Answer:
(1, 4)
Don't worry, I feel the same way sometimes, :)
Please give me Brainliest :)Step-by-step explanation:
Substitute the bottom equation into the top.
If y=3x+1, than the first y will equal 3x+1.
3x+1 = x+3
Subtract 1 from 3
3x = x+2
Subtract x from 3x.
2x=2
Divide everything by 2.
x=1
Now substitute it in the equation.
1. y=1 + 3
y=4
2. y= 3(1) + 1
y=3+1
y=4
(1, 4)
Find the highest common factor (HCF) of 12x^12 and 16x^16
Answer:
Step-by-step explanation:
To find the highest common factor (HCF) of 12x^12 and 16x^16, we need to factor both expressions.
12x^12 = 2^2 * 3 * (x^2)^6
16x^16 = 2^4 * (x^2)^8
The common factors of 12x^12 and 16x^16 are 2^2 and (x^2)^6. To find the HCF, we take the product of these common factors:
HCF = 2^2 * (x^2)^6 = 4x^12
Therefore, the highest common factor (HCF) of 12x^12 and 16x^16 is 4x^12.
Please help this is for a test and i need a good grade lollll
"the wind force f on a sail varies jointly as the area al of the sall and the square of the wind speed w.
the force on a sail with area an area of 500 p? is 64.8 pounds when the wind speed is 18 mph. what
would be the force for a sail with an area of 250 f12 with a wind speed of 35 mph"
please show step by step work tysmmmm <3
The force on a sail with an area of 250 f12 and a wind speed of 35 mph would be 108.72 pounds.
How to find force on sail?We are given that the wind force F on a sail varies jointly as the area A and the square of the wind speed W. We can represent this relationship mathematically using the equation:
F = k * A * W²
where k is a constant of proportionality.
We are also given that the force on a sail with an area of 500 p and wind speed of 18 mph is 64.8 pounds. We can use this information to solve for k:
64.8 = k * 500 * 18²
Solving for k, we get:
k = 64.8 / (500 * 18²)
k = 0.0000768
Now, we can use the equation to find the force for a sail with an area of 250 f12 and a wind speed of 35 mph:
F = 0.0000768 * 250 f12 * 35²
F = 108.72 pounds
Therefore, the force on a sail with an area of 250 f12 and a wind speed of 35 mph would be 108.72 pounds.
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A boat heading out to sea starts out at point a, at a horizontal distance of 996 feet from a lighthouse/the shore. from that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 6^{\circ} ∘. at some later time, the crew measures the angle of elevation from point b to be 4^{\circ} ∘. find the distance from point a to point b. round your answer to the nearest foot if necessary.
The distance from point A to point B is approximately 998 feet (rounded to the nearest foot).
Let's denote the distance from point A to the lighthouse as "x", and the distance from point B to the lighthouse as "y". Also, let's denote the height of the lighthouse as "h". Then we have the following diagram:
Lighthouse
|\
| \
| \ h
| \
|θ2 \
|____\
x y
A B
From the diagram, we can see that:
tan(6°) = h/x (equation 1)
and
tan(4°) = h/y (equation 2)
We need to find the value of "d", the distance from point A to point B. We can use the following equation:
d^2 = x^2 + y^2 (equation 3)
We can solve equation 1 for h:
h = x tan(6°)
Substitute this into equation 2:
x tan(6°) / y = tan(4°)
Solve for y:
y = x tan(6°) / tan(4°)
Substitute this into equation 3:
d^2 = x^2 + (x tan(6°) / tan(4°))^2
Simplify:
d^2 = x^2 (1 + tan^2(6°) / tan^2(4°))
Solve for d:
d = x sqrt(1 + tan^2(6°) / tan^2(4°))
Substitute the given values:
d = 996 sqrt(1 + tan^2(6°) / tan^2(4°))
Using a calculator, we get:
tan(6°) / tan(4°) = 0.1051
So,
d = 996 sqrt(1 + 0.1051^2) ≈ 998.38 feet
Therefore, the distance from point A to point B is approximately 998 feet (rounded to the nearest foot).
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Find-F+2G+H-R using the Graphical Tail-to-Tip method.
F = 45.0 N [S 45° W]
G= 25.0 N[35° N of W]
H=70.0 N [E 15° S]
To find -F+2G+H-R using the Graphical Tail-to-Tip method, measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.
How to solveTo find the vector sum F+2G+H-R using the graphical tail-to-tip method, follow these steps:
Draw vector F: 45.0 N [S 45° W]Draw 2G: Multiply G by 2: 2 x 25.0 N [35° N of W] = 50.0 N [35° N of W]Draw vector H: 70.0 N [E 15° S]Draw vector R: Since we want to find the sum F+2G+H-R, R should be drawn in the opposite direction to balance the equation.Now, place the vectors tail-to-tip in the following order: F, 2G, H, and R (in opposite directions).
The sum of these vectors can be found by connecting the starting point (tail of F) to the endpoint (tip of R in the opposite direction).
Measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.
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Find the difference. Express the answer in scientific notation. (8. 64 times 10 Superscript 20 Baseline) minus (7. 83 times 10 Superscript 20 Baseline) 8. 1 times 10 Superscript 19 0. 81 times 10 Superscript 20 8. 1 times 10 Superscript 21 0. 81 times 10 Superscript 40
In scientific notation, the difference between (8.64 x 10^20) and (7.83 x 10^20) is expressed as 8.1 x 10^19.
To find the difference between (8.64 x 10^20) and (7.83 x 10^20), we subtract the second number from the first:
8.64 x 10^20 - 7.83 x 10^20 = 0.81 x 10^20
Since the difference is less than one, we express the answer in scientific notation by moving the decimal point one place to the left and increasing the exponent by one:
0.81 x 10^20 = 8.1 x 10^19
Therefore, the difference between (8.64 x 10^20) and (7.83 x 10^20) expressed in scientific notation is 8.1 x 10^19.
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Consider the following series: (-1)^ 71n n We will test this series for convergence or divergence. (i) What test(s) is(are) applicable to test this series? Click for List (i) Determine whether this series converges or diverges. O Converges O Diverges (iii) What is the sum of the series? Note: Write the exact answer not the decimal approximation (for example write 1 / not 0.8). Answer: The sum of the series is PO
The series given is (-1)^71n*n. To test for convergence or divergence, the alternating series test as the series alternates in sign. Also, the absolute value of the terms of the series is decreasing as n increases. In conclusion, the given series (-1)^71n * n diverges, and it does not have a finite sum.
According to the alternating series test, if a series alternates in sign, and the absolute value of its terms is decreasing as n increases, then the series converges.
Thus, the series converges.
To find the sum of the series, we use the formula for the sum of an alternating series:
Sum = (-1)^71*1 - (-1)^71*2 + (-1)^71*3 - (-1)^71*4 + ...
= (-1)^71*(1 - 2 + 3 - 4 + ...)
= (-1)^71*(n(n+1)/2)
= 0
Therefore, the sum of the series is 0.
I'd be happy to help you with your question. To determine the convergence or divergence of the series (-1)^71n * n, we can follow these steps:
(i) Since the series has terms that alternate in sign, we can use the Alternating Series Test to test for convergence.
(ii) To apply the Alternating Series Test, we must first verify that the sequence of positive terms is decreasing and has a limit of zero. In this case, the sequence of positive terms is given by "n". As "n" goes to infinity, the sequence increases, not decreases, and the limit is not zero. Therefore, the series (-1)^71n * n does not pass the Alternating Series Test, and it diverges.
(iii) Since the series diverges, it does not have a finite sum.
In conclusion, the given series (-1)^71n * n diverges, and it does not have a finite sum.
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Which is true about the relationship between 1 inch and 1 foot?
A. 1 inch is 12 times as long as 1 foot. B. 1 foot is 12 times as long as 1 inch. C. 1 foot is 6 times as long as 1 inch. D. 1 inch is 6 times as long as 1 foot
Option B is true about the relationship between 1 inch and 1 foot.
What is conversation?
A unit's use depends on the context; for example, a room's area is expressed in meters, yet a pencil's length and thickness are expressed in centimeters and millimeters, respectively. Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion. When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.
There are 12 inches in 1 foot. This means that 1 foot is 12 times longer than 1 inch. Therefore, option B is correct. Option A is incorrect because it states that 1 inch is 12 times as long as 1 foot, which is the opposite of the correct relationship. Option C is incorrect because it states that 1 foot is 6 times as long as 1 inch, which is half of the correct relationship. Option D is incorrect because it states that 1 inch is 6 times as long as 1 foot, which is the opposite of the correct relationship.
Hence, Option B is true about the relationship between 1 inch and 1 foot.
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!!PLEASE HELPP!! (check if I’m right pls)
Answer: It's correct
Step-by-step explanation:
When you don’t replace the marble for the second draw what kind of probability is it?
If you do not replace the marble after the first draw, the probability calculation depends on whether you are dealing with a dependent or an independent event.
The possibility or chance of an event occurring is measured by probability. It is a number between 0 and 1 (inclusive), where 0 denotes an impossibility and 1 denotes a certainty. By dividing the number of favorable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. The field of mathematics known as probability studies the possibility that a certain event will take place. It is a way to quantify the possibility or likelihood that something will really happen.
For an independent event, assuming that the first draw had no bearing on the outcome of the second draw, in the case of an isolated occurrence, the chance of drawing a specific marble on the second draw would be the same as the likelihood of drawing that same marble on the first draw. For a dependent event, the outcome of the first draw would determine the possibility of drawing a specific marble on the second draw.
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HELP!!! PLEASE
97. Sri is weighing things on a scale, and he finds out that the following items have equal
weights:
5 marbles = 3 toy soldiers
7 toy soldiers = 5 plush chipmunks
3 plush chipmunks = 14 jujubes
How many jujubes equal the weight of one marble?
1 marble is equal in weight to 84 jujubes.
Let's start by writing down the given information in equations:
5m = 3s (where m represents one marble and s represents one toy soldier)
7s = 5c (where c represents one plush chipmunk)
3c = 14j (where j represents one jujube)
We want to find out how many jujubes equal the weight of one marble, so we need to eliminate all the other variables except for j and m. We can do this by using substitution and algebraic manipulation.
First, we can solve the second equation for s in terms of c:
7s = 5c
s = (5/7)c
Then, we can substitute this expression for s in the first equation:
5m = 3s
5m = 3(5/7)c
m = (3/7)c
Next, we can solve the third equation for c in terms of j:
3c = 14j
c = (14/3)j
Now we can substitute this expression for c in the previous equation:
m = (3/7)c
m = (3/7)(14/3)j
m = 2j
So we have found that one marble is equal in weight to 2 jujubes. But the question asks for the weight of one marble in terms of jujubes, not in terms of jujubes and toy soldiers and plush chipmunks. We can use the other equations to eliminate the other variables:
5m = 3s
5m = 3(5/7)c
5m = (15/7)c
m = (3/7)c
7s = 5c
7s = 5(14/3)j
s = (10/3)j
Putting this all together:
m = (3/7)c
m = (3/7)(7s/5)
m = (3/5)s
m = (3/5)(10/3)j
m = 2j
So we have found that one marble is equal in weight to 2 jujubes. Finally, we can use the third equation to find how many jujubes are equal in weight to 1 marble:
3c = 14j
c = (14/3)j
m = (3/7)c
m = (3/7)(14/3)j
m = 2j
1 marble = 2 jujubes
1 jujube = 1/2 marble
1 marble = 2 jujubes = 2(84) = 168 jujubes
Therefore, one marble is equal in weight to 84 jujubes.
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Kennedy makes $7 per hour babysitting. Hours (h) dollars (d) 1 7 2 14 3 21 4 28 which equation represents the amount kennedy makes babysitting? 7 = hd h = 7d d = 7h h = d
The correct equation represents the amount Kennedy makes babysitting is,
⇒ d = 7h
We have to given that,
Kennedy makes $7 per hour babysitting.
Let us assume that,
'h' represent the number of hours
And, d represent amount in dollars.
Hence, By given condition, we get;
⇒ d = 7h
Thus, The correct equation represents the amount Kennedy makes babysitting is,
⇒ d = 7h
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The formula that Kennedy uses to calculate how much money she makes babysitting is:d = 7h
We have,
Kennedy makes $7 per hour babysitting.
let "d" represents the amount of dollars Kennedy makes, and "h" represents the number of hours she babysits.
Since Kennedy earns $7 per hour, the equation can be written as
d = 7h
which relates the dollars earned (d) to the number of hours worked (h).
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the circumstances of the base is 48π cm. if the volume if the cone is 8640π cm cubed, what is the height?
Answer:
h = 15 cm
Step-by-step explanation:
Given:
C (base's circumstance) = 48π cm
V (volume) = 8640π cm^3
Find: h (height) - ?
[tex]c = 2\pi \times r[/tex]
[tex]2\pi \times r = 48π[/tex]
[tex]r = 24[/tex]
We found the radius
[tex]v = \frac{1}{3} \times \pi {r}^{2} \times h[/tex]
[tex] \frac{1}{3} \times \pi \times {24}^{2} \times h = 8640π[/tex]
Multiply the whole equation by 3 to eliminate the fraction:
[tex]1728\pi \times h = 25920\pi[/tex]
[tex]h = 15[/tex]
on a standardized test, phyllis scored 84, exactly one standard deviation above the mean. if the standard deviation for the test is 6, what is the mean score for the test?
The mean score for the test Phyllis scored 84, exactly one standard deviation above the mean is 78.
One of the statistics used in the generalised Cochran-Mantel-Haenszel tests is the mean score statistic. When the answer levels (columns) are assessed using an ordinal scale, it is applicable.
The chi-square distribution with (R-1) degrees of freedom, where R is the number of treatment groups, serves as the asymptotic distribution of the mean score statistic if the two variables are independent of one another in all strata (rows).
If the mean scores of the response differ between the treatment groups in at least one stratum, the mean score statistic tends to have larger values. The term "nonparametric ANOVA statistic" also applies to this statistic.
x = 84
[tex]\sigma=6[/tex]
since, x is 1 standard deviation above mean so,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]1=\frac{84-\mu}{6}\\ \\[/tex]
[tex]\mu[/tex] = 84-6
[tex]\mu[/tex] =78.
therefore, mean = 78.
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Identify the angle or side that is common to triangle SUT and triangle SVT
A. B. SV
C. D. ST
Angle S, Angle T and side ST are common to triangle SUT and triangle SVT.
To identify the angle or side that is common to triangle SUT and triangle SVT, based on given information, we can evaluate them as follows:
A. Angle S is common to both triangles SUT and SVT, as it is the vertex where the two triangles share a point.
B. Side SV is not common to both triangles, as it is only a side of triangle SVT.
C. Side ST is common to both triangles SUT and SVT, as it connects the shared vertex S to points U and V in each respective triangle.
D. Angle T is also common to both triangles SUT and SVT, as it is the other vertex where the two triangles share a point.
Therefore, Angle S, side ST, and Angle T are all common to triangle SUT and triangle SVT.
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The cost after the coupon is $21. 25 she decides to add a 20% tip. How much is she adding for a tip
If the cost after the coupon is $21.25 and she decides to add a 20% tip, she will be adding $4.25 for the tip.
Find out how much a 20% tip would be on a cost of $21.25 after applying a coupon.
Identify the total cost after the coupon.
In this case, the cost is $21.25.
Determine the percentage for the tip.
The tip percentage is given as 20%.
Convert the percentage to a decimal.
To do this, divide the percentage by 100. So, 20% divided by 100 is equal to 0.2.
Multiply the total cost by the tip percentage in decimal form.
Now, multiply $21.25 (total cost) by 0.2 (tip percentage as a decimal).
$21.25 x 0.2 = $4.25
Calculate the tip amount.
The tip amount is $4.25.
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can anyone answer?
Please
Answer:
145.7 cm
Step-by-step explanation:
You want the perimeter of a shape bounded by 4 semicircles of radius 10 cm and two straight lines 10 cm long.
PerimeterThe circumference of a circle with radius 10 cm is ...
C = 2πr
C = 2(3.142)(10 cm) = 62.84 cm
The shape is bounded (in part) by 4 semicircles, so 2 full circles. The length of the curved boundary is ...
curve length = 2 · (62.84 cm) = 125.68 cm
The two straight edges at either end of the figure are equal in length to the radius. That total length gets added to the curve length to form the perimeter.
P = straight length + curve length
P = 2·10 cm + 125.68 cm ≈ 145.7 cm
The perimeter is about 145.7 cm.
B. Constructing a parallel through a point (rhombus method) Steps: 1. Place the compasess on the point K and set it width to a little more than the distance to the PQ. The exact distance is not important. 2. Draw a wide arc from the right of K around so it crosses the PQ at two points. Label the left point J.
3. Without adjusting the opening of the compass, move the compass to J and draw an arc across the PQ Label this point E.
4. Without adjusting the span of the compass , move the compass to E and draw an arc across the large arc to the right of K. Label this point S.
5. Draw a straight line through points K and S.
6. Done. The KS is parallel to the PQ.
please paki sagot po.
The rhombus method is a useful technique for constructing parallel lines, especially in geometry problems where creating accurate drawings is essential.
Constructing a parallel line through a point using the rhombus method involves the following steps:
1. Place the compass on point K and set its width slightly more than the distance to line PQ. The exact distance is not crucial.
2. Draw a wide arc from the right of K, crossing line PQ at two points. Label the left point J.
3. Without adjusting the compass opening, move the compass to point J and draw an arc across line PQ. Label this point E.
4. Keeping the compass width unchanged, move the compass to point E and draw an arc across the large arc to the right of K. Label this point S.
5. Draw a straight line through points K and S.
6. The line KS is now parallel to line PQ, as desired.
The rhombus method is a useful technique for constructing parallel lines, especially in geometry problems where creating accurate drawings is essential. The process relies on the compass's fixed width to ensure the angles and distances remain consistent, resulting in parallel lines.
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Find the absolute maximum and absolute minimum values off on each interval. (If an answer does not exist, enter DNE.) F(x) = 2x² - 16x + 850 (a) (0,4) Absolute maximum: Absolute minimum: (b) (0,4) Absolute maximum: Absolute minimum:
From the above information we get:
Absolute maximum: 850
Absolute minimum: 800
To find the absolute maximum and minimum values of the function f(x) = 2x² - 16x + 850 on the given interval (0,4), we will follow these steps:
1. Find the critical points by taking the first derivative of f(x) and setting it equal to zero.
2. Determine if the critical points are within the interval (0,4).
3. Evaluate f(x) at the critical points and endpoints of the interval.
4. Identify the absolute maximum and minimum values based on the results.
Step 1: Find the critical points
f'(x) = 4x - 16
Setting f'(x) equal to zero:
4x - 16 = 0
4x = 16
x = 4
Step 2: Determine if the critical point is within the interval (0,4)
The critical point x = 4 is within the interval (0,4).
Step 3: Evaluate f(x) at the critical points and endpoints of the interval
f(0) = 2(0)² - 16(0) + 850 = 850
f(4) = 2(4)² - 16(4) + 850 = 850 - 64 + 850 = 800
Step 4: Identify the absolute maximum and minimum values based on the results
Absolute maximum: f(0) = 850
Absolute minimum: f(4) = 800
To answer the question:
(a) Interval (0,4)
Absolute maximum: 850
Absolute minimum: 800
(b) It seems you have repeated the interval (0,4), so the answer remains the same.
Absolute maximum: 850
Absolute minimum: 800
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The tax on a bicycle costing $400 is $32 how much will the tax be on a bicylce costing $700 if the tax remains the same
The tax on a bicycle costing $700, with the tax remaining the same as a bicycle costing $400 with a tax of $32, will be $56.
To calculate the tax on a bicycle costing $700, we need to know the percentage of tax charged on the $400 bicycle. The tax on the $400 bicycle is $32. To find the tax rate, we divide the tax by the cost of the bicycle and multiply by 100 to get a percentage.
tax rate = (tax / cost of bicycle) x 100%
tax rate = (32 / 400) x 100%
tax rate = 8%
Therefore, the tax rate is 8%. We can use this tax rate to calculate the tax on a bicycle costing $700.
tax on $700 bicycle = (tax rate / 100) x cost of bicycle
tax on $700 bicycle = (8 / 100) x $700
tax on $700 bicycle = $56
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Yuriy and anduray will mail rectangular packages that meet the weight and height requirements of their delivery service. their packages are described in
the table.
yurly's package
package
height
4 in.
7 in.
length
21 in.
18 in.
width
9 in.
14 in.
part 1. the delivery service also requires that both the length and width of the packages to be 22 inches or less and that the length plus the width be no
more than 30 inches. write a system of inequalities to represent this situation. don't forget to define your variables and show your work
The complete system of inequalities for Anduray's package is:
x ≤ 22
y ≤ 22
x + y ≤ 30
14xy ≤ 3696
Let's define:
x: length of the package in inches
y: width of the package in inches
Then, the system of inequalities that represents the delivery service requirements is:
x ≤ 22 (length must be 22 inches or less)
y ≤ 22 (width must be 22 inches or less)
x + y ≤ 30 (length plus width must be no more than 30 inches)
We also know that Yuriy's package has a height of 7 inches, so we can add the following constraint:
4xy ≤ 840 (the product of length, width, and height must be no more than 840 cubic inches)
Therefore, the complete system of inequalities for Yuriy's package is:
x ≤ 22
y ≤ 22
x + y ≤ 30
4xy ≤ 840
Anduray's package has a height of 14 inches, so we can add the following constraint to his system of inequalities:
14xy ≤ 3696 (the product of length, width, and height must be no more than 3696 cubic inches)
Therefore, the complete system of inequalities for Anduray's package is:
x ≤ 22
y ≤ 22
x + y ≤ 30
14xy ≤ 3696
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Find a formula for the slope of the graph of fat the point (x, f(x)). Then use it to find the slope at the two given points.
The slope at the given points are -1/36 and -1/16 respectively.
Given is a function f(x) = 1/x+6 we need to find the slope of the function,
The slope of a function is given by dy/dx, therefore,
dy/dx = -1/(x+6)²
Therefore, at point (0, 1/6),
The slope = -1/(0+6)² = -1/36
At point (-2, 1/4),
The slope = -1/(-2+6)² = -1/16
Hence the slope at the given points are -1/36 and -1/16 respectively.
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The original selling price of a jacket was s dollars. The selling price was then changed on two occasions by the store owner. Its price is now represented by 0. 85 (1. 4s). Which expression could explain what happened to the price of the jacket?
The expression 0.85(1.4s) explains what happened to the price of the jacket through the two changes made by the store owner.
The original selling price of the jacket was s dollars.The store owner made the first change, increasing the selling price by 40%. This can be represented by multiplying the original price (s) by 1.4: 1.4s.The store owner then made a second change, reducing the selling price by 15%. This can be represented by multiplying the new price (1.4s) by 0.85: 0.85(1.4s).So, the expression 0.85(1.4s) explains what happened to the price of the jacket through the two changes made by the store owner.
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Please Help me with this problem! No links or files, I will report.
The area of the preimage is 400units²
What is dilation?Dilation is a transformation, which is used to resize a given object. We can use dilation to either make the objects larger or smaller.
A scale factor shows the relationship between the old shape and new shape.
The scale factor is expressed as ;
scale factor = dimension of the new length / dimension of old length
scale factor = 3/2 = 1.5
old length = x
therefore 1.5 = 30/x
1.5x = 30
divide both sides by 1.5
x = 30/1.5 = 20units
therefore the area of the preimage = l²
= 20²
= 400units²
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The lengths of the sides of a triangle are given. Classify each triangle as acute,
right, or obtuse.
19. 3, 4, 6
To start, compare c 2 to a 2 + b2
. Substitute the greatest length for c.
20. 9, 11, 16
19. The triangle with sides 3, 4, 6 is obtuse triangle.
20. The triangle with sides 9, 11, 16 is acute triangle.
How to Classify Triangles?In a triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side for the triangle to be considered "non-degenerate," which means it is a valid triangle with a positive area.
19. We have sides of 3, 4, and 6. We can check whether this triangle is non-degenerate using the above formula:
3² + 4² = 9 + 16 = 25, which is less than 6² = 36.
Therefore, this triangle is non-degenerate and we can classify it based on the size of its angles.
To do so, we can use the Pythagorean Theorem to find that the longest side (6) is opposite the largest angle, which is obtuse. Therefore, triangle #19 is an obtuse triangle.
20. For triangle #20, we have sides of 9, 11, and 16. Checking again with the above formula:
9² + 11² = 81 + 121 = 202, which is less than 16² = 256. So this triangle is also non-degenerate.
Using the same method as before, we can find that the longest side (16) is opposite the largest angle, which is acute. Therefore, triangle #20 is an acute triangle.
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Sally earns a weekly salary of $450 plus a 6. 5% commission on sales at a boutique. How much would she make in a work week if she sold $650 worth of merchandise?
To find out Sally's total earnings for the week, we need to consider her base salary and the commission on her sales. Her base salary is $450, and she earns a 6.5% commission on $650 worth of merchandise.
First, let's calculate her commission:
6.5% of $650 = 0.065 * $650 = $42.25
Now, we can add her base salary to the commission:
Total earnings = Base salary + Commission
Total earnings = $450 + $42.25
Total earnings = $492.25
So, Sally would make $492.25 in a work week if she sold $650 worth of merchandise.
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Bus stops A, B, C, and D are on a straight road. The distance from A to D is exactly 1 km. The distance from B to C is 2 km. The distance from B to D is 3 km, the distance from A to B is 4 km, and the distance from C to D is 5 km. What is the distance between stops A and C? AC=_ km
The distance between bus stops A and C is exactly 1 km.
To find the distance between bus stops A and C, we can use the fact that the distance from A to D is 1 km and the distance from C to D is 5 km.
This means that the total distance from A to C, passing through D, is 6 km (1 km + 5 km).
However, we need to subtract the distance between B and D (3 km) and the distance between B and C (2 km) since we don't want to double count the stretch between B and D.
Therefore, the distance between A and C is 6 km - 3 km - 2 km = 1 km.
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A baker makes 20 loaves of bread
each day. The loaves are either
white or brown.
The ratio of white loaves to brown
loaves is always 7 : 3.
After how many days would the
baker have made 180 loaves of
brown bread?
Every day, a baker produces 20 loaves of bread. The loaves come in white or brown. It would take him 30 days to make 180 loaves of brown bread.
Let the ratio be x,
We have been given the ratio of 7 : 3 in which 3 part is of brown bed.
So the number of brown bread will be 3x and white bread will be 7x.
Now, we have to find out the days for 180 loaves of brown bread. This means that 3x = 180. Now we will find out the value of x to find the total loaves of bread from this equation.
3x = 180
x = 180 / 3
x = 60
So, the total amount of bread = brown bread + white bread
Total amount of bread = 3x + 7x
= 10x
= 10 × 60
= 600
We know that in 20 loaves of bread are made in one day, so
time taken to make 600 loaves of bread = 600 / 20
= 30 days
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The International Links long-distance phone company charges no monthly fee but charges 18 cents per minute for long-distance calls. The World Connections long distance company charges $50 per month plus 10 cents per minute for long-distance calls. Compare the World Connections long-distance plan to that of International Links. Under what circumstances is it cheaper to use International Links?
If the number of minutes used is less than 625 per month, it is more affordable to use International Links if not, you can go for World Connections.
Let us assume that the number of minutes used = x
Cost per minute = 18 cents
Total cost for International calls = 0.18x
Basci cahrge = 50 per month
If we use x number of minutes for calls for world connections then the total cost will be:
50 + 0.10x
To find the value of x where International Links cost is less than the total cost for World Connections
0.18x < 50 + 0.10x
0.08 < 50
8x < 50
x < 625
Therefore, we can infer that if the number of minutes used is less than 625 per month, it is cheaper to use International Links.
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Your gross pay is $2,500 and your net pay is $1,750. How much was withheld from your pay?
a: $250
b: $500
c:750
d:4,250
$750 was withheld from my pay after deductions form the gross pay
How to calculate the amount of money that was withheld from my pay?
Gross pay is the money that an employee gets before tax and other deduction are made
Net pay is the amount of money given to am employee after deduction of tax and other mandatory expenses
The gross pay is $2,500
The net pay is $1,750
The money withheld can be calculated as follows
= 2500 - 1750
= 750
The money withheld from the gross pay is $750
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Please help me with this
Answer:
B f(x)=1(8)^x
Step-by-step explanation:
1 is the 0 value, you can see it's exponential by the rapid growth and how it grows by a lot each time