Answer:
A) Suppose we have an onedimensional situation.
in the 0 of our x-axis, we have a fruit tree, and we want to rest at a distance no bigger than 6 ft of the tree, then all the possible positions of our resting place are:
x ∈(-6ft, 6ft)
we can write this as: IxI < 6ft
b) now we think the opposite situation, we want to rest at least 6ft away from the tree, then we have that:
x ∉ [-6ft, 6ft].
or IxI > 6ft.
So you can see that the difference in those two cases is if we want to be "inside a given range" (for the first case) or "outside a given range" (for the second case).
to prepare for a new year john praticed marching and playing his tuba for 45 minutes he took a break and then practiced 15 more minutes how many did john practice in all
Answer:
60 minutes/1 hour
Step-by-step explanation:
45+ 15=60
look for prefixes and suffixes in these words and move each word into its correct category
Answer:
words with prefixes: pro-duce. uni-cycle.
words with suffixes: hope-ful. goof-y.
words with both: multi-function-al. un-fix-able.
Produce
Unicycle
Words with Suffixeshopeful
Goofy
Words with BothMultifunctional
Unfixable
Hope this helped. If it did, please mark as brianliest as it helps me and others find the correct answer. Thank you! :)
A.line d
B.line c
C.line b
D.line a
Answer:
B. Line c
Step-by-step explanation:
looking at the points, 3, -2 is on line c.
// have a great day //
|x-1|=14 solve the equation
Answer:
x = 15 x = -13
Step-by-step explanation:
|x-1|=14
There are two solutions to the absolute value equation, one positive and one negative
x-1 = 14 and x-1 = -14
Add 1 to each side
x-1+1 = 14+1 x-1+1 = -14+1
x = 15 x = -13
Answer:
x= 13 or -13
Step-by-step explanation:
Substitute x for 13
|13+-1|=14
13+1=14
14=14
Now try -13
|-13+-1|=14
13+1=14
14=14
Find the center, vertices, and foci of the ellipse with equation 3x2 + 7y2 = 21.
Answer:
Center [tex]= (0,0)[/tex]
Vertices [tex]=(-\sqrt{7},0)\text{ and }(\sqrt{7},0)[/tex]
Foci [tex]=(-2,0)\text{ and }(2,0)[/tex].
Step-by-step explanation:
The standard form of an ellipse is
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex] ...(1)
where, a>b, (0,0) is center, (±a,0) are vertices and (±c,0) are foci.
[tex]c=\sqrt{a^2-b^2}[/tex]
The given equation of ellipse is
[tex]3x^2+7y^2=21[/tex]
Divide both sides by 21.
[tex]\dfrac{3x^2+7y^2}{21}=\dfrac{21}{21}[/tex]
[tex]\dfrac{x^2}{7}+\dfrac{y^2}{3}=1[/tex] ...(2)
On comparing (1) and (2), we get
[tex]a^2=7,b^2=3[/tex]
[tex]a=\sqrt{7},b=\sqrt{3}[/tex]
Now,
[tex]c=\sqrt{a^2-b^2}=\sqrt{7-3}=\sqrt{4}=2[/tex]
Therefore,
Center [tex]= (0,0)[/tex]
Vertices [tex]=(\pm a,0)=(\pm \sqrt{7},0}=(-\sqrt{7},0)\text{ and }(\sqrt{7},0)[/tex]
Foci [tex]=(\pm c, 0)=(\pm 2,0)=(-2,0)\text{ and }(2,0)[/tex].
Question 1
In this hanger, the weight of the triangle is x and the weight of the square is y.
a. Write an equation using x and y to represent the hanger.
B. If x is 6, what is y ?
Answer:
a. -3x = -2y
When x=6, y=9
Step-by-step explanation:
From the hanger, There are two sides
If x=triangle and y=square
First side has 1 triangle and 3 squares
It can be represented by
x+3y
Second side has 4 triangles and 1 square
It can be represented by
4x+y
Equate the first and second side
x+3y=4x+y
Collect like terms
x+3y-4x-y=0
-3x+2y=0
-3x=-2y
Find y when x=6
-3(6)=-2y
-18=-2y
Divide both sides by -2
-18/-2=-2y/-2
9=y
y=9
The value of y when x = 6 is 9
Given that the weight of the triangle is x and the weight of the square is y.
For the hanger at the left, the resulting equation will be:
x + 3y (1 triangle and 3 square)
For the right-hand side
4x + y (4 triangles and 1 square)
Equating both expressions
x + 3y = 4x + y
x - 4x = -2y
-3x = -2y
3x = 2y
If x = 6, hence;
3(6) = 2y
2y = 18
y = 9
Hence the value of y when x = 6 is 9
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Martha types a 4−digit code into a keypad to unlock her car doors. The code uses the numbers 1 and 0. If the digits are selected at random, what is the probability of getting a code with exactly two 1's? Enter your answer as a simplified fraction.
The probability of getting two 1's is_________.
Answer:
3/8
Step-by-step explanation:
1. We list all codes that start with 0 and have 0 as second digit:
2. We list all codes that start with 0 and have 1 as second digit:
3. We list all codes that start with 1 and have 0 as second digit:
4. We list all codes that start with 1 and have 1 as second digit:
5. We find the number of codes which have exactly 2 zeros: 6 codes
6. The total number of outcomes is: 16 codes
7. We find the probability that the number of codes has exactly 2 zeros: 6/16 3/8
Answer:
The probability of getting two 1's is 3/8
Step-by-step explanation:
Martha types a 4−digit code into a keypad to unlock her car doors.
The code uses the numbers 1 and 0
So the sample space of all the possible combinations is given by
1. 0 0 0 0
2. 0 0 0 1
3. 0 0 1 0
4. 0 0 1 1
5. 0 1 0 0
6. 0 1 0 1
7. 0 1 1 0
8. 0 1 1 1
9. 1 0 0 0
10. 1 0 0 1
11. 1 0 1 0
12. 1 0 1 1
13. 1 1 0 0
14. 1 1 0 1
15. 1 1 1 0
16. 1 1 1 1
So there are total 16 possible outcomes.
Now count the number of combinations that has exactly two 1's
4. 0 0 1 1
6. 0 1 0 1
7. 0 1 1 0
10. 1 0 0 1
11. 1 0 1 0
13. 1 1 0 0
So there are 6 possible outcomes with exactly two 1's
The required probability is
P(two 1's) = Number of outcomes with two 1's/Total number of outcomes
P(two 1's) = 6/16
P(two 1's) = 3/8
Therefore, the probability of getting two 1's is 3/8
The volume, V, of a rectangular solid is found using the equation V= Iwh, where I is the length, w is the width, and h is the height of the solid. A rectangular solid has length of 16 and height of 5. Which equation represents the volume of the solid, in terms of its width?
Answer:
Volume = length × width × height
length = 16
height = 5
V= 16 × w × 5
V = 80w
Hope this helps.
Consider the function f(x) = x5 – 3x2 + 5x. Let g(x) = f(–x + 4). Which shows the graphs of f(x) and g(x)
Answer:
The first graph
Step-by-step explanation:
I think it is the first one because I remember doing this. If this is wrong please forgive me. Have a wonderful day!
First graph shows the function f(x) and g(x).
What is graph?" Graph is representation of the coordinates on the coordinate plane along x-axis and y-axis."
According to the question,
Given function,
[tex]f(x) = x^{5} -3x^{2} +5x\\\\g(x) = f(-x+4)[/tex]
Plot the given functions on the graph we get,
Compare the drawn graph with the given graph.
First graph is same as graph drawn for the function f(x) and g(x).
Hence, we conclude that first graph shows the function f(x) and g(x).
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Using the quadratic formula to solve x2 = 5 – x, what are the values of x?
Answer:
[tex]\dfrac{-1+\sqrt{21}}{2}[/tex] and [tex]\dfrac{-1-\sqrt{21}}{2}[/tex].
Step-by-step explanation:
The given quadratic equation is
[tex]x^2=5-x[/tex]
It is can written as
[tex]x^2+x-5=0[/tex]
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
In the given quadratic equation [tex]a=1,b=1,c=-5[/tex]. So,
[tex]x=\dfrac{-1\pm \sqrt{1^2-4(1)(-5)}}{2(1)}[/tex]
[tex]x=\dfrac{-1\pm \sqrt{1+20}}{2}[/tex]
[tex]x=\dfrac{-1\pm \sqrt{21}}{2}[/tex]
[tex]x=\dfrac{-1+\sqrt{21}}{2},\dfrac{-1-\sqrt{21}}{2}[/tex]
Therefore, the values of x are [tex]\dfrac{-1+\sqrt{21}}{2}[/tex] and [tex]\dfrac{-1-\sqrt{21}}{2}[/tex].
Help! Look at the picture
Answer:
171 square ft
Step-by-step explanation:
Area of side walk of the pool = Are of outer square - Area of inner square
[tex] = {30}^{2} - {27}^{2} \\ = (30 + 27)(30 - 27) \\ = 57 \times 3 \\ = 171 \: {ft}^{2} [/tex]
The graph shows the speed of a particle over a 10 second time interval find an estimate for the distance travelled by the particle
Answer:
240
Step-by-step explanation:
(2x36)/2=36
(36+39)x2/2=75
(31+39)x2/2=70
(14+31)x2/2=45
(2x14)/2=14
14+45+70+75+36=240
IO
80
14x + 2
The figure is a parallelogram.
Solve for x.
'S
2
7
Answer:
x = 7
Step-by-step explanation:
The consecutive angles in a parallelogram are supplementary, thus
80 + 14x + 2 = 180
14x + 82 = 180 ( subtract 82 from both sides )
14x = 98 ( divide both sides by 14 )
x = 7
In the given parallelogram QRST, x = 7°.
What are adjacent angles?In a quadrilateral, adjacent angles are the pair of angles, that come is formed by the intersection of any common line.
How do we solve the given question?In the question, we are shown a parallelogram QRST and are asked to find the value of x.
We know that ∠TQR and ∠QRS are adjacent, as they include a common side, QR.
∠TQR = 80°, ∠QRS = (14x + 2)°
Now, we know that adjacent angles of a parallelogram are supplementary, that is their sum = 180°
∴ ∠TQR + ∠QRS = 180°
or, 80° + (14x + 2)° = 180°
or, 14x = 180° - 80° -2° = 98°
or, x = 98°/14 = 7°
∴ In the given parallelogram QRST, x = 7°.
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20 POINTS!! Let logb A = 3; log, C = 2; log, D= 5
What is the value of logb(a5c2/d6)?
Answer:
-11
Step-by-step explanation:
logb ( a^5 c^2 / d^6)
Splitting these into log (xy/z) = log x + log y - logz
logb ( a^5) +logb ( c^2) - logb( d^6)
We also know that log x^y = y log x
5logb ( a) +2logb ( c) - 6 logb( d)
Given logb ( a)=3 logb ( c) =2 logb( d)=5
5 * 3 + 2* 2 - 6* 5
15 +4 -30
19 - 30
-11
Answer: -11
Step-by-step explanation:
just got it right on ap3x
Select the correct product.
(y+ z)3
y 3+3y2z+ 3yz 2 + z 3
y 3 y+ 3 z
y 3 z 3
y 3 + z 3
Answer:
Step-by-step explanation:
Can someone help me on this math question?
Answer:
23°.
Step-by-step explanation:
Look closely at the spots where A and C connect. They end in the same exact place, suggesting that they are the same number of degrees.
It's a no-brainer.
3. What is the solution to the equation 3x = 15? Express the
solution as a logarithm, make an estimate, and then evaluate.
Round to the nearest thousandth.
Answer:
x=2.4650
Step-by-step explanation:
I assume that you mean [tex]3^x=15[/tex]
so let s use the ln() function
[tex]ln(3^x)= xln(3)=ln(15)[/tex]
so x = ln(15)/ln(3)
x = 2.4650
Help!!!
Point A(-5,8) is reflected across the line y = x. What are the coordinates of A’?
Show your work an explain!
Answer:
(8, -5)
Step-by-step explanation:
When you reflect across the line y = x, you switch the two numbers in the coordinate. The point (a, b) turns into (b, a).
A bullet exits the barrel of a gun at 625 m/s. How long does it take to
hit a target that is 2.0 km away?
Answer: 3.2 seconds
Step-by-step explanation:
Time = Distance / speed
= 2000 / 625
= 3.2 seconds
Please answer, I need help.
Brandon decided to take his family to a water park and celebrate the end of the school year. The cost is $9.50 for parking and $15 for each person for the entire day.
a. Define the variable and write a linear equation for the situation
b. Use the equation to find the cost if Brandon has 5 members in his family
Answer: a) Cost(x) = $9.50 + $15*x
b) $84.50
Step-by-step explanation:
a) If x is the number of members in the family, we can model this situation with a linear equation, where x is the variable.
We have:
A fixed $9.50 (this does not depend on the number of members in the family)
and $15 for each member, so the equation that represents this is:
Cost(x) = $9.50 + $15*x
b) now we have x = 5, then:
Cost(5) = $9.50 + $15*5 = $84.50
Answer:
a. y = 9.50 + 15a
b. total cost(y) = 84.5
Step-by-step explanation:
Brandon decided to take his family to a water park to celebrate the end of the school year.
The cost for parking is $ 9.50 which is a flat rate and compulsory rate for parked cars. The cost for each person is $15 .
a. The linear equation can be expressed below. The variable required in the linear equation will be the number of people that entered the water park(a) and the total cost (y)
let
a = number of person for the entire day
total cost = y
y = 9.50 + 15a
b. To find the cost for a whole family of 5 member can be calculated below.
Using the linear equation
total cost = 9.50 + 15a
total cost = 9.50 + 15(5)
total cost = 9.50 + 75
total cost(y)= 84.5
Use the discriminant to determine the number of real solutions to the quadratic equation. −100a2+20a−1=0 What is the number of real solutions? Select the correct answer below: 0 1 2
Answer:
1 real solution
Step-by-step explanation:
20² - 4 (-100) (-1)
400 - 400
0
When the discriminant is 0, there is one real solution.
Answer:
1 real solution
Step-by-step explanation:
20² - 4 (-100) (-1)
400 - 400
0
What is the answer? To this question
Answer:
x = 5
Step-by-step explanation:
In a parallelogram, the diagonals bisect each other.
Therefore,
4x - 5 = 3x
4x = 3x + 5
4x - 3x = 5
x = 5
question in attachment
Answer:
The range within 1 standard deviation :155.12 ,328.38
Step-by-step explanation:
Data: 338+160+210+180+166+272+128+409+240+250+160+300+340+200+194+132+202+180+420+380+325+185+233+198
[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}[/tex]
[tex]Mean =\frac{338+160+210+180+166+272+.........+233+198}{24}[/tex]
Mean =241.75
[tex]\text{Standard deviation} = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]
Standard deviation = [tex]\sqrt{\frac{(338-241.75)^{2}+(160-241.75)^{2}+......+(185-241.75)^{2}+(233-241.75)^{2}+(198-241.75)^{2}}{24-1}}[/tex]
Standard deviation =86.63
Range within 1 standard deviation :[tex](\mu-\sigma,\mu+\sigma)[/tex]
Range within 1 standard deviation :(241.75-86.63,241.75+86.63)
Range within 1 standard deviation :155.12 ,328.38
Hence The range within 1 standard deviation :155.12 ,328.38
2. Daniel paid $22 for a water bottle. This amount includes 5% tax. What was the cost of the item before tax?
Answer:
$20.9
Step-by-step explanation:
100%=22
95%=x
95x22=2090/100=20.9
Answer:
$20.95 (rounded)
Step-by-step explanation:
To solve this, you need to first make an equation where x is the original cost before tax. So it would be 22=1.05x. You know it is 1.05 because 1 is the "whole" original cost and 0.05 is the 5% tax in decimal form. To solve the equation, you divide both sides by 1.05 to get x=20.95
measurement of these angles
Answer:
1= 105, 2= 75
Step-by-step explanation:
Based on the 75 degree angle, since alternate interior angles have the same measurements, angle 2 will also measure 75 degrees. Furthermore, since angle 1 and angle 2 are supplementary angles, angle 1 will be 105 degrees because 105 + 75 is 180.
solve for x
9^x/9^3=9^5
Answer:
9^x =9^5.
9^3
cross multiply
9^x=9^5×9^3
the nine cancel themselves .
x=5+3=8.
Answer:
x=8
Step-by-step explanation:
when dividing, you subtract the indicies (powers) and vice versa
rearrange the equation:
9^x=9^5*9^3
5+3= 8 (add because when multiplying with indicies you need to add the indicies)
check answer:
9^8/9^3=9^5
8-3=5 ✓
whar does it mean that one object has more density than the other object.
pls i need this it is due in not long i put 31 pts for who answers pls.
find the area of this figure
Answer: 49.12 ft²
Step-by-step explanation:
To find the area of this figure, we can separate it into 2 parts. We can find the area of the semi circle and the area of the triangle. Then we add together to areas.
Area of Triangle
A=bh/2
A=6(8)/2
A=48/2
A= 24 ft²
Area of Semi Circle
A=πr²/2 (Divide by 2 because semi circle is half of a circle, so we divide the area by 2)
A=π(4)²/2
A=(3.14)(16)/2
A=25.12 ft²
Total area
A=24+25.12=49.12 ft²
Complete the equation of the line through (-8,-2)and (-4,6)
use exact number
y=................
Answer: y=2x+14
Step:
substitute into y=mx+b
m= slope
b = y-int.
1) Factor x2 +7x+ 10.
The answer is (x+2)(x+5)
The middle number is 7 and the last number is 10.
What numbers when multiplied get 10 AND when added together get 7?
I hope this helped :)
