Answer: No
Step-by-step explanation: They are not perpendicular due to the slopes. Perpendicular will have the same slopes value wise, but one is negative and one positive.
Solve the equation without using a calculator
[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex]
Answer:
x = 5 ± √26-------------------------
Convert the given equation as below:
[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+10x^9(9x)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+90x^{10}[/tex][tex](x^2-9x-1)^{10}+9x^{10}=10x^9(x^2-9x-1)[/tex][tex](x^2-9x-1)^{10}-9x^9(x^2-9x-1)=x^9(x^2-9x-1)-9x^9x[/tex]Let's substitute x² - 9x - 1 = t, then the equation is:
[tex]t^9t-9x^9t=x^9t-9x^9x[/tex]Comparing both sides, we see that x = t, so:
x² - 9x - 1 = xx² - 10x - 1 = 0Solving this quadratic equation we get:
x = 5 ± √26Mr Tan calculated the average amount of money collected by all the students in his class during a fund-raising event. If three of his students each collected $32 less, the average amount of money collected would be $146. If eight of his students each collected $18 more, the average amount of money collected would be $156. How many students were there in Mr Tan's class?
There were 56 students in Mr Tan's class.
To solve this problem, we can use the formula for average: average = (sum of all values) / (number of values). Let's assume that there were initially n students in Mr Tan's class, and the average amount collected was x. Then, we can write:
nx = sum of all amounts collected
Now, if three students each collected $32 less, the new sum of amounts collected would be:
(nx - 3*32) = (n-3)(x-32)
And the new average would be:
(n-3)(x-32) / n = 146
Similarly, if eight students each collected $18 more, the new sum of amounts collected would be:
(nx + 8*18) = (n+8)(x+18)
And the new average would be:
(n+8)(x+18) / n = 156
Now we have two equations with two unknowns (n and x). We can solve them using algebraic manipulation. After some simplification, we get:
n = 56 and x = 104
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PLEASE SOLVE THIS QUICKLY!!!!!
The ratio of the two arc lengths is equal to a / b. (Correct choice: B)
How to find the ratio of two arc lengths
In this problem we must determine the ratio of two arc lengths, that is, the ratio between two circular arcs. The length of a circular arc is described by the following expression:
s = θ · r
Where:
s - Arc length
θ - Angle, in radians.
r - Radius
And the ratio of the length JK to the length MN is:
JK / MN = (θ · a) / (θ · b)
JK / MN = a / b
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Solve for k and graph the solution. 0≥ k+14 3 > – 2
The graph of the solution set for the inequality -14 ≥ k > -20 is on the image at the end.
How to solve the inequality for k?To do this we just need to isolate the variable k in the middle.
We start with:
0 ≥ (k+14)/3 > – 2
We can multiply both sides by 3:
3*0 ≥ (k+14) > – 2*3
0 ≥ (k+14) > - 6
Now subtract 14 in both sides:
-14 ≥ k > -6 - 14
-14 ≥ k > -20
Then we need to draw an open circle at k = -20 and a closed circle at k = -14, and connect them with a line, like in the image below.
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what does scaled version mean in this case its 3:5 scaled version but i just want to know what it means asap please help
Scaled version means adjusted value from the original size. For example, 3:5 could be a scaled version of 6:10.
Understanding Scale VersionScale Version of an object is a replica or model of the original object that has been proportionally reduced or enlarged in size. The scale of a model is the ratio of the size of the model to the size of the original object. For example, if a model of a building is one-tenth the size of the actual building, then the scale of the model is 1:10, which means that every measurement on the model is one-tenth of the corresponding measurement on the actual building.
Scale versions of objects are often used in engineering, architecture, and design to create smaller or larger versions of objects that can be studied, tested, or used for other purposes. For example, architects might create scale models of buildings to study their design and appearance, while engineers might create scale models of machines or structures to test their performance under different conditions.
Scale versions can also be used in maps, where the scale is used to indicate the relationship between the size of the map and the size of the area it represents. In this case, the scale might be represented as a ratio, such as 1:10,000, or as a statement of the size of a unit of measurement on the map, such as 1 inch equals 1 mile.
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Javier and Naida are discussing the elevation of Lima, Peru.
200
150 Lima
100
50+
0+Sea level
-50-
-100+
-150
-200
The elevation of Lima, Peru is 154 meters.
Javier: Lima is 154] meters from sea level.
Naida: Lima is 154 meters above sea level.
Whose statement is true?
Choose 1 answer:
Answer:
Naida's statement is true
Step-by-step explanation:
Since the elevation of Lima, Peru is a positive number, you can automatically tell that it is above sea level since sea level is zero
WILL GIVE BRAINLIEST IF CORRECT
Will report is answer is a guess. Include reasoning behind answer
The image of point R by rotation is equal to R'(x, y) = (- 4, 7).
How to find the image of a point by rotation
The statement of the problem asks us to find the image of point by a kind of rigid transformation known as rotation, whose formula is:
(x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
x, y - Coordinates of the original point.θ - Angle of rotation, in degrees.If we know that x = 4, y = 7 and θ = - 180°, then the coordinates of the image of point R are:
R'(x, y) = (4 · cos 180° - 7 · sin 180°, 4 · sin 180° + 7 · cos 180°)
R'(x, y) = (- 4, 7)
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Help please!!!!
Whoever answers right gets brainliest!
When w = 10 and z = 2, the value of expression 2w⁻²z⁰ is equal to 1/50. So, correct option is A.
The expression 2w⁻²z⁰ can be simplified as follows:
2w⁻²z⁰ = 2/w² * z⁰
Since z⁰ = 1 for any non-zero value of z, we can simplify further:
2w⁻²z⁰ = 2/w² * 1
Now we can substitute w = 10 into the expression:
2(10)⁻² * 1 = 2/100 = 1/50
In general, when we have a negative exponent in an expression, we can rewrite it as a positive exponent in the denominator. In this case, w⁻² can be rewritten as 1/w². Additionally, any number raised to the power of 0 is always 1, so z⁰ = 1. By simplifying the expression, we can easily substitute the given values of w and z to evaluate the expression.
So, correct option is A.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
A. x² + (y - 3)² = 36.
D. x² + (y + 8)² = 36.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = diameter/2 = 12/2 = 6 units.
Center, (h, k) = (0, 3).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 3)² = 6²
x² + (y - 3)² = 36.
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A shopper has $430 to spend on a winter coat. Write and solve an inequality to find the prices p of coats that the shopper can buy. Assume that p is greater than or equal to 175.
The inequality that represents the range of prices of winter coats the shopper can buy as 175 ≤ p ≤ 430
To write the inequality, we can use the variable p to represent the price of the coat. The inequality we can write is:
p ≥ 175
This inequality means that the price p of the coat must be greater than or equal to $175.
Now, we also know that the shopper has a budget of $430 to spend on a winter coat. This means that the price p of the coat must be less than or equal to $430. We can represent this inequality as:
p ≤ 430
This inequality means that the price p of the coat must be less than or equal to $430.
To find the range of prices that the shopper can buy, we need to find the values of p that satisfy both of these inequalities. We can do this by finding the intersection of the two inequality regions on a number line, or by solving the system of inequalities:
p ≥ 175
p ≤ 430
To solve this system, we simply need to find the values of p that satisfy both inequalities simultaneously. We can do this by taking the intersection of the two inequality regions:
175 ≤ p ≤ 430
This means that the price p of the winter coat must be greater than or equal to $175 and less than or equal to $430. Therefore, the shopper can buy any winter coat with a price in this range.
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show that f= 16 is
R
equivalent to
fpm = 12
RPM in fluid flow through porous media
Complete part (a) and part (b) given the following system of equations. x+y=0 -3x+4y=14. Solve this system graphically.
Answer:
Step-by-step explanation:
[tex]\left \{ {{x+y=0} \atop {-3x+4y=14}} \right.[/tex] ⇔ [tex]\left \{ {{y=-x} \atop {y=\frac{3}{4} x+ \frac{7}{2} }} \right.[/tex]
If your starting salary is $50,000 and you receive a 4% increase at the end of
every year, what is the total amount, in dollars, you will earn over the first 16
years that you work?
Round your answer to the nearest whole dollar, and express your answer
without using commas.
Answer here
SUBMIT
Answer:
Total amount of becomes after 16 year is $93649 .
the expression when c=56 and d=10
The numeric value of the expression 3c + 4d when c = 56 and d = 10 is given as follows:
208.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The expression for this problem is given as follows:
3c + 4d.
Hence the numeric value of the expression is given as follows:
3 x 56 + 4 x 10 = 208.
Missing InformationThe expression is:
3c + 4d.
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Julieta says that it is not possible to draw a quadrilateral that is not a trapezoid and a parallelogram. Is Julieta correct explain why or why not.
Julieta's claim about the quadrilateral is false.
How to prove or disprove Julieta claim?The statement is given as:
It is impossible to draw a quadrilateral that is not a trapezoid and not a parallelogram.
The condition for a shape to be a quadrilateral is that the shape must have four sides.
An irregular shape that has four sides is a quadrilateral, but neither a quadrilateral nor a parallelogram
Therefore, Julieta's claim is false
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An angle measures 158.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
the 2 angles are 169.1° and 10.9°
Step-by-step explanation:
Supplementary angles add to 180
x = first angle
y = second angle = x - 158.2
x + y = 180
x + (x - 158.2) = 180
2x = 180 + 158.2
2x = 338.2
x = 338.2/2 = 169.1
y = 169.1 - 158.2 = 10.9
x + y = 169.1 + 10.9 = 180
I may be able to figure out part (b) of this one, but I do need help with parts (a) and (c). Any help would be greatly appreciated.
(a) The shape of sampling distribution is not too close to 0 or 1 (b) The mean of standard deviation = 0.033
(c) [tex]P(Z > (P-P + 0.03) / 0.033) = P(Z > 0.91)[/tex]
According to given information:(a) The sampling distribution of p-p is approximately normal by the Central Limit Theorem because both sample sizes are large enough (n₁ = n₂ = 240) and the sample proportions of orange candies are not too close to 0 or 1.
(b) The mean of the sampling distribution of p-p is equal to the difference between the population proportions, which is 0.20 - 0.23 = -0.03. The standard deviation of the sampling distribution of p-p is given by:
sqrt[(p₁q₁/n₁) + (p₂q₂/n₂)]
= sqrt[(0.200.80/240) + (0.230.77/240)]
= 0.033
The standard deviation represents the amount of variation we expect to see in the differences between sample proportions of orange candies from multiple random samples of the same size.
(c) To find P(P-P>0), we need to standardize the difference between the sample proportions and the population difference and then find the probability that the standardized difference is greater than 0. That is:
(P-P - (p₁ - p₂)) / sqrt[(p₁q₁/n₁) + (p₂q₂/n₂)]
= (P-P - (-0.03)) / 0.033
= (P-P + 0.03) / 0.033
Using a standard normal distribution table or calculator, we can find the probability that a standard normal variable is greater than this value. For example, if we use a calculator, we get:
P(Z > (P-P + 0.03) / 0.033) = P(Z > 0.91)
where Z is a standard normal variable. The probability is approximately 0.18. This means that if we take many random samples of 240 M&M's milk chocolate candies and 240 peanut M&M's and calculate the difference between the sample proportions of orange candies, about 18% of the time we would expect to see a difference of 0.03 or greater (favoring M&M's milk chocolate candies).
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Which of the following are solutions to the system of inequalities y<−x+5 and y≥3x+1?
A)
(1,0)
cross out
B)
(−2,2)
cross out
C)
(1,6)
cross out
D)
(0,1)
cross out
E)
(1,4)
cross out
F)
(−2,7)
From the graph attached below, the solution to the system of linear inequalities are (1, 4)
What is the solution to the system of linear inequalities?A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.
In the problem given;
y < - x + 5 ...eq(i)
y ≥ 3x + 1 ...eq(ii)
To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.
From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E
Kindly find attached graph below
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find the missing sides of this triangle (Hint: is this a special right triangle?)
(10 on the adjacent and two 45° angles on both ends if anyone can’t see)
Answer:
Both sides are equal, and are equvalent to 5 square root of 2
Step-by-step explanation:
This is a special right angled triangle known as the 45-45-90 triangle
The hypotenuse of a 45-45-90 triangle is x square root 2, with x being both sides of the triangle
10=x square root of 2 (Divide both sides by square root of 2)
10/square root of 2=x (Rationalize)
x=5 square root of 2
The graph of an equation is sketched in the figure.
Describe five ordered-pair solutions of this equation by
using a table.
X
-6
-3
0
3
6
y
☐
I
8-
10-88427
6
40
10
The value of five ordered-pair solutions of this equation by using a table are,
x y
- 6 - 1
- 3 - 2
0 3
3 - 4
6 - 5
We have to given that;
The graph of an equation is sketched in the figure.
Hence, From graph we get;
The value of five ordered-pair solutions of this equation by using a table are,
x y
- 6 - 1
- 3 - 2
0 3
3 - 4
6 - 5
Thus, The value of five ordered-pair solutions of this equation by using a table are,
x y
- 6 - 1
- 3 - 2
0 3
3 - 4
6 - 5
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Determine whether y=9(-5)^x represents an exponential function
Answer: Yes, y = 9(-5)^x represents an exponential function.
An exponential function is a function in the form y = ab^x, where a and b are constants and b is a positive real number not equal to 1. The base, b, is raised to the power of x, and the resulting value is multiplied by the constant a.
In the given function, we have a = 9 and b = -5. Although b is negative, it is still a real number not equal to 1, so the function is still considered exponential. Furthermore, the exponent x is a variable, which is raised to a constant base -5, meeting the definition of an exponential function.
Therefore, y = 9(-5)^x is an exponential function.
Step-by-step explanation:
Consider the letters in the word SAMPLE. In how many ways can you arrange 5 of the letters?
Answer: 720
Step-by-step explanation: There are 6 choices for the first letter, 5 for the second, 4 for the third and so on. 6*5*4*3*2=720
Step-by-step explanation:
according to the law of combination
⁵C6 note 6 is a base numberCombining formula: 6!/(6-1)! 6!solving 6!/5! 6! :120waysWhich equation has the variable, or missing number, in the correct place to match the given situation? The Mansour family drove a total of 687 miles, starting on Friday and ending on Sunday. They drove 313 miles on Friday and 164 miles on Saturday. How many miles did they drive on Sunday?
part a.
The equation that has the variable in the correct place to match the given situation is: Sunday's mile
part b
the Mansour family drove 210 miles on Sunday.
What is an equation?An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign =..
We have that the equation that has the variable in the correct place to match the given situation is: Sunday's mile
Sunday's miles = Total miles - Friday's miles - Saturday's miles
Sunday's miles = 687 - 313 - 164
Sunday's miles = 210
In conclusion, the Mansour family drove 210 miles on Sunday.
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Navid earns a basic wage of $10.25 an hour. He works for 40 hours a week. He earns 20% more than his basic wage when he works overtime. Navid wants to earn at least $500 this week. Calculate the total number of hours he needs to work. Give your answer to the nearest hour.
A child at a day care can choose one type of writing tool and one type of paper for an art project. The chart shows
the types of writing tools and paper that are available.
Art Project
Type of Writing Tool Type of Paper
Crayon
Marker
Pencil
Construction
Newsprint
Which list shows all the combinations of one type of writing tool and one type of paper that can be used for the art
project?
The list that shows all the combinations is given as follows:
{Crayon, Construction}, {Marker, Construction}, {Pencil, Construction}, {Crayon, Newsprint}, {Marker, Newsprint}, {Pencil, Newsprint}.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.
This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The options are given as follows:
Writing Tool: Crayon, Marker and Pencil. -> 3 options.Type of Paper: Construction and Newsprint -> 2 options.The total number of options is given as follows:
3 x 2 = 6.
Hence the list is:
{Crayon, Construction}, {Marker, Construction}, {Pencil, Construction}, {Crayon, Newsprint}, {Marker, Newsprint}, {Pencil, Newsprint}.
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In QA, if m/DBG= 32° and mGFE = 149°, find mDG.
A. mDG = 62°
B. mDG=85°
C. mDG = 107°
D. mDG = 117°
E
Mark this and return
The tangent secant exterior angle measure theorem indicates that the measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°, the correct option is the option B.
B. m[tex]\widehat{DG}[/tex] = 85°
What is the tangent secant exterior angle measure theorem?The tangent secant exterior angles theorem states that if two secant or tangent or a secant and tangent intersect on the exterior to a circle, the measure of the angle formed is half the difference of the arcs they intercept.
The possible options in the question indicates that the possible drawing in the consists of a tangent and a secant, with the angle m∠DBG, being external to the circle.
The tangent secant exterior angle measure theorem indicates that we get;
m∠DBG = (1/2) × (m[tex]\widehat{GFE}[/tex] - m[tex]\widehat{DG}[/tex])
The question indicates; m[tex]\widehat{GFE}[/tex] = 149°
m∠DBG = 32°
Therefore;
32 = (1/2) × (149° - m[tex]\widehat{DG}[/tex])
149° - m[tex]\widehat{DG}[/tex] = 2 × 32° = 64°
m[tex]\widehat{DG}[/tex] = 149° - 64° = 85°
The measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°
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what is y= -2/9x +2 in standard form?
Answer:
2x+9y=18
Step-by-step explanation:
HOW MANY WAYS ARE THERE TO PICK 3 ASTRONAUTS TO GO TO THE MOON OUT OF 10 CANDIDATES
The number of ways to pick 3 astronauts from 10 candidates can be found using the combination formula, which is:
nCk = n! / (k!(n-k)!)
where n is the total number of candidates, k is the number of candidates to be chosen, and "!" denotes the factorial function.
In this case, we want to choose 3 astronauts from a pool of 10 candidates, so we can plug these values into the formula:
10C3 = 10! / (3!(10-3)!)
= (10 x 9 x 8) / (3 x 2 x 1)
= 120
Therefore, there are 120 ways to pick 3 astronauts to go to the moon out of 10 candidates.
Answer:
120 or 220
Step-by-step explanation:
The radius of a circle is 7 inches the radius of circle, B is 3inches greater than the radius of circle A. If the radius of circle C is 4 inches greater than the radius of circle B the radius of circle D is 2 inches less than the radius of circle C, see what is the area of each circle
The area of each circle would be given below:
Circle A= 153.86 in²
Circle B = 314in²
Circle C = 615.44in²
Circle D = 452.16 in²
How to calculate the area of circle?To calculate the area of a circle, the formula that should be used is given below such as follows:
Area of circle = πr²
For circle A;
radius = 7 in
area = 3.14×7×7 = 153.86 in²
For circle B;
radius = 3+7 = 10in
area = 3.14×10×10 = 314in²
For circle C;
radius = 10+4 = 14 in
area = 3.14×14×14
= 615.44in²
For circle D;
radius = 14-2 = 12in
radius = 3.14×12×12
= 452.16 in²
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Charges for advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is a percentage of the population of 110 million TV households. The CBS television show 60 Minutes recently had a rating of 7.8, indicating that 7.8% of the households were tuned to that show. An advertiser conducts an independent survey of 100 households and finds that at least b+1 were tuned to 60 Minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting at least 5+1 tuned to
60 Minutes.
The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.
How to calculate the probabilityP(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)
P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)
Using a calculator or software, we can find that:
P(X <= 4) = 0.000203
This means that the probability is 0.02%.
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Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?