Answers
Answer:
\(\fbox{\begin{minipage}{16em}Option D: y = (4/7)x + 8 is correct\end{minipage}}\)
Step-by-step explanation:
(1) A typical form of equation of a line is:
\(y = Mx + b\)
with, \(M\) is slope and \(b\) is y-intercept.
(2) Another straight line has equation in form of:
\(y = Nx + c\)
with \(N\) is slope and \(c\) is y-intercept
(3) If these two lines are perpendicular, according to the property of two perpendicular lines on the two-dimensional plane, we have:
\(M\) x \(N\) = -1
(4) Transform the given equation of original line into typical form:
\(7x + 4y = -24\\\)
<=> \(4y = -7x - 24\)
<=> \(y = (\frac{-7}{4})x - \frac{24}{4}\)
<=> \(y = (\frac{-7}{4})x - 6\)
=> \(M = \frac{-7}{4}\)
=> \(N = \frac{-1}{M} = \frac{-1}{\frac{-7}{4} } = \frac{-4}{-7} = \frac{4}{7}\)
=> Option D: \(y = (\frac{4}{7})x + 8\) is correct (Slope = \(\frac{4}{7}\))
Hope this helps!
:)
Related Questions
Solve this system of 3 variables with elimination. Once you eliminate 1 variable to get down to only 2, you can use Desmos but show all work/steps first.
3x − 4y + z = 2
−9x + 12y − 3z = − 6
4x − 2y − z = -16
Answers
The solution of the system of the equations are; x = -2/3, y = -1/2 and z = 1.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The system of equation is given by;
3x − 4y + z = 2 ---- (1)
−9x + 12y − 3z = − 6 -------(2)
4x − 2y − z = -16 -----(3)
Now we add equations 1 from equation 3;
(3x − 4y + z ) + (4x − 2y − z ) = 2 -16
7x - 6y = -14 -----(4)
Further we multiply equation 3 by 3 and subtract from equation 2;
3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6
12x - 6y - 3z + 9x - 12y + 3z = 42
21x - 18y = 42-----(5)
Now we multiply equation 4 by 3 and add it to equation 4
3(-3x + 3z) + (9x + 4z) = 5×3 - 2
-9x + 9z + 9x + 4z = 15 -2
13z = 13
z = 1
Now we put z = 1 in equation number 5
-3x + 3×1 = 5
-3x + 3 = 5
-3x = 5 - 3
-3x = 2
x = -2/3
y = -1/2
Therefore, the solution of the system of the equations are; x = -2/3, y = -1/2 and z = 1.
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What is the value of 9x - 4y if x = 3 and y = 2
Answers
Answer:
19
Step-by-step explanation:
plug both values in
Answer:
19
Step-by-step explanation:
Since it gives you the values of x and y, all you need to do is plug in the numbers, like so:
9x - 4y
9(3) - 4(2)
27 - 8
19
A $5,$10,$20,$50, or $100 bill is mapped to all the sets of coins that are the same as the total value of the bill. Tell whether this situation represents a function. Explain your reasoning. If the situation represents a function, give the domain and range.
Answers
Answer:
This situation represents a function. The domain is {A, B, C, D, E} and the range is {$5, $10, $20, $50, $100}.
Step-by-step explanation:
Firstly, we need to know what a function is:
It is simply something that relates an input to an output. Like for instance a mirror is a function that relates your face to your image. In lay terms we can call something a function if and only if it can relate one thing to another. Mathematically, a function is called a function if and only if every input has a distinct output, just as how one face can't produce two images at a time when looked at the mirror. The input is called the domain and output range.
Now, in the question we are told that all the bills are mapped – related in lay terms – to some set of coins that are exactly the same number of the bills. This means each bill has a distinct input. Here is a clearer picture:
A to 5 usd
B to 10usd
C to 20usd
D to 50usd
E to 100usd
Where A, B, C, D and E respectively stand for the distinct coins that are mapped to the distinct bill.
From here, each coin has it distinct output. Therefore it is a function.
The domain is {A, B, C, D, E} and the range is {$5, $10, $20, $50, $100}.
Which is the polynomial function of lowest degree that has –5, –2, and 0 as roots? f(x) = (x – 2)(x – 5) f(x) = x(x – 2)(x – 5) f(x) =(x 2)(x 5) f(x) = x(x 2)(x 5)
Answers
The polynomial function of the lowest degree that has -5, -2, and 0 as roots is f(x) = (x - 2)(x - 5).
To find the polynomial function of the lowest degree with -5, -2, and 0 as roots, we can use the factored form of a polynomial. If a number is a root of a polynomial, it means that when we substitute that number into the polynomial, the result is equal to zero.
In this case, we have the roots -5, -2, and 0. To construct the polynomial, we can write it in factored form as follows: f(x) = (x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots.
Substituting the given roots, we have: f(x) = (x - (-5))(x - (-2))(x - 0) = (x + 5)(x + 2)(x - 0) = (x + 5)(x + 2)(x).
Simplifying further, we get: f(x) = (x^2 + 7x + 10)(x) = x^3 + 7x^2 + 10x.
Therefore, the polynomial function of the lowest degree with -5, -2, and 0 as roots is f(x) = x^3 + 7x^2 + 10x.
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The polynomial function of lowest degree that has –5, –2, and 0 as roots is f(x) = x(x + 2)(x + 5). Each root is written in the form of (x - root) and then multiplied together to form the polynomial.
Explanation:The question asks for the polynomial function of the lowest degree that has –5, –2, and 0 as roots. To find the polynomial, each root needs to be written in the form of (x - root). Therefore, the roots would be written as (x+5), (x+2), and x. When these are multiplied together, they form a polynomial function of the lowest degree.
Thus, the polynomial function of the lowest degree that has –5, –2, and 0 as roots is f(x) = x(x + 2)(x + 5).
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when the “a” value is negative in any quadratic what do you know about the graph?
Answers
Answer:
when a is negative, the parabola opens downward
Step-by-step explanation:
Write 128 as a product of its prime factors
Answers
Answer:
The prime factorization of 128 is 2 x 2 x 2 x 2 x 2 x 2 x 2.
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Help? ;-;
If an item became sentient, and changed it's own price from $18 to $45, what is that percent of change, AND what would be the total price that someone would pay if the sales tax was 5%?
A.150%; $47.25
B.150%, $2.25
C.60%; $47.25
D.60%; $2.25
Answers
What’s the answer????
Answers
(-2)^3 = -8.
So if you take the cubed root of -8, raised to the 3rd power: [3√(-8)]^3
and (-2)^(-3), the answer will be -2.
Therefore, the correct answer is x = -8.
a five card hand of cards is dealt from a deck of 52 cards. how many ways can the hand have 3 hearts and 2 diamonds?
Answers
The number of ways to have 3 hearts and 2 diamonds in a 5 card hand is 286 * 78 = 22,308 ways.
The number of ways to choose 3 hearts from the 13 available hearts is given by the binomial coefficient C(13,3). The number of ways to choose 2 diamonds from the 13 available diamonds is given by C(13,2). The total number of ways to choose 3 hearts and 2 diamonds from the deck of 52 cards is the product of these two binomial coefficients: C(13,3) * C(13,2).
i.e.
There are 13 hearts and 13 diamonds in a deck of 52 cards.
To choose 3 hearts, we have C(13,3) = 13!/(3!(13-3)!) = 286 ways.
To choose 2 diamonds, we have C(13,2) = 13!/(2!(13-2)!) = 78 ways.
Therefore, the number of ways to have 3 hearts and 2 diamonds in a 5 card hand is 286 * 78 = 22,308 ways.
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3. Which equation shows a correct
trigonometric ratio for angle A in the right
triangle below? (MGSE9-12.G.SRT.6)
B
8 cm
A.
B. tan A
sin A =
C. cos A
17 cm
15 cm
D. tan A =
15| 17 3/17 15/17 15-2
8
8
A
Answers
Answer:
C) cos A = 15/17
cos A = adjacent/hypotenuse = 15/17
What is trigonometric ratio for right angle triangle?
The trigonometric ratios for a right angle triangle are sine, cosine, and tangent. The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side.
The following are the trigonometric ratios of a right angle triangle:
Sine (sin): Opposite Side/Hypotenuse
Cosine (cos): Adjacent Side/Hypotenuse
Tangent (tan): Opposite Side/Adjacent Side
Cosecant (csc): Hypotenuse/Opposite Side
Secant (sec): Hypotenuse/Adjacent Side
Cotangent (cot): Adjacent Side/Opposite Side
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Find the solution to the initial value problem. y′′(θ)−16y(θ)=3sin(4θ)−4e3θ;y(0)=1,y′(0)=−1 y(θ)=
Answers
Therefore, the solution to the initial value problem is:
y(θ) = (65/64) cos(4θ) - (25/272) sin(4θ) - (1/64)e3θ. To solve the initial value problem y′′(θ)−16y(θ)=3sin(4θ)−4e3θ;y(0)=1,y′(0)=−1, we can use the method of undetermined coefficients.
First, we find the general solution to the homogeneous equation y′′(θ)−16y(θ)=0. The characteristic equation is r^2 - 16 = 0, which has roots r = ±4i. So the general solution to the homogeneous equation is y_h(θ) = c1 cos(4θ) + c2 sin(4θ).
Next, we find a particular solution to the non-homogeneous equation. Since the right-hand side of the equation contains both sin(4θ) and e3θ, we guess that the particular solution has the form y_p(θ) = A sin(4θ) + Be3θ.
Taking the derivatives of y_p(θ), we have y_p′(θ) = 4A cos(4θ) + 3Be3θ and y_p′′(θ) = -16A sin(4θ) + 9Be3θ.
Substituting y_p(θ), y_p′(θ), and y_p′′(θ) into the original equation, we get:
(-16A sin(4θ) + 9Be3θ) - 16(A sin(4θ) + Be3θ) = 3sin(4θ) - 4e3θ
Simplifying and collecting like terms, we get:
-16A sin(4θ) + 3sin(4θ) = 4e3θ - 16Be3θ
Solving for A and B, we get A = -3/272 and B = -1/64.
So the particular solution is y_p(θ) = (-3/272) sin(4θ) - (1/64)e3θ.
Therefore, the general solution to the non-homogeneous equation is y(θ) = y_h(θ) + y_p(θ) = c1 cos(4θ) + c2 sin(4θ) - (3/272) sin(4θ) - (1/64)e3θ.
Using the initial conditions y(0) = 1 and y′(0) = -1, we can solve for c1 and c2:
y(0) = c1 + 0 - (3/272) (0) - (1/64)(1) = 1
So c1 = 1 + (1/64) = 65/64.
y′(0) = 0 + 4c2 - (3/272)(4) - (1/64)(-3) = -1
So c2 = (-1 + (3/272)(4) + (3/64))/4 = (-25/68)(1/4) = -25/272.
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how do i find the 13th term?
Answers
D=8
Now
t13=a*12D
=2*12*8=192
Answer= 192
Misty correctly determined the equation of the linear function represented by the table of values below to be y = negative 2 x + 9 in slope-intercept form by using the ordered pairs (1, 7) and (2, 5).
x
y
1
7
2
5
3
3
4
1
What would she have gotten for the equation of the linear function if she had used the ordered pairs (2, 5) and (4, 1) instead?
y = negative 4 x + 9
y = negative 4 x + 18
y = negative 2 x + 9
y = negative 2 x + 18
Answers
Answer:
y = negative 2 x + 9
Step-by-step explanation:
In the figure below what is the value of x?
Answers
Answer:
The value of x is 106
Step-by-step explanation:
Let us solve the question
In the given figure
∵ The triangle in the given figure has two sides equal
→ That means the triangle is an isosceles triangle
∴ The triangle is isosceles
∵ In the isosceles triangle, the base angles are equal in measures
∵ The measure of one base angle is 37°
∴ The measure of other base angle is 37°
→ The sum of the measures of the interior angles of a Δ is 180°
∵ 37° + 37° + x = 180°
→ Add the like terms
∴ 74° + x = 180°
→ Subtract 74 from both sides
∵ 74 - 74 + x = 180 - 74
∴ x = 106
∴ The value of x is 106
if expected frequencies are not all equal, then we can determine them by enp for each individual category, where n is the total number of observations and p is the probability for the category. b. if expected frequencies are equal, then we can determine them by , where n is the total number of observations and k is the number of categories. c. expected frequencies need not be whole numbers. d. goodness-of-fit hypothesis tests may be left-tailed, right-tailed, or two-tailed.
Answers
If the expected frequencies are not all equal, we can determine them by using the equation enp for each individual category, where n is the total number of observations and p is the probability for the category. This equation helps us calculate the expected frequency for each category based on their probabilities and the total number of observations.
On the other hand, if the expected frequencies are equal, we can determine them by using the equation n/k, where n is the total number of observations and k is the number of categories. This equation helps us distribute the total number of observations equally among the categories when the expected frequencies are equal.
Expected frequencies do not necessarily have to be whole numbers. They can be decimals or fractions depending on the context and calculations involved.
Goodness-of-fit hypothesis tests can be left-tailed, right-tailed, or two-tailed. These different types of tests allow us to assess whether the observed data significantly deviates from the expected frequencies. The choice of the tail depends on the specific research question and the alternative hypothesis being tested.
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322 Out of 450 is What Percent?
Answers
The percentage of 322 out of 450 using the percentage formula was found out to be approximately 71.56%.
To find the percentage of 322 out of 450, we can use the following formula:
percentage = (part/whole) x 100
where, "part" is the value we want to express as a percentage (in this case, 322), "whole" is the total value (in this case, 450), and "x" means "multiply".
Using the formula mentioned above, we get:
percentage = (322/450) x 100
percentage = 0.7156 x 100
percentage = 71.56%
Therefore, percentage of 322 out of 450 is approximately 71.56%.
A percentage is a way to express a number as a fraction of 100. It is often denoted using the "%" symbol.
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Write the equation of line in slope-intercept form, which is parallel to y=−2x+5 and passing through the point (1, −4)
What would Y = ?
Answers
Answer:
y = -2x-2
Step-by-step explanation:
y = -2x+5
This is in slope intercept form so y = mx+b where m is the slope
The slope is -2
Parallel lines have the same slope so the new line has a slope of -2
y= -2x+b
We have a point on the line of (1,-4)
-4 = -2(1)+b
-4 = -2+b
Add 2 to each side
-4+2 = -2+b+2
-2 =b
y = -2x-2
Witch of the following is equal to -2 -5
Answers
the answer of given expression is -7.
What are mathematics operations?
A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Given mathematics expression is :
-2-5
Simply add 2 and 5 with negative sign as there sign is same :
-2-5 = -7
Therefore, the answer of given expression is -7.
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How does h(x)=5^(x) change over the interval from x=1 to x=3 ?
Answers
The function \(h(x) = 5^x\) exhibits exponential growth over the interval from x = 1 to x = 3. It starts at 5 and increases significantly to 125 within this interval.
The function h(x) = 5^x represents exponential growth, where the base 5 is raised to the power of x. To understand how h(x) changes over the interval from x=1 to x=3, let's evaluate the function at these values.
At x = 1, h(1) = 5^1 = 5.
At x = 3, h(3) = 5^3 = 125.
Therefore, over the interval from x = 1 to x = 3, the function h(x) = 5^x increases from 5 to 125. This demonstrates the rapid increase characteristic of exponential functions with a base greater than 1.
The function exhibits exponential growth, where the values increase rapidly as the exponent increases. In this case, the base 5 raised to increasing powers results in a substantial increase in the function's values over the given interval.
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PLEASE PLEASE PLEASE Solve the literal equation a+4b=5b-3a for a.
Answers
Answer:
a=b/4
Step-by-step explanation:
subtract 4b from both sides to end up with a=b-3a and then add 3a to both sides to get 4a=b, and divide both sides by 4 to get a=b/4.
Answer:
a + 4b + 5b - 3a can only be solved by a little.
Step-by-step explanation:
a + 3a =3a.
4b + 5b = 9b.
we can't solve 9b - 3a, since they have different functions, so 9b - 3a is the answer.
the width of a rectangle is 2x²+9x-7 and the length is x²-9. Find the perimeter of the rectangle.
Answers
Answer:
---
Step-by-step explanation:
W=2x²+9x-7
L=x²-9
2(3x²+9x-16)
6x²+18x-32
The bold is the perimeter.
---
hope it helps
Work out the surface area of this cylinder.
12 cm
35 cm
Answers
pi x r^2 which means pi x 12^2 =452.3893421(if you round it in 2dp its 452.39)
If you need the volume then you times it by 35.
Casho has a bag that contains pineapple chews, lemon chews, and lime chews. She performs an experiment. Casho randomly removes a chew from the bag, records the result, and returns the chew to the bag. Casho performs the experiment 54 times. The results are shown below:
A pineapple chew was selected 9 times.
A lemon chew was selected 15 times.
A lime chew was selected 30 times.
Based on these results, express the probability that the next chew Casho removes from the bag will be pineapple chew as a percent to the nearest whole number.
Answers
Answer:
17% the next chew Casho pulls out is pineapple
Step-by-step explanation:
pineapple chew 9/54
lemon chew 15/54
lime chew 30/54
9/54 = 0.1666666... make this a percent and you get 17% of the time Casho will pull out a pineapple chew.
Answer:
...................................................................
Step-by-step explanation:
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answers
Answer:
10
Step-by-step explanation:
Equation=5*2^3/2^2
Alexa gets $100 every week from her parents and earns $25 per hour tutoring. Jenna gets $150 from her parents every week and earns $15 per hour baby-sitting. How many hour per week will they have to work to have the same amount?
Answers
Answer: 5 hours/week
They will have to work 5 hours/week to get their amount equal.
What is equation?An equation is the statement of equality between two expressions consisting of variables and/or numbers.
Given that, Alexa gets $100 every week from her parents and earns $25 per hour tutoring. Jenna gets $150 from her parents every week and earns $15 per hour baby-sitting.
Let the number of hours they work be n, then according to question,
100 + 25n = 150 + 15n
10n = 50
n = 5
Hence, They will have to work 5 hours/week to get their amount equal.
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please help me it would be apprciated
Answers
Answer: 1
Step-by-step explanation: 1
Your hospital has just reset the safety stock level for sleeping pills to be 220 pills.
If your hospital consumes an average of 1,155 per day with a standard deviation of 81 pills, what is the chance that your hospital will run out of sleeping pills on any day? (Keep four decimal places in your answer, which should be a number not a percentage)
Answers
The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).
To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.
First, let's calculate the Z-score using the formula:
Z = (X - μ) / σ
Where:
X = consumption rate per day (1,155 pills)
μ = average consumption rate per day (1,155 pills)
σ = standard deviation (81 pills)
Z = (1,155 - 1,155) / 81
Z = 0
Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.
We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.
To find the probability of running out of sleeping pills, we subtract this probability from 1:
Probability of running out of sleeping pills = 1 - 0.5000
Probability of running out of sleeping pills = 0.5000
Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.
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pleaseee help
BRAINLIESt!!!!
Answers
Answer:
C y cause it was already there plus ik super late but hey sum points
Step-by-step explanation:
2^x × 3^3 = 108 find the value of x
Answers
Answer:
It's 2
Step-by-step explanation:
2^x × 3^3 = 108
2^x = 108 / 27
2^x = 4
2^x = √4
x = 2
A well-mixed cookie dough will produce cookies with a mean of 7 chocolate chips apiece. What is the probability of getting a cookie with no more than 4 chips? Round
your answer to four decimal places
Answers
Answer:
I have solved this on Paper and attached an image in the explanation part!
Step-by-step explanation:
