Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n

According to the image we can infer that both figures are similar. Their ratio is 11:4; their scale factor is 1:2 and their areas are: 40cm² and 14.54cm²

We know that the two figures are similar because they have the same angles. Therefore they are similar. In this case it can be inferred that they have a scale factor close to half because the small triangle represents more or less half of the large triangle.

The value of the ratio can be found taking as reference the measurements of the base of the triangles. Then it would be a ratio of 11:4, that is to say that for every 11cm of large triangle, the small one has a 4cm base.

Finally, if the area of the large triangle is 40cm², the area of the small triangle would be the following:

11cm base = 40cm²

4 cm base = cm²

4 * 40 / 11 = 14.54cm²

Yes they are similar because they have the same angle values.

According to the graph we can infer that the scale factor of the similarity transformation that takes ABC to CDE is 1:2.

According to the information, we can infer that the ratio of the area of both triangles is 11:4 because those values correspond to their base length.

if the area of the large triangle is 40cm², the area of the small triangle would be the following:

11cm base = 40cm²

4 cm base = cm²

4 * 40 / 11 = 14.54cm²

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Answer:

Molly is correct in stating that the two functions are not inverses of each other.

To be inverses of each other, two functions must satisfy the property that when they are composed in either order, they result in the identity function, which is represented by f(x) = x.

In this case, we have:

f(g(x)) = (x + 5) + 5 = x + 10

g(f(x)) = (x + 5) + 5 = x + 10

Since both compositions of the functions result in x + 10, which is not equal to x, the two functions are not inverses of each other.

Step-by-step explanation:

Answer:

Molly is correct. The fact that $f(g(x)) = g(f(x)) = x+5$ indicates that the two functions, $f$ and $g$, are symmetric about the line $y=x$, which means that they are not inverses of each other.

To determine whether two functions are inverses of each other, we need to show that their composition results in the identity function. That is, if $f(x)$ and $g(x)$ are two functions, then $f(g(x)) = g(f(x)) = x$ for all $x$ in the domain of $f$ and $g$.

In this case, we see that $f(g(x)) = g(f(x)) = x+5$, which is not the identity function. Therefore, the two functions are not inverses of each other.

The value of 'x' using the Triangle sum theorem is found as: x = 80°.

180° = 65°+35°+x

180° = 100°+x

180° - 100° = x

x=80° (value of x)

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The diagram for the question is attached:

Answer: The correct answer would be Graph H.

Step-by-step explanation:

Answer:

top right

Step-by-step explanation:

600 per 10 hours is a rate of 60/hour.

You need a graph that has a slope of 60 and includes the point (1, 60).

Answer: top right

Answer:

x=4, y=-2

Step-by-step explanation:

[tex]2y=x-8\\2y-x=-8\\2(2x-10)-x=-8\\4x-20-x=-8\\3x-20=-8\\3x=-8+20\\x=12/3\\x=4\\\\\\y=2x-10\\y=2(4)-10\\y=8-10\\y=-2[/tex]

Answer:

No R30000 will be enough as the gate of 1.2m width cost R500

If we know the length of the garden and the cost per meter of fencing, we can determine if Mr. Khumalo has sufficient funds to fence off the garden, taking into account the cost of the gate.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To determine if Mr. Khumalo will have sufficient funds to fence off the garden,

We need to calculate the total cost of the fence excluding the cost of the gate.

Let's assume the length of the garden is L meters.

The perimeter of the garden is then 2L + 1.2 meters (due to the gate on one side).

If the cost of fencing per meter is R, then the total cost of the fence will be:

Cost of the fence.

= (2L + 1.2) × R

Since Mr. Khumalo has a budget of R30000, we can set up an inequality to determine if the cost of the fence is within his budget:

(2L + 1.2) × R + 500 ≤ 30000

Simplifying the inequality, we get:

(2L + 1.2) × R ≤ 29500

Therefore,

If we know the length of the garden and the cost per meter of fencing, we can determine if Mr. Khumalo has sufficient funds to fence off the garden, taking into account the cost of the gate.

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The division (4+3i)/(5-7i) is performed and the result is (-1/74)+(43/74)i.

The division (4+3i)/(5-7i) is performed by multiplying the numerator and denominator by the complex conjugate of the denominator. In this case, the complex conjugate of (5-7i) is (5+7i).

So, the division can be performed as follows:

(4+3i)/(5-7i) * (5+7i)/(5+7i) = (4+3i)(5+7i)/(5-7i)(5+7i)

Multiplying the numerator and denominator gives:

(20+28i+15i+21i^2)/(25+35i-35i-49i^2)

Simplifying the numerator and denominator gives:

(20+43i-21)/(25+49)

Combining like terms gives:

(-1+43i)/(74)

Finally, dividing the numerator and denominator by 74 gives:

(-1/74)+(43/74)i

So, the division (4+3i)/(5-7i) is performed and the result is (-1/74)+(43/74)i.

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This is the equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10.

The equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10 can be found using the X=P+TD vector equation. In this equation, X represents the point on the line, P represents the point through which the line passes, T represents a scalar parameter, and D represents the direction vector of the line.

To find the direction vector of the line, we can use the normal vector of the plane, which is given by the coefficients of the x, y, and z terms in the equation of the plane. The normal vector of the plane is (2,-1,3).

Since the line is orthogonal to the plane, the direction vector of the line will be parallel to the normal vector of the plane. Therefore, the direction vector of the line is also (2,-1,3).

Now, we can plug in the values of P and D into the X=P+TD equation to find the equation of the line:

X = (2,1,-1) + T(2,-1,3)

X = (2+2T, 1-T, -1+3T)

The equation of the line in parametric form is:

x = 2+2T
y = 1-T
z = -1+3T

This is the equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10.

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Answer:

50

Step-by-step explanation:

good

Answer:

-4

Step-by-step explanation:

3x + 4 = -8

3x = -8 -4

3x = -12 /3

x = -4

The given functions f(x) = x² + 4x – 5 and g(x) = x - 1 are to be evaluated.
(f+g)(9). The addition of two functions is denoted by (f+g)(x) = f(x) + g(x). Now, we need to find the value of (f+g)(9). Substituting the values in the formula, we get:
(f+g)(x) = f(x) + g(x)f(x) = x² + 4x – 5g(x) = x - 1
(f+g)(9) = f(9) + g(9) = (9)² + 4(9) – 5 + (9) - 1= 81 + 36 – 5 + 9 - 1= 120
Therefore, (f+g)(9) = 120.

The subtraction of two functions is denoted by (f-g)(x) = f(x) - g(x). Now, we need to find the value of (f-9)(9). Substituting the values in the formula, we get:(f-g)(x) = f(x) - g(x)f(x) = x² + 4x – 5g(x) = x - 1(f-9)(9) = f(9) - g(9) = (9)² + 4(9) – 5 - (9) + 1= 81 + 36 – 5 - 9 + 1= 104
Therefore, (f-9)(9) = 104.3. (fog)(9)The composition of two functions is denoted by (fog)(x) = f(g(x)). Now, we need to find the value of (fog)(9).
Substituting the values in the formula, we get:
(fog)(x) = f(g(x))
f(x) = x² + 4x – 5
g(x) = x - 1
(fog)(9) = f(g(9)) = f(9 - 1) = f(8)= 8² + 4(8) – 5= 64 + 32 – 5= 91
Therefore, (fog)(9) = 91.4. g(x) = x - 1
Now, we need to evaluate g(9). Substituting x = 9 in the formula, we get:
g(x) = x - 1
g(9) = 9 - 1= 8
Therefore, g(9) = 8.

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The real zeros of the polynomial p(x) are 7/2, -7, and 7. Option D is the correct answer.

According to the algebraic principle known as the Factor Theorem, if a polynomial f(x) has a factor of (x - a), then f(a) = 0. To put it another way, if (x - a) is a factor of f(x), then the polynomial f(x) is equal to zero when x equals a. By finding the components of the polynomial and computing the values of x that make each factor equal to zero, this theorem may be used to locate the roots or zeros of a polynomial. The effective factorization and solution of polynomial problems are made possible by the Factor Theorem, a potent algebraic tool.

The given polynomial can be written as follows:

p(x) = (2x - 7)(x + 7)(x - 7)

The real zeros are the values of x that make the polynomial equal to zero. Therefore, the real zeros are:

x = 7/2, -7, 7

Therefore, the real zeros of the polynomial p(x) are 7/2, -7, and 7.

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The equation for the line that passes through the point (3,−2) , and that is perpendicular to the line with the equation x=2, is given by y = -2

To find the equation for the line that passes through the point (3, -2) and is perpendicular to the line x = 2, we need to find the slope of the perpendicular line and use the point-slope form of an equation.

The slope of the line x = 2 is undefined, since it is a vertical line. A line that is perpendicular to a vertical line is a horizontal line, and the slope of a horizontal line is 0.

Using the point-slope form of an equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can plug in the values for the slope and the point:

y - (-2) = 0(x - 3)

Simplifying the equation, we get:

y + 2 = 0

y = -2

So the equation for the line that passes through the point (3, -2) and is perpendicular to the line x = 2 is y = -2. This is a horizontal line that passes through the y-axis at -2.

Answer: y = -2

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The average rate of change of f(x)=x^2+3x+1 from x=−5 to x=−3 is −5.

The average rate of change of a function f(x) over an interval [a,b] is given by the formula:
average rate of change = (f(b) - f(a)) / (b - a)

In this case, we are given the function f(x)=x^2+3x+1 and the interval [−5,−3], so we can plug in the values into the formula:
average rate of change = (f(−3) - f(−5)) / (−3 - (−5))

First, we need to find the values of f(−3) and f(−5):
f(−3) = (−3)^2 + 3(−3) + 1 = 9 − 9 + 1 = 1
f(−5) = (−5)^2 + 3(−5) + 1 = 25 − 15 + 1 = 11

Now, we can plug these values back into the formula:
average rate of change = (1 - 11) / (−3 - (−5)) = (−10) / 2 = −5

Therefore, the average rate of change of f(x)=x^2+3x+1 from x=−5 to x=−3 is −5.

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Ramu bought 12 metre long ribbon, and he cut it into different pieces then the length of remaining ribbon is equals to the 10 metre.

Ramu bought a long ribbon with lengths in meters. We have to calculate the length of remaining ribbon.

Total length of ribbon, L = 12 meters

After that he cut it into 2 and 3 by 4 m and 1 and 1 by 2 meter long. Two pieces of ribbon has length of 3/4 metre in each piece. So, total length of two pieces

= 2×3/4 = 3/2 meters

Also, he cut one piece of ribbon

length of this piece = 1/2 meter

Thus, total length of cutting pieces of ribbon = 3/2 metre + 1/2 metre

= 4/2 = 2 metre

The length of remaining ribbon = total length of ribbon - cutting pieces length

= 12 metre - 2 metre

= 10 metre

Hence, the required length is 10 metre.

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Answer:

y=1

Step-by-step explanation:

Answer:1

Step-by-step explanation: 7y = 7

divide both sides by 7 to isolate y

y = 1

Thus, the drawing's scale factor is 8:1, or simply 8. This implies that each function measurement on the design is eight times bigger than its actual-world equivalent.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

One inch on the illustration equals one eighth of an inch in reality if the scale is 1 inch = 1/8 inch.

We must divide the length of the drawing by the comparable length in reality to determine the scale factor. The scale factor is: because one inch on the design corresponds to 1/8 inch in reality.

1 / (1/8) = 8

Thus, the drawing's scale factor is 8:1, or simply 8. This implies that each measurement on the design is eight times bigger than its actual-world equivalent.

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Answer:

h(-2) = 13, h(0) = 9, and h(5) = -1.

Step-by-step explanation:

To evaluate h(x) = -2x + 9 for the given values of x, we can substitute each value of x into the expression and simplify:

h(-2) = -2(-2) + 9 = 13

h(0) = -2(0) + 9 = 9

h(5) = -2(5) + 9 = -1

Therefore, h(-2) = 13, h(0) = 9, and h(5) = -1.

Answer:

Step-by-step explanation:

slope of line = 7/3

y-intercept is = 7

In regards to question A:

P(G) = 0.2

P(W) = 0.32

P(B) = 0.48

B: we can estimate that the friends will choose approximately 90 glass beads, 144 wood beads, and 216 brass beads if they select a total of 450 beads from the crate.

a. The probability model for choosing a bead can be represented by a discrete probability distribution, where the sample space consists of the three types of beads - glass, wood, and brass - and the probabilities of selecting each type are proportional to their respective frequencies. Let P(G) denote the probability of selecting a glass bead, P(W) denote the probability of selecting a wood bead, and P(B) denote the probability of selecting a brass bead. Then:

P(G) = [tex]\frac{60}{300}[/tex] = 1 ÷ 5 = 0.2

P(W) = [tex]\frac{96}{300}[/tex] = 8 ÷ 25 = 0.32

P(B) = [tex]\frac{144}{300}[/tex] = 12÷ 25 = 0.48

b. To estimate the number of each type of bead that will be chosen if the friends select a total of 450 beads from the crate, we can use the probabilities calculated above to find the expected number of beads of each type. Let X_G, X_W, and X_B denote the random variables representing the number of glass, wood, and brass beads, respectively, that are selected out of the 450 total selections. Then:

E(X_G) = P(G) × 450 = (1 ÷ 5) × 450 = 90

E(X_W) = P(W) × 450 = (8 ÷ 25) × 450 = 144

E(X_B) = P(B) × 450 = (12 ÷ 25) × 450 = 216

Therefore, based on the frequencies in the table, we would expect approximately 90 glass beads, 144 wood beads, and 216 brass beads to be chosen if the friends select a total of 450 beads from the crate.

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Answer:

Step-by-step explanation:

So first you have to divide the monkey by the + sign then when you did that you take the exponent and turn it into a ratio. When you are done doing that you have to multiply and divide and then you have your answer.

When x=6, the value of [tex]y=ax^2[/tex] is 11a.

What is expression?

One or more variables or numbers are combined with one additional action to form an expression.

Assuming that the function [tex]y=ax^2[/tex] is defined for all real numbers x, we can use the pattern of the differences of consecutive y-values to write an expression for y when x=6.

The differences of consecutive y-values for the function y=ax^2 are given by:

[tex]a(2^2 - 1^2), a(3^2 - 2^2), a(4^2 - 3^2), ...[/tex]

Simplifying these expressions, we get:

3a, 5a, 7a, ...

We can see that the differences between consecutive values are all the same, namely 2a. Therefore, we can express any y-value of the function

[tex]y=ax^2[/tex] as:

y = y(1) + (x-1)Δy

where y(1) is the value of y when x=1, and Δy is the common difference between consecutive y-values, which in this case is 2a.

Substituting the values x=6, y(1)=a(1^2)=a, and Δy=2a into this expression, we get:

y = a + (6-1)(2a) = a + 10a = 11a

Therefore, when x=6, the value of [tex]y=ax^2[/tex] is 11a.

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The two possible solutions for w are 6 and -3/4.

To solve for w, we need to use algebraic manipulation to isolate w on one side of the equation. Here are the steps:

1. Multiply both sides of the equation by (w+1)(w-7) to clear the fractions: -(7) = 4(w+1)(w-7) + 3(w+1)

2. Distribute the 4 and 3 on the right side of the equation: -(7) = 4w^2 - 24w - 28 + 3w + 3

3. Combine like terms on the right side of the equation: -(7) = 4w^2 - 21w - 25

4. Move all terms to one side of the equation: 4w^2 - 21w - 18 = 0

5. Use the quadratic formula to solve for w: w = (-(-21) ± √((-21)^2 - 4(4)(-18)))/(2(4))

6. Simplify the equation: w = (21 ± √(441 + 288))/(8)

7. Simplify the equation further: w = (21 ± √729)/(8)

8. Solve for the two possible values of w: w = (21 + 27)/(8) or w = (21 - 27)/(8)

9. Simplify the two possible values of w: w = 48/8 or w = -6/8

10. Simplify the two possible values of w further: w = 6 or w = -3/4

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Answer:

Starting with the given equation:

√x³ - 100 = 5

Adding 100 to both sides:

√x³ = 105

Squaring both sides:

x³ = 11025

Taking the cube root of both sides:

x = 15

Therefore, the exact solution to the given equation is x = 15.

Note that no inverse functions were needed to solve this equation

Step-by-step explanation:

Answer:

A. Tim's pay rate is $3/hr than Susie's

B. Tim worked 6 years longer than Susie

Step-by-step explanation:

Timmy makes $720 in 40 hrs

=> he makes 720/40 = $18.00/hr

Susie makes $600 in 40 hrs

=> she makes 600/40 = $15.00/hr

So Tim makes 18 - 15 = $3/hr than Susie

50 cent = $0.5

If pay raise is $0.5/yr

=> 3/0.5 = 6 yr

Tim worked 6 years longer than Susie

Answer:

Step-by-step explanation:its 18.50

Using IQR would be the appropriate measure of variability to compare the consistency of temperatures between Desert Landing and Flower Town.

What is Graph ?

A graph is a visual representation of data that displays the relationship between variables or sets of data. Graphs are commonly used in various fields such as mathematics, statistics, economics, and science to help people understand and analyze data.

IQR, because it is a measure of variability that is resistant to outliers and is appropriate for both symmetric and skewed distributions. It measures the spread of the middle 50% of the data, which gives a good indication of how consistent the temperatures are around the median.

Therefore, using IQR would be the appropriate measure of variability to compare the consistency of temperatures between Desert Landing and Flower Town.

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The value of  y = 57.86 when x = 1331.

We are given that y varies directly as the cube root of x. This means that the equation relating y and x is of the form:

y = k * cube_root(x)

Where k is the constant of proportionality. We are also given that y = 100 when x = 6859. We can use this information to find the value of k:

100 = k * cube_root(6859)

k = 100 / cube_root(6859)

k = 100 / 19

k = 5.26

Now we can use the value of k to find y when x = 1331:

y = 5.26 * cube_root(1331)

y = 5.26 * 11

y = 57.86

Therefore, y is approximately 57.86 when x is 1331. We can round this answer to two decimal places to get:

y = 57.86

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Answer:

Just help your mother to wash your dise

The total cost at an activity level of 8,000 units is $55,000.

The total cost at an activity level of 8,000 units can be found by plugging in the value of X into the cost formula Y= $15,000 + $5X.

Step 1: Plug in the value of X into the cost formula:
Y= $15,000 + $5(8,000)

Step 2: Simplify the equation by multiplying $5 and 8,000:
Y= $15,000 + $40,000

Step 3: Add $15,000 and $40,000 to get the total cost:
Y= $55,000

Therefore, the total cost at an activity level of 8,000 units is $55,000. The correct answer is $55,000.

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