A=5
b=12
c=10
d=2

2a to the power of 2-c

The surface area of the triangular prism is of 162 cm².

The surface area of a prism is given by the sum of all the areas of the prism.

This prism is composed by:

For a rectangle, the area is the multiplication of the dimensions, hence:

A1 = 10 x 15 = 150 cm².

For a right triangle, the area is half the multiplication of the sides, hence:

A2 = 0.5 x 6 x 4 = 12 cm².

Hence the surface area is:

A = A1 + A2 = 150 cm² + 12 cm² = 162 cm².

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The overall algebraic  expression will be:   [tex]\frac{5(x+11)}{3(x+8)}[/tex]

Definition of algebraic expression -

An expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

Five times the sum of a number and eleven, divided by three times the sum of the number and eight.

Let the number be x.

Five times the sum of a number and eleven means 5 multiplied to the sum of x and 11. In expression this will be written as:

5(x + 11)

Three times the sum of the number and eight means 3 multiplied to the sum of x and 8. In expression this will be written as:

3(x + 8)

So, the overall algebraic expression will be:    [tex]\frac{5(x+11)}{3(x+8)}[/tex]

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Answer:

Since the graph looks like this, I would say solid line

The answers are :

y = 3ˣ ⇒ b

y = 3⁻ˣ ⇒ a

y = -3ˣ ⇒ c

For y = 3ˣ, we will get a graph that will increase exponentially in the direction of positive y-axis.

For y = 3⁻ˣ, we will get a graph that will decrease exponentially in the direction of positive x-axis.

For y = -3ˣ, we will get a graph that will decrease exponentially in the direction of negative y-axis.

The characteristic that  is necessary to create a table that compares two functions  is D. Choose the same values for each functions .

The Mathematical tables can be regarded as the lists of numbers which is used in showing the results of a calculation  and these can have  varying arguments.

It should be noted that when necessary to creating a table that compares two functions it  is important to Choose the same values for each functions .

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Using a system of equations, it is found that one large jar holds 6 ounces and one small jar holds 4 ounces.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

One large jar and five small jars can hold 26 ounces of jam, hence:

l + 5s = 26, which is the first equation in matrix form.

Then:

l = 26 - 5s.

One large jar minus one small jar can hold 2 ounces of jam, hence:

l - s = 2, which is the second equation in matrix form:

Then:

l = 2 + s = 26 - 5s

2 + s = 26 - 5s

6s = 24

s = 4.

l = 26 - 5s = 6.

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Based on the given task content; the product of StartFraction 4 n Over 4 n minus 4 EndFraction times StartFraction n minus 1 Over n + 1 EndFractiontartFraction 2 Over x EndFraction is (4n² - 8n) / (4n²x - 5nx - x)

Product of numbers refers to the multiplication of two or more values to arrive at a single result.

4n / (4n - 1) × (n - 1) / (n + 1) 2/x

= 4n / (4n - 1) × 2(n - 1) / x(n + 1)

= 4n / (4n - 1) × (2n - 2) / (nx + x)

= 4n(2n - 2) / (4n - 1) (nx + x)

= 4n² - 8n / (4n²x - 4nx - nx - x)

= (4n² - 8n) / (4n²x - 5nx - x)

Therefore, the product of 4n / (4n - 1) × (n - 1) / (n + 1) 2/x is (4n² - 8n) / (4n²x - 5nx - x)

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A rule which describes the transformations that maps ΔJKL to ΔJ"K"L" is: D. translation of -2 units x, 0 units y composition 90 degree rotation about point 0.

A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on the diagram (see attachment), we can infer and logically deduce that a rule which describes the transformations that maps triangle JKL to triangle J"K"L" is a rotation of 90 degrees about the origin and then translated 2 units left.

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In the linear equation, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.

A linear equation is modelled in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept of the equation, which is the initial value of y when x is zero.

Using two pair of points from the table, say, (1, 3) and (2, 5), find the slope (m) of the linear equation:

Slope (m) = change in y / change in x = (5 - 3)/(2 - 1)

Slope (m) = 2/1

Slope (m) = 2

To find the y-intercept (b), substitute (x, y) = (1, 3) and m = 2 into y = mx + b

3 = 1(2) + b

3 = 2 + b

Subtract 2 from both sides

3 - 2 = 2 + b - 2

1 = b

b = 1

Thus, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.

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The value of w is 12.5 when x = 5 , y= 5  and z = 10.

What is Equation of variation?

Equation of variation w = [tex]\frac{kxy^{2} }{z}[/tex]

Constant of variation  k = [tex]\frac{wz}{xy^{2} }[/tex]

Find k when w = 1/2, x = 2 and z = 36

k = [tex]\frac{wz}{xy^{2} }[/tex]

[tex]k = \frac{\frac{1}{2} * 36 }{2 * 3^{2} }[/tex]

[tex]k = \frac{18}{2 * 9}[/tex]

[tex]k = \frac{18}{18}[/tex]

k= 1

find the value of w when x = 5 , y = 5 and z = 10

[tex]w = \frac{kxy^{2} }{z} \\w= \frac{1 * 5 * 5^{2} }{10}[/tex]

[tex]w = \frac{5^{3} }{10}[/tex]

w = 125 /10

w = 25 /2

w = 12 . 5

Therefore, the value of w is 12.5 when x = 5 , y= 5  and z = 10

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Answer: 12 square units

Step-by-step explanation: first you must count hom many units there are between points A and B, which is 4, and then count the points between B and C, which is 6.

Now that we have the units we do 6 x 4 = 24, however, you may be asking why we do not do 24 then, well if you were to be doing 6 x 4, you would be getting the area of a rectangle, and half of a rectangle is a triangle, so we have to do 24/2 which equals 12.

Since the product of the slope is -1, hence the lines are perpendicular

Two lines are known to be parallel if they have the same slope while if two lines are perpendicular if the product of the slope is -1

Given the coordinates of line 1 passing through (0, 6) and (6, 4), the slope is given as;

Slope = 4-6/6-0
Slope = -2/6
Slope = -1/3

Similarly for the coordinate points (-1, -7) and (1, -1).

Slope = -1+7/1+1
Slope of line 2 = 6/2

Slope = 3

Take the product of the slopes

Slope = -1/3 * 3
slope = -1

Since the product of the slope is -1, hence the lines are perpendicular

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Answer:

[tex]\frac{a^3b^4}{ab^2}[/tex] which is the last choice in the question

Step-by-step explanation:

Simplify

[tex]\frac{a^3b^{-2}}{ab^{-4}} = \frac{a^3}{a}\frac{b^{-2}}{b^{-4}}[/tex]

Using the fact that [tex]\frac{x^m}{x^n} =x^{m-n}[/tex]

We get

[tex]\frac{a^3}{a} = a^{3-1} = a^2[/tex]

[tex]\frac{b^{-2}}{b^{-4}} = b^{-2-(-4)} = b^2[/tex]

So

[tex]\frac{a^3b^{-2}}{ab^{-4}} =a^2b^2[/tex]

Multiplying numerator and denominator by [tex]ab^2[/tex] gives

[tex]a^2b^2 \frac{ab^2}{ab^2}[/tex]

= [tex]\frac{a^3b^4}{ab^2}[/tex] ANSWER

Hint:

We can eliminate first choice since negative exponents still remain

We can eliminate third choice because the expression has a minus sign which is not possible

That just leaves second and fourth choices to work with

The solution to the system of equations is x = 1, y = 10 and z = 4

The system of equations is given as:

3x +2y +4z = 11

2x -y +3z = 4

5x -3y +5z = -1

Multiply the second equation by 2

So, we have

4x - 2y + 6z = 8

Add this equation to the first equation

3x + 4x + 2y - 2y + 4z + 6z = 11 + 8

Evaluate the like terms

7x + 10z = 19

Multiply the second equation by 3

So, we have

6x - 3y + 9z = 12

Subtract this equation from the third equation

6x - 5x - 3y + 3y + 9z - 5z = 12 + 1

Evaluate the like terms

x + 4z = 13

Make x the subject

x = 13 - 4z

Substitute x = 13 - 4z in 7x + 10z = 19

7(13 - 4z) + 10z = 19

Expand

91 - 28z + 10z = 19

Evaluate the like terms

-18z = -72

Divide

z = 4

Substitute z = 4 in x = 13 - 4z

x = 13 - 4 * 4

Evaluate

x = 1

We have:

2x -y +3z = 4

This gives

2(1) - y + 3 * 4 = 4

Evaluate

2 - y + 12 = 4

This gives

y = 10

Hence, the solution to the system of equations is x = 1, y = 10 and z = 4

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Recall that for [tex]|x|<1[/tex], we have the convergent geometric series

[tex]\displaystyle \sum_{n=0}^\infty x^n = \frac1{1-x}[/tex]

Now, for [tex]\left|\frac x5\right| < 1[/tex], we have

[tex]\dfrac1{5 - x} = \dfrac15 \cdot \dfrac1{1 - \frac x5} = \dfrac15 \displaystyle \sum_{n=0}^\infty \left(\frac x5\right)^n = \sum_{n=0}^\infty \frac{x^n}{5^{n+1}}[/tex]

Integrating both sides gives

[tex]\displaystyle \int \frac{dx}{5-x} = C + \int \sum_{n=0}^\infty \frac{x^n}{5^{n+1}} \, dx[/tex]

[tex]\displaystyle -\ln(5-x) = C + \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}[/tex]

If we let [tex]x=0[/tex], the sum on the right side drops out and we're left with [tex]C=-\ln(5)[/tex].

It follows that

[tex]\displaystyle \ln(5-x) = \ln(5) - \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}[/tex]

or

[tex]\displaystyle \ln(5-x) = \boxed{\ln(5) - \sum_{n=1}^\infty \frac{x^n}{5^n n}}[/tex]

[tex]3x + y = - 4 \\ 3x + 0 = - 4 \\ 3x = - 4 \\ x = \frac{ - 4}{3} = - 1.333[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex] \bm{Last \: option \: (D.)}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Write the equation in slope-intercept form. Then solve y.

▪ [tex]\small\longrightarrow \sf{3x-3x + y = −3x -4}[/tex]

▪ [tex]\small\longrightarrow \sf{y= -3x-4}[/tex]

Identify the x-intercept,

[tex]\small \sf \longrightarrow{3x + 0 = - 4}[/tex]

[tex]\small\longrightarrow \sf{3x=-4}[/tex]

[tex]\small\longrightarrow \sf{x = - \dfrac{4}{3} }[/tex]

[tex]\small\longrightarrow \sf{x = -1.33}[/tex]

The graph has the next properties:

[tex]\small\longrightarrow \sf{Slope: \: 3}[/tex]

[tex]\small\longrightarrow \sf{x-intercept: \: (-1.33,0)}[/tex]

[tex]\small\longrightarrow \sf{y-intercept: \: (0,4) }[/tex]

The height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.

Volume of a rectangular prism = Base area × height

Height = Volume of a rectangular prism ÷ Base area

3x³ + 16x² + 5x cubic units = (x² + 5x) square units × h

h = (3x³ + 16x² + 5x) cubic units ÷ (x² + 5x) square units

h = (3x³ + 16x² + 5x) / (x² + 5x) units

Therefore, the height of the rectangular prism. given its volume and base area is (3x³ + 16x² + 5x) / (x² + 5x) units.

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A locus is a set of a given point that satisfies certain/ stated conditions. This could be in the form of a curve, circle, or line. The required construction is wherewith attached to this answer.

Construction is a topic that requires following some steps to complete or solve a given question. This majorly requires the use of materials and instruments for drawing the expected figure.

A locus is a set of a given point that satisfies some given conditions. This could be in the form of a curve, circle, or line satisfying the required condition(s).

An equidistant locus is one that is at the same distance to a reference point or a line.

In question 14, the required locus should be at the same distance to points A, B, C, and D.

In question 15, the required locus should be at the same distance to sides KJ and KL. This should pass through point C.

The required construction is herewith attached to this answer.

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See my explanation in the pic

Answer:

angle a = [tex]\boxed{154}^{\circ}[/tex]

Step-by-step explanation:

The angles in a triangle add up to 180°.

∴ ∠a + 13° + 13° = 180°

⇒ ∠a + 26° = 180°

⇒ ∠a = 180° - 26°

⇒ ∠a = 154°

Answer:

Angle a equals= 154°

Step-by-step explanation:

you have two angles which add up to 26°

remember that triangle always adds up to 180°

so you calculate 180-26 and you get 154

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

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Answer:

In standard form x^2/64 + y^2/100 = 1

Step-by-step explanation:

The major axis is the y axis because 10 has a larger value than 8.  

8x8 = 64

10 x10 = 100

Inequality can be used to find the domain of f(x) is (B) 4x+9 greater-than-or-equal-to 0.

To find the domain:

Therefore, inequality can be used to find the domain of f(x) is (B) 4x+9 greater-than-or-equal-to 0.

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The correct question is given below:

If f (x) = start root 4 x 9 enroot 2, which inequality can be used to find the domain of f(x)?

(A) startroot 4 x endroot greater-than-or-equal-to 0                                        

(B) 4x+9 greater-than-or-equal-to 0

(C) 4 x greater-than-or-equal-to 0

(D) startroot 4 x 9 endroot 2 greater-than-or-equal-to 0

Answer:

(B)- 4X+9 greater than or equal to 0

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

(-3, -1), (-5, 5)

Each point is (x, y).

slope = (difference in y)/(difference in x)

slope = (-1 - 5)/(-3 - (-5)) = -6/(-3 + 5) = -6/2 = -3

The slope is -3

Answer + Step-by-step explanation:

10 × 5 × 2

= 10 × (5 × 2)   (associative property)

= 10 × (10)

= 10 × 10

= 100