Question 11-(3 marks available)
Find the total surface area of this triangular prism.
13 cm
5 cm
12 cm
9 cm
20 cm

Answer:

slope = - [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 10 ) and (x₂, y₂ ) = (24, 6 )

m = [tex]\frac{6-10}{24-0}[/tex] = [tex]\frac{-4}{24}[/tex] = - [tex]\frac{1}{6}[/tex]

Answer:

Step-by-step explanation:

dees

Answer:

Hmm I am not sure, but I think you should try 44 and 26!

Step-by-step explanation:

Reply back if its right :)

The equation the function after the transformation is g(x) = x/10

The equation of the function is given as

y = x

Express as a function

f(x) = x

The sequence of transformations is given as follows:

Vertically stretched by a factor of 1/10

When the above transformations are combined, we have:

Vertically stretched by a factor of 4: g(x) = 1/10f(x)

So, we have

g(x) = 1/10f(x)

Substitute x for f(x)

So, we have

g(x) = 1/10 * x

Evaluate

g(x) = x/10

Hence, the function g(x) is g(x) = x/10

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Step-by-step explanation:

The answer is: A=210÷26.2=8.2

B=now we have to turn minutes in to haurs 210:60=3.5 now 26.2÷3.5=29.7

Answer:

A) 26.2/210= .125 miles per minute

B) 210/26.2= 8.02 minutes per mile

C) the other runner talks about the same rate as b), not a).

Step-by-step explanation:

A)[tex]\frac{26.2}{210\\}[/tex] and B)[tex]\frac{210}{26.2}[/tex] :)  

C)the runner was referring to the time they took to run one mile, so the other runner ran 10 minutes to cover one mile, or as they say, "10 minute miles", which is the rate in minutes per mile.

If they were referring to the rates in a), that would imply the other runner ran 10 miles per minute... which is very unlikely.

The volume of the given figure is 5760 [tex]cm^{3}[/tex].

According to the question,

We have the following information:

We have a figure where two cuboids are joined together. So, the volume of the figure will be the sum of the volume of these cuboids.

We know that the following formula is used to find the value of cuboid:

Volume of cuboid = Length*breadth*height

Volume of larger cuboid = 40*8*12

Volume of larger cuboid = 3840 [tex]cm^{3}[/tex]

Volume of smaller cuboid = 20*8*12

Volume of smaller cuboid = 1920 [tex]cm^{3}[/tex]

Volume of the figure = 3840+1920

Volume of the figure =  5760 [tex]cm^{3}[/tex]

Hence, the correct option is B (the second option).

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Answer:

5760

Step-by-step explanation:

Answer:

The number to the ration

Step-by-step explanation:

The dimensions of the ticket are width is 11 cm and  length is 18 cm.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

An airplane ticket has a perimeter of 58 cm and an area of 198 square cm.

Let W is the width of the ticket and L is the length of the ticket

The area of a credentials= L × W

198 = L × W ...(i)

The perimeter of a ticket = 2(L+W)

58 = 2(L+W)

29 = L + W

L = 29 - W ...(ii)

Substitute the value of L = 99 - W in equation (i)

198 = (29 - W) × W

198 = 29W - W²

0 = W² - 29W + 198

[tex]0=\left(W^2-11W\right)+\left(-18W+198\right)[/tex]

[tex]0=W\left(W-11\right)-18\left(W-11\right)[/tex]

[tex]0=\left(W-11\right)\left(W-18\right)[/tex]

W = 18 or 11

Substitute the value of W = 11 in equation (ii)

L = 29 - 11

L = 18

Thus, the dimensions of the ticket are width is 11 cm and length is 18 cm.

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Answer:

26x-56y

Step-by-step explanation:

First you open the bracket and collect like terms

55x-29x-46y-10y

26x-56y

Answer:

Step-by-step explanation:       Step 1

1 of 2

step 1.2659 ;[26 Discovery Group

October 20

Last

Trade Time

Chg

Open

52-week High

52-week Low

Sales in 100s

High

Low

​

$38.50

4:00 P.M. ET

$1.56

$37.22

$76.19

$22.78

19,700

$40.10

$36.77

​

\begin{matrix} \text{Discovery Group} & \text{}\\ \text{October 20} & \text{}\\ \text{Last} & \text{\$42.00}\\ \text{Trade Time} & \text{4:00 P.M. ET}\\ \text{Chg} & \text{\$1.50}\\ \text{Open} & \text{\$42.50}\\ \text{52-week High} & \text{\$76.19}\\ \text{52-week Low} & \text{\$22.78}\\ \text{Sales in 100s} & \text{23,600}\\ \text{High} & \text{\$42.50}\\ \text{Low} & \text{\$42.00}\\ \end{matrix}

Discovery Group

October 20

Last

Trade Time

Chg

Open

52-week High

52-week Low

Sales in 100s

High

Low

​

$42.00

4:00 P.M. ET

$1.50

$42.50

$76.19

$22.78

23,600

$42.50

$42.00

​

The product of (4i-5)(4i+5) is -41.

What are complex numbers?

Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted i, also known as the imaginary unit, and satisfies the equation i² = - 1.

Here, we have

Given function

= (4i-5) (4i+5)

After applying the product rule, we get

=  16i² + 20i - 20i - 25

= 16i² - 25

after putting i² value, we get

= 16(-1) - 25

= -41

Hence, the product of (4i-5)(4i+5) is -41.

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The slope and the intercepts of the graph are determined.

Given:

the equation is :

2x+3y=6

we first find the slope of the equation:

m = -a/b

m = -2/3

now solve the intercepts:

to find x intercept, substitute in 0 for y and solve for x.

⇒ 2x+3y=6

⇒ 2x+3(0)=6

⇒ 2x+0=6

⇒ 2x=6

⇒ x=6/2

⇒ x=3

hence we get (3,0)

now, to find y intercept, substitute in 0 for x and solve for y.

⇒ 2x+3y=6

⇒ 2(0)+3y=6

⇒ 0+3y=6

⇒ 3y=6

⇒ y=6/3

⇒ y=2

hence we get (0,2) as the intercepts.

Therefore we plot the required graph.

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Answer: x=4

Step-by-step explanation: simplify expression and divide polynomials

Answer:

Step-by-step explanation:

-8-6y=-8-2y

+2y +2y

-8-4y=-8

+8 +8

-4y=0

Y=0

Answer:

2. ax=m and ​ay=n​

4. mn=a(x+y)

6. power property of logarithms.

I took the quiz.

k12

i took the quiz this is the right answers

The relation that can be formed by obersving the Cartesian Plane is y = 5x

What is Co-ordinate Geometry?

The study of geometry using coordinate points is known as coordinate geometry (or analytic geometry). It is possible to estimate the distance between two points, divide lines in a m:n ratio, identify the midpoint of a line, calculate the area of a triangle in the Cartesian plane, and so on using coordinate geometry.

Solution:

By analysing the given Cartesian Plane

it can be observed that the rate of change of y with respect to x

is 5 times

Therefore, the relation that can be formed by obersving the Cartesian Plane is y = 5x

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Money  she will have after 52 weeks = rs.2,700

acc to our question-

Unit rate of change here is =

⇒ Unit rate of change here is =

⇒ Unit rate of change here is = 50%

Part B

Equation to calculate the amount of money Greta will have after any number of weeks = ?

Money after 'x' number of weeks =

⇒ Money after 'x' number of weeks =

Part C

Money Greta will have after 1 year= ?

In a year there are 52 weeks

So, putting x = 52 in the solution of Part B

⇒ Money after 52 weeks =

⇒ Money after 52 weeks =

⇒ Money after 52 weeks = 2,700

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Step-by-step explanation:

I skipped the answer line because they are pasted below.

Since there is a ten dollar difference for two people, each guest is 5 dollars. If each guest is 5 dollars, the party room is 120. If we want to create an equation, we have:

y=5x(each guest is 5 dollars)+120(the basic fee).

If we use 15 here, we have that it will be $195.

ANSWERS DOWN HERE:

1. $120

2. $5

3. y=5x+120

4. $195

The value of k so that the system of equation has no solution is k = -4

Since we have the system of equations

kx + 6y = 6

y = 2/3x - 4

For the system of equations to have no solution, the determinant coefficient matrix must be zero.

Re-arranging the equations, we have

kx + 6y = 6

-2/3x  + y = - 4

So, the coefficient matrix is

[tex]\left[\begin{array}{ccc}k&6\\-2/3&1\end{array}\right][/tex]

So, the determinant D = k × 1 - (-2/3) × 6

= k + 2/3 × 6

= k + 2 × 2

= k + 4

Since the determinant must be zero for the system of equations to have no solution, we have that

D = 0

k + 4 = 0

k = -4

So, the value of k = -4

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The greater factor of 432, if 12 is the greatest common factor between the two factors is 36

The Greatest Common Factor is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.

The factors of 432 are 36,12, 24 ,18,4,108

But the two factors of 432 that has a multiple of 12 is 12 and 36

12× 36 = 432

The factors of 12 = 1,2,3,4,6,12

The factors of 36 = 1,2,3,4,6,9,12,18,36

the common factors are ; 1,2,3,4,6 and 12

therefore the greatest common factor = 12

since the GCF between 12 and 36 is 12, the second number will be 36

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The numeric value of the expression sec²(54º) - 1, using a trigonometric identity, is given as follows:

tan²(54º) = 1.8944.

Before applying the trigonometric identity, we have to define the secant and the tangent of an angle, as follows:

The identity that exists between the squares of these measures is given as follows:

tan²(x) + 1 = sec²(x).

Hence, isolating the tangent:

tan²(x) = sec²(x) - 1.

In this problem, the expression is given as follows:

sec²(54º) - 1

Applying the identity, the expression is given as follows:

sec²(54º) - 1 = tan²(54º).

Using a calculator, the numeric value of the expression is given as follows:

tan²(54º) = 1.8944.

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The length of segment DE on the rectangle, considering the midpoint, is given as follows:

DE = 22.67.

The midpoint of a segment divides a segment into two segments of equal length, having half the length of the entire segment.

In this problem, the diagonal of the rectangle represented by segment AC has midpoint E, hence the measure of x is calculated as follows:

EC = AE.

The measures are as follows:

Hence:

7x - 3 = 4x + 8

7x - 4x = 8 + 3

3x = 11

x = 11/3.

Segment DE is also half of a diagonal, hence it's length is obtained with the numeric value of any segment EC or AE, as follows:

DE = EC = 7x - 3 = 7 x 11/3 - 3 = 77/3 - 9/3 = 68/3 = 22.67.

The rectangle is given by the image at the end of the answer.

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The factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).

Given expression:

= 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex]

divide by 18 .

= 4[tex]a^{9} b^{3}[/tex] - [tex]a^{7} b^{5}[/tex]

divide by [tex]a^{7}[/tex]

= 4[tex]a^{2}b^{3}[/tex] - [tex]b^{5}[/tex]

divide by [tex]b^{3}[/tex]

= 4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]

= 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).

Therefore the factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).

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The solution to the quotient for 2.0 and 4.0 is 0.50

From the question, the mathematical statement is given as

The quotient for 2.0 and 4.0

The quotient of numbers is their division

This in other words mean that:

The quotient for a and b is a/b

Using the above highlights as a guide, we have

The quotient for 2.0 and 4.0 to be 2.0/4.0

Evaluate the quotients

So, we have the following representation

The quotient for 2.0 and 4.0 to be 0.50

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Answer:

360 of 10%

360 x 10/100

36

now, 360 - 36 = 324

therefore, 324 students attended haley elementry this yr.

The mixture of 13% disinfectant solution needs to be made with 8 gallons of 11% solution and 4 gallons of 17% solution respectively.

Let

x + y = 12

0.11x + 0.17y = 0.13 × 12

x + y = 12

0.11x + 0.17y = 1.56

From (1)

x = 12 - y

Substitute into (2)

0.11x + 0.17y = 1.56

0.11(12 - y) + 0.17y = 1.56

1.32 - 0.11y + 0.17y = 1.56

- 0.11y + 0.17y = 1.56 - 1.32

0.06y = 0.24

divide both sides by 0.06

y = 0.24/0.06

y = 4

x + y = 12

x + 4 = 12

x = 12 - 4

x = 8

So therefore, the gallons of 11% solution and

gallons of 17% solution needed are 8 and 4 gallons respectively.

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The function whose graph is shifted 2 units to the left is y = (x + 2)² .

In the question ,

it is given that the equation is given as y = x² .

we know that when the function y = x² is shifted " a units " to the left , the shifted function becomes y = (x + a)²  ,

we have to find the equation of the graph that is shifted 2 units to the left ,

So , the value of a is 2 ,

and the equation becomes

y = (x + 2)²

so , the equation is y = (x + 2)² .

the graph is shown below .

Therefore, The function whose graph is shifted 2 units to the left is y = (x + 2)² .

The given question is incomplete , the complete question is

Write the function whose graph is the graph of y = x², but is shifted to the left 2 units ?

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The solution of quadratic equation 8x² = 6 + 22x is x = 3 and x = -1/4

What is a Quadratic equation ?

A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.

Given expression is,

8x² = 6 + 22x

Rewrite this expression as,

8x² - 6 - 22x = 0

8x² - 22x - 6 = 0

Now, we get the form quadratic equation i.e, ax² + bx + c = 0

Solve the equation and find roots

8x² - 22x - 6 = 0

2(4x² - 11x - 3) = 0

4x² - 11x  - 3 = 0

4x² - 12x + x - 3 = 0

Take common terms out,

4x(x - 3) + 1(x - 3) = 0

we get the brackets same that means we're on right way,

(4x + 1) (x - 3) = 0

split the values into two,

4x + 1 = 0      and  x - 3 = 0

4x = -1                    x = 3

x = -1/4

Therefore, the solution of quadratic equation 8x² = 6 + 22x is x = 3 and   x = -1/4

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