Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal. Is Kyle's claim Incorrect or correct? In two or more complete sentences, Justify your answer.

The ratio of rise to run between points B and C is the same as the slope of line AB

An equation is an expression that shows the relationship between two or more numbers and variables.

Slope of a line = ratio of rise to run = rise / run

Hence:

The ratio of rise to run between points B and C is the same as the slope of line AB

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Answer:

x = 1

Step-by-step explanation:

Step 1: Combine like terms.

Step 2: Divide both sides by 30.

Step 3: Check if solution is correct.

Therefore, x = 1.

Solution: X=1

[tex]\searrow[/tex]

Detailed explanation:

Here we need to solve for x. x is our unknown. It's what we should find.

[tex]\searrow[/tex]

Note right up front that we can add the x's. This is a process that is known as "Combining Like Terms". We can combine them by adding, like here.

[tex]\twoheadrightarrow\sf 29x+x=30[/tex]

"x" is the same as 1x.

[tex]\twoheadrightarrow\sf 30x=30[/tex]

We're getting closer to finding the value of the unknown!

Now we know that if we multiply 30 times the unknown, we will get 30.

What will we get if we multiply 1 times the unknown? 1 is what we will obtain upon dividing by 30.

So our unknown, or x, is 1.

Voila! There's our answer!

_____________________________

Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

_____________________________

The Area of carpet for the given dimension is 72m².

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.

Let the width of the room w = x m

     and the length, L = 1.5x

Length of carpet + 6 = length of room

2(x-6)+6=1.5x

2x-12+6=1.5x

0.5x=6

  x = 6 / 0.5

  x = 12

length of room x = 12 m

width of room = 18 m

18-6 by 12-6    =    12 by 6 dimensions of carpet

Area of carpet = 12 X 6=72 m²

Thus, the Area of carpet for the given dimension is 72m².

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Answer:

75 Seconds

Step-by-step explanation:

First divide 90,000 by 16 then square root that answer for 75 and when you plug it in you'll end up with -90,000 + 90,000

The mid point of the segment with the following endpoints. (-9, 8) and (-4, -2) is (-6.5, 3)

The mid point of the segment can be found as follows;

The endpoint is a follows:

(-9, 8) and (-4, -2)

Therefore,

mid point = (x₁ + x₂ / 2,  y₁ + y₂ / 2)

hence,

mid point = (-9 - 4 / 2, 8 - 2 / 2)

mid point = (-13 / 2 , 6 / 2)

mid point = (-6.5, 3)

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The value of a₃₃ is 1.

Matrices is a plural form of a matrix, which is a rectangular array or a table where numbers or elements are arranged in rows and columns.

Here,  aₓₙ is the element of matrix in which x represents the number of row and n represents the number of column of element.

So, a₄₃ means element from 4th row and 3rd column.

3rd row  =  [6   7   1   8]

3rd column = [tex]\left[\begin{array}{ccc}8\\6\\1\\3\end{array}\right][/tex]

the common value between them is 1.

Thus, the value of a₃₃ is 1.

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Answer:

pqr²+pr-rp²+rq²

Step-by-step explanation:

pq(r²+1)-r(p²+q²)

pqr²+pr-rp²+rq²

Answer:

When 68.321 rounded to the nearest tenth the result is 68

Answer:

6 Slices

Step-by-step explanation:

Total units = 1 + 3 + 2 = 6 Units

6 Units = 18 Slices of Pizza

Iris shared 2 units.

1 Unit = 18/6 = 3 Slices of Pizza

2 Units = 2 * 3 = 6 Slices of Pizza

Answer:

y = 2

Step-by-step explanation:

Y varies indirectly with x (as x gets bigger, y gets smaller)

You have to find k, the constant of proportionality.

y = [tex]\frac{k}{x}[/tex]

Plus in the x & y values you are given

58 = [tex]\frac{k}{9}[/tex]  Multiply both sides by 9 to solve for k

k= 522

Now plug in the new value of x to solve for y

y = [tex]\frac{522}{261}[/tex]

y = 2

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: slope \:\: of \:\: line = \cfrac{3}{2}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The equation of line is written in slope - intercept form

[tex]\qquad \tt \rightarrow \: f(x) = \dfrac{3}{2} x - 4[/tex]

if we compare it with general slope - intercept equation of line :

[tex]\qquad \tt \rightarrow \: f(x) = mx + c[/tex]

[ m represents slope of line ]

[tex]\qquad \tt \rightarrow \: m = \dfrac{3}{2} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]\frac32[/tex]

Step-by-step explanation:

Hello!

An equation of a line is usually written in slope-intercept form.

Slope Intercept Form: [tex]y = mx + b[/tex]

If we compare our given equation with the format:

This means that [tex]\frac32[/tex] would be our slope for the line.

The speed that Jo walked for the first 15 minutes is; 6 km/hr

The distance - time graph is missing and so i have attached it.

Now, the formula for speed is;

Speed = Distance/time

The distance after 15 minutes from the graph is 1.5km.

Now, 15 minutes when converted to hours is 15/60 = ¹/₄ hr

Thus, the speed that Jo walked for the first 15 minutes is;

Speed = 1.5/(¹/₄)

Speed = 6 km/hr

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The slope of CD, which is parallel to AB must be: A. -5.

If two line segments are parallel to each other, their slope value (m) would be equal to each other.

Side AB and CD in the parallelogram are parallel segments, therefore, their slope (m) would be the same.

Slope (m) of AB = -5, therefore, the slope of CD must be: A. -5.

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D option is correct by SSS congruence rule

Answer:

0.74

Step-by-step explanation:

A tree diagram is a visual way of showing combinations of two or more events. The outcome of each branch is labelled at the end of the branch line and its probability is written alongside the branch.

To calculate the probabilities of each combination, follow the branches and multiply the probabilities together.

There are two possible combinations to get a final outcome of D:

Therefore, the probability of D is:

⇒ P(D) = P(A and D) OR P(B and D):

⇒ P(D) = 0.42 + 0.32

⇒ P(D) = 0.74

Answer: Difference in membership costs after m months = -($24.96m + $34.94)

Step-by-step explanation:

Cost of Zippy health club = $49.95 + $19.95 per month

Cost of Be strong = $24.99 per month and $10 off the first month

Total cost after m months of Zippy health club = $49.95 + $19.95m

Total cost after m months of Be strong = $24.99 (m - 1) + $ 10

Difference in membership costs after m months ={ $24.99m - $24.99 + $10 ]-[$49.95m + $19.95}

=$(24.99 - 49.95) m -$14.99 - $19.95

= -$24.96m - $34.94

=-($24.96m + $34.94)

So Difference in membership costs after m months =-($24.96m + $34.94)

therefore jada have to pay more if she joins Be strong.

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The steps arranged in the right order are:

45,000,000 = [tex]100(1 + 1.5)^{t}[/tex]

45,000,000 = [tex]100(2.5)^{t}[/tex]

450,000 = [tex](2.5)^{t}[/tex]

log 450,000 = log [tex](2.5)^{t}[/tex]

log 450,000 = log t (2.5)

[tex]\frac{log 450,000}{log 2.5} = t[/tex]

5.632 / 0.3979 = t

t = 14.21 hours

The equation that can be used to represent the growth rate of the bacteria is an exponential equation. The form of exponential equations is:

FV = P(1 + r)^t

Where:

45,000,000 = 100( 2.5)^t

t = log 450,000 / log 2.5

t = 14.21 hours

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Answer:

No. There should be 210 small triangles

Step-by-step explanation:

The number of small triangles in these figures forms a sequence

Fig         No Small Triangles
1             1
2            3  (1+2)
3            6  (1+2+3)

So the nth figure should have 1+2+3+.....+(n-1)+ n

1+2+3+.....+(n-1)+ n = [tex]\frac{n (n-1)}{2}[/tex]
So for 20th figure, n = 20 and number of small triangles = 20 x 21 /2 = 420/2 = 210

Answer:

10

Step-by-step explanation:

cos(30) = b / c

c = b / cos(30)

c = 5xsqrt(3) / 0.866

c = 10

Answer:

Tax 3.78 $ and tip 7.56 $

Step-by-step explanation:

42*0.09 = 3.78

42*0.18 = 7.56

Inequalities help us to compare two unequal expressions. The correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequality -6 ≤y + 2x < 15 can be broken into two small inequality, as shown below.

Now, if we plot the inequality as shown below, then the area in which both the shaded region overlap is the area of the this inequality.

Hence, the correct option is B.

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We need radius

Now

LSA

Answer:

813.4 cm² (nearest tenth)

Step-by-step explanation:

Volume of a cylinder

[tex]\sf V=\pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Use the Volume of a Cylinder formula and the given values to find the radius of the cylinder:

[tex]\implies \sf 1715=\pi r^2 (18)[/tex]

[tex]\implies \sf r^2=\dfrac{1715}{18 \pi}[/tex]

[tex]\implies \sf r=\sqrt{\dfrac{1715}{18 \pi}[/tex]

Surface Area of a Cylinder

[tex]\sf SA=2 \pi r^2 + 2 \pi r h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Substitute the given value of h and the found value of r into the formula and solve for SA:

[tex]\implies \sf SA=2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)^2 + 2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)(18)[/tex]

[tex]\implies \sf SA=2 \pi \left(\dfrac{1715}{18 \pi} \right) + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)[/tex]

[tex]\implies \sf SA=\dfrac{1715}{9} + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)[/tex]

[tex]\implies \sf SA=813.3908956...[/tex]

Therefore, the surface area of the cylinder is 813.4 cm² (nearest tenth)

Answer:

4 ^3sqrt(2)

Step-by-step explanation:

two 2's can come out of the square root and it leaves one left in it and 2x2 is 4 which is on the outside.

Answer:

Since both of the coordinates are positive, we have:

Find the hypotenuse of the right triangle using values of both legs:

Find sine:

Find cosine:

Answer:

g(x) = (x-4)² +9

Step-by-step explanation:

If f(x) is moved up 9 units, it becomes x² + 9, as only the 'y' value is changed by 9. Then, if it is moved 4 units to the right, it becomes (x+4)² +9, as only the 'x' value is changed by -4.

The function g(x) that represents the translation of f(x) = x² with 9 units up and 4 units to the right is,

⇒ g(x) = (x-4)² + 9.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Now, To translate the function f(x) = x² with 9 units up and 4 units to the right, we need to use the following formula:

⇒ g(x) = f (x - 4) + 9

Substituting f(x) with its equivalent form:

⇒ g(x) = ( x - 4 )² + 9

Therefore, The function g(x) that represents the translation of f(x) = x² with 9 units up and 4 units to the right is,

⇒ g(x) = (x-4)² + 9.

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The Volume and Surface Area of Prism is 462  in² and 637  in³.

What is Prism?

Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross-sections.

Surface area of rectangular prism,

= 2( lb +bh +lh)

= 2 ( 13*7 + 7*7+ 13*7)

=2*231

= 462  in²

Now, Volume,

= bhl

= 13*7*7

= 637  in³

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