Right triangle ABC is reflected over AC, then dilated by a scale factor of Two-thirds to form triangle DEC. Which statements about the two triangles must be true? Select three options.

△ABC ~ △DEC
∠B ≅ ∠E
3BC = 2EC
3DE = 2AB
3m∠A = 2m∠D
2m∠A = 3m∠D

Answer:

X=3+-√5/3

Step-by-step explanation:

x=-b+-√b^2-4ac/2

=3+-√(-3)^2-4(1)(1)/2

The algebraic rule that best describes the translation of quadrilateral ABCD to quadrilateral A'B'C'D' is P'(x, y) = (x + 8, y + 7). (Correct answer: A)

According to the image attached we understand that the quadrilateral ABCD is transformed into quadrilateral A'B'C'D' by applying pure translation. Translations are a kind of rigid transformation, defined as a transformation applied on a geometric locus such that Euclidean distance is conserved at every point of the construction.

Vectorially speaking, translations are described by the following formula:

P'(x, y) = P(x, y) + T(x, y)     (1)

Where:

By direct comparison, we conclude that the quadrilateral ABCD is translated 8 units in the +x direction and 7 units in the +y direction. Hence, the algebraic rule that describes the translation of quadrilateral ABCD to quadrilateral A'B'C'D' is:

P'(x, y) = (x, y) + (8, 7)

P'(x, y) = (x + 8, y + 7)

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Answer:

a. 40000pi ft^3

b. 5 times

Step-by-step explanation:

a. the volume of a cylinder is pi * h * r^2

r = 20ft, h = 100ft

so V = pi * 100 * 20^2 = 40,000pi or around 125663.7 ft^3

b. to find the number of times, divide the volume by the amount of salt needed per storm then round down:

40000pi/21000 = 5.98 so 5 times. notes: depending on the teacher you might just round to the nearest integer

Answer:

M is target to the circle

the assumption being that the tax is added to the amount advertised for the vehicle, namely 23289.26 + 6.5% of that.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.5\% of 23289.26}}{\left( \cfrac{6.5}{100} \right)23289.26}\implies 1513.8~\hfill \underset{\textit{total selling price}}{\stackrel{23289.26~~ + ~~1513.8}{24803.06}}[/tex]

Answer:

D. 2.19

Step-by-step explanation:

ok so the formula for the surface area of a sphere is 4[tex]\pi[/tex][tex]r^2[/tex]

We see that 4[tex]\pi[/tex][tex]r^2[/tex]=60.

To find the radius we must isolate r on one side of the equations.

[tex]r^2[/tex]=60/4[tex]\pi[/tex]

[tex]r^2[/tex] = 4.77464829276

r = [tex]\sqrt{4.77464829276}[/tex]

That is approximately equal to 2.19

The solution to the equations are:

The equation is given as:

[tex]9x\² - 36x + 36 = 0[/tex]

The above equation is a quadratic equation which can be represented as:

[tex]ax\² + bx + c = 0[/tex]

The discriminant (d) is calculated as:

[tex]d = b\² - 4ac[/tex]

So, we have:

[tex]d = (-36)\² - 4 * 9 * 36[/tex]

[tex]d = 0[/tex]

A discriminant of 0 means that the equation has two equal real solutions

Hence, 9x² - 36x + 36 = 0 has two equal real solutions

The equation is given as:

[tex]x\² - x + 4 = 0[/tex]

The above equation can be represented as:

[tex]ax\² + bx + c = 0[/tex]

The discriminant (d) is calculated as:

[tex]d = b\² - 4ac[/tex]

So, we have:

[tex]d = (-1)\² - 4 * 1 * 4[/tex]

[tex]d = -15[/tex]

A discriminant of -15 means that the equation has no real solutions

Hence, x² - x + 4 = 0 has no real solutions

We have:

[tex]4x\² + 23 - 35[/tex]

Evaluate the difference

[tex]4x\² -12[/tex]

Factor out 4

[tex]4(x\² -3)[/tex]

Hence, the factored expression of 4x² + 23 – 35 is 4(x² -3)

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Answer: B

Step-by-step explanation:

The ratio of the areas of similar figures is the square of the scale factor.

So, the ratio of the areas is 16, and thus the area of DEF is (16)(90)=1440

Answer:

zero

Step-by-step explanation:

pemdas

The range of the exponential function f(x) = 2.7ˣ will be from zero to infinity that is (0, ∞).

The domain means all the possible values of x and the range means all the possible values of y.

The exponential function is given below.

f(x) = 2.7ˣ

We know the value of the exponential function is always positive.

Then the range of the exponential function f(x) = 2.7ˣ will be from zero to infinity that is (0, ∞).

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Answer:

What exactly is the question here?

Answer:

Width = 2

Length = 5

Step-by-step explanation:

let A be the area of the rectangle

   L be the length of the rectangle

   w be the width of the rectangle

Formula: ‘area of a rectangle’

A = L × w

…………………………………………………

A = L × w

⇔ 10 = (w + 3) × w

⇔ 10 = w² + 3w

⇔ w² + 3w - 10 = 0  

Solving the quadratic equation w² + 3w - 10 =  0 :

Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49

then √Δ = 7

[tex]\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2[/tex]

  [tex]or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5[/tex]

-5 is not valid ,because w represents the width

which must be a positive number

Then  w = 2

Conclusion:

Width = 2

Length = 2 + 3 = 5

Answer: 134°

Step-by-step explanation:

Since angle ABC is equal to 75, we know that the arc in front of it (arc AC) is 150. We then start to add all the know arc angle measures together. So, our equation to finding arc BEC 360-150+76= BEC arc.

Answer:

134

Step-by-step explanation:

cause yeah

Answer:

2ax−2ay−2x2−2xy+2a+4x+2y

Step-by-step explanation:

Let's simplify step-by-step.

(x+y)(2)−2(x+y)(a+x)+(a+x)(2)

Distribute:

=(x)(2)+(y)(2)+−2ax+−2ay+−2x2+−2xy+(a)(2)+(x)(2)

=2x+2y+−2ax+−2ay+−2x2+−2xy+2a+2x

Combine Like Terms:

=2x+2y+−2ax+−2ay+−2x2+−2xy+2a+2x

=(−2ax)+(−2ay)+(−2x2)+(−2xy)+(2a)+(2x+2x)+(2y)

=−2ax+−2ay+−2x2+−2xy+2a+4x+2y

Answer:

=−2ax−2ay−2x2−2xy+2a+4x+2y

Answer:

45 minutes

Step-by-step explanation:

If you're trying to find the total number of minutes, they practiced you'd have to add.

So, if they did free throws for 17 minutes

Ran for 12 minutes

And passed the ball for 16

You'd add those up

17+16+12 = 45

In conclusion they practiced for a total of 45 minutes.

The formula that can be used to find the area of the figure shaded green is 9² - 4². The correct option is c 9² - 4²

From the question, we are to determine the formula that could be used to find area of the figure shaded green

From the formula for calculating area of a square

A = s²

Where A is area

and s is the side length

Then, the area of the bigger square will be

A = 9²

NOTE: Side length of the bigger square is 9m

Then,

For the smaller square, which is not shaded green

A = 4²

NOTE: Side length of the smaller square is 4m

∴ Area of the figure shaded green = 9² - 4²

Hence, the formula that can be used to find the area of the figure shaded green is 9² - 4². The correct option is c 9² - 4²

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Answer: See below

Step-by-step explanation:

Given:

AB = CD and BC = DE

To prove:

AC = CE

            Statements                                       Reasons

Therefore, AC = CE has been proved                

The x-intercept is 4, and the asymptote is located at y = 3 , Option C is the correct answer.

An asymptote is a line that a curve approaches but it never reach.

The given equation

y = log₅(x-3)

To find the asymptote

Set the argument of the logarithm equal to zero.

x - 3 = 0

The vertical asymptote occurs at

x = 3

The equation can also be written as

[tex]\rm 5^y = x-3[/tex]

To find the x intercept we will put the value of y = 0 ;

therefore

5⁰ = x -3

1=x-3

x = 4

Therefore ,The x-intercept is 4, and the asymptote is located at y = 3 , Option C is the correct answer.

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Answer:

The x-intercept is 4, and the asymptote is located at x = 3.

Step-by-step explanation:

I got it right on the test.

Answer:

I feel that is would be D

Step-by-step explanation:

This is the most reasonable awnser.

The pie chart for the expenditure of a housewife for a particular day is shown below.

A map wherein the round is split into segments, each one representing a percentage of the total.

The data below show the expenditure of a housewife for a particular day

Item amount

Rice - 120

Yam - 100

Beans - 140

Vegetable - 140

Meat - 180

Sugar - 40

Palm oil - 60

The pie chart is given below.

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Answer:

[tex]\displaystyle \log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex] OR [tex]\displaystyle 3+\log\frac{z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]

Choose the more appropriate answer

Step-by-step explanation:

I read your problem as [tex]3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y[/tex]:

[tex]\displaystyle 3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y\\\\\log1000+\log z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log1000z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2}{(x+1)^2}+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]

Answer:

All of the following are answers:

B) It has a slope of 2

C) It goes through the origin

D) It is a straight line

Step-by-step explanation:

trust me

The equation of the circle with center at (2,-4) and tangent to the line x = -2 is given by:

(2) (x - 2)² + (y + 4)² = 16

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The circle has center at (2,-4), hence [tex]x_0 = 2, y_0 = -4[/tex].

The center is tangent to the line x = -2, hence it has a point at x = -2, since |-2 - 2| = 4, r = 4 -> r² = 16.

Hence the equation of the circle is given by:

(2) (x - 2)² + (y + 4)² = 16

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0.3 is a Rational Number written in Decimal Form

0.3 is neither an Integer nor a Whole number.

Answer:

$10955.6157151671

Step-by-step explanation:

Amount [A] = [tex]P(1+r)^{t}[/tex]

Here, P = principal (which is $5000)

r = rate of interest in decimal form(which is 0.04)

t = time in years (which is 20)

Substituting,

[tex]$5000(1+0.04)^{20}[/tex] = $10955.6157151671

Step-by-step explanation:

so, we have a large triangle made of the 2 cables as legs and the ground distance AB as baseline.

the tower is the height to the baseline of that large triangle.

let's call the top of the tower T.

and remember, the sum of all angles in a triangle is always 180°.

we know the angle A = 62°, and angle B = 72°.

assuming that AB is a truly horizontal line that means that the 2 legs (cables) have different lengths, the triangle is not isoceles, and the tower is not in the middle of the baseline.

so, the height (tower) splits the baseline into 2 parts. let's call them p and q.

p + q = 12 m

p = 12 - q

let's simply define that p is the part of the baseline on the A side, and q is the part of the baseline on the B side.

we have now 2 small right-angled triangles the large height (tower) splits the large triangle into.

one has the sides

AT, height (tower), p

angle A = 62°

angle T = 180 - 90 - 62 = 28°

the other has the sides

BT, height (tower), q

angle B = 72°

angle T = 180 - 90 - 72 = 18°

now remember the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with the sides and the associated angles being opposite.

p/sin(28) = height/sin(62)

q/sin(18) = height/sin(72)

we know from above that

p = 12 - q

so,

(12 - q)/sin(28) = height/sin(62)

height = (12 - q)×sin(62)/sin(28)

q/sin(18) = height/sin(72)

height = q×sin(72)/sin(18)

and therefore, as height = height we get

(12 - q)×sin(62)/sin(28) = q×sin(72)/sin(18)

(12 - q)×sin(62)×sin(18) = q×sin(72)×sin(28)

12×sin(62)×sin(18) - q×sin(62)×sin(18) =

= q×sin(72)×sin(28)

12×sin(62)×sin(18) = q×sin(72)×sin(28) + q×sin(62)×sin(18) =

= q×(sin(72)×sin(28) + sin(62)×sin(18))

q = 12×sin(62)×sin(18) / (sin(72)×sin(28) + sin(62)×sin(18))

q = 4.551603755... m

p = 12 - q = 7.448396245... m

height = q×sin(72)/sin(18) = 14.00839594... m ≈ 14 m

the cell tower is about 14 m tall.

Hey there!

Solve for x :

x = 6 ✅

3x - 2 = 16

>> Add 2 to both sides :

3x - 2 + 2 = 16 + 2

3x = 18

>> Divide each side by 3 :

3x / 3 = 18 / 3

x = 6

▪️Let's verify :

3(6) - 2 ⇔18 - 2 ⇔ 16

Therefore, your answer is x = 6

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3x−2=16

Add 2 to both sides.

3x=16+2

Add 16 and 2 to get 18.

3x=18

Divide both sides by 3.

x = 18 /3

Divide 18 by 3 to get 6.

x = 6 ===> Answer

Let x = 6

3×6−2=16

18-2= 16

16 = 16

Checked ✅

This function shows a horizontal translation of the parent function to the left and 2 units up.

The parent function of a square root function is expressed as:

f(x) = √x

According to the question, we are to plot the expression f(x) = √x+ 3 - 2

This function shows a horizontal translation of the parent function to the left and 2 units up. The required graph will be in the 2nd quadrant of the graph as shown;

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Answer:

It should be the first one.