Type SSS, SAS, ASA, AAS, or HL to justify why AABC = ADEF.

AC FD and AB = DE

Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

To determine which planks Amanda should use to build the triangular-shaped kennel:

Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

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Answer: c = 520

Step-by-step explanation:

     f(2) = 578 means that when x = 2, the value is equal to 578. We will plug these knowns in and then solve for c.

Given:

    f(x) = 4x³ + 7x² - x + c

Substitute:

    578 = 4(2)³ + 7(2)² - (2) + c

Distribute:

    578 = 4 * 2³ + 7 * 2² - 2 + c

Raise to the power of 3 and 2:

    578 = 4 * 8 + 7 * 4 - 2 + c

Multiply:

    578 = 32 + 28 - 2 + c

Add:

    578 = 60 - 2 + c

Subtract:

    578 = 58 + c

Subtract 58 from both sides:

    520 = c

Reflexive property:

   c = 520

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

Given:

[tex]\longrightarrow\bold{f(x) = 4x^3 + 7x2 −x + c}[/tex]

[tex]\longrightarrow\sf{578= 32+28 −2+ c}[/tex]

[tex]\longrightarrow\sf{578 =58+ c}[/tex]

[tex]\longrightarrow\sf{c = 578-58}[/tex]

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

[tex]\longrightarrow\sf{c= 520}[/tex]

The solution to the inequality 4 ≥ b is represented in the graph

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

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Inequality shows the non equal comparison between two or more numbers and variables.

Given the inequality:

4 ≥ b

Rearranging gives:

b ≤ 4

The solution to the inequality 4 ≥ b is represented in the graph

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Answer: 57

I'm pretty sure that's what it is

Step-by-step explanation:

the units of measurement for the composite function f(w(h)) are - furniture/weeks

function composition is an operation. that takes two functions f and g, and produces a function h = g . f such that h(x) = g. In this operation, the function g is applied to the result of applying the function f to x.

                               [tex]f(w(h)) = \frac{furniture}{hours} (\frac{hours}{week} )\\f(w(h)) = \frac{furniture}{week}[/tex]

The units of measurement for the composite function f(w(h)) is furniture/weeks.

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The complete fractional question given in the above picture is 55/3 = 1 + 52/3 = 2 + 49/3 = 5 + 40/3 = 8 + 31/3 = 10 + 25/3

Let

55/3 = 1 + x/3

55/3 = (3+x) / 3

55/3 × 3 = 3 + x

55 = 3 + x

55 - 3 = x

52 = x

55/3 = 2 + x/3

55/3 =(6+x) / 3

55/3 × 3 = 6+x

55 = 6 + x

55 - 6 = x

49 = x

55/3 = x + 40/3

55/3 = (3x+40) / 3

55/3 × 3 = 3x + 40

55 = 3x + 40

55 - 40 = 3x

15 = 3x

x = 15/3

x = 5

55/3 = x + 31/3

55/3 = (3x+31) / 3

55/3 × 3 = 3x + 31

55 = 3x + 31

55 - 31 = 3x

24 = 3x

x = 24/3

x = 8

55/3 = 10 + x/3

55/3 = (30+x) / 3

55/3 × 3 = 30 + x

55 = 30 + x

55 - 30 = x

25 = x

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Answer:

84

Step-by-step explanation:

4 (-4)^2 - 5(-4)

4 × 16 - 5 × -4

64 + 20

84

Yes. [tex]f(x)[/tex] is a PDF if

• [tex]f(x) \ge 0[/tex] for all [tex]x[/tex] in the support; this is true, since [tex]e^{-x}>0[/tex] for all [tex]x[/tex], and multiplying a positive number [tex]x[/tex] doesn't change this fact;

• the integral of [tex]f(x)[/tex] over its support is 1; this is also true, since

[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = \int_0^\infty xe^{-x} \, dx = 1[/tex]

which can be computed by parts.

Answer:

  (a)  The two triangles are similar by AA

Step-by-step explanation:

Similar triangles have congruent corresponding angles and proportional corresponding side lengths.

The third angle in triangle ABC is found using the fact that the sum of angles is 180°.

  ∠C = 180° -∠A -∠B

  ∠C = 180° -97° -46° = 37°

Two of the angles, A and C, match the measures of two of the angles in triangle DEF. The matches are ...

  ∠A = ∠D = 97°

  ∠C = ∠F = 37°

The two triangles are similar by AA.

__

Additional comment

The similarity statement can be ΔABC ~ ΔDEF.

Considering the situation described, the classification of the runners is given as follows:

Dan - Ben - Alex - Curtis.

The oldest came in second place. Ben is older than Alex, and Curtis is older than Dan, hence either Ben or Curtis finished second.

Alex ran the distance faster than Curtis, and Dan ran faster than Ben and Curtis, hence considering the above observation Ben finished second and the classification is:

Dan - Ben - Alex - Curtis.

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Using proportions, it is found that 1685% of an hour passes between 11:24 am and 415 am.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

One hour is composed by 60 minutes. Between 11:24 am and 4:15 am, there are 16 hours and 51 minutes, hence the number of minutes is given by:

M = 16 x 60 + 51 = 1011 minutes.

As a percentage of one hour = 60 minutes, we have that this measure is:

1011/60 x 100% = 1685%.

Hence 1685% of an hour passes between 11:24 am and 415 am.

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Answer:

y=-5x-12/5

Step-by-step explanation:

First you need to find y intercept

y=mx+b

plug in the points (0,12)

12=mx+0

now plug in -5

12=-5x+0

subtract 0 from both side

12=-5x

divide -5 from both side.

x=12/-5

Answer:

Step-by-step explanation:

A= π(5)²

 = 3.14(5)²

 = 3.14(25)

 = 78.5 ans

The vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)

The coordinates of the quadrilateral ABCD are given as:

A(0,0), B(0,3), C(5,3), and D(5,0)

When dilated by a scale factor of 2.5, we have the following equation

A' = A * 2.5

So, we have:

A' = (0,0) * 2.5

A' = (0, 0)

B' = (0,3) * 2.5

B' = (0, 7.5)

C' = (5,3) * 2.5

C' = (12.5, 7.5)

D' = (5,0) * 2.5

D' = (12.5, 0)

Hence, the vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)

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the interval in which g(x) is positive is [3, ∞].

Here we have the function:

g(x) = ∛(x - 3)

The interval in which the function is positive is defined by:

g(x) > 0.

Then we have:

∛(x - 3) > 0.

We need to solve that inequality for x.

∛(x - 3) > 0

The cube root respects the sign of the argument, then:

x - 3 > 0

x > 3

Then the interval in which g(x) is positive is [3, ∞].

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Answer:

see explanation

Step-by-step explanation:

let x be the amount Kweku gets then Kofi gets 3x , so

x + 3x = 4800

4x = 4800 ( divide both sides by 4 )

x = 1200

that is

Kweku gets $1200

Kofi gets 3 × $1200 = $3600

Answer:

182000

Step-by-step explanation:

4.82 x 10^5

1.

10^5 is equal to 10 being multiplied 5 times. So this can be expressed as:

10 x 10 x 10 x 10 x 10.

When you multiply 10s, you just add the number of zeros next to one.

==> 100000 (5 zeros total)

2.

We multiply 100000 to 4.82.

100000 x 4.82 = 182000

So our final answer will be 182000.

Answer:

482,000.

Step-by-step explanation:

The 5 tells us this number is 6 digits long.

The answer is

482,000

Place value of 5 in 5107465 is equal to 5,000,000.

According to the statement

we have given that the a value and we have find the place value of a digit 5 in this numbers.

So, For this purpose,

The given digit is 5107465

And we have find the value of digit 5 in it so,

we know that,

A Place value is the position or place of a digit in a given number .

As we can see that, in given number 5107465:-

5 is at one million place = 5 * 1,000,000 = 5,000,000

1 is at hundred thousand place = 1 * 100000 = 100000

0 is at ten thousand place = 0 * 10000 = 0

7 is at thousand place = 7 * 1000 = 7000

4 is at hundred place = 4 * 100 = 400

6 is at tens place = 6 * 10 = 60

5 is at unit place = 5 * 1 = 5

Therefore,

Place value of 5 in 5107465 is equal to 5,000,000.

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The Laplace transform of the given function is [tex]f(s)=\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]

Given,

[tex]f(t)=\left \{ {{t, 0\leq t < 5} \atop {0,t\geq 5}} \right.[/tex]

Write the function in unit step function.

[tex]f(t)=t(u_{0}(t)-u_{5} (t))[/tex]

      = [tex]t(1-u_{5}(t))[/tex]                       ∵[tex]u_{0} (t)=1[/tex]

      = [tex]t-tu_{5} (t)[/tex]

[tex]f(t)=t-tu_{5} (t)[/tex]

In order to make it easier to take the Laplace transform of the function, we can follow the steps:

[tex]f(t)=t-tu_{5} (t)[/tex]

      = [tex]t-(t-5+5)u_{5} (t)[/tex]

      = [tex]t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]

[tex]f(t)=t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]

We need to find the Laplace transform of f(t).

Apply Laplace transform on both sides,

£[tex][f(t)=[/tex]£[tex](t)-[/tex]£[tex](t-5)u_{5} (t))+5[/tex]£[tex](u_{5} (t))[/tex]

         = [tex]\frac{1}{s^{2} } -e^{-s}[/tex]£[tex](t)+5(\frac{e^{-5s} }{s} )[/tex]

         = [tex]\frac{1}{s^{2} } -e^{-5s} (\frac{1}{s^{2} } )+\frac{5se^{-5s} }{s^{2} }[/tex]

        = [tex]\frac{1-e^{-5s}+5se^{-5s} }{s^{2} }[/tex]

       = [tex]\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]

[tex]f(s) =\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]

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Answer:

227.02

Step-by-step explanation:

[tex]400.00-172.98 \\ \\ =300 - 72.98 \\ \\ =230-2.98 \\ \\ =228-0.98 \\ \\ =227.02[/tex]

Answer:

227.02

Step-by-step explanation:

[tex]400.00\\-172.98[/tex]

To solve: First subtract 172 from 400, resulting in 228, then you may subtract the 0.98, leaving 227.02.

Answer:

A) f(x) = x^2 +8(x+2)

Step-by-step explanation:

We will start by putting y=0

0 = x^2+8(x+2) -Apply distributive property

0 = x^2+8x+16

0=(x+4)(x+4)

0=x+4, 0=x+4

x=-4

There is only one zero, and that is x=-4

Brainiest would be appreciated.

First one

Because

If we solve for x

Option A

Answer:

Future Amount ≈ 32

Step-by-step explanation:

substitute x = 8 into the given formula , that is

future amount = 16[tex](1.09)^{8}[/tex] = 16 × 1.99256.. ≈ 32 ( nearest whole number )

13.1 = 13.10

---> 13.1 > 13.01

---> 13.01 < 13.1

The correct answer is <

Answer:

f(3) = g (3)

Step-by-step explanation:

graphically, we notice that the graphs of f and g intersect

at the point of coordinates (3 , 0)

Then

f(3) = 6 = g(3)

Then

f(3) = g (3)

Answer:

I mean, I think it varies by house and by location but a general range would be:

Min: 64 *F

Max: 74 *F

Answer:

Solution:

here,

6 cans cost = 9 dollars

1 can costs = 9÷6 dollars

= 1.5 dollars

Now,

8 cans cost = 8×1.5 dollars

= 12 dollars

The property best describes the Function f IP 4- to- 1 Correspondance.

f is Nat Bijective since Not one-one.

x1= 010101 = 010111

then 2 and 7 2 maps to 0101

So f is mat one-one.

fip Mat 2 - to- 1 correspondance

Since

2 , = 0101 vo , 212 = 0101 01 , 23 = 010 / 1 1

One point 0101

go,

f is Not 2 - to- 1 correspondance.

7 12) is the storing a with the last two

bits mold so we have only $ possibility

of 4 strings going to a single storing.

f can not be 16 - to - 1 correspondance.

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9 hours long after the second runner started will the second runner overtake the first runner.

What does it mean to do speed?

Runner I = 6 mph

Runner II = 7 mph

Difference in time= 90 minutes

Train A will have covered 9 miles before Runner II starts

catch up distance= 9 miles

catch up speed = 7-6 mph

catch up speed = 1 mph

Catchup time = catchup distance/catch up speed

catch up time= 9/1

catch up time= 9 hours

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The measure of angle C is 35°.

Given that, ΔABC≅ΔDEF, ∠A=70°, ∠E=3x and ∠F=x+10.

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

In ΔABC and ΔDEF, corresponding angles are equal.

That is, ∠A=∠D=70°, ∠B=∠E=3x and ∠C=∠F=x+10

Now, ∠A+∠B+∠C=180° (∵angle sum property)

⇒70°+3x+x+10=180°

⇒4x=100°

⇒x=25°

Thus, ∠C=x+10=35°.

Therefore, the measure of angle C is 35°.

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