Joshua has a ladder that is 15 feet long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 14.2 feet above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 78 degrees. Will the ladder be safe at this height? Show your work and label the diagram

Answer:

4.25 gallons of juice

Step-by-step explanation:

4 quarts = 1 gallon

3 quarts = 3/4 gallon

2 1/2 + 1 + 3/4 = 3 2/4 + 3/4 = 3 5/4 = 4 1/4

4 1/4 = 4.25

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The length of EF which lie on line EC is 8.66 units.

Parallel lines are the lines that do not intersect or meet each other at any point in a plane. They are always parallel and are at equidistant from each other. Parallel lines are non-intersecting lines.

Here,    EG = 6.9 ,        FC = 6.4,           GD = 5.1

Also. FG || CD

By Basic Proportionality Theorem,

               [tex]\frac{EF}{FC} = \frac{EG}{GD}[/tex]

               [tex]EF = \frac{EG . FC}{GD}[/tex]

               EF =  (6.9 X 6.4) / 5.1

               EF = 8.66 units

Thus, The length of EF which lie on line EC is 8.66 units.

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The given shape in the image is not an equilateral triangle.

The triangle with all three sides equal and all the angles equal is called an equilateral triangle.

In the given figure we can see a triangle this triangle is not an equilateral triangle because the figure is formed between a square grid now if you see closely the base of the triangle can not be equal to the two sides of the triangle.

Because these two sides are the hypotenuse for the remaining right-angle triangle. So the base of the highlighted triangle can not be equal to the other two sides of the triangle.

Therefore given shape in the image is not an equilateral triangle.

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Answer:

she will need about 7 baskets, the proper number is 6.7 but round up and its 7

Step-by-step explanation:

hope this helps!

Inspired by the works of Neil Dawson and Bert Flugelman, Kassidy drafts a design for a modern sculpture, the amount of steel Kassidy will need is mathematically given as

SA=16.094711 ft^2

Generally, the equation for the surface area of a cone is mathematically given as

SA=πr(rπ+√(h^2+r^2))

Therefore

SA=πr(rπ+√(h^2+r^2))

SA=π*1(1+√(4^2+1^2))

SA=16.094711 ft^2

In conclusion,  the amount of steel Kassidy will need is

SA=16.094711 ft^2

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Answer:

[tex]\text{1st term} = 3\\\\\text{Common ratio} = 2[/tex]

Step by step explanation:

[tex]\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\[/tex]

The following represents the factorization of the trinomial is -3x [ (x+2)(x+4)].

What is Trinomial?

A trinomial is a polynomial consisting of three terms or monomials.

Given polynomial:

-3x³-18x²-24x

Taking -3x as common, we get

=-3x(x²+6x+8)

Now, by factorization

=-3x (x²+4x+2x+8)

= -3x[x(x+4) + 2(x+4)]

= -3x [ (x+2)(x+4)]

Hence, the factorization is -3x [ (x+2)(x+4)].

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Answer:

y=3x-10

Step-by-step explanation:

Slope: (y2-y1)/(x2-x1)

(2-8)/(4-6)

slope= -6/-2 = 3

Point: (6,8)

Slope-intercept: y-y1=m(x-x1)

y-8=3(x-6)

y-8=3x-18

y=3x-10

Answer:

A=108

B=22

C=51

D=28

Step-by-step explanation:

A= AFB is a vertical angle opposite 108

B= congruent angles congruent sides, 11 x 2 sides

C= using angle rules, alternate interior angles of 21 puts 21 in the

triangle with 108, all triangles sum total 180, so (180-21=51)

for the 3rd angle ACD

D=last answer

The graph that shows the information on the table is On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (2, 300) and (4, 600).

The independent variable is the number of ounces of salad dressing which means that it will be shown on the x axis.

The total calories is the dependent variable which means that it will be on the y axis.

The line drawn will pass through the points on the table of (2,300) and (4 ,600) so option A is correct.

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Step-by-step explanation:

using elimination method because this is a simultaneous equation

3×x+6×y=111

x+y=27

1×[3x+6y=111]

3×[x+y=27]

3x+6y=111—equation 1

3x+3y=81—equation 2

substrate equation 1 from equation 2

3y=30

divide both sides by 3

y=10

substitute 10 for y in equation 1

3x+6y=111

3x+6(10)=111

3x+60=111

3x=111-60

3x=51

divide both sides by 3

x=17

Answer:

it would be a vertical shift of 5 down

Step-by-step explanation:

I'm learning the same thing rn and that's right

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}[/tex]

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

  | 2  -7    8  -3

1 |      2   -5   3

  | 2   -5    3  0

1 |      2     -3  

    2   -3     0

So the factorization is (x-1)² (2x-3)=0. So:

                     [tex]\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}[/tex]

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

      |  1  -1  0  -4

  2  |     2  2    

         1  2  2  0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

                   [tex]\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}[/tex]

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

   | 6    7       9      2

-2 |      -12    10     -2

     6    -5     1       0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

         [tex]\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}[/tex]

                     [tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}[/tex]

Answer: B

Step-by-step explanation:

    We will test the options and see if they apply to the given values.

[A]  ✗

1 * 6 = 6 ✓

4 * 6 ≠ 15✗

[B] ✓

1 * 3 = 3, 3 + 3 = 6 ✓

4 * 3 = 12, 12 + 3 = 15 ✓

6 * 3 = 18, 18 + 3 = 21 ✓

[C] ✗

1 * 8 = 8, 8 - 2 = 6 ✓

4 * 8 = 32, 32 - 2 = 30, 30 ≠ 15 ✗

By using trigonometric relations, we will see that the distance between Carlos and the tree is:

D = 781.23 ft

We can model this with a right triangle. We know that Carlos is 6ft tall, and the height of the tree is 275ft.

Then one of the cathetus of the triangle is equal to:

275ft - 6ft = 269ft.

That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.

Then we can use the relation:

tan(a) = (opposite cathetus)/(adjacent cathetus).

Where:

Replacing that, we get:

tan(19°) = 269ft/D

Solving for D, we get:

D = 269ft/tan(19°) = 781.2ft

So we conclude that Carlos is at 781.23 ft of the tree.

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Answer:

d

Step-by-step explanation:

your answer to your question is D

The values for time is  1.361 and 0.828.

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .

Given: h=-16t²+35t+2

so if the height is going to be 20ft,

20 = 2+35t-16t²

16t²-35t18=0

Solve the above quadratic equation

x= -b±√b²-4ac/2a

a=16, b=-5, c=18

x=[-(-35)±√(-35)²-4*16*18]/2*16

x= [35±√73]/32

x= 35+√73/32  and x= 35-√73/32

x=1.361 and 0.828.

Hence, the values for time is  1.361 and 0.828.

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the probability of getting a black one given that in the first draw we got a black one is P = 1/2 = 0.5

We will assume that all the beads have the same probability of being randomly selected.

Then the probability of picking a black bead is equal to the quotient between the number of black beads and the total number of beads.

Originally, there are 4 black ones and 3 red ones ( a total of 7).

We want to get the probability of getting a black one given that in the first draw we got a black one.

If in the first draw we got a black one, then now there are 3 blacks and 3 reds (a total of 6 beads).

So the probability of getting another black one is:

P = 3/6 = 1/2 = 0.5

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Answer:

$699.80

Step-by-step explanation:

$640 - 18% = 524.80

(640x18)/100 = 115.20

640-115.20 = 524.80

524.80+175 = 699.80

Answer:

$699.80

Step-by-step explanation:

640(18%)

640 x 18

100

reduce fraction

640 x 9

50

simplify

64 x 9

5

576

5. or 115 1

5. of 115.20

640 - 115.20 = 524.80 (dishwasher)

524.80 + 175 = 699.80 (total including installation)

Answer:

B.) 4,096 feet

Step-by-step explanation:

You were given a time, and time in the equation is represented by "t". To find the height, represented by "h", you just need to plug the given value in for "t" and simplify to find "h".

t = (1/4)√x                                         <--- Original equation

16 = (1/4)√x                                      <--- Plug 16 in "t"

64 = √x                                            <--- Divide both sides by (1/4)

4,096 ft = x                                    <--- Square both sides

The object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.

The equation is t=1/4 √x , where t is time in seconds and x is height in feet. To determine the height  x at which an object should be dropped to reach the ground in 16 seconds, you can plug in the value of t=16 into the equation:

16 = 1/4 √x

Simplify the equation by multiplying both sides by 4:

4⋅16= √x

64= √x

Now, square both sides to isolate x:

64²=x

4096 = x

Therefore, to have the object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.

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Answer:

slope is undefined

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 ) = (6, 4 ) and (x₂, y₂ ) = (6, - 2 )

m = [tex]\frac{-2-4}{6-6}[/tex] = [tex]\frac{-6}{0}[/tex]

division by zero is undefined, therefore the slope of the vertical line is undefined.

Answer:

101 degrees

Step-by-step explanation:

The third angle in the first triangle would be  180 - (26+53) = 101 degrees

the angle in triangle 2 could be the 101 degree one

Answer:

choose option 1

Step-by-step explanation:

option one is going to take a longer time to pay off but option 2's annual fees are going to make you spend at least $200 more dollars than option 1

Answer:

1. I went to a store four days in a row and only bought chocolate bars each day. All chocolate bars were the same and cost the same. On the first day, I bought 2 chocolate bars for $2.38. On the second day I bought 1 chocolate bar for $1.19. On the third day, I bought 10 chocolate bars for $11.90. On the fourth day, I bough 4 chocolate bars for $4.76.

2. A sink is full. It contains 20 gallons of water. The stopper is removed and water starts draining out. One minute after the stopper is removed, the volume of water in the sink is 18 gallons.  Two minutes after the stopper is removed, the volume of water in the sink is 16 gallons.  Four minutes after the stopper is removed, the volume of water in the sink is 12 gallons.  Ten minutes after the stopper is removed, the sink is empty.  

Answer:

C

Step-by-step explanation:

the 2 angles form a linear pair and sum to 180° , that is

3x + 12 + x = 180

Using compound interest, it is found that Dante was 6.6 years old when the balance in the account reached $13,000.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

In this problem, we have that the parameters are given as follows:

A(t) = 13000, A(0) = 10000, r = 0.04, n = 12.

Hence the time in years is found as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]13000 = 10000\left(1 + \frac{0.04}{12}\right)^{12t}[/tex]

[tex](1.0033)^{12t} = 1.3[/tex]

[tex]\log{(1.0033)^{12t}} = \log{1.3}[/tex]

[tex]12t\log{1.0033} =  \log{1.3}[/tex]

[tex]t = \frac{\log{1.3}}{12\log{1.0033}}[/tex]

t = 6.6

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Answer:

3/4 (A)

Step-by-step explanation:

replace x with -2 in the function

3 · 2^-2  = 3 · 0.25

3 · 0.25 = 0.75

0.75 = 3/4