I need help!!!!

The square below has the given side lengths. x is positive

The distance I can see from the  top of the sears tower in Chicago is 46.41 mi.

The equation for direct proportionality = y = b√x

where:

b = y /√x

41 / √1135

b = 1.217

y = 1.217√1454

y = 46.41 mi

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Answer:

sqrt(11)

Step-by-step explanation:

a^2+b^2 = c^2

a = 5

c = 6

b = ?

25 - b^2 = 36

36 - 25 = b^2

b = sqrt(11)

The ladder should be 7.81 feet long.

Pythagoras theorem tell us the relation between the sides of a right-angled triangle, it states, the sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.

Given that, Aubrey is building a slide for her kids. If the ladder is 6 feet tall, and she wants the bottom of the slide to be 5 feet from the ladder,

This slide is in the form of a right triangle, therefore applying the Pythagoras theorem, we have,

a²+b² = c² (refer to the figure attached)

5²+6² = c²

c² = 25+36

c² = 61

c = √61

c ≈ 7.81

Hence, the length of the slide should be 7.81 feet.

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#SPJ2

After x half-lifes, the amount of the isotope is:

A(x*T) = 90mg*e{-x*ln(2)}

And after 70 days, there are 5.628 mg

We define the half-life as the time such that the inital amount of a given substance reduces to half of it.

If the half-life is T, the amount of the substance can be written as:

A(t) = a*e^{-λ*t}

Where λ = ln(2)/T.

and a is the initial amount.

In this case, T = 17.5 days, then:

λ = ln(2)/17.5 days = 0.0396 / day

And we also have a = 90mg

Then the exponential equation is:

A(t) = 90mg*e^{-t*0.0396 / day}

After x half-lifes, the amount of the isotope left is:

A(x*T) = 90mg*e^{-x*T*ln(2)/T} = 90mg*e^{-x*ln(2)}

And after 70 days the amount is:

A(70 days) = 90mg*e^{-70 days*0.0396 / day} = 5.628 mg

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Answer:

Y=90mg(0.5)^5

1.86 after 70 days

Step-by-step explanation:

Answer:

14.4

Step-by-step explanation:

We have hypotenuse so cannot use tangent. We have adjacent so we can't use sine, therefore, we have to use cosine.

x = cos(59) x 28

x = 14.4

Answer:

D.

Step-by-step explanation:

Okay, so 8:15 to 12:00 is 225 minutes, or 3.75 hours

12:45 to 17:30 is 285 minutes, or 4.75 hours

3.75 + 4.75 = 8.5 hours (total)

She earns 14.50 dollars per hour

8.5 * 14.5 = 123.25 dollars

D.

Answer:

The answers is D: 8.5 hours x $14.50 = $123.25

Step-by-step explanation:

This employee worked a total of 8.5 hours on Monday (3.75 hours in the morning and 4.75 hours in the afternoon).

Then, you have to multiply the total amount of hours worked by the number of dollars paid per hour.

8.5 hours x $14.50 = $123.25

Answer:

-4n + 49

Step-by-step explanation:

it is going down by 4 each step, hence, -4 and 45 -- 4 = 45 + 4 = 49.

Answer:

Step-by-step explanation:

45, 41, 37, 33, 29, ....

a₁ = 45

a₂ = 45 - 4 = 41

a₃ = 41 - 4 = 37

a₄ = 37 - 4 = 33

a₅ = 33 - 4 = 29

...

It's an arithmetic sequence.

a₁ = 45, d = -4

A general term of an arithmetic sequence:

aₙ = a₁ + (n - 1)d

Substitute:

aₙ = 45 + (n - 1) · (-4) = 45 - 4n + 4 = -4n + 49

Answer:

17%

Step-by-step explanation:

subtract/originial*100=lercent change

4.08/24=0.17*100=17

The answer is 17%

The cost of the horse given the amount received at the end of 6 months is 600

let

6/12 × 1200 + 6h/12 = 400 + h

700 + 6h / 12 = 400 + h

700 - 400 = h - 6h/12

300 = 12h - 6h / 12

300 = 6h/12

300 × 12 = 6h

3600 = 6h

h = 3600 / 6

h = 600

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Using the Central Limit Theorem, it is found that the mean of the sampling distribution is of 78 and the standard deviation is of 2.84.

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem, for the population, we have that [tex]\mu = 78, \sigma = 11[/tex].

Then, considering samples of n = 15, we have that the standard deviation is given by:

[tex]s = \frac{11}{\sqrt{15}} = 2.84[/tex].

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The amount Don must pay on his card without  going over the credit limit is $125.

Don's credit limit is $500. If Don does not want to go over the limit, he must not exceed the $500 limit. In order to determine the amount he should pay, add the sum of the charges and subtract it from the credit limit.

Amount to be paid = (425 + 200) - 500 = $125

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For the line and the plane to be perpendicular, they have to meet at right angles

The equation for the plane is x + 2y + 3z= 26

From the complete question, we have:

Point = (5,0,7)

Plane perpendicular to ⟨1,2,3⟩

The general equation is:

a * x+b * y+c * z = d

So, we have:

d = 5 * 1 + 2 * 0 + 7 * 3

Evaluate

d = 26

Recall that:

d = 5 * 1 + 2 * 0 + 7 * 3

Replace the points with x, y and z.

So, we have:

d = x * 1 + 2 * y + 3 * z

Evaluate

d = x + 2y + 3z

So, we have:

d = x + 2y + 3z and d = 26

Equate both equations

x + 2y + 3z= 26

Hence the equation for the plane is x + 2y + 3z= 26

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Answer: 75, 40, 65

Step-by-step explanation:

Let the angles measure 15x, 8x, and 13x.

Since the sum of the angles of a triangle is 180 degrees,

15x+8x+13x=180, meaning that x=5.

So, the angles are 15(5)=75 degrees, 8(5)=40 degrees, and 13(5)=65 degrees.

Answer:

6.25 weeks

Step-by-step explanation:

Take 18.75 and divide it by 3, since the crew is finishing 3 km per week. You get 6.25, so it took the crew 6.25 weeks to finish the road.

Hopefully this helps- let me know if you have any questions!

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

We need to know two formulas before we start ~

Taking value of pi as 3.14

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \:d = 7.4[/tex]

[tex]\qquad \sf  \dashrightarrow \:r = d \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:r = 7.4 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:r = 3.7 \: \: units[/tex]

[tex]\qquad \sf  \dashrightarrow \:area = 3.14 \times (3.7) {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:a = 42.9866 \approx43 \: \: unit {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:r = 2.2 \: yd[/tex]

[tex]\qquad \sf  \dashrightarrow \: circumference = 2 \times 3.14 \times 2.2[/tex]

[tex]\qquad \sf  \dashrightarrow \: c =13.816 \: yd[/tex]

[tex]\qquad \sf  \dashrightarrow \:d = 5 \: cm[/tex]

[tex]\qquad \sf  \dashrightarrow \:circumference = 3.14 \times 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:c = 15.7 \: \: cm[/tex]

[tex]\qquad \sf  \dashrightarrow \:d = 6 \: cm[/tex]

[tex]\qquad \sf  \dashrightarrow \:circumference = 3.14 \times 6[/tex]

[tex]\qquad \sf  \dashrightarrow \:c =18 .84 \: \: cm[/tex]

[tex]\qquad \sf  \dashrightarrow \:r = 2.1 \: m[/tex]

[tex]\qquad \sf  \dashrightarrow \:area = 3.14 \times (2.1) {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:a = 3.14 \times 4.41[/tex]

[tex]\qquad \sf  \dashrightarrow \:a \approx13.85 \: \: m {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:r = 1.3 \: mm[/tex]

[tex]\qquad \sf  \dashrightarrow \:c = 2 \times 3.14 \times 1.3[/tex]

[tex]\qquad \sf  \dashrightarrow \:c = 8.16 \: \: mm[/tex]

Answer:

7.8 feet

Step-by-step explanation:

Use the formula of tan to find his height.

tan Θ = [tex]\frac{opposite}{adjacent}[/tex]

tan 48 = [tex]\frac{x}{7}[/tex]

x = tan 48 × 7

x = 7.8 ft

1.1 2.4 3.3 right

Step-by-step explanation:

no have

Answer:

Last option

Step-by-step explanation:

In order to manipulate a, you have to divide by 3 on both sides.

Answer:

the formula to use is R = 100I/ PT

Step-by-step explanation:

R = rate, I = interest = $1100, P = $ 1000, T= 5years

Based on the speed Alyssa used to get to London and the speed back to Boston, the average speed was 540 mph.

The average speed that Alyssa was going can be found by the formula:

= (Initial speed + Final speed) / 2

Solving gives:

= (480 + 600) / 2

= 1,080 / 2

= 540 mph

In conclusion, Alyssa's average speed was 540 mph.

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Answer:

Correct option is A)

Given,a,b are distance roots of x

3

+3x

2

−1=0

⇒a

3

+3a

2

−1=0 and b

3

+3b

2

−1=0

let the third root be c

then c

3

+3c

2

−1=0

product of roots =

a

−d

=

1

−(−1)

=1

⇒

abc=1

c=

ab

1

but c is root of x

3

+3x

2

−1=0

⇒c

3

+3x

2

−1=0

⇒

(ab)

3

1

+

(ab)

2

3

−1=0

⇒

1+3ab−(ab)

3

=0

.....(1)

in equation (1)

(ab)

3

−3(ab)−1=0

⇒ab is root of

x

3

−3x−1=0

∴(ab) is root of

x

3

−3x−1=0

Answer:

Step-by-step explanation:

Slope intercept form

y + 7 = 3(x  + 4)                 Change all the double minuses to pluses.

y + 7 =  3x + 12                  Remove the brackets.

y + 7 - 7 = 3x + 12-7           Subtract 7 from both sides

y = 3x + 5

Slope

Whatever number is in front of the x is the slope Answer: 3

y intercept

Whatever comes after the plus sign (or minus sign) is the y intercept. It is a single number.  Answer: 5

x intercept.

This occurs when y = 0

0 = 3x + 5                      Subtract 5 from both sides

-5 = 3x + 5 -5

-5 = 3x                            Divide by 3

-5/3 = 3x / 3

-5/3 = x                          

Answer: x_intercept = -5/3

Answer:

No, (-4, 6) is not a solution to y = -9.

Step-by-step explanation:

y= -9 has a horizontal line graph.  Every point on this line has -9 as its y-coordinate.  (-4, 6) does not lie on that line and is therefore not a solution to y = -9.

Answer:

Step-by-step explanation:

The relations describing the two numbers can be written as equations. First, we need to assign variables: let x and y represent the first and second numbers, respectively.

The given relations are then ...

  7x +6y = 31

  3x -10y = 29

__

Such a system of equations can be solved many ways. One that is usually convenient is to use a graphing calculator. It tells us ...

Answer:

19 the explanation is 19 46

Answer: 90.

Step-by-step explanation: According to the question above, 54 Thin Mints cookies were 60% of the total amount of cookies she sold in one afternoon and the remaining 40% is still missing. 54 / 3 is 18, which is part of our answer, because if 54 is 60%, then 18 is 20%. 18 x 2 is 36, and 36 is 40%. Now that we've found the remaining 40%, the rest is adding 54 and 36, which gives you an answer of 90.

Rectangle GHIJ with the vertices G(2,-1) H(7,-1) I(7,-4) J(2,-4) is reflected across the line y= -5 to give G'(2, 3) H'(7, 3) I'(7, -3) J'(2, -3)  

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Rectangle GHIJ with the vertices G(2,-1) H(7,-1) I(7,-4) J(2,-4) is reflected across the line y= -5 to give G'(2, 3) H'(7, 3) I'(7, -3) J'(2, -3)  

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