You lean a 6 foot ladder against the wall. If the base is 4 feet from the wall, what angle does the ladder make with the ground? Round to the nearest tenth.

Answer:

See below

Step-by-step explanation:

2x = 10

Divide by 2.

x = 5

x has to equal 5 to make the first statement true.

Proof:

2x = 10

2(5) = 10

10 = 10

-3x = 21

Divide by -3.

x = -7

x has to equal -7 to make the second statement true.

Proof:

-3x = 21

-3(-7) = 21

21 = 21

1/3(x) = 6

Multiply by 3 to cancel the fraction.

x = 18

x has to equal 18 to make the third statement true.

Proof:

1/3(x) = 6

1/3(18) = 6

6 = 6

-1/2(x) = -7

Multiply by -2 to cancel the fraction.

x = 14

x has to equal 14 to make the fourth statement true.

Proof:

-1/2(x) = -7

-1/2(14) = -7

-7 = -7

Answer:

4. t>16

hope it helps......

Answer:

96 people.

Step-by-step explanation:

Exponential equation for a decreasing amount:

The exponential equation for a decreasing amount is given by:

[tex]A(t) = A(0)(1-r)^t[/tex]

In which A(0) is the initial rate and r is the decay rate, as a decimal.

Currently, the number of people entering a shopping mall is 109.

This means that [tex]A(0) = 109[/tex]

It is estimated that the number of people entering the shopping mall will decrease by 3% each hour.

This means that [tex]r = 0.03[/tex]

So

[tex]A(t) = A(0)(1-r)^t[/tex]

[tex]A(t) = 109(1-0.03)^t[/tex]

[tex]A(t) = 109(0.97)^t[/tex]

Find the total number of people entering the shopping mall at the end of 4 hours.

This is A(4). So

[tex]A(4) = 109(0.97)^4 = 96.49[/tex]

Rounding to the nearest whole number, 96 people.

Answer:

y = (5/4)x+1

Step-by-step explanation:

[tex]\frac{y+4}{x+4} =\frac{-4-6}{-4-4}[/tex]

[tex]\frac{y+4}{x+4} = \frac{-10}{-8} \\or, 4(y+4) = 5(x+4)\\or, 4y= 5x+20-16\\or, y= \frac{5}{4}x+1[/tex]

Answer:

Required expression = (g+h) - 11

Answer:

[tex]\frac{1}{x^21y^12}[/tex]

Step-by-step explanation:

9514 1404 393

Answer:

  y = -3x

Step-by-step explanation:

Your solution will be in the form ...

  y = (something)

In order to get the y-term by itself, you need to add the opposite of everything else*:

  3x +y +(-3x) = 0 +(-3x)

  y = -3x . . . . . simplify

_____

* Anything you do to one side of the equation must also be done to the other side. Here, we added -3x to both sides.

Answer:

blank area = 1.5π units²

Step-by-step explanation:

area of full circle = πr² = π6² = 36π units²

blank area = (15/360)(36π) = 1.5π units²

The area blank in a circular mosaic pattern is 4.71 square units.

A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.

For the given situation,

The diagram shows the circle with a central angle cutout.

The central angle, θ = 15°

Radius of the circle, r = 6 units

The formula of area blank in circle is

[tex]Area_{blank} = \frac{\theta}{360}\pi r^{2}[/tex]

⇒ [tex]Area_{blank} = \frac{15}{360}(3.14) (6)^{2}[/tex]                [∵ π = 3.14 ]

⇒ [tex]Area_{blank} = 0.0416(3.14) (36)[/tex]

⇒ [tex]Area_{blank} = 4.71[/tex]

Hence we can conclude that the area blank in a circular mosaic pattern is 4.71 square units.

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Answer:

Step-by-step explanation:

g(x) =  -|x-3| +4

Answer:

p =favorable outcome/possible outcome

p(not 3)=3/4

Answer:

5

Step-by-step explanation:

Answer:

x+y= 30

8x+7.5y=234

you need to work 18 hours as a dog walker and 12 hours at the carwash

Step-by-step explanation:

x is the number of hours spent dog walking

y is the number of hours spent at the car wash

x+y is to total number of hours work (30)

8x is the amount made dog walking

7.5y is the amount made working at the carwash

234 is the total amount made by working 30 hours

x+y= 30

8x+7.5y=234

to solve:

x+y=30  (isolate the variable x) x=30-y

8(30-y)=234 (substitute in the 30-y for x)

240-8y+7.5y=234 (distribute the 8)

240-.5y=234 (combine like terms)

-.5y=-6 (subtract 240 from each side)

y=12 (divide by .5)

x+12=30 (put 12 in for y)

x=18 (subtract 12 from both sides)

you need to work 18 hours as a dog walker and 12 hours at the carwash

Answer:

B

Step-by-step explanation:

if you connect and extend to points it forms a line with a y-intercept of 2 when x is zero

   y = mx + b      m the slope equals 1

   y = x +2

Answer:

It's (B), using L'Hopital's Rule.

Answer:

f(x) = 25,000(0.1)^5x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The intersections of a transversal with two lines create various types of pairs of angles: consecutive interior angles, consecutive exterior angles, corresponding angles, and alternate angles.

Answer:

B. 12^3 - 12^2 - 11

Step-by-step explanation:

........

Answer:

The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.

Step-by-step explanation:

An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating:

At the null hypothesis, we test if the mean is the same, that is:

[tex]H_0: \mu = 59.5[/tex]

At the alternate hypothesis, we test that it is different, that is:

[tex]H_a: \mu \neq 59.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

59.5 is tested at the null hypothesis:

This means that [tex]\mu = 59.5[/tex]

After testing 250 vans, they found a mean MPG of 59.2. Assume the population standard deviation is known to be 1.9.

This means that [tex]n = 250, X = 59.2, \sigma = 1.9[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{59.2 - 59.5}{\frac{1.9}{\sqrt{250}}}[/tex]

[tex]z = -2.5[/tex]

Pvalue of the test and decision:

The pvalue of the test is the probability of finding a mean that differs from 59.5 by at least 0.3, which is P(|Z|>-2.5), which is 2 multiplied by the pvalue of Z = -2.5.

Looking at the z-table, Z = -2.5 has a pvalue of 0.0062

2*0.0062 = 0.0124

The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.

Answer:

a = –2, b = 4, c = – 3

Step-by-step explanation:

We are given the following quadratic equation in the question:

-2x^2 + 4x - 3 = 0−2x

2

+4x−3=0

General form of quadratic equation:

ax^2 + bx + c = 0ax

2

+bx+c=0

Comparing the given equation to general quadratic equation, we get,

a = -2, b = 4, c = -3a=−2,b=4,c=−3

Thus, the correct answer is

Option D) a = –2, b = 4, c = – 3

The values of a, b, and c in the given quadratic equation are a = -2, b = 4, c = -3

The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given is a quadratic equation -2x²+4x-3 = 0, we need to find the values of a, b, and c in the given quadratic equation.

The standard equation of a quadratic equation is ax²+bx+c = 0,

Comparing the given equation with the standard equation,

We get, a = -2, b = 4, c = -3

Hence, the values of a, b, and c in the given quadratic equation are a = -2, b = 4, c = -3

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Answer:

The perimeter of rectangle JKLM is 16 units.

Step-by-step explanation:

Perimeter is the area around the shape, so if you look at the space between K and J, the units there are 7. Multiply 7 by 2 (since there are two sides), and then add 2. 2 + 14 = 16.

Answer:

17 units

Step-by-step explanation:

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Answer:

482.5 ft^2.

Step-by-step explanation:

The figure can be regarded as a rectangle with a triangle cut out of one corner.

The base of the triangle = 25-20 = 5 in and the height = 20 - 13 = 7 in.

The required area = area of rectangle - area of triangle

= 25*20 - 1/2 * 5 * 7

= 500 - 17.5

= 482.5 ft^2

9514 1404 393

Answer:

  482.5 square inches

Step-by-step explanation:

The figure can be considered to be a 25 in by 20 in rectangle with a 5 in by 7 in triangle cut off the corner. Then the area of the figure is the area of the rectangle, less the area of the triangle.

  A = LW - 1/2bh

  = (25 in)(20 in) - 1/2(5 in)(7 in) = 500 in² -35/2 in² = 482 1/2 in²

The area of the figure is 482.5 square inches.

Answer:

p

Step-by-step explanation:

If angle BOC in circle is 68° then the measure of angle BAC is 34°.

Given that angle BOC in the circle is 68°.

We have to find the angle BAC.

We have that m∠BOC=arc BC ------by central angle.

we have m∠BOC=68°.

therefore arc BC=68°.

We know that the inscribed angle is half that of the arc it comprises so m∠BAC=1/2 *(arc BC)-----1

In geometry one of the theorem states states that angle at the center of a circle is twice angle at the circumference.

We have that arc BC=68°

substitute arc BC in equation 1 to get the measurement of ∠BAC.

m∠BAC=[tex]68/2[/tex]

=34°

Hence if angle BOC in circle is 68° then the measure of angle BAC is 34°.

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Answer:

540 in³

Step-by-step explanation:

v = lwh

v = 18 * 10 * 3

c = 540 in³

Answer:

v= length x width x height so 10x18x3= 540in cubed

Step-by-step explanation:

Answer:

[tex]56666\frac{2}{3}[/tex]

Step-by-step explanation:

Answer:56,666.666

Step-by-step explanation:

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