The base of the mountain is 6,500 feet above sea level and lineAB measures 230 feet across. Given that the measurements for angleQAP is 20° and angleQBP is 35°, how far above sea level is peak P? Express your answer to the nearest foot.

The area of triangle ABC is given as follows:

A = 5.5 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The base AB has the length given as follows:

[tex]AB = \sqrt{(-4  - (-8))^2 + (-7 - (-8))^2}[/tex]

b = 4.12.

The midpoint of the base AB is given by the mean of the coordinates, hence:

M = (-6, -7.5).

The height is given by the distance MC, as follows:

[tex]h = \sqrt{(-6 - (-5))^2 + (-7.5 - (-5))^2}[/tex]

h = 2.69.

Hence the area of the triangle is given as follows:

A = 0.5 x 4.12 x 2.69

A = 5.5 square units.

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The family traveled from Camp Carol to Phoenix at an average speed of approximately 84.44 kilometers per hour.

Speed is simply referred to as distance traveled per unit time.

It is expressed mathematically as:

Speed = Distance / time

Given that the family traveled 38 km from Camp Carol to Phoenix in 27 minutes:

Distance traveled = 38 kilometers

Time taken = 27 minutes

First, convert the time from minutes to hours:

Time taken = ( 27 / 60 ) hours

Time taken = 0.45 hour

We can now calculate the average speed using the above formula as follows:

Average speed = Distance / time

Average speed = 38 km / 0.45 h

Average speed = 84.44 km/h

Therefore, the average speed is approximately 84.44 km/h.

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1 2/3 yards is equal to 5 1/3 feet.

To convert from yards to feet, we know that 1 yard is equal to 3 feet. Therefore, we can calculate:

1 2/3 yards = (1 + 2/3) yards = (3/3 + 2/3) yards = 5/3 yards

Now, to convert yards to feet, we multiply by 3:

5/3 yards * 3 feet/1 yard = 15/3 feet = 5 feet

Therefore, 1 2/3 yards is equal to 5 1/3 feet.

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Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;

Statement                                 Reason

AC bisects ∠BAD                      Given

∠BAC ≅ ∠DAC                         Definition of an angle bisector.

∠BCA ≅ ∠DCA                         Congruent angles of a triangle (SAS).

AC ≅ AC                                   Reflexive property

ΔABC ≅ ΔADC                         AAS postulate

In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

By applying the angle bisector theorem to the given triangle, the variable y can be calculated by using the following mathematical equation (formula):

AC bisects ∠BAD       Given

∠BAC ≅ ∠DAC           Definition of an angle bisector.

Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can logically deduce that ∠BCA is congruent to ∠DCA

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Answer:

30% increase

Step-by-step explanation:

percentage increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase = $35.10 - $27 = $8.10 , then

percentage increase = [tex]\frac{8.10}{27}[/tex] × 100% = 0.3 × 100% = 30%

Answer:

Step-by-step explanation:

step 1:       35.10-27 =8.1

step 2:       8.1/27 x 100 = 30%

so therefore = 30% increase

They are similar because AB is four more than ED, AC is three more than DF, and BC is three more than EF.

To determine if two triangles are similar, we need to compare the ratios of the corresponding sides.

In this case, the given information allows us to compare the lengths of the corresponding sides of triangle ABC and triangle DEF.

We have:

AB = 16 and ED = 12 (AB is four more than ED)

AC = 12 and DF = 9 (AC is three more than DF)

BC = 1 and EF = 9 (BC is three more than EF)

The corresponding sides are proportional because the ratios of the lengths are consistent:

AB/ED = 16/12 = 4/3

AC/DF = 12/9 = 4/3

BC/EF = 1/9

Since the ratios of the corresponding sides are the same, we can conclude that triangle ABC and triangle DEF are similar

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Sure. Here are the steps on how to solve the equation 3|x + 1| ≥-6:

Divide both sides of the equation by 3.

Simplify both sides of the equation.

Isolate x on the left-hand side of the equation.

Test each solution in the original equation to make sure it makes the equation true.

Write the solution in interval notation.

Here are the detailed steps:

Divide both sides of the equation by 3:

3|x + 1| ≥-6

|x + 1| ≥ -2

Simplify both sides of the equation:

|x + 1| ≥ -2

x + 1 ≥ -2 or x + 1 ≤ -2

Isolate x on the left-hand side of the equation:

x + 1 ≥ -2

x ≥ -2 - 1

x ≥ -3

x + 1 ≤ -2

x ≤ -2 - 1

x ≤ -3

Test each solution in the original equation to make sure it makes the equation true.

Test x = -3 in the original equation:

3|-3 + 1| ≥-6

3|-2| ≥-6

3(2) ≥-6

6 ≥-6

True

Test x = -4 in the original equation:

The scale factor used to create the image is given as follows:

4.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

In the context of this problem, we have that each vertex of A'B'C'D' is obtained with the multiplication of each of the coordinates of ABCD by four.

For example, we have that vertex A has the coordinates A(1, -2), while the equivalent vertex A' has the coordinates of A'(4, -8).

Hence the scale factor used to create the image is given as follows:

4.

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Answer:

  f(x)=40(2.25)^x

Step-by-step explanation:

You want the equation of the exponential function that goes through points (0, 40) and (1, 90).

The exponential function can be written ...

  f(x) = a·b^x

When x = 0, this is ...

  f(0) = a·b^0 = a·1 = a

Using the given point, we have a = 40.

When x = 1, this is ...

  f(1) = 40·b^1 = 40b

Using the given point, we have ...

  90 = 40b

  b = 90/40 = 2.25

The function equation is ...

  f(x) = 40(2.25^x)

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It should be noted that when b = 8, the expression b/2 - 3 evaluates to 1.

In order to evaluate the expression b/2 - 3 when b = 8, we substitute the value of b into the expression and perform the calculations.

Given that b = 8, we have:

8/2 - 3

Now we simplify the expression:

8/2 is equal to 4, so we have:

4 - 3

Finally, subtracting 3 from 4 gives us the result:

4 - 3 = 1

Therefore, when b = 8, the expression b/2 - 3 evaluates to 1.

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b/2-3 Evaluate the expression you got in part d for b = 8

Answer:

[tex]\sf m = -2\\\\y-intercept =\dfrac{-5}{4}[/tex]

Step-by-step explanation:

Slope and y-intercept of the line:

     Write the equation in slope y-intercept form: y =mx +c

Here, m is the slope and c is the y-intercpet.

To isolate y, add 8x to both side,

            -8x - 4y = 5

                   -4y  = 8x + 5

Now, divide the entire equation by (-4),

                        [tex]\sf \dfrac{-4y}{-4}=\dfrac{8x}{-4} + \dfrac{5}{-4}\\\\\\y = -2x -\dfrac{5}{4}[/tex]

Now, compare with y = mx +c

          [tex]\boxed{\sf m= -2}\\\\\\\boxed{\sf y-intercept=\dfrac{-5}{4}}[/tex]

Answer:

y-intercept = -5/4

slope = -2

Step-by-step explanation:

To quickly find the slope and y-intercept of a given linear equation, we can express it in the following form, called the slope-intercept form:

[tex]\boxed{y = mx + c}[/tex],

where:

m ⇒ slope

c ⇒ y-intercept

In order to take the given equation into the slope-intercept form, we have to  make y the subject of the equation:

[tex]-8x - 4y = 5[/tex]

⇒ [tex]-4y = 8x + 5[/tex]                 [Adding 8x to both sides of the equation]

⇒ [tex]y = -\frac{1}{4}(8x + 5)[/tex]              [Dividing both sides of the equation by -4]

⇒ [tex]y = -2 x - \frac{5}{4}[/tex]

Comparing the above equation with the slope-intercept form, we can see that m = -2 and c = -5/4.

Therefore, y-intercept = -5/4, and slope = -2.

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The area of the square A is 19.98 square feet

From the question, we have the following parameters that can be used in our computation:

Two squares constructed on the sides of a rectangle.

Let the side lengths of square C be x

Let the side lengths of rectangle B be x and y

So, we have

x² = 5

xy = 10

Solving for x and y, we have

x = 2.24 and y = 4.47

The area of square A is

Area = y²

So, we have

Area = 4.47²

Evaluate

Area = 19.98

Hence, the area of the square A is 19.98 square feet

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By the complex conjugate root theorem, there must also be another zero -  [tex]5-i[/tex].

Therefore

[tex]f(x)=(x-2)(x-(5+i))(x-(5-i))\\f(x)=(x-2)(x-5-i)(x-5+i)\\f(x)=(x-2)((x-5)^2+1)\\f(x)=(x-2)(x^2-10x+25+1)\\f(x)=(x-2)(x^2-10x+26)\\f(x)=x^3-10x^2+26x-2x^2+20x-52\\f(x)=x^3-12x^2+46x-52[/tex]

hello

the answer to the question is:

Tan (x) = 6.7/4.9 = 1.3673 ----> x = 53.81° or 54°

Answer:

Unknown but formula (Check step by step solution)

Step-by-step explanation:

Without the image of the base of the crayon, I cannot determine the exact dimensions of the triangular prism or calculate the volume of a single crayon. However, I can give you a general formula for calculating the volume of a triangular prism and use it to find the total volume of wax needed to make a box of 8 crayons.

The formula for the volume of a triangular prism is:

Volume = (1/2) x base x height x length

where base is the area of the base of the triangular prism, height is the height of the triangular prism, and length is the length of the triangular prism.

Assuming all the crayons in the box have the same dimensions, let's say the base of the triangular prism has a length of L and a width of W. We can calculate the area of the base of one crayon as:

Base area = (1/2) x L x W

Since the crayon is 90 millimeters long, its height is 90 millimeters. Therefore, the volume of one crayon is:

Volume of one crayon = (1/2) x L x W x 90

To find the total volume of wax used to make a box of 8 crayons, we can multiply the volume of one crayon by the number of crayons:

Total volume of wax = Volume of one crayon x 8

Total volume of wax = (1/2) x L x W x 90 x 8

Total volume of wax = 360 x L x W

Again, without knowing the exact dimensions of the triangular prism, I cannot calculate the total volume of wax used to make a box of 8 crayons. But you can use the formula above and substitute the values of L and W based on the dimensions of the base of the crayon to find the answer.

Yes, the mass of the Earth is much larger than the mass of an atom of hydrogen.

A hydrogen atom weighs around 1.67 x 10⁻²⁷ kilograms (kg) in mass. The mass of a hydrogen atom is approximately 1051 times smaller than that of the Earth, which has a mass of about 5.97 x 10²⁴ kg.

The majority of the mass of the Earth is made up of the following elements: iron, oxygen, silicon, magnesium, Sulphur, nickel, calcium, and aluminium. Despite its minor presence, hydrogen does not significantly contribute to the mass of the Earth.

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Answer: B   =[tex]x^{\frac{4}{5} }[/tex]

Step-by-step explanation:

Rules needed:

When you have a root, you can write it in exponented form.  It becomes a fraction.

             EX.

                          [tex]\sqrt[5]{x} =x^{\frac{1}{5} }[/tex]

When you have a number that is multiplied to another number both have exponents and same bases, you can combine the two by adding the exponents

            EX.

                       [tex]x^{\frac{1}{5} } *x^{\frac{1}{5} } = x^{\frac{2}{5} }[/tex]

Your problem:

[tex]\sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}* \sqrt[5]{x}[/tex]              >convert to exponent form

=[tex]x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} } *x^{\frac{1}{5} }[/tex]                >add all exponents [tex](\frac{1}{5} +\frac{1}{5} +\frac{1}{5}+\frac{1}{5})[/tex]

=[tex]x^{\frac{4}{5} }[/tex]

B

The correct statement regarding the exponential functions in this problem is given as follows:

D. The functions both have the same y-intercept.

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The functions in this problem are given as follows:

Hence the y-intercept for each function is given as follows:

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As it only told interest i asume its simple interest for compound interest the answer would be different

The equation for the parabola in the graph is the one in option C:

y = (-1/4)x² -2x - 7

Remember that a parabola with leading coefficient a and a vertex (h, k) can be written as:

y = a*(x - h)² + k

Here the vertx is at (-4, -3), then:

y = a*(x + 4)² - 3

And we can see that it passes through the point (0, -7), replacing that we will get:

-7 = a*(0 + 4)² - 3

-7 = a*16 - 3

-7 + 3 = a*16

-4 = a*16

-4/16 = a

-1/4 = a

The quadratic is:

y = (-1/4)*(x + 4)² - 3

Expanding that, we will get:

y = (-1/4)x² -2x - 4 - 3

y = (-1/4)x² -2x - 7

The correct option is C.

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Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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Answer:B,C

hope it helps

Michelle pays $1365 in total.

Option D is the correct answer.

We have,

To calculate the total amount Michelle pays for the T-shirts, we need to consider the cost per shirt and the shipping fee.

The cost per shirt is $6.50, and she ordered 200 shirts, so the cost of the shirts alone is:

= $6.50 x 200

= $1300

The shipping fee is 5% of the total order, which is:

= 5% x $1300

= $65

To find the total amount Michelle pays, we add the cost of the shirts and the shipping fee:

= $1300 + $65 = $1365

Therefore,

Michelle pays $1365 in total.

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Answer:  d. Y=2

Step-by-step explanation:

The revenue function for the cakes can be shown as: R(x1, x2, x3, x4, x5) = $9x1 + $12x2 + $4x3 + $5x4 + $8x5

The revenue function is described as  the total amount of money earned from selling a certain quantity of cakes.

We make the following  

Cake 1 sold =  x1

Cake 2 =  x2

Cake 3 = x3,

Cake 4 =  x4,

Cake 5=  x5.

The revenue generated from selling each cake is:

Revenue1 = $9 * x1

Revenue2 = $12 * x2

Revenue3 = $4 * x3

Revenue4 = $5 * x4

Revenue5 = $8 * x5

Total revenue = Revenue1 + Revenue2 + Revenue3 + Revenue4 + Revenue5

Total revenue = $9 * x1 + $12 * x2 + $4 * x3 + $5 * x4 + $8 * x5

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hi

what's the title of the question?

We can see here that matching the steps for constructing a congruent line segment to their pictures, we have:

Step 1 - Picture a

Step 2 - Picture b

Step 3 - Picture c

Step 4 - Picture c.

Any portion of a line with two ends and a set length is referred to as a line segment. It differs from a line that has neither a beginning nor an end and can be stretched in both directions.

The endpoints of a line segment can be used to define it. The portion of the line that begins at point A and finishes at point B, for instance, is known as the line segment AB.

A ruler or measuring tape can be used to determine the length of a line segment. The distance between two line segments' endpoints is the segment's length.

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Answer:

Step-by-step explanation:

Hello !

100% - 60% = 40%

=> 40% of police officers have ride-alongs

                                                                      total

number of policier            258          ?           ??

frequency in %                  60%        40%      100%

3.1 Calculate the number of of the police officers have ride-alongs with teenagers who want to join the police force

? = 258 x 40 ÷ 60 = 172

3.2 Calculate the total

?? = 258 + 172 = 430

In total there are 430 police officers.

Have a good day !

To create a cubic model, we need to find a cubic equation in the form of [tex]y = ax^3 + bx^2 + cx + d[/tex] that fits the given data. Let's use the data provided in the table and the equation [tex]y = 0x^3 + x^2 + x + 0[/tex].

Since the coefficient of [tex]x^3[/tex] is 0, the cubic term does not contribute to the equation. Therefore, the cubic model simplifies to [tex]y = x^2 + x[/tex].

The equation [tex]y = x^2 + x[/tex]represents a quadratic function rather than a cubic function.

Thus, if we assume that the cubic term is indeed meant to be 0, we can use the simplified equation [tex]y = x^2 + x[/tex] as the cubic model based on the given data.

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