Alexander is drawing a map of the Federal Triangle in Washington, D.C. The actual Federal Triangle has a base of 30 feet and height of 1200 feet. Alexander needs his drawing to fit on his paper, so he decides to make the base of his triangle 10 inches. What scale is Alexander using?

Elena should put a point where the two circles intersect and draw line segments connecting that point to points A and B to finish her triangle.

ΔABC and ΔABD are the required Triangle.

Geometric constructions are precise drawings of geometrical shapes, angles, and lines. We will need a pencil, a ruler (or other straight edge), and compasses to do this. Perpendicular bisector and angle bisector are the fundamental constructions.

We have,

Elena is trying to draw a triangle with side lengths 4 inches, 3 inches, and 5 inches.

Elena should find the intersection of two circles at point C and point D.

Connect point B and C, A and C or connect them.

ΔABC and ΔABD are the required Triangle.

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Answer:

Substitution.

Step-by-step explanation:

x+y=2

y=-x+2

2x+(-x+2)=4

x=2

(2)+y=2

y=0

Solution: (2,0)

Answer:

subsitution

Step-by-step explanation:

It’s a and c

Step-by-step explanation:

The true statements about the given geometric sequence are as follows:

A) It can be represented using the formula f(x + 1) = 6/5(f(x)) when f(1) = 10/3.

C) It can be represented using the formula f (x) = 10/3(6/5)/\x-1

The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.

The given sequence is as follows:

10/3, 4, 24/5, 144/25, ...

The sequence is a geometric sequence with a common ratio of 6/5.

The first term is 10/3, so we can use the formula f(x + 1) = (6/5)(f(x)) to represent the sequence.

We have

f(x) = 10/3

Also, for f(x+1) we can have

x = 1,

f(1)= 10/3

f(2)= 4

So, f(x + 1) = 6/5(f(x))

Thus, the correct options are A and C.

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The complete question is as follows:

Which statements are true regarding the sequence below? Check all that apply.

10/3, 4, 24/5, 144/25, ...

A) It can be represented using the formula f(x + 1) = 6/5(f(x)) when f(1) = 10/3.

B) It can be represented using the formula f (x) = 4 (6/5) /\x.

C) It can be represented using the formula f (x) = 10/3(6/5)/\x-1

D) The Domain of the sequence is all real numbers

E) The range of the sequence is all natural numbers.

Answer:

B. 264

Step-by-step explanation:

Although the figure may look odd, This is just a square pyramid on it's side.

So, to find the surface area, we need to find the area of the base and the area of the faces and add them together.

To find the area of the base:

Since the base is a square, all we have to do is multiply 8 by itself.

8 * 8 = 64

The area of the base is 12.5 in^2

To find the area of the faces:

Since the faces are triangles, we have to multiply the length by the height and divide by 2.

8 * 12.5 = 100

100/2 = 50

The area of one face is 50 in^2

To find the surface area:

Add the area of the base to the area of all 4 sides.

64 + 4(50)

64 + 200 = 264

The surface area of the pyramid is B. 264 in.^2

Information on the number of tall buildings and their heights in China and the United States can be interpreted from the histograms, with specific focus on the tallest buildings and the number surpassing the 390-meter mark.

From the provided histograms comparing the heights of the tallest buildings in China and the United States, several pieces of information can be gathered. If the histograms indicate that the tallest bar on the chart for China is over the 390-meter mark and more numerous compared to the United States' histogram, then Choice B would be correct, indicating that China has more buildings over 390 meters tall. To verify Choice A, we would need to look at the highest point on both histograms; if the highest bar on the U.S. histogram extends further than the Chinese one, then it would mean the United States has the tallest building of the two. Without seeing the histograms, these judgments are based on typical interpretations of histogram data.

When considering data on tall buildings such as the number of stories and their height, constructing a histogram can help illustrate the frequency distribution of these heights. For example, using the rule of thumb that one story is approximately equal to the height of two adult humans, it is possible to establish some basic estimates for building heights. However, for detailed statistical analysis, including the identification of linear relationships or outliers, the data would need a closer examination, possibly using a least-squares or best-fit line.

Answer:

x=37

Step-by-step explanation:

We know that the angles in a triangle must add to 180 degrees

So, the three angles: x, 3x-5 and x must be equal to 180

x+3x-5+x=180

Combine like terms

x+3x+x-5=180

5x-5=180

Add 5 to both sides

5x=185

Divide both sides by 5

x=37

Answer:

The cost will be the same after 1 month

Step-by-step explanation:

Step 1: set up the equation

club A= 28x+24  club B= 35x+17

club A=club B: 28x+24=35x+17

Step 2: Get rid of the smallest X

28x+24=35x+17

-28         -28

24=7x+17

Step 3: Get rid of the constant next to the variable to isolate the variable

24=7x+17

-17       -17  

7=7x

Step 4: Inverse operation to remove variable

7÷7x=7x÷7x

1=1

I hope this helped, im not too good at explaining but im positive the solution is correct.

Answer:

With $35, a member is paying 100%.

Since the reduction is 5%, that means his is paying now 95% of $35,

that means $35 x 0.95 = $33.25, So the decrease in fees is 35-33.25 = $1.75

Another method: the reduction was 5% on the $35 or 5% x 35 = 0.05x35=$1.75

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

B. 1/3

Step-by-step explanation:

We know that:

- There are 24 total chocolates

- 10 + 6 of them do not have caramel centers, the rest of them do.

The first step is to evaluate how many chocolates have caramel centers. To do this, add 10 and 6.

10 + 6 = 16

Now, subtract that number from 24 to get the amount of chocolates with caramel centers.

24 - 16 = 8

8 of the chocolates have caramel centers. This means that the ratio of caramel centered chocolates to all chocolates is 8:24, or 8 out of 24.

Since the question is looking for a fraction answer, convert the ratio to a fraction. 8:24 becomes 8/24.

Now, simplify the fraction. 8/24 becomes 1/3.

The final answer is 1/3.

Answer:  A

Step-by-step explanation:

Answer:

DV = numbers of chairs needed (c)

IV = number of tables (t)

IV × 4 = DV     OR    t × 4 = c

Step-by-step explanation:

DV dependent variable

IV independent variable

brainliest please?

The dependent variable means that it depends on how the independent variable is being manipulated. The independent variable is a variable that represents an amount that is being manipulated.

The dependent variable is "c" because it depends on the number of chairs it needs if there are t tables.

The independent variable is "t" because it manipulates the amount chair there are by the amount of tables there are.

Equation: 4t = c

4t represents the amount of chairs there are for the amount of tables there are. c represents the total amount of chairs.

Best of Luck!

1. C. 538.56

2. A. $1478.40

3. A. $2295.60

4.A.  $795.60

Answer:

2r-5

Step-by-step explanation:

Answer:

2r-5

Step-by-step explanation:

Answer:

B. 0.06

D. 6/100

E. 3/50

Answer:

find the average of the 2 numbers in the direct middle.

Step-by-step explanation:

1,2,4,4,4,4,6,6,6,6,6,6

4,6

4+6=10

10/2=

=5

Answer:

17

Step-by-step explanation:

The Interquartile range is the difference between the Quartile 1 and 3. Those quartiles are the median of the left and right side.

Ex: 1, 2, 3, 4, 5

Median = 3, so quartile 1 = median of left side of 3 and quartile 3 = median of right side of 3

First we should organize the data from least to greatest.

38 < 45 < 47 < 50 < 55 < 58 < 60 < 64 < 70 < 71

The median is 56.5.

Quartile 1 = 47

Quartile 3 = 64

64-47 = 17

Hope this helps!

Answer:

Q1 is 38,45,47,50,55

Q2 is 58,60,64,70,71

middle numbers are 47 and 64

64-47=17

Step-by-step explanation:

Answer:

10?

Step-by-step explanation:

20 • .5= 10

The price per unit can be determined by adding the total cost of production to the target profit and then dividing by the quantity produced. This assumes the market will tolerate this price.

In order to determine pricing in Steeze Co., using the total cost approach, you would need to add the total cost of producing the units to the target profit and then divide by the quantity to get the price per unit. Here's the step-by-step calculation:

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Answer:

B) y = -4/3 x + 31/3

y = 2 x + 7

Step-by-step explanation:

The equations above match the description given about them.

If this answer is correct, please make me Brainliest!

Answer:

THEREFORE

Step-by-step explanation:

THERE SHOULD BE 7 TEENAGERS IN THE SAMPLE.

HOPE, THIS MAY HELP YOU BRO!!..

The sample should include 18 teenagers, as they constitute 60% of visitors aged 13-19 among the total sample of 30.

To determine the number of teenagers that should be in the sample, we first need to calculate the proportion of teenagers among the total visitors and then apply that proportion to the sample size.

From the cumulative frequency table, we can see that:

- The total number of visitors is 350.

- The number of teenagers (ages 13-19) is 210.

The proportion of teenagers among all visitors is:

[tex]\[\frac{\text{Number of teenagers}}{\text{Total number of visitors}} = \frac{210}{350}\][/tex]

Now, we need to apply this proportion to the sample size of 30 to find out how many teenagers should be in the sample:

[tex]\[\text{Number of teenagers in the sample} = \text{Proportion of teenagers} \times \text{Sample size}\][/tex]

[tex]\[\text{Number of teenagers in the sample} = \frac{210}{350} \times 30\][/tex]

[tex]\[\text{Number of teenagers in the sample} = \frac{3}{5} \times 30\][/tex]

[tex]\[\text{Number of teenagers in the sample} = 18\][/tex]

So, there should be 18 teenagers in the sample.

Answer:

The zeros are -1/2, 1/3 and 2.

The factors are (x - 2)(3x - 1)(2x + 1)

Step-by-step explanation:

h(x)= 6x^3 - 11x² - 3x + 2 = 0

As the last term is 2 we try  to see if +/-1 or +/- 2 are zeros

f(1) = -6, f(-1) = -18  so  they are not zeros.

f(2) = 6*8 - 11*4 - 3(2) + 2

= 48 - 44 - 6 + 2

=  4 - 6 + 2

= 0.  

So x = 2 is a zero and x - 2 is a factor.

Dividing by x - 2:

x - 2 ) 6x^3 - 11x² - 3x + 2 ( 6x^2 + x - 1 <--------Quotient

         6x^3  - 12x^2

                      x^2 - 3x

                      x^2 - 2x

                             - x+ 2

                             -x + 2

Factoring the quotient:

6x^2 + x - 1

= (3x - 1)(2x + 1) =  0

x = 1/3, x = -1/2..

Answer:

Step-by-step explanation:

hello :

cosx= -1/2    0°≤x≤360°

x = 120°

x=240°

Answer:

y=15

Step-by-step explanation:

We know that the angles in a triangle add to 180 degrees

∠ABC+∠BAC+∠ACB=180

We don't know what ∠ACB is, but we know it is on a straight line with another angle (∠ACD). They are supplementary, and must add to 180

∠ACB+ ∠ACD=180

∠ACB+146=180

Subtract 146 from both sides

∠ACB=34

Now, we know ∠ABC is 4y+8, ∠BAC is 5y+3 and∠ACB is 34, so we can substitute them in

∠ABC+∠BAC+∠ACB=180

4y+8+5y+3+34=180

Combine like terms

4y+5y+8+3+34=180

9y+45=180

Subtract 45 from both sides

9y=135

Divide both sides by 9

y=15

Answer:

12. [tex]x=10[/tex]

13. [tex]x=4[/tex]

14. [tex]x=5[/tex]

15. [tex]x=1[/tex]

16. [tex]x=8[/tex]

17. [tex]x=14[/tex]

Step-by-step explanation:

for these i also used the pythagorean theorem ([tex]a^{2}+b^{2}=c^{2}[/tex])

[tex]a[/tex] and [tex]b[/tex] are the legs, [tex]c[/tex] is the hypotenuse

12.

[tex]x^{2} +x^{2} =(10\sqrt{2} )^{2}[/tex]

[tex]2x^{2} =200[/tex]

[tex]x^{2} =100[/tex]

[tex]x=10[/tex]

13.

[tex]x^{2} +x^{2} =(4\sqrt{2} )^{2}[/tex]

[tex]2x^{2} =32[/tex]

[tex]x^{2} =16[/tex]

[tex]x=4[/tex]

14.

[tex]x^{2} +x^{2} =(5\sqrt{2} )^{2}[/tex]

[tex]2x^{2} =50[/tex]

[tex]x^{2} =25[/tex]

[tex]x=5[/tex]

15.

[tex]x^{2} +x^{2} =(\sqrt{2} )^{2}[/tex]

[tex]2x^{2} =2[/tex]

[tex]x^{2} =1[/tex]

[tex]x=1[/tex]

16.

[tex]x^{2} +x^{2} =(8\sqrt{2} )^{2}[/tex]

[tex]2x^{2} =128[/tex]

[tex]x^{2} =64[/tex]

[tex]x=8[/tex]

17.

[tex]x^{2} +x^{2} =(14\sqrt{2} )^{2}[/tex]

[tex]2x^{2} =392[/tex]

[tex]x^{2} =196[/tex]

[tex]x=14[/tex]

Given:

The base of the triangle = 6 ft

The height of the triangle = 5 ft

The other two side of the triangle = 5.5 ft and 5.5 ft

The height of the prism = 9 ft

To find the measurement of the fabric to make the tent.

We need to find the surface area of the triangular prism.

Formula

The surface area of the triangular prism is

[tex]SA = bh+(a+b+c)H[/tex]

where, b be the base of the triangle

h be the height of the triangle

a and c be other two sides of the triangle

H be the height of the prism

Now,

Putting,

b = 6, h = 5, a = 5.5, c = 5.5 and H = 9 we get,

[tex]SA = (6)(5)+(6+5.5+5.5)(9)[/tex] sq ft

or, [tex]SA = 30+153[/tex] sq ft

or, [tex]SA = 183[/tex] sq ft

Hence,

Based on the given dimension 183 sq ft fabric is needed to make the tent.

Answer:

183 sq. ft. fabric is needed to make the tent.

Step-by-step explanation:

The base of the triangle = 6 ft

The height of the triangle = 5 ft

The other two side of the triangle = 5.5 ft and 5.5 ft

The height of the prism = 9 ft

To find the measurement of the fabric to make the tent.

We need to find the surface area of the triangular prism.

a=1/2bh   1/2(6)(5)*2=30

a=(6*5)+2(9*5.5)+(9*6)=183 sq. ft.

30+99+54=183 square ft.

Answer: 300[tex]\pi[/tex]

Step-by-step explanation:

Let's use the arc-length formula to solve this problem, and plug in the values that we have. Arc length is 50[tex]\pi[/tex] and the arc is 60°

Arc-length = [tex]2\pi r (\frac{x}{360})[/tex]

[tex]50\pi =2\pi r(\frac{60}{360})[/tex]

Cancel the [tex]\pi[/tex] and simplify the fraction.

[tex]50 = 2r(\frac{1}{6})[/tex]

Simplify further.

[tex]50 = r(\frac{1}{3} )[/tex]

Pass the 3 to the other side.

[tex]150=r[/tex]

So our radius is 150.

To find the circumference, we use the formula [tex]2\pi r[/tex]

Plug in r.

[tex]2\pi (150) = 300\pi[/tex]

To find the full circumference of a circle, multiply the given arc length for 60 degrees (50π) by 6, yielding a total circumference of 300π.

To find the circumference of a circle when given the arc length of a particular section, we can use the relationship between the arc's degree measure and the circle's total circumference. Since the arc length of 60 degrees is 50π, we recognize that 60 degrees is one-sixth of a circle's full 360 degrees. Therefore, to find the full circumference of the circle, we multiply the arc length by 6 (because 360° / 60° = 6).

50π times 6 equals 300π, which is the circumference of the circle. This process uses the fact that the circumference of the circle is proportionate to the circle's rotation angle, which completes at 360°, corresponding to an angle of 2π radians.

Given:

The line parallel to the given line containing the points (-3,3) and (-2,1).

Also, the parallel line passes through the point (4,1).

We need to determine the equation of the line in slope - intercept form.

Slope:

Since, the two lines are parallel, then their slopes are equal.

Thus, the slope of the parallel line can be determined using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the points (-3,3) and (-2,1), we get;

[tex]m=\frac{1-3}{-2+3}[/tex]

[tex]m=\frac{-2}{1}[/tex]

[tex]m=-2[/tex]

Thus, the slope of the line is [tex]m=-2[/tex]

Equation of the line:

The equation of the line can be determined using the formula,

[tex]y-y_1=m(x-x_1)[/tex]

Since, the line passes through the point (4,1), let us substitute the point (4,1) in the above formula, we have;

[tex]y-1=-2(x-4)[/tex]

Thus, the equation of the line is [tex]y-1=-2(x-4)[/tex]

Hence, Option a is the correct answer.

To find the equation in point-slope form of a line parallel to the given line and passing through a point, we use the fact that parallel lines have the same slope.

To find the equation in point-slope form of a line parallel to the given line and passing through the point (4, 1), we need to use the fact that parallel lines have the same slope.

The given line has an equation in point-slope form as y - 1 = -2(x - 4). The slope of this line, which is -2, will be the slope of the parallel line we are looking for.

Using the point-slope form equation y - y1 = m(x - x1), and substituting the values y1 = 1, x1 = 4, and m = -2, we can write the equation as y - 1 = -2(x - 4).

Answer:

Side y = 109. 3

Step-by-step explanation:

Step 1 The two sides we are using are Opposite (y)

and Adjacent (162).

Step 2 SOHCAHTOA tells us to use Tangent.

Step 3 Put our values into the tangent function:

tan 34° = Opposite/Adjacent

= y/162

Step 4 Solve:

Start with: tan 34° = y/162

Swap: y/162 = tan 34°

Multiply both sides by 162: y = 162 tan 34°

y = 109.27

 y = 109.27 (to 2 decimal places)

Side y = 109. 3

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

About 530cm²

Step-by-step explanation:

C=2×pi×radius

81.58=2×3.14×radius

81.58=6.28r

81.58÷6.28=6.28r÷6.28

About 12.99cm is radius.

A=pi×radius²

A=3.14×12.99²

A=3.14×168.7401

A=529.843914

Area is about 530cm²