A surveyor has taken measurements, a ft, b ft, and the angle y in degrees, as seen in the figure below.
If a = 217 ft, b = 347 ft, and y = 53°, find the distance across the lake.
a ft
Yo
The distance across the lake is how many ft?

Answer:

8.  x = 9

9.  x = 9

10. x = 36

11.  x = 8

Step-by-step explanation:

Question 8

As the base of the triangle has been bisected, set the expressions either side of the perpendicular bisector equal to each other and solve for x:

[tex]\implies 5x-15=2x+12[/tex]

[tex]\implies 5x-15-2x=2x+12-2x[/tex]

[tex]\implies 3x-15=12[/tex]

[tex]\implies 3x-15+15=12+15[/tex]

[tex]\implies 3x=27[/tex]

[tex]\implies \dfrac{3x}{3}=\dfrac{27}{3}[/tex]

[tex]\implies x=9[/tex]

Question 9

As the base of the triangle has been bisected, set the expressions either side of the perpendicular bisector equal to each other and solve for x:

[tex]\implies 8x-63=4x-27[/tex]

[tex]\implies 8x-63-4x=4x-27-4x[/tex]

[tex]\implies 4x-63=-27[/tex]

[tex]\implies 4x-63+63=-27+63[/tex]

[tex]\implies 4x=36[/tex]

[tex]\implies \dfrac{4x}{4}=\dfrac{36}{4}[/tex]

[tex]\implies x=9[/tex]

Question 10

Angles on a straight line sum to 180°.  Therefore, as the other angle on the line is a right angle, equate the given expression to 90° and solve for x:

[tex]\implies (3x-18)^{\circ}=90^{\circ}[/tex]

[tex]\implies 3x-18=90[/tex]

[tex]\implies 3x-18+18=90+18[/tex]

[tex]\implies 3x=108[/tex]

[tex]\implies \dfrac{3x}{3}=\dfrac{108}{3}[/tex]

[tex]\implies x=36[/tex]

Question 11

Interior angles of a triangle sum to 180°.  Therefore, equate the sum of the given angles to 180° and solve for x:

[tex]\implies 90^{\circ}+(3x)^{\circ}+(8x+2)^{\circ}=180^{\circ}[/tex]

[tex]\implies 90+3x+8x+2=180[/tex]

[tex]\implies 11x+92=180[/tex]

[tex]\implies 11x+92-92=180-92[/tex]

[tex]\implies 11x=88[/tex]

[tex]\implies \dfrac{11x}{11}=\dfrac{88}{11}[/tex]

[tex]\implies x=8[/tex]

Answer:

  57 cm²

Step-by-step explanation:

You have a composite figure and you want to find its area.

There are several ways you can decompose the given figure. Three of them are shown in the attachments. The missing dimensions are found by realizing that the sum of the right-side dimensions is equal to the left-side dimension, and the sum of the bottom-side dimensions is equal to the top dimension.

Extending the vertical boundary line divides the figure into a left rectangle that is 7 cm high and 7 cm wide, and a right rectangle that is 2 cm high and 4 cm wide. This is shown in the first attachment.

The area of each rectangle is the product of its height and width, and the total area is the sum of these:

  Area = (height)×(width) . . . . . area formula for one rectangle

  Area = (7 cm)(7 cm) +(2 cm)(4 cm) = 49 cm² +8 cm² = 57 cm²

Extending the horizontal boundary line divides the figure into a top rectangle 2 cm high and 11 cm wide, and a bottom rectangle 5 cm high and 7 cm wide. This is shown in the second attachment. The total area is ...

  Area = (2 cm)(11 cm) +(5 cm)(7 cm) = 22 cm² +35 cm² = 57 cm²

A line can be drawn corner-to-corner to divide the figure into two trapezoids. This is shown in the third attachment.

The upper right trapezoid has bases 11 cm and 4 cm, and height 2 cm.

The lower left trapezoid has bases 7 cm and 5 cm, and height 7 cm.

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

Then the total area is ...

  Area = 1/2(11 cm +4 cm)(2 cm) +1/2(7 cm +5 cm)(7 cm) = 15 cm² +42 cm²

  Area = 57 cm²

The rectangle that encloses the entire figure is 7 cm high and 11 cm wide, so has an area of ...

  A = HW = (7 cm)(11 cm) = 77 cm²

From that area, the lower right corner space is cut out. It has dimensions 5 cm high by 4 cm wide, so an area of (5 cm)(4 cm) = 20 cm².

The area of the figure itself is the difference between the area of the bounding rectangle and the area of the cut-out space at lower right:

  Area = 77 cm² -20 cm² = 57 cm²

The area of the figure in the picture is 57 cm².

The equation of the parabola as described in the task content is; f (x) = -3 (x - 5)² + 9.

It follows from the task content that the equation of the parabola which has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f (x) = a (x-h)² + k be determined.

Recall that the vertex of a quadratic equations of the given form is defined by the coordinates (h, k).

On this note, the required equation of the parabola by substitution of h and k is;

f (x) = -3 (x - 5)² + 9.

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The solution of the system of equations using substitution is, (2500, 5).

What is substitution method?

In the "by substitution" method, one of the equations is solved for one of the variables (you choose which one), which is then plugged back into the other equation where the chosen variable is "substituted" for and the second equation is then solved for. The first variable is then back-solved.

The equations are,

d = 200m + 1500             ..(1)

d = 500m                         ..(2)

Substitute d = 500m in equation (1),

500m = 200m + 1500

300m = 1500

      m = 5

Plug m = 5 in equation (2),

d = 500(5) = 2500

Hence, the solution of the system of equations using substitution is, (2500, 5).

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Answer:

1. [tex]\frac{4}{27}[/tex]

2. D

Step-by-step explanation:

1. [tex]3^{-2} * 1 * 4^3 * 3^{-1}*4^{-2[/tex]

= [tex]3^{-3} * 4^1[/tex]

= [tex]\frac{4^1}{3^3}[/tex]

= [tex]\frac{4}{27}[/tex]

2. Remember the rule that 1/a^b is equal a^-b, in this case, [tex]\frac{1}{2^3}[/tex] is the same as [tex]2^{-3}[/tex], now 6 + (-3) = 3 -- which will be the exponent. [tex]2^3[/tex] is correct.

Answer:

D)

Can you please mark me as "Brainliest"

Answer:

u= 3

Step-by-step explanation:

Isolate a square root on the left hand side

Original equation

    √5u-10-√2u-1 = 0

    Isolate

    √5u-10 = √2u-1+0

Eliminate the radical on the left hand side

Raise both sides to the second power(√5u-10)2 = (√2u-1)2 After squaring

5u-10 = 2u-1

Solve the linear equation

Rearranged equation

     3u  -9 = 0

    Add  9  to both sides

     3u  = 9

    Divide both sides by 3

    A possible solution is :

    u = 3

Answer:

Take a look at the attachments...

Hope this helps! :)

The total surface area of the cylinder is 175.84 squared inches

The surface area of a cylinder can be defined as the amount of space covered by the flat surface of the bases of the cylinder and the curved surface of the cylinder. The total surface area of the cylinder includes the area of the 2 bases of the cylinder which are in the shape of a circle and the area of the curved surface.

The formula is given as

A = 2πrh + 2πr²

We can substitute the values into the equation and solve

A = 2(3.14 * 4 * 3) + 2(3.14 * 4²)

A = 175.84 in²

The cylinder has a surface area of 175.84 in²

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Answer: 175.84

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

7x + 18 = 81

     -18     -18

------------------------

7x = 63

÷7    ÷7

-----------

x = 9

I hope this helps!

Answer: 16720yd

Step-by-step explanation:

Henry biked 9.5 miles to the park. How far is this in yards?

5280 ÷ 3 x 9.5 = 16720yd

Answer:  64.95/5= C, C= 12.99

Step-by-step explanation:

If you want to figure out what the cost of 1 book you must divide the total cost of the books ($64.95) by how many books Jamal bought (5).

So the equation should look like this 64.95/5=C. Each book is $12.99.

Hope this helped!

The translation rule is T<5, 2> and the image of U' is (0,3)

Translation.

The transformation of a shape in a plane that preserves length, which means that the object is transformed without getting its dimensions affected. i.e., it may just be shifted to left/right/up/down is referred as translation.

Given,

The vertices of a rectangle are R(-5, -5), S(-1,-5), T(-1, 1), and U(-5, 1). A translation maps R to the point (0, -3).

Here we need to find the translation rule and the image of U

Here we know the given the vertices of rectangle which are  R(–5, –5), S(–1, –5), T(–1, 1), and  U(–5, 1).

And it is also given that the translation maps R(-5,-5) to the point (0, -3). we have to find the translation rule and the image of U.

In order to find the translation rule,

First we have to identify the Horizontal shift for the given point

That is calculated as,

=> 0 - (-5) = 5 unit

Which means R is shifted to 5 units horizontally.

Now, the Vertical shift is calculated as,

=> -3 - (-5) = 2 units

Which means R is shifted to 2 units vertically.

Therefore, the translation rule is < 5, 2 >  

So, the image of U(-5, 1) is calculated as,

=> -5 + 5 = 0

=> 1 + 2 = 3

Therefore, the point of the image U' is (0, 3)

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Answer:

Step-by-step explanation:

we cant see it so this is not able to answer

Answer:

C

Step-by-step explanation:

the directrix and focus are equidistant from the vertex

vertex = (0, 1 ) and focus = (0, - 2 ) then directrix is a horizontal line above the vertex with equation

y = 4

the focus and directrix are equidistant from any point (x, y ) on the curve.

using the distance formula

[tex]\sqrt{x-0)^2+(y-(-2))^2}[/tex] = | y - 4 |

[tex]\sqrt{x^2+(y+2)^2}[/tex] = | y - 4 | ( squaring both sides )

x² + (y + 2)² = (y - 4)²

x² + y² + 4y + 4 = y² - 8y + 16 ( subtract y² from both sides )

x² + 4y + 4 = - 8y + 16 ( add 8y to both sides )

x² + 12y + 4 = 16 ( subtract x² + 4 from both sides )

12y = - x² + 12 ( divide through by 12 )

y = - [tex]\frac{1}{12}[/tex] x² + 1

Answer: Y = -[tex]\frac{1}{12}[/tex][tex]x^{2}[/tex] + 1

Step-by-step explanation: Correct on Edmentum

3)The first angle in the triangle is three times that of the second angle. The second angle is two times that of the third angle. The ratio of angles in the triangle is 6:2:1.

4)The scale of a map measures 1 inch : 1250 miles. If the distance between two cities measures 3 inches on the map. The actual distance between the two cities on the ground is 3750 miles.

5)A sum of 2700 dollars is shared among Eric, Jo and Richard. Jo's share is two times that of Richard's share. Eric's share is three times that of Jo's share. Eric's share is 1800 dollars.

3) Let A,B,C are the angles of a triangle.

Given that, A =3B, B=2C

A = 3B =3(2C) = 6C

B=2C

Thus, A:B:C = 6C: 2C: C = 6:2:1

4) Given, scale of the map is 1 inch : 1250 miles

The distance between two cities is given as 3 inches.

The actual distance between two cities is 3*1250 = 3750 miles.

5) J is Jo's share, E is Eric's share, R is Richard's share

Given that, J=2R, E=3J

E=3J = 3*2R = 6R

E+J+R = 2700

6R + 2R + R = 2700

9R = 2700

R = 300 dollars

Eric's share = 6R = 6(300) = 1800 dollars

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The run is 9x miles long, while the bike race is 22y miles long.

The distance between two points in mathematics is referred to as the distance. The distance formula, which is simply a derivation of the Pythagorean theorem, which is used to find the length of any one side of a right triangle when you know the lengths of the other two sides, can be used to calculate this distance.

Therefore,

d = vt

where:

d = distance (miles)

v = speed (mph)

t = time (hours)

Let  x = run time

Let  y = bike time

Total time:      x + y = 4

We can create an equation that represents the formula using these variables.

d total = d bike + d run

49 = 9x + 22y

The equation is then only expressed in terms of x or y. We're going to get it in terms of x.

49 = 9x +22(4 - x)

49 = 9x + 88 - 22x

-39 = -13x

3 = x

To determine the distance between each part, enter this value of x into the variables.

run distance = 9x

bike distance = 22(4 - x)

Let x be run time, y be the bicycle race time.

Total time

x+y = 4

Run distance R = 9x

Bicycle race distance  B = 22y

Total distance

9x + 22y = 49

Replace y in the second equation with 4 - x to solve this system.

You'll obtain

y = 1

x = 3

so

R = 9x = 27

B = 22y = 22

Hence, The run is 9x miles long, while the bike race is 22y miles long.

The complete question is:

Suppose you have entered a 49?-mile biathlon that consists of a run and a bicycle race. During your? run, your average velocity is 9 miles per? hour, and during

Suppose you have entered a 49?-mile biathlon that consists of a run and a bicycle race. During your? run, your average velocity is 9 miles per? hour, and during your bicycle? race, your average velocity is 22 miles per hour. You finish the race in 4 hours. What is the distance of the? run? What is the distance of the bicycle? race?

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The point estimate of the population mean is 30 and margin of error for the confidence interval with lower bound 25 and upper bound 35 is 5.

Point Estimate = Upper bound + Lower bound /2

Point Estimate = 35 + 25 /2

Point Estimate = 60/2

Point Estimate =30

Margin of error = Upper bound − Lower bound /2

Margin of error =  35 -25/2

Margin of error = 10/2

Margin of error =5

Therefore the  point estimate is 30 and the margin of error is 5.

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Answer:

x=([tex]\sqrt{41}[/tex]+7)/4, (-[tex]\sqrt{41}[/tex]+7)/4

Step-by-step explanation:

2x²+1=7x

2x²-7x+1=7x-7x

2x²-7x+1=0

2(x²-7x/2+1/2)=0

x²-7x/2+1/2=0

x²-7x/2+8/16=0

x²-7x/2+49/16-41/16=0

(x-7/4)^2-41/16=0

(x-7/4)^2-41/16+41/16=0+41/16

(x-7/4)^2=41/16

x-7/4=[tex]\sqrt{41}[/tex]/4    x-7/4=-[tex]\sqrt{41}[/tex]/4

x=[tex]\sqrt{41}[/tex]/4+7/4    x=-[tex]\sqrt{41}[/tex]/4+7/4

x=([tex]\sqrt{41}[/tex]+7)/4, (-[tex]\sqrt{41}[/tex]+7)/4

Answer:

Decimal: 0.08

Fraction: 2/25

Step-by-step explanation:

To convert a percentage to a decimal, we divide the percentage by 100, or move the decimal point to the left 2 times:

8/100 = 0.08

To convert a percentage to a fraction, we need to understand what a percentage is first. A percentage is a "number or ratio expressed as a fraction of 100". This means that percentages are numbers out of 100 (x% = x/100). Therefore, to convert 8% to a fraction, we divide 8 by 100:

8% = 8/100

Next, simplify the fraction

8/100 = 2/25

Answer:

shsjsjsjsjshsh#6#7#7##+-##6#3

The value of expression when r = 0.1 , n = 12 and t = 2 is,

⇒ 24.192

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (1 + r/n) nt

Now, We can put r = 0.1 , n = 12 and t = 2 in above equation as;

⇒ (1 + r/n) nt

⇒ (1 + 0.1/12) 12 x 2

⇒ (1 + 0.008) 24

⇒ 1.008 x 24

⇒ 24.192

Thus, The value of expression when r = 0.1 , n = 12 and t = 2 is,

⇒ 24.192

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By using CPCTC theorem ∆ ADC congruence ∆ BCD.

According to CPCTC, which stands for "corresponding parts of congruent triangles are congruent," if two or more triangles are congruent, their corresponding angles and sides must also be congruent.

Corresponding parts of Congruent triangles is the abbreviation for this phrase. According to the CPCT theorem, if two or more congruent triangles are selected, their corresponding sides and angles are also selected as congruent.

AD = BC and angle ADC = angle BCD

we have to prove AC = BD

Let's see ∆ ADC and ∆ BCD

Given AD = BC

angle ADC = angle BCD

CD = CD

from S - A - S, we get

∆ ADC congruence ∆ BCD

Therefore, by using CPCTC theorem ∆ADC congruence ∆BCD.

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The coordinates of the point on the directed line segment are (7/2,21/4).

What is a line segment?

A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon.

Here, we have

A line segment with coordinates partitioned in some ratio.

Let's say that the ends of the segment are A and B.

We have to find the coordinates of C.

Coordinates of point A are = (2,9)

Coordinates of point B are = (8,-3)

Considering the point C as (x,y) and the partition ratios as m:n i.e 1:3

By applying the section formula, we get

x = mx₂ + nx₁ /(m+n) ,  y = my₂ + ny₁ /(m+n)

x = 1 × 9 + 3 × 2 / (1+3) , y = 1×(-3) + 3 × 8 / (1+3)

x = 14/4,   y = 21/4

x = 7/2 , y = 21/4

Hence, the coordinates of the point on the directed line segment are (7/2,21/4).

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m=y₂-y₁/x₂-x₁ we use this formula for line with slope 4 and y intercept is negative

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Let us consider a equation with slope 4 and a negative y intercept

y=4x-3

In the above equation 4 is the slope and -3 is the y intercept

x    0      1        2      3

y     -3    1        5      9

We have to plot this graph and the graph is given in attachment.

We get to know the slope is 4 by taking any two points (2,5) and (3,9) and applying in formula

m=y₂-y₁/x₂-x₁

Hence m=y₂-y₁/x₂-x₁ we use this formula for line with slope 4 and y intercept is negative

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Answer: 6/10

Step-by-step explanation: Six parts are shaded and even though the shaded parts are not touching each other, they will still count as shaded. 4 parts are not shaded and there is a total of 10 parts so the answer would be 6/10.

Hoped This Helped!

Answer:

If it is asking for the fraction of shaded parts the answer is A

If it is asking for the fraction of non-shaded parts the answer is B

Step-by-step explanation:

I would most likely go with A, because I have very rarely gotten a question asking for the non-shaded parts.

The value of x is x = -3.

What is solving an equation?

Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics. Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.

Consider the given equation,

27 = (1/3)^x

This equation can be written as,

[tex]27 = \frac{1^x}{3^x}[/tex]

Here 1^x

1[tex]27 = \frac{1}{3^x}[/tex]

Take 3^x on numerator.

[tex]27 = 3^-^x[/tex]

Now 27 can be written as,  [tex]27 = (3)(3)(3) = 3^3[/tex]

⇒ [tex]3^3 = 3^-^x[/tex]

Applying the exponent rule: [tex]a^b=a^c[/tex] ⇒ b = c

So we get,

3 = -x

Multiply both sides by -1.

-3 = x

x = -3

Hence the value of x is x = 3.

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