36/42 = 24/r solve the proportion to find r

Answer:

G.) 23 meters

Step-by-step explanation:

makeing it into a proportion would be the easiest -

9/x = 21/54

21x = 486

/21      /21

x = 23.14

rounded out would be x = 23 meters

hope this helps!!

The height of the tree is 23 meters

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Let  the height of the tree as 'x'.

The proportion can be set up as:

(height of the tree) / (length of the tree's shadow) = (height of the building) / (length of the building's shadow)

Plugging in the given values:

x / 9 = 54 / 21

To solve for x, we can cross-multiply:

21x = 54×9

21x = 486

Dividing both sides by 21:

x = 486 / 21

= 23.143

Hence,  the height of the tree is 23 meters.

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Answer:

Step-by-step explanation:

Using law of indies;

√Xᵃ = Xᵃ/²

√(0.08¹²) = (0.08¹²ˣ¹/²)

                  = 0.08⁶

The correct answer is A; (0.08)⁶

For this case we must simplify the following expression:

[tex](\sqrt {0.08 ^ {12}}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So, we can rewrite the given expression as:

[tex]0.08 ^ {\frac {12} {2}} =\\(0.08) ^ 6[/tex]

Answer:

[tex](0.08) ^ 6[/tex]

Option A

total distance of 24 laps

29.6km - 0.2km

=29.4km

total distance of each lap

24 laps = 29.4km

1 lap = ?

Use cross-multiple

24 laps × X = 29.4km × 1 lap

X = 29.4km / 24

X = 1.225km

Answer

1.225km

Answer:

1.225km is equal to each laps

Step-by-step explanation:

Since Kristy total distance traveled = 29.6km

And Kristy ran 24 laps and later walk 0.2km. it simply implies that

Total distance traveled = distance covered running + distance covered walking

Since we know that

Total distance traveled = 29.6km

distance covered running = 24 laps

distance covered walking = 0.2km

Distance covered running in km = total distance traveled - distance covered walking

Distance covered running in km = 29.6km - 0.2km = 29.4km.

To now find the distance for each lap.

Since we have:

Distance covered running in km = 29.4km.

Distance covered running in lap = 24 laps

i.e

24 laps = 29.4km

1 lap = x

Use cross-multiple

24 laps * x = 29.4km × 1 lap

x = 29.4km / 24

x = 1.225km

Therefore

1.225km is equal to each laps.

Answer:

the first one is (cylinder) and second one is (6 units)

The radius of base is, 5 units

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Since, it has a perimeter of 32 units and it is to be rotated about the line, the solid to be created it is a cylinder. As you can see below.

Hence, Let's calculate its radius, based on the information given, i.e. the perimeter as,

2p = 32

Since, We know that;

2p = b + b + h + h

2p = 2 (b + h)

2 (b + h) = 32

b + h = 16

And, bh = 60

This gives solutions,

b = 10 and h = 6

Since, the line of rotation is the center, and the radius is half the line segment of the basis,

Then, The radius is 5.

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Complete question is this,

Rectangle ABCD has a perimeter of 32 units and will

be rotated about line k.

What is the three-dimensional solid created?

cylinder

What is the radius of a base?

10 units

Answer:

m2 or inch2 or pulg2

Step-by-step explanation:

Answer: square units

Step-by-step explanation: when you hear of a shape area like 26 square feet or units

The answer is D 30 .85x30=25.5

Answer:

D

Step-by-step explanation:

Answer is D

Answer: 5/4, or 1.25

Step-by-step explanation:

To solve, get a variable on one side. First, add 5 on both sides.

g(x) = 4x-5+5

Next, divide by four.

5/4 = 4x/4

Now, solve.

5/4, or 1.25 = x

75+75=150

180-150=30

your missing angle is 30 degrees

Answer: 132%

Step-by-step explanation:

In the function y= -1/2(x-1)^2+3, the negative sign inverts the graph so that it opens downwards unlike y=x^2 that opens upwards. This is due to the negative slope which implies a descent in the graph when moving left to right, showing a negative correlation between x and y.

In the function y= -1/2(x-1)^2+3, the negative sign in front of the fraction plays a vital role in the graph's orientation. Unlike the graph of y=x^2 which opens upwards, the negative sign causes the graph of the given function to open downwards. This occurs because the negative sign affects the slope of the function. Graphically, a negative slope means that as we move from left to right along the graph, it descends; showing a negative correlation between x and y. Thus in the concoction of a graph, when x increases, y decreases, or when x decreases, y increases. This is a fundamental rule in graphing quadratic functions.

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The negative sign in the function [tex]y = -1/2(x-1)^2+3[/tex]inverts the graph compared to[tex]y = x^2[/tex], making the parabola open downwards and indicating a negative relationship between the x and y values.

The negative sign in the function [tex]y = -1/2(x-1)^2+3[/tex] in comparison to the function [tex]y = x^2[/tex]inverts the graph of the parabola. While the graph of[tex]y = x^2[/tex]opens upwards, the negative coefficient causes the graph of the given function to open downwards. This means that instead of the parabola having a minimum point which occurs in [tex]y = x^2[/tex], the parabola will have a maximum point at the vertex (1, 3). As the x-value increases or decreases from the vertex, the y-value will decrease due to the negative sign, indicating that the two variables are negatively related. The general shape of the graph remains a parabola, but it is flipped vertically over the x-axis.

Answer:

300 students

Step-by-step explanation:

Since 4/5 of students do not wear glasses, 1/5 of students do.  

There are 60 students who wear glasses, so let 'x' represent the number of students who wear glasses

(1/5)x = 60     is our equation.  "One-fifth of the number of students who wear glasses is 60"

Now solve for x

(1/5)x = 60

    x = 300    (multiply both sides by 5 to get rid of the fraction)

Answer:

See attached picture

Step-by-step explanation:

This is a linear equation. To graph it, use the model y = mx + b where m is the slope and b is the y-intercept. Here m = 2 and b = 4. Start at the point (0,4) on the y-axis. Mark this point because it is the y-intercept. Then move up 2 units and over 1 to the point (1, 6). Mark this point. And connect. This is the correct graph. See attached picture.

Alex have 200 cards.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

According to the question

Alex, Gil and Meg shared 740 cards.

Alex had 20 fewer cards than Gil and 120 fewer cards than Meg.

Assuming Alex have x cards

Based on the given condition, write equation

[tex]x+(x+20)+(x+120)=740[/tex]

Solving the equation

[tex]3x =740-20-120[/tex]

[tex]3x=600[/tex]

[tex]x=200[/tex]

Hence, Alex have 200 cards.

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Alex had 193 cards. Meg had 120 more, Gil 20 more than Alex, for a total of 740 shared.

Let x be the number of cards Gil had.

Alex had x - 20 cards.

Meg had x + 120 cards.

The total number of cards is x + (x - 20) + (x + 120) = 740.

Combining like terms, we get 3x + 100 = 740.

Subtracting 100 from both sides, we get 3x = 640.

Dividing both sides by 3, we get x = 213.33.

Since the number of cards must be a whole number, we can round 213.33 down to 213.

Therefore, Alex had 213 - 20 = 193 cards.

So the answer is 193

Answer:

K=31

Step-by-step explanation:

17=(-14)+K

We want to isolate k

Add 14 to each side

17+14=(-14)+14+K

31 = K

Answer:

k=31

Step-by-step explanation:

Answer:

The bottom left

Step-by-step explanation:

As one variable increases so does the other and it goes through the origin.

it looks like somebody else is already answering this for you, but if you are in need of an answer for a question like this fast just go to desmos.com and input your function it will show you what the graph will look like

Answer:

D (9,13)

Step-by-step explanation:

Substitute the points into the equation

y =x+4

A (0,0)

0=0+4

0=4  False  This point is not a solution

B (5,54)

54 = 4+4

54=8  False  This point is not a solution

C (7,28)

28 = 7+4

28 = 11  False  This point is not a solution

D (9,13)

13 = 9+4

13=13  True This point is a solution

Answer:

plug in 13 for y you get x = 9  D(9,13)

Answer:

63

Step-by-step explanation:

80+69+78+73+75+63= 438

438/6 = 73

Hope this helps you! :)

Answer:

Correct Answer: B

Step-by-step explanation:

Answer:

The area of the polygon is [tex]116\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of the polygon is equal to the area of the triangle ADE plus the area of triangle ACD plus the area of triangle ABC

step 1

Find the area of triangle ADE

The area is equal to

[tex]A=\frac{1}{2}(AD)(EG)[/tex]

substitute the values

[tex]A=\frac{1}{2}(16)(3)=24\ units^{2}[/tex]

step 2

Find the area of triangle ACD

The area is equal to

[tex]A=\frac{1}{2}(AD)(CH)[/tex]

substitute the values

[tex]A=\frac{1}{2}(16)(7)=56\ units^{2}[/tex]

step 3

Find the area of triangle ABC

The area is equal to

[tex]A=\frac{1}{2}(AC)(BF)[/tex]

substitute the values

[tex]A=\frac{1}{2}(12)(6)=36\ units^{2}[/tex]

step 4

Find the area of the polygon

[tex]A=24\ units^{2}+56\ units^{2}+36\ units^{2}=116\ units^{2}[/tex]

Answer:

This is a relation not a function

Step-by-step explanation:

This is not a function

The input x=-2 goes to both the output 2 and -2

Each input can only go to one output to be a function

Answer:

A - 0.6 repeating

Step-by-step explanation:

An irrational number cannot be written as a fraction - it is a number without end (like a repeating number)

Answer:

12.56

Step-by-step explanation:

C= 2 x 3.14 x 2

(the other 2 is half of the circumference)

To find the circumference of a round hut floor with a diameter of 4 meters, use the formula Circumference = π x Diameter, resulting in 12.56 meters.

The circumference of a round hut with a floor diameter of 4 meters can be calculated using the formula Circumference = π x Diameter.

Answer:

-1

Step-by-step explanation:

To find the slope of a line, you would need to use the slope formula, and that is [tex]slope=\frac{y2-y1 }{x2-x1}[/tex]

This equation should be used every time you need to find a slope with two given points. If you remember this, you would find questions like this more easy.

First, you would need to plug in your coordinate points into the formula.

You would plug -7 in y2, 2 in y1. And then you will plug in 4 in x2, and -5 in x1.

Your equation should look like this:

[tex]\frac{-7-2}{4-(-5)}[/tex]

Then you solve.

For the top portion of your equation you would get -9. The -5 turns into a positive 5 because when you carry the negative over (distribute it), the negative cancels out and turns into a positive. When you add the 5 and the 4 together, it will get you 9. The bottom portion of the equation will be 9.

Your equation should now look like this:

[tex]\frac{-9}{9}[/tex]

Now, you divide.

When you divide, the two 9's end up as a whole, and you keep the negative since the negative doesn't cancel out in this situation. When you finish dividing, you would get -1.

Your FINAL answer would be -1.

Answer:

-1

Step-by-step explanation:

    Slope formula:

             ↓

 [tex]{\huge\frac{Y_2-Y_1}{X_2-X_1}[/tex]

[tex]\frac{(-7)-2}{4-(-5)}=\frac{-9}{9}=-1[/tex]

Therefore the slope is -1.

-1 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

Step-by-step explanation:

The perimeter of the given figure is equal to the circumference of whole circle.

The formula of a circumference of a circle:

[tex]C=\pi d[/tex]

d - diameter

We have d = 70 cm. Substitute:

[tex]C=70\pi\ cm[/tex]

The area of given figure is equal to the area of rectangle 70cm × 35cm.

(look at the picture).

The area of a rectangle:

[tex]A=(70)(35)=2,450\ cm^2[/tex]

The area of a circle is given by the formula A = πr², where π represents pi, and r the radius. The area can be left in terms of pi to avoid rounding errors, with the example of a circle with 1.2-meter radius having an area of approximately 4.5 m² when considering significant figures.

The area of a circle is expressed as A = πr², where π (pi) is approximately 3.14159265, and r is the radius of the circle. In terms of pi, this formula is often left in the form of πr² to retain the exact value without rounding. For example, if we have a circle with a radius of 1.2 meters, the area would be calculated as A = π(1.2 m)² = 4.5238934 m² using a calculator with eight-digit precision. However, since the radius is given with two significant figures, the appropriate representation of the area would be A=4.5 m².

It is important to note that when expressing the area in terms of pi, you may encounter different contexts such as finding the area of a semicircle using the definite integral that results in r²/2 for the semicircle's area, or understanding proportionalities in a circle divided into slices.

Answer:

24-q

Step by Step Explanation :

24 decreased by q is basically saying 24 minus q which is 24-q

The true statement is the side lengths will form a triangle because 6+7>4. So option (d) is correct.

To determine if the given side lengths can form a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's denote the side lengths as follows:

a = 4  meters

b = 6  meters

c = 7  meters

We'll check each possible combination:

1. \( a + b > c \): \( 4 + 6 > 7 \) (True)

2. \( a + c > b \): \( 4 + 7 > 6 \) (True)

3. \( b + c > a \): \( 6 + 7 > 4 \) (True)

Since all three conditions are true, the given side lengths (4, 6, 7 meters) can indeed form a triangle.

Thus, the correct option is D. The side lengths will form a triangle because 6 + 7 > 4.

Complete Question:

A triangular garden is being formed with stones. The three sides measure 4 meters by 6 meters by 7 meters. Which of the following is a true statement about the side lengths of the triangle?

A. The side lengths will not form a triangle because 6+4>7.

B. The side lengths will form a triangle because 4+6<7.

C. The side lengths will not form a triangle because 7+4<6.

D. The side lengths will form a triangle because 6+7>4.

0.05 ---> 1/18

square root of 0.25 ------> 0.05

1/7------> 0.142857 repeating

0.6 -------> 2/3

Answer:

0.05 ---> 1/18

1/7 ---> 0.142857

0.6 ---> 2/3

0.25 ---> 0.05

Step-by-step explanation:

Answer:

At = 21.5 cm2

Step-by-step explanation:

At = Asqr - Acircle

At = A1 - A2

A1 = 10^2  = 100

A2 = Pi*(5)^2 = 78.5

At = 100 - 78.5

At = 21.5 cm2

Best regards

For this case we have that by definition:

The area of a circle is: [tex]A_ {c} = \pi * r ^ 2[/tex]

Where r is the radius of the circle.

The area of a square is: [tex]A_ {s} = l ^ 2[/tex]

Where l is the side of the square.

The area of the shaded region will be:

[tex]A_ {sr} = A {s} -A_ {c}[/tex]

So:

[tex]A_ {s} = 10 * 10\\A_ {s} = 100 \ cm ^ 2[/tex]

On the other hand:

[tex]A_ {c} = \pi * (\frac {10} {2}) ^ 2\\A_ {c} = \pi * 25\\A_ {c} = 78.5375cm ^ 2[/tex]

Finally:

[tex]A_ {sr} = 100-78.5375\\A_ {sr} = 21.4625[/tex]

Rounding out, we have that the area of the shaded region is 21.5 square centimeters.

Answer:

Option D

Answer:

44=y

Step-by-step explanation:

27+x=y

We know x = 17, so we can substitute x=17 into the equation

27 + 17 = y

44=y

Answer:

[tex]y=44[/tex]

Step-by-step explanation:

Substitute 17 for x in the equation since [tex]x=17[/tex]

[tex]27+(17)=y[/tex]

[tex]44=y[/tex]