SOH CAH TOA TRIG RATIOS

The grade of a highway up a hill is 26%, therefore the amount of change in horizontal distance if the vertical height of the hill is 600 feet is 2307ft.

This is referred to as the numerical or occasionally qualitative measurement of how far apart objects or points are.

First, express the grade as a decimal.

26% → 0.26

Grade = (change in vertical height) / (change in horizontal distance)

0.26 = (600 ft) / x

x = (600 ft) / 0.26 = 2307 ft

That is the change in horizontal distance.

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answer :

9(2p+1)

steps

(10p+10)+(8p−1)

18p+9

9(2p+1)

chatgpt

The missing angle measures for the similar triangles are given as follows:

Similar triangles share these two features listed as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle C is obtained as follows:

m < C + 22 + 75 = 180

m < C = 180 - 97

m < C = 83º.

The equivalent vertices on the similar triangles share the same angle measures, hence:

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on solving the provided question we can say that length of the major arc angle  is [tex](29/6)\pi or 4.83\pi[/tex].

In Euclidean geometry, an angle is a shape that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to form an angle in the plane where they are positioned. When two planes collide, an angle is also created. These are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays or lines that share a termination. The origin of the English term "angle" is the Latin word "angulus," which meaning "horn." The vertex is the point where the two rays, also known as the sides of the angle, converge.

circle with center K has an arc with a radius = 3 yards

angle subtended at the center = 70 degrees.

Angle  = 360 - 70  = 290

Length of arc = (∅/360) x 2πr

Angle   = 290,

r = 3,

Length of arc

[tex]= (290/360) X 2 X\pi X 3\\= (29/36) X 6\pi \\= (29 X \pi X 6)/36\\= 29\pi /6[/tex]

= (29/6)π or 4.83π

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Answer:

i think the answer may be (2,infinity)

(1, 2)​ and (-∞, 0)​

===========================================================

Explanation:

The function curve is increasing when going uphill as you move to the right. This happens on the interval (-∞, 0)​ aka -∞ < x < 0​ aka x < 0. This is why choice D is one of the answers.

The function is also increasing when 1 < x < 2 which translates to the interval notation (1,2). This is why choice B is the other answer.

Choices A and C are eliminated since they describe decreasing intervals.

The formula for the volume of a cone, V = (1/3)·π·r²·h, indicates that doubling the radius, quadruples the volume while doubling the height doubles the volume. Therefore;

A cone is a three dimensional figure formed by lines that extend between a point and the circumference of the circular base, where the point is located on the a line perpendicular to and passing through the center of the circular base.

The formula for the volume of a cone is; V = (1/3) × π × r² × h

Where;

V = The volume of the cone

r = The radius of the cone

h = The height of the cone

Therefore;

When the radius is doubled, we get;

V₁ = (1/3) × π × (2·r)² × h = (1/3) × π × 4 × r² × h = 4 × (1/3) × π × r² × h

When the radius of the cone is doubled, the volume of the cone increases 4 times the initial volume

When the height of the cone is doubled, we get;

V₂ = (1/3) × π × r² × 2·h = 2 × (1/3) × π × r² × h = 2·V

When the height of the cone is doubled, the volume of the cone is doubled.

Therefore, doubling the radius of the cone which increases the volume to four times the initial volume has the greater effect on the volume of the cone than doubling the height which doubles the volume of the cone.

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To calculate the lateral surface area, you should add the areas of C. B, C, and E

A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry.

If the sides of a right triangular prism are not rectangular, the prism is oblique.

We know that

The lateral area for a triangular prism is the sum of the areas of its side faces (which are 3 rectangles).,

From the given images, the side faces are B, C and E which is option C.

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The solution is Option B.

The equation of line is y = x + 8 , where the slope is m = 1

Yolanda had eight books and bought one new book each week

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P (

Let the second point be Q (

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we getWhat is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 8 )

Let the second point be Q ( 1 , 9 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 9 - 8 ) / ( 1 - 0 )

Slope m = 1

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = 1 ( x - 0 )

On simplifying the equation , we get

y - 8 = x

Adding 8 on both sides of the equation , we get

y = x + 8

Hence , the equation of line is y = x + 8

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Answer: B

Step-by-step explanation:

Answer:

Height = 16

Step-by-step explanation:

Area = (Base * Height) / 2

Height = (2 * Area) / Base

Height = (2 * 10) / (5/4)

Height = (2 * 10) / (5/4) * (4/4)

Height = (2 * 10 * 4) / 5

Height = (80 / 5)

Height = 16

The weight of the other children are 37.5 kg and 31.25 kg

The weight of the three children are 6:5:4

6x, 5x and 4x

The weight of the smallest child is 4x

4x= 25

x= 6.25

The weight of the other two children can be calculated as follows

6(6.25)

= 37.5

5(6.25)

= 31.25

Hence the weight of the other two children are 37.5 kg and 31.25 kg

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Answer:240

Step-by-step explanation:

8x30=240

Answer:

240

Step-by-step explanation:

30x2x8 so that is your answer

The height of the pyramid given by the Pythagoras theorem will be 90.66 inches.

One of the first areas of mathematics is geometry, along with maths. It is preoccupied with spatial characteristics including the separation, form, size, and relative placement of objects. A geometer is a mathematician who specializes in shape.

A square pyramid-shaped steel patio heater. One of the base's sides is 21.6 inches in length. The pyramid's slant height is 91.3 inches.

The height of the pyramid is perpendicular to the base of the pyramid. Then the height is given as,

(91.3)² = h² + (21.6 / 2)²

8,335.69 = h² + 116.64

h² = 8,219.05

h = 90.66 inches

The height of the pyramid given by the Pythagoras theorem will be 90.66 inches.

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The angles in the quadrilateral are as follows;

x = 77°

y = 103 degrees

z = 52 degrees

The diagram above is a quadrilateral. The angles x, y and z can be found as follows:

x + 103 = 180(sum of angles on a straight line)

x = 180 - 103

x = 77 degrees

Therefore,

y = 103 degree(vertically opposite angles)

Vertically opposite angles are congruent.

The sum of angles in a triangle is 180 degrees.

Therefore,

103 + 25 + z = 180

z = 180 - 128

z = 52 degrees.

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Stuart has enough money to buy 4 kg of onions.

we must first  find the cost of 4 kg of onions.

We know that 2.5 kg of onions and 2 kg of carrots cost £2.36.

The cost of 15 2.5 kg of onions is 15 × 2.5 = 37.5 kg of onions.

The cost of 1 kg of onions is 2.36 ÷ 37.5 = 0.06293 = £0.063.

3 kg of carrots cost £1.74. and we need to find how much 1kg of carrots cost.

Therefore, the cost of 1 kg of carrots is 1.74 ÷ 3 = 0.58 = £0.58.

Now we can use the above information to find the cost of 4 kg of onions:

The cost of 1 kg of onions is £0.063.

Hence, the cost of 4 kg of onions is 4 × 0.063 = £0.252.

We then can say since Stuart has £2, and we have found that the cost of 4 kg of onions is £0.252. Stuart has enough money to buy 4 kg of onions.

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Using arithmetic equation, each students gets 2 cookies and 1 fruit.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. That will be regarded as a phrase.

Given that, Total number of students are 16

total cookies and fruit are 48 items including 1 piece of fruit for each student

let each student get x cookies

16x + 16 = 48

subtract 16 from both side we get

16x = 48-16

16x = 32

both side divided by 16 we get

x = 32/16

x = 2

So that, each students gets 2 cookies and 1 fruit.

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Answer:

67,914

Step-by-step explanation:

Let x = total employees.

18.7% of x = 12,700

0.187x = 12,700

x = [tex]\frac{12700}{0.187}[/tex] = 67914.438 → 67,914

The value of XW is 11

XW = ZW/tan 81

= 0.158 ZW

We should recall that tan 81 = ZW/XW

WY = ZW/tan22

= 2.475ZW

We should recall that tan 22 = ZW/WY

XW = 0.158/0.158 + 2.475 + XY

= 0.158/2.633 x 180

= 11

Therefore, the value of XW is 11

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Answer:

d. 6

Step-by-step explanation:

Given, a-5> -1

Both sides add 5, and we get

a > 4

So a is 6.

The population size in 1951 can be predicted to be :  2,551,970,500

Population is the term typically used to refer to the number of people in a single area. Governments conduct a census to quantify the size of a resident population within a given jurisdiction.

here, we have,

Applying Malthus's  population  projection

P = P₁ ( 1 + r ) n  ----- ( 1 )

where :

P ( projected population ) = ?

P₁ ( Recent population ) = 2,515,000,000

r ( intrinsic rate ) = 1.47 %

n ( number of years ) = 1

Given that the population grows exponentially

P = 2,515,000,000 ( 1 + 0.0147 ) * 1

 = 2,551,970,500.

Hence we can conclude that The population size in 1951 can be predicted to be  2,551,970,500

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Answer: 11

Step-by-step explanation:

We need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), to simplify the expression:

1: First, we solve the exponent 3², which is 3 multiplied by itself, or 3 x 3 = 9.

2: So, the expression now becomes: (3 x 4) ÷ 6 + 9

3: Next, we solve the multiplication, which is 3 x 4 = 12.

4: So, the expression becomes: 12 ÷ 6 + 9

5: Then, we solve the division, which is 12 ÷ 6 = 2.

6: So, the expression becomes: 2 + 9

7: Finally, we solve the addition, which is 2 + 9 = 11.

answer :

a. Multiply each side of the equation by x(x+5)

(so you can have 1 denominator)

b. square each side (to get rid of the square root sign on the left side

c. Raise each side of the equation to the power 2/5

(its helps get rid of ^5/2 in (x+5)^5/2 & on the right side of the equal sign 2 is 5th root of 32)

d. Let u=(x+5)^1/3 and u² = (x+5)^2/3

(u is usually used when x has big exponent &

needs to be factored so it looks like

u^2 - u - 2 = 0 which is easier to factor.

after factoring you can bring back the original

(x+5)^2/3 & (x+5)^1/3 )

e. Cube each side of the equation

(cube root is the same on the left & right side of the equal sign so you can take it out)

The subtraction problem represented by the fraction model is given above.

Given is a figure as shown in the image.

We can write the fractional problem as -

" A rectangle is divided into eight equal rectangles. Smith colored six of these rectangles. How much percentage fraction of the image is colored."

Therefore, the subtraction problem represented by the fraction model is given above.

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The measure of the complement of angle is 45 degrees.

Let's call the measure of the angle "x". The complement of the angle is defined as 90 degrees minus the measure of the angle, so the complement of the angle is 90 - x.

If the measure of the angle is less than its complement, then we can write the following inequality:

x < 90 - x

Now we can isolate x by subtracting x from both sides:

0 < 90 - 2x

And then dividing both sides by -2:

0 > -45 + x

Finally, subtracting x from both sides:

-x > -45

So, we have:

x < 45

So, the complement of the angle is 90 - x, which is greater than 90 - 45 = 45 degrees.

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The equation for how tall the flag pole is h = 12sin(35)

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

Angle = 35 degrees

Distance = 12 feet

Using the above as a guide, we have the following:

sin(angle) = height/distance

So, we have

sin(35) = h/12

This gives

h = 12sin(35)

Hence, the equation is h = 12sin(35)

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I don’t have an answer for number one but

2) Angle I = 59. From lowest to greatest it goes G,I,H

Answer:

Problem 1
From smallest to largest:
∠y , ∠w, ∠x

Problem 2

m∠I = 39°

Sides from shortest to longest
GH, HI, GI

Step-by-step explanation:

For question 1

The ratios of the sides of a triangle to the sine of the angle opposite them is the same

That means the ratios of the sides to each other is the same as the ratio of the sines of the angles opposite them

Since the sine of an angle increases with increasing angle value, the longest side will opposite the greatest angle measurement and the smallest length will be opposite the smallest angle measurement

So in order from smallest to largest
m∠y < m∠w < m∠x

For question 2

Since three angles of a triangle add up to 180°

Missing angle = 180 - (83 + 58)
= 180 - 141

= 39°

From shortest to longest it would be
Side GH < side HI  < side GI

If Mr.Curry has 264 pictures on 4 shelves in his house.

The number of pictures on each shelf can be found by dividing the total number of pictures by the number of shelves:

264 ÷ 4 = 66

So, there are 66 pictures on each shelf.

To find the number of tens Mr. Curry regrouped as ones, we can use long division to see the process of dividing 264 by 4.

When dividing 264 by 4, the first step is to divide 2 by 4, which gives a quotient of 0 with a remainder of 2. Then, you bring down the next digit (6), and form the number 26. Dividing 26 by 4 gives a quotient of 6 with a remainder of 2. Finally, you bring down the last digit (4), and form the number 264. Dividing 264 by 4 gives a quotient of 66 with no remainder.

Therefore, Mr. Curry regrouped 2 tens as ones (or 20 as 10 + 10), which is the same as regrouping 20 ÷ 10 = 2 tens as ones.

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The number of years for the speculation to reach from £785 to £1,105.58 will be 23 years.

Let 'A' is the amount, 'P' is the initial amount, 'r' is the rate of interest, and 'n' is the number of years.

Then the compound interest is written as,

A = P(1 + r)ⁿ

Then the equation is given as,

£1,105.58 = £785 × (1 + 0.015)ⁿ

1.40838 = (1.015)ⁿ

n log 1.015 = log 1.40838

n = 23 years

The number of years for the speculation to reach from £785 to £1,105.58 will be 23 years.

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