5
Copy the diagram and write in the size of all the other angles.
Work out the unknown angles a, b and c
(It’s question 5)

To find the missing  sides of the special right angle,

The ratio for 45°,45°and 90°,   1:1:√2,

and for 60°, 30°, 90°,   1:√3:2.

Special right triangles are right triangles with three defined interior angles and fixed side ratios. If one side is known in these right-angled triangles, we can find the value of the two missing sides. The 45°- 45°- 90° triangle and the 30°- 60°- 90° triangle are additional names for the two exceptional right triangles.

Given finding the  missing sides of the special right angle,

Only right triangles with other internal angles of 30° and 60° or 45°and 45°. are valid according to this criteria. Furthermore, it makes no difference whatever side's length you know in order for the rule to function.

for 45°,45°and 90°.

The 45°,45°,90° theorem states that triangles with these angles will have sides in a ratio 1:1:√2,

where the side opposite 45° equates to 1 in the ratio and the side opposite to 90° equates to √2. To find the missing side, just put the given value in the following ratio and find the value.

For 60°, 30°, 90°

Similar to this, according to the 30°, 60°, 90° theorem, triangles with these angles will have sides in the ratio 1:√3:2,

where the side opposite to 30° equates to 1 in the ratio, the side opposite to 60° equates to √3, and the side opposite to 90° equates to 2 in the ratio. Simply enter the given amount into the following ratio to determine the value to discover the missing side.

Hence the ratios are for 45°,45°and 90°,   1:1:√2,

and for 60°, 30°, 90°,   1:√3:2.

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Answer:

you have it correct sir

Step-by-step explanation:

The percent reduction in the price of the car is given as follows:

12%.

The percent reduction in the price of the car is obtained applying the proportions in the context of this problem.

A proportion is applied because the percentage reduction is obtained dividing the reduction by the initial value, and then multiplying by 100%.

The parameters for this problem are given as follows:

Hence the percent reduction is given as follows:

1416/11800 x 100% = 12%.

The problem asks for the percent reduction in the price of the car.

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Answer:

26 students

Step-by-step explanation:

We know

The ratio of students failing the test to students passing the test was 2/9

For every 11 students, 2 students fail the test, and 9 passes it.

2:9 = 11

143 students took the test. How many did not pass?

To get from 11 to 143, we time 13. To find how many did not pass, we take

2 times 13 = 26 students did not pass the test.

So, 26 students did not pass the test.

Answer: it's less than 6.87...

The required system of equations equation besides y = 8x + 7 is y = 8x + 15  has no solution.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,

A system of equations has no solution when the equations describe lines that are parallel and do not intersect. In other words, there is no common solution for both equations, or in other words, there is no ordered pair that satisfies both equations.

If y = 8x + 7 is one of the equations, the other equation could be any line that is parallel to it and does not intersect it. This means that the other equation would have the same slope as y = 8x + 7, which is 8, but a different y-intercept.

For example, y = 8x + 15 is a line that is parallel to y = 8x + 7 and does not intersect it. Thus, the system of equations

y = 8x + 7 and y = 8x + 15 has no solution.

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Answer:

2.29

Step-by-step explanation:

add the 2 numbers in decimal form then divide by 2

Answer: (1/3, -1)

Step-by-step explanation: substitue 0 for x to find the y

y=-3x-1

y=-3(0)-1

y=-1

then substitue -1 in for y to find the x

3x-y=1

3x-(-1)=1

3x=1

x=1/3

Answer:

Step-by-step explanation:

2790.47619048

Answer:

2790.47619048

Step-by-step explanation:

To solve 5,860 ÷ 2.1, we are finding how many times 2.1 goes into 5,860.

We start by dividing 5,860 by 2.1 and keep dividing until the result can no longer be divided evenly.

5,860 ÷ 2.1 = 2790.47619048

The result, 2790.47619048, is the number of times 2.1 goes into 5,860. So, the answer to 5,860 ÷ 2.1 is 2790.47619048.

Answer:

y=4x-1

Explanation:

looking at the x row, as you can see, it goes up by 1 each time. In the y row, it goes up by 4, because -1+4=3, 3+4=7, etc. So your slope is 4, and in the funtion y=mx+b given, that would go in the “m” spot. Then for the “y” spot you need to figure out if x is 0, what is y. Well, that is given to you in the picture. It shows that when x=0, y=-1. So that is you y intercept, going into the b spot. If you put it together, it looks like this: “y=4x-1”.

Answer:

[tex]1 \frac{7}{12} [/tex]

Step-by-step explanation:

First you subtract the whole numbers

4-3

Then you

Subtract the fractions which will give 7/12

Combining them together we get

[tex]1 \frac{7}{12} [/tex]

The area of the square block is 48,881 m2, which is calculated by multiplying the length of each side (221 m) by itself.

The area of a square can be calculated by multiplying the length of one side by itself. In this case, the length of each side is 221 m. To find the area of the square block, we need to multiply 221 m by itself. This gives us 48,881 m2 as the final answer. To summarize, the area of the square can be found by multiplying the length of one side by itself. In this case, the length of each side of the block was 221 m, so 221 m multiplied by 221 m results in a total area of 48,881 m2.

The complete question: In one city there are four straight streets that form  a square block. The length of each side of the block is 221 m. Find the area of the square defined by this city block.

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Answer:

e = 190

Step-by-step explanation:

Rearrange to:

e/(-95)+6-(4)=0

Now we simplify, and get this:

(e/-95 + 6) - 4 = 0

Rewrite the equation to get this:

6 = 6/1 = 6x(-95)/-95

after adding fraction with a common denominator we get:

(570 - e)/95 - 4 = 0

Rewrite the whole as an equivalent fraction:

4 = 4/1 = 4x95/95

After adding fractions with a common denominator we get:

190-e/95 = 0

Now we must get the numerator to equal 0:

190-e/95 x 95 = 0 x 95

We get:

190 - e = 0

So we solve:

-e + 190 = 0

Subtract 190 from both sides:

-e = -190

Multiply both sides by (-1):

e = 190

The ratio of wins to losses is 5:6.

The ratio of losses to ties will be 3:2

The ratio of losses to games played will be 2:5.

The ratio of wins to games played will be 1:3.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

The ratio of wins to losses is:

= 10 / 12

= 5:6.

The ratio of losses to ties will be:

= 12 / 8

= 3:2

The ratio of losses to games played will be:

= 12 / (10 + 12 + 8)

= 12 / 30

= 2:5.

The ratio of wins to games played will be:

= 10 / 30

= 1:3

The ratio of children to adult will be:

= 165 / 66

= 5:2

The ratio of good bothes to games boothes will be:

= 6/15.

= 2:5

The ratio of children to games booths will be:

= 165 / 15

= 11:1

The ratio of female lions to make lions will be:

= 20 / 8

= 5:2

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Among the 3 cards the probability of picking an odd number and then picking an odd number is 1/3.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The probability of picking a card with odd number is -

Probability = Favourable outcomes / Total outcomes

Substitute the values in the equation -

P(odd1) = Odd number of cards / Total number of cards

P(odd1) = [tex]\frac{^1C_1}{^3C_1}[/tex]

P(odd1) = 1/3

This is followed by picking up a second card without putting the first card back.

So, out of remaining two cards an odd card needs to be picked.

Probability = Favourable outcomes / Total outcomes

Substitute the values in the equation -

P(odd2) = Remaining odd number of cards / Remaining number of cards

P(odd2) = [tex]\frac{^0C_1}{^1C_1}[/tex]

P(odd2) = 0/1

P(odd2) = 0

The probability of both the events is -

P(odd1) + P(odd2)

1/3 + 0

1/3

Therefore, the probability value is 1/3.

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The two numbers are 3 and 6. We can then solve for y using the quadratic formula:y = [9 ± √(81 - 120)]/2 , y = 3 or 6

The sum of two numbers (x + y) = 9

The product of two numbers (x * y) = 30

We can solve for x and y using the following equations:

x + y = 9

x * y = 30

We can solve for x by dividing both sides of the equation by y:

x = (30/y)

We can then substitute this into the first equation:

(30/y) + y = 9

We can then solve for y by subtracting 30/y from both sides:

y = 9 - (30/y)

We can then solve for y by multiplying both sides by y:

y^2 = 9y - 30

We can then solve for y using the quadratic formula:

y = [9 ± √(81 - 120)]/2

y = 3 or 6

Therefore, the two numbers are 3 and 6.

the complete question is :

What are the two numbers has a sum of 9 and a product of 30 ?

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The initial graph shows [tex]f(x)= 2(3)^{x}[/tex]

A function is a mathematical object that assigns a unique output (or "value") to each input in its domain. It is a rule that takes an input (or "argument"), performs some operations on it, and returns a corresponding output. Functions are often written using the notation f(x), where x is the input, and f(x) is the corresponding output. For example, the function f(x) = x^2 maps the input value x to its square. Functions are a key concept in mathematics and are used to model various phenomena in science, engineering, economics, and more.

The function provided is,

[tex]f(x)= 2(3)^{x}[/tex]

making x = 1

[tex]f(x)= 2(3)^{1}=f(x)= 2(3)=6[/tex]

The point (1, 6) that is (x, f(x)) must therefore satisfy the condition or be on the curve of the function.

The point (1, 6) only lies on the curve in the first graph.

As a result, the first graph accurately depicts the function.

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a) The value of x is 20 cm

b) The area of cones that sought is 680π cm²

a) To find the length of x

Compare the ratio and height of the small cone with the large cone

4/x= 7/35

4.35=7x

x= 20 cm, x is the radius of the large cone

b) To calculate the area of the whole cone

The area you are looking for = (Area of the large cone - Area of the small cone) + area of the circle

The area sought = (π20.35 - π4.7) + 2π4

The area sought = 700π-28π+8π

Area sought = 680π cm²

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An expression which does not represent the perimeter of the rug in feet include the following: C. 2(6 7/8) + w.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W) or P = 2L + 2W

Where:

Substituting the given parameters into the perimeter of a rectangle formula, we have the following expressions;

Perimeter, P = 2(6 7/8 + W)

Perimeter, P = 2(6 7/8) + 2W = 2W + 13 6/8

Perimeter, P = 6 7/8 + W + 6 7/8 + W

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The graph that represents the situation on the gymnast paying membership for yoga is Graph C.

The equation given for the amount spent in total by the gymnast is y = 10 + 20 x. What this means is that even if the gymnast takes no classes, he still has to pay the monthly fee of $ 10.

The graph should therefore begin at $10. If the gymnast takes 1 class, then the total cost for the month is:

= 10 + 20 ( 1 )

= $ 30

This is shown in the third graph so this is the correct graph.

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We can start by finding the diameter of the larger pizza in inches:

41.91 cm ÷ 2.54 cm/inch = 16.5 inches (rounded to one decimal place)

The diameter of the larger pizza is about 16.5 inches. Using this value, we can find the circumference (length of the crust) of the larger pizza using the formula:

C = πd

where C is the circumference and d is the diameter.

C = 3.14 × 16.5 inches

C ≈ 51.81 inches (rounded to two decimal places)

Therefore, the length of the crust around the larger pizza is about 51.81 inches.

The slope is negative three halves for option 2 and the y-intercept is 2. Hence option 2 is the correct answer.

A line's steepness and direction are determined by the line's slope. Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not.

Any two clearly separated points on a line can be used to calculate the slope of any line. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined.

The y-intercept is obtained when the x coordinate is 0.

From the given options the y-intercept is 2 for option 1 and 2.

The slope is given as:

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

For option 1:

m = (0 - 2) / (3 - 0)

m = -2/3

For option 2:

m = (-1 - 2) / (2 - 0)

m = -3/2

So, the slope is negative three halves for option 2 and the y-intercept is 2. Hence option 2 is the correct answer.

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a) Ninety percent is not a trustworthy estimate of the percent of all students who are outraged.

It is important to note that a sample of 5000 responses, while large, may not necessarily be representative of the entire population of students. The sample may have biases or limitations that affect the results of the survey. For example, the survey may have only been distributed to certain groups of students or there may have been a higher response rate from students who are particularly passionate about the issue.
In order to accurately estimate the percent of all students who are outraged, a representative sample of the entire population of students would need to be surveyed, and the survey would need to be designed and administered in a manner that minimizes biases and limitations.

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Complete question:

The university newspaper posts a survey question to its readers asking for opinions on the recently approved increase in fees for parking in a garage. The newspaper receives more than 5000 responses and reports that 90% of students are outraged over the approval of the garage parking fee. Which of the following is true?

a) Ninety percent is not a trustworthy estimate of the percent of all students who are outraged.

b) Ninety percent is an accurate estimate of the percent of all students who are outraged, since the sample size is so large.

Answer: n=8

Step-by-step explanation:

7n-2=6n+6

add 2 to 6 and subtract 6 from 7

this gets you n=8

53.9 degree is the angle of the compass direction of a line connecting your starting point to your final position measured from north of west.

A compass is a tool for orientation and navigation that displays direction in relation to the four cardinal directions of the earth (or points). The directions north, south, east, and west are typically represented on the compass face as initialised abbreviations in a design called a compass rose. The rose can be aligned with the corresponding geographic directions when the compass is employed; for instance, the rose's "N" mark points northward. Compass roses are frequently joined with (or occasionally replaced by) marks indicating angles in degrees. East is 90° degrees, south is 180° degrees, and west is 270° degrees, with north being 0° and the angles increasing clockwise.

Here,

You started by travelling west to north.

Your entire distance from the beginning location is your hypotenuse.

[tex]H^{2}= P^{2}+ B^{2} \\\\H^{2}= 17.5^{2}+ 24^{2}\\\\H^{2}= 306.25+ 576\\\\H=\sqrt{882.25} \\\\=29.7 meters[/tex]

You are moving in the northwest.

Use trigonometry now:

[tex]sin\alpha =\frac{B}{H}\\\\sin\alpha =\frac{24}{29.70} \\\\=0.808\\\\\alpha =53.9 degree[/tex]

That's the angle of the compass direction.

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Solve the following problem using analytical techniques: Suppose you walk 17.5 m straight west and then 24.0 m straight north. How far are you from your starting point, & what is the compass direction of a line connecting your starting point to your final point?

The expression to represents the phrase: "6 times a number plus 3." is:

6n + 3

Here, "n" represents an unknown number, and "6" and "3" are constants. The expression means that 6 is being multiplied by "n" to get an intermediate result, and then 3 is being added to that result to get the final answer.

For example, if n = 2, then the expression would evaluate to 6 * 2 + 3 = 12 + 3 = 15. So, the expression "6n + 3" represents the mathematical relationship between the unknown number "n" and the final result.

Therefore, the expression "6 times a number plus 3" can be represented as "6n + 3".

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The length, width, and height of the right square prism are all equal to 7units, i.e., 7units * 7units * 7units.

The volume of a right square prism can be expressed as the product of its length, width, and height. If the volume is 360 cubic units, and the prism is a square prism, then we can assume that its length, width, and height are all equal, so we can call them x. The volume formula can be expressed as:

V = x * x * x = 360

Taking the cube root of both sides of the equation, we get:

x = ∛(360) = 7.11

The cube root of 360 is approximately 7, so the length, width, and height of the square prism are all equal to 7 units.

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Answer: The equation 63 = 9k is correct.

To solve for k, you can divide both sides of the equation by 9:

63/9 = 9k/9

k = 7

So, k = 7 is the solution to the equation 63 = 9k.

Step-by-step explanation:

The value of k in the equation 63= 9k is 7

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

The equation 63 = 9k is a type of linear equations with one variable.. The variable here is K

To find k;

63 = 9k

divide both sides by 9

63/9 = 9k/9

k = 7

therefore the value of k is 7

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Step-by-step explanation:

The potential energy of an object can be calculated as the sum of its kinetic and gravitational potential energy. At its highest point, the ball has zero kinetic energy, so the potential energy is equal to its gravitational potential energy.

The gravitational potential energy of an object is given by:

PE = m * g * h

where m is the mass of the object (7 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height above a reference point. In this case, the reference point is the ground, so h = 100 m.

Substituting in the given values, we find:

PE = 7 * 9.8 * 100 = 686 J

This is the potential energy of the ball at its highest point.

Answer:

answeransweransweranswer is 686 Joules(J)

Step-by-step explanation: