Topic 21 Angles of Triangles
3.
88 1
180'
姐
5.
(8x-35)
For questions 3 and 4, find the measure of each missing angle.
11 180
ई
-64
(3x-1)
(6r-5)
6.5
642
•92⁰
m22 = 24
m21 =
m23-
m24 =
m25=
80
For questions 5 and 6, find the value of x.
6.
(i=11)
2x+20)
(11X-63)
mel-
m/2=
m23-
m24
m25-
m26-
m47 =

Answer:

12 ft

Step-by-step explanation:

To find the height of a rectangular box with a base measuring 3 feet by 6 feet and a volume of 72 cubic feet, we need to use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

We are given the volume of the box and the length and width, so we can substitute the values and solve for the height:

72 = 3 x 6 x Height

72 / (3 x 6) = Height

12 = Height

So, the height of the box is 12 feet.

Answer:

Each bucket will be [tex]\dfrac{1}{2}[/tex] full

Step-by-step explanation:

First add up all the different fractions to find out how many buckets of water are in all 3 buckets combined.

Adding up the fractions we get the expression:

[tex]\dfrac{5}{12} + \dfrac{3}{4} + \dfrac{1}{3}[/tex]

To add these fractions first find the LCM(least common multiple of the denominators, 12, 4 and 3

This is the smallest number divisible by all 3 numbers without a remainder

There are several strategies for finding the LCM but here we can see that 12 is evenly divisible by12, 4 and 3

We convert each of the fractions to have the same denominator as the LCM of 12 and adjust the numerator accordingly

Multiply each of the fractions by the LCM

12 x 5/12 = 5

12 x 3/4 = 9

12 x 1/3 = 4

These will become the numerators in the addition with the common denominator of 12

[tex]\dfrac{5}{12} + \dfrac{3}{4} + \dfrac{1}{3}\\\\= \dfrac{5 + 9 + 4}{12}\\\\= \dfrac{18}{12}\\\\[/tex]

This is how many buckets it will take to hold the water from all three buckets

Divide numerator and denominator by 6 to reduce to lowest fraction

[tex]\dfrac{18 \div 6}{12\div6} = \dfrac{3}{2}[/tex]

This is 1 1/2 buckets. If this amount of water is to be evenly divided among 3 buckets then the amount of water in each bucket

[tex]\dfrac{3}{2} \div 3\\\\= \dfrac{3}{2} \times \dfrac{1}{3}\\\\= \dfrac{1}{2}[/tex]

So each bucket will be half full

The graph of the equation can be seen on the image at the end, and when she uses 17 cups of flour, she will use 76.5 cups of honey.

We assume that the relation is linear.

Remember that a general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the linear equation passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the two pairs:

(27, 6)

(45, 10)

First, you can graph these two points and connect them with a line, that will be the graph of our equation.

The slope is:

a = (10 - 6)/(45 - 27)

a = 4/18

a = 2/9

y = (2/9)*x + b

To find the value of b we can replace the values of the point (27, 6)

6 = (2/9)*27 + b

6 = 2*3 + b

6 = 6 + b

0 = b

So the equation is just:

y = (2/9)*x

And for 17 cups of flour, she will use:

17 = (2/9)*x

(9/2)*17 = x

76.5 = x

She needs to use 76.5 cups of honey.

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Answer: The total value of the loan with quarterly compounded interest  is $60,109.34.

Step-by-step explanation:

To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A = final amount (loan + interest)

P = principal (the original amount of the loan)

r = annual interest rate as a decimal

n = number of times the interest is compounded in a year

t = time in years

For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.

Substituting the values into the formula, we get:

A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)

A = $50,000 * (1.015375)^(15.7532)

A = $50,000 * 1.22186888

A = $60,109.34

Therefore, To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A = final amount (loan + interest)

P = principal (the original amount of the loan)

r = annual interest rate as a decimal

n = number of times the interest is compounded in a year

t = time in years

For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.

Substituting the values into the formula, we get:

A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)

A = $50,000 * (1.015375)^(15.7532)

A = $50,000 * 1.22186888

A = $60,109.34

Therefore, the total value of the loan with the quarterly compounded interest would be $60,109.34.

Answer:

The equation for the new graph is e^(x -6)

The solution is, a) Negative linear; b) about 48

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

a) Type of correlation

The graph shows a negative linear correlation.

b) Prediction

It looks like a student who makes 60 in Science would make about 48 in English.

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Answer: 3

Step-by-step explanation:

The probability of ordering meat is 0.7 and the probability of ordering fish is 0.3.

P(+ | M) = 0.8 and P(- | M) = 0.2,

P(+ | F) = 0.95 and   P(- | F)  = 0.05.

P(M and +) = 0.56 and P(M and -) = 0.14,

P(F and +) = 0.285 and P(F and -) = 0.015.

C: the probability that the customer ordered fish is 0.3.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given The Humber, Room advertises two types of entrée, meat and fish,

70% of all customers order meat, and 30% order fish,

M represents the event of ordering meat, F is the event of ordering fish,

probability of M and F,

p(M) = 70% = 0.7

p(F) = 30% = 0.3

and 80% of those who ordered meat and 95% of those who ordered fish were satisfied,

+ is the event of being satisfied, and − is the event of not being satisfied,

probability of satisfied customers with meat,

p(+) = 80% = 0.8

not satisfied with meat,

p(-) = 1 - 0.8 = 0.2

probability of satisfied customers with fish,

p(+) = 95% = 0.95

not satisfied with fish,

p(-) = 1 - 0.95 = 0.05

B: calculating the joint probabilities,

P (M and +) = P(M ∩ +) = p(M)*p(+)

P (M and +) = 0.7*0.8

P (M and +) = 0.56

P (M and -) = P(M ∩ -) = p(M)*p(-)

P (M and -) = 0.7*0.2 = 0.14

P (F and +) = P(F ∩ +) = p(F)*p(+)

P (F and +) = 0.3*0.95

P (F and +) = 0.285

P (F and -) = P(F ∩ -) = p(F)*p(-)

P (F and -) = 0.3*0.05

P (F and -) = 0.015

C:  Determine the conditional probabilities,

P (+ | M) = P(M ∩ +)/p(M)

substitute the values

P (+ | M) = 0.56/0.7

P (+ | M) = 0.8

P (- | M) = P(M ∩ -) /p(M)

P (- | M) = 0.14/0.7

P (- | M) = 0.2

P (+ | F) = P(F ∩ +)/p(F)

substitute the values

P (+ | F) = 0.285/0.3

P (+ | F) = 0.95

P(- | F) = P(F ∩ -)/p(F)

P(- | F) = 0.015/0.3

P(- | F)  = 0.05

D: If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish,

to find P (F | +) = P(F ∩ +)/p(+)

substitute the values

P(F | +) = 0.285/0.95

P (F | +) = 0.3

Hence the probabilities are as followed.

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The probability that Deborah's first flight was delayed can be found to be 0. 85.

To find the probability that Deborah's first flight from Boston to Denver was delayed, use the following formula :

= 1 - probability that the flight takes off on time

Probability that the flight takes off on time = 0. 15 .

The probability that Deborah's first flight from Boston to Denver was delayed is therefore :

= 1 - 0. 15

= 0. 85

In conclusion, there is an 85 % probability that the first flight was delayed.

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If the point (4, -1) is a point on the graph of f, then f(4) = -1.

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

Point ​(4,−​1) is a point on the graph of​ f

The expression "f(4)" represents the output value of the function f, when 4 is plugged into it as the input.

If the point (4, -1) is on the graph of f, it means that for the input value of 4, the output value of the function is -1.

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The bedroom's area in meters squared is 55.1693 m².

finding the area of the basement:

The length of the basement is 2 * 10.5 m = 21 m

The width of the basement is 8 m / 4 = 2 m

The area of the basement is 21 m * 2 m = 42 m²

Next, let's find the equivalent area of the 10 square feet tile in meters:

1 square foot = 0.092903 m²

10 square feet = 10 * 0.092903 m^2 = 0.92903 m²

finding the area of the bedroom:

The length of the bedroom is 10.5 m - 6 m = 4.5 m

The width of the bedroom is 8 m * 34 = 2.72 m

The area of the bedroom is 4.5 m * 2.72 m = 12.24 m²

So the total area covered with carpet and tile is:

12.24 m² + 42 m² + 0.92903 m²

  = 55.1693 m²

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Answer:

Step-by-step explanation:

Wow, that is a lot. You got to give me a brainliest ! Lol

1) 9²+12²=x², x=15

2)10²+24²=x², x=26

3)3²+7²=x², x=7.6

4)6²+x²=10², x=8

5)x²+6²=24², x=23.2

6)1²+1²=x², x=1.4

7)x²+8²=21², x=19.4

8)x²+24²=30², x=18

9)5²+9²=x², x=10.3

A positive and a negative coterminal angle for each given angle is

A. 13π/4 and -3π/4.

B. 97π/36 and -47π/36.

What is the coterminal angle?

Coterminal angles are those with a common terminal side that are in standard position (angles with the starting side on the positive x-axis). Coterminal angles are the angles that have the same initial side and share the terminal sides.

Here, we have

A. 5π/4

We have to find the coterminal angle.

5π/4 + 2π = 13π/4

5π/4 -  2π = -3π/4

Hence, a positive and a negative coterminal angle for each given angle is 13π/4 and -3π/4.

B. 25π/36

We have to find the coterminal angle.

25π/36 + 2π = 97π/36

25π/36 -  2π = -47π/36

Hence, a positive and a negative coterminal angle for each given angle is 97π/36 and -47π/36.

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The pendulum will swing at the velocity of 3.06 m/s at the bottom of the swing.

Velocity is the rate of change of position of an object, usually measured in meters per second (m/s). It is a vector quantity, which means it has both magnitude and direction. Velocity is an essential notion in physics since it is used to describe motion and is one of the fundamental principles of classical mechanics. It is connected to other notions such as acceleration, momentum, and force. Velocity is a measure of how rapidly an item moves in a specific direction, and it is computed by dividing the distance travelled by the time it takes for the object to traverse that distance.

The speed of the pendulum at the bottom of its swing can be calculated using the formula:

v = √(2gh)

where v = velocity, g = gravitational acceleration (9.8m/s2), h = height (1.22m)

Therefore, the speed of the pendulum at the bottom of its swing is:

v = √(2*9.8*1.22)

v = 3.06 m/s

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Therefore , the solution of the given problem of function comes out to be g(x) = ƒ(2x + 3) = f'(-5) = 1.

Mathematics includes the study of numbers, various variations, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship variable between the number of inputs and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a domain. The letter f is frequently used to denote functions (x).

Here,

Given :

=> f(−4) = −2

=> ƒ'(−4) = 6

=> f(-5) = −4

=> f'(-5) = 1

To find :

=> g(x) = ƒ(2x + 3)

=> g(4) = f(2(-4) + 3)

=> g(4) = f(-5)

=> f(-5) = -4

=> f'(-5) = 1

Therefore , the solution of the given problem of function comes out to be g(x) = ƒ(2x + 3) = f'(-5) = 1.

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Answer:

SA = 439.8 in²

Step-by-step explanation:

the surface area (SA) is the total area of the 6 triangular faces and the base

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 10 and h = 6 , then

A = [tex]\frac{1}{2}[/tex] × 10 × 6 = 5 × 6 = 30 in²

so area of 6 triangles = 6 × 30 = 180 in²

Then

SA = 180 + 259.8 = 439.8 in²

On solving the provided question we can say that by fraction, Mike can fill 18 X 1/3 = 6 cups with water

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Each jar holds 1/3 cup.

Mike has 18 cups of water

by fraction, Mike can fill 18 X 1/3 = 6 cups with water

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The correct question is -

Mike will fill jars with water for an experiment. Each jar holds 1/3 cup. Mike has 18 cups of water. How many jars can Mike fill with water?

The equation that represents the given graph is: D. y = 2/5x - 3.

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

here, we have,

To find the equation of a line that passes through two points (x1, y1) and (x2, y2), we can use the following steps:

Find the slope (m) using the formula

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

Plug in the slope and one of the points into the equation

y = mx + b to find b.

So, for the line that passes through the points (0, -3) and (5, -1),

the slope is (-1 - (-3)) / (5 - 0)

                 = 2/5,

and the y-intercept can be found by plugging in the slope and the point (0, -3) into the equation y = mx + b:

-3 = (2/5) * 0 + b

-3 = b

Therefore, the equation of the line that passes through (0, -3) and (5, -1) is:  y = (2/5)x - 3

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La ecuación de la circunferencia que pasa por los puntos (0, 0), (3, 4) y (6, 2) es x² + y² - (55 / 9) · x - (5 / 3) · y = 0.

Según la geometría analítica, la fórmula general de una circunferencia contiene tres coeficientes reales (D, E, F) en la siguiente expresión:

x² + y² + D · x + E · y + F = 0

En consecuencia, se requiere el conocimiento de tres puntos distintos para determinar las condiciones de la ecuación. Es preciso construir un sistema de ecuaciones lineales, cuya forma es:

D · x + E · y + F = - x² - y²

Si sabemos que (x₁, y₁) = (0, 0), (x₂, y₂) = (3, 4) y (x₃, y₃) = (6, 2), entonces tenemos el siguiente sistema de ecuaciones lineales:

F = 0

3 · D + 4 · E + F = - 25

6 · D + 2 · E + F = - 40

Cuya solución se obtiene mediante métodos numéricos:

(D, E, F) = (- 55 / 9, - 5 / 3,  0)

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(a) The maximum number of snack bags he could make,

= 18 snack bags.

(b) 18 juice boxes.

(c) 18 cookies in each bag.

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor.

Given:

Brady is making snack bags with 18 juice boxes and 27 cookies.

He wants each bag to have the same number of juice boxes and the same number of cookies.

(a) The maximum number of snack bags he could make,

= GCF(18, 27)

= 18 snack bags.

(b) 18 juice boxes.

(c) 18 cookies in each bag.

Therefore, all the required values are given above.

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The simplification of (23+16) is 39

Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined.

For example of there are 20 mangoes. 50 cashews and 80 oranges in a store. The total number of fruits the store can be obtained by adding the number of oranges, mangoes and cashew.

This means that 80+20+50 = 150 fruits

Similarly to get the value of( 23+16) , we add the two numbers together

23+16 = 39

therefore the value of 23+16 = 39

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Answer: 4

Step-by-step explanation: i took the test

Answer:

216.25

Step-by-step explanation:

First multiply 4 × 37 = 148

Then add 148 + 68.25 = 216.25

Answer: Let's call the number of gallons of regular gas sold "x". Then, the number of gallons of premium gas sold would be 300 - x.

The total revenue from regular gas would be 2.15 * x dollars. The total revenue from premium gas would be 2.90 * (300 - x) dollars.

We know that the total receipts for the day were $690, so we can set up the following equation:

2.15x + 2.90(300 - x) = 690

Expanding the second term, we get:

2.15x + 870 - 2.90x = 690

Combining like terms, we get:

0.25x = -180

Dividing both sides by 0.25, we get:

x = 720

So, 720 gallons of regular gas and 300 - 720 = -420 gallons of premium gas were sold. However, since it is not possible to sell a negative number of gallons of gas, this solution is not valid.

If we try another value of x that is less than 300, we will find a valid solution. Let's try x = 200:

2.15 * 200 + 2.90 * (300 - 200) = 690

Expanding and simplifying, we get:

430 + 90 = 520

So, 200 gallons of regular gas and 300 - 200 = 100 gallons of premium gas were sold.

Step-by-step explanation:

In order to buy four bananas, then the number of apples that he bought will be 8.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Assume that a consumer has a given budget or income of $10 and that she can buy only two goods, apples or bananas. The price of an apple is $1.00 and the price of a banana is $0.50.

Let 'x' be the number of apples and 'y' be the number of bananas. Then the equation is given as,

1x + 0.50y = 10

x + 0.50y = 10

In order to buy four bananas, then the number of apples that he bought is given as,

x + 0.50 (4) = 10

x + 2 = 10

x = 8

In order to buy four bananas, then the number of apples that he bought will be 8.

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Answer:

C is the answer.

Step-by-step explanation:

Switzerland uses the currency called Switzerland Franc.

PLEASE MARK ME BRAINLIEST.

The required volume of figure 1 is given as 55 ft³, and the volume of all the figures is evaluated by following the same procedure.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
Volume  = 1/3 area of base × height - - - - -(1)

(1)
Area of base = area of triangle = 1/2 × base × height

Area of base = 1/2 × 5 * 6 = 15
Put this value in equation 1
Volume =  1 /3 ×15 × 11
Volume = 55 ft³

Similarly, the volume of each figure can be evaluated.

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Answer:

It isn't measured, but it gives you a ruff representation of what the subject looks like.

Step-by-step explanation:

Kevin has $3840 invested in stocks in total.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Annual interest in first investment - 11%

Annual interest in other investment - 14%

Total interest annually - $480

Let us assume, x is the investment in each stock

or, total investment = 2x

then, making an equation for the total interest

0.11x+.14x=480

Multiplying everything by 100

11x+14x=48000

25x=48000

Divide both sides by 25

x=1920

then, by total investment = 2x

2×(1920) = 3840

Hence, Kevin has $3840 invested in stocks in total.

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the easiest way is to divide, 8068÷31, since it's a big problem, you should use a calculator! When you do, you should get 260.258065, but once you round all the decimals you just get 260, your remainder should be 8. Use 8 as your numerator and 260 as your mixed number! And your finished, and that's why the answer is 260 8/31.