ESSENTIAL QUESTION CHECK-IN
17. Tell how you can determine whether a number is a solution of an
equation.
324 Unit 4

Answer:

y = -1

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

To find slope we look for the rise/run or (y2 - y1) / (x2 - x1)

The slope here is 0, and the y-intercept is located at (0,-1), so the equation is

y = -1

Answer:

y = -1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

$21,200

Step-by-step explanation:

Given the best fit equation:

y= 34,000 - 1,600x

Where ;

y = value of vehicle in $

x = Age of vehicle in years

The predicted value of vehicle aged 8 years ;x = 8

y = 34000 - 1600(8)

y = 34000 - 12800

y = 21,200

Hence, the predicted value of car aged 8 years is $21,200

Answer:

1/6

Step-by-step explanation:

if one kid shared 1/3 of cookies then each kid would have 1/3 of cookies

Answer:

A, y = x

Step-by-step explanation:

Slope is equal to one

Y-intercept is origin

Answer:

A.) Y=X

Step-by-step explanation:

It intercepts with origin

Answer: [tex]35x+9\leq 310,\ 8[/tex]

Step-by-step explanation:

Given

A group of friends has $310 to spend

Parking costs $9 and ticket cost $35 per person

Suppose  there are x friends who go to amusement park

So, the cost of tickets and parking must be less than or equal to $310

[tex]\Rightarrow 35x+9\leq 310\\\text{Subtract 9 from both sides}\\\Rightarrow 35x\leq 301\\\text{Divide both sides by 35}\\\Rightarrow x\leq 8.6[/tex]

This indicates that there sholud be maximum 8 persons who can go to amusement park with this much money.

The height of the Building is 110.01 feet.

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' Theorem.

Given, Finn leaned a 100-foot ladder against the side of a building. The base of the ladder is 14 feet from the base of the building. The top of the ladder is 11 feet from the top of the building.

For the triangle made by ladder

hypotenuse = 100

base = 14

thus, from the Pythagorean theorem

hypotenuse² = base² + height²

100² = 14² + height²

height² = 10000 - 196

height = √9804

height = 99.01

total height of the wall = height of triangle + remaining height of the wall

Thus the total height of the wall  = 99.01 + 11

the total height of the wall  = 110.01

therefore, the building is 110.01 feet tall.

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The four equations of uniformly accelerated motion are:

[tex]v = u + at\\s = ut + (1/2)at^2\\v^2 = u^2 + 2as\\v = u + 2as/t[/tex]

Uniformly accelerated motion is motion in which the acceleration is constant. The four equations of uniformly accelerated motion are:

These equations are derived from the basic kinematic equations of motion which relate velocity, acceleration, distance and time.

The first equation is a result of the definition of acceleration.

The second one is derived from the first equation and the definition of distance.

The third one is derived from the first and second equation by squaring the first equation and then solving for v^2.

The fourth equation is derived by dividing the distance traveled by the time taken.

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Depending on whether a and b are real numbers, they can factor as (a + b) (a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.

When you square an integer, you get perfect squares. The number 81, for example, is a perfect square since it can be derived by squaring 9: 99=81. Because 12 can be squared to make 144, 144 is a perfect square. 13 may be squared to make 169, which is a perfect square. Mathematics-related language. Informally: When an integer (a "whole") number is multiplied by itself, whether the result is positive, negative, or zero, the result is referred to as a square number, a perfect square, or simply "a square." All square numbers are therefore 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

Perfect square trinomials, also referred to as trinomial squares, are the squares of binomial expressions.

Depending on whether a and b are real numbers, they can factor as (a + b)(a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.

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It will cost $10.00 to waterproof a canvas truck cover that is 15' x 24'.

To find this, we need to first convert the dimensions of the canvas truck cover from feet to yards, since the cost is given per square yard. 15' x 24' = 180 sq ft. 1 sq yard is equal to 9 sq ft, so 180 sq ft/9 sq ft/yard = 20 sq yard. Then we multiply the square yards by the cost per square yard to find the total cost:

It's important to note that the measurements of the canvas truck cover are given in feet and the cost is given per square yard. It's important to convert it to square yards to match the unit of measurement and calculate the cost.

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1. The quotients of the following division operations are as follows:

a) 126 ÷ 12 is 10.5.

b) 217 ÷ 4 is 54.25.

c) 75 ÷ 6 is 12.5.

d) 11 ÷ 9 is 1.2222.

e) 200 ÷ 35 is 5.7143.

2a) The quotient of 7 ÷ 2.2 is a nonterminating or repeating decimal.

2b) The quotient of 0.5 ÷ 0.12 is a nonterminating or repeating decimal.

2c) The division operation with a quotient that is nonterminating or repeating decimal is 2 ÷ 2.7.

3) The identification of each resulting quotient as a terminating or nonterminating, repeating decimal is as follows:

4) The quantity of meat in one piece of hamburger, if they are evenly shared or divided, is 41.67 g.

The quotient is the result of the division operation.

Every division operation involves the dividend (the numerator), the divisor (the denominator), the division operand (÷), and the equal sign (=).

2)

a) 7 ÷ 2.2 = 3.181818

b) 0.5 ÷ 0.12 = 4.16667

c) 3 ÷ 0.8 = 3.75

9 ÷ 0.16 = 56.25

2 ÷ 2.7 = 0.740740

3)

a. 2 ÷ 3 = 0.6667

b. 5 ÷ 1.2 = 4.16667

c. 0.3 ÷ 0.9 = 0.3333

d. 2.4 ÷ 1.8 = 1.3333

4) Total weight of ground pork = 1.25 kilograms

1 kg = 1,000 g

1.25 kg = 1,250 g

The pieces of patties = 30

The weight of each piece = 41.67 g (1,250/30)

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Answer:

The height of the triangle = 6 inches

The base of the triangle = 10 inches

Step-by-step explanation:

The formula for the Area of a Triangle = 1/2 × Base × Height

Area = 30 in²

h = b - 4

Hence

30 = 1/2 × b × b - 4

Cross Multiply

30 × 2 = b² - 4b

60. = b² - 4b

b² - 4b - 60

We factorise the Algebraic expression to find b

b² - 4b - 60 = 0

b² - 10b + 6b - 60 = 0

b(b - 10) + 6(b - 10) = 0

(b - 10) + (b + 6 ) = 0

b - 10 = 0 , b = 10

b + 6 = 0, b = -6

We are going to take the positive answer of b as the value of b

b = 10 inches

Solving for h

h = b - 4

h = 10 - 4

h = 6 inches

Therefore, the height of the triangle = 6 inches

base of the triangle = 10 inches

The trigonometric ratio as a fraction for sinC is  , and the decimal is 0.80.

The trigonometric functions are actual functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

The widely used trigonometric functions are sine, cosine and tangent. The trigonometric functions also operate the inverse of the functions.

For the given triangle the trigonometric values are as follows:

For angle A the opposite side is CB, the adjacent side is AB and the hypotenuse is AC.

For angle C the opposite side is AB, the adjacent side is CB and the hypotenuse is AC.

[tex]sinC = \frac{\text{Opposite side }}{Hypotenuse} = \frac{4}{5} =0.80\\ \\ cosC = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{3}{5} = 0.60\\\\tanA =\frac{\text{Opposite side }}{Adjacent side} = \frac{3}{4} = 0.75\\\\tanC= \frac{\text{Opposite side }}{Adjacent side} =\frac{4}{3} = 1.33\\\\cosA = \frac{\text{Adjacent side }}{Hypotenuse} =\frac{4}{5} = 0.80\\\\sinA= \frac{\text{Opposite side }}{Hypotenuse}=\frac{3}{5} =0.60[/tex]

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Answer:

Los jugadores dan 36 palmadas en total.

Step-by-step explanation:

Dado que 9 jugadores de un equipo de baloncesto chocan palmadas unos con otros, para determinar cuántas palmadas dan en total, sabiendo que 2 jugadores dan una palmada, 3 jugadores, tres palmadas, 4 jugadores, seis palmadas, y 5 jugadores, diez palmadas, se debe realizar el siguiente cálculo:

Cada jugador da un número de palmadas igual al número de jugadores en el campo, menos 1. A su vez, esa palmada es recíproca con el otro jugador que la recibe, con lo cual el número de jugadores a contar va disminuyendo.

8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = X

15 + 6 + 5 + 4 + 3 + 2 + 1 = X

21 + 5 + 4 + 3 + 2 + 1 = X

26 + 4 + 3 + 2 + 1 = X

30 + 3 + 2 + 1 = X

33 + 2 + 1 = X

35 + 1 = X

36 = X

Por lo tanto, dan 36 palmadas en total.

Answer: o.7619

Step-by-step explanation: i used the standard algorithm i am sorry i cant do a more in depth just hard to do with words ;)

Answer: 0.7619

:)

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

Open up the parenthesis

R - 8 - R - 15

R - R - 8 - 15

-23

Answer:-23    ITS SUPER EASY:0

Step-by-step explanation:

Open up the parenthesis

R - 8 - R - 15

R - R - 8 - 15

-23

Answer:

Step-by-step explanation:

The system of linear equations has no solution when the lines are parallel. It means the lines have same slope but different y-intercepts.

The y-intercepts are different:

For the given system to have no solution we need n = -4.

Answer:

x = 29

y = 119

Step-by-step explanation:

51 + x = 90

x = 90 - 51

x = 29

y = 90 + x

= 90 + 29

y = 119

If $10,000 is invested at x percent simple annual interest for n years, the total amount of interest would be F = 10,000n(x/100)

Simple interest is calculated based on the principle of a loan or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.

F = P(1+rt), formula for simple rate of interest

Here,

=> Future value is F

Present value is P

=> Rate is R

=> Time is t

Substituting x for r

And, n for t

Also, 10,000 in for P

F = 10,000(1+xn)

The formula tells us principal + interest,

F = 10,000(xn)

Now, to get the x into terms of a percentage,

F = 10,000(n * x/100)

F = 10,000n(x/100)

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Answer:

C. xy²

Step-by-step explanation:

You have to add the exponents:

(xy) exponent is 1

(x) exponent is 1

Combine the (x):

xy²

A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).

The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.

Using a standard t-test and the following formula, you can determine a t-value: t is equal to (X - ц0) / (s / √n), where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.

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A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).

The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.

Using a standard t-test and the following formula, you can determine a t-value: t is equal to [tex](X - ц0) / (s / √n)[/tex], where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.

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Answer:

[tex]-\sqrt{7/4}[/tex]

Step-by-step explanation:

[tex] \sin( \theta) = \frac{ \sqrt{3} }{2} [/tex]

Answer:

Mary bought the most flour

Step-by-step explanation:

Ana bought 12 3/6 kg of flour

12 3/6 = 75/6 = 12.5 kg of flour

Mary has brought 14 2/8 kg of flour

14 2/8 = 114/8 = 14.25 kg of flour

Kristina bought 11 8/12 kg of flour.

11 8/12 = 140/12 = 11.66 kg of flour

So, Mary bought the most flour.

Answer:42.875 feet3

Step-by-step explanation:

Answer:

Step-by-step explanation:

V=a³

=[tex](3\frac{1}{2})^3=42\frac{7}{8}[/tex]in³

Answer:

B: weather occurs because the climate is constantly changing

Step-by-step explanation:

Eight 1/2s are in 4. This can be visualized with pattern blocks, as four triangles (each triangle is 1/2) would be needed to make up a square (4).

Visualization is the process of creating graphical representations of data and information. It can take the form of charts, graphs, diagrams, maps, and other visual representations of data and patterns. Visualization can be used to explore, analyze, and communicate data in an effective and meaningful way, helping to make complex data more accessible and easier to understand. Visualization can also help to uncover trends and relationships that might otherwise be difficult to detect.

b. Three 2/3s are in 2. This can be visualized with pattern blocks, as three hexagons (each hexagon is 2/3) would be needed to make up a rectangle (2).
c. Six 1/6s are in 1. This can be visualized with pattern blocks, as six rhombuses (each rhombus is 1/6) would be needed to make up a hexagon (1).

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Answer:

18.84

Step-by-step explanation:

x is the hypotenuse of the triangle.

For the 48° angle, 14 is the opposite leg.

The trigonometric ratio that relates the opposite leg to the hypotenuse is the sine.

sin 48° = opp/hyp

sin 48° = 14/x

x × sin 48° = 14

x = 14/sin 48°

x = 18.84

Consequently, there is a 0.89736 percent chance or probability that he weighs fewer than 258 kilograms.

Probability fundamentals. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Here,

we use the z-score algorithm to answer this query.

Score Z = x - μ/σ

x = the raw score

 population mean= μ 

Population standard deviation is σ

Hence,

x = 258, μ = 220, σ = 30

Z = 258 - 220/30

=1.26667

Probability based on the Z-Table:

P(x<258) = 0.89736

Consequently, there is a 0.89736 percent chance that he weighs fewer than 258 kilograms.

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