parallel lines, transversals

When y = -x² + 15x - 56 then coordinates are is (c) (-7, 0); (8, 0).

Quadratic functions are a type of polynomial function of degree 2, which can be expressed in form f(x) = ax² + bx + c, where a, b, and c are constants, and x is the variable.

The graph of the given quadratic equation y = -x² + 15x - 56 can be plotted using a graphing calculator or any graphing tool. The x-intercepts are the points on the x-axis where the graph intersects the x-axis, i.e., the points where y = 0. By plotting the graph, we can determine the x-intercepts to be (-7, 0) and (8, 0), which correspond to option (c) (-7, 0); (8, 0).

Option (a) and (b) have incorrect x-coordinates for the x-intercepts, and option (d) has both positive x-coordinates for the x-intercepts, which is not correct based on the graph of the given quadratic equation.

Hence, option (c) is the correct answer.

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Answer:4

Step-by-step explanation:

2+2 is 4

a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.

a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:

Industry Average Salary = 96% of Firm B's Average Salary

= 0.96 * $58,000

= $55,680

b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:

Firm A's Average Salary = 93% of Industry Average Salary

= 0.93 * $55,680

= $51,718.40

c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:

Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100

= ($58,000 / $51,718.40) * 100

≈ 112.27%

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Answer:

65000 metres

Step-by-step explanation:

65*1000=65000

Answer: 10/40 or 1/4

Step-by-step explanation:

Add up all the amount of rolls, so 10+6+4+8+6+6=40

then add the probability of rolling a 3 or 6 = 10

divide that quantity out of the whole

answer is 10/40 and simplified is 1/4

hope it helps

Answer:

22 in.

Step-by-step explanation:

Perimeter = Length + Length + Breadth + Breadth

Perimeter = 7 in. + 7 in. + 4 in. + 4 in.

Perimeter = 22 in.

Answer:

mean= sum of all observations /no.of observation

mean=45+80+15+10+94/5

mean=244/5

mean=48.8

this is how the calculator gets 48.8

Answer:

Step-by-step explanation:

Use a simple Equation

Price = Number x Price

So Price = 536.

Since it was 67% off we multiple the price of the original by .67.

So

536 = .67x

Solve for x = 536/.67 = 800

The original Price is $800.

check by multiplying by the sale %.

Answer:

81

Step-by-step explanation:

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

1inch : 3.9miles

Explanation:

Given that the distance between the museum which is 7.8miles apart is represented by 2inches, then;

7.8miles = 2inches

To get the scale used;

x = 1 inch

Divide both expressions

Cross multiply

Divide both sides by 2

Hence the scale used is 1inch : 3.9miles

Answer:

ok ok ok ok ok

Step-by-step explanation:

Answer:

ok?

Step-by-step explanation:

The sampling method used in this problem is classified as:

Simple Random Sampling

Samples may be classified as:

In this problem, all the options are assigned a number and then taken, hence a Simple Random Sample is used.

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Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

The concentration of the type of antibiotic after 4 hours is; 11.04 parts per million

We are told that the equation that models the concentration in parts per million of a type of antibiotic in a human's bloodstream after h hours is;

A(h) = -0.06h² + 2h + 4

where h is the time in number of hours after which the concentration is recorded.

Now, we want to find the concentration after 4 hours and as such we will input 4 for h in the equation to get;

A(4) = -0.06(4²) + 2(4) + 4

A(4) = -0.96 + 12

A(4) = 11.04 parts per million

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Answer:

10/7= $1.43 per kg

...........

0.7 kg = $1

7 kg - $10

? kg - $1

7 / 10 = 0.7

0.7 kg = $1

Let me know if I did something wrong :)

The appropriate alternative hypothesis for the investigation is: Ha: proportion < 0.38

The correct option is option D)

What is null and alternate hypothesis?

Null and alternate hypothesis are hypothesis in statistical testing. A null hypothesis assumes that is no difference. where as an alternate hypothesis assumes that there is a difference. A null hypothesis is denoted by H0 and alternate hypothesis is denoted by H1.

The null hypothesis is the proportion of people in Region X with blood type O positive is equal to the proportion in Region W. And that proportion is 0.38

Hence by null hypothesis we have

H0: proportion = 0.38

The alternative hypothesis, denoted by Ha, is the hypothesis that we want to test against the null hypothesis.

In this case, we want to investigate whether the proportion of people in Region X with blood type O positive is less than the proportion in Region W. So, the appropriate alternative hypothesis is:

Ha: proportion < 0.38

Hence, The appropriate alternative hypothesis for the investigation is: Ha: proportion < 0.38

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Answer:

The simplest form of 48 is 12.

Step-by-step explanation:

hope that helps :)

The simplest form of the expression 4 x 1/8 will be 1 / 2.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that there are two numbers 4 and 1 / 8 multiplied by each other.

The solution of the expression 4 x 1/8 will be:-

E = 4 x ( 1 / 8 )

E = 4 / 8

E = 1 / 2

Therefore, the simplest form of the expression 4 x 1/8 will be 1 / 2.

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Answer:

D?

Step-by-step explanation:

I'm not completely sure, but there are 2 different 180 degree lines that y falls on. On one line (y+70=180) it is for sure 110 degrees

When measured on the other line it is (y+70+x=180) I'm not too familiar with this??

Answer:

C

Step-by-step explanation:

Answer:

\(9 + 7i\)

Step-by-step explanation:

\(7i^5+9i^8\)

\(i^5 = i\\ i^8 = 1\)

Answer:

A)  4.5

Step-by-step explanation:

you can set up a ratio comparing AB/CB to (AB + BD)/5

3/2 = 3 + BD/5

cross-multiply to get 15 = 2(3 + BD)

15 = 6 + 2BD

9 = 2BD

9/2 = BD

The length of AD will be 7.5

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Lines BC and DE are both vertical.

Now,

Since,  Lines BC and DE are both vertical.

So, We get by definition of proportionality;

⇒ AB / CB =  (AB + BD) / 5

⇒ 3/2 = (3 + BD) / 5

⇒ 3×5 / 2 = 3 + BD

⇒ 15/2 = 3 + BD

⇒ 15/2 - 3 = BD

⇒ BD = 9 / 2

⇒ BD = 4.5

Thus, The length of AD = 3 + 4.5

                                    = 7.5

Therefore, The length of AD will be 7.5.

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The cube root of -2i,

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

We can represent -2i in polar form as,

r(cosθ + i sinθ)

by computing its magnitude and angle.

The magnitude of -2i is 2

Since the absolute value of any imaginary number is equal to its magnitude.

To find the angle θ,

We can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case,

The opposite side is -2 and the adjacent side is 0.

Therefore, we have tanθ = -2/0, which is undefined.

However,

We can use the fact that the cube root of a complex number is equal to the cube root of its magnitude times exp(iθ/3) to find the cube root of -2i.

So, the cube root of -2i is equal to the cube root of 2 times exp(iθ/3).

Now, we need to find the value of θ/3. Since θ is undefined,

we will represent it as π/2 + 2πn,

where n is any integer.

So, θ/3 = (π/2 + 2πn)/3 = π/6 + 2πn/3.

Therefore, the cube root of -2i is equal to

⇒  ∛2 [ cos(π/6 + 2πn/3) + i sin(π/6 + 2πn/3) ]

Now put n = 0

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

This is the final form of the cube root of -2i in the required form.

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ANSWER:

Juan went to a toy store to buy his favorite toy on sale that cost 4 dollars, but when he arrived the sale had ended and the price of the toy is 10 dollars. How much money does Juan need to be able to buy his toy without the discount?

The x variable represents the amount Juan needs to buy the toy.

STEP-BY-STEP EXPLANATION:

We have the following equation:

We must represent in the word problem. We do it in the following way:

Juan went to a toy store to buy his favorite toy on sale that cost 4 dollars, but when he arrived the sale had ended and the price of the toy is 10 dollars. How much money does Juan need to be able to buy his toy without the discount?

The x variable represents the amount Juan needs to buy the toy.

We solve for x:

Juan needs a total of 6 dollars

The following percentages are listed below:

In this question we have seven cases of real life situations in which percentages are used. Mathematically speaking, percentages are represented by the following expression:

x = r / r' × 100       (1)

Where:

Now we proceed to determine quantities related to percentages:

2.8 mm as a per cent of 2.24 cm

x = (2.8 mm / 22.4 mm) × 100 %

x = 12.5 %

What per cent of 1.5 m is 60 cm?

x = (60 cm / 150 cm) × 100 %

x = 40 %

What per cent of 2 kg is 125 g?

x = (125 g / 2000 g) × 100

x = 6.25 %

What per cent of R 6 to 40 p?

x = (40 / 600) × 100

x = 6.667 %

What per cent of a day is 10 h?

x = (10 h / 24 h) × 100

x = 41.667 %

What per cent of 7 1 / 3 m in 5 1 / 2 m ?

x = [(11 / 2) / (22 / 3)] × 100 %

x = 75 %

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Answer: B (3,333 yards, 1 foot)

Step-by-step explanation: 10,000 feet / 3yards= 3,333.33 yards

3 feet in every yard so divide 10,000 by 3 and get 3,333.33 yards. since there are 3 feet in every yard the .33 is 1 foot.

899,452 is greater than 756,451

899,452 > 756,451

Given,

899,451

756,451

We need to compare these numbers.

Consider 967543

3 - ones

4 - tens

5 - hundreds

7 - thousands

6 - ten thousands

9 - hundred thousands

Find the highest place value in 899,452.

-  8 hundred thousands

We can read this as eight hundred ninety-nine thousand four hundred fifty-two.

Find the highest place value in 756,451.

- 7 hundred thousands

Seven hundred fifty-six thousand four hundred fifty one

Thus,

899,452 is greater than 756,451

899,452 > 756,451

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Answer:

Not a random variable

Step-by-step explanation:

The last book a person read in City A is not a random variable because it is not a number as there is no numerical description for the outcome of this experiment.

Thus, the last book read by someone in City A is not a random variable.

Answer:

not random

Step-by-step explanation:

Answer:

a=−3

Step-by-step explanation:

a−2+3=−2

Step 1: Simplify both sides of the equation.

a−2+3=−2

a+−2+3=−2

(a)+(−2+3)=−2(Combine Like Terms)

a+1=−2

a+1=−2

Step 2: Subtract 1 from both sides.

a+1−1=−2−1

a=−3