Given the following function, find the coordinates of the vertex of f(x):
f(x)=x²- 2x - 15
A. (1, -16)
B. (-1, -12)
C. (-1, -14)
D. (1, -17)
Ο.Α.
OB
O C
OD.

Answer:

79

Step-by-step explanation:

(8+2)^2 - 7(3)

10^2 - 21

100 - 21

79

The expression is simplified to n = 3/ 25

Algebraic expressions are expressions made up of arithmetic operations such as addition, subtraction, multiplication, division, etc.

They also consist of variables, terms, factors, constants and coefficients.

Given the expression;

\(5( n- \frac{1}{10} ) = \frac{1}{2}\)

expand the bracket

\(5 ( \frac{10n - 1}{10} ) = \frac{1}{10}\)

\(\frac{50n - 5}{10} = \frac{1}{10}\)

cross multiply

10( 50n - 5) = 10

expand the bracket

500n - 50 = 10

collect like terms

500n = 60

Make 'n' the subject

n = 60/ 500

n = 6/ 50

n = 3/ 25

Thus, the expression is simplified to n = 3/ 25

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The equation of a linear function is given by the following general form:

y = mx + b

Where m is the slope of the line and is given by the following formula:

Where (x1, y1) and (x2, y2) are two points of the function. In this case, we can take points (3, 0) and (4, 6) from the table, then we get:

With m = 6 we can rewrite the equation like this:

y = 6x + b

By replacing another point, like (5, 12), we get:

12 = 6(5) + b

12 = 30 + b

12 - 30 = 30 - 30 + b

-18 = b

b = -18

Then, the equation of the linear function can be written like this:

h(x) = 6x - 18

Conditional relative frequency that a customer prefers pepperoni given that the customer is female is 0.318, or approximately 31.8%.

Conditional relative frequency that a customer is male given that he prefers veggies pizza is 0.667, or approximately 66.7%.

The conditional relative frequency that a customer prefers pepperoni given that the customer is female is calculated as follows:

P(pepperoni | female) = P(pepperoni and female) / P(female)

The number of females who prefer pepperoni is 14, so P(pepperoni and female) = 14/90. The total number of females is 44, so P(female) = 44/90.

Therefore,

P(pepperoni | female) = (14/90) / (44/90) = 14/44 = 0.318

The conditional relative frequency that a customer is male given that he prefers veggies pizza is calculated as follows:

P(male | veggies) = P(male and veggies) / P(veggies)

The number of males who prefer veggies pizza is 16, so P(male and veggies) = 16/90.

The total number of customers who prefer veggies pizza is 24, so P(veggies) = 24/90.

Therefore,

P(male | veggies) = (16/90) / (24/90) = 16/24 = 0.667

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Answer:

300kg

Step-by-step explanation:

240(25/100)

240(.25) = 60

25% of 240 = 60, so add that 60 to get an extra 25% for this month

240 + 60 = 300

Answer:  12.6 ft

Step-by-step explanation:

a = 8.8 ft

b = 9 ft

c = ?

Since it is a right triangle, we can use the Pythagorean Theorem to solve for missing side c, the hypotenuse.

a^2 + b^2 = c^2

(8.8)^2 + (9)^2 = c^2

158.44 = c^2

(158.44)^(1/2) = c

12.5873 = c

c = 12.6 ft (rounded to the nearest tenth)

Answer:

enlargement ; 2

Step-by-step explanation:

dilation is change in the size of the figure.

in the given scenario, figure's size is increasing so dilation is called enlargement and scale factor must be greater than 1.

scale factor = dimension of new shape / dimension of original shape

let's calculate the difference in terms of boxes of both figures to calculate the scale factor,

scale factor = 6/3

thus, in the given dilation we have enlargement of 2

Answer:

729

Step-by-step explanation:

27^2 =

Answer:

A

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Each time you divide or multiply by a negative number, you must change the direction of the inequality symbol.

If Mirka is 5 years old, her parents start to give her pocket money of 50p per week , then the amount of pocket money does Mirka get in the first year is £26 .

the amount that Mirka gets per week is = 50p ;

Age of Mirka is = 5 years ;

When Mirka is 5 years old, she starts to receive 50p per week in pocket money. On her birthday, her parents increase her pocket money by 50p.

that means ;

So, for the first year, the pocket money will be 50p per week for 52 weeks (1 year),

Pocket money in the first year = 50p × 52 weeks = £26 .

Therefore , Mirka will get £26 in the first year of her birthday .

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The statement " An interval estimate is a range of values within which the actual value of the population parameter, such as μ, may fall" is true.

An interval estimate is a range of values within which the actual value of the population parameter, such as μ, may fall with a certain degree of confidence. The interval estimate is based on sample data and statistical methods, and it provides a measure of the uncertainty associated with the estimate of the population parameter.

Interval estimates are important in statistics because it is often not possible to determine the true population parameter with absolute certainty. Instead, statistical inference provides us with a range of plausible values for the parameter based on the data that has been collected. This range of plausible values is called a confidence interval.

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Simplify/Multipy/Find the product: −80x^5y^2z − 10x^3y^2z

The number of different ways of distributing the scholarships is 32,760.


consider the situation: fifteen students are competing for 4 Rotary scholarships.
consider each scholarship  is to be a position In which a student assigned.
This is a permutation problem as:
   

A) each student selected from the same set.  
b) No students can be selected twice.
c) The order in which students are assigned to three scholarships.  

Four students  are assigned in 4 activities For scholarships.

Activity A1: select a student from the set of 15 students for giving away the first scholarship.

Activity A2: select a student from remaining 14 students for giving away the second scholarship.

Activity A3: select a  student from remaining 13 students for giving away the third scholarship.

Activity A4: Select a student from remaining 12 students for giving away the forth scholarship.

According to multiplication rule of accounting the number of different arrangements is  A1 X A2 X A3 X A4  
15 X 14 X 13 X 12=32760  

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Answer:

128

Step-by-step explanation:

couculator mhm thats all

Answer:

\(160cm^{2}\)

Step-by-step explanation:

Surface Area = \(2(wl+hl+hw)\)

w = 4

l = 8

h = 4

\(2((4*8)+(4*8)+(4*4))\)

\(2(32+32+16)\)

\(A = 160\)

Answer:

C, D, F

Step-by-step explanation:

She walked 12 miles. Then she walked 1/4 that distance. "That distance" is 12 miles.

That means she walked 12 miles plus 1/4 of 12 miles.

She walked

12 + 1/4 * 12

You can factor out 12 from the expression above, and write it as

12(1 + 1/4)

Now you can do the addition in parentheses.

12(1 + 1/4) = 12(4/4 + 1/4) = 12(5/4)

Answer:

C, D, F

Answer:

12 + 1/4 x 12, 12 x 5/4, and 12 (1 + 1/4)

Step-by-step explanation:

To solve this, you need to add 1/4 of 12 to 12. 1/4 of 12 is 3, and 12 + 3 is 15. All of these equations are equal to 15, therefore they are all correct.

1/4 x 12 = 3 + 12 = 15

12 x 5/4 = 60/4 = 15

1 + 1/4 = 5/4

5/4 x 12 = 60/4 = 15

The required 1st term and third term in the given expressions are   -3x and  -12pqr

Expressions are mathematical equations separated by signs.

For instance, a + b + c is an expression having three terms

First-term is a

Second term is "b"

Third term is "c"

Given the expression -3x + 7, we are to identify the first term. Based on the explanation above, the first term will  be  - 3x

For the expression 9pq - 3pr - 12pqr​, the third term from this equation will be -12pqr

Hence the required 1st term and third term in the given expressions are   -3x and  -12pqr

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Here is the answer :

people who like both the songs is 35 and

people who like only folk songs is 100.

MathPapa Algebra Calculator is an online tool that allows users to solve algebraic equations step-by-step. The calculator can handle a wide range of algebraic expressions, including equations, inequalities, and systems of equations. The tool simplifies expressions, solves equations, and graphically represents solutions to problems.

Users can enter algebraic equations directly into the calculator, and the software automatically breaks the equation down into individual steps. MathPapa Algebra Calculator can help users better understand the underlying concepts behind algebraic equations by showing them how to solve problems using logical steps.

In addition, the calculator has an extensive library of tutorials and video lessons that explain various algebraic concepts, including solving equations, factoring, graphing, and more.

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Answer:

QUESTION 1:  (-3,0), (1,1), (5, 2), (9,3)

QUESTION 2: Draw a mapping diagram (see question 3)

QUESTION 3: Yes, the image below is a function.

Step-by-step explanation:

For question 1, you can pair the domains (x-values) with any y-value. The y-values can repeat.

For question 3b, you must understand that domains cannot repeat, but ranges (y-values can). In 3b, every x-value has a unique y-value which means that it is a function. You can also determine is something is a function by seeing if its graph passes the vertical line test.

Yes

As per definition

Every domain of the function has an unique range

Here

Hence it's a function

The expression "4(3.2 + n) = n - 1" accurately represents the given word sentence "Four times the sum of 3.2 and a number is the number less 1."

The expression that represents the given word sentence "Four times the sum of 3.2 and a number is the number less 1" is "4(3.2 + n) = n - 1". Let's break down the sentence and analyze it step by step to understand how this expression is derived.

The sentence states "Four times the sum of 3.2 and a number." In mathematical terms, this can be represented as "4 * (3.2 + n)". Here, "n" represents the unknown number we are referring to.

The sentence further states "is the number less 1." Mathematically, "the number less 1" can be expressed as "n - 1". Therefore, we combine the two expressions to form the equation "4(3.2 + n) = n - 1".

To understand why this equation represents the given sentence, let's evaluate it using an example. Let's assume the unknown number "n" is 5.

When we substitute 5 for "n" in the equation, we have:

4(3.2 + 5) = 5 - 1

4(8.2) = 4

Simplifying further:

32.8 = 4

As we can see, the equation holds true in this case. The left side of the equation represents "Four times the sum of 3.2 and a number," which is 32.8. The right side of the equation represents "the number less 1," which is 4.

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Answer:

There is no picture

Step-by-step explanation:

Answer:

option D is correct

x=O and x=-8

Answer:

Hope this helps!!

Step-by-step explanation:

Notice that:

Therefore, the given equation is factored as follows:

The solutions of the above equation are x=-7 and x=3.

Answer:

Answer:

4:3

Step-by-step explanation:

16:12=8:6=4:3

Answer:

4:3

Step-by-step explanation:

16 and 12 can both be divided by 4

16/4 = 4 12/4 = 3

so your simplified ratio is 4:3

The error that Bobby most likely made in verifying if the relation is a function is given as follows:

C. Bobby drew the incorrect arrow diagram. The correct arrow diagram of the relation is a function. Bobby's arrow diagram is not a function.

A relation represents a function if each value of the input is mapped to only one value of the output.

The ordered pairs from this data-set are given as follows:

(​4,​5), ​(​9,​15), ​(14​,​22), ​and (​18,​37).

The input and the output for the pairs are given as follows:

Each value of the input is mapped to only one value of output, hence the relation represents a function.

However, Bobby made a mistake, in mapping the point (9, 15), as he mapped an input of 14 to an output of 9, and thus it would not represent a function. Hence the correct statement is given by option C.

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Answer:

Since all triangle angles sum to 180 then we can say

2x + 3x + 7x = 180

12x = 180

x = 15

There fore the angles are

2 * 15 3 * 15 and 7 * 15 or

30 45 and 105

Those 3 total 180 degrees

Step-by-step explanation: