For the function f(x) = 5x - 7 answer the following questions:
1. Is the function increasing or decreasing?
2. What is the y-intercept?
3. What is the slope?
4. What is f(-2)?
5. If f(x) = 0, what is x?

Answer:

10. x ≈ 15,9

11. x ≈ 17,5

Step-by-step explanation:

10. Use the Pythagorean theorem:

\( {x}^{2} = {17}^{2} - {6}^{2} = 289 - 36 = 253\)

\(x > 0\)

\(x = \sqrt{253} ≈15.9\)

11.

\( {x}^{2} = {9}^{2} + {15}^{2} = 81 + 225 = 306\)

\(x > 0\)

\(x = \sqrt{306} ≈17.5\)

Answer:

This is ur ans

Step-by-step explanation:

a.y=5x or x=y/5

b.y=60

y/x=5

y/12=5

y=60

Answer:

\(6\sqrt{2}+3\sqrt{10}\)

Step-by-step explanation:

Use the Distributive Property. Remember that you can multiply the numbers under a square root whether or not they're the same. But you can ONLY add square roots when the square root part is the same.

\(\sqrt{3}(2\sqrt{6}+\sqrt{30})\\= \sqrt{3}(2\sqrt{6})+\sqrt{3}(\sqrt{30})\\=2\sqrt{18}+\sqrt{90}\)

Simplify each square root part:

\(2\sqrt{18}+\sqrt{90}\\=2(3\sqrt{2})+3\sqrt{10}\\=6\sqrt{2}+3\sqrt{10}\)

Since the square root parts are different, you cannot simplify any further.

Answer:

0

Step-by-step explanation:

It is zero,   since -6+6 is bassicly 6-6 which is 0

Answer:

9 months

Step-by-step explanation:

peter is saving 35 dollars per month.  

295=35x

295/35=8.42 which is less than 295

9 is an approximate answer

35*9 equals 315, which is enough to pay 295 and have 20 dollars left over

Main Answer: The probability that a randomly selected passenger has a waiting time greater than 3.25 minutes is 0.59375.

Explaination:

Calculation of the probability:

Since The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 8 minutes.

So, here the probability is

= 0.59375

Hence, The probability that a randomly selected passenger has a waiting time greater than 3.25 minutes is 0.59375

Answer:

3, 9, 15, 21

Step-by-step explanation:

6n-3

n = 1: 6(1) - 3 = 3

n = 2: 6(2) - 3 = 9

n = 3: 6(3) - 3 = 15

n = 4: 6(4) - 3 = 21

Answer:

35 units

Step-by-step explanation:

Perimeter of rectangle ABCD =2(L + W)

L = AD or BC (we only need to calculate one of the two)

W = AB or DC. (we only need to calculate one of the two).

Distance between A(-2, 6) and D(-8, -4):

\( AD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( A(-2, 6) = (x_1, y_1) \)

\( D(-8, -4) = (x_2, y_2) \)

\( AD = \sqrt{(-8 -(-2))^2 + (-4 - 6)^2} \)

\( AD = \sqrt{(-6)^2 + (-10)^2} \)

\( AD = \sqrt{36 + 100} = \sqrt{136} \)

\( AD = 11.7 \) (nearest tenth)

Distance between A(-2, 6) and B(3, 3):

\( AD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( A(-2, 6) = (x_1, y_1) \)

\( B(3, 3) = (x_2, y_2) \)

\( AB = \sqrt{(3 -(-2))^2 + (3 - 6)^2} \)

\( AB = \sqrt{(5)^2 + (-3)^2} \)

\( AB = \sqrt{25 + 9} = \sqrt{34} \)

\( AB = 5.8 \) (nearest tenth)

Perimeter of rectangle ABCD =2(AD + AB)

= 2(11.7 + 5.8)

= 2(17.5)

= 35 units

The expression which correctly represents the factored form of the given expression such that the coefficient of the variable is factored is; 3/10 (x - 2).

It follows from the task content that the expression given to be factored such that the coefficient of the variable is factored out is; 3/10 x - 3/5.

Therefore, in a bid to factorise the expression; we must express each term of the expression as follows;

3/10 x - 3/5

= (3/10 × x) - (3/10 × 2)

By factoring out the common factor of each term; we therefore have;

= 3/10 (x - 2)

Ultimately, the expression which correctly represents the factored form of the given expression such that the coefficient of the variable is factored is; 3/10 (x - 2).

Read more on factorisation;

https://brainly.com/question/22048680

#SPJ1

As a result, the borrower can qualify for a loan amount of $476,757.76, expression resulting in a monthly principal and interest payment of $1,587.50, assuming a monthly escrow requirement of $360.

In mathematics, an expression is a grouping of representations, digits, and huge corporations that resemble a clear relationship or regimen. An expression can be a real number, a transitory, or a combination of the two. Addition, subtraction, pervasiveness, division, and exponentiation are examples of mathematical operators. Expressions are common in arithmetic, mathematics, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

To solve this problem, we must use the loan program's single ratio, which is 45%. This is the maximum debt-to-income (DTI) ratio a borrower can have in order to qualify for the loan.

$65,000 divided by 12 months equals $5,416.67 per month

$5,416.67 divided by 45% equals $2,437.50 per month

$2,437.50 minus $360 equals $2,077.50 per month

$2,077.50 minus $490 equals $1,587.50 per month

This means that the borrower can afford a $1,587.50 monthly principal and interest payment.

Loan amount = (Monthly payment) / (Monthly interest rate)

The loan amount is ($1,587.50) divided by the loan term (0.00333)

The loan amount is $476,757.76.

As a result, the borrower can qualify for a loan amount of $476,757.76, resulting in a monthly principal and interest payment of $1,587.50, assuming a monthly escrow requirement of $360.

To know more about expression visit :-

https://brainly.com/question/14083225

#SPJ1

Answer:

n = 3

Step-by-step explanation:

1) Divide both sides by 3.5

n = 10.5/3.5

2) Simplify 10.5/3.5 to 3

n = 3

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

For more such question on function. visit :

https://brainly.com/question/11624077

#SPJ8

Answer:

D

Step-by-step explanation:

Answer:

10+12x

Step-by-step explanation:

9−4x+2x+8x+1+6x

(9+1)+(−4x+2x+8x+6x)

10+12x

There is a 65.54% probability that the average age of those doctors is under 48.8 years.

Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.

It is written as a number between 0 and 1, or between 0% and 100% when represented as a percentage.

The possibility of an event occurring increases as it gets higher.

True mean = mean (or average)+/- Z*SD/sqrt (sample population)

Then,

Mean (average) = 48.0 years

The true mean must be less than 48.8 years.

SD = 6.0 years, and

Sample size (n) = 9 doctors

Using Z as the formula's subject:

Z= (True mean - mean)/(SD/sqrt (n))

Inserting values:

Z=(48.8-48.0)/(6.0/sqrt (9)) = 0.4

From the table of normal distribution probabilities:

At Z= 0.4, P(x<0.4) = 0.6554 0r 65.54%

Therefore, there is a 65.54% probability that the average age of those doctors is under 48.8 years.

Know more about probability here:

https://brainly.com/question/24756209

#SPJ1

Complete question:

The average age of doctors in a certain hospital is 48.0 years old. suppose the distribution of ages is normal and has a standard deviation of 6.0 years. if 9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 48.8 years. assume that the variable is normally distributed.

Answer:

1/27 if that's what u want

Step-by-step explanation:

How to solve your problem

3

6

3

1

0

⋅

3

1

\frac{3^{6}}{3^{10}} \cdot 3^{1}

31036​⋅31

Solve

1

Evaluate the exponent

3

6

3

1

0

⋅

3

1

\frac{{\color{#c92786}{3^{6}}}}{3^{10}} \cdot 3^{1}

31036​⋅31

7

2

9

3

1

0

⋅

3

1

\frac{{\color{#c92786}{729}}}{3^{10}} \cdot 3^{1}

310729​⋅31

2

Evaluate the exponent

7

2

9

3

1

0

⋅

3

1

\frac{729}{{\color{#c92786}{3^{10}}}} \cdot 3^{1}

310729​⋅31

7

2

9

5

9

0

4

9

⋅

3

1

\frac{729}{{\color{#c92786}{59049}}} \cdot 3^{1}

59049729​⋅31

3

Divide the numbers

7

2

9

5

9

0

4

9

⋅

3

1

{\color{#c92786}{\frac{729}{59049}}} \cdot 3^{1}

59049729​⋅31

1

8

1

⋅

3

Answer:

a. 49 + 0.89c

b. $400

Step-by-step explanation:

Given

Delivery = $49

Cost per Centrepiece = $0.89

Solving (a): Expression that represents the equation.

From the question, we have that the number of centrepiece is represented by c

The expression can be gotten by the following formula.

Cost of Delivery + Cost per centrepiece * Number of centrepieces

This gives

49 + 0.89 * c

49 + 0.89c

Hence, the expression that represents the scenario is 49 + 0.89c

Solving (b): Payment for 400 centrepieces

To solve this, we simply substitute 400 for c in the expression in (a)

This gives:

Payment = 49 + 0.89 * 400

Payment = 49 + 356

Payment = 405

Hence, Mrs. Thompson will pay $405 for 400 centerpieces

The approximate area to the left of z= 2​ is 0.978

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

The left of z= 2​

The area to the left of z is calculated by calculating the probability that the z-score is less than 2

In other words, this is represented as

Area = (z < 2)

This can then be calculated using a statistical calculator or a table of z-scores,

Using a statistical calculator, we have the area to be

Area =  0.97725

When this value is approximated, we have the approximated area to ve

Area =  0.978

Hence, the area is 0.978

Read mroe about z-scores at

brainly.com/question/25638875

#SPJ1

Answer:

275.

Step-by-step explanation:

Answer:

35.64

Step-by-step explanation:

solution,

36% × 99

= 36 × 99

100

= 3564

100

=35.64

Answer:

= 4 0

Step-by-step explanation:

/ 1 0 + 8 =1 2

/1 0+ 8 − 8 = 1 2 − 8

SIMPLIFY

1 0 = 4

Multiply all terms by the same value to eliminate fraction denominators

1 0 = 4

1 0 ⋅ /1 0= 1 0 ⋅ 4

Simplify

n=40

Answer:

7

Step-by-step explanation:

subtracting a negative is the same as just adding the number, so five minus negative seven is just five plus seven

We are to obtain the radius of a circle with a radius 7mm.

The area;

So, substituting r = 7mm, we have;

Answer:

9 years

Step-by-step explanation:

Based on the result shown in the table below, a statement which is true include the following: A. exactly 1/5 of the students chose pizza as their favorite food.

In Mathematics, a fraction simply refers to a numerical quantity which is not expressed as a whole number. In order to determine the true statement, we would evaluate them as follows;

"Exactly 1/5 of the students chose pizza as their favorite food."

Total number of students that chose pizza = 6 + 4

Total number of students that chose pizza = 10 students.

Total number of students = 26 + 24

Total number of students = 50 students.

Therefore, the fraction of students that chose pizza as their favorite food is given by:

Fraction = 10/50

Fraction = 1/5.

Read more on fraction here: brainly.com/question/2194108

#SPJ1

Complete Question:

Two classes were asked what was their favorite food at a local restaurant. The results are shown in the table below.

Which statement is true?

Exactly 1/5 of the students chose pizza as their favorite food.

Less than 25% of students chose tacos as their favorite food.

More students prefer French fries than prefer tacos.

Exactly 1/2 of students prefer either pizza or hamburgers.

Answer:

The number can be expressed in multiple forms

Fraction form \(x=\frac{2962}{67}\)  or decimal form  \(x=44.21\)

Step-by-step explanation:

Lets break the problem down

"times" is multiplication *

The difference between 2 numbers is subtraction  \((x-y)\)

A number plus a number is addition \(x+y\)

\(68(x-45)=x+-98\)

Lets solve for \(x\).

Lets start on the left side.

Distribute 68 to the terms inside the parenthesis.

\(68x-3060=x+-98\)

A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign.

\(68x-3060=x-98\)

Subtract \(x\) from both sides of the equation.

\(68x-3060-x=-98\)

Subtract \(x\) from \(68x\).

\(67x-3060=-98\)

Add 3060 to both sides of the equation.

\(67x=2962\)

Divide both sides of the equation by 67.

\(x=\frac{2962}{67}\) or as a decimal \(x=44.21\)

Answer:

Either way, whether that's 3 and 4, 3, 4, or 34, the product will still be bigger than 12.

Step-by-step explanation:

The only thing that would lessen 12 would be if it were multiplied by a negative number.

The values of the variables are;

x = 7

y = -9

From the information given, we have that;

5x−y=44

−3x−y=−12

Using the elimination method of solving simultaneous equations

Subtract equation (2) from equation (1), we get;

5x - y - (-3x - y) = 44 - (-12)

Now, expand the bracket

5x - y+ 3x + y = 56

collect the like terms

5x + 3x = 56

add the terms

8x = 56

Make 'x' the subject of formula

x= 7

Now, substitute the value of x in equation (2)

-3x - y = -12

-3(7) - y = -12

expand the bracket

-21 - y= - 12

collect like terms

-y = 9

y = -9

Learn about simultaneous equation at: https://brainly.com/question/16863577

#SPJ1

The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even. so the correct option is D.

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of a/b  

where a and b are integers.

Irrational numbers are those real numbers which are not rational numbers.

Here, Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

A composite number is a number divisible by another number than 1 and the number itself.

To find example, a sum of two composite numbers, which is not a composite number, is needed.

The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even.

Hence so the correct option is D.

Learn more about composite number;

https://brainly.com/question/19312484

#SPJ1