The graph of a quadratic function with vertex (0, -2)
Write the range and domain using interval notation

Answer:

[tex]x=-\frac{43}{3}[/tex]

Step-by-step explanation:

[tex]-4(6x+7)=-316 \\ \\ 6x+7=-79 \\ \\ 6x=-86 \\ \\ x=-\frac{43}{3}[/tex]

Answer:

x=12

Step-by-step explanation:

hope this helps! -4(6x + 7) = -316=x=12

Step-by-step explanation:

this is a college question ????

and you don't know how to do it ? what happened to you in elementary school ?

there are many different techniques. everybody thinks theirs is the fastest or easiest to understand.

after all, this is just "playing" with numbers, the factors embedded within the dividend.

this is mine. when I was in elementary school, we called this the "long division" :

62.79 ÷ 23 =

we pick the first few positions from the left of the dividend, where we are sure, the divisor fits at least once.

in our case here : 62.

we do an integer divide of 62/23 = 2 (for 3 the dividend would have to be at least 69). this 2 is our first digit of the quotient.

62.79 ÷ 23 = 2

now we multiply the divisor by that digit and subtract the result from the dividend. this gives us a remainder of 16, and we pull down the next position (7) :

62.79 ÷ 23 = 2

- 46

---------

167

now, we pulled the first digit after the decimal point, and we need to set the decimal point there in our quotient :

62.79 ÷ 23 = 2.

- 46

---------

167

now, we repeat the process by integer dividing this new dividend (167) by the divisor (23)

167/23 = 7

this 7 becomes the next digit in our quotient. and we repeat the process of multiplying this by the divisor and subtracting the result from the dividend. this gives us a remainder (6), and we pull down the next digit (9).

62.79 ÷ 23 = 2.7

- 46

---------

167

- 161

----------

69

and again, we repeat by integer dividing the new dividend (69) by the divisor (23)

69/23 = 3

this 3 is the next digit in our quotient.

we multiply it with the divisor and subtract the result from the dividend.

if the remainder is still not 0, we need to repeat the process by pulling the next digit, which would be an invisible 0. and continue.

but luckily, after this the remainder is 0, and we are finished.

62.79 ÷ 23 = 2.73

- 46

---------

167

- 161

----------

69

- 69

--------------

0

so, 62.79 ÷ 23 = 2.73 and 0 remainder.

Answer:2nd down on the first one and 3rd one down on the second question

Each  player will get 9 cards.

According to our question-

total people= 6

cards=52

52/6= 8.66

rounding off

=9

hence, each  player will get 9 cards.

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Answer: 1/8, Division equation: 1/3 divided by 8/3

Step-by-step explanation:

Step 1: Write this problem as an equation, of means multiply so the equation is 1/3 x 3/8.

Step 2: Solve the equation by multiplying the numerators and the denominators. You get 3/24.

Step 3: Simplify by dividing the numerator and denominator by their gcf. In this case it is 3. So, 1/3 of 3/8 is 1/8.

Step 4: Now we need to get the division equation of 1/3 x 3/8, for this you do the same thing as if we had to actually solve the division equation with fraction, just for changing multiplication to division instead. I am talking about keep change flip. You keep the first fraction the same. you change the operation to it's opposite ,and you flip the numerator and denominator in the second fraction. When we do this we get our division equation of 1/3 divided by 8/3.

The   proceeds  is  $7,566.67 and  the effective rate charged by the bank to the nearest is 6.87%.

Given data:

Principal = $8,000

Rate =6 1/2% or 6.5%

Term= 300 Days

a. Proceeds

Interest  = Principal  x Rate  x Time

Interest  = $8,000 x 6.50% x 300/360

Interest = $8,000 x 0.065 x 0.8333

Interest  = $433.33

Now let find the Proceeds:

Proceeds = $8,000 - 433.33

Proceeds = $7,566.67

b. Effective Interest Rate:

Effective Interest Rate = 433.33 / 7566.67 x 300/360

Effective Interest Rate = 433.33 / 6305.56

Effective Interest Rate = 0.0687 × 100

Effective Interest Rate = 6.87%

Therefore  $7,566.67 is the proceeds and 6.87% is the interest rate.

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Answer: Yellow Greed

Step-by-step explanation: Maths

The number is defined by the two inequalities:

x > -3

x  ≤ -6

If we define x as the number, the number increased by 3 is written as:

x + 3

If this is greater than zero or less than or equal to negative three, we can write two inequalities:

x + 3 > 0

x + 3 ≤ -3

Solving both inequalities for x (isolting it) we will get:

x > 0 - 3

x > -3

and:

x  ≤ -3 - 3

x  ≤ -6

So we have the two inequalities that define the number:

x > -3

x  ≤ -6

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Answer:

Step-by-step explanation:

The question about how many people ONLY had a drink is asking to solve some simultaneous equations .   Know this?

People = 92

soup = SP = 33

sandwich = SW = 45

drink = D = 52

9(SP+SW+D)

5(SP+SW)

10(SW+D)

5(SP+D)

for a drink 9+10+5 people had a drink with something else

24 had a drink with something else so 52-24=28 only had a drink

28 people only had a drink

The height of the arrow at 2.5 seconds is 71 feet.

Given:

An arrow released from a bow, traveling towards a target 200 yards away,reaches a max height of 42.6 ft in only 1.5 seconds.

1.5 seconds = 42.6 feet

divide by 1.5 on both sides.

1 sec = 28.4 feet

0.5 sec = 28.4/2

0.5 sec = 14.2 feet

2.5 sec = 1.5 sec + 1 sec

= 42.6 + 28.4

= 71 feet

Therefore The height of the arrow at 2.5 seconds is 71 feet.

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The rate change is $1.50 per miles

The one time pickup fee of every ride = $3.50

The rate charges for every miles traveled = $1.50

Consider the number of miles traveled = x

Then the equation will be

y = 1.50x + 3.50

Where y is the total cost

x is the number of miles traveled

The slope intercept from is

y = mx + b

Where m is the slope of the line

b is the y intercept

Comparing the slope intercept form the given equation

y intercept of the line b = $3.50

Slope of the line m = $1.50 per mile

Hence, the rate change is $1.50 per miles

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(a) The common ratio R is 3/10.

What do you mean by Geometric progression?

Every following word in a sequence known as a geometric progression (GP) is created by multiplying every previous term by a constant amount, or "common ratio." Another name for this progression is a pattern-following geometric sequence of numbers.

To find out the common ratio we have to divide the second term by the first term,

in the given example to find out the common ratio we have to divide [tex]P_{2[/tex] by  [tex]P_{1}[/tex],

so, we are getting, common ratio(R)= 9/30

                                                          =  3/10

Hence,The common ratio(R) is 3/10.

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Answer:

$247,517

Step-by-step explanation:

Hello,

Assets

(Car Value) $29,850

(Savings Account Balance) $12,409

(Treasury Bonds) $10,000

(Checking Account Balance) $19,419

(Home Value) $194,450

29850+12409+10000+19419+194450 = 266128

Liabilities

(Car Loan) $10,560

(Student Loans) $13,824 since the students loans are payed of we don't include it into the final net worth.

(Credit Card Balance) $8,051

10560+8051=18611

assets - liabilities = net worth

266128 - 18611 = 247517

So, if the banker pays off the students loans of a credit union banker their net worth will be $247,517.

a) Probability that the number of college students who say they use credit cards because of the rewards program is​ exactly​ two is;

P(X = 2) = 0.1419

b) Probability that the number of college students who say they use credit cards because of the rewards program is​ more than two is;

P(X > 2) = 0.9402

c) Probability that the number of college students who say they use credit cards because of the rewards program is​ between two and five inclusive is; P(2 ≤ X ≤ 5) = 0.8054

The formula for Binomial Probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

p is probability of success

n is number of trials

x = the number of expected successful outcomes

We are given;

p = 38% = 0.38

n = 10

Thus;

a) Probability that the number of college students who say they use credit cards because of the rewards program is​ exactly​ two is;

P(X = 2) = 10C2 * 0.38^(2) * (1 - 0.38)^(10 - 2)

P(X = 2) = 0.1419

b) Probability that the number of college students who say they use credit cards because of the rewards program is​ more than two is;

P(X > 2) = 1 - P(X ≤ 2)

P(X > 2) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

P(X > 2) = 0.9402

c) Probability that the number of college students who say they use credit cards because of the rewards program is​ between two and five inclusive is;

P(2 ≤ X ≤ 5) =  [P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)]

P(2 ≤ X ≤ 5) = 0.8054

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Answer:

3) m= 3/310

4) x > -1

6) 1:a)-4

2:b)-2

3:c)2

4:d)4

7) f(-4.2)=46.06

Step-by-step explanation:

hope this helps

Answer: The ratio of the total number of marbles in Orlandria’s marble collection is 7:28, where 7 is the yellow marbles and 28 is the total number of marbles Orlandria has.

Answer:

if you mean 0.14 + 3.5 the answer is 3.64

Step-by-step explanation:

Line the numbers and decimal point when adding

Answer:

It can send 2,666 kids to school for a year.

Examining the rainfall data for the two periods a conclusion is that the range of the values are period 1 has low variability while period 2 has high variability

period 1: 0.6

period 2: 4

The range in statistics refers to the distribution of data between the lowest and greatest value in the distribution. It is a widely used indicator of variation.

Measurements of variability provide you with descriptive statistics for summarizing your data set in addition to measures of central tendency.

By deducting the lowest value from the greatest value, the range is computed. A short range indicates low variability in a distribution, whereas a big range denotes significant variability.

The range is

period 1: 2.5 - 1.9 = 0.6

period 2: 4.7 - 0.7 = 4

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The growth formula for the given population is P = 182eⁿˣ and the population in 2004 is 186.98 million

Growth function:

Basically, the growth function means the pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Given,

A country's population in 1994 was 182 million. In 2002 it was 186 million.

Here we need to find the growth formula and the population in 2004.

According to the given problem, let us consider that the

final population P,

the starting population A, and

the time passed t.

Here we need to determine the value of the growth factor k.

And it can be calculated using the information for the years 1994 and 2002.

Here we know that, A will be 182 million (the population in 1994), P will be 186 million (the population in 2002), and t will be 8 years (the number of years between 1994 and 2002):

⇒186 = 182eⁿˣ⁸

⇒186/182 = e⁸ⁿ

Now, by applying ln to both sides of the equation:

⇒ln(186/182) = ln(e⁸ⁿ)

Using the laws of logarithms:

=> 8n = ln(186) - ln(182)

=> n = [ln(186) - ln(182)] / 8

=> n = 0.0027

Now, let's use this information to determine P in 2004.

Here the value of A will still be 182 million, but t will be 10 years.

Now, we have to apply these values then we get,

=> P = 182e⁰°⁰⁰²⁷ˣ¹⁰

=> P = 182e⁰°⁰²⁷

=> P = 182 x 1.0273

=> P = 186.98

Therefore, there are  186.98 million in 2004.

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The length and width of the rectangle is 31 inches and 7 inches.

Given:

The length of a rectangle is 10 inches more than 3 times the width and the area is 217 square inches.

Let l and w be the length and breadth.

l = 10 + 3w

lw = 217

w = 217/l

l = 10 + 3(217/l)

l = 10 l + 651 / l

[tex]l^{2} -10l -651=0[/tex]

on solving

l = 31 inches

lw = 217

w = 217/31

w = 7 inches.

Therefore the length and width of the rectangle is 31 inches and 7 inches.

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The amount engine oil which should be added to a jerry can that contains 4.3 gallons of​ gas is 0.172 gallons.

Given that arborist is preparing the fuel mix for her chainsaw before climbing a tree to remove a dead limb when two-stroke chainsaw requires a 4​% mix of engine oil to gas and the amount of oil should be 4​% of the amount of gas.

We want to find the amount of engine oil which should be added to a jerry can that contains 4.3 gallons of​ gas.

To find the amount of engine oil convert the mixture of engine oil to gas into decimal.

4%=4/100

4%=0.04

Now, we will multiply the above mixture with 4.3 gallons of gas is

4.3×0.04=0.172 gallons

Hence, the amount of engine oil which should be added to a jerry can that contains 4.3 gallons of​ gas when two-stroke chainsaw requires a 4​% mix of engine oil to gas is 0.172 gallons.

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The values of f(2) = 0 & f(3) = 2.

Here given that,

f(0) = f(1) = 1

f(n+1) = (n)/(n-1)

We have to solve the equation if n = 1:

putting the value of n = 1 in the given equation f(n+1) = (n)/(n-1)

= f(1+1) = 1/(1-1)

= f(2) = 0

In the same way we have to solve the equation if n = 2:

putting the value of n = 2 in the given equation f(n+1) = (n)/(n-1)

= f(2+1) = 2/(2-1)

= f(3) = 2/1

= f(3) = 2

Hence the answer is the values of f(2) = 0 & f(3) = 2.

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The result of adding the two given equations (-2x + 7y = -5 and -2x - 4y = 6) is -4x + 3y = 1

From the question, we are to determine the result of adding the two given equations.

The given equations are

-2x + 7y = -5 and -2x - 4y = 6

Now, we will add the equations

    -2x + 7y = -5

+ ( -2x - 4y = 6

------------------------------

-2x + (-2x) + 7y + (-4y) = -5 + 6

-2x - 2x + 7y - 4y = 1

Simplifying

-4x + 3y = 1

Hence, the result of adding the equations is -4x + 3y = 1

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by converting the decimal number 0.65 to the simples fraction, the result will be 13 / 20

The given decimal number = 0.65

The decimal number consist of a whole number part and fractional part. The whole number and the fractional part are separated by a decimal point.

Multiply the given decimal number by 100/100

Then the result will be

0.65 × (100/100) = (0.65×100) / 100

Multiply the numerator terms

(0.65×100) / 100 = 65 / 100

Divide both numerator and denominator by 5

Then the expression will be

(65/5) / (100/5) = 13 / 20

Hence, by converting the decimal number 0.65 to the simples fraction, the result will be 13 / 20

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The derivative of the given function is 4x³ / (x²+1) ²

What is derivative mean?

d(u/v) = [ u(dv/dx) + v(du/dx) ] / v²

Given:

f(x) = x²/x²+1

Applying the formulae:

=  x²[ d(x²+1)/dx] + (x²+1) [ d(x²)/dx ] / (x²+1) ²

= x²(2x+0) + (x²+1)2x / (x²+1) ²

= 2x³ + 2x³ / (x²+1) ²

= 4x³ / (x²+1)²

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Answer:

  (a)  The graph has a domain of all real numbers.

  (d)  The graph has a y-intercept of (0, 1).

  (e)  The graph has an x-intercept of (-7, 0).

Step-by-step explanation:

You want to know the correct descriptors of the domain, range, slope, and intercepts of the graph of y = ∛(x-1) +2.

The domain of the cube root function is all real numbers. Hence the graph has a domain of all real numbers.

The range of the cube root function is all real numbers. Hence the graph is not restricted to a range of y ≥ 1.

The slope of the cube root function is positive everywhere. The graph of y is increasing as x is increasing.

The x-intercept is the value of x that makes y = 0.

  0 = ∛(x -1) +2

  -2 = ∛(x -1)

  -8 = (x -1)

  -7 = x . . . . . . . the x-intercept

The y-intercept is the value of y when x = 0.

  y = ∛(0 -1) +2

  y = -1 +2 = 1 . . . . . . the y-intercept

The true statements about the graph are ...

  (a)  The graph has a domain of all real numbers.

  (d)  The graph has a y-intercept of (0, 1).

  (e)  The graph has an x-intercept of (-7, 0).

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The probability of the event E i.e an odd number less than 9 is 0.4.

The probability of an event is a ratio of number of favorable outcomes to total number of outcomes. The sum of all probabilities of events must be equal to one. The probability of an event must not be greater than 1.

In event E i.e an odd number less than 9, the number of favorable outcome is 4 i.e. {1,3,5,7}.

The total number of outcomes is whole set S i.e. 10.

So, the probability of event E will be,

P(E) [tex]=\frac{4}{10}[/tex]

=0.4

Therefore, the probability of the event E i.e an odd number less than 9 is 0.4.

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