Type the correct answer in each box. Use numerals instead of words.

This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

The answer to the inequality is expressed as x< 1 and x< -4

Inequalities are mathematical expressions having both sides unequal or rather not equivalent to each other.

Given the inequality;

4x (x+3) < -24

First, expand the bracket

4x² + 12x < -  24

Let's turn to quadratic inequality

4x² + 12x - 24 < 0

Factorize further

4 ( x² + 3x - 4) < 0

4 ( x² + 4x - x - 4) < 0

4 ( x(x + 4) - 1 (x + 4) ) < 0

4(x - 1) ( x + 4) < 0

expand the bracket

4x - 4 < 0

x < 1

And

4x + 16 < 0

x < -4

Thus, the answer to the inequality is expressed as x< 1 and x< -4

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The ratio of the patterned circles to plain circles is 6 : 7.

We are given the four arrays of the circles.

In the first array, we have only 1 plain circle.

In the second array, we have 4 patterned circles and 1 plain circle.

In the third array, we have 1 patterned circle and 4 plain circles.

In the fourth array, we have only 1 plain circle.

So, total patterned circles = 5 + 1

Total patterned circles = 6

Total plain circles = 1 + 1 + 4 + 1

Total plain circles = 7

Ratio of patterned circles to plain circles will be given as:

6 : 7

Therefore, we get that, ratio of the patterned circles to plain circles is 6 : 7.

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Answer:

pic 1 goes first second pic second slot

Step-by-step explanation:

Answer:

32 or +-8 depending on question

Step-by-step explanation:

If question is 2x = 64, then x= 32

If question is x^2 = 64, then x= +-8

Answer: 27/45

Step-by-step explanation:

[tex]\displaystyle\\\frac{3}{5} =\\\\\frac{3}{5}*1=\\\\ \frac{3}{5}*\frac{9}{9} =\\\\\frac{3*9}{5*9}= \\\\\frac{27}{45}[/tex]

Answer:

The graph is provided in the image

Answer:from least to greatest:

1) g (x)

2) f (x)

3) h (x)

Step-by-step explanation:

Answer:

For f (x):

f (x) = (x + 3) ^ 2 - 2

For x = -1

f (-1) = (-1 + 3) ^ 2 - 2

f (-1) = (2) ^ 2 - 2

f (-1) = 4 - 2

f (-1) = 2

For x = 3

f (3) = (3 + 3) ^ 2 - 2

f (3) = (6) ^ 2 - 2

f (3) = 36 - 2

f (3) = 34

AVR = ((34) - (2)) / ((3) - (- 1))

AVR = 8

For g (x):

linear graph with and intercept of negative 3 over 2 and x intercept of 3

y = mx + b

b = -3/2

For me we have:

0 = m (3) - 3/2

3m = 3/2

m = 1/2

The function g (x) is:

g (x) = (1/2) x - 3/2

For x = -1

g (-1) = (1/2) (- 1) - 3/2

g (-1) = -1/2 - 3/2

g (-1) = -4/2

g (-1) = -2

For x = 3

g (3) = (1/2) (3) - 3/2

g (3) = 3/2 - 3/2

g (3) = 0

AVR = ((0) - (- 2)) / ((3) - (- 1))

AVR = 1/2

For h (x):

Using the table we have:

AVR = ((62) - (14)) / ((3) - (- 1))

AVR = 12

Step-by-step explanation:

Number 7:

-8=x-20

-8+20=x

12=x

The product of √6 and √12 is option b 6√2.

Given,

Two square roots : √6 and √12

We have to find the product of these square roots:

That is,

√6 × √12

Multiplying square roots:

So here,

Multiply the numbers,

√6 × √12 = 6 × 12 = 72

Now consider the square root of 72

√72 = √36 × √2 = 6√2

That is, the product of the square roots √6 and √12 is 6√2

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7 students in the class can speak more than one language.

Given that,
Total student = 36
For every four students who could only speak one language
For every five students who could only speak one language.
To determine how many students in the class can speak more than one language.

Since,
For every five students who could only speak one language,
= 36 / 5
quotient = 7 ; remainder = 1

Implies that, 7 students in the class can speak more than one language.

Thus, 7 students in the class can speak more than one language.

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Answer:

A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven

Step-by-step explanation:

Answer:

Theorems and postulates are statements of geometrical truth.

Explanation:

We create theorems based on postulates.

Postulates are the mathematical statements we assume to be true without any proof while theorems are mathematical statements we can or must prove as true.

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

Hope this helps!

Have a great day and God bless! :)

The new percentage of broth to solution 25/60 is 41.67

Broth, also known as bouillon is a savory liquid made of water in which meat, fish or vegetables have been simmered for a short period of time .It can be eaten alone, but it is most commonly used to prepare other dishes, such as soups.

Commercially prepared liquid broths are available, typically chicken, beef, fish, and vegetable varieties. Dehydrated broth in the form of bouillon cubes were commercialized beginning in the early 20th century.

Broths have been used as a nutrition source for the sick in Great Britain since at least the early 1700s, such as for dysentery patients

Let,

60 represents the 100% of the broth to solution

25 represents the x percentage of the broth to solution

Now,

Solving for the 25 which represents the x percentage of the broth to solution.

25/100 = x/100*

25/60 = x/100*x

25(100) = 60x

x = 2500/60

x = 41.67

Therefore,

25 represents the 41.67 percentage of the broth to solution.

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Answer:

a) 25/60=x/100

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

Remember Bedmas/Pedmas

P/B = Bractets or parentheses ( )

E = Exponents 3⁵

D = Division ÷

M = Multiply ×

A = Addition

S = Subtract

(4x1)+6-9x3-6

4+6-(9×3)-6

(4+6)-27-6

(10-27)-6

-17-6

-23

The total number of labels collected by the students in the third month is equal to 525 by the equation 3 x + x = 2100.

Let the number of labels collected in the first two months be 3 x.

We are given that the number of labels collected in the first two months was three times the number of labels collected in the third month.

So, the number of labels collected in the third month = 3 x / 3 = x

Now, we are also given that:

The total number of labels collected by the students at the school = 2100.

So, we get the equation as:

3 x + x = 2100

4 x = 2100

x = 2100 / 4

x = 525 labels.

Therefore, we get that, the total number of labels collected by the students in the third month is equal to 525 by the equation 3 x + x = 2100.

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Answer:

2n² + n

Step-by-step explanation:

Given sequence:

3, 10, 21, 36, ...

Work out the first differences between terms:

[tex]3 \underset{+7}{\longrightarrow} 10 \underset{+11}{\longrightarrow} 21 \underset{+15}{\longrightarrow} 36[/tex]

As the first differences are not the same, work out the second differences.

[tex]7 \underset{+4}{\longrightarrow} 11 \underset{+4}{\longrightarrow} 15[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of n² is always half of the second difference. Therefore, as the second difference is 4, the coefficient of n² is 2.

To work out the nth term of the sequence, write out the numbers in the sequence 2n² and compare with the given sequence:

[tex]\begin{array}{|l|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4 \\\cline{1-5} 2n^2 & 2 & 8 & 18 & 32\\\cline{1-5} \sf Operation & +1 & +2& +3& +4\\\cline{1-5} \sf Sequence & 3 & 10 & 21 & 36\\\cline{1-5}\end{array}[/tex]

Therefore, we need to add n to 2n² to match the sequence.

Therefore, the nth term of this sequence is 2n² + n.

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Answer:

Step-by-step explanation: I'm not sure it's an interesting question I hope you figure it out soon(:  

Answer: x<45.9?

Step-by-step explanation:

25.5+24.3+24.8+23.5=98.1

So (x+98.1)/6<24?

x<45.9?

Answer:

x = -7

Let the first integer be x.

Given the next two integers are consecutive, it would be: x+1, x+2

The problem states: "4 more than the smaller number plus twice the 3rd number is 7 less than the 2nd number."

Translating English to Algebra, you'll get:

(x + 4) + 2(x + 2) + 7 = x + 1

x + 4 + 2x + 4 + 7 = x + 1

3x + 15 = x + 1

2x = -14

x = -7

That would be the third option.

Answer:

14x

Step-by-step explanation:

We just add the bases because they have the same variable terms, (they are like terms)

9 + 5 = 14

14x

Random assignment means participants have an equal chance of being in the control group or in the experimental group.

Assignment refers to putting people into experimental or control group. In this, the Random assignment involves dividing the participants into two groups through randomization. That is, selection is on random. Tis method provides equal chance for the participants to be in the experimental or control group.

This kind of assignment will be unbiased and the participants in two groups does not differ in any way. So random assignment makes the experiment and control group equivalent. Also this makes the experimental study more accurate, acceptable and scientific too.

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Using equations, the solutions for the problems are given as follows:

1. She played 5 games.

2. Gary had 7 rebounds.

3. The width of the rectangle is of 38 inches.

4. Mark had 21 rebounds.

5. Tony spent 45 minutes studying for his Biology test.

6. The length of the rectangle is of 72 inches.

7. He rented the limousine for 6 hours.

8. The two numbers are 11 and 26.

9. Pamela is 8 years old.

10. Debra is 1 year old now.

The situation is modeled by the following linear function:

P(n) = 2.75 + 4.25n.

We have that P(n) = 24, hence we have to solve for n.

24 = 2.75 + 4.25n.

n = (24 - 2.75)/4.25

n = 5.

She played 5 games.

The situation is modeled by the following system of equations:

Hence:

3y + y = 28

4y = 28

y = 7.

Gary had 7 rebounds.

Considering the equations for the perimeter of the triangle, and the situation described, we have that:

Hence:

2(2w - 4 + w) = 220

2(3w - 4) = 220

3w - 4 = 110

3w = 114

w = 114/3

w = 38.

The width of the rectangle is of 38 inches.

Solution x for item 2, hence:

x = 3y = 3 x 7 = 21.

Mark had 21 rebounds.

This situation is modeled by the following equation:

3x + 5 = 140

3x = 135

x = 135/3

x = 45.

Tony spent 45 minutes studying for his Biology test.

This is the solution for l of item 3, hence:

l = 2w - 4 = 2 x 38 - 4 = 72.

The length of the rectangle is of 72 inches.

The situation is modeled by the following equation:

P(x) = 125 + 50x.

We have that P(x) = 425, hence we solve for x as follows:

425 = 125 + 50x

50x = 300

x = 300/50

x = 6.

He rented the limousine for 6 hours.

The situation is modeled by the following system:

Hence:

15 + y + y = 37

2y = 22

y = 11.

x = 15 + 11 = 26.

The two numbers are 11 and 26.

The situation is modeled by the following system:

Hence:

x + 6 = 2(x - 7 + 6)

x + 6 = 2(x - 1)

x + 6 = 2x - 2

x = 8.

Pamela is 8 years old.

This is the solution for y of the previous item, hence:

y = x - 7 = 8 - 7 = 1.

Debra is 1 year old now.

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Answer-

The cost of one tetra is $2.5 and one rainbow fish is $8.5

Explanation

Let the cost one tetra be 'x';

Cost of rainbow fish = x + 6;

According to question;

8x + 2(x + 6) = 37;

10x = 25

x = $2.5;

the amount or equivalent paid or charged for something : price

The average cost of a university training has gone up dramatically.

the outlay or expenditure (as of attempt or sacrifice) made to acquire an item

He executed repute, but at the fee of dropping numerous buddies.

loss or penalty incurred specially in gaining some thing

the price of lives during war

three

costs plural : charges incurred in a judicial process

particularly : those given by the law or the courtroom to the triumphing party in opposition to the dropping birthday party

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The measure of the complement of angle K is (78 - 6x)°. The correct option is D. (78 − 6x)°

From the question, we are to determine the complement of the given angle measure

From the given information, the measure of angle K (m ∠K) is (6x + 12)°

NOTE: If two angles are complementary, the measures of the angles sum up to 90°

Let the complement of angle K be angle L.

Thus,

∠K + ∠L = 90°

(6x + 12)° + ∠L = 90°

6x° + 12° + ∠L = 90°

∠L = 90° - 12° - 6x°

∠L = 78° - 6x°

∠L = (78 - 6x)°

Hence, the measure of the complement of angle K is (78 - 6x)°. The correct option is D. (78 − 6x)°

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in that function x would be -2

The expression for r is n(4t-v) and the expression for the width is (P-2l)/2

This is a way of representing a variable with another variable.

Given the expression below:

r/n + t = 4v

Making r the subject

r/n = 4v - t

r =. n(4t-v)

Hence the expression for r is n(4t-v)

For the expression

P = 2l + 2w

P - 2l = 2w

2w = P - 2l

w = (P-2l)/2

Hence the expression for the width is (P-2l)/2

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Answer:

5

2

8

4

6

1

3

7

Step-by-step explanation:

Using a proportional relationship, it is found that:

The graph for this relationship is given at the end of the answer.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

For this problem, we have that the variables are:

Hence the proportional relationship between these two variables is given by:

y = 2x.

Then:

The linear graph of the relationship, considering the given points, is given at the end of the answer.

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Answer:

Vertex: (-1, 4)

Domain: All Real Numbers

Range: y < or equal to 4

Step-by-step explanation:

Vertex: Using my calculator, i determined the vertex. The vertex is the most bottom/top point of the parabola, depending on if it opens down or up.

Domain: All the answers have all real numbers so its obvious.

Range: the parabola opens down at (-1, 4), so all the numbers on the y axis below 4 fit in with the line