The graph of the function f(x) = (x - 3)(x + 1) is shown.
Which describes all of the values for which the graph is
positive and decreasing?

Answer:

1

Step-by-step explanation:

It would be 1 because it is the least number there

we can alsoways find the slope by simply using two points off the table, bearing in mind  that slope goes by different names

rate of change

average rate of change

delta difference

rise over run

however is the same cat disguised in different costumes.

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} time&distance\\ \cline{1-2} 15&2\\ 30&4\\ 45&5\\ 60&6\\ \cline{1-2} \end{array} \begin{array}{llll} \\[1em] \leftarrow \\\\ \leftarrow \end{array}\qquad \qquad (\stackrel{x_1}{30}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{60}~,~\stackrel{y_2}{6})[/tex]

[tex]\bf \stackrel{\textit{\large average rate of change}}{\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{60}-\underset{x_1}{30}}}\implies \cfrac{2}{30}\implies \cfrac{1}{15}}[/tex]

Answer:r

Step-by-step explanation:

let x and y this numbers : x +y = -103 and x = y +59

so : y+59 +y = -103

2y +59 = -103

2y +59-59 = -103-59

2y = -162

y = -162/2

y = -81  but  x = y +59

so : x = -81+59

x = -22

The two numbers satisfying the given condition is -22 and -81.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have sum of two numbers is -103. One number is 59 less than the other.

Assume that the first number is [x]. Then, another number would be (x - 59).

We can write -

x + (x - 59) = - 103

2x - 59 = - 103

2x = - 103 + 59

2x = - 444

x = - 22

Another number would be -

x - 59 = - 22 - 59 = - 81

Therefore, the two numbers satisfying the given condition is -22 and -81.

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Answer: 0.58333333333333

Step-by-step explanation: To find the decimal that is equivalent to 7/12, remember that fractions are division problems so we can divide the numerator by the denominator.

Numerator = 7

Denominator = 12

7 ÷ 12 = 0.58333333333333.

Answer:

_

.583

Step-by-step explanation:

In order to convert 7/12 to a decimal you must divide 7/12. The answer won't be a rational number, but will be a repeating decimal. You end up with .583 with 3 repeating. To show that this is repeating, you must put a little bar over the 3 (Because the 3 is the only repeating number) like so:

_

.583

I hope I was helpful!

Answer: -6

Step-by-step explanation:

When X = - 3, then Y = -6

Slope is 2.

Answer:

When x = -3, then y = -6

Step-by-step explanation:

We need to find out the value of y when x=-3

From the graph we look at the value of y

x is the input of the graph and y is the output .

In x axis the positive numbers on the right side and negative numbers on the left side . In y axis the positive numbers at the top and negative numbers at the bottom.

Given x=-3, Lets find the value of

At x=-3 the graph is at the bottom of x axis

Draw a line down at x=-3 , the line meets the graph at -6

So at x=-3 the value of y is -6

When x = -3, then y = -6

Answer:

x=9

Step-by-step explanation:

-2(-5x - 4) + 2x - 2 = 114

-2(-5x - 4) + 2x = 116

10x + 8 + 2x = 116

12x + 8 = 116

12x = 108

x = 9

Answer:

(x + 4) × (2x - 5)

Step-by-step explanation:

Hope this helps!!

Answer:

Answer:

(2x−5)(x+4)

Step-by-step explanation:

Factor 2x2+3x−20

2x2+3x−20

=(2x−5)(x+4)

Answer:

(2x−5)(x+4)

A trapezoid has exactly one pair of parallel sides.

I hope I was helpful! :)

Answer:  (a) 3     (b) -4      (c) 8      (d) 8i        (e) 11

Step-by-step explanation:

For a cubed root, you need three like terms on the inside to make one on the outside.

[tex]a)\quad \sqrt[3]{27}\quad = \sqrt[3]{3\cdot3\cdot3}\quad =\large\boxed{3}\\\\b)\quad \sqrt[3]{-64}\quad = \sqrt[3]{-4\cdot-4\cdot-4}\quad =\large\boxed{-4}[/tex]

For a square root, you need two like terms on the inside to make one on the outside. Reminder that √-1 = i

[tex]c)\quad \sqrt{64}\quad = \sqrt{8\cdot8}\quad =\large\boxed{8}\\\\d)\quad \sqrt{-64}\quad = \sqrt{-1\cdot8\cdot8}\quad =\large\boxed{8i}\\\\e)\quad \sqrt{121}\quad = \sqrt{11\cdot11}\quad =\large\boxed{11}[/tex]

Answer:

The dolphin speed in miles per hour is 6

Step-by-step explanation:

we know that

1 mi=1,609.34 m ------> 1 m=1/ 1,609.34 mi

1 h= 3,600 sec ----> 1 sec=1/3,600 h

we have

[tex]2.68\frac{m}{sec}[/tex]

Convert to mi/h

[tex]2.68\frac{m}{sec}=2.68\frac{(1/1,609.34)}{(1/3,600)}=6\frac{mi}{h}[/tex]

Answer:

6

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

-y₁ + y₂\-x₁ + x₂ = m

[tex] \frac{0 + 8}{ - 2 - 6} = - \frac{8}{8} = - 1[/tex]

I am joyous to assist you anytime.

The required expression would be -2(y+7) represents which is negative two times the sum of y and 7.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

We have been given that y represents a number.

To determine the expression for negative two times the sum of y and 7.

As per the given statement,

So the expression would be -2(y+7).

Hence, the required expression would be -2(y+7) represents which is negative two times the sum of y and 7.

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Answer: 5b = 15

Step-by-step explanation:

5b + 2 = 17

     - 2     -2

5b = 15

The two steps are:

step 1  : 5b = 17 - 2

step 2 : b = 15/5

Given,

5b + 2= 17

Now,

The equation given two us is in linear form with one variable .

So,

Simplifying the equation,

5b + 2= 17

Take 2 from LHS to RHS

5b = 17 - 2

5b = 15

b = 15/5

b = 3

Thus the value of b is 3 .

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Answer:

True

Step-by-step explanation:

The base angles of an isosceles triangle are equal.

The sum of the 3 angles in a triangle = 180°, thus

vertex angle = 180° - (55 + 55)° = 180° - 110° = 70°

Answer:

21, 35 , 49

Step-by-step explanation:

21 = 3 * 7

35 = 5 * 7

49 = 7 * 7

GCF = 7

Answer:

840,000 / 306,000 = 2.7450980392

So, Greenland is about 2 and 3/4 times larger than New Guinea.

Step-by-step explanation:

Greenland, the largest island in the world, is 534,000 square miles larger than New Guinea.

Greenland is 840,000 square miles and New Guinea is 306,000 square miles. To find out how much larger Greenland is than New Guinea, we subtract the area of New Guinea from the area of Greenland:

840,000 - 306,000 = 534,000 square miles

Therefore, Greenland is 534,000 square miles larger than New Guinea.

To determine how much larger Greenland is than New Guinea, one must subtract the size of New Guinea from the size of Greenland. Given that Greenland, the largest island in the world, is 840,000 square miles and New Guinea is 306,000 square miles, you would perform the following calculation:

840,000 - 306,000 = 534,000 square miles

Therefore, Greenland is 534,000 square miles larger than New Guinea.

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Answer:The volcano has a height of nearly 22 km (13.6 mi or 72,000 ft) as measured by the Mars Orbiter Laser Altimeter (MOLA). Olympus Mons is about two and a half times Mount Everest's height above sea level.

Olympus Mons - Wikipedia

Step-by-step explanation:

Olympus Mons on Mars is the tallest mountain in the solar system, standing over 20 kilometers above its surroundings and nearly 30 kilometers above the lowest points on Mars.

The height of Olympus Mons, which is the tallest mountain in the solar system, located on Mars, is incredibly impressive in comparison to mountains on Earth. Olympus Mons towers more than 20 kilometers above its surroundings, reaching nearly 30 kilometers above the lowest elevation areas on Mars. When converted to more familiar units, this equals approximately 22 miles in height, a figure that dwarfs the height of Mount Everest, which stands at 29,029 feet or about 8.848 kilometers.

Answer:

Step-by-step explanation:

It's highly advisable to find and use the LCD in problems like this.

21/32 has the denominator 32; if we multiply numerator and denominator each of 3/4, we get the equivalent fraction 24/32.

Now, compare 21/32 and 24/32.  It's pretty obvious that "21/32 greater than 3/4" is false; 24/32 is greater than 21/32, so 3/4 is greater than 21/32.

For this case we must solve the following equation:

[tex]\frac {2} {5} + p = \frac {4} {5} + \frac {3} {5}[/tex]

Since the denominators on the right side of the equation are equal, then we add the fractions:

[tex]\frac {2} {5} + p = \frac {4 + 3} {5}\\\frac {2} {5} + p = \frac {7} {5}[/tex]

We subtract [tex]\frac {2} {5}[/tex]on both sides of the equation:

[tex]p = \frac {7} {5} - \frac {2} {5}\\p = \frac {7-2} {5}\\p = \frac {5} {5}\\p = 1[/tex]

Thus, the value of p is 1.

Answer:

[tex]p = 1[/tex]

The solution to the linear equation is; p= 1.

The equation given in the task content is;

On this note, By isolating the unknown variable, p, we have;

By taking the LCM, we have; p = (4+3-2)/5

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2/3x=36

multiply by 3 both sides

2x=108

divide by 2

x=54

The value of the number whose two thirds part is equal to the number 36 is number 54.

A fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,

[tex]\dfrac{a}{b}[/tex]

Here (a) is the numerator and (b) is the denominator.

Two thirds of a number is 36. Let suppose the number is x. As it is given that the two third of this number x is equal to the 36.

Thus, we have to multiply the fraction 2/3 to x and equate it to 36.

[tex]x\times\dfrac{2}{3}=36\\x=\dfrac{36\times3}{2}\\x=54[/tex]

Hence, the value of the number whose two thirds part is equal to the number 36 is number 54.

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Answer:

Option D. 1

Option E. 1/2

Step-by-step explanation:

we know that

Looking at the graph

The domain is the interval ----> [-1,1]

[tex]-1\leq x\leq 1[/tex]

The domain is all real numbers greater than or equal to -1 and less than or equal to 1

The range is the interval ----> [0,1]

[tex]0\leq y\leq 1[/tex]

The range is all real numbers greater than or equal to 0 and less than or equal to 1

therefore

The values that are in the range are

1 and 1/2

Answer:

D.1

E.[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We have to find the values lie in the range of function in given graph.

Let f(x) be given function

Domain takes along x- axis and range takes along y- axis.

From given graph , we can see that

Domain of function =[-1,1]

It means

[tex]-1\leq x\leq 1[/tex]

Range of function:[0,1]

It means

[tex]0\leq y \leq 1[/tex]

The value of range of given function  from 0 to 1.

Hence, option D and E are correct.

D.1

E.[tex]\frac{1}{2}[/tex]

Check the picture below.

so, bearing in mind that vertical angles are equal, thus ∡AED = ∡BEC, and we know that ∡BEC = 52 = ∡AED, so those two angles added up are 104°.

now, a circle has a total of 360°, if we take away those 104° from the red angles, what's leftover is just 256°, well, the green angles there are also vertical angles and thus twins, so each one will take half of 256°.

∡BEA = 128° = ∡CED.

Answer:

x = y + 8

Step-by-step explanation:

Given

y = x - 8 ( add 8 to both sides )

y + 8 = x

Final answer:

To make x the subject of the equation y = x - 8, simply add 8 to both sides of the equation to get x = y + 8, which is the rearranged equation.

Explanation:

To rearrange the equation y = x - 8 to make x the subject, you need to isolate x on one side of the equation. Here are the steps to do so:

Add 8 to both sides of the equation to get y + 8 = x.

Once you have done that, the equation is already solved for x, and the new equation with x as the subject is x = y + 8.

This process is common in algebra when solving linear equations or finding the equation of a line, similar to when you want to determine the line of best fit in a set of data points. For example, in the equation y = 9 + 3x, rearranging to solve for x would involve subtracting 9 from both sides and then dividing by 3.

Hey!

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

Steps To Solve:

~Follow PEMDAS

6.4 − 2.4 ÷ 0.1

~Divide

6.4 − (2.4 ÷ 0.1)

~Simplify

6.4 - 24

~Subtract

(6.4 - 24)

~Simplify

-17.6

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

Answer:

[tex]\large\boxed{-17.6}[/tex]

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

Hope This Helped! Good Luck!

Answer:

-17.6

Step-by-step explanation:

6.4 - 2.4 ÷ 0.1

6.4 - 24 *Order of operations tells you

to divide first

-17.6 *Subtract

Answer:

$5.20 x 20 = $104.00

$104.00 ×8= $832.00

Answer:36%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

3 ribbons/ 12ribbons= 1/12

If You simplify dividing by 3 it becomes =1/4 = 0.25

so.. this is the 25 %

Answer:

I am not sure but the answer might be: $1688.1816

Step-by-step explanation:

A rectangle with sides 15 and w has perimeter

[tex]2p = 2(15+w) = 2w+30[/tex]

We want this quantity to be at most 50, so it must be less than or equal to 50:

[tex]2w+30\leq 50[/tex]

For the record, this implies that

[tex]2w\leq 20 \iff w \leq 10[/tex]

So, the width can be at most 10.

Answer:

2x+30< 50   ...answer : A

Step-by-step explanation:

the perimeter is :  P = 2(L+W)

let : L= x   given : L=15

P= 2(x+15)

The perimeter of the rectangle is, at most, 50:   P<50

2(x+15) < 50

2x+30< 50   ...answer : A

To solve the given equation, w need to review some rules:

The given equation is :

  ⇒⇒⇒⇒ rule (2)

  ⇒⇒⇒⇒ rule (1) and rule (2)

          ⇒⇒⇒⇒ rule (3)

removing the nature logarithm from both sides

∴ x = 4

So, the correct answer is option (2) ⇒⇒⇒⇒ x = 4

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The solution of the logarithmic equation is x = 4

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

[tex]ln[e^{ln ( x )} ] + ln[e^{ln (x^{2} )} ] = 2ln(8)[/tex]

On simplifying , we get

The value of ln e = 1

From the laws of logarithm , we get log Aⁿ = n log A

ln ( x ) ln ( e ) + ln ( x )² ln ( e ) = 2 ln ( 8 )

On further simplification , we get

ln ( x ) + ln ( x )² = ln ( 8 )²

From the laws of logarithm , we get log A + log B = log AB

ln ( x )³ = ln ( 64 )

ln ( x )³ = ln ( 4 )³

So , the value of x = 4

Hence , the logarithmic equation is solved

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Answer:

(a). $20,000

(b). The estimate will be lower than the actual amount.

Step-by-step explanation:

We have been given that Michael saves $423 dollars a month for college.

(a). We know that 1 year equals 12 months.

4 years = 4*12 months = 48 months.

[tex]\text{Actual amount saved}=\$423\times 48[/tex]

Since we are asked to find the estimated amount of money Michael will save in 4 years, so we will estimate both quantities as:

[tex]423\approx 400\\\\48\approx 50[/tex]

[tex]\text{Actual amount saved}=\$400\times 50[/tex]

[tex]\text{Actual amount saved}=\$20,000[/tex]

Therefore, Michael will save approximately $20,000 in 4 years.

(b).

The estimate will be lower than the actual amount as we rounded $423 down $23 to nearest hundred that is $400 and rounded 48 up 2 to nearest ten that is 40.

Therefore, the estimate will be lower than the actual amount.