Which graph represents g(x)=−(x−3)2−5 ?

Answer:

The solution for the given equation is 0 and 2.

Step-by-step explanation:

Given equation:

[tex]2-9|-8b+8|=-70[/tex]

To solve for [tex]b[/tex].

Solution:

In order to solve the given equation, we will first isolate the absolute value expression:

Step 1: Isolating the absolute value expression

[tex]2-9|-8b+8|=-70[/tex]

Subtracting both sides by 2.

[tex]2-2-9|-8b+8|=-70-2[/tex]

[tex]-9|-8b+8|=-72[/tex]

Dividing both sides by -9.

[tex]\frac{-9|-8b+8|}{-9}=\frac{-72}{-9}[/tex]

[tex]|-8b+8|=8[/tex]

Step 2: Set the value of the absolute value expression to positive and negative.

[tex]-8b+8=8[/tex]              and       [tex]-8b+8=-8[/tex]

Step 3: Solve for the unknown.

Solving for [tex]b[/tex].

Subtracting both sides by 8.

[tex]-8b+8-8=8-8[/tex]       and       [tex]-8b+8-8=-8-8[/tex]

[tex]-8b=0[/tex]                  and       [tex]-8b=-16[/tex]

Dividing both sides by -8.

[tex]\frac{-8b}{-8}=\frac{0}{-8}[/tex]          and       [tex]\frac{-8b}{-8}=\frac{-16}{-8}[/tex]

[tex]b=0[/tex]       and       [tex]b=2[/tex]     (Answer)

Thus, the solution for the given equation is 0 and 2.

Answer:

The answer is x^8

Step-by-step explanation:

x^4(x^4)

=x^4*x^4

=(x*x*x*x)*(x*x*x*x)

=x*x*x*x*x*x*x*x

=x8

Answer:

B

Step-by-step explanation:

For Plan A ---> you pay $50 per month flat

For Plan B,

average usage = 6 GB

cost per GB = $5 per GB

average cost per month = $5 per GB x 6 GB = $30

comparing the cost per month between the 2, we can clearly see that for plan B, $30 a month is the least expensive option

Plan B would be the least expensive option for someone who uses about 6 GB of data per month, costing $30, compared to Plan A's flat rate of $50 per month. It is important to also consider other costs and usage patterns when selecting a phone data plan.

When finding the least expensive phone data plan between a flat rate plan and a pay-per-gigabyte plan, you need to calculate the total costs based on the average data usage. In this case, Plan A offers unlimited data for a flat rate of $50 per month, while Plan B charges $5 per gigabyte of data used, with no monthly base cost.

For an average use of 6 GB of data per month:

Plan A would cost $50 every month, regardless of how much data you use.

Plan B would be 6 GB x $5/GB = $30 per month.

Comparing the two plans, Plan B is the least expensive option for someone who uses about 6 GB of data each month, as it would cost $30 as opposed to the $50 charged by Plan A.

However, it's important to consider your personal usage patterns and other potential costs, such as monthly charges for other services, occasional charges for peripherals or repairs, and any relevant annual costs or major costs when choosing a plan that fits your budget effectively.

Answer:

Step-by-step explanation:

Total staff is 32

Security guards = 5/8 of 32

= 5/8 × 32

= 5 × 4

= 20 security guards

There were total 20 security guards.

Fractions are used to represent smaller pieces of a whole.

Given that, There are a total of 32 staff members working in the aquarium, 5/8 of the staff are security guards.

Total staff is 32

Security guards = 5/8 of 32

= 5/8 × 32

= 5 × 4

= 20

Hence, there were 20 security guards.

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Answer:

Height of an oak tree= 9 meters

Height of a pine tree = 12 meters

Step-by-step explanation:

Given:

The combined height of 1 oak tree and 1 pine tree = 21 meters

Height of 4 oak trees = 24 meters more than 1 pine tree

To find the height of 1 pine tree and height of one oak tree.

Solution:

Let the height of one oak tree be = [tex]x[/tex] meters.

Let height of one pine tree = [tex]y[/tex] meters.

Combined height can be given as :

[tex]x+y=21[/tex]-------------[1]

Height of 4 oak trees = 24 meters more than 1 pine tree

The above statement can be given as :

[tex]4x=24+y[/tex]------------[2]

Rearranging equation [2] by subtracting both sides by [tex]y[/tex].

[tex]4x-y=24+y-y[/tex]

[tex]4x-y=24[/tex]-------------[2]

Adding rearranged equation [2] to [1].

[tex]x+y=21[/tex]

[tex]4x-y=24[/tex]

+--------------------

[tex]5x\ = 45[/tex]

Dividing both sides by 5.

[tex]\frac{5x}{5}=\frac{45}{5}[/tex]

∴ [tex]x=9[/tex]

Plugging in  [tex]x=9[/tex] in equation [1]

[tex]9+y=21[/tex]

Subtracting both sides by 9.

[tex]9-9+y=21-9\\\therefore y=12[/tex]

Height of an oak tree= 9 meters

Height of a pine tree = 12 meters

Answer:his total sales be $6500 in a week if he is to make a total of $675

Step-by-step explanation:

The total amount of money that Tito receives as weekly salary at an appliance store is $350.

He also receives a 5% commission on a total dollar amount of all sales he makes.

Let x represent his total sales in a week.

The amount of commission that he receives would be

5/100 × x = 0.05x

if he is to make a total of $675 in a week, it means that

0.05x + 350 = 675

0.05x = 675 - 350 = 325

x = 325/0.05 = $6500

By setting up an equation to represent Tito's total earnings and solving for total sales, we find that Tito must make $6500 worth of sales to earn a total of $675 in a week.

The subject of this question is Mathematics, specifically dealing with algebraic calculations to find the value of the variable. The variable in this case is the total sales Tito must make to earn a total of $675 in a week.

We know that Tito earns a fixed weekly salary of $350 and he also receives a 5% commission on his total sales. He wants to know how much he needs to sell to reach a total earning of $675.

To solve this, we set up an equation to represent the total earnings that Tito wishes to make: $350 (salary) + 0.05x (sales commissions) = $675.

Now we solve the equation for x (total sales). First, subtract $350 from both sides to get 0.05x = $675 - $350, which simplifies to 0.05x = $325.

Next, divide both sides of the equation by 0.05 to find x, so x = $325 / 0.05.

Therefore, Tito's total sales in a week must be $6500 for him to make a total of $675.

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Step-by-step explanation:

Height of shadow of basketball hoop = 109 inches

Height of person = 5 foot 8 inches = 68 inches

Height of shadow of person = 62 inches

[tex]\frac{\texttt{Height of person}}{\texttt{Height shadow of person}}=\frac{68}{62}=\frac{34}{31}[/tex]

[tex]\frac{\texttt{Height of basketball hoop}}{\texttt{Height of shadow of basketball hoop}}=\frac{34}{31}\\\\\frac{\texttt{Height of basketball hoop}}{109}=\frac{34}{31}\\\\\texttt{Height of basketball hoop}=119.55inches=120inches[/tex]

Height of the basketball hoop = 120 inches

Answer:

-2yx/15?

Step-by-step explanation:

Answer: distance = 5

Step-by-step explanation:

The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Where

x2 represents final value of x on the horizontal axis

x1 represents initial value of x on the horizontal axis.

y2 represents final value of y on the vertical axis.

y1 represents initial value of y on the vertical axis.

From the graph given,

x2 = 1

x1 = - 2

y2 = 0

y1 = - 4

Therefore,

Distance = √(1 - - 2)² + (0 - - 4)²

Distance = √3² + 4² = √9 + 16 = √25

Distance = 5

Answer:

22 yards

Step-by-step explanation:

Use a (+) sign for yards gained and a (-) sign for yards lost.

Geno gained 4 yards 3 times: (+4) × 3.

Geno lost 1 yard twice: (-1) × 2.

Geno gained 6 yards twice: (+6) × 2.

Net change

in field position

=

(4 × 3) + (-1 × 2) + (6 × 2)

=

12 − 2 + 12

=

10 + 12

=

22.

Geno gained 22 yards.

The net change in the position of Geno if In the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice, is 22 yards.

In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.

Given:

In the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice,

Calculate the net change in position as shown below,

The net change = Total  gained - Total  lost,

Total gained = 4 × 3 + 6 × 2

Total gained = 12 + 12

Total gained = 24

Total lost = 1 × 2

Total lost = 2

The net change = 24 - 2

The net change = 22

Thus, the net change in the Geno position is 22 yards.

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The complete question is:

Geno is a running back for the Bayside Barn Owls. During the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice. Find the net change in the position of Geno.

[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})] = \frac{-1}{8}[/tex]

Solution:

Given that, we have to perform the indicated operation

[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})][/tex]

We can use BODMAS rule to perform the operation

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right

So, in the given expression, we have to solve for brackets first

Solve the innermost bracket

[tex]\frac{5}{8}-[\frac{1}{2}+\frac{1}{4}][/tex]

Now solve the bracket again

[tex]\frac{5}{8}-[\frac{1}{2}+\frac{1}{4}] = \frac{5}{8}-[\frac{4+2}{8}] = \frac{5}{8}-[\frac{6}{8}][/tex]

Now remove the parenthesis

[tex]\rightarrow \frac{5}{8} - \frac{6}{8}[/tex]

Now perform subtraction operation

[tex]\rightarrow \frac{5}{8} - \frac{6}{8} = \frac{5-6}{8} = \frac{-1}{8}[/tex]

Thus we got,

[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})] = \frac{-1}{8}[/tex]

Thus the indicated operation is performed

Answer:

Step-by-step explanation:

Total number of questions in the test is 80.

To receive a grade of A on the 80 question test, 90% of the questions must be answered correctly. It means that the number if questions that must be answered correctly would be

90/100 × 80 = 0.9 × 80 = 72.

Therefore, the maximum number of questions that can't be missed to still receive an A is 72

Answer: you have 118 text messages.

Step-by-step explanation:

Let x represent the number of text messages that you have or sent.

A cell phone company charges a monthly fee plus $.25 for each text message. The monthly fee is $30. This means that the total cost of x sending x messages in a month would be

0.25x + 30

If you owe $59.50, then your total cost is $59.50

Therefore,

59.50 = 0.25x + 30

0.25x = 59.50 - 30

0.25x = 29.5

x = 29.5/0.25

x = 118

Answer:

The dog ran 15 miles

Step-by-step explanation:

The combined speed of the 2 hunters is 7mph, therefore, they will met in 21/7 = 3 hours, becuse they are walking in opposite directions. In this 3 hours the dog kept running and thus it ran 3*5 = 15 miles. Note that the position of the dog is always between the position of both hunters, therefore when both hunters met each other, the dog will be alredy there.  

The correct statement is,

⇒ The product of (2x−5)(x²+3x−1) is 2x³+x²−17x+5 because the following are like term pairs: 6x²−5x² and −2x−15x.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

To find the correct statement about the expression.

Now, We have;

The expression is,

⇒ (2x - 5) (x² + 3x - 1)

Hence, We can simplify as;

⇒ (2x - 5) (x² + 3x - 1)

⇒ (2x³ + 6x² - 2x - 5x² - 15x + 5

⇒ 2x³ + x² - 17x + 5

Thus., The correct statement is,

⇒ The product of (2x−5)(x²+3x−1) is 2x³+x²−17x+5 because the following are like term pairs: 6x²−5x² and −2x−15x.

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ANSWER: Paz have $267.30

STEP BY STEP EXPLANATION

Let be Z for Zacarías and P for Pax

Z+P= 756.80

Z= 489.50

P=756.8 - Z

P=756.80 - 489.50

P= 267.30

Answer:

Step-by-step explanation:

The square base measures 8 inches by 8 inches. The slant height is 10 inches.

The formula for determining the area of the square base of the pyramid is l^2. Therefore,

Area of the base = 8^2 = 64 inches^2

The formula for determining the perimeter of the square base is

4l. It becomes

4 × 8 = 32 inches

The amount of construction paper needed to make this pyramid is the total surface area of the pyramid. Therefore,

Total surface area = (1/2 × 32 × 10) + 64

= 160 + 64 = 224 inches^2

Nick will need approximately 224 square inches of construction paper for his square based pyramid project with a base measuring 8 inches by 8 inches and a slant height of 10 inches.

To find the amount of construction paper needed for Nick's square based pyramid project, we need to calculate the surface area of the pyramid. The surface area of a pyramid includes the area of the base plus the area of the four triangular sides.

The area of the base (Abase) is the side length squared:
Abase = side × side = 8 inches × 8 inches = 64 square inches.

The area of one triangular side (Atriangular side) is given by the formula:
Atriangular side = 1/2 × base × slant height.
For Nick's project, the base of a triangular side is equal to the side of the square, so:
Atriangular side = 1/2 × 8 inches × 10 inches = 40 square inches.

Since there are four identical triangular sides:
Total area of triangular sides = 4 × 40 square inches = 160 square inches.

Adding the base and triangular sides areas together gives us the total construction paper needed:
Total construction paper needed = Abase + Total area of triangular sides = 64 square inches + 160 square inches = 224 square inches.

Therefore, Nick will need approximately 224 square inches of construction paper for his project. To get the nearest whole number, we round 224 to 224.

Answer:  80%

Step-by-step explanation:

Since we have given that

Number of erasers sold in May = 80

Number of erasers sold in June = 16

Decrement in 1 month gap is given by

16-80=-64

So, Percentage of change in erasers sold from May to June is given by

[tex]\frac{-64}{80}[/tex] × 100

= -80% (Decreased 80%)

Answer:

80%

Step-by-step explanation:

I took a test with this question on it

Answer:

22.9 feet

Step-by-step explanation:

You are using Tangent because you have the opposite and adjacent sides

Tan 5 = 2/x

x Tan 5= 2

x= 2/Tan5

= 22.860

To find the horizontal run length of a wheelchair ramp with a 5-degree angle and a 2-foot rise, use the tangent function of trigonometry. Plug the given values into the tangent formula, rearrange to solve for 'Run', and calculate to get a run length of approximately 22.8 feet.

The question is referring to the use of trigonometry to solve real-life problems. Here, we are going to use the tangent of the angle, which is defined as the ratio of the opposite side (the rise) to the adjacent side (the run). In this case, we know that the angle is 5 degrees and the rise is 2 feet.

In mathematical terms, this can be written as:

Tan(ρ) = Rise/Run

Substituting the values into the equation, we get:

Tan(5°) = 2/Run

Solving for Run, we get:

Run = 2/Tan(5°)

You can find this value using a calculator, rounding to the nearest tenth, to get the run as approximately 22.8 feet.

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Answer:

Correct number : c = 16

Step-by-step explanation:

The triangle theorem states that each side of the triangle is smaller than the sum of the other two and larger than their difference. We denote the three sides of a triangle as a, b, and c.

Suppose that a = 8 and b = 10 and as we see b is greater than a , b > a

b - a < c < b + a  => 10 - 8 < c < 10 + 8  =>  2 < c < 18

from the offered answers we choose number 16

c = 16

God is with you!!!

Answer:

Step-by-step explanation:

if a,b,c are three sides of a triangle,then a<b+c,b<c+a,c<a+b

or in general we can say any side < sum of other two sides.

third side<8+10

or third side <18

Here third side=16

if you are asked smallest side then any side >difference of other two sides.

third side >10-8 or>2

Answer:

x = 6 or x = -4

Step-by-step explanation:

x^2 - 2x - 24 = 0

(x - 6)(x + 4) = 0

x - 6 =0 or x + 4 = 0

x = 6 or x = -4

Answer:

1 is concentric circles

2 is concentric circles, they have same center

3 is congruent circles, they have equal radii

4 is correct

5 is correct

Step-by-step explanation:

Congruent circles are circles of the same size while concentric circles are circles that have same center but different radii. Diameter is the line passing through the center of a circle joining two points on the circumference while radius is the joining the center of the circle to any point on the circumference.

Answer:

The correct order of fractions in descending order will be:

[tex]\frac{2}{5}, \frac{11}{30}, \frac{1}{3}[/tex]

Step-by-step explanation:

Given fraction:

[tex]\frac{1}{3}, \frac{2}{5}, \frac{11}{30}[/tex]

To arrange them in descending order.

Solution:

In order to arrange the fractions in descending order, we will have to find the least common denominators.

To find the least common denominator, we will find the least common multiple of the denominators 3,5, and 30.

Since 30 is a common multiple of all 3 numbers, so it will be the least common denominator.

So, we multiply the numerators and denominators with same numbers in order to make the denominators = 30.

So, we have:

[tex]\frac{1}{3}, \frac{2}{5}, \frac{11}{30}[/tex]

⇒ [tex]\frac{1\times 10}{3\times 10}, \frac{2\times 6}{5\times 6}, \frac{11\times 1}{30\times 1}[/tex]

⇒ [tex]\frac{10}{30}, \frac{12}{30}, \frac{11}{30}[/tex]

Now, we compare the numerators and arrange them accordingly.

[tex]\frac{12}{30} > \frac{11}{30} > \frac{10}{30}[/tex]

So, the correct order of fractions in descending order will be:

[tex]\frac{2}{5}, \frac{11}{30}, \frac{1}{3}[/tex]

Answer:

B. 120.5 ft

Step-by-step explanation:

Given:

Length of Martins drive way = 121 ft

We need to find the minimum possible length of the driveway

Solution:

Now we know that ;

When a number is rounded to nearest whole number.

We can say that the number is in decimal format.

Also rounding techniques applies when the decimal number has digit 5 or more in ten's place after decimal then the number in increase by 1 as a whole number.

Here the number is rounded to nearest foot which is 121 ft.

So we an say that;

Number ranging from 120.50 to 120.99 can be made to 121 as nearest foot.

Hence the minimum possible length of the drive way could be 120.5 ft

Answer:

[tex]3\sqrt{29}[/tex] or approximately 16.16

Step-by-step explanation:

The diagonal (hypotenuse) mesures 19 inches.

The height of the computer monitor is 10 inches.

Use the Pythagorean theorem:

a and b are the triangle's legs

h is the hypotenuse

[tex]a^{2} + b^{2} = c^{2}\\ \\a^{2} + 10^{2} = 19^{2}\\ \\361 - 100 = a^{2}\\ \\a = \sqrt{261} \\\\a = 3\sqrt{29}[/tex]

Answer:

67

Step-by-step explanation:

48=6

35=8.5

67

Answer:

A.)$68

B.)$32

Step-by-step explanation:

For 8.5 hours of babysitting, Tiva will earn $ 68

If Tiva babysits for  4 hours, she will earn $32.

Answer:

On that day 75 soft drinks and 45 popcorn were sold.

Step-by-step explanation:

Given:

Let the number of soft drinks be 'x'.

Let the number of popcorn be 'y'.

Number of cups sold = 120

Now we know that;

Number of cups sold is equal to sum of the number of soft drinks and the the number of popcorn.

framing in equation form we get;

 [tex]x+y=120 \ \ \ \ equation \ 1[/tex]

Also Given:

Cost of Soft drink = $2 .00

Cost of popcorn = $4.00

Total amount collected = $330.00

Now we know that;

Total amount collected is equal to sum of the number of soft drinks multiplied by Cost of Soft drink and the number of popcorn multiplied Cost of popcorn.

framing in equation form we get;

 [tex]2x+4y = 330 \ \ \ \ eqaution \ 2[/tex]

Hence The System of equation to determine the number of softdrinks and cups sold is  [tex]\left \{ {{x+y=120} \atop {2x+4y=330}} \right.[/tex].

Now to find the number of each type of cups sold we will solve the above equations.

First we will multiply equation 1 with 2 we get;

 [tex]2(x+y)=120\times2\\\\2x+2y =240 \ \ \ \ equation \ 3[/tex]

Now we will subtract equation 3 from equation 2 we get;

 [tex]2x+4y-(2x+2y)=330-240\\\\2x+4y-2x-2y=90\\\\2y = 90[/tex]

Now Dividing both side by 2 we get;

 [tex]\frac{2y}{2}= \frac{90}{2}\\\\y=45[/tex]

Now we will substitute the value of 'y' in equation 1 we get;

 [tex]x+y=120\\\\x+45 =120\\\\x=120-45 = 75[/tex]

Hence On that day 75 soft drinks and 45 popcorn were sold.

Answer: 455ways

Step-by-step explanation:

This can be done according to rule of combination because it talks about selection.

In order to select r object from a pool of n objects, it is represented as nCr = n!/(n-r)!r!

Therefore to select 3 students from a class of 15students, this will give us 15C3.

15C3 = 15!/(15-3)!3!

= 15!/12!3!

= 15×14×13×12!/12!×6

= 15×14×13/6

= 455ways

This selection can be done in 455ways

The question is an illustration of combination

There are 455 ways of selecting the students

The number of students is 15, and the students to select are 3.

So, the number of selections is:

[tex]*nC_r = \frac{n!}{(n -r)!r!}[/tex]

This gives

[tex]^nC_r = \frac{15!}{(15 -3)!3!}[/tex]

Evaluate

[tex]^nC_r = 455[/tex]

Hence, there are 455 ways of selecting the students

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Four out of twelve converts to the fraction

4/12

if both sides are divided by four, you can simplify this fraction to

1/3

therefore, a is correct

1/3 times two makes

2/6

therefore, c is correct

1/3 has no more multiples in this selection

The equivalent fraction are 1/3 and 2/6.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.

How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned in the fraction's upper portion.

Given:

Four out of twelve converts to the fraction

= 4/12

Now, simplifying the fraction we get

= 4/12

= 1/3

Now, 3/6 = 1/2

2/6 = 1/3

Hence, the equivalent fraction are 1/3 and 2/6.

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Answer:

x^2−18x+81

x^2+2x+1

Step-by-step explanation:

we know that

A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself

so

[tex]a^2\pm2ab+b^2=(a\pm b)(a\pm b)=(a\pm b)^2[/tex]

Verify each case

case a) x^2−10x−25

we know that

[tex](x-5)^2=x^2-10x+25[/tex]

therefore

Is not a perfect square trinomial

case b) x^2−18x+81

we know that

[tex](x-9)^2=x^2-18x+81[/tex]

therefore

Is a perfect square trinomial

case c) x^2+2x+1

we know that

[tex](x+1)^2=x^2+2x+1[/tex]

therefore

Is a perfect square trinomial

case d) x^2+7x+49

we know that

[tex](x+3.5)^2=x^2+7x+12.25[/tex]

therefore

Is not a perfect square trinomial