Find the roots and the vertex of the quadratic on a calculator. Round all values to 3
decimal places (if necessary).
y=-x² + 6x + 72

For the given problems we have:

1) The solution of the inequality is:

x ≤ 2

2) The absolute value equation has two solutions:

z= 2

z = -12

3) The correct matches are:

Remember that solving means to isolate the variable in one side of the expression.

1) We have the inequality:

-4x + 17 ≥ 9

-4x  ≥ 9 - 17

x ≤ -8/-4

x ≤ 2

This is the solution of the inequality.

2) We have the absolute value function:

|5 + z| + 3 = 10

|5 + z| = 10 - 3 = 7

We can decompose this into:

5 + z = 7

5 + z = -7

Then the two solutions are:

z = 7 - 5 = 2

z = -7 - 5 = -12

3) The correct matches here are:

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He will cover total 247.5  kilometers on day 30 of his programe .

When there are identical differences between every two next words, the series is known as an arithmetic progression (AP). There is a chance to find a formula for the nth term of the AP using this kind of development. The series 2, 6, 10, 14, etc., for instance, is an example of an arithmetic progression (AP) because it follows a pattern in which each number is acquired by adding 4 to the preceding word. Nth term in this series equals 4n-2.

Given that :Lerato begins a new cycling programme with 2 km on the first day. Each day, he will increase his cycling by 500 m.

The formula to find Sum of an arithmetic progression is

S = [tex]\frac{n}{2}[2a+(n-1)d][/tex]

here , a = 2km

n = 30

d = 0.5km

S =[tex]\frac{30}{2}[2(2)+(30-1)0.5][/tex]

S = 247.5 km

He will cover total 247.5  kilometers  on day 30 of his programe

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Answer:

[tex]{ \tt{\% savings = \frac{savings}{total \: income} \times 100\%}} \\ \\ { \tt{ = \frac{720}{3000} \times 100\%}} \\ \\ = { \tt{24\%}}[/tex]

Answer:

24%

Step-by-step explanation:

[tex]\boxed{\sf Percent=\left(\dfrac{Value}{Total\:value}\right) \times 100}[/tex]

Given information:

Substitute the given values into the formula and solve for percent:

[tex]\begin{aligned}\implies \textsf{Percent} & =\dfrac{720}{3000} \times 100\\\\& = \dfrac{720\times 100}{3000} \\\\& = \dfrac{72000}{3000} \\\\& = \dfrac{72}{3} \\\\& = 24\% \end{aligned}[/tex]

Therefore, 24% of Tanisha's budget is savings.

When we write an inequality in the form:

In a number line, we can draw it, mark the endpoints (1 and 5) and then we highlight the parts at which the x is, which is in the middle:

Notice that we marked the endpoints as empty dots, which indicates that the endpoints are not included in the interval.

Given that equation

1) [tex]x^{2} - 2x - 2[/tex]  using the general quadratic equation, x = 1

2)[tex]x^{2} -6x -4[/tex] using the general quadratic equation, x= [tex]\frac{6 - \sqrt{20} }{2}[/tex]

According to the question, given that

1) [tex]x^{2} - 2x - 2[/tex]

2)[tex]x^{2} -6x -4[/tex]  

this equation cannot be factored but using general quadratic equation. we solved it easily.

When asked to solve a quadratic equation that you just can’t seem to factor (or that just doesn’t factor), you have to employ other ways of solving the equation, such as by using the quadratic formula. The quadratic formula is the formula used to solve for the variable in a quadratic equation in standard form.

Given a quadratic equation in standard form ax2 + bx + c = 0,

[tex]x = \frac{- b - \sqrt{b^{2} - 4 ac } }{2a}[/tex] and  [tex]x = \frac{- b + \sqrt{b^{2} - 4 ac } }{2a}[/tex]

solve [tex]x^{2} - 2x - 2[/tex] = 0, you first say that a = 1, b = –2, and c = 2. The a, b, and c terms simply plug into the formula to give you the values for x:

    1) [tex]x^{2} - 2x - 2[/tex]    

 [tex]x = \frac{- (-2) + \sqrt{(-2)^{2} - 4 (1)(1) } }{2(1)}[/tex]

[tex]x = \frac{2 + \sqrt{4 -4} }{2}[/tex]

x = [tex]\frac{2}{2}[/tex]

[tex]x = 1[/tex]

and    [tex]x = \frac{- (-2) - \sqrt{(-2)^{2} - 4 (1)(1) } }{2(1)}[/tex]

         [tex]x = \frac{2 - \sqrt{4 -4} }{2}[/tex]

         x = [tex]\frac{2}{2}[/tex]

         [tex]x = 1[/tex]

equation  [tex]x^{2} - 2x - 2[/tex]  and x= 1

2)[tex]x^{2} -6x -4[/tex]  

solve [tex]x^{2} - 6x - 4[/tex] = 0, you first say that a = 1, b = –6, and c = 4. The a, b, and c terms simply plug into the formula to give you the values for x:

[tex]x^{2} -6x -4[/tex]  

[tex]x = \frac{- (-6) + \sqrt{(-6)^{2} - 4 (1)( 4) } }{2(1)}[/tex]

[tex]x = \frac{6 + \sqrt{36 - 16} }{2}[/tex]

x = [tex]\frac{6 \sqrt{20} }{2}[/tex]

and    [tex]x = \frac{- (-6) - \sqrt{(-6)^{2} - 4 (1)(4) } }{2(1)}[/tex]

         [tex]x = \frac{6 - \sqrt{36 - 16} }{2}[/tex]

         x = [tex]\frac{6 - \sqrt{20} }{2}[/tex]

equation  [tex]x^{2} - 6x + 4[/tex]  and x= [tex]\frac{6 - \sqrt{20} }{2}[/tex]

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Answer: 17 million

Step-by-step explanation:

      We will set up a proportion to solve. We also will divide 26% by 100 to get a decimal, 0.26. We know that 26% of college students was 4.4 million, but we want to find 100%.

     [tex]\displaystyle \frac{0.26}{4.4\text{ million}} =\frac{1}{x\text{ million}}[/tex]

      Now, we will cross-multiply.

0.26 * x = 1 * 4.4

0.26x  = 4.4

      Lastly, we will divide both sides of the equation by 0.26. Then, we will round to the nearest million.

x = 16.923

x ≈ 17 million

The sum of the first 31 terms of the arithmetic series is 114.

What is arithmetic series?

In mathematics, arithmetic series is the sequence of the number whose common difference between the two consecutive number is always constant. And the sum of the series is depend on the first term as well as on the last term.

According to the question, the given series is an arithmetic series. In the common difference is same.

The given series is:

4, 11, 18,....4, 11, 18,....4, 11, 18,....

To know the sum of the given series, first calculate the sum of the first three numbers. And later multiply by ten.

Using standard formula for the sum of the arithmetic series:

[tex]S_{3} =\frac{(first term + last term)}{2} = \frac{4+18}{2} =11[/tex]

Therefore to calculate the sum of the 31 terms:

s(31 terms) = 10(11) + first term = 110 + 4 = 114

Hence, the sum of the first 31 terms of the arithmetic series is 114.

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The cost of the car the Gilberts purchased before tax is  $13,820.52.

Tax is a compulsory amount that is levied on a good or service by the government. A sales tax is a tax that is levied on the purchase of a good and service. Taxes increase the cost of a good or service.

The equation that can be used to determine the cost of the car after tax is:

(1 + sales tax) x cost before tax = cost after tax

(1 + 0.05) x c = $14,512

1.05c = $14,512

In order to determine the value of c, divide both sides of the equation by 1.05:

c = $14,512 / 1.05

c = $13,820.52

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Answer:

Step-by-step explanation:

Multiply both sides by 14 to find the missing value:

The function represents the area of the walkway along the width of the flower patch.

Rule, or law that establishes the link between an independent variable and a dependent variable is known as function.

Functions can be found everywhere in mathematics, and they are essential for building physical connections in the sciences.

The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837.

The total area taken up by the flower patch and walkway by multiplying the functions modeling the new total length and width represents  the area of the walkway along the width of the flower patch.

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Examples of each survey question that relates to organic farm produce are as follows;

a) Dichotomous

Do you prefer organic farm produce?

Yes/No

b) Multiple choice

How many of your colleagues make use of organic farm produce

c) Rating scale

On a scale of 1 to 5, with 10 being happiest, how happy are you about our customer service?

1, 2, 3, 4, 5

d) Completion

Eating organic produce _______ improve my health

Will

Will not

e) Open-ended

Tell us why you prefer organic farm produce ___________

A survey involves the administration of questions or the examination of a process that is aimed at obtaining data with regards to a service, process or product.

a) Dichotomous questions are questions that can have only two possible responses. Such questions are used in a survey in which the two possible responses are stated such as Agree/Disagree, Yes/No, Fair/Unfair, True/False, or Cold/Hot. Based on the definition of the responses, the opinion of the responder is made clear

An example of a dichotomous question asked with respect to organic farm produce is 'Do you prefer organic farm produce?'

The possible responses are; Yes/No

b) Multiple choice survey question

Multiple choice questions provide the opportunity for a respondent to have more options to choose a response from. The multiple choice questions also allow researcher to obtain detailed information on the subject.

An example of multiple choice question is as follows;

How many of your colleagues make use of organic farm produce

c) Rating Scale

In rating scale survey questions the respondents are asked to select a rating of their experience in a response that offers a rating such as 1 to 10 or 1 to 100

An example of a rating scale question in a survey is as follows;

On a scale of 1 to 5, with 10 being happiest, how happy are you about our customer service?

1, 2, 3, 4, 5

d) Completion

Completion type question assesses the level of cognition on a subject matter

Example;

Eating organic produce _______ improve my health

e) Open–ended

Open–ended questions gives respondents the latitude to express themselves with regards to the question in written text in a detailed or in a brief response.

Example;

Tell us why you prefer organic farm produce ___________

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Answer:

Step-by-step explanation:

=−10.44−4.2−(−6.85)

=−14.64−(−6.85)

=−7.79

Answer:

-7.79

Step-by-step explanation:

Given problem,

→ -16.26 - (-5.82) - (4.20) - (-6.85)

Let's simplify the problem,

→ -16.26 - (-5.82) - (4.20) - (-6.85)

→ -16.26 + 5.82 - 4.20 + 6.85

→ -10.44 + 2.65 = -7.79

Hence, the answer is -7.79.

TO find the zeros of a quadratic function we should factorize the function

So we have to find numbers that multiplied are -20 and added are -1. So we get -5 and 4

so the zeros of the function are 5 and -4

We are to solve using completing the square:

1/4x² + x + 1/4 = 0

Let's collect like terms:

1/4x² + x = -1/4

Divide both sides by the coefficient of x-squared:

x² + 4x = -1

Take half of the coefficient of x, square it, then add to both sides:

x² + 4x + 4 = -1 + 4

factor the left side of the equation:

(x + 2)² = 3

Take the root of both sides;

x + 2 = ±√3

Add 2 to both sides:

x = ±√(3) - 2

x = -2 + √3 or x = -2 - √3

herefore, the correct option is B, which is x = -2 + √3 or x = -2 - √3

To write  3.656 X 10^-5 in standard form 0.00003656

What is Standard Form ?

A mathematical item's canonical, normal, or standard form refers to how the object is typically expressed mathematically in both mathematics and computer science. It is frequently the one that offers the most straightforward illustration of the thing while yet enabling distinctive identification.

Move the decimal in the number that many spaces to the right when multiplying a number by 10 to the power of a positive exponent

(for example, (10)^3)).

For example, 4.5x(10)^3=4500.

Move the decimal in the number (the absolute value of) that many spaces to the left when multiplying a number by 10 to the power of a negative exponent

(for example, (10)^4)).

For example, (4.5x10)^4=(0.00045)

Move the decimal five spaces to the left for (3.656x 10)^-5:

0.00003656

Hence , 0.00003656 is Standard form of  (3.656x 10)^-5

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Answer: I believe the answer is 3.

Step-by-step explanation:

a wood cutter has 1/4 + 2/4 + 3/4 So we add those up to get 6/4.

Then he buys the same amount again which would make 12/4.

We are not done probably, so we MUST simplify.

how many times can 4 fit into 12? 3! so we have whole number 3 and since 4 fit into 12 3 times perfectly all we have is 3

C. add 6 from the previous term

To get the next term in the sequence, you subtract 6 from the previous term.

The values of m that can fit into the equation m² = 16 will be m = ±4.

It should be noted that a equation is simply used to illustrate the relationship between the variables that are given. From the information, it should be noted that the equation is illustrated as m² = 16.

Since m² = 16, we need to find the square root. This will be illustrated as:

m² = 16

m = ✓16

m = 4

It should be noted that (-4) × (-4) = 16 and 4 × 4 = 16.

Therefore, the correct option is m = ±4

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Total ticket = 675

Child tickrt sold = 243

percentage of child tickets sold

The equation for each line will be y=-x+2.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that,

The coordinate of the points are (2,0) and (0,2)

The slope of the line is,

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1} \\\\ m = \frac{2-0}{0-2} \\\\ m = -1[/tex]

The standard equation of the line is,

y-y₁ = m(x-x₁)

y-0=-1(x-2)

y=-x+2

Thus, the equation for each line will be y=-x+2.

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From the question;

Point A is at (2,2)

Point B is the reflection of point A across the x-axis;

The rule for reflection across the x-axis is;

So, point B will be;

The point C is 5 units directly left of point B;

So, point C will be;

Therefore, the coordinates of the Points A, B and C are;

Shown as;

So, the length AB is;

The length BC is;

The value of the expression in the options is (a) three raised to the sixth power divided by six raised to the fifteenth power

The expression is given as

A fraction with six raised to the negative third power in the numerator and the quantity three raised to the negative second power times six squared end quantity in the denominator and the entire fraction is cubed.

Rewrite the expression properly

So, we have

[6^-3/(3^-2 x 6^2)]^3

Apply the law of indices to the expression

So, we have

[6^-3/(3^-2 x 6^2)]^3 = [6^(-3 - 2)/(3^-2)]^3

Evaluate the difference

[6^-3/(3^-2 x 6^2)]^3 = [6^-5/(3^-2)]^3

Apply the change of power rule

[6^-3/(3^-2 x 6^2)]^3 = [3^2/6^5]^3

Evaluate the product of exponents

[6^-3/(3^-2 x 6^2)]^3 = 3^6/6^15

In words, the result is (a) three raised to the sixth power divided by six raised to the fifteenth power

Hence, the value of the expression is (a)

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Answer:

hi

Step-by-step explanation:

i dot no because i dot spak in english because im frach

The formula to show the height and time an object is in the air :

when the object hits the ground the height will become 0

so, put h(t) = 0

and simplify :

Simplfy the equation by using discrimination rule :

The general form of quadratic equation is : ax² + bx + c

and the roots are express a s :

On compare the given equation with the general equation we get :

a = -16, b = 48 and c = 50

Substitute the value and simplify :

New width: 10 cm, new length: 15 cm

Or new width 15 and new length 10

1) Since this rectangle, has been scaled up by a factor k=5 (since 5 >1 then the rectangle has been enlarged)

2) Then we can write the following about their new dimensions:

w = 2 x 5 = 10

l = 3 x 5 = 15

3) So the answer is 10 x 15

The most appropriate choice for combination will be given by-

Models can wear 112 different types of outfit.

What is combination?

Combination determines the number of ways of selecting some number of particular items from a group of given item, here the order of selection do not matter.

If there are n objects and from there, r objects are chosen, number of ways will be given by

                                  [tex]n \choose r[/tex] = [tex]\frac{n!}{(n - r)! \times r!}[/tex]

Here,

Number of tops = 7

Number of pants = 2

Number of jackets = 8

From 7 tops the designer can choose 1 top in [tex]7 \choose 1[/tex] ways

                                                                        = [tex]\frac{7!}{(7-1)!\times 1 !}[/tex]

                                                                        = [tex]\frac{7!}{6!}[/tex]

                                                                        = [tex]7[/tex]

From 2 pants the designer can choose 1 pant in [tex]2 \choose 1[/tex] ways

                                                                        = [tex]\frac{2!}{(2-1)!\times 1 !}[/tex]

                                                                        = [tex]\frac{2!}{1!}[/tex]

                                                                        = [tex]2[/tex]

From 8 jackets the designer can choose 1 jacket in [tex]8 \choose 1[/tex] ways

                                                                        = [tex]\frac{8!}{(8-1)!\times 1 !}[/tex]

                                                                        = [tex]\frac{8!}{7!}[/tex]

                                                                        = [tex]8[/tex]

Total number of different outfits models can wear = [tex]7 \times 2 \times 8[/tex]

                                                                             = 112

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The quotient of 2.538 ×10^9 and 2.7×10^2 expressed in scientific notation is : 0.94 × 10^6.

Given:

2.538 × 10^ 9 and 2.7 × 10^ 2

We have to first of all formulate before determining the scientific notation

(2.538 × 10^ 9) ÷ (2.7 × 10^2)

Rewrite as fraction

2.538 × 10^9 ÷ 2.7 × 10^2

simplify

2.538 ÷ 2.7 × 10^ 9-2

=  2.538 ÷ 2.7 × 10^7

Convert the fraction to decimal

0.94 × 10^7

Now let express it in scientific notation

Scientific notation = 94 × 10^6

Therefore the scientific notation is 94 × 10^6.

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The correct question is:

What is the quotient of 2.538 ×10^9 and 2.7×10^2 expressed in scientific notation

Explanation:

The question involves dividing radicals

To resolve the question, we will follow the steps below

Step 1: Write the expression

Step 2: simplify the expression in parts and apply the laws

Thus

For the second part

simplifying further

Hence, we have

Finally, we will combine the simplified terms, so that we will have

Hence, we will have

By canceling out the common parts, we will have the answer to be

Answer:

360ft

Step-by-step explanation:

Here,

Given,

→Area=57600ft²

→Width=160ft

Now,

→Length=Area/Width
→Length=57600ft²/160ft=360ft

Answer:

19.5

Step-by-step explanation: