The zeros of a quadratic function are 1 and 4. How would you use this information to write the equation for the function? If the equation cannot be written, explain why. Use complete sentences in your answer.

The result of the expression (5x[tex]10^{-3}[/tex]) (7×[tex]10^{-2}[/tex])  in scientific notation is 35×[tex]10^{-5}[/tex].

What is scientific notation?

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ [tex]10^{8}[/tex].

The expression in scientific notation is

(5x[tex]10^{-3}[/tex]) (7×[tex]10^{-2}[/tex]) = 5×7 × [tex]10^{-3-2}[/tex]

                           = 35 × [tex]10^{-5}[/tex]

Therefore, the result of the expression (5x[tex]10^{-3}[/tex]) (7×[tex]10^{-2}[/tex]) in scientific notation is 35×[tex]10^{-5}[/tex].

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If a (30cm by 40cm) page of a book includes a 2cm margin on each side, then the margins occupy 11.67 percentage of the total surface area of one side of the pages.

As per the question statement, a (30cm by 40cm) page of a book includes a 2cm margin on each side.

We are required to calculate the percentage of the total surface area of one side of the pages, occupied by the margins.

To solve this question, first we will need to calculate the total surface area of one side of the pages, and also the surface area occupied by the margins on one side, and then simply, calculate the percentage amount between the two area values.

Since the dimensions of the pages of the book are (30cm by 40cm), therefore, area of one side of each page = (30 * 40) sq. cm.

                                                                    = 1200 sq. cm.

And, area occupied by the margins on each side of the page

= [(2 * 30) + (2 * 40)] sq. cm.

= (60 + 80) sq. cm.

= 140 sq. cm.

Therefore, percentage of the total surface area of one side of the pages, occupied by the margins = [(140/1200) * 100] = 11.67%

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Answer: [tex]y= \frac{-12}{5}x -2[/tex]

Step-by-step explanation:

1) Move x to the right.

1/4y = -1/2 - 3/5x

2) Multiply both sides by 4 to make y by itself.

-1/2 * 4 = -2 (Multiply the top by 4 and you will get -4/2 = -2)

-3/5x * 4 = -12/5x (Multiply the top by 4 and you will get -12/5x)

y= -2 - 12/5x

3) Reorder the terms so that x goes first.

y= -12/5x -2

Answer: y=-12/5(x-2)

Step-by-step explanation:

Move x to the right.

1/4y = -1/2 - 3/5x

2) Multiply both sides by 4 to make y by itself.

-1/2 * 4 = -2 (Multiply the top by 4 and you will get -4/2 = -2)

-3/5x * 4 = -12/5x (Multiply the top by 4 and you will get -12/5x)

y= -2 - 12/5x

3) Reorder the terms so that x goes first.

y= -12/5x -2

Answer:

22

Step-by-step explanation:

The x-coordinates are the same, so we can find the positive difference between the y-coordinates, which is 22.

the answer is D) 22.

There are 450 triangles, we can pick that do not form an equilateral triangles when 15 dots are evenly spaced on the circumference of a circle.

Let's calculate the total no. of possible triangles, it depends on the combination. To make a triangle, we have to choose 3 dots out of 15.

Here, we will use the combination rule to find out the possible triangles,Thus, the total number of possible triangles = 15C3                                                                      = (15.14.13) / (1.2.3) = 455

Note that an equilateral triangle would be formed by connecting 3 equally spaced dots.

For an equilateral triangle, out of 15 dots, there would be 15 - 3 = 12 dots that will not be connected.

And 12/3 = 4 dots would be between any two connecting dots.

Taking 1st connecting dot, the second connecting dot would be

1 + 4 + 1 = 6th

Similarly, the third connecting dot would be 6 + 4 + 1 = 11th

So, the following connecting dots will form equilateral triangles: (1, 6, 11); (2, 7, 12); (3, 8, 13); (4, 9, 14); (5, 10, 15);

After applying the combination rule we found the total number of the possible triangle and there are 5 equilateral triangles:

So, there are 455 - 5 = 450 triangles that are not equilateral triangles.

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Answer:

f=4

Step-by-step explanation:

I think it's right but not 100% sure

Answer:

x = 70

Step-by-step explanation:

(2x - 5) and 45 are same- side interior angles and sum to 180° , that is

2x - 5 + 45 = 180

2x + 40 = 180 ( subtract 40 from both sides )

2x = 140 ( divide both sides by 2 )

x = 70

Answer:

i dunno

Step-by-step explanation:

hard man

Answer:

(y+5)(y-3)

Step-by-step explanation:

..........

Answer:

y^2-3y+5y-15

y(y-3)+5(y-3)

(y-3) (y+5)

The Slope of the line q equals 3.

Given the slope of line r is -

slope = perpendicular / base

Finding the equation of line using coordinates (2,3) and (-1,4)

putting the values in the equation,

y2 - y1 / x2 - x1

⇒ 4-3 / -1 -2

⇒ 1/-3

⇒ -1/3

Slope of the line r is -1/3

As line q is perpendicular to line r,

Using the property, 2 lines perpendicular to each other have slope = negative reciprocal of slope 1

the slope of line q becomes 3

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The maximum height of the skateboarder is 40.25 feet after 0.875 seconds

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let h(t) represent the height of the skateboarder after t seconds.

h(t) = -16t² + 28t + 8

The maximum height is at h'(t) = 0

h'(t) = -32t + 28

-32t + 28 = 0

32t = 28

t = 0.875s

h(0.875) = -16(0.875)² + 28(0.875) + 8 = 40.25 feet

Maximum height is 40.25 feet

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Answer:

2.28 or 2.2

Step-by-step explanation:

46 angle and 18x+5 angle make a z formation and the interior is always the same

46 -5 =41

41/18 =2.2777

round it off and you get 2.2

you can always verify it by putting it in the place of x

Description of a Function : Consider two nonempty sets, X and Y. A relation that links exactly one element from X to Y is known as a function from X into Y.

f(x) = 5x-2 ?

Solution:

f(x) = 5x-2

5x-2 = 0

 5x = 2

    x = 0.4

f(0.4) = 5(0.4)-2

          = 0

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Using proportions, it is found that the scale of the rectangle is of 1:14.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division to find the unit rates.

One example of application of proportions is for scale problems, as the scale is given by the following equation:

Scale = Drawn distance : Actual distance.

For this problem, we have that:

Hence the scale is of:

6.1 : 85.4.

We can simplify dividing 85.4 by 6.1, hence:

85.4/6.1 = 14.

Hence the simplified scale is:

1:14.

This problem is incomplete and could not be found on any search engine, hence we are going to suppose that it asks for the scale of the drawing of the rectangle.

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[tex]x^{2} + 2x - 15 = 0[/tex] -> [tex](x+1)^{2} - 16 = 0[/tex]

-> [tex](x+1)^{2} = 16[/tex]
-> x+ 1 = 4 or -4
-> x = 3 or -5

Answer:

[tex]x=3, \quad x=-5[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]x^2+2x-15=0[/tex]

Step 1

Move the constant to the right side of the equation:

[tex]\implies x^2+2x-15+15=0+15[/tex]

[tex]\implies x^2+2x=15[/tex]

Step 2

Add the square of half the coefficient of the term in x to both sides to form a perfect square trinomial on the left side:

[tex]\implies x^2+2x+\left(\dfrac{2}{2}\right)^2=15+\left(\dfrac{2}{2}\right)^2[/tex]

[tex]\implies x^2+2x+1=15+1[/tex]

[tex]\implies x^2+2x+1=16[/tex]

Step 3

Factor the perfect square trinomial on the left side:

[tex]\implies (x+1)^2=16[/tex]

Step 4

Square root both sides:

[tex]\implies \sqrt{(x+1)^2}=\sqrt{16}[/tex]

[tex]\implies x+1=\pm4[/tex]

Step 5

Subtract 1 from both sides:

[tex]\implies x+1-1=-1\pm4[/tex]

[tex]\implies x=-1\pm4[/tex]

Solutions

[tex]\implies x=-1+4=3[/tex]

[tex]\implies x=-1-4=-5[/tex]

Therefore, the solutions of the given quadratic equation are:

[tex]x=3, \quad x=-5[/tex]

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Answer:

D. The last 26/8, 3-32, -Pi, -4 2/3

Step-by-step explanation:

26/8= 3.25

3-32=3.17

-Pi= -3.14

-4 2/3= -4.67

Step-by-step explanation:

3 ................

.

........................

Answer:

3

Step-by-step explanation:

–4 + (–16) + 23

–4 – 16 + 23

–20 + 23

= 3

Answers:

a)  2710 kg/m³

b)  5149 kg

====================================================

Work shown for part a)

density = mass/volume

density = (6775 kg)/(2.5 m³)

density = (6775/2.5) kg/m³

density = 2710 kg/m³

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

Work shown for part b)

density = mass/volume

mass = density * volume

mass = (2710 kg/m³) * (1.9 m³)

mass = (2710*1.9) kg

mass = 5149 kg

From the division property, the required kansui is 5/32 tablespoon.

What is division?

One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.

Given that a batch of mooncake contains 1/4 tablespoon of kansui.

Given batch of mooncake is 1 3/5 = 8/5

Therefore,

[tex]\frac{\frac{1}{4}}{\frac{8}{5}}\\=\frac{1}{4} \times \frac{5}{8}\\=\frac{5}{32}[/tex]

Hence, the required kansui is 5/32 tablespoon.

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If the sales tax in your city is 4.4% and an item costs $3 before tax the amount of tax you would  pay on that item is $0.132.

Sales tax is the tax amount that is charge on goods customers buys.

Using this formula to determine the sales tax

Sales tax = Sales tax percentage × Cost of item

Where:

Sales tax percentage = 4.4% or 0.044

Cost of item = $3

Let plug in the formula so as to find the sales tax

Sales tax = 0.044 × $3

Sales tax = $0.132

Therefore the sales tax amount is $0.132.

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For triangle UTV reflection across y = 1 would be,

U' = (0, 2)

T' = (-3, 3)

V' = (-1, 5)

And for triangle HIJ the reflection across y = -2 would be,

H' = (-5, 1)

I' = (-3, -3)

J' = (-2, -1)

1)

In this question, we have been given a triangle UTV.

We need to find the the coordinates of the triangle if it is reflected across the line y = 1

Coordinates of UTV are:

U = (1, 2)

T = (-3, -1)

V = (-1, -3)

If we take the reflection across line y = 1 then,

U(1, 2) --> U'(0, 2)

T(-3, -1) --> T'(-3, 3)

V(-1,-3) --> V'(-1, 5)

2)

In this question, we have been given a triangle HIJ.

We need to find the the coordinates of the triangle if it is reflected across the line y = -2

Coordinates of HIJ are:

H = (-5, -5)

I = (-3, -1)

J = (-2, -3)

If we take the reflection across line y = -2 then

H(-5, -5) --> H'(-5, 1)

I(-3, -1) --> I'(-3, -3)

J(-2, -3) --> J'(-2, -1)

Therefore, for triangle UTV reflection across y = 1 would be,

U' = (0, 2)

T' = (-3, 3)

V' = (-1, 5)

And for triangle HIJ the reflection across y = -2 would be,

H' = (-5, 1)

I' = (-3, -3)

J' = (-2, -1)

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The midpoint of the given coordinates of points (0,-10) and (-6,-8) is  ( -3,-9 )

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point 1( 0,-10 )

Point 2( -6,-8 )

Midpoint = ?

To determine the midpoint, plug the given points into the midpoint formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ( 0 + (-6) )/2, ( (-10) + (-8) )/2 )

M = ( ( 0 - 6) )/2, ( -10 - 8 )/2 )

M = ( ( -6 )/2, (-18 )/2 )

Midpoint M = ( -3,-9 )

Therefore, the midpoint of the coordinates is ( -3,-9 ).

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Answer:

21

Step-by-step explanation:

You are 14 right now if you were 7 yo 7 years ago. Add 7 more years to 14 and you get 21

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: Correct \:\: Choice\:\: D[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

For being the sides of an Isosceles triangle, the measure of two sides should be equal. and it should also fulfil the criteria of being a triangle.

i.e sum of either two sodes shouldn't exceed the third one, and difference between any two sides shouldn't be smaller than the third side.

So, keeping that in mind, the only option that satisfy the criterias is :

D. 4, 4, 6

As it has two equal sides measuring 4 each, and it fulfils the criteria of being a triangle too.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Step-by-step explanation:

I beleive it would be D

The likes and dislikes of the people is given the priority and the product is altered according to the taste of the consumers , in order to increase the sale of the product .

It refers to the method of sampling , where the data or information is collected from a certain specified group of people , is referred to as quota sampling .

The method is helpful for marketing the goods and services of the company .

The likes and dislikes of the people is given the priority and the product is altered according to the taste of the consumers , in order to increase the sale of the product .

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Answer: ales revenue = 1,386,000 dollars Increase sales in percent = 10 percent Increase sales in dollars = 1,386,000 dollars * 0,1 = 138,600 dollars New sales goal in dollars = 1,386,000 dollars + 138,600 dollars = 1,524,600 dollars

New sales goal is 1,524,600 dollars.

Step-by-step explanation:

For every mile the car is driven the cost increases by $ 0.74 or 74 cents.

It is given in the question that the equation y = 0.74x + 64 gives the cost y of renting a car if the car is driven x miles.

It is a linear equation in 2 variable.

We have to find, for every mile the car is driven the cost increases by how much.

As we can observe from the equation, 64 is the fixed cost of renting a car, $ 0.74 is the cost of driving per mile.

Hence, for every mile the car is driven the cost increases by  $ 0.74 or 74 cents.

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a collection of 65 coins contains one with two heads. the remainder of the coins are fair. if a coin, selected randomly from the collection, turns up heads 6 times in 6 tosses, 1/65 is the probability it’s a two-headed coin

Definition of probability

(1) : the chance that a given event will occur. (2) : the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

We know that one coin in a collection of 65 has two heads. If a coin, chosen at random from the lot and then tossed, turns up heads 6 times in a row. We calculate the probability that it is the two-headed coin.

We calculate  the number of possible combinations:

C₁⁶⁵= 65!/1!(65-1)!

     = 65

Number of favorable combinations is 1.

Therefore, the probability is

P=1/65.

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