Work out
m
and
c
for the line:
2
y
−
4
x
=
2

To write an equation for a parabola with the vertex and y-intercept, the equation of vertex form y=a(x-h)^2+k is used.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

Consider an example where vertex is (2,1) and y-intercept is (0,-3).

The equation of parabola needs to be deduced using these points.

The equation of a parabola in vertex form is -

y=a(x-h)^2+k

Here, a is a constant and (h ,k) are the coordinates of the vertex.

So, (h,k)=(2,1)

⇒y=a(x−2)^2+1

To obtain the value of a, substitute (0,−3) into the equation -

-3=4a+1

4a=-4

a=-1

⇒y=-1(x−2)^2+1

Now, distribute and simplify -

y=-1(x−2)^2+1

y=-(x^2-4x+4)+1

y=-x^2+4x-4+1

y=-x^2+4x-3

On, graphing this equation a parabola is obtained.

Therefore, to write an equation of parabola vertex form is used.

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⟹ Numbers that are less than zero are known as negative numbers (or integers). They fall on the left side of the number line.

⟹ Numbers that are greater than zero are known as positive numbers (or positive integers). They fall on the right side of the number line.

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꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

40

Step-by-step explanation:

Perimeter of sqaure:

= 4 × side

= 4 × 10

= 40 m

Answer:

I'm not good with math lol

As per the graph, there is no restrictions for the domain but the range has a minimum value at y = - 4.

The domain is any real number:

The range is any real number not less than - 4:

The ordered pair that would be needed by the company for shipment can be loaded in the trailer as the pair will take only 3200ft³ of the volume of the trailer which is 3800 cubic feet.

The total volume of the trailer = 3800 cubic feet

The volume of each recliner = 40 cubic feet

The volume of each sofa = 80 cubic feet

The number of recliner needed = 30

The number of sofas needed = 25

The volume that the sofa will cover = 25 × 80 = 2000

The volume that the recliner will cover= 30 × 40 = 1200

Therefore the total volume both will take = 3200 cubic feet.

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Answer:

x=29, y= 14

Step-by-step explanation:

y=16-2(move the 2 over to isolate y.) y=14. now input 14 in the bottom equation. x= 2(14)+1, 2×14=28, 28+1=29. x=29, y=14

Answer:it’s 5.36

Step-by-step explanation:

The perimeter of a trapezoid is 28ft.

An isosceles trapezoid is a trapezoid whose non-parallel sides (the legs) are equal in length.

The perimeter of an  isosceles trapezoid (P) = a + b+ 2c

where a is the top, b is the bottom, and c is the leg of the trapezoid

According to the question,

perimeter = 38ft

leg of an isosceles trapezoid = 8ft

        38 = a +b +2 × 8

    ⇒ 38 = a+b +16

   ⇒a +b = 38 -16

    ⇒a +b = 22

Another similar trapezoid has a leg measuring 3ft.

Perimeter of this trapezoid is =( 22 + 2× 3) ​ft

                                                   = (22 +6)ft

                                                   = 28 ft

So, the perimeter of a trapezoid is 28ft.

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Answer:

Total cost =3over8 x 48 x0. 55=9.9

Answer:

$9.90

Step-by-step explanation:

First, we need to find the number of vanilla cupcakes.

The question tell us that 3/8 of the 48 cupcakes are Vanilla flavored, so we can start by dividing 48 by 8 to find what 1/8 of 48 is:

48/8 = 6

1/8 of 48 = 6

Now to find 3/8, we just need to multiply that number by 3:

6 x 3 = 18

3/8 of 48 = 18

So now we know that she bought 18 vanilla cupcakes.

Finally to find the price, we just need to multiply the price per cupcake by the number of cupcakes:

$0.55 per cupcake x 18 cupcakes = 0.55 x 18 = $9.90

The total cost of the vanilla cupcakes was $9.90

Hope this helped!

Answer: x = 60

Step-by-step explanation:

the equation is a^2 + b^2 = c^2.

If you draw out the problem, you plug in the information into the formula, so it would be...

x^2 + 80^2 = 100^2.

80^2 = 6,400 and 100^2 = 10,000.

x^2 + 6,400 = 10,000.

You subtract 6,400 from itself and 10,000 and then you get...

x^2 = 3,600.

You square both of those and your final answer will be x = 60.

The degree of the polynomial 2x² 5x³ 7 is 5.

The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the highest exponent of the variable is 5, which appears in the term 5x³. The degree of a polynomial is a whole number that tells us how many times the variable is multiplied by itself. The degree of the polynomial is 5.

It's worth noting that polynomials can be constant or non-constant, meaning they don't have to have a variable in them, in that case the degree is 0. And also a polynomial with only one term, the degree of that polynomial is the exponent of that term.

In this case, we only have one term with variable x in it, 5x³, and the degree is the exponent of that term which is 5.

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Answer:

56

Step-by-step explanation:

Gluten-free choices:

Main dishes:  4

Rice dishes:  7

Bread:  2  (40% of 5 is 2)  0.40 x 5 = 2

Multiply numbers of choices together:  4 x 7 x 2 = 56

There are a total of 112 meal deals.

'In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole.'

According to the given problem,

For gluten free choices,

Main dishes = 22 × [tex]\frac{4}{11}[/tex]

                    = 8

Bread choices = [tex]\frac{40}{100}[/tex] × 5

                        = 2

Total possible meal deals = 8 × 7 × 2

                                           = 112

Hence, we can conclude, 112 possible meal deals are gluten free.

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Answer:

[tex]3 \div \frac{3}{4 } \\ = 3 \times \frac{4}{3} \\ = 4[/tex]

The margin of error is $148.89. The upper limit is $2215 and lower limit is $1914.

In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.

First we need to name some of the variables we are given:

n = 38 the sample size

x = 6.88 the sample mean

= 1.86 the population standard deviation

We need to find a 90% confidence interval for the mean price per 100 lbs of watermelon:

= 1-.90 = .10

/2 = .05

z(/2) = -1.64

-z(/2) = 1.64

This can give us a probability expression:

P(-1.645 < z < 1.645) = .90

The margin of error is calculated with the formula: E = z(/2)(/√n)

E = 1.645(1.86/√38) = $.4963(300) = $148.89  

Then to calculate the upper and lower limit we add and subtract E from x:

lower limit = 6.88 - .4963 = $7.38(300) = $2214

upper limit = 6.88 + .4963 = $6.38(300) = $1914

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Answer:

k < 10

Step-by-step explanation:

An inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers.

Let k represent Ken. The closed side of < is the side the smaller number is going to be on. Ken has fewer marbles then Joe, therefore, k < 10 because Joe has 10 marbles.

Answer:

x = 62°

y = 118°

Step-by-step explanation:

Since the sum of interior angles of any quadrilateral is 360°, all of the interior angles in this image will add up to 360°.

Since the shape of the trapezoid is symmetrical, x is equivalent to 62°.

This means 62 + 62 + x + x = 360°

(360-(62+62))/2 = 118°

118 + 118 + 62 + 62 = 360°

x = 62°

y = 118°

Step-by-step explanatio

On solving the provided question, we can say that by fraction they will have the same amount of fish in 5 months.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Month / Brent / Gretel

0/4/ 128

1/ 16 / 256

2 / 64 / 512

3 / 256 / 1024

4 / 1024 / 2048

5 / 4096 / 4096

They will have the same amount of fish in 5 months.

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Answer:

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

Step-by-step explanation:

The center is at x = 3 and y = 2:  (3, 2).  The radius is 2.  Starting with the standard equation of a circle with radius r and center (h, k), we get:

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

Answer:

c is the independent variable and f is the dependent variable

Step-by-step explanation:

Answer:

(a) The complete table

[tex]\begin{array}{cccccc}Hours & {1} & {2} & {3} & {4} &{5}\ \\ {Amount} & {\$9.50} & {\$19.00} & {\$28.50} & {\$38.00} & {\$47.50} \ \end{array}[/tex]

(b) $38.00

(c) 3 hours

Step-by-step explanation:

Given

[tex]Earnings = \$9.50[/tex] per hour

See attachment for complete question;

Solving (a): Complete the table

To complete the table, we simply multiply the earnings by the number of hours.

So, we have:

[tex]Hours = 2 \to Earnings = \$9.50 * 2 = \$19.00[/tex]

[tex]Hours = 3 \to Earnings = \$9.50 * 3 = \$28.50[/tex]

[tex]Hours = 4 \to Earnings = \$9.50 * 4 = \$38.00[/tex]

[tex]Hours = 5 \to Earnings = \$9.50 * 5 = \$47.50[/tex]

Solving (b): Earnings, if Megan works for 4 hours

In (a) above, we have:

[tex]Hours = 4 \to Earnings = \$9.50 * 4 = \$38.00[/tex]

This implies that Megan will earn $38.00

Solving (c): Hours to earn $28.50

In (a) above, we have:

[tex]Hours = 3 \to Earnings = \$9.50 * 3 = \$28.50[/tex]

This implies that Megan will work for 3 hours to earn $28.50

The algebraic expression to show Jill's age will be;

Jill = 1/3 x b

Algebraic expressions are the mathematical statements that are derived when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.

There are different parts of an algebraic expression and they are; Variables - a symbol that doesn't have a fixed value is called a variable. It can take any value assigned to it.

Constants - a symbol that has a fixed numerical value is called a constant. All numbers are constants.

Terms - A term is a variable alone (or) a constant alone (or) it can be a combination of variables and constants and the operation of multiplication or division with it.

Coefficients - the numbers that are multiplying the variables are called coefficients.

Beth's age = b

Jill's age = 1/3 of Beth's age

Jill's age = 1/3 x b

Jill's age = 1/3b

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Answer:

$59.40

Step-by-step explanation:

Multiply the amount of watermellon (12) by the price (4.95) giving you 59.40

Answer:

$59.40

Step-by-step explanation:

take $4.95 and times it by twelve to get $59.40

Answer:

66

Step-by-step explanation:

Replace t with 9 in the equation.

[tex]28(1.1)^9[/tex]

Simplify.

[tex]28(2.358)[/tex]

[tex]66.023[/tex]

Rounded, it equals 66

Answer:

[tex]x + 5y = 6[/tex] is perpendicular to [tex]y = 5x + \frac{6}{5}[/tex] and parallel to [tex]y = -\frac{1}{5}x + 2\\[/tex]

Step-by-step explanation:

First, convert the equation to standard form so that y is isolated.

x + 5y = 6 --> x - 6 = -5y (divide both sides by -5) --> [tex]y = -\frac{1}{5}x + \frac{6}{5}[/tex]

A perpendicular line will have a slope that is the opposite reciprocal of the original slope (meaning you flip the numerator and denominator then make it negative).

[tex]-\frac{1}{5}[/tex] is perpendicular to [tex]-(\frac{-5}{1} )[/tex] which simplifies to 5.

A parallel line will have the same slope, but the y-intercept will be different. It can be pretty much any number as long as the original slope is used in the new equation.

[tex]y = -\frac{1}{5}x + \frac{6}{5}\\[/tex] is parallel to [tex]y = -\frac{1}{5}x + 2\\[/tex] just like [tex]y = -\frac{1}{5}x - \frac{100}{23}[/tex].

Answer:

8

Step-by-step explanation:

3x6 = 18

18-10 = 8