Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.

Determine the equation for the parabola graphed below.
y =
x2 +
x +

Answer:

Carrie read at a rate of 21 2/3 pages per hour

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Time Ms. Graves gave her class to read = 18 minutes

Number of pages Carrie read in 18 minutes = 6 1/2 pages

2. At what rate, in pages per hour, did Carrie read?

Rate = Number of pages/Time given

For getting the exact rate per hour, we should use the Rule of Three Simple, this way:

Number of pages in 60 minutes * 18 = 6 1/2 * 60

Number of pages in 60 minutes = (6.5 * 60)/18

Number of pages in 60 minutes = 390/18 = 21.67 or 21 2/3

Carrie read at a rate of 21 2/3 pages per hour

Answer:

the boat travel one way = 2 x 14.16 = 28.32 miles

Step-by-step explanation:

the return trip only takes 1.7 miles (?) ... is it 1.7 hours (?)

the boat travels 2.5 miles (per hour ?) faster downstream

I calculate it on the assumption of my guess stated above ...

X: represent the boat speed / hour

distance one way = 2X

and Distance also = 1.7 * (x + 2.5 ) on return

2x = 1.7 x + 1.7 * 2.5 = 1.7x + 4.25

0.3 x = 4.25

x = 14.16

the boat travel one way = 2 x 14.16 = 28.32 miles

Answer:

7000

Step-by-step explanation:

because 6532 is closer to 7000 then 6000.

Step-by-step explanation:

|h-3|<5

This implies that

h-3<5 or h-3<-5

h<5+3 or h<-5+3

h<8 or h<-2

Hence the solution set is {h:h<-2 or h<8 }

Therefore the number line in the picture shows the solution set for |h-3|<5

The inequality |h-3|<5 means that h is a numerical value between -2 and 8. A number line representing this solution set would be marked between these two values.

The inequality |h-3|<5 represents all numbers that are less than 5 units from 3 on the number line. It leads to two simple inequalities. When we remove the absolute value we get -5 < h-3 < 5, which simplifies to -2 < h < 8. So the number line that shows the solution set will have a line drawn between -2 and 8, indicating all the numbers between these two values satisfy the inequality.

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Option B

-0.249851765 is a irrational number

Solution:

Given number is -0.249851765

We have to classify the number

Let us first understand about irrational, real, whole, integer and rational numbers

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043

Every integer can be expressed as a decimal, but most numbers that can be expressed as a decimal are not integers. If all the digits after the decimal point are zeroes, the number is an integer. If there are any non-zero digits after the decimal point, the number is not an integer.

Thus -0.249851765 has non zero digits after decimal point. So it is not a integer

Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."

But the given number -0.249851765 is negative number. So it is not a whole number

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc. Natural numbers are also called "counting numbers" because they are used for counting.

A decimal is a natural number if it is non-negative and the only digits after its decimal points are zero

So the given number -0.249851765 is a negative number and so it is not a natural number

A rational number is a number that can be expressed as a fraction (ratio) in the form [tex]\frac{p}{q}[/tex] where p and q are integers and q is not zero.

The rational numbers includes all positive numbers, negative numbers and zero that can be written as a ratio (fraction) of one number over another.

When a rational number fraction is divided to form a decimal value,  it becomes a terminating or repeating decimal.

So -0.249851765 is not a rational number

An irrational number is real number that cannot be expressed as a ratio of two integers.

When an irrational number is expressed in decimal form, it goes on forever without repeating

So the given number -0.249851765 is irrational number

We can conclude that:

-0.249851765 is a irrational number, So Option B is correct

Answer:

Therefore values of a and b are

[tex]a=3\ and\ b = 2[/tex]

Step-by-step explanation:

Rewrite [tex]x^{2}-6x+7=0[/tex] in the form

[tex](x-a)^{2}=b[/tex]

where a and b are integers,

To Find:

a = ?

b = ?

Solution:

[tex]x^{2}-6x+7=0[/tex] ..............Given

Which can be written as

[tex]x^{2}-6x=-7[/tex]

[tex](\frac{1}{2} coefficient\ of\ x)^{2}=(\frac{1}{2}\times -6)^{2}=9[/tex]

Adding half coefficient of X square on both the side we get

[tex]x^{2}-6x+9=-7+9=2[/tex] ...................( 1 )

By identity we have (A - B)² =A² - 2AB + B²

Therefore,

[tex]x^{2}-6x+9=x^{2}-2\times 3\times x+3^{2}=(x-3)^{2}[/tex]

Substituting in equation 1 we get

[tex](x-3)^{2}=2[/tex]

Which is in the form of

[tex](x-a)^{2}=b[/tex]

On comparing we get

a = 3 and b = 2

Therefore values of a and b are

[tex]a=3\ and\ b = 2[/tex]

Answer 2: a = 3 and b = 2

Answer:

All real numbers are solution for the inequality.

Step-by-step explanation:

Given expression:

[tex]2(-6n-5)<-3(4n+2)[/tex]

Solving the inequality.

Using the distribution.

[tex](2(-6n))+(-2(-5)<(-3(4n))+(-3(2))[/tex]

[tex]-12n-10<-12n-6[/tex]

Adding [tex]12n[/tex] to both sides.

[tex]-12n+12n-10<-12n+12n-6[/tex]

We have,

[tex]-10<-6[/tex]

The above statement is always true and thus the inequality has all real number solutions.

The number line graph for the inequality can be shown.

Answer:

If today is Saturday, the probability that tomorrow is Sunday.

Step-by-step explanation:

Answer:

5.   m < 1 = 72 degrees.

6.    m < 1 = 80 degrees.

Step-by-step explanation:

5. < 1 = 72 degrees.

If we draw a line through the point of < 1,  We see that  We have have 2 angles  of 40 and 32 ( alternate angles).

6.  By the same reasoning m < 1 = 60 + 20

= 80 degrees.

Answer: 250 grams.

Step-by-step explanation:

Let x be the weight of the solution.

Given : There are 80 grams of salt in a 32% solution.

That means , 32% of x = 80 grams

[tex]\Rightarrow\ 0.32x=80[/tex]  [convert percent into decimal by dividing it by 100]

[tex]\Rightarrow\ x=\dfrac{80}{0.32}=\dfrac{8000}{32}=250[/tex]

i.e. Total solution = 250 grams.

Hence, the weight of the solution = 250 grams.

Answer:

The answer is 6 ratio because when you divide these two number then the anwer is 6

Answer:

ratio of food costs to take away home 1:6

Step-by-step explanation:

$1500: $250

150:25

30:5

6:1

Answer:

70%

Step-by-step explanation:

69 - 20.70 = 48.3

48.3 / 69 = 0.7

0.7 x 100 = 70

The discount percentage for the JCPenney dress, discounted from an original price of $69.00 to a final price of $20.70, is calculated to be 70% off.

To calculate the discount percentage for the JCPenney dress, we need to find the difference between the original price and the final price, and then divide that by the original price. We can then multiply the result by 100 to get the percentage.

The original price of the dress is $69.00, and the final price is $20.70. The difference between these two prices is $69.00 - $20.70 = $48.30. This is the amount of the discount.

To find the discount percentage, we divide the discount amount by the original price: $48.30 / $69.00 = 0.7. To convert this decimal to a percentage, we multiply by 100: 0.7  imes 100 = 70%.

Thus, the dress is discounted by 70%.

Answer:

8 ounces of vinegar

36 ounces of dressing

Step-by-step explanation:

Marco makes his famous salad Jackson by mixing 5 1/4 ounces of olive oil with 1 1/2 ounces of vinegar.

Olive oil                 Vinegar

5 1/4                           1 1/2

28                                x

Write a proportion:

[tex]\dfrac{5\frac{1}{4}}{28}=\dfrac{1\frac{1}{2}}{x}\\ \\5\dfrac{1}{4}\cdot x=28\cdot 1\dfrac{1}{2}\ [\text{Cross multiply}]\\ \\\dfrac{21}{4}x=28\cdot \dfrac{3}{2}\\ \\\dfrac{21 x}{4}=42\\ \\x=42\div \dfrac{21}{4}\\ \\x=42\cdot \dfrac{4}{21}\\ \\x=2\cdot 4\\ \\x=8\ ounces[/tex]

Marco will make

[tex]28+8=36[/tex] ounces of dressing

Answer:

23*0.15=$3.45

Step-by-step explanation:

23*0.15=$3.45

Answer:

$103

Step-by-step explanation:

192.62 divided by 1.87

answer is $103

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If the markup price of the shoes is $192.61 then the original price of the shoes will be equal to $25.04.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the given information in the question,

Let the original price of the shoes is x.

Markup Price = $192.61, which is 87% more than the original price.

Price markup = 192.61 × 87/100 = $167.57

Original Price, x = $192.61 - $167.57

x = $25.04.

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Answer:

maximum value of P is 33

Step-by-step explanation:

Sketch the lines represented by the constraints

5x + y = 16

with intercepts ([tex]\frac{16}{5}[/tex], 0) and (0, 16)

2x + 3y = 22

with intercepts (11, 0) and (0, [tex]\frac{22}{3}[/tex])

The solutions to both are below the lines.

Solve 5x + y = 16 and 2x + 3y = 22 simultaneously to find the point of intersection at (2, 6)

The coordinates of the vertices of the feasible region are

(0, 0), (0, 16), (2, 6), 11, 0)

Evaluate the objective function at each vertex

P = 3(0) + 2(0) = 0 + 0 = 0

P = 3(0) + 2(16) = 0 + 32 = 32

P = 3(2) + 2(6) = 6 + 12 = 18

P = 3(11) + 2(0) = 33 + 0 = 33

The maximum value of P is 33 when x = 11 and y = 0

Answer:

Step-by-step explanation:

x = 60

ΔMAD ≅ Δ SUN

So corresponding parts of congruent triangle are congruent.

∠MDA = ∠NSU

Answer:

x = 90

Step-by-step explanation:

Remember you have to post complete questions in order to get good and exact answers. So here I'll assume a diagram shown below. From the statement. we know that:

△MAD ≅ △SUN

This implies that triangle MAD is congruent to triangle SUN meaning that corresponding sides and angles measure the same. In other words:

∠M = ∠S

∠A = ∠U

∠D = ∠N

And:

MA = SU

AD = UN

MD = SN

So, from the figure:

∠S = ∠M = 30°

As the sum of internal angles of every triangle measures 180°, then:

∠S + ∠U + ∠N  = 180°

And:

∠U = x°

So:

30° + x° + 60°  = 180°

x° = |80° - 30° - 60°

x° =  90°

So:

x = 90

_________________________________________________________

Brainliest?, also let me know if i am wrong, Good Luck.

To find the height of the baby giraffe given the average height of it and a giraffe is 6m, and it is 2/3 the giraffe's height, first solve for the giraffe's height to find it is 7.2m. Then, calculate 2/3 of this to get the baby giraffe's height, which is 4.8m.

The question asks to determine the height of a baby giraffe given the average height of a giraffe and a baby giraffe together is 6m, and the baby giraffe's height is 2/3 that of the giraffe's height. Let X be the height of the giraffe. Then, the baby giraffe's height would be 2/3 X. Given the average of these two heights is 6m, the equation to find the height of the baby giraffe is:

(X + (2/3)X) / 2 = 6

By solving this equation:

Hence, the height of the baby giraffe is 4.8m.

Answer:

Angular cut

Step-by-step explanation:

If you cut it horizontally, the cross-section would be a square.

If you cut it vertically, it would be  result as a triangle.

If you cut angular, it would result as a trapezoid.

Answer: Horizontal cut

Step-by-step explanation:

NO. The mirror will not fit in a space that is 15 inches by 16 inches

Solution:

Given that area of mirror is 225 square inches

[tex]width = 13\frac{3}{4} \text{ inches }[/tex]

Converting the above mixed fraction we get,

[tex]width = 13\frac{3}{4} = \frac{13 \times 4 + 3}{4} = \frac{55}{4} \text{ inches }[/tex]

Let us find the length of mirror

The area of mirror is given as:

area of mirror = length x width

Substituting the given values,

[tex]225 = length \times \frac{55}{4}\\\\length = 225 \times \frac{4}{55}\\\\length = 225 \times 0.0727\\\\length = 16.36[/tex]

Thus length of mirror is 16.36 inches

Will the mirror fit in a space that is 15 inches by 16 inches?

NO. The mirror will not fit in a space that is 15 inches by 16 inches

Because length of mirror is 16.36 inches whereas the given space is 15 inches long

16.36 > 15 so the length of mirror will not fit inside the space

Also width of mirror is [tex]\frac{55}{4} = 13.75[/tex] inches which is less than the given space whose width is 16 inches

13.75 < 16 so the width of mirror will not fit inside the space

The answer is 25.12 exactly

Answer:

3800 square centimeters

Step-by-step explanation:

We need to find the surface of the rectangular prism shown.

The surface area is the area of all the surfaces (including the bottom and top).

There are 6 surfaces, top and bottom is squares and 4 sides are rectangles.

The area of square is side * side, and

The area of rectangle is length * width

Top Area = 10 * 10 = 100

Bottom Area = 10 * 10 = 100

Area of 1 side = 90 * 10 = 900

Hence, area of 4 of these same sides is:  900 * 4 = 3600

Total Surface Area = 3600 + 100 + 100 = 3800

Total Carpet Needed = 3800 square centimeters

Answer:

3800

Step-by-step explanation:

Answer:

SAS

Step-by-step explanation:

WX = ZY

ANGLE W = ANGLE Y (90 DEGREE)

YZ = YZ

SAS CONGRUENCY

I hope this answer is correct

Anyways do confirm

Answer:

y - 8 = (-2/3)(x + 3)

y - 8 = (-2/3)x - 2

y = (-2/3)x + 6

Answer:

the answer will be -5 and 1/2

Answer:

5 is a regular number and 1/2 is a fraction

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Step-by-step explanation:

If cos x= sin(20 + x)° and 0° < x < 90° then value of x is 35 degrees

Solution:

Given that:

[tex]cos x= sin (20 + x)[/tex]

We know that,

[tex]sin (a+b)=sin a \times cos b+cos a \times sin b[/tex]

[tex]cos x= sin (20 + x) = sin 20 cos x + cos 20 sin x[/tex]

[tex]cos x-sin20 \times cos x=cos 20 \times sin x[/tex]

Taking cos x as common,

[tex]cos x(1-sin 20)=cos 20 \times sin x[/tex]

[tex]\frac{(1-sin 20)}{(cos 20)}=\frac{sin x}{cos x }\\\\tan x = \frac{(1-sin 20)}{(cos 20)}[/tex]

By trignometric functions,

sin 20 = 0.34202

cos 20 = 0.939692

So,

[tex]tan x = \frac{1 - 0.34202}{0.939692}\\\\tan x = 0.7002[/tex]

Therefore,

x = arc tan (0.7002)

x = 35 degrees

Therefore value of x is 35 degrees

cos x = sin (20 + x)

sin and cos are co - functions, which means that:

cos x = cos [90 - (20 + x)]

cos x = cos (90 - 20 - x)

cos x = cos (70 - x)

Therefore, x = 70 - x

x + x = 70

2x = 70

x = 35

Therefore value of x is 35 degrees

Answer:

f(3)=11

Step-by-step explanation:

given f(x)=4x-1.............(1)

put x=3

f(3)=[tex]4\times3[/tex]-1

f(3)=12-1

f(3)=11 answer

Answer: y = (4/3)x + 8

Step-by-step explanation:

Answer:

The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)

Step-by-step explanation:

we have

[tex]f(x)=2x^{2}+3x-5[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex is a minimum

The coordinates of the vertex is the point (h,k)

step 1

Find the vertex of the quadratic function

Factor the leading coefficient 2

[tex]f(x)=2(x^{2}+\frac{3}{2}x)-5[/tex]

Complete the square

[tex]f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-5-\frac{9}{8}[/tex]

[tex]f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-\frac{49}{8}[/tex]

Rewrite as perfect squares

[tex]f(x)=2(x+\frac{3}{4})^{2}-\frac{49}{8}[/tex]

The vertex is the point (-\frac{3}{4},-\frac{49}{8})

step 2

Find the x-intercepts (values of x when the value of f(x) is equal to zero)

For f(x)=0

[tex]2(x+\frac{3}{4})^{2}-\frac{49}{8}=0[/tex]

[tex]2(x+\frac{3}{4})^{2}=\frac{49}{8}[/tex]

[tex](x+\frac{3}{4})^{2}=\frac{49}{16}[/tex]

take the square root both sides

[tex]x+\frac{3}{4}=\pm\frac{7}{4}[/tex]

[tex]x=-\frac{3}{4}\pm\frac{7}{4}[/tex]

[tex]x_1=-\frac{3}{4}+\frac{7}{4}=1[/tex]

[tex]x_2=-\frac{3}{4}-\frac{7}{4}=-2.5[/tex]

therefore

The function f(x) is negative in the interval (-2.5,1)

The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)

see the attached figure to better understand the problem