ESSENTIAL QUESTION How do graphs
and equations reveal information about a
relationship between two quantities?

Answer:

100

Step-by-step explanation:

Hey there!

First, to find the cost of one apple, 50 ÷ 25, which equals 2.

At this point, i am not very sure if you meant to say 75 apples, or $75 apples, so I am just going to give both solutions.

If you meant 75 apples: 75 x 2 = $150

If you meant $75 apples: $75 ÷ 2 = 37.5

Since it isn't realistic to buy 37 apples and one half, round it to 37 apples.

Hope this helps!

Have a great day!

Answer:

The answer is A f(x) = -2x + 40

Step-by-step explanation:

it has a negative 2 because the dumps are decreasing by 2 every week and x is the amount of weeks and + 40 because that is the amount you started with.

Answer:

d = 55.5  

x = 1

c = 11

m = [tex]\frac{1}{122}[/tex]

k = [tex]\frac{a}{(c + 5)}[/tex]

Step-by-step explanation:

Sorry, the formatting is slightly hard to understand, but I think this is what you meant.

Q1.

[tex]\frac{1}{6}[/tex]d - 8 = [tex]\frac{5}{8}[/tex] x 2

Step 1. Simplify.

[tex]\frac{5}{8}[/tex] x 2 = [tex]\frac{5}{8}[/tex] x [tex]\frac{2}{1}[/tex] = [tex]\frac{10}{8}[/tex]

Step 2. Cancel out the negative 8.

[tex]\frac{1}{6}[/tex]d - 8 = [tex]\frac{10}{8}[/tex]

+ 8 to both sides (do the opposite: [tex]\frac{1}{6}[/tex]d is subtracting 8 right now, but to cancel that out, we will do the opposite of subtraction, i.e. addition)

[tex]\frac{1}{6}[/tex]d = [tex]\frac{10}{8}[/tex] + 8

Step 3. Simplify.

[tex]\frac{10}{8}[/tex] + 8 = [tex]\frac{10}{8}[/tex] + [tex]\frac{8}{1}[/tex] = [tex]\frac{10}{8}[/tex] + [tex]\frac{64}{8}[/tex] = [tex]\frac{74}{8}[/tex] = [tex]\frac{37}{4}[/tex]

Step 4. Cancel out the [tex]\frac{1}{6}[/tex].

[tex]\frac{1}{6}[/tex]d = [tex]\frac{37}{4}[/tex]

÷ [tex]\frac{1}{6}[/tex] from both sides (do the opposite: d is multiplied by [tex]\frac{1}{6}[/tex] right now, but to cancel that out, we will do the opposite of multiplication, i.e. division)

÷ [tex]\frac{1}{6}[/tex] = x 6

So....

x 6 to both sides

d = [tex]\frac{37}{4}[/tex] x  6 = [tex]\frac{37}{4}[/tex] x [tex]\frac{6}{1}[/tex] = [tex]\frac{222}{4}[/tex] = [tex]\frac{111}{2}[/tex] = 55.5

Step 5. Write down your answer.

d = 55.5

Q2.

3x - 4 + 5x = 10 - 2x × 3

Step 1. Simplify

3x - 4 + 5x = 3x + 5x - 4 = 8x - 4

10 - 2x × 3 = 10 - (2x × 3) = 10 - 6x

Step 2. Cancel out the negative 6x

8x - 4 = 10 - 6x

+ 6x to both sides (do the opposite - you're probably tired of reading this now - right now it's 10 subtract 6x, but the opposite of subtraction is addition)

14x - 4 = 10

Step 3. Cancel out the negative 4

14x - 4 = 10

+ 4 to both sides (right now it's 14x subtract 4, but the opposite of subtraction is addition)

14x = 14

Step 4. Divide by 14

14x = 14

÷ 14 from both sides (out of the [14 × x] we only want the [x], so we cancel out the [× 14])

x = 1

Step 5. Write down your answer.

x = 1

Q3.

7(c - 3) = 14 × 4

Step 1. Expand the brackets

7(c - 3) = (7 x c) - (7 x 3) = 7c - 21

Step 2. Simplify

14 x 4 = 56

Step 3. Cancel out the negative 21

7c - 21 = 56

+ 21

7c = 56 + 21

7c = 77

Step 4. Cancel out the ×7

7c = 77

÷ 7

c = 77 ÷ 7

c = 11

Step 5. Write down your answer.

c = 11

Q4.

11([tex]\frac{m}{22}[/tex] + [tex]\frac{3}{44}[/tex]) = 87m + m × 5

Step 1. Expand the brackets

11([tex]\frac{m}{22}[/tex] + [tex]\frac{3}{44}[/tex]) = (11 x [tex]\frac{m}{22}[/tex]) + (11 x [tex]\frac{3}{44}[/tex]) = ([tex]\frac{11}{1}[/tex] x [tex]\frac{m}{22}[/tex]) + ([tex]\frac{11}{1}[/tex] x [tex]\frac{3}{44}[/tex]) = [tex]\frac{11m}{22}[/tex] + [tex]\frac{33}{44}[/tex] = [tex]\frac{m}{2}[/tex] + [tex]\frac{3}{4}[/tex]

Step 2. Simplify.

87m + m x 5 = 87m + 5m = 92m

Step 3. Cancel out the add [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] + [tex]\frac{3}{4}[/tex] = 92m

- [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = 92m - [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = [tex]\frac{92m}{1}[/tex] - [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = [tex]\frac{368m}{4}[/tex] - [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = [tex]\frac{368m - 3}{4}[/tex]

Step 4. Cancel out the ÷ 4

[tex]\frac{m}{2}[/tex] = [tex]\frac{368m - 3}{4}[/tex]

x 4

2m = 368m - 3

Step 5. Cancel out the 368m

2m = 368m - 3

- 368m

-366m = - 3

Step 6. Cancel out the × -366

-366m = -3

÷ -366

m = [tex]\frac{-3}{-366}[/tex]

m = [tex]\frac{1}{122}[/tex]

Step 7. Write down your answer.

m = [tex]\frac{1}{122}[/tex]

Q5.

ck + 5k = a

Step 1. Factorise

ck + 5k = (c × k) + (5 × k) = (c + 5) x k = k(c + 5)

Step 2. Cancel out the × (c + 5)

k(c + 5) = a

÷ (c + 5)

k = a ÷ (c + 5)

k = [tex]\frac{a}{(c + 5)}[/tex]

Answer:

19 of 95% grades

Step-by-step explanation:

90= (0+95(x-1))/x

90x=0+95(x-1)

90x=95(x-1)

90x=95x-95

90x-95x=-95

-5x=-95

x=-95/-5

x=19

Answer:

12 inches

Step-by-step explanation:

A=1/2bh

30=1/2b5

(30*2)/5=b

B=12

Answer:

Step-by-step explanation:

Let the price of the item = Rs x

13% of x = 390

[tex]\frac{13}{100}*x=390\\\\\\x = 390*\frac{100}{13}\\\\\\[/tex]

x = Rs. 3000

Answer:The first issue one most notice is the words “at least” We are trying to find the probability of at least 2 girls.

The five possible outcomes for girls are 0,1,2,3,4. The odds of 1 girl out of 4 is .25 and the odds of 1 boy out of 4 is .25 (same as the odds of 3 out of 4 girls). Therefore the odds of 1 OR 3 girls must be .5 because 1 girl and 3 girls each has a .25 probability. If the probability of (1 OR 3 girls) equals .5, then the probability of 2 girls must be a different number.

The probability of 2 or more girls, is the sum of the probability of 4 girls (.06125)(—-.5 to the 4th power—— ), plus the probability of 3 girls (.25)——(the same as the probability of 1 boy)—- plus the probability of 2 girls. Since we know the probability of zero boys is .0625 (again, .5 to the 4th power) and the probability of 1 boy is .25 (the same as the probability of 3 girls )———then the probability of 2 girls is ((1 minus (the sum of the probability of 0 OR 1 boys) plus the (sum of the probability of 3 or 4 girls)), or 1-((.0625+.25)+(.0625+.25)), or .375. We had to derive the probability of two from the other known probabilities. Therefore .375+.25+.0625=.6875 is the probability of both AT LEAST 2 girls and also NO MORE than 2 boys. Notice this adds up to 1.375 because the probability of the central number 2 (i.e., .375) appears on both sides.

Answer:

(1/2, [tex]\frac{\sqrt{3} }{2}[/tex])

Step-by-step explanation:

Don't totally trust me on this...

Answer:

Step-by-step explanation:

To model the equation for the cost of Each Arrangement.

We need to itemize all parameters needed.

An arrangement consists of

1. one vase

2. twelve roses

Given that 1 vase cost $2 and

The cost of one rose is r

Let the total cost of the arrangement be C

Hence C is the  cost of the vase plus the cost of 12 roses combined, this is given as

[tex]C = 12r + 2[/tex]

Answer:

Step-by-step explanation:

Given,

Principal ( P ) = N 250

Time ( T ) = 4 years

Amount ( A ) =N 330

Rate ( R ) = ?

First, finding the Interest :

According to definition of Amount ,

Amount = Principal + Interest

plug the values

⇒[tex] \sf{330 = 250 + I}[/tex]

Move i to left hand side and change it's sign

⇒[tex] \sf{ - I = 250 - 330}[/tex]

Calculate

⇒[tex] \sf{ - I = - 80}[/tex]

Change the signs of the both equation

⇒[tex] \sf{I = 80 }[/tex]

Interest = 80

Finding the rate :

Simple Interest = [tex] \sf{ \frac{PTR}{100} }[/tex]

plug the values

⇒[tex] \sf{80 = \frac{250 \times 4 \times R}{100} }[/tex]

Multiply the numbers

⇒[tex] \sf{80 = \: \frac{1000 \: R}{100} }[/tex]

Apply cross product property

⇒[tex] \sf{1000R = 100 \times 80}[/tex]

Multiply the numbers

⇒[tex] \sf{1000R = 8000}[/tex]

Divide both sides of the equation by 1000

⇒[tex] \sf{ \frac{1000R}{1000} = \frac{8000}{1000} }[/tex]

Calculate

⇒[tex] \sf{R = 8 \: \% \: }[/tex]

Thus, Rate = 8 %

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

Let's learn about Principal , Interest , Time , Rate and Amount :

Hope I helped!

Best regards!!

Answer:

The correct option is;

45°

Step-by-step explanation:

By angle sum theorem, we have that the sum of angles in a triangle = 180°

Therefore, we have;

When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;

The third angle + 60° + 75° = 180°

Which gives;

The third angle  = 180°- 60° - 75° = 180°- 135° = 45°

The measurement of the third angle by the angle sum theorem will be 45°

The correct option is ∠third angle = 45°.

Answer:  B) 5 inches

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

Explanation:

1 ft = 12 in

9 ft = 108 in ... multiply both sides by 9

9 ft, 9.5 in = 108 in + 9.5 in = 117.5 in

The board's length of 9 ft, 9.5 inches is the same as 117.5 inches.

It's cut into sections of 11.25 inches, so we have (117.5)/(11.25) = 10.44 approximately which rounds down to 10.

Having 10 sections of length 11.25 inches each, takes up 10*11.25 = 112.5 inches so far. That leaves 117.5 - 112.5 = 5 inches as the remaining piece of the board.

Answer:

ΔABC ~ ΔQPR by the Angle-Angle (AA) similarity theorem of two triangles

Step-by-step explanation:

The coordinates of the vertices are given as follows;

A = (1, 2), B =(9, 8), C = (1, 8)

P= (5, -3), Q = (-7, 6), R = (-7, -3)

The given dimensions of AB and PQ are 10, and 15 respectively

The, l lengths of the sides of triangles are found as follows;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

For segment BC, we have;

B =(9, 8), C = (1, 8)

(x₁, y₁) = (9, 8), (x₂, y₂) = (1, 8), substituting gives;

Length BC = 8

For length CA, C = (1, 8) A = (1, 2)

(x₁, y₁) = (1, 8)

(x₂, y₂) = (1, 2)

The length found by substituting the values for (x₁, y₁), (x₂, y₂) in the length equation gives; Length CA = 6

Given that length  CA² + BC² = 8² + 6² = 64 + 36 = 100 = BA², we have by Pythagoras theorem, we have ΔABC is a right triangle

Similarly, for ΔQPR, we have;

Length QR, Q = (-7, 6), R = (-7, -3) = 9

Length PR, P= (5, -3), R = (-7, -3) = 12

QR² + PR² = 9² + 12² = 225 = 15² = PQ²

∴ ΔQPR is a right triangle

By comparing the ratio of the sides, we have;

cos(θ) = PR/PQ = 12/15 = 4/5, θ = cos⁻¹(4/5) = 36.9°

∠RPQ = 36.9°

sin(θ) = QR/PQ = 9/15 = 3/5

Similarly in triangle ΔABC, we have;

cos(θ) = BC/AB = 8/10 = 4/5

∠CBA = 36.9°

Therefore, ∠CBA ≅ ∠RPQ = 36.9°

Also ∠PRQ ≅ ∠BCA = 90° (Angle opposite hypotenuse side of right triangle

Therefore, ΔABC and ΔQPR are similar triangles by the Angle-Angle (AA) similarity theorem of two triangles.

Answer:

(3,0) lie between quadrants I and II. (-9, -3) lie in quadrant III

First subtract the amount the bow takes from the total:

70 - 32 = 38 inches

The width is 14 on top and bottom so subtract 14 x 2 = 28 from 38:

38-28 = 10

Divide 10 by the 2 sides:

10/2 = 5

The height is 5 inches.

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

You don't get a free answer. I am, after all, a high school math teacher, so there has to be a lesson in with this.

The discriminant is part of the quadratic formula. It is:

[tex]b^2-4ac[/tex]. If this value is found to be > 0 and a perfect square, there are 2 real roots; if this value is found to >0 and not a perfect square, there are 2 complex roots; if this value is found to be = 0, then there is 1 real root with a multiplicity of 2; and finally, if this value is found to be < 0, then there are 2 imaginary roots. Also, it would help to know that, because we are dealing with the discriminant, which comes from the quadratic formula, and quadratics, by definition, have 2 solutions, you must have 2 solutions listed as the possible roots for the equation. Our equation is:

[tex]-4x^2=-8-10x[/tex] but in order to determine the a, b, and c for the discriminant, that equation has to be in standard form, set equal to 0:

[tex]-4x^2+10x+8=0[/tex]

From this we can see that a = -4, b = 10, and c = 8. Filling in the discriminant:

[tex]10^2-4(-4)(8)[/tex] which gives us a value of

100 - [4(-4)(8)] (don't forget orders of operation here!)

100 - (-128) = 100 + 128 = 228

This value is greater than 0 but is not a perfect square, so there are 2 complex roots. That means that there will be radicals in the solutions.

Answer:

B. [tex] \frac{HI}{GI} [/tex]

Step-by-step explanation:

The trigonometric ratio formula for tangent of any angle in a right triangle is given as:

tan(θ) = [tex] \frac{opposite}{adjacent} [/tex]

Note: it is the length of the side opposite to the θ, and the length of the side adjacent to θ.

Thus, in the right triangle given, ∆GHI,

θ = <G

The length of side the opposite <G = HI

The length of the side adjacent to <G = GI

Therefore, the equivalent of tan(<G) = [tex] \frac{HI}{GI} [/tex]

Answer:

Step-by-step explanation:

j    -  total number of cars she installed axles on

2    - number of axles she installed on one car

2·j   - total number of axles she installed on

46   - total number of axles she installed on

2·j = 46              {divide both sides by 2}

Answer:

136^3 cm

Step-by-step explanation:

Big square:

5 × 4 × 6 = 20 × 6 = 120

Small rectangle:

7 - 5 = 2

2 × 2 × 4  = 4 × 4 = 16

Both:

120 + 16 = 136

The volume of this figure is 136 cm^3.

Hope this helped.

Answer:

Below

Step-by-step explanation:

First you can find the front area and just multiply it by the length

Find the area of the small square

A = lw

   = (2)(2)

   = 4 cm^2

Find the area of the large square

A = lw

   = (6)(5)

   = 30 cm^2

Now just multiply the area of the two by the length

34 x 4 = 136 cm^3

Hope this helps!

Answer:  -1 < x < 3

Step-by-step explanation:

[tex]\dfrac{5}{(x+2)(4-x)}<1[/tex]

Step 1   The denominator cannot equal zero:

x + 2 ≠ 0    and     4 - x ≠ 0

     x ≠ -2                4 ≠ x

Place these restrictive values on the number line with an OPEN dot:

    <----------o-------------------o--------->

                -2                       4

Step 2   Find the zeros (subtract 1 from both sides and set equal to zero):

[tex]\dfrac{5}{(x+2)(4-x)}-1=0\\\\\\\dfrac{5}{(x+2)(4-x)}-\dfrac{(x+2)(4-x)}{(x+2)(4-x)}=0\\\\\\\dfrac{5-(-x^2+2x+8)}{(x+2)(4-x)}=0\\\\\\\dfrac{5+x^2-2x-8}{(x+2)(4-x)}=0\\\\\\\dfrac{x^2-2x-3}{(x+2)(4-x)}=0\\\\\\\text{Multiply both sides by (x+2)(4-x) to eliminate the denominator:}\\x^2-2x-3=0\\(x-3)(x+1)=0\\x-3=0\quad x+1=0\\x=3\quad x=-1[/tex]

Add the zeros to the number line with an OPEN dot (since it is <):

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 3    Choose test points to the left, between, and to the right of the points plotted on the graph. Plug those values into (x - 3)(x + 1) to determine its sign (+ or -):

Left of -2: Test point x = -3: (-3 - 3)(-3 + 1) = Positive

Between -2 and -1: Test point x = -1.5: (-1.5 - 3)(-1.5 + 1) = Positive

Between -1 and 3: Test point x = 0: (0 - 3)(0 + 1) = Negative

Between 3 and 4: Test point x = 3.5: (3.5 - 3)(3.5 + 1) = Positive

Right of 4: Test point x = 5: (5 - 3)(5 + 1) = Positive

          +         +        -          +       +

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 4  Determine the solution(s) based on the inequality symbol. Since the original inequality was LESS THAN, we want the solutions that are NEGATIVE.

Negative values only occur between -1 and 3

So the solution is:     -1 < x < 3

Answer:

b^12

Step-by-step explanation:

(b^4)^3

We know that x^y^z = x^(y*z)

b^4^3 = b^*4*3) = b^12

Answer:

Below

Step-by-step explanation:

Notice that x is between 10 and -10 but takes only the values that are integers.

The inequalities:

● we can write an inequality that includes all these values.

● -10 《 x 《 10

This is a possible inequality

Multiply both sides by 2 and you will get a new one:

● -20 《 2x 《 20

You can multiply it by any number to generate a new inequality.

Or you can add or substract any number.

Answer:

1.

(a) The Domain is the set of inputs of the function.

Considering that the function takes a period of 3 weeks (21 days), the domain is [0, 21], once we can't evaluate what happens after the 21st day.

[tex]\text{Domain is } [0, 21][/tex]

Otherwise, it could be [tex][0, \infty)[/tex]

Note: We include 0 and 21.

Once the greatest balance was $400, it will not exceed $400, either it doesn't show negative values.

[tex]\text{Range is } [0, 400][/tex]    

Note: We include 0 and 400.

(b)

Once the greatest balance was $400, when x=0, it seems that the y-value is half of $400, therefore, approximately $200. It also represents the initial value, the amount of money when she opened the account.

(c)

[tex]f(x)=B(d)[/tex]

[tex]B(12)=0[/tex]

(d)

It is in segment 4.

The balance equal to zero means that the y-value of the graph is zero, therefore in the x-axis.

Answer: False. This expression is a monomial!

Answer:

false

Step-by-step explanation:

it is molonomial

Answer:A

Step-by-step explanation:

The phrase can be described broadly as adjusted gross income (AGI) minus allowable tax deductions.

"Adjusted gross income, or AGI, is your gross income minus certain adjustments. The IRS uses this number as a basis for calculating your taxable income. AGI can also determine which deductions and credits you may qualify for."

Since, Taxable income is the portion of your gross income used to calculate how much tax you owe in a given tax year.

It can be described broadly as adjusted gross income (AGI) minus allowable itemized or standard deductions.

Taxable income includes wages, salaries, bonuses, and tips, as well as investment income and various types of unearned income.

Hence, the phrase can be described broadly as adjusted gross income (AGI) minus allowable tax deductions.

Learn more about adjusted gross income visit:

brainly.com/question/6705479

#SPJ5

Answer:

x^2 -10x+2

Step-by-step explanation:

(3x^2 - 11x - 4) – (x – 2) (2x + 3)

FOIL

(3x^2 - 11x - 4) – (2x^2-4x+3x-6)

Combine like terms

(3x^2 - 11x - 4) – (2x^2 -x-6)

Distribute the minus sign

3x^2 - 11x - 4 – 2x^2 +x+6

Combine like terms

x^2 -10x+2

This is the same as writing  v = sqrt(ar)

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

Work Shown:

[tex]a = \frac{v^2}{r}\\\\ar = v^2\\\\v^2 = ar\\\\v = \sqrt{ar}\\\\[/tex]

I multiplied both sides by r to isolate the v^2 term, then I applied the square root to fully isolate v.

Answer:

75 pounds

Step-by-step explanation:

(x) + (x) + (x+20) = 185

3x + 20 = 185

3x = 165

x = 55

Large dog = 55 + 20 = 75

Answer:

7.9 * 10 ^-6

Step-by-step explanation:

Move the decimal 6 places to the left so there is one number before the decimal

0.0000079

7.9

The exponent is -6  ( negative because we moved it to the left)

7.9 * 10 ^-6

Answer:

Hey there!

7.9 × 10-6 is your answer.

Hope this helps :)