Karen received a $50.75 gift card for a photo center. She used it to buy prints that cost 10 cents each. The remaining balance, B (In dollars), on the card after
buying x prints is given by the following function
B(x) = 50.75 -0.10x
What is the remaining balance on the card if Karen bought 30 prints?

The factory must produce 6,400 parts  so that there is 1 ton of scrap aluminum for recycling.

It is given that For every part produced by a factory there are 5 ounces of scrap aluminum that can be recycled there are 16 ounces in 1 pound and 2,000 in 1 ton we need to find how many parts must the factory produce so that there is 1 ton of scrap aluminum for recycling

What is a Ratio?

A quantitative relation between two amounts showing the number of times one value contains in another

1 part produced  ⇒ 5 ounces scrap aluminium recycled.

So, the ratio of parts produced : Scrap of aluminium = 1   : 5  .... (a)

Let us assume for m parts produced ,  1 ton of scrap is recycled.

Also, 1 ton = 2, 000 pounds

and 1 pound = 16 ounces

⇒ 1 ton = 2000 x (16 ounces)  = 32,000 ounces

So, for m parts made in the  factory, 32,000 ounces scrap is recycled.

So, the ratio of parts produced : Scrap of aluminium =  m   : 32,000  .... (b)

From both the given ratio, we get

1   : 5  = m   : 32,000

m=32000/5

m=6400

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Answer:

Smaller Angle = 60°

Larger Angle = 120°

Step-by-step explanation:

Step 1:

2x + x = 180°

Step 2:

3x = 180°

Step 3:

x = 60°

Step 4:

60° times 2 = 120°

Answer:

Smaller Angle = 60°

Larger Angle = 120°

Hope This Helps :)

Answer:

r=6 and 9 × 6

the equation is basically telling us what 54 ÷ 9 is and the answer is r = 6

Answer:

54 × 9 I guesssssssss

Step-by-step explanation:

54÷r=9

it is the same things as

r/54=9

then cross multiply

then, r=54×9

r= 486

Answer:

no.

Step-by-step explanation:

12/30 =  0.4

15/45 = 1/3

Answer:

X = 3.2

Step-by-step explanation:

sin(42) = x/4.6

0.7 = x/4.6

3.2 = x

A quadrilateral is a polygon with four sides. All trapezoids have two pairs of parallel sides. Option (a) is correct.

A quadrilateral is a polygon with four sides, and there are several properties and characteristics that can be true about a quadrilateral. Some possible true statements about a quadrilateral include:

1. A quadrilateral has four angles.

2. A quadrilateral has four vertices.

3. The sum of the interior angles of a quadrilateral is always 360 degrees.

4. A quadrilateral can have sides of different lengths.

5. A quadrilateral can have parallel sides.

Compare each of the properties above to the given options.

Options:

a) All trapezoids have two pairs of parallel sides.

b) Only some rectangles have four right angles.

c) All squares are rectangles.

d) Some rhombuses are trapezoids.

We can conclude that option (a) is correct because it correspond to the property 5 of a quadrilateral.

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Answer:

Step-by-step explanation:

You want to identify the x-intercepts on the graph.

An "x-intercept" is a point where the graph crosses or touches (intercepts) the x-axis. The y-value there is always 0.

The given graph crosses the x-axis where x = -2 and x = 3. This means the x-intercept points are ...

  (-2, 0) and (3, 0)

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Answer:

The integers are  9 and 22

Step-by-step explanation:

Step one:

given data

let the smaller integer be x

and the bigger be y

x+y=31-----------1

so

y=(2x+4)

Step two:

put y=(2x+4 in equation 1 we have

x+2x+4=31

3x+4=31

3x=31-4

3x=27

divide both sides by 3

x=27/3

x=9

the smaller integer is 9

the bigger is 2(9)+4= 18+4=22

Answer:

line b

Step-by-step explanation:

you can tell because x and y equal the same number on line b

Answer:

Step-by-step explanation:

Answer:

6x+6x2+3

Step-by-step explanation:

6x2+5x+1+x+2

Combine 5x and x to get 6x.

6x2+6x+1+2

Add 1 and 2 to get 3.

6x2+6x+3

According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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Answer:

$71.4

Step-by-step explanation:

Answer:

$71.40

Step-by-step explanation:

an item with an original price tag of $102 that is marked down by 30% will have a sales price of $71.40 -- a savings of $30.60.

A triangle is a three-edged polygon with three vertices. The measure of ∠C is 18°.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Let the measure of ∠C be represented by x. Given the measure of ∠A= 2(∠B), while the measure of ∠B=3(∠C). Therefore, the measure of angles can be written as,

∠A = 2(∠B) = 2[3(∠C)] = 6x

∠B = 3x

∠C = x

Now, since the sum of all the angles of a triangle is 180°. Therefore,

∠A + ∠B + ∠C = 180°

6x + 3x + x = 180°

10x = 180°

x = 18°

Hence, the measure of ∠C is 18°.

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

{3, 4, 5, 6, 7, 8} and {8, 7, 6, 5, 3}

Step-by-step explanation:

The sets {3, 4, 5, 6, 7, 8} and {3, 4, 5, 6, 7, 8} will be constraint through {x | x < 9 and x >2} so option (A) and (C) will be correct.

A set is a combination of specific quantities in which the meaning of each variable must be the same.

For example {1,2,3,4,5,6...} is a set of natural numbers in which each variable is representing a natural number so the overall meaning is the same among all.

Another example could be a set of the whole number like that.

Given the constraint

{x | x < 9 and x >2}

It means x should be greater than 2 and less than  9

So all possible values are

3,4,5,6,7,8

Now set associated with these number is {3, 4, 5, 6, 7, 8} and {8, 7, 6, 5, 3}.

Hence "The sets {3, 4, 5, 6, 7, 8} and {3, 4, 5, 6, 7, 8} will be constraint through {x | x < 9 and x >2}".

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Answer: -66.67%, but if the answer is supposed to positive then the answer is 66.67%.

* Hopefully this helps:)

The ladder is 10 feet long, and the base of the ladder at least 3 feet away from the wall the ladder is leaning on.

So, By making a right triangle, the ladder will represent the hypotenuse of the triangle

So, we need to find how high will the ladder reach up?

So, using a Pythagorean theorem

which stated that at the right triangle, the sum of the squared of the sides adjacent to the right angle is equal to the squared of the hypotenuse

so, let the height = h , the length of the ladder = 10 ft

and the base is 3 feet away from the wall

The ladder will represents the hypotenuse of the triangle

So,

So, The height that can the ladder reach up is 9.54 feet

After evaluating f(x) = 3x - 5, the answer is f(x-2) = 3x - 11

What do you mean by functions?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). Expressions of well-known functions can be found in many frequently used mathematical formulas. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The set X is called the domain of the function and the set Y is called the codomain of the function.

Given function:

f(x) = 3x - 5

For f(x-2) substitute x as (x-2) in given function

f(x-2) = 3(x - 2) - 5 = 3x - 6 - 5 = 3x - 11

therefore, f(x-2) = 3x - 11

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Answer:

1/27

Step-by-step explanation: I took the quiz and the right answer is 1/27

The value of the given expression would be 0.25 which is simplified by using the PEMDAS rule in the expression.

The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.

The given expression would be below as:

⇒ [(1 1/4−3/4)⋅(−2/3)3]÷(−4)

Using the PEMDAS rule in the above expression,

⇒ [(5/4−3/4)⋅(−2/3)3]÷(−4)

Apply the subtraction operation,

⇒ [(2/4)⋅(−6/3)]÷(−4)

Reduce the fractions, and we get

⇒ [(1/2)⋅(−2)]÷(−4)

Cancel out the terms of 2 to each other

⇒ (−1)÷(−4)

Cancel out the negative sign to each other

⇒ 1 / 4

Apply the division operation to get

⇒ 0.25

Therefore, the value of the given expression would be 0.25 which is evaluated.

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Answer:

$7.50

Step-by-step explanation:

the question can be represented with:
12.5/5 and x/3

12.5/5 is 2.5, so that means each bag of dog food is $2.5  
So then you multiply 2.5 by 3, = 1.20, so 3 bags of dog food is $7.50.

Answer:

Step-by-step explanation:

Remark

I take it you mean 5 and not 0.5.

If that is the case, this is a proportion question. A proportion consists of 4 parts. If you know 3 of the parts, you can solve for the 4th one.

Formula

Number of bags/Cost = new number of bags/Cost of the new number

Givens

original Number of bags  = 5

Cost = 12.50

New number of bags = 3 bags

Cost = x

Solution

5/12.50 = 3/x           Cross Multiply

5x = 12.50 * 3          Combine the right

5x = 37.5                  Divide by 5

5x/5 = 37.5/5

x = 7.5

Answer: 3 bags cost 7.50 dollars.

Answer:

Amount = $6614 and 19 cent

Step-by-step explanation:

Formula for compound interest is

A= p(1+r/n)^(nt)

Compounded daily

So n= 365*2= 730

T= 2

r= 0.13

P= 5100

A= p(1+r/n)^(nt)

A= 5100(1+0.13/730)^(730*2)

A= 5100(1+1.78082*10^-4)^(1460)

A= 5100(1.000178082)^1460

A= 5100(1.2969)

A= 6614.19

Amount = $6614 and 19 cent

Answer:

I think it is 3.1

Step-by-step explanation:

make me brainlyest pls

a. The secant slope through (-2,4) and (0,0) is -2.

b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.

The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.

To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.

a. (-2,4) and (0,0):

The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:

msec = (y2 - y1) / (x2 - x1)

Plugging in the values, we get:

msec = (0 - 4) / (0 - (-2))

= -4 / 2

= -2

So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.

b. (-1.5, 2.25) and (-0.5, 0.25):

The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:

msec = (0.25 - 2.25) / (-0.5 - (-1.5))

= (-2) / (1)

= -2

So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.

By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.

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No. The reported return rate appears lower than expected.

To determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.

First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.

Then, we can use the following formula to calculate the expected rate of return:

Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1

Plugging in the given values, we get:

n = 1 (since we are only given information for a single quarter)

Initial investment = 26,245

Ending value = 26,292

Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%

Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.

Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.

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Answer:

80 tablespoons of flour for 2 pounds of butter

Step-by-step explanation:

5 tablespoons = 2 ounces.

2=5

4=10

6=15

8=20

10=25

12=30

14=35

16=40

18=45

20=50

22=55

24=60

26=65

28=70

30=75

32=80

Answer:

Step-by-step explanation:

The first step in evaluating the expression is to perform the calculations inside the parentheses. This involves subtracting 3.6 from 7.4.

Step 1: Evaluate the expression inside the parentheses.

7.4 - 3.6 = 3.8

After evaluating the expression inside the parentheses, the expression becomes:

12 ÷ 3.8 + 8 - 2

Step 2: Perform the division.

12 ÷ 3.8 = 3.158

After performing the division, the expression becomes:

3.158 + 8 - 2

Step 3: Perform the addition and subtraction from left to right.

3.158 + 8 = 11.158

11.158 - 2 = 9.158

Therefore, the value of the given expression is approximately 9.158.

The first step is:

Work/explanation:

The expression is:

12 ÷ (7.4 − 3.6) + 8 − 2

Let's recall the order of operations first:

So we evaluate

\(\sf{12\div(7.4-3.6)+8-2}\)

\(\sf{12\div3.8+8-2}\)

Next, division:

\(\sf{3.158+8-2}\)

Next, addition & subtraction:

\(\sf{9.158}\)

Answer:

a = 2

b = 3

c= 8

Step-by-step explanation:

a) 4 = \(2^{2}\)  We want to have all of the bases the same in the powers, so we will convert 4 to a base of 2.

b) When we divide with powers with the same baes, we subtract the exponents.  (5-2 =3)

c) \(2^{3}\) means 2x2x2 or 8