A baker has 10 cups of sugar to make cookies. Each batch calls for 113 cups of sugar.

How many batches of cookies can he make?

Enter your answer, as a mixed number in simplest form, in the box.

Answer:

The rule of translation (x,y) → (x+6 , y-8)

Step-by-step explanation:

The rest of the question is the coordinates of the ΔABC and ΔA'B'C'

The coordinates of the ΔABC: A(-6,2) , B(-5,5) , C(-1,3)

The coordinates of the ΔA'B'C': A'(0,-6) , B'(1,-3) , C'(5,-5)

It is required the rule of translation.

By Comparing between any of the points and its image

For example between A and A'

Let A(-6,2) = (x,y)  and  A'(0,-6) = (x+h , y+k)

So, x = -6 and y = 2

And x+h = 0 , y+k = -6

Substitute with x and y to find h and k

So, -6 + h = 0 ⇒ h = 6

And 2 + k = -6 ⇒ k = -8

So, the rule of translation (x,y) → (x+6 , y-8)

Answer: 23x305 = n , n = 7,015 square feet

Step-by-step explanation:

1 office = 305 square feet

If we want to calculate the area of 23 offices, we just need to multiply the area of one office, by the number of total offices.

That's 305 square feet * 23 = 7015 square feet

The correct answer is 23x305 = n , n = 7,015 square feet

Hope I helped!

120% is "x" is 50, meaning "x" must be the 100%.

if 50 is 120% of "x", and "x" is the 100%, what is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 50&120 \end{array}\implies \cfrac{x}{50}=\cfrac{100}{120}\implies \cfrac{x}{50}=\cfrac{5}{6}\implies 6x=250 \\\\\\ x = \cfrac{250}{6}\implies x = \cfrac{125}{3}\implies x = 41\frac{2}{3}\implies x = 41.\overline{6}[/tex]

Answer:

35

Step-by-step explanation:

Final answer:

To determine the least number of years from 2023 until the year rounds to 2060, subtract 2023 from 2055, the first year that rounds to 2060, resulting in 32 years.

Explanation:

The question is asking for the least number of years it will take for the current year to be rounded to nearest ten to become 2060. To answer this, we consider the year closest to 2060 that when rounded will result in exactly 2060. We are considering that the current year is 2023, optimizing the rounding rule of being closer to or equal to the next multiple of ten (2055-2064 would round to 2060). Following this logic, the first year that rounds to 2060 is 2055, therefore the least number of years from 2023 until we reach a year that rounds to 2060 is 2055 minus 2023, which is 32 years.

Answer:

9

Step-by-step explanation:

12x+40 = 7x + 85

12x - 7x = 85 - 40

5x = 45

x=9

so designing 9 shirts will take for the 2 stores to cost the

same.

Final answer:

To find the number of shirts, set up a system of equations and solve for the cost of each store. It will take 9 shirts for the two stores to cost the same.

Explanation:

To find the number of shirts it will take for the two stores to cost the same, we need to set up a system of equations. Let's assume the number of shirts needed is 'x'.

For Stylish Shirts: Total Cost = (Price per shirt * Number of shirts) + Design Fee = ($12 * x) + $40.

For Decatur Clothing: Total Cost = (Price per shirt * Number of shirts) + Design Fee = ($7 * x) + $85.

Setting the two total costs equal to each other, we have: ($12 * x) + $40 = ($7 * x) + $85. Solving this equation gives us x = 9. Therefore, it will take 9 shirts for the two stores to cost the same.

Answer:

I think it is option B. and option C.

Step-by-step explanation:

an instance of a form of reasoning in which a conclusion is drawn from two given or assumed propositions. a common or middle term is present in the two premises but not in the conclusion, which may be invalid.

Brady bought items totaling $42.13 from the hardware store. After giving a hundred-dollar bill, he received $57.87 in change.

To calculate the change Brady gets back from the hardware store, we need to add up the cost of the items he purchased and then subtract this total from the amount of the hundred-dollar bill he provided to the owner. First, we add the cost of the wrench ($9.63), the nail gun ($28.01), and the dozen nails ($4.49) to find the total spending. Once we have the total, we subtract it from $100 to find out how much change Brady should receive.

Let's calculate:

Brady will receive $57.87 in change from the hardware store.

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Answer:

The total cost for 8 skiers=316 dollars

Step-by-step explanation:

Given that the expression 15n+12n+100 represents the total cost in dollars for skis,boots and a lesson for n skiers.

To simplify the given expression :

15n+12n+100=27n+100

27n=-100

Therefore [tex]n=\frac{-100}{27}[/tex]

Now to find the total cost for 8 skiers.

The total cost for 8 skiers can be written as below

Put n=8 in the given expression 15n+12n+100

15(8)+12(8)+100

=120+96+100

=316

Therefore the total cost for 8 skiers is 316 dollars

The total cost for 8 skiers=316 dollars

It will take 6 years for the trees to be same height.

Step-by-step explanation:

Given,

Initial height of Type A = 7 feet = 7*12 = 84 inches

Growth rate = 2 inches per year

Let,

x be the number of years

Total height = T

T = 2x+84      Eqn 1

Initial height of Type B = 5 feet = 5*12 = 60 inches

Growth rate = 6 inches per year

T = 6x+60     Eqn 2

For same height;

Eqn 1 = Eqn 2

[tex]2x+84=6x+60\\84-60=6x-2x\\24=4x\\4x=24[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4}=\frac{24}{4}\\x=6[/tex]

It will take 6 years for the trees to be same height.

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Answer:

1246 sq cm

Step-by-step explanation:

you can break this shape into two rectangles, find the area of each, and then add them together

Answer:

First we need to find the area of the whole shape which would be the length times width

Length= 39

Width= 34

39*34=1,326

This is the area if the shape were shaded in

Now we want to find the area of the missing section which is again length times width

Length=10

Width=8

10*8=80

This is the area of the missing section, so to find the area of the shape you would take your total area minus your missing section area

1,326-80= 1,246

Your final answer would be 1,246 sq. cm

Hope this helps ;)

Step-by-step explanation:

Answer:

Explanation:

First, you must find the y-value returned by the line in the graph for a time (x) of five minutes, and then use the deviation of 3º to conclude the range of the real temperature.

1. y- value at x = 5 min.

The trend line (blue line in the graph) passes through the point (5,15), which means that it predicts a temperature of 15ºF when the time (x) is 5 minutes, or five minutes after the freezer was turned on.

2. Actual temperature value

It is stated that the temperature was actually three degrees from what the trend line shows, that means that the actual temperature could be 3ºF more or 3ºF less than the predicted temperature of 15ºF.

Mathematically:

The values that the actual temperature could be after the freezer was on for five minutes are 12°F or 18°F.

A trendline is sometimes referred to as a line of best fit and it is a statistical tool which is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any form of correlation (either positive or negative) between a given data.

By critically observing the scatter plot, we can logically deduce that the trend line passes through the point (5, 15), which implies that the temperature is 15°F, 5 minutes after the freezer was turned on.

Since the actual temperature deviates by 3°F from what the trend line shows, we have:

Actual temperature = 15 ± 3

Actual temperature = 15 - 3 = 12°F

Actual temperature = 15 + 3 = 18°F

Answer:

Step-by-step explanation:

10=z+6

subtract 6 from both sides

4=z

z=4

Answer:

The answer is 4

Step-by-step explanation:

To get the answer for this equation, take 6 and subtract from both sides.. meaning 6-6 and they will cancel and then subtract 6 from 10 and that will give you your answer of 4.

Answer:

Any U

Step-by-step explanation:

Hey there. Here isbyour solution:

2.7-2.8=0

0/u=0

Statement is always true. So u[tex]\in[/tex]R

Answer:

487887

Step-by-step explanation:

The correct answer is The graph stretches because 7 is bigger than 1.

The graph of [tex]\( f(x) = 7|x-5|+9 \)[/tex] experiences a vertical stretch, not a shrink, despite the coefficient ( 7 ) being greater than 1.

The absolute value function ( |x| ) reflects any negative values of ( x ) to their positive counterparts, essentially mirroring the negative portion of the graph onto the positive side.

When you apply a coefficient greater than 1 to [tex]\( |x| \), as in \( 7|x| \),[/tex] it vertically stretches the graph.

This means that the graph of ( f(x) ) will be vertically stretched by a factor of 7 compared to the graph of ( |x| ).

In this case, since [tex]\( |x-5| \)[/tex] is the argument of the absolute value, it implies a horizontal shift of the graph of [tex]\( |x| \)[/tex] by 5 units to the right.

So, the absolute value graph [tex]\( |x| \)[/tex] gets shifted 5 units to the right before it is stretched vertically by a factor of 7.

The ( +9 ) at the end of the function only moves the entire graph up by 9 units.

Thus, the graph of [tex]\( f(x) = 7|x-5|+9 \)[/tex] experiences a vertical stretch by a factor of 7.

Therefore, the correct statement is: "The graph stretches because 7 is bigger than 1."

Question

Does the absolute value graph below stretch or shrink? Support your answer. F(x) = 7|x-5|+9

The graph shrinks because 7 is between 0 and 1.

The graph stretches because 7 is bigger than 1.

The graph shrinks because 7 is bigger than 1.

The graph stretches because 7 is between 0 and 1.

Answer:

23 over 3 will give you a mixed number / whole number of 8

Step-by-step explanation:

your answer is 8

Answer:

the answer to this is

24/3= 8 ( edited again as I TOOK THE wrong values )

Answer:

right 2, down 9

Step-by-step explanation:

move point A' two places to the right, and down nine to get to point A

Answer:

80.4

Step-by-step explanation:

To remember all of the ratios for trigonometry, using the acronym "SohCahToa". You always divide two sides for trig. ratios.

'S' is sine or sin for short.

'C' is cosine or cos for short.

'T' is tangent, or tan for short.

'h' means hypotenuse, the longest side in the triangle.

'o' means the side that's opposite, or not touching the angle of reference.

'a' means the side that's adjacent, or touching the angle of reference.

The angle of reference means the angle you are talking about (use the symbol θ to mean angle). In this question, the angle of reference is 15°.

We have the adjacent side, 300, and we need to find the opposite side, x.

The trig. ratio that has the side adjacent and opposite is tangent or 'tan'.

tanθ = opposite / adjacent     Trig. ratio for tangent

tan15° = x / 300     Substitute what we know. Isolate 'x'.

x = 300tan15°     This means 300 times tan15°. Use a calculator.

x = 80.3847..... Exact decimal answer on your calculator

x ≈ 80.4       Answer rounded to nearest tenth (first decimal)

When rounding, you decide to round up or down using the decimal place after where you will cut off.

In 80.3847..... '8' tells us to round up because it is 5 or greater.

If  the second decimal place was 4 or less, we round down (the answer would be 80.3).

Answer:

10 liters of solution should be drained off  and replaced with water.

Step-by-step explanation:

As forty liters of a 60% salt solution are being reduced to a 45% solution, and we have to determine the amount in liters that must be drained and replaced with distilled water so that the resulting solution will  contain only 45% salt solution.

So, the equation becomes

[tex]0.60(40-x) = 0.45(40)[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]

[tex]0.6\left(40-x\right)=0.45\cdot \:40[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:0.45\cdot \:40=18[/tex]

[tex]0.6\left(40-x\right)=18[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}10[/tex]

[tex]0.6\left(40-x\right)\cdot \:10=18\cdot \:10[/tex]

[tex]\mathrm{Refine}[/tex]

[tex]6\left(40-x\right)=180[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}6[/tex]

[tex]\frac{6\left(40-x\right)}{6}=\frac{180}{6}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]40-x=30[/tex]

[tex]\mathrm{Subtract\:}40\mathrm{\:from\:both\:sides}[/tex]

[tex]40-x-40=30-40[/tex]

[tex]-x=-10[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]

[tex]\frac{-x}{-1}=\frac{-10}{-1}[/tex]

[tex]x=10[/tex]

Therefore, 10 liters of solution should be drained off  and replaced with water.

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Answer:

10 liters of solution should be drained off  and replaced with water.

Step-by-step explanation:

;) brainliest???????

Answer:

15.68

Step-by-step explanation:

22/15=23/x

cross product

15*23=22*x

345=22x

x=345/22

x=15.68

Answer:

12x-8y

Step-by-step explanation:

10x+2x=12x

-5y-3y=-8y

Answer: 12x-8y

Step-by-step explanation: add like terms 10x and 2x, and -3-5= 8 so 8y

Answer:

Step-by-step explanation:

breadth = x

length = 2x

Perimeter = 540m

2*( length + breadth ) = 540

2 *(2x + x) = 540

3x = 540/2

3x = 270

x = 270/3

x = 90 m

Breadth = 90m = 90 *100 = 9000 cm

Length = 2*90 = 180 m = 180 * 100 = 18000 cm

No.of bricks = Area of room/ area of one brick

= 9000 * 18000 / 20 * 12

= 675000 bricks

The nth term of the quadratic sequence 1, 12, 29, 52, 81 is T(n) = 2n² - n - 2.

1. Check for a Quadratic Sequence:

To determine if a sequence is quadratic, we look at the differences between consecutive terms, and then the differences between those differences (second differences).

First differences: 11, 17, 23, 29

Second differences: 6, 6, 6

The sequence is quadratic since the second differences are constant.

2. General Form of a Quadratic Sequence:

The quadratic sequence formula in general is:

T(n) = an² + bn + c

Where:

T(n) is the nth term

a, b, and c are constants to be determined

3. Forming Equations:

We can use the first three terms of the sequence to create three equations:

For n = 1: a(1)² + b(1) + c = 1

For n = 2: a(2)² + b(2) + c = 12

For n = 3: a(3)² + b(3) + c = 29

Simplifying these equations, we get:

a + b + c = 1

4a + 2b + c = 12

9a + 3b + c = 29

4. Solving the Equations:

By concurrently solving this set of equations, we arrive at:

a = 2

b = -1

c = -2

5. Finding the nth Term:

Substituting the values of a, b, and c into the general formula, we get: T(n) = 2n² - n - 2

The solution of this system of linear equations is [tex](x,y,z) = (1,2,4)[/tex]. (Correct choice: C)

The system of equations is represented by the following augmented matrix:

[tex]\left[\begin{array}{cccc}2&1&4&16\\5&-2&2&-1\\1&2&-3& -9\end{array}\right][/tex] (1)

Where the fourth column represents the vector column of independent coefficients. After making some operations, we find that the reduced row-echelon form of the augmented matrix is:

[tex]\left[\begin{array}{cccc}1&0&0&1\\0&1&0&2\\0&0&1& 4\end{array}\right][/tex]

The solution of this system of linear equations is [tex](x,y,z) = (1,2,4)[/tex]. (Correct choice: C) [tex]\blacksquare[/tex]

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Final answer:

To solve the system of equations, we need to find the reduced row-echelon form of the augmented matrix. Applying row operations, we can reduce the matrix to row-echelon form. Then, using backward substitution, we can find the values of x, y, and z. The solution to the system of equations is (-10, 2, 8.5).

Explanation:

To solve the system of equations, we can represent it as an augmented matrix and find its reduced row-echelon form. The augmented matrix for the given system of equations is:

[2 1 4 | 16]
[5 -2 2 | -1]
[1 2 -3 | -9]

Next, we need to apply row operations to reduce the matrix to its row-echelon form. Following the Gaussian elimination method, we perform the row operations:

R2 → R2 - 5R1, and
R3 → R3 - R1

The resulting matrix in row-echelon form is:

[2 1 4 | 16]
[0 -7 -18 | -81]
[0 0 0 | 0]

Now, we can apply backward substitution to find the values of x, y, and z. From the last row of the row-echelon form, we know that 0z=0. We can assign any value to z, such as 1, and then solve for x and y. Plugging in z=1, we get:

2x + 1y + 4(1) = 16

x + 2y - 3(1) = -9

Simplifying these equations, we get:

2x + y + 4 = 16 → 2x + y = 16 - 4 → 2x + y = 12

x + 2y - 3 = -9 → x + 2y = -9 + 3 → x + 2y = -6

Using these equations, we can solve for x and y by setting up a system of linear equations:

2x + y = 12
x + 2y = -6

Solving this system, we can find the values of x and y: x = -10 and y = 2. Finally, substituting these values back into one of the original equations, we can find z:

2(-10) + 1(2) + 4z = 16 → -20 + 2 + 4z = 16 → 4z = 34 → z = 8.5

So, the solution to the system of equations is (-10, 2, 8.5).

Answer:

18.7 feet far

Step-by-step explanation:

Based on the information given we can conclude that our set up will be a Right triangle (i.e. one angle is 90°), where the hypotenuse will be denoted by the guy wire of [tex]20ft[/tex]  and angle of 21° is the angle formed between then hypotenuse and the base (i.e. ground).

Thus we want to find the base length (lets call it [tex]x[/tex] ) of this triangle, so we can use trigonometry as we have one angle and the hypotenuse, as follow:

[tex]cos(21)=\frac{adjacent side}{hypotenuse}=\frac{baselength}{guywire}\\\\ cos(21)=\frac{x}{20} \\x=20cos(21)\\x=18.671\\x=18.7ft[/tex]

So the base is approximately 18.7 feet far from the tree of the anchored wire.

The distance from the base of the tree to the stake anchoring a guy wire that is 20 ft long and makes a 21-degree angle with the ground is approximately 18.8 ft, found using the cosine function of trigonometry.

The student asked for help in determining the distance from the base of the tree to the stake anchoring a guy wire that is 20 ft long and makes a 21-degree angle with the ground. To solve this problem, we need to employ trigonometry, specifically the cosine function which relates the adjacent side of a right triangle (the distance we're looking for) to the hypotenuse (the length of the guy wire) and the angle between them.

Using the formula cosine(angle) = adjacent/hypotenuse, we can set up our equation as cos(21°) = distance/20 ft. Rearranging the equation to solve for the distance, we get distance = 20 ft * cos(21°). After calculating, we find that the distance from the base of the tree to the stake is approximately 18.8 ft.

If the given function is h(x)=5x-1 then  h(1)h(1) would be equal to 16.

Function is a type of relation, or rule, that maps one input to specific single output.

Given;

h(x)=5x-1

In order to find the  h(1)h(1)

substitute x = 1 in the function h(x)

h(x)=5x-1

h(1) = 5(1) - 1

h(1) = 5 -1 = 4

So, h(1)h(1) = 4 x 4 = 16

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Answer:

270 miles

Step-by-step explanation:

Let the total distance be d.

Then (2/3)d = 180 miles.

Solve for d by multipying both sides by (3/2):

(3/2)(2/3)d  = (3/2)(180 miles) = 270 miles

The total distance is 270 miles.

Answer:

C, B

Step-by-step explanation:

4x * 1 = 4x

4x * y = 4xy

4x + 4xy

Next

5 * x = 5x

5 * 3 = 15

5x + 15

Answer:

17(c)

18(b)

Step-by-step explanation:

17) (4x*1)+(4x*y)

4x+4xy

18) (x+3)5

(5*x)+(3*5)

5x+15