If rectangle ABCD is dilated by a scale factor of 1.5 with a center of dilation at vertex A, how does the area of A'B'C'D' compare with the area of ABCD?

Answer:

Problem 1. Answer: D

Problem 2. Answer: A

Problem 3. Answer: C

Problem 4. Answer: D

Step-by-step explanation:

Problem 1:

A pack is targeted to weigh 9.25 oz.

A pack can be up to 0.23 oz off, either over or under weight.

The pack cannot weigh less than 9.25 oz - 0.23 oz or more than 9.25 oz + 0.23 oz.

The following compound inequality represents the rejected weights.

x < 9.25 - 0.23  or x > 9.25 + 0.23

Subtract 9.25 from both sides of both inequalities.

x - 9.25 < -0.23 or x - 9.25 > 0.23

Change to an absolute value inequality.

|x - 9.25| > 0.23

x - 9.25 < -0.23 or x - 9.25 > 0.23

x < 9.02 or x > 9.48

Problem 2:

Almond trees produce 12a

Macadamia nut trees produce 8m

Yield is 250

12a + 8m = 250

Problem 3:

8.8 m/s converted into km/h

1000 m = 1 km

60 sec = 1 min

60 min = 1 hr

8.8 m/s * (1 km)/(1000 m) * (60 s)/(1 min) * (60 min)/(1 hr) =

= 31.68 km/h

Problem 4.

Let number of alternative schools be a.

Let number of charter schools be c.

"the number of charter schools is 4 less than twice the number of alternative schools"

c = 2a - 4

There are 48 charter schools, so c = 48. Now we solve for a.

48 = 2a - 4

52 = 2a

a = 26

Answer:

Do the MAth yourself

Step-by-step explanation:

Hope this helps!

2/9, 2/7, 2/3, 9/7

Answer:

2/9, 2/7, 2/3, 9/7

Step-by-step explanation:

9th are smaller than 7th so 2/9 goes first.

7th are smaller than thirds so 2/7 goes second

9/7 is an improper fraction so it is more than one, so 2/3 goes third

Then 9/7

Problem 14 and problem 16 are missing the diagrams needed to answer the questions. Thankfully, there is enough info for me to answer problem 15, which I'll do so below.

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If we have a triangle with side lengths a,b,c then we can write this compound inequality

b-a < c < b+a

If we knew the value of a and b, then we can find a range for c.

In our case, a = 5, b = 12, c = n, so,

b-a < c < b+a

12-5 < n < 12+5

7 < n < 17

The value of n is between 7 and 17. The value of n cannot equal 7, and it also can't equal 17 either.

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Final Answer for problem 15 is choice C) 7 < n < 17

Answer:

 [tex]3y+7x=-5[/tex]  is the required equation.

Step-by-step explanation:

We have been given two points: (-2,3) and (1,-4)

We have a formula to find the equation with two points:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot (x-x_1)[/tex]

Here, we have:

[tex]x_1=-2,x_2=1,y_1=3,y_2=-4[/tex]

On substituting the values in the formula we get:

[tex]y-3=\frac{-4-3}{1-(-2)}\cdot (x-(-2))[/tex]

[tex]\Rightarrow y-3=\frac{-7}{3}\cdot (x+2)[/tex]

On further simplification:

[tex]3y-9=-7(x+2)[/tex]

[tex]\Rightarrow 3y-9=-7x-14[/tex]

After rearranging the terms

[tex]3y+7x=-14+9[/tex]

After final simplification we get:

[tex]3y+7x=-5[/tex]

Answer:

m=[tex]\frac{-7}{3}[/tex]

Step-by-step explanation:

Given:

(-2,3)(1,-4)

(x₁,y₁)(x₂,y₂)

m=(y₂-x₂)÷(y₁-x₁)

m=(-4 - 3) ÷ (1+2)

m= [tex]\frac{-7}{3}[/tex]

Answer:-3 less than -1

Step-by-step explanation: -3 is less than -1

Final answer:

The integers that satisfy the given condition of the equation x^2 + 2 = 10x - 7 are 1 and 9. To find these integers, the quadratic equation x^2 - 10x + 9 = 0 was factored and solved.

Explanation:

To find the integer(s) that satisfies the given condition, we need to set up an equation based on the description. The condition states: if 2 is added to the square of an integer x, the result equals 10 times that integer minus 7. Mathematically, this can be expressed as x2 + 2 = 10x - 7. To solve this, first rearrange the terms to one side to form a quadratic equation:

x2 - 10x + 9 = 0

Now we factor the quadratic equation:

(x - 1)(x - 9) = 0

Setting each factor equal to zero gives us the solutions:

x - 1 = 0 ⇒ x = 1

x - 9 = 0 ⇒ x = 9

The integers that satisfy the given condition are 1 and 9.

Answer:

Area of plane surface of cylinder = 2772 sq.cm.

Step-by-step explanation:

Let r be the radius and h be the height of the cylinder.

Curved Surface Area = 1848 sq.cm

2πrh = 1848

2×[tex]\frac{22}{7}[/tex]×rh = 1848

rh = 1848 × [tex]\frac{7}{22}[/tex] × [tex]\frac{1}{2}[/tex]

rh = 294

Sum of radius and height = 35

r + h = 35 --- (1)

Now,

r - h = [tex]\sqrt{(r+h)^{2}-4rh }[/tex]

= [tex]\sqrt{35^{2}-4(294) }[/tex]

= [tex]\sqrt{1225-1176}[/tex]

= [tex]\sqrt{49}[/tex]

= 7

r - h = 7 --- (2)

Adding (1) and (2),

2r = 42

r = 21  cm.

Area of the plane surface = 2 × π[tex]r^{2}[/tex]

= 2 × [tex]\frac{22}{7}[/tex] × 21 × 21

= 2772 sq.cm.

To calculate the plane surface area of a cylinder, subtract the area of the two circular bases from the curved surface area. Use the given formula and equations to find the radius and height, then calculate the area of one circular base. Finally, subtract the area of the bases from the curved surface area to find the plane surface area.

To calculate the plane surface area of a cylinder, we need to subtract the area of the two circular bases from the curved surface area.

The formula for finding the curved surface area of a cylinder is given as:

CSA = 2πrh

So, the curved surface area is 1848 cm² and the sum of the radius and height is 35 cm. We can use these values to find the radius and height of the cylinder.

Solving the equation 2πrh = 1848 and r + h = 35 simultaneously will give us the values of r and h.

Once we have the values of r and h, we can calculate the area of one circular base using the formula Area = πr². Finally, we can calculate the plane surface area by subtracting the area of the two circular bases from the curved surface area.

Answer:

MaybeIf you do 12,000 times 5.5 and didved by 100?

Step-by-step explanation:

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&12000\\ P=\textit{original amount deposited}\dotfill\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]\bf 12000=P\left(1+\frac{0.055}{12}\right)^{12\cdot 3}\implies 12000=P(1.00458\overline{3})^{36} \\\\\\ \cfrac{12000}{(1.00458\overline{3})^{36}}=P\implies 10178.56\approx P[/tex]

The fraction form of the given expression is 29/40.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The expression in the percentage form is given as 72.5%.

Divide by 100 to obtain fraction as,
72.5%

= 72.5/100

= 725/1000

= 29/40

Hence, the given expression can be written in fraction as 29/40.

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Answer:

The enlargement will be 30 ft by 7.5 ft.

Step-by-step explanation:

A scale drawing is a larger or smaller version of an object. To find the dimensions of the new drawing, multiply each measurement by the scale factor. The scale factor here is 5/2 or 2.5.

12(2.5)=30 ft

3(2.5)=7.5 ft

Question

Which two numbers does the √12 fall between? √4 √9 √16 √25

Answer:

√9 √16

Step-by-step explanation:

√4 = 2

√9 = 3

√12 = 3.5

√16 = 4

√25 = 5

Answer:

5 hours 40 minutes can they stay out.

An algebraic equation, y =6x

Step-by-step explanation:

Unit rate defined as the rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.

Let x represents the hours and y represents the cost.

As per the statement: Erica babysits for 4.5 hours and is paid $27.

Unit rate per hour(m) = [tex]\frac{27}{4.5}= $6[/tex]

Line of equation with no intercept is given by:

y = mx  .....[1]; where m represents the slope or unit rate.

Also, it is given if the people she babysits for have $34 to pay her.

⇒ y = $34

substitute the given values in [1] to solve for x;

[tex]34 = 6 \times x[/tex]

Divide both sides by 6 we get;

[tex]x = \frac{34}{6} = 5\frac{4}{6}[/tex] hours

or

x = 5 hours 40 minutes

Therefore, 5 hours 40 minutes can they stay out.

Also, algebraic equation: y =6x

The orthocenter is only outside of a triangle when the triangle is obtuse. The only obtuse triangle shown is the 25-45-110 triangle.

The orthocenter is only outside of a triangle when the triangle is obtuse. The only obtuse triangle shown is the 25-45-110 triangle.

In a triangle, the orthocenter is the point where the altitudes of the triangle intersect.

Altitudes are lines drawn from each vertex of the triangle perpendicular to the opposite side.

In some cases, the orthocenter can be located outside of the triangle.

One example of a triangle where the orthocenter is located outside of the triangle is an obtuse triangle.

In an obtuse triangle, one of the angles is greater than 90 degrees.

When you draw the altitudes, they will intersect outside the triangle, forming the orthocenter.

For instance, consider a triangle with angle measures of 100 degrees, 40 degrees, and 40 degrees. When you draw the altitudes, you will find that they intersect outside the triangle. Thus, an obtuse triangle can have an orthocenter located outside of the triangle.

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Answer:

(28*12)-(18*5) or 246 meters squared

Step-by-step explanation:

It is actually easy really, all you have to do is find the area of the larger polygon (28*12) or 336 and subtract the smaller polygon (18*5) or 90 and subtract it from the larger polygon getting you 246 meters squared

Answer:

The geometric mean of 2 and 8 comes out to equal 4.

Step-by-step explanation:

Answer:

56/6

Step-by-step explanation:

3 1/2 * 2 2/3

first evaluate 3 1/2 = (6+1)/2=7/2

so for that multiply 2 * 3 and +1 and divide by 2

second evaluate 2 2/3 = (6+2)/3 = 8/3

now the product = 7/2 * 8/3 =  (7*8) / (2*3) = 56 / 6

Answer:

40 students

Step-by-step explanation:

Lets multiply:

5:3 = 10:6 = 20:12 = 25:15

Since 25 is 10 more than 15, these are the actual numbers we need.

25 + 15 = 40 students.

Answer:

If the ratio is 5:3 boys to girls and there are 10 more boys than girls, there would be 15 girls and 25 boys, for a total of 40 people.

Step-by-step explanation:

To solve the ratio, we need to set up a proportion and assign a variable to solve for.  In this case, we can make 'x' the number of girls and 'x+10' the number of boys.  We know that the ratio of boys to girls is 5 to 3, so we can set up a proportion where 5/3 = (x+10)/x.  In order to solve a proportion, we would cross-multiply and divide in order to get a two-step equation to solve for the variable.  When we cross-multiply, we get 5x=3(x+10), or 5x=3x + 30.  Using inverse operations, first subtracting the '3x' from both sides to get 2x=30, and then dividing both sides by 2 to get x=15.  Remember, that 15 represents the number of girls.  The number of boys is equal to  'x+10' or 15 +10=25.  Then the total number of people is 15+25=40.

Answer:

-5120

Step-by-step explanation:

Replace the n in the formula by 6.

a6 = -5(4)^(6-1)

= -5 * 4^5

= -5120

Answer:

[tex]a_{6}[/tex] = - 5120

Step-by-step explanation:

To obtain the sixth term substitute n = 6 into the formula

[tex]a_{6}[/tex] = - 5 × [tex]4^{5}[/tex] = - 5 × 1024 = - 5120

Answer:

12n +6

Step-by-step explanation:

5n + 6 + (7n)

The first step is to combine like terms

I put the like terms next to each other.

5n + 7n +6

12n +6

Answer:

The total [tex]\frac{3}{8}[/tex] lb flour is used to make brownies.

Step-by-step explanation:

Let x lb flour is used to make brownies.

She used 1/4 pound more flour to make cookies than to make brownies. So, the total flour is used to make cookies is

[tex]x+\frac{1}{4}[/tex]

she used 1/8 lb less flour to make the bread then to make the cookies. So, the total flour is used to make bread is

[tex]x+\frac{1}{4}-\frac{1}{8}[/tex]

It is given that she used a half pound of flour to make bread.

[tex]x+\frac{1}{4}-\frac{1}{8}=\frac{1}{2}[/tex]

[tex]x+\frac{2-1}{8}=\frac{1}{2}[/tex]

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

[tex]8x+1=4[/tex]

[tex]8x=3[/tex]

[tex]x=\frac{3}{8}[/tex]

Therefore total [tex]\frac{3}{8}[/tex] lb flour is used to make brownies.

Answer:

It would be 2 hours and 15 minutes

Step-by-step explanation:

Answer:2.26 hours

Step-by-step explanation:

Given

Rich is driving from Philadelphia to Pittsburgh at 70 mph

and Michelle speed is 65 mph

If Philadelphia and  Pittsburgh is 305 miles apart

Let Rich travels x miles in t time

therefore

Michelle travels 305 -x

[tex]\frac{x}{70}=\frac{305-x}{65}[/tex]

[tex]13x=14\times 305 -14x[/tex]

27x=4270

[tex]x=\frac{4270}{27}[/tex]

[tex]x=158.148\approx 158.15 miles[/tex]

time taken t[tex]=\frac{158.15}{70}=2.259 \approx [/tex] 2.26 hours

Answer:

8 piles for basketball

4 piles for football

3 piles for baseball

Step-by-step explanation:

1. Find the GCF of all three #s

2. 8 is the GCF, so divide each # by 8

3. You get the # of piles for each type of card

Answer:

413.44 but the whole decimal is 413.4375

Step-by-step explanation:

first I turned the fractions into percents...

1/3- 30% and 1/8- 12.5

$750-10%= $675

675-12.5%= 590.63 (or 590.635)

590.63-30%= 413.441

Hope it helps some!

Answer:

C. 6x - 4y

Step-by-step explanation:

Difference means subtract

8x-5y - (2x-y)

Distribute the minus sign

8x-5y - 2x+y

Combine like terms

6x-4y

Answer:

C

Step-by-step explanation:

Answer:

8 and 13

Step-by-step explanation:

8+13 = 21

13-8 = 5

Answer:

24

48

72

96

Step-by-step explanation:

I just know

Answer:

31 ft²

Step-by-step explanation:

(1) Area of square

A = l²

A = 12²

A = 144 ft²

=====

(2) Area of circle

A = πr²

A = π × 6²

A = π × 36

A = 113 ft²

=====

(3) Remaining area

A = 144 – 113

A = 31 ft²

The area of the remaining board is 31 ft².

Answer:

Step-by-step explanation:

30