The balance of Susu’s savings account can be represented by the variable b. The inequality describing her balance is b greater-than 30 dollars. Which could be a solution to the inequality?

Answer:

10 m/s

Step-by-step explanation:

Unit stands for one so

120 meters in 12 seconds in 10 meters a sec

Answer:

Step-by-step explanation:

1. regroup terms

\(125x^3+343+525x^2+735x\)

2. Rewrite \(125x^3\) as  \((5x)^3\) and 343 as \(7^3\)

\((5x)^3+7^3+525x^2+735x\)

3. Since both terms are perfect cubes, factor using the sum of cubes formula, \(a^3+b^3 = (a+b)(a^2-ab+b^2)\), where \(a=5x\) and \(b=7\)

\((5x+7)((5x)^2-(7)(5x)+(7)^2)+525x^2+735x\)

\((5x+7)(25x^2-35x+49)+525x^2+735x\)

4. Factor \(105x\) out of \(525x^2+735x\)

\((5x+7)(25x^2-35x+49)+105x(5x+7)\)

5. Regroup

\((5x+7)(25x^2-35x+49+105x)\)

\((5x+7)(25x^2+70x+49)\)

6. Factor again

\((5x+7)(5x+7)^2\)

\((5x+7)^3\)

Answer:

(5x+7)^3

Step-by-step explanation:

(a+b)^3=a^3+3a^2b+3ab^2+b^3

The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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The coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.

During translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.

Given the question above, we need to find the coordinates of the vertices for the image of the pre image that are translated 4 units right.

So,

\(\rightarrow\sf \boxed{\boxed{-5+4=1=\bold{(-1,2)}}}\)

\(\rightarrow\sf \boxed{\boxed{1+4=5=\bold{(5,3)}}}\)

\(\rightarrow\sf \boxed{\boxed{-3+4=1=\bold{(1,0)}}}\)

Thus, the coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

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Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

1) x = -6, 8

2) x = -1 + i√2

Step-by-step explanation:

1)

\( {x}^{2} - 2x - 48 = 0\)

\((x - 8)(x + 6) = 0\)

x = -6, 8

2)

\(3 {x}^{2} + 2x + 1 = 0\)

x = (-2 + √(2^2 - 4(3)(1))) / (2 × 1)

x = (-2 + √(4-12)) / 2

x = (-2 + √-8) / 2

x = (-2 + 2i√2) / 2

x = -1 + i√2

The lengths of the other two sides of the right triangle are 24m and 25m, respectively.

Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we have the equation:

\(7^2 + x^2 = (x + 1)^2\)

Expanding and simplifying this equation, we get:

\(49 + x^2 = x^2 + 2x + 1\)

Now, we can cancel out \(x^2\) from both sides of the equation:

49 = 2x + 1

Next, we can isolate 2x:

2x = 49 - 1

2x = 48

Dividing both sides by 2, we find:

x = 24

Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.

Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.

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Answer:

C (2)

Step-by-step explanation:

• √32 = 4√2 ( bc √32 = √16×2 = √16×√2 = 4×√2 )

• √8 = 2√2 ( bc √8 = √4×2 = √4×√2 = 2×√2 )

So √32 ÷ √8 is equal to 4√2 ÷ 2√2

And there √2 cancels for both

So what you're left with is 4 ÷ 2

And 4÷2 = 2

The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

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The answers are

1). warmer

2). higher

3). end behavior

A refrigerator is a device which is designed to remove heat from a space that is at lower temperature than its surroundings.

When Gianna initially placed the two cups in the refrigerators, the liquid placed in refrigerator A was warmer than the liquid placed in refrigerator B.

The end behavior of the two functions implies that refrigerator A is set to a higher temperature than refrigerator B.

The graph for the question given below.

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Integral that would give the volume V generated by rotating the region bounded by the given curves will be 200 pi unit³

Finding the volume of rotation is similar to finding the area of the bounded region of the graphs of the functions. The only difference is the added component added due to the rotation of the bounded region. Now whether we are using disk method or cylindrical shell method to find the volume, we will first set up the integral and its limits of integration, then evaluate this integral.

To find the volume of the solid generated by rotating the region bounded by curves:

(y = x^3 and y = 0) around the y-axis

We use the Cylindrical Shells Method.

First, we need to set up the integral.

We have:

2π∫\(0^5\) x (\(x^3\)) dx.

To solve this integral, we use the power rule for integration.

This states that if we have an integral of \(x^n\), the antiderivative is

x^(n+1)/(n+1).

Therefore, the antiderivative of our integral is 2π∫\(0^5\) x (\(x^3\)) dx.. Now that we have the antiderivative, we can solve the integral by applying the fundamental theorem of calculus.

This states that the integral of a function is equal to the difference between the evaluated antiderivative at the upper and lower limits of the integral.

Therefore, the volume of the solid generated is

V = \([x^5/5]^5_0\) = 2π(\(5^5/5\)) = 200π\(unit^3\).

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Answer:

0

Step-by-step explanation:

7 is in the ones

0 is in the tens

6 is in the hundreds

5 is in the thousands

4 is in the ten thousands

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Let's assume Width of rectangle be x feet and length be 2 +x. to Find the are of the rectangle firstly we need to the length and width of the Rectangle:

Using formula:

→ 32 = 2(x + 2 + x)

→ 32 = 2(2x + 2)

→ 32 = 4x + 4

→ 32 - 4 = 4x

→ 28 = 4x

→ 28/4 = x

→ 7 = x

Hence,

Now,

→ Area of rectangle = Length × Width

→ Area fo rectangle = 9 × 7

→ Area of rectangle = 63 feet²

Answer:

⠀

Step-by-step explanation:

⠀

⠀

So, let us assume the width of the rectangle as w ft and therefore the length will (w + 2) ft .

⠀

Now,

⠀

\({\longrightarrow \qquad{ {{\boldsymbol {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}}\)

⠀

\({\longrightarrow \qquad {\rm{2(w + 2 + {w})= 32 \ }}}\)

⠀

\({\longrightarrow \qquad {\rm 2({2w + 2= 32 ) }}}\)

⠀

\({\longrightarrow \qquad {\rm{4w +4= 32 \ }}}\)

⠀

\({\longrightarrow \qquad {\rm{4w = 28\ }}}\)

⠀

\({\longrightarrow \qquad {\rm{w = \dfrac{28}{4} }}}\)

⠀

\({\longrightarrow \qquad{ \mathfrak{{\pmb{w = 7 }}}}}\)

⠀

⠀

Now, We are to find the length of the rectangle:

\({\longrightarrow \qquad{ {{\rm{Length = w + 2 }}}}}\)

⠀

\({\longrightarrow \qquad{ {{ \rm{Length = 7 + 2 }}}}}\)

⠀

\({\longrightarrow \qquad{ { \frak{ \pmb{Length = 9}}}}}\)

⠀

Now, we are to find the area of the rectangle :

⠀

\({\longrightarrow \qquad{ {{\boldsymbol{ Area_{(Rectangle)} = Length \times Breadth }}}}}\)

⠀

\({\longrightarrow \qquad{ {{ \rm{ Area_{(Rectangle)} = 9 \times 7 }}}}}\)

⠀

\({\longrightarrow \qquad{ { \pmb{\boldsymbol{ Area_{(Rectangle)} = 63 }}}}}\)

⠀

Therefore,

⠀

Answer:

ice has kinetic enery

Step-by-step explanation:

Ice has heat energy

Answer:

Option 2

Step-by-step explanation:

Parallelograms have 2 parallel sides, and Option 2 proves that AB and DC are equal, which makes sides AD and BC Parallel according to lines AE and EC.

Answer:

According to my calculations, 1.6 goes into 10.8 a total of 6 times with a remainder of 1.1999999999999993. If you continue the long division beyond the decimal point, the result would be 6.75.

Step-by-step explanation:

Answer:

6.75 miles

Step-by-step explanation:

1.6 km = 1 mile

   1 km = 1/1.6  mile

10.8 km = \(\frac{1}{1.6}*10.8\)

             = 6.75 miles

Answer:

x = 7 and

y = 4\(\sqrt{2}\)

Step-by-step explanation:

as you can see from the image we need to draw a line and when we do so we get a special right triangle with angle measures 90-45-45 and side lengths represented by a-a-a\(\sqrt{2}\)

since the line we drew is parallel to the rectangle's length it's = 4 and so the number represented with a is also = 4

from there on we see x = 7 and y = 4\(\sqrt{2}\)

Answer:

I can confirm, it is B! x=7 and y=4sqrt2

Step-by-step explanation:

edge

Answer: B

Shape: Diamond (4 triangles)

Formula: A = 1/2bh

so...

A = 4(1/2bh) <------ Multiply by 4 because a diamond has 4 triangles)

A = 4(1/2(5)(10))

A = 4(5(5))

A = 4(25)

A = 100 in^2

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

A graphing calculator does this nicely.

The radius of the base is 8.245 cm

Given, a vase with a circular base exerts

Pressure = 700 N/m²

Force = 15 N

Area = ?

∴ area = πr²

By finding out the area of the vase we can calculate the radius.

We know that Pressure = Force/Area

According to the equation, pressure is inversely related to area but directly related to force. Pressure rises at a constant area as the force exerted increases in strength.

therefore apply the above the formula to find out the area and radius.

700 = 15/πr²

 πr² = 15/700

 πr² = 3/140

  r² = 3/140 × 3.14

since π value is 3.14

  r² = 0.0068

   r = √0.0068

   r = 0.0824 m

   r = 0.0824 × 100

   r = 8.245 cm

we get radius as 8.245 .

Hence we get the radius of the base of the vase as 8.245 cm.

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Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

The distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.

In other words, the distance between two points in space is the magnitude of the vector formed by said points.

So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:

distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

In this case, you know:

Replacing in the definition of distance:

distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)

distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)

distance= \(\sqrt{7^{2} +(-5)^{2} }\)

distance= \(\sqrt{49+25 }\)

distance= √74= 8.6023

Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

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Answer:

5x+7 > 17 matches with 3.

1+3x > -5 matches with 2.

2x+1 < 3 matches with 1.

5-3x > 11 matches with 4.

Step-by-step explanation:

Answer:

Hi, option A). 3 to 1 is the correct option.

Step-by-step explanation:

See there are 6 yellow and 2 red.

It will be 6:2

And if we simplify it further both of the numbers are multiples of 2.

Therefore:

The answer is option A). 3:1

Answer: B. 4 to 1

Step-by-step explanation:

green = (3/4) purple

Substituting the expression for green from the first conversion, we get:

yellow = (5/6) (3/4) purple

yellow = (5/8) purple

Finally, we can use the third ratio to convert purple to red:

5 purple = 2 red

purple = (2/5) red

Therefore, the ratio between yellow to red is 4 to 1.

Answer:

415 miles

Step-by-step explanation:

Start with the speed equation:

speed = distance/time

Now solve the speed equation for distance:

distance = speed × time

Apply the speed equation solved for distance to the two parts of the trip.

4 hours at 55 mph:

distance = 55 mph × 4 hours = 220 miles

3 hours at 65 mph:

distance = 65 mph × 3 hours = 195 miles

Add the two distances to find the total distance:

total distance = 220 miles + 195 miles = 415 miles

Answer: 415 miles

Answer:

415 miles

Step-by-step explanation:

Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.

How far did he drive?

d=rt

For the first part of the trip:

d = 55 * 4 = 220 miles

For the second part of the trip:

d = 65*3 =195 miles

Add the miles together

220+195 = 415 miles

Answer:

C

Step-by-step explanation:

So I don’t know if you don’t know how to do it but imagine right to explain it ... You good have to add oh yeah P2 together and all numbers together and all the p together see this is why I did use different colors. Have an amazing day :)

Step-by-step explanation:

putting x= 7

2x7x7

2x49

98(ans)

Answer:

13 packages

Step-by-step explanation:

We need to find the highest common factor, in order to solve this problem.

So, we have to find the highest common factor of 39 and 13.

We find the highest common factor of 39 and 13 because it says in the problem” Tim has 39 pairs of headphones and 13 music players.”

And than you just find the highest common factor, after you find the highest common factor... YOU ARE DONE SOLVING THE PROBLEM!

The highest common factor will be 13

13: 1,13

39:1,3,13,39

ANSWER:13

Hope this helps!

Answer:

13

Step-by-step explanation:

Greatest number of packages Tim can make =

H. C. F of 39 and 13

Factors of 39 = 13 * 3 * 1

Factors of 13 = 13 * 1

H.C.F = 13

Therefore, Greatest number of identical packages Tim can make is 13.