Use the Distributive Property to simplify the expression 6 • 68.
Evaluate the expression 48 ÷ m for m = 10.
Solve the equation 3.8 = x ÷ 7.7. Then check the solution.
Solve x + 5.1 = 13.4
Use mental math to solve the equation 8x = 64.
Solve the equation 22 = m + 1. Then check the solution.
Evaluate the expression 45 – 4x for x = 5.
. Find the missing term Box, 256, 64, 16.

Answer:

So the value of u is [tex]24[/tex] degree.

Step-by-step explanation:

Given;

Three angle [tex]2u[/tex] , [tex](u+18)[/tex] degree and [tex]90[/tex] degree in a Triangle.

We know;

Addition of three angle in a triangle is equal [tex]180[/tex] degree

[tex]2u+u+18+90=180[/tex]

[tex]3u=180-90-18[/tex]

[tex]3u=72[/tex]

[tex]u=\frac{72}{3}[/tex]

[tex]u=24[/tex]

∴ The value of u is [tex]24[\tex] degree.

Answer:

Length = 32 feet

Width = 10 feet

Step-by-step explanation:

The area of a rectangle = length (L) x width (W)

The relationship between the length and width is that

L = 12 + 2W -------------- (i)

therefore

Area = L x W can be rewritten as (12 + 2W) x W

320 =  (12 + 2W) x W

320 = 12W + 2W^2

this can then be turned into a quadratic equation:

2W^2 + 12W - 320 = 0

Divide through by 2

W^2 + 6W - 160 = 0

W^2 - 10W + 16W - 160 = 0

W(W- 10) + 16(W- 10) = 0

(W- 10)(W + 16) = 0

hence W = -16 and 10

since width cannot be a negative value,

Width = 10

hence substituting for width = 10 into equation (i)

L = 12 + 2(10)

L = 12 +20 = 32

Answer: Square

Step-by-step explanation: It has 4 equal sides that are all the same length.

The shape with four equal right angles and sides of the same length is a square, a fundamental concept in Euclidean geometry discussed in middle school mathematics.

The shape that has right angles and sides that are the same length is a square. In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or right angles). To identify a square, you can look for these two characteristics. .

The understanding of similar triangles is relevant when considering shapes and their properties, such as when using the properties of similarity to prove that two right triangles are similar based on their equal angles.

To create the image of a figure under a dilation with a scale factor of 1/2 centered at the origin, multiply each vertex coordinate by 1/2. The new coordinates for vertices j, k, l, and m would be j'(-1, 1), k'(2, 1), l'(2, -1), and m'(-1, -1), respectively.

The student is asking for the image of a figure after performing a dilation with a scale factor centered at the origin. To perform this dilation, you need to multiply the coordinates of each vertex by the scale factor. For a scale factor of 1/2, each coordinate of the vertices is halved. Therefore, the new vertices after the dilation will be:

These new vertices j', k', l', and m' will give you the dilated figure.

Answer:

45%

Step-by-step explanation:

The formula to work out the decrease is:

Percentage Decrease= actual decrease / original amount X 100%

1) So firstly, we have to work out the decrease, to do this we have to do is do $750-$412.50= $337.50

2) We can now substitute this into our formula which will now be. (We will also add the original amount, which is $750.00)

Percentage Decrease= 337.50 / 750.00 X 100% = 45

The percentage decrease is 45%

Answer:

m = - 8 ± 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

m² + 16m - 8 = 0 ( add 8 to both sides )

m² + 16m = 8

To complete the square

add ( half the coefficient of the m- term )² to both sides

m² + 2(8)m + 64 = 8 + 64

(m + 8)² = 72 ( take the square root of both sides )

m + 8 = ± [tex]\sqrt{72}[/tex] = ± [tex]\sqrt{36(2)}[/tex] = ± 6[tex]\sqrt{2}[/tex]

Subtract 8 from both sides

m = - 8 ± 6[tex]\sqrt{2}[/tex]

Answer:

Its no Solution

Step-by-step explanation:

If you use elimination both 7x and the 4y will be 0 and you'll get

0=-26 and 0=-2

So

No Solution

sorry for my hand writing

Answer:

2 milion

Step-by-step explanation:

2,000 x 2,000= 4,000,000

4,000,000÷ 2= 2,000,000

Half the number of square root of a number is 2k is [tex]2k^2[/tex].

Let's break down the problem step by step to find half of the number. We start with the given information: the square root of a number is [tex]2k[/tex]. Our goal is to find half of this number.

Let the number be [tex]x[/tex]. The problem tells us that the square root of [tex]x[/tex] is [tex]2k[/tex].

We write this mathematically as:
[tex]\sqrt{x} = 2k[/tex]

To find [tex]x[/tex], we square both sides of the equation to remove the square root:
[tex]x = (2k)^2[/tex]

Simplify the right side:
[tex]x = 4k^2[/tex]

Now, we need to find half of [tex]x[/tex]. Half of [tex]x[/tex] is:
[tex]\text{Half of } x = \frac{x}{2} = \frac{4k^2}{2}[/tex]

Simplify the fraction:
[tex]\frac{4k^2}{2} = 2k^2[/tex]

Answer:

see explanation

Step-by-step explanation:

Any integer n > 1 multiplied by 2 will be even, that is

2n ← is even

Given

n² - (n - 2)² - 2 ← expand parenthesis

= n² - (n² - 4n + 4) - 2

= n² - n² + 4n - 4 - 2 ← collect like terms

= 4n - 6 ← factor out 2 from each term

= 2(2n - 3)

Hence 2(2n - 3) ← will always be even for n > 1

The statement can be proved by parenthesis that the expression [tex]n^{2} - (n - 2)^{2} - 2[/tex] is always an even number.

=  [tex]n^{2} - (n - 2)^{2} - 2[/tex]

=  [tex]n^{2} - (n^{2} - 4n + 4) - 2[/tex]

=  [tex]4n - 4 - 2[/tex]

=  [tex]4n - 6[/tex]

= [tex]2(2n - 3)[/tex]

As the expression 2(2n - 3) is always a multiple of 2 and also it is given that n>1 therefore by the parenthesis, the expression [tex]n^{2} - (n - 2)^{2} - 2[/tex] is always an even number.

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Answer:

First question is D: F varies directly with x and y, and inversely with z.

Second Question is B Y=kx^3/sq root z

Edge Verified

Answer:

part 1 = d

part 2= b

Step-by-step explanation:

I just got it right on edg

Answer:

D) approximately bell-shaped

Step-by-step explanation:

a bell-shaped histogram is where you can draw a vertical line to the top of the histogram (in this case to the blue line at frequency 12) and a "mirror" line going back down (1 (200-249) ) where the bell-shape can make the shape going through all the lines of the histogram.

I hope I explained that well, and I hope that helps!

Answer: X= 4

Step-by-step explanation:

24+0.44x=19+1.69x exp equation like:

24+44x/100=19+169x/100

Multiply left and right side of equation with 100

2400+44x=1900+169x

2400-1900=169x-44x

500=125x

x=500/125

x=4

The solution of the equation is 4.

To solve the equation 24+0.44x=19+1.69x, we want to collect like terms and isolate the variable x on one side. This type of equation is a linear equation, not a quadratic equation, since the highest power of x is one. First, let's move the terms containing x to one side and the constant terms to the other side:

Subtract 1.69x from both sides: 24 - 19 = 1.69x - 0.44x

Combine like terms: 5 = 1.25x

Divide both sides by 1.25: x = 5 / 1.25

Solving for x gives us: x = 4

Answer:

n +(-8)=14

Step-by-step explanation:

a number is 'n'

is adding negative of 8

i. e. -8

is eaual to 14

then n=14+8

or; n =22

therefore the number is 22.

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-7)^2=x^2-2(x)(7)+7^2=x^2-14x+49\\\\\bold{METHOD\ 2:}\\\\\text{We know:}\ a^2=a\cdot a\\\\(x-7)^2=(x-7)(x-7)\\\\\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x)(x)+(x)(-7)+(-7)(x)+(-7)(-7)\\\\=x^2-7x-7x+49\qquad\text{combine like terms}\\\\=x^2-14x+49[/tex]

Answer:

27[tex]\frac{27}{4x^{6}y^{8}  }[/tex]

Step-by-step explanation:

your going to raise the power on the numerator by 3 and the denominator 4  so you get [tex]\frac{4*27x^{6} y^{12} }{16x^{12}y^{20}  }[/tex] then reduce and simplify

[tex]\rightsquigarrow[/tex] [tex]\bold{\dfrac{4(3x^2 y^4)^3}{(2x^3 y^5)^4} }[/tex]

[tex]\rightsquigarrow[/tex] [tex]\bold{\dfrac{4(3x^5 y^{12})}{2x^{12} y^{20}} }[/tex]

[tex]\rightsquigarrow[/tex] [tex]\bold{\dfrac{ 12x^5 y^{12}}{2x^{12} y^{20}} }[/tex]

[tex]\rightsquigarrow[/tex] [tex]\bold{ \dfrac{\cancel{12x^5 y^{12}}}{\cancel{2x^{12} y^{20}}}}[/tex]

[tex]\rightsquigarrow[/tex] [tex]\bold{\dfrac{6}{x^7 y^8} }[/tex]

Answer:

8p + 56 + 16q

Step-by-step explanation:

To distribute, we must multiply all numbers/terms inside the paranthesis by '8.'

So:

8(p) = 8p

8(7) = 56

8(2q) = 16q

So your expression would be 8p + 56 + 16q  ^-^

Answer:

[tex]\rm{8p+56+16q[/tex]

Step-by-step explanation:

Hi there!

The Distributive Property states that

a(b+c)=ab+ac

Let's use this property to simplify our expression:

[tex]\rm{8(p+7+2q)[/tex]

[tex]\rm{8p+56+16q[/tex]

Thus, [tex]\rm{8p+56+16q[/tex] is our final answer.

[tex]\star\star[/tex]Hope it helps! Enjoy your day!

[tex]\bold{GazingAtTheStars(:}[/tex]

Answer:

600

Step-by-step explanation:

20%=0.2

120/0.2=600

Equation: 1.15 c = 40

Solution: $34.78

Step-by-step explanation:

The given is:

We need to write an equation that can be used to find c, and then

find the value of c

∵ The cost of the printer cartage = $c

∵ The computer game costs 15% more than a printer cartridge

- That means add the cost of the cartage by 15% of it to find the

   cost of the computer game

∴ The cost of the computer game = c + 15% × c

∵ 15% = 15 ÷ 100 = 0.15

∴ The cost of the computer game = c + 0.15 c

- The two terms of c (1 + 0.15)

∴ The cost of the computer game = $1.15 c

∵ The cost of the computer game = $40

- Equate the two expressions of the cost of the game

∴ 1.15 c = 40

The equation that can be used to find c is 1.15 c = 40

Solve the equation to find c

∵ 1.15 c = 40

- Divide both sides by 1.15

∴ c = $34.78

The cost of the printer cartridge is $34.78

Equation: 1.15 c = 40

Solution: $34.78

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Answer:

Factor the numerator and denominator and cancel the common factors.

−1

Answer:

it is -1 when all calculated

Step-by-step explanation:

Answer:

8.1 gallons of gas

Step-by-step explanation:

240/9=216/x

simplify 240/9 into 80/3,

80/3=216/x

cross product

3*216=80*x

648=80x

x=648/80

x=8.1

Answer:

20*s+30*l = 280

4*s=l

Step-by-step explanation:

Let's say that the number of small boxes is s and the number of large boxes is l. Then, 20*s equals the amount of books in small boxes (as there are 20 books per small box), and 30*l for the amount of books in large boxes. Then, we know that 4 times the amount of small boxes, s, equals l, so 4*s=l. Then, as we know that the amount of books that can be held is 280, we can add the amount of books for each type of box, or 20*s+30*l, to get 280. Our equations are as follows:

20*s+30*l = 280

4*s=l

As we can define l in terms of s, making it so that we can limit the top equation to 1 variable, we can use this to determine the number of each type of box

Answer:

1152? 36÷32=1152 I think?

Mr. Hanson needs to multiply the number of students (32) by the number of pencils required per student (36) to find out he needs to purchase a total of 1152 pencils for the school year.

Mr. Hanson needs to calculate the total number of pencils required for his class for the entire school year. With 32 students and the need for each student to have 36 pencils, the calculation is straightforward:

Multiply the number of students by the number of pencils each student requires.

32 students imes 36 pencils per student = 1152 pencils.

Therefore, Mr. Hanson needs to purchase 1152 pencils in total.

By having this quantity of pencils, Mr. Hanson ensures that each student has a pencil for each week of the school year, contributing to a well-prepared classroom environment.

The length of NT in isosceles triangle RST is 7.

In an isosceles triangle, the base angles are congruent, and the sides opposite those angles are also congruent. Let's denote the length of RS (and RT) as r, and the length of MN as m  Since M and N are midpoints, MN is parallel to the base, and its length is half the length of the base. Therefore, [tex]\( m = \frac{r}{2} \).[/tex]

The perimeter of the triangle is the sum of the three sides, so [tex]\( 2r + r = 25 \) (as RS = RT).[/tex] Solving for r, we get [tex]\( r = \frac{25}{3} \).[/tex]

Now, we know that [tex]\( m = \frac{r}{2} \),[/tex] so [tex]\( m = \frac{25}{6} \)[/tex]. Finally, the length of NT is the difference between RT and MN, which is [tex]\( \frac{25}{3} - \frac{25}{6} = 7 \).[/tex]Therefore, the length of NT is 7 units.

QUESTION:Consider isosceles triangle RST, where RS = RT. Let M and N be the midpoints of sides RS and RT, respectively. A segment MN is drawn with a length of 3.5 units. The perimeter of triangle RST is given as 25 units. Determine and state the length of NT.

Please provide a comprehensive solution to this problem, including step-by-step calculations and explanations.

Final answer:

By applying properties of isosceles triangles and the given conditions, we calculate that the length of segment NT is 4.5 units.

Explanation:

The subject matter is a geometrical problem involving an isosceles triangle with given conditions. In isosceles triangle RST, RS and RT are equal in length, M and N are the midpoints of RS and RT respectively, and MN is drawn with a length of 3.5 units. Given that the perimeter of the triangle is 25 units, we need to find the length of segment NT.

To solve this, we first understand that in an isosceles triangle, the perpendicular from the vertex to the base bisects the base. Therefore, segment MN cuts the base ST equally in two, making each half 3.5 units, since MN = 3.5 units. Furthermore, because M and N are midpoints, segments MS and NT are equal. Finally, by knowing the perimeter, we can deduce that RS + ST + RT equals 25 units.

Thus, we can derive the lengths of RS and RT (which are equal) and then use that information to calculate the length of NT. If RS = RT and we call that length x, then 2x + 2(3.5) = 25. Solving for x gives us x = (25 - 7)/2 = 9. Thus, segment NT as the half of either RS or RT is 9/2 = 4.5 units.

Answer:

C.

Step-by-step explanation:

(∛5)^7

= (5 ^ 1/3)^7

= 5^(7/3)

The cube root of five to the seventh power can be rewritten as a rational exponent as five to the seven thirds power. This is achieved by making the denominator of the exponent the index of the radical and the numerator the power of the radicand.

In mathematics, radical expressions can be rewritten as expressions with rational exponents. In your case, the cube root of five to the seventh power, is represented as [tex]5^(^7^/^3^)[/tex], which is your rational exponent form. So the answer is C: five to the seven thirds power.

To convert a radical expression to an expression with a rational exponent, the denominator of the exponent becomes the index of the radical, and the numerator of the exponent becomes the power of the radicand. In this case, the cube root is the index, which is 3, and the power of the radicand (five) is 7. Hence, five to the seven thirds power.

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Part A: The type of the quadrilateral of the rooftop is a square

Part B: The length of one side of the rooftop is 19 m

Step-by-step explanation:

Let us revise some notes about quadratic expression

The area of a rooftop can be expressed as 9x² + 6x +1

The rooftop is a quadrilateral

We need to find the type of the quadrilateral and the length of

one side of the rooftop

∵ The area of the rooftop = 9x² + 6x +1

- Check if 9x² + 6x +1 is a perfect trinomial

∵ [tex]\sqrt{9x^{2}}=3x[/tex]

∵ [tex]\sqrt{1}=1[/tex]

∵ [tex](3x)(1)(2)=6x[/tex]

∴ 9x² + 6x +1 = (3x + 1)²

∴ 9x² + 6x +1 is a perfect square trinomial

∵ Perfect square trinomial can represent the area of a square

∴ The quadrilateral is a square

Part A: The type of the quadrilateral of the rooftop is a square

∵ The area of the rooftop is 9x² + 6x +1

∵ 9x² + 6x +1 = (3x + 1)²

∵ Area of the rooftop = 361 m²

∴ (3x + 1)² = 361

- Take square root for both sides

∴ 3x + 1 = 19

∵ The area of a square = (side)²

∵ The area of a square = (3x + 1)²

∴ 3x + 1 is the length of the side of the square

∵ 3x + 1 = 19

∴ The length of the side of the square is 19 m

Part B: The length of one side of the rooftop is 19 m

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Answer:

10

Step-by-step explanation:

A bakery makes 40 different flavors of muffins.

25% of the flavors have chocolate as one of the ingredients.

Convert 25% to fraction:

[tex]25\%=\dfrac{25}{100}=\dfrac{1}{4}[/tex]

So, there are

[tex]40\cdot \dfrac{1}{4}=10[/tex]

muffins which have chocolate as one of the ingredients.

In attached tape diagram:

green - with chocolate

blue - without chocolate

Answer:

Step-by-step explanation:

The total number of flavors is 40.

25% of the flavors have chocolate.

To find the number of flavors which have chocolate, we just need to multiply 0.25 by 40, because 0.25 represents 25%

[tex]0.25(40)=10[/tex]

So, there are 10 flavors with chocolate.

Now, if 25% represents flavors with chocolate, then 75% represents flavors without chocolate

[tex]0.75(40)=30[/tex]

So, there are 30 flavors without chocolate.

Answer:

$270.00

Step-by-step explanation:

The ratio of house of babysitting and house is 3:2. If you change the 3 into a 15, you would have to change the 2 into a 10 because 3 x 5 = 15, so 2 x 5 = 10.

After you do those calculations you divide 15 by 5 and that is 3. You then multiply 60 by 3 = 180.

After that you have to divide 10 by 8 and you get 1.25. You then multiply 72 by 1.25 = 90.

Then you add 180 and 90 together to get $270.00

Answer: 6x^2-9x-20

Step-by-step explanation:

(3x+4)(2x-5)

6x^2-15x+6x-20

6x^2-9x-20