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Answer:

The solution is [tex]x=6\ cm[/tex]

Step-by-step explanation:

we know that

The area of rectangle is equal to

[tex]A=LW[/tex]

we have

[tex]A=56\ cm^{2}[/tex]

so

[tex]56=LW[/tex] ------> equation A

[tex]L=x+2[/tex] -----> equation B

[tex]W=2x-5[/tex] -----> equation C

Substitute equation B and equation C in equation A

[tex]56=(x+2)(2x-5)[/tex]

solve for x

[tex]56=(x+2)(2x-5)\\56=2x^{2}-5x+4x-10\\2x^{2}-x-66=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]  

in this problem we have

[tex]2x^{2}-x-66=0[/tex]  

so

[tex]a=2\\b=-1\\c=-66[/tex]

substitute in the formula

[tex]x=\frac{1(+/-)\sqrt{-1^{2}-4(2)(-66)}} {2(2)}[/tex]

[tex]x=\frac{1(+/-)\sqrt{529}} {4}[/tex]

[tex]x1=\frac{1(+)23} {4}=6[/tex]

[tex]x2=\frac{1(-)23} {4}=-5.5[/tex]  

The solution is [tex]x=6\ cm[/tex]

[tex]L=6+2=8\ cm[/tex]

[tex]W=2(6)-5=7\ cm[/tex]

Answer:

43°

Step-by-step explanation:

From the diagram

∠xwy=∠xyw = isosceles triangle where base angles are equal

∠y= ∠w = (180-86)÷2 = 47°

if ∠xzy=90° and ∠xyz =47° then ∠d=?

∠d= 180°-(90°+47°)

∠d=180°-137° =43°

Answer:

D

Step-by-step explanation:

We will solve the equation by using quadratic formula.

x=  (-b ± √(b^2-4ac))/2a

The standard form of quadratic equation is:

ax^2+bx+c=0

So by comparing with the standard form, we get:

a=1

b= -4

c=18

Putting the values in the formula

x=  (-(-4)± √((-4)^2-4(1)(18)))/2(1)  

x =  (4± √(16-72))/2

x =  (4± √(-56))/2

The minus sign in square root will introduce the imaginary symbol.  

x =  (4± √(14*4*(-1)))/2

The minus 1 can be replace by the imaginary i => i^2 = -1

x =  (4± √(14*2^2*i^2 ))/2

The terms with squares can be brought out of the square root

So,

x =  (4± 2i√14)/2

Taking 2 as common

x =  (2(2± i√(14)))/2

x = 2± i√14

Answer:

11

Step-by-step explanation:

8 plus 3 i dunno know if it is forsure but yeah.

This question clearly states that it is a 'find the volume' question.

Given dimensions of the object are :

Length of the object = [tex]40\frac{1}{2}[/tex] inches or 40.5 inches

Depth of the object = 10 inches

Height of the object is = 8 inches

So, the volume becomes = [tex]40.5\times10\times8[/tex] = 3240 cubic inch

Hence, the amount of cement needed is 3240 cubic inches.

To fill the form, you use the formula for the volume of a rectangular prism (length x width x height) to find that 3240 cubic inches of cement is needed.

The student is asking about the volume of cement needed to fill a form with specified dimensions. To calculate the volume, we need to use the formula for the volume of a rectangular prism, which is length x width x height. In this case, we need to convert the mixed number into an improper fraction before multiplying, or we could convert it to a decimal.

First, convert the length from 40 1/2 inches to 40.5 inches. Then, use the formula:

Volume = length x width x height

Volume = 40.5 in x 10 in x 8 in

Volume = 405 in x 8 in

Volume = 3240 cubic inches

Therefore, to fill the form, 3240 cubic inches of cement is needed.

Answer:

(x+1)(x2+1)

Step-by-step explanation:

Factor x3+x2+x+1

x3+x2+x+1

=(x+1)(x2+1)

also a great website for your problems is called mathpapa-algebra calculator

The slope is

[tex] - \frac{1}{3} [/tex]

Answer:

x = 15; m<(3x) = 45; m<(2x + 15) = 45

Step-by-step explanation:

The measures of the angles measuring 3x and 2x + 15 add up to 90 degrees.

3x + 2x + 15 = 90

5x + 15 = 90

5x = 75

x = 15

m<(3x) = 3 * 15 = 45

m<(2x + 15) = 2 * 15 + 15 = 30 + 15 = 45

Answer:

x ≥ 9

Step-by-step explanation:

Considering the equation is;

-4x (less than or equal to ) 36 , as provided by the questioner;

-4x ≤ 36

Dividing both sides by -4

-4x/-4≤ 36/-4

We get;

x ≥ -9 , the sign ≤ changes to ≥ since we have divided by a negative.

Trace of a matrix is defined only for a square matrix . It is the sum of the elements on the main diagonal, from the upper left to the lower right, of the matrix

Social Studies rate, S = 30/ 1.5 = 20pages/hr

Novel rate, N = 150/2 = 75pages/hr

Novel rate as a % of Social Studies rate...

N/S × 100% = 75/20 × 100% = 375%

percent of Ellie’s social studies reading rate is her Novel reading rate is 375%.

What are mathematics operations?

A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.

• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.

Here, it is given that :

Ellie read 30 pages of her social studies book in 1.5 hours at a constant rate, let first find Ellie's social studies reading rate :

rate = 30 pages/1.5 hours = 20 pages/ hr.

Now, to find out the unit rate, divide the total number of pages reading novel by the total time spent.

rate = 150 pages/ 2 hours = 75 pages/ hr.

To find out the percentage divide Ellie's novel reading rate by  Ellie's social studies reading rate and multiply by 100

percent of Ellie’s social studies reading rate is her Novel reading rate = 75/20 x 100 = 375%.

Therefore, percent of Ellie’s social studies reading rate is her Novel reading rate is 375%.

Read more about mathematics operations at:

https://brainly.com/question/17869111

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Answer:

Step-by-step explanation:

Let "e" represent the number of pounds of Earl Grey tea required for the mix. Then (600-e) is the number of pounds of Orange Pekoe tea required. The total cost of the mix is ...

  6·e + 4·(600 -e) = 4.50·600

  2e = 600·(4.50 -4.00) . . . . . simplify, subtract 4·600

  e = 300/2 = 150 . . . . . . . . . . divide by the coefficient of x

Required are 150 pounds of Earl Grey and 450 pounds of Orange Pekoe.

The amount of Earl Grey and Pekoe tea required for the new blend is :

Price of new blend per pound = $4.50

Price per pound of Earl tea = $6

Price per pound of Pekoe tea = $4

Let :

Pound of Earl tea = a

Pound of Pekoe tea = b

Converting the information to Mathematical expressions :

From (1):

a = 600 - b

Put a = 600 in (2)

6(600 - b) + 4b = 2700

3600 - 6b + 4b = 2700

Collect like terms :

-6b + 4b = 2700 - 3600

-2b = -900

b = 900 ÷ 2

b = 450

Recall :

a = 600 - b

a = 600 - 450

a = 150

Therefore,

Learn more : https://brainly.com/question/11335251

Answer:

(6y+17)

Step-by-step explanation:

1. Subtract 4y from 10y to get 6y

2. 9 is positive and 8 is negative but to subtract a negative is basically adding so you would add 9 to 8

3. You final equation would be (6y+17)

4. (10y+9)-(4y-8)= (6y+17)

Answer:

Step-by-step explanation:

[tex](10y+9)-(4y-8)\\\\=10y+9-4y-(-8)\\\\=10y+9-4y+8\qquad\text{combine like terms}\\\\=(10y-4y)+(9+8)\\\\=6y+17[/tex]

Check the picture below.

Answer

x^2 + 4x - 49

Step-by-step explanation:

you have to do PEMDAS first then add all the like-terms

hope this helps

p.s. you're pretty

Answer:

Vertical angles

x =37

Step-by-step explanation:

Adjacent angles are next to each other and share one side

Vertical angles are across from each other and only share a vertex.

These angles are vertical angles.  Vertical angles are equal

3x-4 = 107

Add 4 to each side

3x-4 +4 =107+4

3x = 111

Divide by 3

3x/3 = 111/3

x=37

Answer:

16

Step-by-step explanation:

Darren completely filled each box before the 21st box.  This means he completely filled 20 boxes.  To find out how many tins fit in each box, divide:

496/20 = 24.8

This means each of the 20 preceding boxes held 24 tins.  To get these filled, Darren used 20(24) = 480 tins of juice.

This left Darren with 496-480 = 16 tins of juice to put in box 21 before lunch.

Final answer:

To find out how many tins are in box 21, we subtracted the number of tins contained in the first 20 fully packed boxes from the total number of tins Darren packed. We found that each of the first 20 boxes must contain 24 tins, hence, there are 16 tins in the partially filled box 21.

Explanation:

The student's question is about finding how many tins were in box 21 before Darren stopped for lunch. To determine this, we need to figure out the pattern of how the tins were packed into the boxes. Since Darren packed the 496th tin in box 21, and since box 21 is not completely full, we can start by assuming that each box before box 21 was filled completely. If we can find the number of tins each box can hold, we will know the number of tins in box 21.

Let's assume the number of tins each box can hold is x. Since 20 boxes are completely full, they would contain a total of 20x tins. Box 21 contains fewer than x tins. The total number of tins, including those in box 21, is 496. Thus, we have the equation 20x + (496 - 20x) = 496. Simplifying, we get 20x = 496 - (496 - 20x), leading to 20x = 20x, which means each of the first 20 boxes contains the same number of tins. To find x, we need to divide the total number of tins not including box 21 by 20. Now we subtract that product from 496 to find the number of tins in box 21.

Since 496 is not evenly divisible by 20, we find that x is a decimal, which is not possible since we cannot have a fraction of a tin. Therefore, we subtract 1 from 496 to make it divisible by 20, giving us 495 tins to be divided evenly among the 20 full boxes. So, 495 ÷ 20 = 24.75, which means each full box holds 24 tins (since we can't have a fraction of a tin). Therefore, the number of tins in box 21 is 496 - 20*24 = 496 - 480 = 16 tins.

Answer:

1 mile

Step-by-step explanation:

f(0) equals 0. When x is 0 in the given function, the result of f(x) is also 0.

To find the value of f(x) when x=0 for the function f(x) = -1x, substitute 0 for x:

f(0) = -1(0) = 0.

Therefore, f(0) equals 0. When x is 0 in the given function, the result of f(x) is also 0.

Answer:

"The values for y are square roots of negative numbers"

Step-by-step explanation:

The steps shown are correct. But at the end we can see that we have to "take the negative square roots".

This means we have to take the square root of -1. In the real number system, we CANNOT take the square root of any negative number. Hence, there is NO SOLUTION to the system.

2nd answer choice, "The values for y are square roots of negative numbers", is right.

The area is 168 yd²

The area of Trapezoid is given by

A= (a+b)/2 * h

Putting the values

A = (5+23)/2 * 12

A = 168 yd²

Answer:

A = 168 Square Yards

Final answer:

The density of the laptop is calculated by dividing the mass (2,300 grams) by the volume (2,850 cubic centimeters), resulting in a density of 0.807 g/cm³, which is approximately 46/57.

Explanation:

To find the density of the laptop in grams per cubic centimeter (g/cm³), we use the formula density = mass/volume. The mass of the laptop is given as 2,300 grams and the volume is given as 2,850 cubic centimeters. By substituting into the formula:

Density = Mass / Volume = 2,300g / 2,850cm³ = 0.807 g/cm³.

When expressed as a fraction in simplest form, this is approximately 46/57 (since 0.807 ≈ 46/57). Hence, the answer is D. 46/57.

Answer:

D

Step-by-step explanation:

I'm assuming you're looking for area here.

The formula is b * h = A

So all you're doing is multiplying 30 by 18 to get 540.

[tex]\bold{Hey\ there!} \\ \bold{-5+\frac{2}{8}} \\ \bold{-5=-\frac{5}{1}}\\ \bold{Problem\ becomes\rightarrow -\frac{5}{1}+\frac{2}{8}} \\ \bold{\frac{2\div2}{8\div2}=\frac{1}{4}}\\ \bold{-\frac{5}{1}+\frac{1}{4}} \\ \bold{-5\times4=-20}\\ \bold{1\times4=4} \\ \bold{Problem\ becomes:\frac{-20+1}{4}} \\ \bold{-20+1=-19} \\ \bold{4=4} \\ \boxed{\boxed{\bold{Answer:\frac{-19}{4}}}}\checkmark[/tex]

[tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]

Answer:

(-1, -1) Let me know if the explanation didn't make sense.  

Step-by-step explanation:

If we graph the three points we can see what looks like a quadrilateral's upper right portion, so we need a point in the lower left.  This means M is only connected to N here and P is only connected to N.  So we want to find the slope of these two lines.

MN is easy since their y values are the same, the slope is 0.

NP we just use the slope formula so (y2-y1)/(x2-x1) = (-1-3)/(5-4) = -4.

So now we want a line from point M with a slope of -4 to intersect with a line from point P with a slope of 0.  To find these lines  weuse point slope form  for those two points.  The formula for point slope form is y - y1 = m(x-x1)

y-3 = -4(x+2) -> y = -4x-5

y+1 = 0(x-5) -> y = -1

So now we want these two to intersect.  We just set them equal to each other.

-1 = -4x -5 -> -1 = x

So this gives us our x value.  Now we can plug that into either function to find the y value.  This is super easy of we use y = -1 because all y values in this are -1, so the point Q is (-1, -1)

D.Bed because if you were to split the word BED in half horizontally you would be able to put them together and it match up.

Answer:

Step-by-step explanation:

Unfortunately not...

The shape is a triangle, and the area formula is A=[tex]\frac{1}{2}[/tex]bh.

b = 5 ft.

h = 4 ft.

Therefore:

A = [tex]\frac{1}{2}[/tex](5)(4)=10ft

Johnny currently owns fewer than 200 records.

Let's denote:
- \( x \) as the number of records Johnny currently owns.

Given:
- Gina has 400 records.
- Johnny would still have fewer than Gina has if he were to double the number of records he owns.

We can set up the following inequality:

[tex]\[ 2x < 400 \][/tex]

To find the maximum value of \( x \), we solve for it:

[tex]\[ x < \frac{400}{2} \]\[ x < 200 \][/tex]

So, Johnny currently owns fewer than 200 records.

Answer:

NO

Step-by-step explanation:

To find if they are equivalent, we need to simplify them first.

Using the distributive property we get:

6(4x-5) = 24x - 30

In this case we need to combine like terms.

3 + 22x - 33 - 2x =  20x - 30

So now we can compare.

24x - 30 ≠ 20x - 30

So we can conclude that the two expressions are not equal because 24x - 30 and 20x - 30 are obviously not equal.

Answer:

Not equivalent

Step-by-step explanation:

We are given an expression [tex] 6 ( 4 x - 5 ) [/tex] and we are to check if it is equal to [tex] 3 + 22 x - 33 - 2 x [/tex] or not.

Evaluation the given expression first:

[tex] 6 ( 4 x - 5 ) = 24 x - 30 [/tex]

While adding the terms in [tex] 3 + 22 x - 33 - 2 x [/tex], we get:

[tex] 22 x - 2 x - 33 + 3 = 20 x - 30 [/tex]

[tex] 24 x - 30 \neq 20 x - 30 [/tex]

Therefore, [tex] 6 ( 4 x - 5 ) [/tex] is not equivalent to [tex] 3 + 22 x - 33 - 2 x [/tex].

Answer:

x = -17

Step-by-step explanation:

Divide both sides by two and get:

x = -17

Answer:

x=-17

Step-by-step explanation:

-2x=34

-2x/-2=34/-2

x=-17