Solve this problem
Step by step


​

Answer:

The area of the shaded region is, [tex]24mm^{2}[/tex]

Step-by-step explanation:

First we have to calculate the area of ΔABC and ΔXYZ.

Area of ΔABC = [tex]\frac{1}2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]

Area of ΔABC = [tex]\frac{1}{2}[/tex]×[tex]5mm[/tex]×[tex]12mm[/tex]

Area of ΔABC =[tex]30mm^{2}[/tex]

and,

Area of ΔXYZ = [tex]\frac{1}{2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]

Area of ΔXYZ = [tex]\frac{1}{2} X3mmX4mm[/tex]

Area of ΔXYZ = [tex]6mm^{2}[/tex]

Now we have to calculate the area of the shaded region.

Area of the shaded region = Area of ΔABC - Area of ΔXYZ

Area of the shaded region = [tex]30mm^{2} - 6mm^{2}[/tex]

Area of the shaded region = [tex]24mm^{2}[/tex]

Therefore, the area of the shaded region is, [tex]24mm^{2}[/tex]

The coefficient of [tex]x^{2}[/tex] in [tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex] is -3.

A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves. The coefficient in an expression that is not related to any variables is called the constant coefficient (also known as constant term or free coefficient).

Given equation,

[tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex]

= [tex]2x^{2}-3x-4-5x^{2}-6x+7[/tex]

= [tex]-3x^{2}-9x+3[/tex]

Hence, coefficient of [tex]x^{2}[/tex] is -3.

To learn more about coefficient here:

https://brainly.com/question/28975079

#SPJ4

False. Using the unit rate of cost per pound, 5 pounds of apples cost $6.00.

Cost per pound = $12.00 / 8 pounds = $1.50

5 pounds of apples cost = 5 pounds x $1.50 = $7.50

The unit rate of cost per pound can be calculated by dividing the total cost of 8 pounds of apples by the total number of pounds. In this case, the unit rate of cost per pound is $1.50. This means that for every pound of apples, the cost is $1.50. To calculate the cost of 5 pounds of apples, we need to multiply the unit rate of cost per pound by the number of pounds. In this case, 5 pounds of apples cost $7.50, which is calculated by multiplying $1.50 by 5. Therefore, the statement that using the unit rate of cost per pound, 5 pounds of apples cost $7.50 is false.

Learn more about unit here

https://brainly.com/question/19866321

#SPJ4

Answer:

$8173

Step-by-step explanation:

For this problem you will use the formula P(t)=Pe^r(t). P=5800 r=4.9%=0.049

t=7 years. With using this formula you should get your answer. I hope this helps!

Answer: The length of each side of the triangle is; 

Equal sides, x = 21.02 = PQ = PR

QR = 28.03

Step-by-step explanation: The trusses made by the manufacturer have the shape of an isoscellestriangle and as such two congruent sides PQ ≅ PR) are equal and QR is the third side whose length is 4/3 of the congruent sides.

The perimeter of each truss is 70ft.

Let the length of each congruent side be x ft.

Therefore,

Perimeter = x + x + (4/3)x

Perimeter, p = 70 = 3.33x

x = 70/3.33

x = 21.02

Therefore, Length of QR is; QR = (4/3) x

QR = (4/3) × 21.02

QR = 28.03

Answer:

x = 14

Step-by-step explanation:

Vertical angles are congruent ( equal to each other )

If ∠A and ∠B are vertical angles

Then 5x + 2 = 6x - 12

                     ^ ( Note that we just created an equation that we can use to                                   solve for x )

The rest comes down to basic algebra

5x + 2 = 6x - 12

step 1 subtract 5x from each side

5x - 5x cancels out

6x - 5x = x

we now have 2 = x - 12

step 2 add 12 to each side

- 12 + 12 cancels out

2 + 12 = 14

we're left with x = 14

Therefore , the solution of the given problem of equation comes out to bem² + p² =z².

The Latin word equ has the meaning of equivalent. Many of the English language's changeable terms, including adequate, temperate, and equality, contain Latin roots in their base words. The Latin root word equ enters our lexicon rather easily because both sides of an equation are, by essence, "equal" to one another.

Here,

Given : a triangle of m,p,z of length of right triangle :

By using Pythagoras theorem :

The relationship comes out to be :

=> m² + p² =z²

Thus , relationship between m , p and z is m² + p² =z² as per Pythagoras theorem.

Therefore , the solution of the given problem of equation comes out to be m² + p² =z².

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

y = -3/2 or -1.5

Step-by-step explanation:

-2/3 + y = -2 1/6

-2 1/6 = -13/6

So, our equation is

-2/3 + y = -13/6

Add 2/3 to both sides

y = -3/2

So, the answer is

y = -3/2 or -1.5

Answer:
Y= -3/2
in decimal form it is -1.5
in mixed number form it is -1 1/2

Step-by-step explanation:

Answer:

85 units²

Step-by-step explanation:

Add up your given areas to find the missing area using the Pythagorean Theorem:

a²+b²=c²

35+50=c²

85=c²

Therefore, the area of the blue square is 85 units²

Answer:

85 units²

Step-by-step explanation:

Answer:

o, we should add 16 on both sides in order to make it a complete square

Step-by-step explanation:

For making a perfect square we will add 16 on both sides of the given equation.

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Given equation is:-

x² - 8x = 5

x² - 8x + 16  = 5 + 16

x² - 4x -4x + 16  = 5 + 16

x ( x - 4 ) -4 (x - 4 ) = 21

( x - 4 )²  =  21

Therefore to make a perfect square we will add 16 on both sides of the given equation.

To know more about quadratic equations follow

https://brainly.com/question/1214333

#SPJ2

The flowers on the float would be 6.000 flowers. The result is obtained by using fraction multiplication.

Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.

For example:

It means one of four parts and two of five parts.

We have four thousand two hundred carnations on the float. It was 7/10 of flowers needed. Find the whole flowers on the float!

The carnations of a set of flowers is 7/10. It is 4200 carnations.

The carnations part is 7 and the whole part of flowers is 10.

Using fraction, the whole flowers would be

= 10/7 × 4200

= 6.000 flowers

Hence, the number of flowers needed to be on the float is 6.000 flowers.

Learn more about fraction here:

brainly.com/question/30156711

#SPJ4

Step-by-step explanation:

The way that you would multiply polynomials is pretty easy. Say we had a binomial and a trinomial and we wanted to multiply them. As an example, we will use (2x + 4) (x^2 + x + 4).

You have to multiply each number with each other number. For example, we would multiply 2x by x^2, 2x by x, and 2x by 4 to get the first part of the bigger equation. These come out to being 2x^3 + 2x^2 + 8x when multiplied and added.

Then, you have to do the same thing for the 4 in the binomial. Multiply 4 by x^2, 4 by x, and 4 by 4 to get the second part of the bigger equation. These come out as 4x^2 + 4x + 16 when added and multiplied.

After both of those are done, simply add the two parts together and simplify.

2x^3 + 2x^2 + 8x + 4x^2 + 4x + 16

2x^3 + 6x^2 + 12x + 16

That is your example answer, and that is how you multiply polynomials.

Answer:

Number of smaller ropes she can make from the larger rope = 2/3

Step-by-step explanation:

Total length of rope = 2/5 ft

Length of smaller rope = 3/5 ft

How many smaller ropes can she make from the larger rope?

Number of smaller ropes she can make from the larger rope = Total length of rope / Length of smaller rope

= 2/5 ÷ 3/5

= 2/5 × 5/3

= (2*5)/(5*3)

= 10/15

= 2/3

Number of smaller ropes she can make from the larger rope = 2/3

Given:

Consider the sides of the rectangle are (x+7) and (x+5) units.

To find:

The area of the entire rectangle in standard form.

Solution:

The area of the rectangle is:

[tex]A=l\times w[/tex]

Where, l is length and w is width of the rectangle.

So, the area of the given rectangle is:

[tex]A=(x+7)\times (x+5)[/tex]

[tex]A=(x)(x)+(x)(5)+(7)(x)+(7)(5)[/tex]

[tex]A=x^2+5x+7x+35[/tex]

[tex]A=x^2+12x+35[/tex]

Therefore, the area of the rectangle is [tex]A=x^2+12x+35[/tex].

Answer:

5/8

Step-by-step explanation:

15/3=5 and 24/3=8

Answer:

5/8

Step-by-step explanation:

divide both by 3

Answer: O x<12

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

5x+25<85

Step 2: Subtract 25 from both sides.

5x+25−25<85−25

5x<60

Step 3: Divide both sides by 5.

5x/5 < 60/5

x<12

Answer: 60

Step-by-step explanation:

If you subtract how much money you already had(54.75) from what you spent(79.99) you get 25.24. You then add 25.24 to the koney you had left(34.76) to get you answer of 60

Answer:

166 square units

Step-by-step explanation:

Let’s find the area of the shapes that in the net.

First, we can see two of the triangles have a base of 2 and a height of 13. The formula for surface area of a triangle is bh÷2. (13x2)÷2=13. Since there are two triangles, we multiply 13 by 2 and get 26.

Second, we can see two of the triangles have a base of 10 and a height of 12. (10x12)÷2=60. Since there are two triangles, we multiply 60 by 2 and get 120.

Third, we can see a rectangle has a base of 10 and a height of 2. The formula for surface area of a rectangle is bh. 10x2=20.

Last, we add up all the areas:

20+120+26=166.

The effective annual rate of interest if you do not make any payments for a year is 35%.

Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

where -

[A] = final amount

[P] = initial principal balance

[r] = interest rate

[n] = number of times interest applied per time period

[t] = number of time periods elapse

Given is that You just bought a new tablet computer for $500, including tax. There are no required payments for six months, but the company does charge 30% annual interest, compounded monthly, on any unpaid balance.

We can write -

A = 500(1 + 0.3/12)¹²⁽¹⁾

A = 500(1 + 0.025)¹²

A = 500 x (1.025)¹²

A = 675

Effective annual interest rate for a year is as follows -

A = 500(1 + r/1)⁽¹⁾⁽¹⁾

675 = 500(1 + r)

1 + r = 675/500

1 + r = 1.35

r = 0.35

r = 35%

Therefore, the effective annual rate of interest if you do not make any payments for a year is 35%.

To solve more questions on compound interest, visit the link below -

brainly.com/question/14295570

#SPJ1

Answer:

d. alternate interior angles are congruent

The third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.

Given an isosceles triangle with an angle and two equal sides, we can use the Pythagorean Theorem to calculate the missing side.

The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. Therefore, we can use this formula to calculate the missing side of the triangle.

First, let's call the two equal sides of the triangle 'a', and the angle opposite to them 'A'.

We can then use the Pythagorean Theorem to calculate the missing side, 'c', which is the third side of the triangle.

[tex]c^2 = a^2 + a^2\\c^2 = 2a^2\\c = sqrt(2a^2)[/tex]

To calculate 'c', we can first calculate 'a' by using the formula:

a = c * sin(A)

Then we plug 'a' into the equation for 'c':

c = sqrt(2*(c * sin(A))^2)

c = sqrt(2)*c*sin(A)

Therefore, the third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.

Learn more about isosceles triangle here:

https://brainly.com/question/2456591

#SPJ4

Answer:

She bought 10 apples and 10 bananas

Step-by-step explanation:

10 apples - $1.50 each x 10 apples = $15.00

10 bananas - $1.25 each x 10 bananas = $12.50

15.00+12.50=$27.50

x+y=28.00

1.50x+1.25y=28

Blank space 1: 3

Blank space 2: 4.242

Blank space 3: 6

Blank space 4: 6

Blank space 5: 3

This can be solved using triangle theorem.

Given that,

Liling is making a quilt. She starts with two small squares of material and cuts them along the diagonal.

The bigger square = 36 sq. in.

Then the side of the bigger square = √36 inch = 6 inch

Next, The side of the bigger square = Diagonal of the smaller square

Let the side of the smaller square = a (let)

Diagonal (smaller square): a√2 = 6 inch

so, a = 3√2 inch

Thus,  a = 3 x 1.414 = 4.242

To know more about triangle theorem refer to:

https://brainly.com/question/30105529

#SPJ4

The complete question is as follows:

Answer:

A

Step-by-step explanation:

check the above attachment to verify the answer.

Answer:  sqrt(2)

Step-by-step explanation:

Remember that sec x = 1/cos x.

That means that sec 7pi/4 = 1/cos(7pi/4)

cos(7pi/4) = -cos(7pi/4 - pi)

                 = -cos(3pi/4)

cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.

Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2

Since cos(7pi/4) is equal to -cos(3pi/4),

cos(7pi/4) is equal to sqrt(2)/2.

Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).

Rationalizing the answer 2/sqrt(2) gives sqrt(2)

Answer:

A.   2w² + 8w

Step-by-step explanation:

rectangle:  A = w(w+4) = w² + 4w

triangle:  A = 1/2(2(w+4)(w)) = 1/2(2w+8)(w) = 1/2(2w²+8w) = w² + 4w

Total Area = w² + 4w + w² + 4w = 2w² + 8w

Answer:

-------------------------------

The width of the space for computer stations is:

Each computer station has a space of: