The sum of x and y is 7. The value of y is three more than the value of x. Write a system of equations to model this.

Answer:

Part A ) Option A, Option C, Option E

Part B ) 1200 cm^2

Step-by-step explanation:

The area of a kite can be identified through 1 / 2 of the multiplication of each diagonal. The first diagonal is equivalent to the addition of 50 cm and 10 cm, while the second is of length 20 cm + 20 cm.

[tex]1 / 2 * ( 50 + 10 ) * ( 20 + 20 ),\\1 / 2 * ( 60 ) * ( 40 ),\\( 30 ) * ( 40 ),\\\\Area of Kite = 1200 square cm[/tex]

Consider the first option. If we take a look at the bit 2 * ( 1 / 2 * 20 * 50 ) the 2 and 1 /2 cancel each other out, leaving you with 20 * 50 = 1000 . Respectively in the expression 2 * ( 1 / 2 * 20 * 10 ) the 2 and 1 / 2 cancel each other out, leaving you with 20 * 10 = 200;

[tex]1000 + 200 = 1200 square cm,\\Option A - Correct![/tex]

The second option considers the expression 2 * ( 1 / 2 * 20 * 60 ). Again, the 2 and 1 / 2 cancel each other out, leaving you with 20 * 60;

[tex]20 * 60 = 1200 square cm,\\Option B - Correct![/tex]

Option C is a similar version of option a, besides the fact that the 1 / 2 doesn't exist. Thus, Option C is incorrect!

Option D is a similar version of option a as well, but as the 2 doesn't exist, it is incorrect!

This last option, option E is taken as 1 / 2 of the multiplication of the diagonals, and thus is correct!

[tex]1 / 2 * ( 40 * 60 ),\\1 / 2 * ( 2400 ),\\1200 square cm\\\\Correct![/tex]

Hope that helps!

Answer: -7, -1, 5, -5

Step-by-step explanation:

In order to find the inverse, swap the x's and y's and solve for y.

[tex]y=\dfrac{5x+1}{-x+7}\\\\\\\underline{Swap\ the\ x's\ and\ y's}:\\x=\dfrac{5y+1}{-y+7}\\\\\\\underline{\text{Multiply both sides by -y+1 to clear the denominator}}:\\x(-y+7)=5y+1\\-xy+7x=5y+1\\\\\\\underline{\text{Add xy and subtract 1 from both sides}}:\\7x-1=xy+5y\\\\\\\underline{\text{Factor out the y from the right side}}:\\7x-1=y(x+5)\\\\\\\underline{\text{Divide x+5 from both sides}}:\\\dfrac{7x-1}{x+5}=y[/tex]

Since the boxes you need to fill in show -x in the denominator, multiply the equation by -1/-1:

[tex]y=\dfrac{-1}{-1}\bigg(\dfrac{7x+1}{x+5}\bigg)\\\\\\\large\boxed{f^{-1}(x)=\dfrac{-7x-1}{-x-5}\qquad for\ x \neq -5}[/tex]

Answer:

Step-by-step explanation:

Depends on what you mean by multiplying by - 1.  I assume you are not going to multiply the y or f(x) term by - 1.

If that is so, take an example. Suppose you have a graph that is y=x^2

That's a parabola that opens upwards and it has a line going through its focus which is a point on the +y axis.

When you multiply the right hand side by - 1, the graph you get will be y = - x^2.

That opens downward and the focus is on the - y axis.

That means that the effect of the graph is that it flips over the x axis, which I think is the third answer.

Answer:

c

Step-by-step explanation:

ape x

Answer:

25 x 10^6 in standard form

= 25,000,000

Step-by-step explanation:

brainleist!

Answer:25,000,000

Step-by-step explanation:

Answer: x + 12.7 = -25.2 ✓given

x + 12.7 -12.7 = -25..2 -12.7 ✓ Subtraction property of equality

x + 0 = -37.9 ✓ Additive inverse and simplification

x = -37.9 ✓ Identity property

Step-by-step explanation: Put the steps in order. Then it makes some sense. Why is the step "legit"?

Answer:

y=x_1 is the solution of system

Answer:

A=1.5 units²

Step-by-step explanation:

a²+b²=c²

2.5²+1.5²=c²

a²+2.25=6.25

a²=4.00

a=2

A=1/2 x b x h

A=1/2 x 1.5 x 2

A=1.5 units²

Answer:

1.5

Step-by-step explanation:

Use the pythagorean theorem.  a^2+b^2=c^2.  a and b are the legs, or the shorter sides of the triangle.  If you don't know which ones are shorter, just know that c is opposite of the right angle which is 2.5 in this case.  So c is 2.5 and a is 1.5.  Now you plug the values into the equation

1.5^2+b^2=2.5^2

2.25+b^2= 6.25 .Simplify the equation

b^2= 4 .Subtract 2.25 from both sides.

b= 2.  Square root both sides.  

Based on the picture, a is the base and b is the height.  The area of a triangle is 1/2(bh) .You already know the base and height you you plug it in again

1/2(1.5*2)= 1/2(3)= 1.5  

Answer:

Step-by-step explanation:

D is the answer

Answer:

Step-by-step explanation:

Similarity property,

" If the two triangles are similar then their corresponding sides will be proportional."

14). If ΔPQR ~ ΔUVW,

     [tex]\frac{PQ}{UV}=\frac{QR}{VW}=\frac{PR}{UW}[/tex] [Statement}

     [tex]\frac{15}{10}=\frac{9}{6}=\frac{6}{4}[/tex]

     [tex]\frac{3}{2}=\frac{3}{2}=\frac{3}{2}[/tex]  [True}

Therefore, ΔPQR ~ ΔUVW [Theorem - SSS]

15). If ΔFHE ~ ΔDHG,

     [tex]\frac{EH}{HG}=\frac{HF}{DH}[/tex] [Statement]  

     [tex]\frac{24}{6}=\frac{36}{9}[/tex]

     4 = 4

Therefore, ΔFHE ~ ΔDHG [Theorem - AA]

Answer:

529 plan

Step-by-step explanation:

The 529 plan investment account is a type of account used to save for future education purposes and are sponsored by educational institutions and the state. They are of two types, The prepaid tuition plan and the education saving plan. The prepaid tuition plan is used to pay for future tuition fee at present rates while the education saving plan are used to pay for qualified education expenses

Answer:

529 plan

Step-by-step explanation:

A 529 college savings plan works much like a Roth 401(k) or Roth IRAby investing your after-tax contributions in mutual funds, ETFs and other similar investments. Your investment grows on a tax-deferred basis and can be withdrawn tax-free if the money is used to pay for qualified higher education expenses.

Answer: 58°

Step-by-step explanation:

They say the triangles are equal. And they give us more information for the triangle on the right.

∠E = ∠B

We know ∠C and ∠D, so you should add them all up to equal 180. (degree of a triangle)

74 + 48 + ∠E = 180

122 + ∠E = 180

∠E = 58

So therefore ∠B = 58

Answer:

x = 29

Step-by-step explanation:

Focus on ΔDEC first. We know that two of its angles are ∠C = 48° and ∠D = 74°.

All of a triangle's angles must add up to 180° by the Triangle Sum Theorem. 48° + 74° = 122°. 180° - 122° is 58°. So ∠E is 58°.

Because the triangles are congruent, ∠E corresponds to ∠B.

Because ∠B is "2x," divide 58° by 2. 58° ÷ 2 = 29°. 29° × 2 = 58°, so this checks out.

I hope this helps!!

The answer of this is C: 43

Answer:

C)43ft

Step-by-step explanation:

Area= pi*r(squared)

Pi*3.7(squared)=43.00

So answer=43pi(squared)

Answer:

3/10

Step-by-step explanation:

Josh and Lucy share some money in the ratio 3:7.

3+7=10

The fraction Lucy gets is 7/10

The fraction Josh must get is 3/10.

Answer:

see below

Step-by-step explanation:

2/3y + 15 = 9

Subtract 15 from each side

2/3y + 15-15 = 9-15

2/3y = -6

Multiply each side by 3/2 to isolate y

3/2 * 2/3y = -6 *3/2

y = -9

Answer:

y = - 9

Step-by-step explanation:

2/3y + 15 = 9

Subtract 15 on both sides.

2/3y = 9 - 15

2/3y = - 6

Multiply both sides by 3/2.

y = - 6 × 3/2

y = -18/2

y = -9

Answer:

C. 5

Step-by-step explanation:

XY= -1-(-5)= 4

ZA= A-1= 4 ⇒ A=1+4= 5

A=5

Answer:

y = -1/2x + 2

Step-by-step explanation:

If two lines are perpendicular then the product of their slopes are -1

m1*m2 = -1

where m1 amd m2 is slope of two lines.

_______________________________________

Given line

y = 2x-3\

it is in form of y = mx+c (slope intercept form)

where m is slope and c is y intercept

Thus, slope of line  y = 2x-3 is 2

Now we know that product of two lines are -1

let m be slope of other line

then m*2 = -1

m = -1/2

thus, slope of required line is -1/2

let the line be y = mx+c but m = -1/2

thus

y = -1/2 x + c

given that point(-6,5) lies on it

we use -6 in plca of x and 5 in place of y

5 = -1/2 *-6 + c

=>5 = 3 +c

=> c = 5-3 = 2

Thus, equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5) is y = -1/2x + 2

Answer:

The correct answer is

n = 3038

Step-by-step explanation:

Where we have;

We note that 1000! = An even number

Since Even × Even = even

Even × Odd = Even

Also, 7ⁿ is an Odd number since odd × odd = odd

Therefore 7ⁿ will divide 1000! with some fractions as follows;

1000! divided by 7ⁿ

When 7ⁿ = 1000!

log(7ⁿ) = log(1000!) = log(4.02×10²⁵⁶⁷)

n·log(7) = 2567.604

n = 2567.604/(log(7)) = 3038.23

Therefore, the largest integer n such that 7ⁿ divides 1000! = 3038

Which gives, 1000! ÷ 7³⁰³⁸ = 1.5733.

Answer:

From the sum of angles on a straight line, given that the rotation of each triangle attached to the sides of the octagon is 45° as they move round the perimeter of the octagon, the angle a which is supplementary to the angle turned by the triangles must be 135 degrees

Step-by-step explanation:

Given that the triangles are eight in number we have;

1)  (To simplify), we consider the five triangles on the left portion of the figure, starting from the bottom-most triangle which is inverted upside down

2) We note that to get to the topmost triangle which is upright , we count four triangles, which is four turns

3) Since the bottom-most triangle is upside down and the topmost triangle, we have made a turn of 180° to go from bottom to top

4) Therefore, the angle of each of the four turns we turned = 180°/4 = 45°

5) When we extend the side of the octagon that bounds the bottom-most triangle to the left to form a straight line, we see the 45° which is the angle formed between the base of the next triangle on the left and the straight line we drew

6) Knowing that the angles on a straight line sum to 180° we get interior angle in between the base of the next triangle on the left referred to above and the base of the bottom-most triangle as 180° - 45° = 135°.

Answer:

B

Step-by-step explanation:

The original amount will be the coefficient of (1 + 0.04)^r which is $728.00.

Answer:

17

Step-by-step explanation:

Plot in the points for each variable to find the y-intercept.

1=-4(4)+c

1=-16+c

1+16=c

17=c

9=-4(2)+c

9=-8+c

9+8=c

17=c

Answer:

Step-by-step explanation:

Given:

2 Points

(4,1) and

(2,9)

Slope

m = (y2 - y1)/(x2 - x1)

y2 = 9

y1 = 1

x2 = 2

x1 = 4

m = (9 - 1) / (2 - 4)

m = 8 / - 2

m = - 4

y intercept

y = mx + b

y = -4x + b

Use (9, 1) to find the y intercept

1 = - 4*9 + b

1 = - 36 + b

b = 37

Answer

The equation is y = - 4x + 37

Answer:

B.)The volume of the triangular prism is not equal to the volume of the cylinder.

Step-by-step explanation:

Let A be the cross-sectional area of both congruent right triangular prism and right cylinder.

Since the prism has height 2 units, its volume V₁ = 2A.

Since the cylinder has height 6 units, its volume is V₂ = 6A

Dividing V₁/V₂ = 2A/6A =1/3

V₁ = V₂/3.

The volume of the prism is one-third the volume of the cylinder.

So, since the volume of the prism is neither double nor half of the volume of the cylinder nor is it equal to the volume of the cylinder, B is the correct answer.

So, the volume of the triangular prism is not equal to the volume of the cylinder.

Answer:

palindromes

Step-by-step explanation:

palindromes are spelled the same forward and backward, thus have vertical symmetry.

Answer:

Hope it helps:) 18j+10

Step-by-step explanation:

(2)(3j+5+6j)

(2)(3j)+(2)(5)+(2)(6j)

6j+10+12j

18j+10

Answer:

x=-9

Step-by-step explanation:

3 x=-27

x = -9

Answer:

-9

Step-by-step explanation:

x3 = -27 OR 3x = -27

3x/3 = -27/3

x = - 9

Answer:

∆v = 32 km/h

the difference, in km/h, between the average speed of their trains is 32 km/h.

Step-by-step explanation:

For Ash's Train;

Distance travelled d1 = 80km

Time taken t1 = 50 minutes = 5/6 hour

Average speed = distance travelled/time taken

v1 = d1/t1

Substituting the values;

v1 = 80/(5/6)

v1 = 96km/h

For Misty's train;

Total distance travelled d2 = 160 km

Time taken t2 = 15:05 - 12:35 = 2 hours 30 minutes

t2 = 2.5 hours

v2 = d2/t2 = 160/2.5

v2 = 64 km/h

the difference, in km/h, between the average speed of their trains is;

∆v = v1 - v2 = 96km/h - 64 km/h = 32 km/h

∆v = 32 km/h

the difference, in km/h, between the average speed of their trains is 32 km/h.

Answer:

32km/h

Step-by-step explanation:

Answer:

Selling price of 5 gives the maximum profit

Step-by-step explanation:

What we do here is to find the first derivative, since at maximum points, the profit will be set to zero.

Mathematically, we have;

dp/dx = -120x + 600

We now equate this to zero

0 = -120x + 600

120x = 600

x = 600/120

x = 5