Substitution for {2x-3y=11 and -x + 2y = -6

Final answer:

Using the properties of similar triangles and the given side lengths, we solve for x and find that ED equals 8 units.

Explanation:

We're dealing with a geometry problem involving parallel lines and the properties of triangles. Since sides AB and CD are parallel, and triangles ABE and DCE share a common vertex at E, we can find the length ED using similar triangles and the given side lengths. The corresponding sides of similar triangles are proportional, so:

AB / AE = CD / ED
9 / (2x + 4) = 6 / (x + 4)

To solve for x, cross multiply and obtain the equation:

9(x + 4) = 6(2x + 4)
Then solve for x:
9x + 36 = 12x + 24
3x = 12
x = 4
Having x, we can find ED:
ED = x + 4 = 4 + 4 = 8 units

Answer:

x=-2

Step-by-step explanation: I gotchu

1. You first apply the -3 to (3x-2) which makes the equation -9x+6=24

2. Then, to isolate "-9x", you subtract 6 from both sides to make the equation -9x=18

3. Lastly, to isolate "x", you divide both sides by -9 which would make x=-2

Answer:

it would be 2x-6

Step-by-step explanation:

since you don't know what the value of "the number" is you would put a variable, x. and there is 2 of this number.

then 6 less would be -6 of this variable.

Answer:

2:3

Step-by-step explanation:

Answer:

2min :3min

Step-by-step explanation:

8 min divided by 4 =2

12 min divided by 4 =3

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

(-3,4) it shows that -3 =x and 4 =y

2x + y ≥ -2

Inserting both values into the equation

2(-3) + 4

-6 +4

-2

Answer confirms equation

For this case we have that by definition, a linear equation is of the form:

[tex]ax + b = 0[/tex]

The variable (s) involved in the equation always have exponent 1.

Some examples of linear equations are:

[tex]x + 5 = 3y\\y + 6 = 3x\\y = 2x + 2[/tex]

Answer:

In a linear equation the variables have exponent 1.

[tex]y = 2x + 2[/tex]

Answer:

Explanation:

The complement of a subset is the subset of elements that are not in the given subset.

You must know which numbers the spinner has.

Assuming the spinner has the numbers 1, 2, 3, 4, the complement of spinning any number less than 3, is spinning a number that is not less than 3.

Then, that is spinning a number that is equal to or greater than 3.

The numbers that are equal to  or greater than four, for a spinner that has the numbers 1, 2, 3, and 4 are 3 and 4.

Thus, the complement of spinning any number less than 3 is spinning a three or a four.

Answer:

C

Step-by-step explanation:

Two sevenths over two fifths = five over seven mile per hour

The unit rate is 5 over 7 miles per hour

Solution:

Given that, Suzanna walked two over seven of a mile in two over five of an hour

We have to find the unit rate in miles per hour

Unit rate means number of miles covered in 1 hour

From given information,

Two over seven of a mile in two over five of an hour

Which means,

[tex]\frac{2}{7} \text{ miles } = \frac{2}{5} \text{ hour }[/tex]

[tex]\text{ So she covered } \frac{2}{7} \text{ miles in } \frac{2}{5} \text{ hour }[/tex]

To find for number of miles covered in 1 hour, divide the [tex]\frac{2}{7} \text{ by } \frac{2}{5}[/tex]

[tex]\text{Unit rate in miles per hour } = \frac{\frac{2}{7}}{\frac{2}{5}}\\\\\text{Unit rate in miles per hour } = \frac{2}{7} \times \frac{5}{2} = \frac{5}{7}[/tex]

Two sevenths over two fifths = five over seven mile per hour

Thus unit rate is 5 over 7 miles per hour

Answer:

two sevenths over two fifths = five over seven mile per hour

Step-by-step explanation:

two sevenths over two fifths = five over seven mile per hour

Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders

Solution:

Let "a" be the orders served by Teresa

Let "b" be the orders served by Charlie

Let "c" be the orders served by Justin

Teresa, Charlie, and Justin served a total of 153 orders

Therefore,

a + b + c = 153 -------- eqn 1

Justin served 4 times as many orders as Charlie

Orders served by Justin = 4( orders served by Charlie )

c = 4b ---------- eqn 2

Teresa served 9 more orders than Charlie

orders served by Teresa = 9 + orders served by Charlie

a = 9 + b ----------- eqn 3

Let us solve eqn 1 and eqn 2 and eqn 3

Substitute eqn 2 and eqn 3 in eqn 1

9 + b + b + 4b = 153

9 + 6b = 153

6b = 153 - 9

6b = 144

b = 24

Substitute b = 24 in eqn 3

a = 9 + 24

a = 33

Substitute b = 24 in eqn 2

c = 4(24)

c = 96

Thus Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders

Answer: X=2.7

Step-by-step explanation:

25*2-8x=12x-4

50-8x = 12x-4

subtract 50 from both sides

-8x = 12x-54

subtract 12x from both sides

-20x= -54

divide both sides by -20

X=2.7

Answer:x=2/5

Step-by-step explanation:

25x2-8x=12x-4

25x2-8x-12x+4=0

25x2-20x+4=0

25x2-10x-10x+4=0

5x(5x-2)-2(5x-2)=0

(5x-2)(5x-2)=0

5x-2=0 and 5x-2=/

5x=2 and 5x=2

X=2/5

The Town Recreation Department ordered 76 baseballs and 24 bats.

Given that, the total number of baseballs = 100, the total purchase = $822, cost of each baseball = $4.50 and the cost of each bat = $20.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Let the number of baseballs be x and the number of bats be y.

Now, the total number of items = The number of baseballs + The number of bats

⇒ 100=x+y ------(I)

Total amount = 4.50x+20y

⇒ 4.50x+20y = 822 ------(II)

Solve the obtained equations:

Put x=100-y in the equation 4.50x+20y = 822

We get, 4.50(100-y)+20y = 822

⇒ 450-4.50y+20y=822

⇒ 15.5y=372

⇒ y=372/15.5

⇒ y= 24

So, x+y =100

⇒ x=100-24=76

Therefore, the Town Recreation Department ordered 76 baseballs and 24 bats.

To learn more about the system of equations visit:

https://brainly.com/question/24065247.

#SPJ2

The question picked from the figure given:

The Town Recreation Department ordered a total of 100 baseballs and bats for the summer baseball camp. Baseballs cost $4.50 each and bats cost 20 each. The total purchase was $822. How many of each item was ordered?

Answer:

small boxes = 5 and large boxes = 10

Step-by-step explanation:

Given:

The volume of each small box is 7 cubic feet.

volume of each large box is 13 cubic fee.

There were twice as many large boxes shipped as small boxes shipped.

Total volume of all boxes was 165 cubic feet.

Question asked:

The number of small boxes shipped and the number of large boxes shipped?

Solution:

Let  number of small boxes shipped = x

Then, the number of large boxes shipped = 2x (given)

Total volume of all boxes = 165 cubic feet.

no. of small boxes [tex]\times[/tex] vol. of each small box +  no. of large boxes [tex]\times[/tex] vol. of each large box =  165 cubic feet. (Total volume of all boxes)

[tex]x \times7 + 2x \times 13 = 165\\7x + 26x = 165\\33x = 165[/tex]

Dividing both side by 33

[tex]x = \frac{165}{33}\\ x = 5[/tex]

The number of small boxes shipped = [tex]x[/tex] = 5

The number of large boxes shipped = 2 [tex]x[/tex] = 2[tex]\times[/tex] 5 = 10

Answer:

Explanation:

The plastic pencil case has form of a triangular prism.

This triangular prism has five faces:

Surface area:

        area = (1/2) base × height

         area of one triangle = 10 cm × 12 cm × (1/2) = 60 cm²

          area of the two triangles = 2 × 60 cm² = 120 cm²

        area of a rectangle = length × width

         area of the trhee triangles = 24 cm × 10 cm + 2 × 24 cm × 13 cm = 240 cm² + 624 cm² = 864 cm².

Answer: first choice, 984 cm²

Answer:

Center (h, k) = (0, 6)

Radius, r = 3 units

Step-by-step explanation:

The given equation of the circle is: [tex]$ x^2 + y^2 + 12y + 27 = 0 $[/tex]

STEP I: Move the constant term to the right hand side.

To do that we subtract 27 on both the sides, we get:

[tex]$ x^2 + y^2 + 12y = -27 $[/tex]

STEP II: Divide the co - effecient of 'x' by 2 and square it.

Here there is no 'x' term. Its co-effecient is 0.

STEP III: Add the result on both sides.

Since, we got 0 in the previous step, there would no change in the equation

STEP IV: We repeat the process for 'y'.

Here, the co-effecient of 'y' is: 12.

Dividing by 2 and squaring it will yield:

[tex]$ \frac{12}{2} = 6; \hspace{5mm} 6^2 = 36 $[/tex]

STEP V: Adding 36 to both the sides of the equation, it becomes:

[tex]$ x^2 + y^2 + 12y + 36 = -27 + 36 $[/tex]

[tex]$ \implies x^2 + y^2 + 12y + 36 = 9 $[/tex]

We have arrived at perfect squares.

STEP VI: Write in the form of perfect squares.

[tex]$ (x - 0)^2 + (y - 6)^2 = 3^2 $[/tex]

STEP VII: Compare it with the standard form.

[tex]$ (x - h)^2 + (y - k)^2 = r^2 $[/tex]

We get: The centre of the circle: (h, k) = (0, 6) and

the radius of the circle, r = 3 units.

Answer:

5u - 20

Step-by-step explanation:

(u - 4)5

Multiply

5u - 20

Hope this helps :)

Answer:

5

(

2

x

+

7

)

Step-by-step explanation:

Answer: 5 (2x-7)

Step-by-step:

Answer:

The third dot

Step-by-step explanation:

I did this question before :)

Answer:

1.75, 0.4375

Step-by-step explanation:

Note there is a common ratio between consecutive terms, that is

r = 28 ÷ 112 = 7 ÷ 28 = 0.25

Thus the sequence is geometric.

To obtain a term in the sequence multiply the previous term by 0.25

7 × 0.25 = 1.75

1.75 × 0.25 = 0.4375

The next 2 terms in the sequence are 1.75, 0.4375

Answer:

25/4 This improper fraction represents how much milk is left in the carton.

Step-by-step explanation:

5×4=20

20+5=25

25/4

Answer:

5z+1

Step-by-step explanation:

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

3z-4+2z+5

3z+2z-4+5

5z-4+5

5z+1

Answer:

5z+1

Step-by-step explanation:

3z-4+2z+5

Group like terms

3z+2z+5-4

Simplify

5z+1

Answer:6350.4

Step-by-step explanation:

Answer:

10 black- 10/20 - 50%

8 red- 8/20 - 40%

2 white - 2/20 -10%

Step-by-step explanation:

The total number of balls = 10 + 8 + 2 = 20 balls

probability of black balls = 10/20 = 50%

probability of red balls = 8/20 = 40%

probability of white balls = 2/20 = 10%

the three probabilities:

probability that the ball is one of the three colors = (10/20) + (8/20) + (2/20)

                                                                              = 1 = 100%

Let's label the number you're trying to find x. You have to set up a system of equations.

1. Five times a number can be labeled as 5x.

2. Subtracted from 20 gives us 5x-20.

3. The problem says this is the same as simply tripling the original number. So set the first equation equal to 3x.

4. 5x-20=3x

5. Move like terms onto the same side. We can do this by subtracting 3x from both sides and adding 20 to both sides.

6. 5x-3x=20

7. 2x=20

8. Divide both sides by 2 to get x by itself.

Answer: x=10

The number is 2.5.

Let the number is = x.

According to the question:

20 - 5x = 3x

Add 5x.

20 = 5x + 3x

20 = 8x

Divide by 8.

x = 20/8 = 2.5

Learn more: https://brainly.com/question/20521181

Answer:

d. thirty residents who live within a 2-miles radius of Natasha’s school

Step-by-step explanation:

got it right

The valid sample for the survey would be students in Natasha’s social studies class and parents who live within a 2-mile radius of Natasha’s school.

The valid sample for the survey would be students in Natasha’s social studies class and parents who live within a 2-mile radius of Natasha’s school.

The students in Natasha's social studies class are directly affected by the speed limit in front of her school, and the parents who live nearby are likely to have an opinion on the matter as well.

While the other options may provide some insight, they are not as directly relevant to Natasha's goal of determining the neighborhood's support for lowering the speed limit.

https://brainly.com/question/9555826

#SPJ2

Step-by-step explanation:

We are asked to draw a triangle.

The information we are given with is AB is a line segment with length 3.9 cm.

∠CAB = 50°.

∠ABC = 63°.

With the given details we need to draw triangle using given angles. We need protractor and ruler to draw the triangle.

Step 1: Draw the line segment of length 3.9 cm using ruler and mark as AB.

Step 2: Using protractor, we need to mark the angle. Keep the center of the protractor at the A and mark with a point at 50°.

Step 3: Draw a line from a passing through the marked point.

Step 4: Repeat step 2 with marking at 63° and step 3 on the other side.

Step 5: Mark the intersection point as C.

Answer: the formula is

(-4) + (-5) = -9

(-9) + (-5) = -14

Step-by-step explanation:

Answer:

an  = 1 − 5n

Explanation:

a1  = 1 − 5 (1) = −4

a2  = 1 − 5 (2) = −9  

a3  = 1 − 5 (3) = −14

Answer:

[tex]a=\dfrac{1}{2}\\ \\b=-3\\ \\c=0[/tex]

Step-by-step explanation:

The general form of the quadratic equation is

[tex]ax^2+bx+c=0[/tex]

You are given the quadratic equation

[tex]0=\dfrac{1}{2}x^2-3x[/tex]

It can be rewritten in standard form as

[tex]\dfrac{1}{2}x^2-3x=0[/tex]

Hence,

[tex]a=\dfrac{1}{2}\\ \\b=-3\\ \\c=0[/tex]

Answer:

58,608

Step-by-step explanation:

Answer:

58,608

Step-by-step explanation:

Answer:

The answer is given in the graph attached.

Step-by-step explanation:

i) The answer is given in the graph attached.

Answer:

Answer: The perimeter of the red polygon is 26 cm.

Step-by-step explanation:

Answer:

Tangents from an external point are equal. This can be used to find the perimeter

Perimeter = 22+22+22+22+27+27+98+98

= 338 in.

Hope this helps!