Please help me find the midpoint

Answer:

t = 7/-4 OR -1 3/4

Step-by-step explanation:

3(t - 3) = 5(2t - 1)​

3t - 9 = 10t - 5

(3t - 3t) - 9 = (10t - 3t) - 5

-9 = 7t - 5

-9 + 5 = 7t (- 5 + 5)

-4 = 7t

-4/-4 = 7t/-4

t = 7/-4 OR -1 3/4

Answer: x = 30°

Concept:

Here, we need to know the idea of an isosceles triangle and the vertical angle theorem.

An isosceles triangle is a triangle that has any two of its sides equal to each other. Also, the angles opposite these equal sides are equal, which is basically the base angles.

The vertical angle theorem states that two vertical angles formed when two lines intersect each other are always equal to each other.

Solve:

Find the other base angle of the isosceles triangle.

Since there are two equal sides, we know that this is an isosceles triangle.

Since the definition said that the base angles are equal, the other base angle would also be x.

Find the value of x

According to the vertical angle theorem, two vertical angles formed by intersection are equal.

Just as angle x and 30°, are vertical angles formed by intersection, therefore, [tex]\boxed{x=30}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

y = 14/3 and 2

x = -13/3 and 1

(-13/3, 14/3) and (1, 2)

Step-by-step explanation:

[tex]x + 2y = 5 - - - (a) \\ {x}^{2} - {y}^{2} = - 3 - - - (b)[/tex]

for equation (a)

make x the subject of the formular:

[tex]x = 5 - 2y - - - (c)[/tex]

for equation (b)

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

substitute for x as 5 - 2y in equation (b):

[tex] {(5 - 2y)}^{2} - {y}^{2} = - 3 \\ (25 - 20y + 4 {y}^{2} ) - {y}^{2} = - 3 \\ 25 - 20y + 3 {y}^{2} = - 3 \\ {3y}^{2} - 20y + 28 = 0 \\ (3y - 14)(y - 2) = 0[/tex]

therefore,

[tex]y = \frac{14}{3} \: \: and \: \: 2[/tex]

substitute for all values of y in equation (c):

for y = 14/3:

[tex]x = 5 - 2( \frac{14}{3} ) \\ \\ x = 5 - \frac{28}{3} \\ \\ x = - \frac{13}{3} [/tex]

for y = 2:

[tex]x = 5 - 2(2) \\ x = 5 - 4 \\ x = 1[/tex]

Answer:

(1, 2)

(-13/3, 14/3).

Step-by-step explanation:

x + 2y = 5

x² - y² = -3​

From the first equation x = 5 - 2y

Substitute for y in the second equation:

(5 - 2y)^2 - y^2 = -3

25 + 4y^2 - 20y - y^2 = -3

3y^2 - 20y + 28 = 0

Factoring:-

(3y - 14(y  -  2)   = 0

y = 2, 14/3.

So when y = 2, x = 5 - 2(2) = 1.

When y = 14/3, x = 5 - 2(14/3) = -13/3.

Checking the results in the second equation:

(1, 2):-

1^2 - 2^2 = -3    Correct.

(-13/3, 14/3):-

(-13/3)^2 - (14/3)^2 = -3   Correct.

Answer:8/25

Step-by-step explanation:

Answer:

Step-by-step explanation:

32/100 = 16/50 = 8/25

Answer:

first part is 32 inches, second part is 16 inches, third part is 11 inches.

Step-by-step explanation:

2x + x + x - 5 =  59

4x + 64

x = 16.

we can then plug 16 in first parts expression, 2x, for 32. second part is just x so 16. 3rd part is 5 less, x-5, so 11.

Answer:

6.5

Step-by-step explanation:

Im not 100% sure because I may have overcomplicated this but im going to submit this anyway.

Answer:

x = 5

Step-by-step explanation:

The opposite sides of a rectangle are equal , then perimeter

2(- 2x - 6) + 2(4x + 4) = 16 ← distribute parenthesis and simplify left side

- 4x - 12 + 8x + 8 = 16

4x - 4 = 16 ( add 4 to both sides )

4x = 20 ( divide both sides by 4 )

x = 5

x=1/4

Step-by-step explanation:

perimeter of a rectangle

2(L+w)

-2x-6(4x+4)

open the bracket

-2x(4x+4)-6(4x+4)

-8x^2-8x-24x-24

-8x^2-32x-24

2(-8x^2-32x-24)

-16x^2-64x-48

coefficient of x is 64

16=64x

x=1/4

Step-by-step explanation:

breadth=x

length is 5m long then breadth

length=x+5

Perimeter=2(length+breadth)

subtitute values in formula:

150=2(x+5+x)

2x+5=150/2

2x+5=75

2x=75-5

2x=70

x=70/2

x=35

breadth=35m

length= x+5

length=35+5

length=40m

[tex] \text{Let us assume the breadth be } \purple{\frak{a}}[/tex]

The length is 5m more than its breadth

[tex] \text{The length be} \: \green{\frak{a + 5}}[/tex]

Here we need to get both breadth and length by finding out a

[tex] \hookrightarrow \frak{{ \sf P}erimeter_{(Rectangle)} =2 (Length + Breadth)} \\ \\ \hookrightarrow \frak{150 =2 (a + 5 + a)} \\ \\ \hookrightarrow \frak{150=2 (2a + 5)} \\ \\ \hookrightarrow \frak{150=4a + 10} \\ \\ \hookrightarrow \frak{4a = 150 - 10} \\ \\ \hookrightarrow \frak{4a = 140} \\ \\ \hookrightarrow \frak{a = \cancel \frac{140}{4} } \\ \\ \star \quad \underline{\boxed{\frak{ \blue{a = 35}}}}[/tex]

[tex] \bigstar \underline{ \frak{Finding \: them}} : [/tex]

[tex] \qquad\odot \: \: \frak{Length = a + 5 = 35 + 5 = \pink{40m}} \\ \\

\qquad\odot \: \: \frak{Breadth = a= \pink{35m}}[/tex]

Answer:

Step-by-step explanation:

If Anna's dad is 36 and is 9 times her age, then Anna's age is 36/9 which is 4.

Check yourself: Anna is 4. Her dad is 9 times her age and 4(9) = 36.

Answer:

Step-by-step explanation:

Given:

Rewrite it as:

Since all A, B, C are integers from 0 to 9, A can be 1 only, then we have:

or

It gives us:

The equation is:

Answer:

ABC=198

Step-by-step explanation:

If you do 11+99+88 then you get 198 which is true to the problem that you have.

Answer:

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

Answer:

8 and 32

Step-by-step explanation:

(19)

x³ ÷ 3 - y ( substitute x = 3, y = 1 into the expression )

= 3³ ÷ 3 - 1

= 27 ÷ 3 - 1

= 9 - 1

= 8

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

(21)

12k - h² ( substitute h = 2, k = 3 into the expression )

= 12(3) - 2²

= 36 - 4

= 32

Answer:

120

Step-by-step explanation:

6!=1x2x3x4x5x6

3!=1.2.3

Answer:

You are correct! But note the syntax:

the computer wants you to type in the box

2/3 x - 2

because "y =" is already written!

Step-by-step explanation:

Answer:

C. 164

Step-by-step explanation:

its self explanitory

Answer:

The measure of angle C is 92°

Step-by-step explanation:

In a quadrilateral opposite angles are supplementary (Angles add up to 180°)

So since we have two opposite angles already set up the equation:

(x+24)+(x+10) = 180

Combine like terms - x+x+24+10 = 180 → 2x+34 = 180

Cancel out the constant to solve for x: 2x+34-34 = 180-34

Divide both sides by 2 so x is isolated: 2x/2=146/2

Solve: x=73

Now that we know x = 73 we can find angle C by setting up the equation:

Let C represent the unknown angle of ∠C

73+15+C=180

Combine like terms: 88+C=180

Isolate C: 88-88+y=180-88

Solve for C: C=92

Answer:

|x| + 1

Adding/subtracting on the outside moves it up/down.

Adding/subtracting on the inside (such as (x - 2) moves it right 2) moves it left/right.

Answer:

the all adult tickets made out 2440$

the all children tickets made out 1548

Answer:

John: 8 Hong: 5 Keith: 7

Step-by-step explanation:

Divided each larger number by three smaller one, and that is how much time each flyer spent.

Answer:

A.) w² + 3w in²

B.) 28 in²

Step-by-step explanation:

A.)

Let w = width and l = length.

    The area of a rectangle can be written as length · width (base · height). The problem informs us that the length of the rectangle is 3 inches greater than the width. Therefore, l can also be written as w + 3. We can use this to form a polynomial that represents the area of the rectangle.

A(rectangle) = lw = (w + 3) · w = w² + 3w

B.)

Use the polynomial we previously found to find the area.

A(rectangle) = (4)² + 3(4) = 16 + 12 = 28 in²

Model:

Answer:

D. 53,650

50,150+3,500=53,650

Answer:

M.  2.5n - (-8.2) = 26. 7

to find n transpose

2.5n + 8.2 = 26. 7

2.5n = 26. 7 - 8.2

2.5n = 18.5

n = 18.5 ÷ 2.5

n = 7.4

L.  [tex]\frac{7a + 1}{2}[/tex] = 18

7a + 1 = 18 ×2

7a + 1 = 36

7a = 36 - 1

7a = 35

a = 35 ÷ 7

a = 5

N.     [tex]\frac{2}{5}[/tex] b + 1 = -11

[tex]\frac{2}{5}[/tex] b   = -11 -1

[tex]\frac{2}{5}[/tex] b   = -12

b = -12 - [tex]\frac{5}{2}[/tex]

b = 20

H.   5 - [tex]\frac{9}{2}[/tex] d = 32

- [tex]\frac{9}{2}[/tex] d = 32 - 5

- [tex]\frac{9}{2}[/tex] d = 27

d =  27 + [tex]\frac{2}{9}[/tex]

d = 6