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1 year ago

What is the value of x + y? How do you know? Show or explain work

Mathematics

1 answer:

enot [183]1 year ago

6 0

The angle (2y - 5)° and 95° are vertical angles, then they are congruent, that is,

$2y-5=95$

Solving for y:

$\begin{gathered} 2y-5+5=95+5 \\ 2y=100 \\ \frac{2y}{2}=\frac{100}{2} \\ y=50 \end{gathered}$

The angle (3x + 55)° and 85° are vertical angles, then they are congruent, that is,

$3x+55=85$

Solving for x:

$\begin{gathered} 3x+55-55=85-55 \\ 3x=30 \\ \frac{3x}{3}=\frac{30}{3} \\ x=10 \end{gathered}$

Finally, the value of x + y is:

$x+y=10+50=60$

You might be interested in

The city is planning to add a fish pond to a neighborhood park. The figure below is a drawing of the fish pond. Its scale is 1/2

faust18 [17]

Answer:

Part a) The area of the actual fish pond is $2,956.50\ ft^{2}$

Part b) The length of the fence will be $244.20\ ft$

Step-by-step explanation:

we know that

The scale drawing is

$\frac{(1/2)}{15}\frac{in}{ft}=\frac{1}{30}\frac{in}{ft}$

step 1

Find the actual dimensions of the fish pond

To find the actual dimensions divide the measure of the drawing by the scale drawing

$0.5\ in=0.5/(1/30)=15\ ft$

$1\ in=1/(1/30)=30\ ft$

$2.5\ in=2.5/(1/30)=75\ ft$

step 2

Find the area of the actual fish pond

The area of the fish pond is equal to the area of a circle p[lus the area of rectangle

$A=\pi r^{2} +bh$

we have

$r=15\ ft$

$b=75\ ft$

$h=30\ ft$

substitute

$A=(3.14)(15)^{2} +(75)(30)=2,956.50\ ft^{2}$

step 3

Find the length of the fence around the entire fish pond

The perimeter of the fish pond is equal to the circumference of a complete circle plus the length of 75 ft two times

$P=2\pir+2(75)$

we have

$r=15\ ft$

substitute

$P=2(3.14)(15)+2(75)=244.20\ ft$

3 0

3 years ago

Solve step by step! Please answer correctly !!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!

Aliun [14]

For the 60°'s topmost line, you can find the angle next to it is 120° because it's a straight line. You can do the same for 95° if you put that the angle opposite it is equal already because it's the opposite angle, so you subtract from 180° again to get 85°. When you extend the lines, you can find the alternate interior angles to the 60° and 85°, which are congruent to them. You then get that for both the formed triangles there is one 85° and one 60°, which together with one more angle should equal 180°. Through knowing that the sun of the triangles angles should be 180°, if you subtract the sum of 60° and 85° from 180°, you get the angle of the 3rd angle in the triangles (35°). This angle also forms 180° with x on a line, so 180°-35°=x, which is 145° seemingly.

4 0

3 years ago

Situation:

Nat2105 [25]

Answer:

${ \bf{A=(P + \frac{r}{100} ) {}^{n} }} \\ { \tt{ = (4000 + \frac{5.5}{100} ) {}^{15} }} \\ \\ { \tt{ = \: 1.074 \times {10}^{54} \: dollars}}$

3 0

3 years ago

11. Isaac wrote two simplified expressions that were not equal to each other. Each equation also had

Elodia [21]

Answer:

The equation has only one solution

Step-by-step explanation:

* Lets explain how to solve the problem

- There are three types of solutions for the equations

Case (1)

# Two sides of the equation have different coefficient of the variable

and same or different numerical terms, then the equation has only

one solution

- Ex: 2x + 5 = x + 5, lets solve it

∵ 2x + 5 = x + 5

- subtract x from both sides

∴ x + 5 = 5

- Subtract 5 from both sides

∴ x = 0

- Zero is a solution

∴ The solution of the equation is x = 0

- If the numerical terms are different x will be any other value, so the

equation has only one solution

∴ The equation has one solution

Case (2)

# Two sides of the equation have same coefficient of the variable,

and different numerical terms, then the equation has no solution

- Ex: 14x - 20 = 14x + 10, lets solve it

∵ 14x - 20 = 14x + 10

- Subtract 14x from both sides

∴ - 20 = 10

- The left hand side not equal the right hand side , then there is

no value of x can make the two sides equal

∴ The equation has no solution

Case (3)

# Two sides of the equation have same coefficient of the variable,

and same numerical terms, then the equation has infinitely

many solutions

- Ex: 3x + 5 = 3x + 5, lets solve it

∵ 3x + 5 = 3x + 5

- Subtract 3x from both sides

∴ 5 = 5

- The left hand side is equal to the right hand side , then x can be

any value because the two sides is already equal without x

∴ The equation has infinitely many solutions

∵ He will write two expressions simplified , not equal , have different

coefficients on the variables and equate them, then it is like

the first case

- That means not same coefficient of the variable, and may be not

same numerical term

∴ The equation has only one solution

5 0

4 years ago

In the number 5.3779, how does the value of the 7 in the hundredths place compare to the value of the 7 in the thousandths place

Sav [38]

C. The value of the 7 in the hundredths place is 10 times the value of the 7 in the thousandths place.

7 0

3 years ago

Read 2 more answers