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3 years ago

Find the value of x.

Mathematics

2 answers:

SVETLANKA909090 [29]3 years ago

8 0

Step-by-step explanation:

58° + 42° + x = 180° -- (Δ sum property)

100° + x = 180°

x = 180° - 100°

x = 80°

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RUDIKE [14]3 years ago

3 0

Answer:

80°

Step-by-step explanation:

42° + 58° + x = 180° [Angle sum property of triangle]

=> 100 + x = 180

=> x = 180 - 100

=> x = 80 (Ans)

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What’s the answer to this?

babymother [125]

Answer:

○ $\displaystyle x > -3 \\ 5y ≥ -4x - 10$

Step-by-step explanation:

This system of inequalities has a shared portion at the origin, so we can easily jump to using the zero-interval test [test point (0, 0)] to verify the inequalities as false or true:

$\displaystyle 5[0] ≥ -4[0] - 10 → 0 ≥ -10$ ☑

$\displaystyle 0 > -3$ ☑

Plus, the top inequality has a dashed line ["<" or ">"], and the bottom inequality has a solid line, so this must have an equivalence line underneath each inequality symbol ["≤" or "≥"].

** Hold on though! Although it looks obvious about what the second inequality is, we need to double-check and make sure anyway, just to be on the safe side ☺:

$\displaystyle \frac{5y}{5} ≥ \frac{-4x - 10}{5} → y ≥ -\frac{4}{5}x - 2$

From the y-intercept of $\displaystyle [0, -2],$ we do $\displaystyle \frac{rise}{run}$ by either moving four blocks north over five blocks west or four blocks south over five blocks east [west and south are negatives]. This IS what our solid graph looks like, so we are correct!

So, from all what was explained, you have your answer.

I am joyous to assist you anytime.

8 0

2 years ago

Sales An apparel shop sells skirts for $45 and blouses for $35. Its entire stock is worth $51,750. But sales are slow and only h

inysia [295]

Answer:

260 skirts and 270 blouses are left in the store after the sale.

Step-by-step explanation:

Let x be the number of skirts and y be the number of blouses.

An apparel shop sells skirts for $45 and blouses for $35

Cost of entire stock = $51,750

Thus, we can write the equation,

$45x + 35y = 51750$

Half the skirts and two-thirds of the blouses are sold for a total of $30,600.

Thus, we can write the equation,

$45(\dfrac{x}{2}) + 35(\dfrac{2y}{3}) = 30600\\\\135x + 140y = 183600$

Solving the two equations by elimination method, we have,

$135x + 140y-(135x + 105y) = 183600 - 155250\\35y = 28350\\\\y = \dfrac{28350}{35} =810\\\\x = \dfrac{51750-35(810)}{45} = 520$

Thus, there were 520 skirts and 810 blouses in the store.

Skirt left =

$520-\dfrac{520}{2} = 260$

Blouses left =

$810 - \dfrac{2}{3}\times 810 = 270$

Thus, 260 skirts and 270 blouses are left in the store after the sale.

5 0

2 years ago

Write 1/10^2 using exponents

Viefleur [7K]

Answer:

I think it would be 100

Step-by-step explanation:

because 10^2 is 10 x 10 which equals 100 and so if you have 1/10^2 it's basically saying 1 divided by 10^2 and 10^2 is 100 so it would be 1 divided by 100 which equals 100.

I hope this helped any.

4 0

3 years ago

Which function has a vertex on the y-axis? f(x) = (x – 2)2 f(x) = x(x + 2) f(x) = (x – 2)(x + 2) f(x) = (x + 1)(x – 2)

strojnjashka [21]

we know that

If the vertex is on the y-axis, then the x-coordinate of the vertex is equal to zero

we are going to verify the vertex of each one of the functions to determine the solution

Remember that

The equation in vertex form of a vertical parabola is equal to

$y=a(x-h)^{2} +k$

where

(h,k) is the vertex

if $a>0$ -------> the parabola open upward (vertex is a minimum)

if $a$ -------> the parabola open downward (vertex is a maximun)

case A) $f(x)=(x-2)^{2}$

This is a vertical parabola open upward

the vertex is the point $(2,0)$

therefore

The function $f(x)=(x-2)^{2}$ does not have a vertex on the y-axis

case B) $f(x)=x(x+2)$

$f(x)=x(x+2)=x^{2}+2x$

convert to vertex form

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)+1=x^{2}+2x+1$

Rewrite as perfect squares

$f(x)+1=(x+1)^{2}$

$f(x)=(x+1)^{2}-1$

the vertex is the point $(-1,-1)$

therefore

The function $f(x)=x(x+2)$ does not have a vertex on the y-axis

case C) $f(x)=(x-2)(x+2)$

$f(x)=(x-2)(x+2)=x^{2}-2^{2}$

$f(x)=x^{2}-4$

the vertex is the point $(0,-4)$

The x-coordinate of the vertex is equal to zero

therefore

The function $f(x)=(x-2)(x+2)$ has a vertex on the y-axis

case D) $f(x)=(x+1)(x-2)$

$f(x)=(x+1)(x-2)\\ \\f(x)= x^{2}-2x+x-2 \\ \\f(x)= x^{2} -x-2$

convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+2= x^{2} -x$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)+2+0.25= x^{2} -x+0.25$

$f(x)+2.25= x^{2} -x+0.25$

Rewrite as perfect squares

$f(x)+2.25= (x-0.50)^{2}$

$f(x)=(x-0.50)^{2}-2.25$

the vertex is the point $(0.5,-2.25)$

therefore

The function $f(x)=(x+1)(x-2)$ does not have a vertex on the y-axis

the answer is

$f(x)=(x-2)(x+2)$

6 0

3 years ago

Read 2 more answers

A bicycle tire has a diameter of 3 feet. How many turns of the wheel could it take for the bicycle to go 792 feet?

Andrew [12]

Answer:

84 complete turns

Step-by-step explanation:

In order to find the number of turns that the bicycle wheel is going to take while going 792 feet, we need to find the circumference of the wheel.

$C = \pi \: d = 3.14 \times 3 = 9.42 \: ft \\ no \: of \: turns = \frac{792}{9.42} \\ = 84.0764331 \\ = 84 \: turns$

7 0

3 years ago