Are the equations -2x = 10 and -5x = 25 equivalent? Explain.

Step-by-step explanation:

To give you a hand for this question, I will show you how to work out one of the equations

One equation is [tex]y - 1 = \frac{-5}{4} (x-2)[/tex]

We know that when x = -2, y = 6

So we can substitute in -2 and see if we get 6

[tex]y - 1 = \frac{-5}{4} (-2-2)[/tex]

[tex]y - 1 = \frac{-5}{4} * (-4)[/tex]

[tex]y - 1 = 5[/tex]

[tex]y = 5 + 1[/tex]

[tex]y=6[/tex]

So this equation is true! Now try the same for the other equations :)

Answer:

Step-by-step explanation:

Answer:

1 ) - 0.04

2 ) 1

3 ) - 0.04

4 ) Less of 0.04 gallons of fuel for every 1 mile.

Answer: B and C

Step-by-step explanation:

the triangle inequality theorem states that any 2 sides of a triangle must be greater than the measure of the third side. now with this rule, let's apply it to all options!

option a:

7 + 5 > 6 .. yes!

6+ 7 > 5 .. yes!

5 + 6 > 7 .. yes!

option b:

9 + 12 > 19 .. yes!

12 + 19 > 9 .. no!

19 + 9 > 12 .. no!

option c:

7 + 11 > 18 .. no!

11 + 18 > 7 .. no!

18 + 7 > 11 .. yes!

option d:

6 + 8 > 11 .. yes!

8 + 11 > 6 .. yes!

11 + 6 > 8 .. yes!

i did this topic years ago so please let me know if there are any mistakes! hope this helped, and good luck! ◝(ᵔᵕᵔ)◜

Answer:

4

Step-by-step explanation:

-3/4m - 1/2 = 2 + 1/4m

The denominators are 4 and 2

If we multiply by the least common multiply we can get rid of the fractions

2 and 4 have a least common multiple of 4

Given:

The inequality is:

[tex]y<\sqrt{x+3}+1[/tex]

To find:

The domain and range of the given inequality.

Solution:

We have,

[tex]y<\sqrt{x+3}+1[/tex]

The related equation is:

[tex]y=\sqrt{x+3}+1[/tex]

This equation is defined if:

[tex]x+3\geq 0[/tex]

[tex]x\geq -3[/tex]

In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set. Thus, -3 is not included in the domain.

So, the domain of the given inequality is x>-3.

We know that,

[tex]\sqrt{x+3}\geq 0[/tex]

[tex]\sqrt{x+3}+1\geq 0+1[/tex]

[tex]y\geq 1[/tex]

The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.

So, the domain of the given inequality is y>1.

Therefore, the correct option is A.

Answer: it’s 111

Step-by-step explanation:

Answer:

11.925

Step-by-step explanation:

9514 1404 393

Answer:

  √20 is not the root of a perfect square

Step-by-step explanation:

4.2^2 = 17.64

4.5^2 = 20.25

The square root of any number between these values that is not a perfect square will be irrational. This includes the roots of the integers 18, 19, or 20.

  4.2 < √20 < 4.5

  √20 ≈ 4.472135954999579...

_____

Of course, there are an infinite number of possibilities. It is easy enough to check to see if a rational number is a perfect square. (Its square root will have half as many decimal digits.) For example, √18.9225 is 4.35 (rational), but √18.9226 ≈ 4.350011494... is irrational.

Square roots are not the only irrational numbers. Polynomial roots, trig function values, logarithms, exponential functions are only some of the ways that irrational numbers can be specified, along with multiples or other combinations of irrational numbers such as π or e. These will be irrational simply because they cannot be expressed exactly as the ratio of two integers.

Answer:

C

Maybe it is B or A as the answer.

Answer:

B.

A'(1,-3), B'(1,-7), C'(-3,-7), D'(-3,-3)

Step-by-step explanation:

study island

Answer:

x = 52

y = 19

Step-by-step explanation:

The degree measure of a straight line is (180) degrees. One can use this to find the measure of the angle that is adjacent to the angle with a measure of (142) degrees. Form an equation and solve for the unknown,

142 + (unknown angle) = 180

unknown angle = 38

The inscribed angle theorem states that twice the measure of an angle with its vertex of the circumference (outer edge) of a circle is equal to the measure of the surrounding arc. Therefore, one can state the following:

(2)(unknown angle) = (surrounding arc)

(2)(38) = (surrounding arc)

76 = surrounding arc

The central angles theorem states that the measure of an angle whose vertex is the center of the circle is equal to the measure of the surrounding arc. Therefore, one can state the following:

m<O = (surrounding arc)

m<O = 76

The radius is the distance from the center of the circle to the circumference of the circle. All radii in a circle are congrunet. Therefore the triangle with angle (x) and vertex (O) is an isosceles triangle, as two of its sides are radii, and are thus congruent. One property of an isosceles triangle is the base angles theorem. This theorem states that the angles opposite the congruent sides in an isosceles triangle are congruent. Moreover, the sum of angles in any triangle is (180) degrees. Therefore, one can make the following statement:

m<O + x + x = 180

76 + 2x = 180

x = 52

Finally, one can use the property that the sum of angles in any triangle is (180) degrees to make the following statement:

(x + 19) + (x + y) + (38) = 180

52 + 19 + 52 + y + 38 = 180

161 + y = 180

y = 19

x=52°

y=19°

Answer:

Solution given:

<OCA=19°[base angle of isosceles triangle]

Since ∆AOC is similar to ∆ BOC

y=19°[corresponding angle of a similar triangle are equal]

<OAB=<OBA=x[base angle of isosceles triangle]

again

<A+<B=180°[exterior angle of a triangle is equal to the sum of two opposite interior angle]

x+19+x+19=142°

2x=142°-38°

x=104/2

x=52°

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the angle, we know the opposite side and the adjacent side. Therefore, we should use the tangent function.

tan(x) = 19 / 35

x = tan^-1(19/35)

x = 28 degrees

Hope this helps!

Answer:

y= 3x -6

Step-by-step explanation:

The equation if a line can be written in the form of y= mx +c, where m is the slope and c is the y- intercept.

Given that the slope is 3, m= 3.

Substitute m= 3 into the equation:

y= 3x +c

To find the value of c, substitute a pair of coordinates into the equation.

Given that it has an x- intercept of -2, the line passes through the point (-2, 0). This is because x- intercept is the point at which the line passes through the x- axis, and this occurs at y= 0.

When x= -2, y= 0,

0= 3(-2) -c

0= -6 -c (expand)

c= -6 (+c on both sides)

Thus, the equation of the line is y= 3x -6.

Let the numbers be 2x and 3x.

According to the Question,

⇒ 2x + 3x = 45

⇒ 5x = 45

⇒ x = 45/5

⇒ x = 9

Now finding the values of both the number,

⇒ 2x = 2 × 9

= 18

⇒ 3x = 3 × 9

= 27

Hence, the value of both the number is 18 and 27 respectively.

Now we have to,

find the both required numbers.

It is given that,

→ Two numbers are in the ratio 2:3.

→ Their sum is 45.

Now assume numbers as,

→ 2y and 3y

As per the given information,

→ 2y + 3y = 45

First we can find the value of y,

→ 2y + 3y = 45

→ 5y = 45

→ y = 45/5

→ [y = 9]

The given ratio is,

→ 2 : 3

Let's find the value of 2y,

→ 2y --- {y = 9}

→ 2 × (9)

→ 18

Let's find the value of 3y,

→ 3y --- {y = 9}

→ 3 × (9)

→ 27

Hence, the number is 18 and 27.

Answer:

Elisa return in time. :)

Step-by-step explanation:

It is given that the bathtub is 17 inches deep.

The water fills the tub at a rate of 3 inches of water for every 5 minutes.

Elisa spent 26 minutes with neighbor.

Let's find whether the tub overflow or did she return in time.

In 5 minutes  water filled is 3 inches

In 10 minutes water filled is 6 inches

In 15 minutes water filled is 9 inches

In 20 minutes water filled is 12 inches

In 25 minutes water filled is 15 inches

In 26 minutes water filled in is 15+1/3 inches , which is same as 15.33 inches.

But the deep of tub is 17 inches.

We could say, she return in time.

Answer:

i think its 24

Step-by-step explanation:

2=2

Answer:

90%

Step-by-step explanation:

63/70 = 0.9 = 90%

Answer:

63 out of 70

63×10÷70=9

9%

Answer:

50

Step-by-step explanation:

Answer:

-4.1

Step-by-step explanation:

Answer:

how do I get started here

Step-by-step explanation:

[tex] {x}^{2} + x = 0 \\ x(x + 1) = 0\\ x = 0 \\ x = - 1[/tex]

is it what ur looking for?

Answer:

Horizontal line

Step-by-step explanation:

uehdjd

Answer:

12

Step-by-step explanation:

24/x = x/6

x^2 =24*6 = 144

x=12

Answer:

y = -x/2 - 14

Step-by-step explanation:

Hint: The slope shows the rise over run, in this case, the slope is going 1 unit to the right and two units down.

Answer:

Step-by-step explanation:

The standard deviation is the square root of the variance, and the variance is found by using the mean. So we will do that first. I will use the population variance as opposed to the sample variance since our set of numbers is small.

The mean: 8 + 12 + 15 + 17 + 18 = 70 and divide that by 5 to get

[tex]\bar{x}=14[/tex] and use this to find the variance in the formula:

[tex]s^2=\frac{\sum(x_i-\bar{x})^2}{n}[/tex] it is a bit difficult to enter that formula in correctly, but here's how it works mathematically:

[tex]s^2=\frac{(8-14)^2+(12-14)^2+(15-14)^2+(17-14)^2+(18-14)^2}{5}[/tex]

Squaring this ensures us that we don't end up with zero, which would be useless.

[tex]s^2=\frac{36+4+1+9+16}{5}[/tex] so

[tex]s^2=13.2[/tex] which means that the standard deviation is

s = 3.633

(If you do it with n-1 = 4 in the denominator of the variance, you get a standard deviation of 4.062)

Answer:

Its your answer ......

hope it will help u

Answer:

I believe its (-3,-2)...........

There are an infinite number of them.

The ten greatest ones are -5, -6, -7, -8, -9, -10, -11, -12, -13, and -14 .

Now that I've given you ten of them, there are only an infinite number more. I'm too busy right now to list them all.

Answer:

p and q are two numbers.whrite down an expression of.

Answer: No solution

Step-by-step explanation:

Given

Pair of lines are

[tex]\Rightarrow y=-2x-6\ \text{and}\ y=-2x+35[/tex]

For lines [tex]a_1x+b_1y+c_1=0\ \text{and}\ a_2x+b_2y+c_2=0[/tex]  will be parallel when

[tex]\Rightarrow \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]

Rewrite the given lines

[tex]y+2x+6=0\ \text{and}\ y+2x-35=0[/tex]

[tex]\Rightarrow \dfrac{2}{2}=\dfrac{1}{1}\neq\dfrac{6}{-35}\\\\\Rightarrow \dfrac{1}{1}=\dfrac{1}{1}\neq\dfrac{6}{-35}[/tex]

Thus, the given lines are parallel. Therefore, there is no solution for the givebn pair of lines.

Answer:

The answer is 2736 cm³

Answer:

What is the volume of this right triangular pyramid?

 2736 cm³

5472 cm³

8208 cm³

16,416 cm³