A water tank fills as shown in the graph below. What is the slope of the line?

Answer:

The x-coordinate of the intersection point (x, y) = (-0.5, -1) of the system is: -0.5

Hence, option A) i.e. -0.5 is correct.

Step-by-step explanation:

Given the system of equations

2.4x - 1.5y = 0.3

1.6x + 0.5y = -1.3

solving the system of equations

[tex]\begin{bmatrix}2.4x-1.5y=0.3\\ 1.6x+0.5y=-1.3\end{bmatrix}[/tex]

Multiply 2.4x - 1.5y = 0.3 by 2

Multiply 1.6x + 0.5y = -1.3 by 3

so the system of equations becomes

[tex]\begin{bmatrix}4.8x-3y=0.6\\ 4.8x+1.5y=-3.9\end{bmatrix}[/tex]

so

[tex]4.8x+1.5y=-3.9[/tex]

[tex]-[/tex]

[tex]\underline{4.8x-3y=0.6}[/tex]

[tex]4.5y=-4.5[/tex]

so the system of equations becomes

[tex]\begin{bmatrix}4.8x-3y=0.6\\ 4.5y=-4.5\end{bmatrix}[/tex]

solve 4.5y = -4.5 for y

[tex]4.5y=-4.5[/tex]

Multiply both sides by 10

[tex]4.5y\cdot \:10=-4.5\cdot \:10[/tex]

Refine

[tex]45y=-45[/tex]

Divide both sides by 45

[tex]\frac{45y}{45}=\frac{-45}{45}[/tex]

Simplify

[tex]y=-1[/tex]

For 4.8x - 3y = 0.6, plug in y = -1

[tex]4.8x-3\left(-1\right)=0.6[/tex]

[tex]4.8x+3\cdot \:1=0.6[/tex]

[tex]4.8x+3=0.6[/tex]

Multiply both sides by 10

[tex]4.8x\cdot \:10+3\cdot \:10=0.6\cdot \:10[/tex]

Refine

[tex]48x+30=6[/tex]

Subtract 30 from both sides

[tex]48x+30-30=6-30[/tex]

Simplify

[tex]48x=-24[/tex]

Divide both sides by 48

[tex]\frac{48x}{48}=\frac{-24}{48}[/tex]

simplify

[tex]x=-\frac{1}{2}[/tex]

or

[tex]x = -0.5[/tex]

Thus,

(x, y) = (-0.5, -1)

Therefore, the x-coordinate of the intersection point (x, y) = (-0.5, -1) of the system is: -0.5

Hence, option A) i.e. -0.5 is correct.

Answer:

3:4:7

Step-by-step explanation:

14-(3+4)

=14-7

=7

red:white:blue

3:4:7

Answer:

Step-by-step explanation:

3 + 4 + 7 = 14 which is the total

The blue balloons number 7 because 14 - (3 + 4) = 14 - 7 = 7

So the ratio is 7 blue / 14 (which is the total)

7/14 = 1/2 or 1 to 2

Answer:

[tex]x =24[/tex]

Step-by-step explanation:

From the question we are told that

Amount of water 1/4x

Gallons added 10

Amount of water after addition 2/3x

Where x is a full container

Generally the parameters above gives the equation

  [tex]\frac{1}{4}x +10=\frac{2}{3}x[/tex]

Therefore

  [tex]\frac{1}{4}x -\frac{2}{3}x =-10[/tex]

[tex]-\frac{5}{12}x =-10[/tex]

[tex]x =\frac{-10}{-\frac{5}{12}}[/tex]

[tex]x =24[/tex]

Therefore the container can hold 24 gallons of water

Answer:

2.)  "My parents will be very disappointed in me."

Step-by-step explanation:

This is the only explanation that will get you out of any bad situations.

1.) I'll try it once: if you try it once, you'll be hooked on it forever.

2.) Correct answer: Only way to get out of a situation like this affectively.

3.) My friends and I prefer weed: This would still suggest you still use drugs.

(I think it's smart to post it in math! :)

Answer:

[tex] \frac{30}{100} = \frac{33}{x} \\ 30x = 3300 \\ x = \frac{3300}{30} = 110[/tex]

Answer:

y = 7/4x

Step-by-step explanation:

All you have to do is find the slope by using the formula change in y divided by change in x of the two points. You can see that y goes up by 14 when x goes up by 8. This means that the slope is 14/8, or 7/4.

The equation would then be y = 7/4x

9)

If y varies directly with x and y = -3 when x = 6, find y when x = 14.

We know if y varies directly with x, we get the equation

y ∝ x

y = kx

k = y/x

where k is called the constant of variation.

we are given y = -3 when x = 6

so substitute y = -3 and x = 6 to determine 'k'

k = y/x

k = -3/6 = -1/2

Now we have to find y when x = 14

so substituting x = 14 and k = -1/2 to find y

y = kx

y =  -1/2 × 14 = -7

Therefore, the value of y = -7 when x = 14

10) If y is directly proportional to x and y = 4 when x = 3, find x when y = -12.

we are given y = 4 when x = 3

so substitute y = 4 and x = 3 to determine 'k'

k = y/x

k = 4/3

Now we have to find x when y = -12

so substituting y = -12 and k = 4/3 to find x

y = kx

x = y/k

x = [-12] / [4/3] = [-12×3] / [4]

x = -36/4

x = -9

Therefore, the value of x = -9 when x = 3

11)

If y varies directly with x and y = -6 when x = 2, find the constant of variation.

We are given

y = -6

x = 2

so substitute y = -6 and x = 2 in the equation

k = y/x

k = -6/2

k = -3

Therefore, the value of the constant of variation will be:

Answer: The total cost of their meal with tax= $23.49

Step-by-step explanation:

Given: Cost of the three dinners before tax = $21.65

Tax = 8.5%

Tax amount = 8.5% of ( Cost of the three dinners before tax)

= (0.085) x 21.65        [0.085 = 8.5%]

= $1.84025 ≈ $ 1.84

The total cost of their meal with tax = Cost + Tax amount

= 21.65 + 1.84

= $23.49

Hence, the total cost of their meal with tax= $23.49

Answer:

y  =  − 2 x  +  5

Step-by-step explanation:

Try this

Answer:

y = −2x+5

Step-by-step explanation:

lmk if you need to see the work shown

Answer:

The value of x = 12.

Step-by-step explanation:

We know that two angles are termed as supplementary when the sum of the measure of their angles is 180°.

We also know that a straight line angle measures 180°.

It is clear that the angles 72° and 9x° line on a straight line. Thus, the sum of the measure of their angles is 180°.

Therefore,

9x° + 72° = 180°

9x° = 180° - 72°

9x° = 108

divide both sides by 9

9x/9 = 108/9

x = 12

Therefore, the value of x = 12.

Answer:

The values of a and b are:

Step-by-step explanation:

We know that the slope-intercept form of the line equation

y = ax+b

where

From the diagram of the line graph, we can fetch the two points

Determining the slope between (0, 2) and (-1, 0)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(-1,\:0\right)[/tex]

[tex]a=\frac{0-2}{-1-0}[/tex]

[tex]a=2[/tex]

Thus, the value of a = 2

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 2

Thus, the y-intercept b = 2

now substituting a = 2 and b = 2 in the slope-intercept form of the line equation

y = ax+b

y = 2x + 2         ∵ a = 2 , b = 2

Thus, the line of equation is:

y = 2x+2

now comparing with y = ax+b

Here:

a = 2

b = 2

Therefore, the values of a and b are:

Answer:

y+4+−4=−6x−36+−4

y=−6x−40

y=−6x−40

slope is -6

y intercept is -40

Answer:

y = -6x - 40

in standard form its:

y + 6x = -40

Step-by-step explanation:

Answer:

[tex](4n + 3) - (3 {n}^{2} + 2) \\ = 4n + 3 - 3 {n}^{2} - 2 \\ = - 3 {n }^{2} + 4n + 1 \\ ( - 3 {n}^{2} - 3n) - (1n + 1) \\ - 3n(n + 1) - 1(n + 1) \\ (n + 1)( - 3n - 1) \\ n = - 1 \\ n= \frac{1}{ - 3} [/tex]

Answer:

[tex]f(n) - g(n) = (4n + 3) - (3 {n}^{2} + 2) \\ = 4n + 3 - 3 {n}^{2} - 2 \\ = \boxed{4n - 3 {n}^{2} + 1}[/tex]

Answer:

multiply and see what you get

Answer:

6 miles

Step-by-step explanation:

Li can walk 6 miles if you divide 135 and 45 you'll get 3 finally if you multiply 2 and 3 you'll get 6 So in total Li walks 6 miles

Answer:

F

Step-by-step explanation:

Square root of 10 is 3.16

Answer:

[tex]\frac{7}{24}[/tex]

Step-by-step explanation:

The cotangent of [tex]m\angle B[/tex] can be represented as [tex]\frac{1}{\tan (m\angle B)}[/tex]. Using trig rules for a right triangle, we can write the following equation:

[tex]\tan B=\frac{24}{7}[/tex].

Therefore, the cotangent of [tex]m\angle B[/tex] is:

[tex]\cot B = \frac{1}{\tan B}=\frac{1}{\frac{24}{7}}=\fbox{$\frac{7}{24}$}[/tex].

The ratio of cotangent of angle B is [tex]\frac{7}{24}[/tex]. for understanding check the calcualtiion here ,

From the given information ,

In ΔABC, the measure of ∠C=90°, CB = 7, BA = 25, and AC = 24

Contangent of any angle is equal to adjacent side divide by opposite side

Cotangent of an angle is a relationship found by dividing the length of  the side adjacent to given angle  by the length of side opposite to the given angle.

The side opposite to angle B is CB  and side opposite of angle B is AC

cot (B) = adjacent side / opposite side

[tex]cot(B)=\frac{CB}{AC}[/tex]

CB = 7, BA = 25, and AC = 24

[tex]cot (B)=\frac{7}{24}[/tex]

The ratio of cotangent of angle B is [tex]\frac{7}{24}[/tex]

Learn more information about 'cotangent ' here

brainly.com/question/10430279

Answer:

480 seconds per day

Step-by-step explanation:

There are 24 hours in a day, 24*20=480 seconds per day

The number of seconds the given clock loses in a day is required.

The number of seconds lost by the clock in one day is 240 seconds.

The clock loses 20 seconds every hour.

A day has 24 hours.

If 20 seconds is lost every hour then the 20 seconds has to be added 24 times or the 20 has to be multiplied by 24.

So,

[tex]20\times 24=480\ \text{s}[/tex]

Learn more about algebra:

https://brainly.com/question/6143254

Answer:

See below.

Step-by-step explanation:

a. Geometric

b. Arithmetic

c. Neither

d. +4

e. 5

f. 2, 4, 6, 8

g. 2, 4, 8, 16

Answer:

x+8.95 and x+24.55

Step-by-step explanation:

im not going to do this

Answer:

1240

Step-by-step explanation:

the explanation is very long but I hope this is correct!

Answer: A

Step-by-step explanation:

Answer:

i believe the y intersept is -4

Answer:

Step-by-step explanation:

F(x) is simply another way of saying y. We are given the x value of -10. We can substitute this in for x and find y.

f(-10) = 7(-10) - 5

f(-10) = -70 - 5

f(-10) = -75

Answer:

Rewrite the equation in term of  

x

and  

y

.

f

(

x

)

=

2

x

2

−

7

x

+

5

Rewrite the equation in vertex form.

Tap for fewer steps...

Complete the square for  

2

x

2

−

7

x

+

5

.

Tap for more steps...

2

(

x

−

7

4

)

2

−

9

8

Set  

y

equal to the new right side.

y

=

2

(

x

−

7

4

)

2

−

9

8

Use the vertex form,  

y

=

a

(

x

−

h

)

2

+

k

, to determine the values of  

a

,  

h

, and  

k

.

a

=

2

h

=

7

4

k

=

−

9

8

Find the vertex  

(

h

,

k

)

.

(

7

4

,

−

9

8

)

Step-by-step explanation:

Answer:

2187+4

= 2191

Step-by-step explanation:

plz brainliest :)

Answer:

First Option: y = 1/2x + 8

Step-by-step explanation:

for lines to be parallel they must have the same slopes

Answer:

56 units long

Step-by-step explanation:

the whole line is 73 units long, and CB is 17 units long. You would subtract 17 from 73 and then you have the missing value which is 56. (or in other words 17 plus what equals 73).

Step-by-step explanation:

[tex]y = 2x + 2 \\ y = 4x - 2 \\ 2x = y - 2 \\ x = 0.5y - 1 \\ y = 4(0.5y - 1) - 2 \\ y = 2y - 4 - 2 \\ - y = - 6 \\ y = 6 \\ x = 0.5 \times 6 - 1 \\ x = 2[/tex]