Montell gets $10.50 each week for doing yard work for his neighbors. He has earned $63 so far. Write and solve an equation to find how many weeks it took for him to earn that amounts.

The equation has only one solution that is x = -15

Step-by-step explanation:

We have to convert the given statement in  form of equation to find the number

Let x be the number

then

According to given statement,

[tex]2x-7 = 3x+8\\-7 = 3x-2x+8\\-7 = x+8\\x = -7-8\\x = -15[/tex]

The equation has only one solution that is x = -15

Keywords: Linear equation, variables

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Final answer:

The equation 'twice a number minus seven equals eight greater than three times the number' simplifies to 2x - 7 = 3x + 8, which has one solution: x = -15.

Explanation:

The original question asks us to solve an algebraic equation where twice a number minus seven is equal to eight greater than three times that number.

To translate this into an algebraic expression, let the unknown number be x.

This gives us the equation 2x - 7 = 3x + 8.

To solve this equation, we can subtract 2x from both sides to get -7 = x + 8 and then subtract 8 from both sides to isolate x, resulting in x = -15.

To answer part B, this type of linear equation will only have one solution because it’s a linear equation with a non-zero coefficient in front of the variable x.

Answer:

-28

Step-by-step explanation:

(-22)-14= -36. (-22)+14= -8. -36-(-8)= -28.

The coordinates of a point on the directed segment from (3,-2) to (8,0) that divides it into a ratio of 3:1 is (6.75, -0.5). The correct option is A.

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Let the line be represented as AB, therefore, the coordinates of points A and B are (3,-2) and (8,0), respectively. The coordinate of the point m that divides the line AB in a ratio of 3:1 is,

x = [(x₂×m)+(x₁×n)]/(m+n)

x = [(8×3)+(3×1)]/(3+1)

  = (24+3)/4

  = 6.75

y = [(y₂×m)+(y₁×n)]/(m+n)

y = [(0×3)+(-2×1)]/(3+1)

  = (0-2)/4

  = -0.5

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Final answer:

The coordinates of the point that divides the directed segment from (3,-2) to (8,0) in the ratio of 3:1 are a) (6.75, -0.5), using the section formula.

Explanation:

When finding the coordinates of a point on a directed segment that divides it into a specific ratio, such as 3:1, the formula for the section formula in coordinate geometry is used. This formula allows us to calculate the coordinates of the point that divides the segment internally or externally in a given ratio (m:n) using the coordinates of the endpoints (x1,y1) and (x2,y2). The formula for the point (x, y) that divides the segment internally in the ratio m:n is:

x = (mx2 + nx1) / (m + n)

y = (my2 + ny1) / (m + n)

For the directed segment from (3, -2) to (8, 0) and a ratio of 3:1, we find the point by this method:

x = (3×8 + 1×3) / (3 + 1) = (24 + 3) / 4 = 27 / 4 = 6.75

y = (3×0 + 1×(-2)) / (3 + 1) = (0 - 2) / 4 = -2 / 4 = -0.5

Thus, the coordinates of the point that divides the segment in the ratio 3:1 are a) (6.75, -0.5).

Answer:

The simplified expression is

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

Step-by-step explanation:

Given expression is

[tex]\frac{4}{5}(\frac{1}{4}c-5)[/tex]

To simplify the given expression:

[tex]\frac{4}{5}(\frac{1}{4}c-5)[/tex]

[tex]\frac{4}{5}(\frac{1}{4}c-5)=(\frac{4}{5}\times \frac{1}{4}c)-(\frac{4}{5}\times 5)[/tex] ( here using the distributive property )

[tex]=(\frac{1}{5}c)-(4\times 1)[/tex] (simplify the factors )

[tex]=\frac{1}{5}c-4[/tex] or

[tex]=\frac{c}{5}-4[/tex]

Therefore the simplified expression is

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

Answer:

Angle 1:  100

Angle 2:  80

Step-by-step explanation:

A linear pair of angles is formed when two lines intersect.  The measure of a straight angle is 180 degrees, so a linear pair of angles is equal to 180 degrees.

Angle 1: x

Angle 2: (x * 3/4) + 5

x + (x * 3/4) + 5 = 180

x + 3/4x + 5 = 180

1 3/4x + 5 - 5 = 180 - 5

1 3/4x = 175

1 3/4x / 1 3/4 = 175 / 1 3/4

x = 100

Check:

(x * 3/4) + 5

(100 * 3/4) + 5

75 + 5

80

100 + 80 = 180

To find the measure of both angles that form a linear pair, set up an equation and solve for x.

To find the measure of both angles, let's assume that one angle is x degrees. According to the given information, the other angle is 3/4 of x degrees plus 5. So the measure of the other angle is (3/4)x + 5 degrees. Since the two angles form a linear pair, their measures sum up to 180 degrees. Therefore, we can write the equation: x + (3/4)x + 5 = 180. Solving this equation, we can find the value of x and then calculate the measures of both angles.

Answer: 0.8mile/min

Step-by-step explanation:please see attachment for explanation

Answer:

Step-by-step explanation:

This Sequence is  Geometric Progression

a = 16

r = 8/16 = 1/2

nth term = ar^(n-1) = 16*(1/2)^(n-1)

The nth term of the geometric sequence 16, 8, 4, 2, 1 can be found using the formula an = 16 * (1/2)^(n-1), where n is the position of the term in the sequence.

The sequence given is 16, 8, 4, 2, 1, which is a geometric sequence where each term is half of the previous term. This means the common ratio r is 1/2. The nth term of a geometric sequence is given by the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

To find the nth term for our sequence, we plug in the values: a_1 = 16 and r = 1/2. Thus, the formula for the nth term becomes an = 16 * (1/2)^(n-1).

The solution is x = 2 and y = -11

Solution:

Given system of equations are:

x + y = -9 --------- eqn 1

5x - 2y = 32 ------------- eqn 2

We have to solve the system of equations

We can solve the system by substitution method

From eqn 1,

x + y = -9

Isolate "y" to one side

y = -9 - x ---------- eqn 3

Substitute eqn 3 in eqn 2

5x -2(-9 - x) = 32

5x + 18 + 2x = 32

Combine the like terms

7x = 32 - 18

7x = 14

x = 2

Substitute x = 2 in eqn 3

y = - 9 - 2

y = -11

Thus the solution is x = 2 and y = -11

Step-by-step explanation:

If two lines cross each other the angles opposite of each other are the same. So left=right and top=bottom. Knowing this the bottom angle must be 120°. if 3x=120° then x=40°

Answer:

-12

Step-by-step explanation:

4x=-48. use inverse operations here so divide -48 by 4

x=-12

Answer:

Step-by-step explanation:

Increases weight  = 80 - 40 = 40 lbs

Percent increase = (40/40)*100 = 1*100 = 100%

Answer:

The percent change is 50%.

Step-by-step explanation

1) 80-40=40

2) 40 divided by 80 which equals 0.5

3) 0.5 multiplied by 100

4) 0.5 x 100=50

The formula for percent change is change divided by the original amount then multiply the answer from that problem by 100.

Answer:

D

Step-by-step explanation:

all of the above

The solution is Option D.

The sources of water pollution are sewage , oil spills and fertilizers

Water contamination is the tainting of bodies of water, typically as a result of human activity, which has a detrimental impact on their uses. Aquifers, reservoirs, lakes, rivers, seas, and groundwater are all examples of bodies of water. When contaminants are introduced into these water bodies, water contamination results. It causes illnesses: consuming contaminated water can lead to serious health problems. From diarrhoea, cholera, hepatitis A, typhoid, to death.

Given data ,

Water scarcity is the situation when available water is not sufficient

And , the sources of water pollution are mainly sewage , oil spills and fertilizers thrown out into the ocean and other water bodies by humans

Toxic substances from farms, towns, and factories readily dissolve into and mix with it, causing water pollution.

Ground water , surface water and ocean water pollution are the three water bodies caused by water pollution

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a. The equation of the line is [tex]y = \frac{28}{15}x+\frac{41}{30}[/tex]

b. The equation of the line is [tex]y = \frac{-7}{5}x+\frac{1}{5}[/tex]

The general equation of the line in slope-intercept form is:

y = mx + c

where m is the slope and c is the y-intercept

1. To get the slope:

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where (x₁ , y₁) and (x₂ , y₂) are two points that belong to the line

2. To get the y-intercept:

We pick any point (x , y) that belong to the line and use this point to substitute in the general equation:

y = mx + c

m is calculated from part 1 and (x , y) is a known point on the line. So, we solve for c which is the only unknown.

Now, for the required lines:

Part a:

The two given points are (2, 5.1) and (-1, -0.5)

representing (x₁ , y₁) and (x₂ , y₂)

i. Getting the slope:

[tex]m = \frac{-0.5 - 5.1}{-1 -2}=\frac{28}{15}[/tex]

ii. Getting the y-intercept:

I will use the point (-1, -0.5)

y = mx + c

[tex]-0.5 = \frac{28}{15}(-1)+c\\\\-0.5=\frac{-28}{15}+c\\ \\ c = \frac{41}{30}[/tex]

iii. Based on the above calculations, the equation of the line is:

[tex]y = \frac{28}{15}x+\frac{41}{30}[/tex]

Part b:

The two given points are (-2, 3) and (3, -4)

representing (x₁ , y₁) and (x₂ , y₂)

i. Getting the slope:

[tex]m = \frac{-4-3}{3--2}=\frac{-7}{5}[/tex]

ii. Getting the y-intercept:

I will use the point (3, -4)

y = mx + c

[tex]-4 = \frac{-7}{5}(3) + c\\ \\-4 = \frac{-21}{5}+c\\ \\c=\frac{1}{5}[/tex]

iii. Based on the above calculations, the equation of the line is:

[tex]y = \frac{-7}{5}x+\frac{1}{5}[/tex]

Hope this helps :)

Marco scored 876 more points than Jasmine.

To find how many more points Marco scored than Jasmine, we subtract Jasmine's score from Marco's score.

Marco scored 1,753 points while Jasmine scored 877 points.

Thus, Marco scored 1,753 - 877 = 876 more points than Jasmine.

Answer:

The price of the shoes should be $13.12

Answer:

infinite solutions

Step-by-step explanation:

−2(2x+3)=−4(x+1)−2 multiply -2 and -4 with inside the parenthesis

-4x -6 = -4x -4 -2 now add like terms

-4x -6 = -4x -6 ➡ -4x +4x = -6+6

that makes equation 0 = 0 this is called infinite solutions which means whatever number you use instead of x there will always be a solution.

Answer: -9

Step-by-step explanation: it is a negative because it is minus 9$ from the price just like adding -9

Answer:

t - 9 = ?

Step-by-step explanation:

Answer: 12 I saw your comment lol

The correct answer is "no solution."

Let's first rewrite the second equation in the system in slope-intercept form (y = mx + b) to make it easier to work with:

[tex]\[ -5y = 10x + 20 \][/tex]

Divide both sides by -5:

[tex]\[ y = -2x - 4 \][/tex]

Now we have the system of equations:

[tex]\[ y = -2x + 5 \][/tex]

[tex]\[ y = -2x - 4 \][/tex]

To find the solution to the system, we can set the two equations equal to each other since they both equal y:

[tex]\[ -2x + 5 = -2x - 4 \][/tex]

Now, we can solve for x:

[tex]\[ 5 = -4 \][/tex]

This equation is not true, which means there is no value of x that satisfies both equations simultaneously. Therefore, the system has no solution.

Answer:

x = 2, y = -1

Step-by-step explanation:

2x + 3y = 1.....(1)

5x + 2y = 8.....(2)

multiply equation (1) by 5 and equation (2) by 2

10x + 15y = 5 .......(3)

10x + 4y = 16......(4)

solving by elimination method

we subtract equation (4) from (3)

hence ...

11y = -11

dividing both sides by 11

y = -1

substituting y = -1 in equation (1) to solve for the value of x

2x + 3(-1) = 1

2x - 3 = 1

rearranging,

2x = 3 + 1

2x = 4

dividing both sides by 2

x = 2

Answer:

19 ft i think

Step-by-step explanation:

hop ethis helps :) have a nice day

Answer:

-18.4z+6

Step-by-step explanation:

1. Always

2. x^2 − 14x + 49

3. x^2 + 10x + 25

4. x^2 − 9

5. 16x^2 − 24xy + 9y^2

6. 4x^2 + 20xy + 25y^2

7. 9x^2 − 49y^2

Some of these may be incorrect as you didn't probably right down the problems... I had to guess what was exponents/ <3

Step-by-step explanation:

parallelogram is a simple quadrilateral with 2 pairs of. parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Thanks..... hope it helped.

Answer: 2.2.3.5 = 60 are the prime factors in ascending order

Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

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

3x+1/2x=3+4

6x+x/2=7

6x+x=14

7x=14

x=14/2

x= 2

Answer:

X = 2

Step-by-step explanation:

- Add 1/2 to both sides

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

7/2x - 4 = 3

- Add 4 to both sides

7/2x - 4 + 4 = 3 + 4

7/2x = 7

- Multiply both sides by 2/7

(2/7) X (7/2x) = (2/7) X (7)

x = 2

Answer:

the answer is 9

Step-by-step explanation:

why it 9 Add '2.7' to each side of the equation.

-2.7 + 2.7 + 0.3x = 9 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0

0.0 + 0.3x = 9 + 2.7

0.3x = 9 + 2.7

Combine like terms: 9 + 2.7 = 11.7

0.3x = 11.7

Divide each side by '0.3'.

x = 39

Simplifying

x = 39

Answer:

0.42

Step-by-step explanation:

use the attached as reference

recall that for a right (90°) triangle, with any acute angle θ,

cos θ = length of adjacent side / length of hypotenuse

in our case, for angle I, the adjacent side is HI = 36 units and the hypotenuse is IJ = 85 units

by the above formula,

cos I = length of adjacent side / length of hypotenuse

= 36 / 85

= 0.42353

= 0.42 (rounded to nearest hundredth)