On an algebra test , the highest grade was 42 points higher than the lowest grade . The sum of the two grades was 138 . Find the lowest grade .

Answers

Answer 1

(x = lowest grade)
x + x + 42 = 138
2x + 42 = 138
-42 -42
2x =96
/2 /2
x = 48

48 was the lowest grade

Answer 2

The lowest grade is 48.

What is substitution method?

The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation.

Let the lowest grade be x and highest grade be y.

According to the given question.

[tex]y = 42 + x[/tex]

Also,

[tex]x + y= 138[/tex]

For finding the points of lowest grade and highest grade substitute

y = 42 + x in x + y = 38.

[tex]x + ( 42 + x ) = 138[/tex]

⇒ [tex]2x + 42 = 138[/tex]

⇒ [tex]x + 21 = 69[/tex]

⇒[tex]x = 69 -21[/tex]

⇒[tex]x = 48[/tex]

Therefore,

[tex]y = 48 + 42 =90[/tex]

Hence, the lowest grade is 48.

Find out more information about substitution method here:

https://brainly.com/question/14619835

#SPJ2

Related Questions

Find two consecutive positive even integers whose product is 168

Answers

Hello There!

The integers you are looking for are 12 and 14.

Hope This Helps You!
Good Luck :)

- Hannah ❤

Write the equation in slope-intercept form of the line that has a slope of -3 and contains the point (4, -5).

Answers

y-(-5) = -3(x-4)
y+5= -3x +12
y= -3x +7

Fabian has a savings account balance of $1,374.73. The interest rate on the account is %3.9 compounded twice a year. If he opened the account nine years ago, what was the value of his deposit?

Answers

The effective interest given that the account is compounded semi-annually is calculated through the equation,

ieff = (1 + i/n)^m - 1

Substituting the known values,
ieff = (1 + 0.039/2)^2 - 1
ieff = 0.0394

The value of the initial investment can be calculated through the equation,
F = P x (1 + ieff)^n

P = F / (1 + ieff)^n

Substituting the known values,
P = ($1374.73) / (1 + 0.0394)^9

P = $971.06

ANSWER: $971.06

evaluate g(x)=3x+1 over the domain of g, {0,1,2,3}. What is the range of g?

Answers

You can do a table like this:

x      g(x) = 3x + 1

0        3(0) + 1 = 0 + 1 = 1

1        3(1) + 1 = 3 + 1 = 4

2        3(2) + 1 = 6 + 1 = 7

3        3(3) + 1 = 9 + 1 = 10

Then, the range is {1, 4, 7, 10}

Remember, the domain is the set of x values for which the function is defined, and the range is the set of images.

Answer: {1, 4, 7, 10}

Using synthetic division, what is the quotient (2x3 − 2x − 12) ÷ (x − 2)? 2x2 + 4x + 6 2x2 − 4x + 6 2x2 + 4x − 6 2x2 + 4x − 6 + 1 over the quantity of x minus 2

Answers

The answer to your question would be 2x^2+4x+6

Answer:

[tex]\text{The quotient is }2x^2+4x+6[/tex]

Step-by-step explanation:

Given the dividend and divisor we have to find the remainder using synthetic division.

The given polynomial [tex]2x^3-2x-12[/tex] is divided by (x-2).

Step 1: Set up the synthetic division.

The dividend goes on the inside of the box.

Step 2: Bring down the leading coefficient to the bottom row.

Step 3: Multiply c i.e 2 by the value just written on the bottom row.

Step 4: Add the column created in step 3 and write the sum in the bottom row.

Repeat steps 1-4 until the last column.

From the last row the remainder becomes

[tex]2x^2+4x+6[/tex]

Hence, option A is correct.

The measures of two complementary angles are in the ratio of 5:7. what is the measure of the smaller angle?

Answers

Final answer:

To find the measure of the smaller angle with a ratio of 5:7 in two complementary angles, set up an equation based on the sum of 90 degrees, leading to a solution where the smaller angle measures 37.5 degrees.

Explanation:

The question asks to find the measure of the smaller angle when two complementary angles have a ratio of 5:7. To solve this problem, we recall that complementary angles sum up to 90 degrees. Since the angles are in a ratio of 5:7, we can denote the measures of the smaller and larger angles as 5x and 7x, respectively.

By combining these ratios, we have 5x + 7x = 90 degrees, which simplifies to 12x = 90 degrees. Solving for x gives us x = 90 / 12 = 7.5. Therefore, the measure of the smaller angle is 5x = 5 × 7.5 = 37.5 degrees.

is -22 an irrational number???

Answers

-22 is not an irrational number

no its a rational number

write an equation of the line that passes through the given point(-2,5) and is parallel to the given line 2y=4x-6

Answers

y=2x+b

substitute -2 for x and 5 for y
5=2(-2)+b4

Solve for b
b=9

The equation is
y=2x+9

write 25.784 in expanded form

Answers

No expanded form is when all the numbers are broke up

I will be writing the 3 different types of expanded form's

Expanded Notation Form:

20+5 + 0.7 + 0.08

Expanded Factors Form:
2 × 10 + 5 × 1 + 7 × 0.1 + 8 × 0.01 + 4 × 0.001

Expanded Exponential Form:

2 × 101 + 5 × 100 + 7 × 10-1 + 8 × 10-2 + 4 × 10-3

Word Form:

twenty-five and seven hundred eighty-four thousandths

Terms and coefficients of 7p - 3r + 6 - 5s

Answers

Final answer:

The terms and coefficients of the expression 7p - 3r + 6 - 5s are 7p, -3r, 6, and -5s, with coefficients of 7, -3, no coefficient, and -5 respectively.

Explanation:

The terms and coefficients of the expression 7p - 3r + 6 - 5s are:

The term 7p has a coefficient of 7.The term -3r has a coefficient of -3.The term 6 is a constant and does not have a coefficient.The term -5s has a coefficient of -5.

Learn more about Terms and Coefficients here:

https://brainly.com/question/23992956

#SPJ12

MATH HELP PLEASE !!!!!!!!!

Answers

3.14 *2r = 157

divide both sides by 3.14

2r = 157/3.14 =50

2r=50

divide both sides by 2

r = 50/2 =25

r = 25

What is the correct evaluation of 3x2 + 4x - 2y2 + 4y + 5, when x is equal to -1 and y is equal to 5?

Answers

Final answer:

The expression 3x^2 + 4x - 2y^2 + 4y + 5 evaluates to -26 when x = -1 and y = 5.

Explanation:

The evaluation of the expression 3x2 + 4x - 2y2 + 4y + 5 when x is equal to -1 and y is equal to 5 is calculated by substituting these values into the equation.

First, substitute x = -1 into 3x2 + 4x, which gives 3(-1)2 + 4(-1) = 3 * 1 - 4 = 3 - 4 = -1.Next, substitute y = 5 into -2y2 + 4y, which gives -2(5)2 + 4*5 = -2 * 25 + 20 = -50 + 20 = -30.Add up the results from step 1 and step 2, and include the constant 5 from the original expression to find the final result: -1 - 30 + 5 = -26.

Therefore, the correct evaluation of the expression when x = -1 and y = 5 is -26.

Find the value of y in the equation

Answers

We want to find y from the equation
[tex] \frac{3}{y-2} =8[/tex]

Multiply each side by (y - 2).
[tex](y-2).( \frac{3}{y-2)}) = 8(y-2) [/tex]
Note that (y-2) in the numerator and denominator cancel out on the left side.
Therefore
3 = 8(y - 2)
3 = 8y - 16
Add 16 to each side.
3 + 16 = 8y - 16 + 16
19 = 8y
Divideach side by 8.
19/8 = y

Answer: [tex]y= \frac{19}{8} [/tex]

SOS!!!!!!!!!!!!!!!!!!!!!!

Answers

Your answer is option 3. Dashed lines because the inequality on either line is NOT an "or equal to" statement.

You eat 3/10 of a pack of hotdogs, your friend eats 1/5 of the pack of hotdogs. what fraction of the hotdogs did you and your friend eat?

Answers

you and your friend ate 1/2 a pack of hotdogs

3/10 + 1/5

(1/5 = 2/10)

3/10+2/10 =5/10 = 1/2

answer math question, 50 pts for brainliest

Answers

slope = (71.75 - 41)/(7 - 4) = 30.75 /3 = 10.25

answer is B.
the slope is 10.25. This means that Dante earns $10.25 each hour

71.75-41 = 30.75

7-4=3

30.75 / 3 =10.25

slope is 10.25

Answer is B

What is the shape of a parallel cross section of a sphere?

Answers

The answer is a circle. Hope this helped :)

a sphere is round so when you take a cross section it would be a circle

Sam packed 42kg of rice into one big bag and 6 small ones which are of the same size. the big bag contained 3/7 of the rice. how many kilograms of rice did each small bag contained?

Answers

if the big bag contained 3/7 of the rice, then the smaller bags contained 4/7.
so the smaller bags contained : 4/7(42) = 168/7 = 24 kg.....and their are 6 small bags...so each bag contained : 24/6 = 4 kg per bag <==

What equation is graphed in this figure?

A.y-4=-1/3(x+2)
B.y-3=1/3(x+1)
C.y+2=-3(x-1)
D.y-5=3(x-1)

Answers

Hello there!

The correct answer is option C

--------------------------------------

Graph using the slope and y- intercept

Slope: -3
Y-intercept: 1

Good luck with your studies!

The sum of a number and its reciprocal is 13/6. find the number

Answers

suppose the number is x, its reciprocal is 1/x
x+1/x=13/6
(x^2+1)/x=13/6
6(x^2+1)=13x
6x^2-13x+6=0
(3x-2)(2x-3)=0
x=2/3 or x=3/2

In 4 years, Harry’s age will be the same as Jim’s age is now. In 2 years, Jim will be twice as old as Harry will be. Find their ages now.

Answers

Jim is 6 / Harry is 2

In 4 years Harry will be 6
In 2 years Jim will be 8 and Harry will be 4 which is twice as much Harry's age.

hope this helps!

Answer: The present age of Harry is 2 years and that of Jim is 6 years.

Step-by-step explanation: Given that in 4 years, Harry’s age will be the same as Jim’s age is now. In 2 years, Jim will be twice as old as Harry will be.

We are to find the present ages of Harry and Jim.

Let x and y represents the present ages of Harry and Jim respectively.

Then, according to the given information, we have

[tex]x+4=y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y+2=2(x+2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Substituting the value of y from equation (i) in equation (ii), we get

[tex]y+2=2x+4\\\\\Rightarrow x+4+2=2x+4\\\\\Rightarrow 2x-x=2\\\\\Rightarrow x=2.[/tex]

From equation (i), we get

[tex]y=x+4=2+4=6.[/tex]

Thus, the present age of Harry is 2 years and that of Jim is 6 years.

sylvie finds the solution to the system of equations by graphing.

y=2/3x+1 and y=-2/3x-1

which graph shows the solution to sylvie’s system of equations?

a) graph 1
b) graph 2
c) graph 3
d) graph 4

Answers

c) graph 3
Point 3,3 satisfies y=2/3x+1

Answer:

solution is (-1.5,0)

Graph 3

Step-by-step explanation:

[tex]y=\frac{2}{3}x+1[/tex]and [tex]y=-\frac{2}{3}x-1[/tex]

In the first equation [tex]y=\frac{2}{3}x+1[/tex]

slope = 2/3 and y intercept is 1

Lets start with graphing y intercept +1

then we slope , move 2 units up and 3 units to the right. stop at (3,3)

Now we graph the second equation

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

slope = -2/3 and y intercept is -1

Lets start with graphing y intercept -1

then we slope , move 2 units down and 3 units to the right. stop at (3,-3)

both graph intersects at a point (-1.5,0)

five cakes cost £4.00 how much do 7 cost

Answers

Greetings!

We can solve this by creating an algebraic equation.
[tex]5/4=7/x[/tex]
Cross Multiply.
[tex]5*x=4*7[/tex]
[tex]5x=28[/tex]
Divide both sides by 5.
[tex](5x)/5=(28)/5[/tex]
The Answer Is:
[tex]x=5.6[/tex]

Seven cakes would cost $5.60.

Hope this helps.
-Benjamin

In an equilateral triangle, what is the relationship between the length of a side and the perimeter?

Answers

1:3
If each side is x, the the perimeter is 3x. x/3x = 1/3

Answer:

1:3

If each side is x, the the perimeter is 3x. x/3x = 1/3

Step-by-step explanation:

The perimeter of a rectangle is 36 inches, and the area is 65 square inches. find the length and width of the rectangle.

Answers

With a perimeter of 36, and a known width of 5, that means the length is 13. This makes the area 65.

Perimeter = (2 x Length) + (2 x Width)Width = [Perimeter - (2 x Length)]/2= [36 -(2 x 13)]/2= (36 - 26)/2= 10/2= 5 inches
Area = Length x Width= 13 x 5 = 65 square inches

Plz can I help me with math

Answers

It will equal £21 for the rifles

£7 divided by 2=1 trifle so 1 trifle=1.50

6x1.50=£9

6trifles=£9

brainliest plz

The leg of a right triangle is 3 units and the hypotenuse is 7 units. What is the length, in units, of the other leg of the triangle?

4
Square root of 40
Square root of 58
10

Answers

7^2 = 3^2 +x^2

49 = 9 +x^2

x^2 = 49-9 =40

x = square root of 40

Answer:

the square root of 40 is the answer your looking for

Step-by-step explanation:

Evan washes two types of vehicles. It takes him 30 minutes to wash a car and 40 minutes to wash a truck. He charges $12 to wash a car and $15 to wash a truck. In 270 minutes, Evan made $105 washing cars and trucks. How many trucks did Evan wash? 2 trucks 3 trucks 4 trucks 5 trucks

Answers

The correct answer is 3 trucks.

The answer is 3 trucks

Find the measure of an angle whose measure is 60 degrees more than the measure of its complement

Answers

Two complementary angles add up to 90 degrees. Hence, the problem can be set up and solved. Let x represents one angle and 5x represent the angle that is 5 times greater:x + 5x = 90 (simplify)6x = 90 (next divide both sides by 6 to find the value of x [the smaller angle])x = 15 (this is the smaller angle, next subtract 15 from 90 to find the greater angle)90 - 15 = 75 (this is the greater angle which is 5 times that of its complement) 90 take away 73...

Answer:

75⁰

Step-by-step explanation:

Angle = x

Complement = 90 - x

Given:

x = 90 - x + 60

2x = 150

x = 75⁰

What is the midpoint m given p(-1, 2) and q(-2, -4)?

Answers

Midpoint = x1+x2/2 , y1+y2,2
= -1 + -2/2 , 2 + (-4)/2
= -3/2,-1
= -1.5, -1

Other Questions