Answer:
#1) 116= -4 + 5(-6 - 5a) : a = -6
#2) 8m + 4(4m -5) = -92 : m = -3
#3) -3(8 - 6x) = -96 : x = -4
#4) -126 = -3 (6+6x) : x = 6
#5) -8 -8(5a + 7)=-224 : a = 4
#6) -2(-5x -1) = 82 : x = 8
#7) -7(4x + 6) = -182 :x = 5
Step-by-step explanation:
Remember: An equation must be equal at all times. This means if something is added to one side, it must also be added to the other. This holds true for addition, subtraction, division, and multiplication.
Problem 1:
116= -4 + 5(-6 - 5a)
move the -4 to the left side by adding 4 to both sides:
116 + 4 = -4 + 5(-6 - 5a) + 4
now 120 = 5(-6 - 5a)
divide both sides by 5:
120/5 = (5(-6 - 5a))/5
now 24 = -6 - 5a
move the -6 to the left side by adding 6 to both sides:
24 + 6 = -6 - 5a + 6
now 30 = - 5a
divide each side by -5:
(30)/-5 = (- 5a)/ -5
now -6 = a or a = -6
___________________________
Problem 2:
8m + 4(4m -5) = -92
begin by diving both sides by 4:
(8m + 4(4m -5))/4 = (-92)/4
now 2m + 4m - 5 = -23
move the -5 to the right side by adding 5 to both sides:
2m + 4m - 5 + 5 = -23 + 5
now 2m + 4m = -18
restate the left side and combine:
now 6m = -18
divide both sides by 6:
6m/6 = -18/6
so m = -3
___________________________
Problem 3:
-3(8 - 6x) = -96
divide both sides by - 3:
(-3(8 - 6x)) / -3 = -96/-3
now 8 - 6x = 32
move 8 to right side by subtracting 8 from both sides:
8 - 6x - 8 = 32 - 8
now -6x = 24
divide both sides by -6:
-6x/ -6 = 24/-6
x = -4
___________________________
Problem 4:
-126 = -3 (6+6x)
divide both sides by - 3:
-126/-3 = (-3 (6+6x)) /-3
now 42 = 6 + 6x
move 6 to left side by subtracting 6 from both sidesL
42 - 6 = 6 + 6x - 6
now 36 = 6x
divide both sides by 6:
36/6 = 6x/6
x = 6
___________________________
Problem 5:
-8 - 8(5a + 7)= -224
add 8 to both sides:
-8 - 8(5a + 7) + 8 = -224 + 8
now -8(5a + 7) = - 216
divide both sides by -8:
(- 8(5a + 7))/-8 = - 216 /-8
now 5a + 7 = 27
move 7 to right side by subtracting 7 from both sides:
5a + 7 - 7 = 27 - 7
now 5a = 20
divide both sides by 5:
5a/5 = 20/5
a = 4
___________________________
Problem 6:
-2(-5x -1) = 82
divide both sides by -2:
(-2(-5x -1))/-2 = 82/-2
now -5x -1 = -41
move -1 to right side by adding 1 to both sides:
-5x - 1 + 1= -41 + 1
now -5x = -40
divide both sides by -5:
-5x/-5 = -40/-5
x = 8
___________________________
Problem 7:
-7(4x + 6) = -182
divide both sides by -7:
(-7(4x + 6))/-7 = -182/-7
now 4x + 6 = 26
move 6 to right side by subtracting 6 from both sides:
4x + 6 - 6 = 26 - 6
now 4x = 20
divide both sides by 4:
4x/4 = 20/4
x = 5
My pumpkin pie recipe (which is listed at the end of this post) is really good. If you want to make my pumpkin pie you will need 1 ¾ cups of pumpkin puree. How many pies would the 2,528- pound pumpkin be able to make?
Answer:
752 pies will be made form the 2,528 pound pumpkin
Step-by-step explanation:
Here, we want to know the number of pies that will be made from the given number of purée
Firstly, we need to know the number of cups in 2,528-pound pumpkin purée
Mathematically, 1 pound = 1.92 cups
So , 2528 pound will be 2,528/1.92 = 1,316.67 cups
1 3/4 cups is needed to make a pie
So the number of pies that 1,316.67 cups will
make would be;
1316.67 divided by 1 3/4
= 1316.67/1.75 = 752 approximately
Translate the following phrase into an algebraic expression. use the variable d to represent the unknown quantity.
The algebraic expression is '4d' for the phrase "The product of 4 and the depth of the pool."
Expressing algebraically means to express it concisely yet easily understandable using numbers and letters only. Most of the Mathematical statements are expressed algebraically to make it easily readable and understandable.
Here, we are asked to represent the phrase "The product of 4 and the depth of the pool" algebraically.
The depth of the pool is an unknown quantity. So let it be 'd'.
Then product of two numbers means multiplying them.
We write the above statement as '4 x d' or simply, '4d' ignoring the multiplication symbol in between.
The question is incomplete. Find the complete question below:
Translate the following phrase into an algebraic expression. Use the variable d to represent the unknown quantity. The product of 4 and the depth of the pool
Learn more about algebraic statements at https://brainly.com/question/4344214
#SPJ4
Mr. Gonzalez invested $4,200 into an account that earns a simple interest rate of 3% per year.
What is the amount of interest Mr. Gonzalez will earn at the end of one year?
Answer:
4326
Step-by-step explanation:
4200/100x3=126
4200 + 126=4326
Answer:
b
Step-by-step explanation:
4326
A sporting goods company produces figure skates and hockey skates. One group of workers makes the blades for both types of skates. Another group makes the boots for both types of skates. It takes 2 hours to make the blade of a figure skate. It takes 3 hours to make the blade of a hockey skate. There is a maximum of 40 hours per week in which the blades can be made for both types of skates. It takes 3 hours to make the boot of a figure skate. It takes 1 hour to make the boot for a hockey skate. There is a maximum of 20 hours per week in which boots can be made for both types of skates. What is the system of inequalities that represents this situation?
Matthew is planning a graduation party at a restaurant. Restaurant A charges $250 to reserve the room and $15 per person to eat. Restaurant B charges $370 to rent the room and $13.50 for each person to eat. How many people would Matthew need to invite for the cost at either restaurant to be the same?
Fill in the blanks to create an equation to represent the situation.
___x + 250 = 13.50x + ____
Considering the definition of an equation and the way to solve it, Matthew would need to invite 80 people.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Number of invitesBeing "x" the number of invites, and knowing that:
Restaurant A charges $250 to reserve the room and $15 per person to eat. → Cost restaurant A= 250 + 15xRestaurant B charges $370 to rent the room and $13.50 for each person to eat. → Cost restaurant B= 370 + 13.50xIf cost at either restaurant is the same, the equation in this case is:
Cost restaurant A= Cost restaurant B
250 + 15x= 370 + 13.50x
Solving:
15x + 13.50x= 370 - 250
1.50x= 120
x= 120 ÷ 1.50
x=80
Finally, Matthew would need to invite 80 people.
Learn more about equations:
brainly.com/question/4983716
brainly.com/question/13314678
#SPJ1
a circular railroad crossing sign has a diameter of 30 inches. Which measurement is closest to the area in square inches?
Answer: it would be 12.
Step-by-step explanation:
The hanger image below represents a balanced equation.
a
9.1
4
Write an equation to represent the image.
Answer:
9.1 = a+4
Step-by-step explanation:
The right side has two different values, variable a, constant 4.
The left side has the constant 9.1.
If both sides are equal, then
a + 4 should equal 9.1
Answer:
9.1 = a+4
Step-by-step explanation:
Find the absolute value of the complex number.
-4+3i
Answer:
5
Step-by-step explanation:
the absolute value is also the modulus to find that it means square root of x^2 + y^2
x is -4 y is 3
=5
find the hcf and lcm of the following. (1) 189 and 84. (2) 315 and 720. (3)616 and 392. (4) 1008 and 1764. (5)560,140 and 224. (6) 378, 567 and 252. (7) 435 and 261
(8) 16, 28, 44, and 68
Answer:
Best and Correct answer gets BRAINLIEST!!!!!
Step-by-step explanation:
Which fraction equals the ratio of rise to run between the points (-3,-4) and (0, 0)?
Answer:
4/3
Step-by-step explanation:
Answer:
THe answer is C
Step-by-step explanation:
45 POINTS!! Pls .. need steps too :(
Answer:
b
Step-by-step explanation:
I need the answer to this ASAP!!!! 30 points!!!
Answer:
Part1: 1L 1s
5: 1 1/4s
1: 1/2
1: 3/4
2: 2
PART 2: 6 1/4
Step-by-step explanation:
For part 1 its just plotting the amount of the numbers in that table
Part 2: there are 5 1 1/4, so I can just multiply that by 5, which gives 6 1/4
pls brainliest
What is the measure of _M?
Answer: I think I cn help bt nt sure
Step-by-step explanation:
X° + 52° + 78° = 180°
X° + 130° = 180°
X° + 130° - 130° = 180° - 130 °
X° = 50°
M is <50°
Find the value of the expression x2−3x+7x+4 when x = 2.
Answer:
x=1/5 or 0.2
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
distribute 2 in for the x and you would get 2^2-3(2)+7(2)+4
and you would get 4-6+14+4= 16
9.
Which two expressions are equivalent?
plsss i have 5 ins to get this questoion pls elp
Mark and his brother David are fighting over a toy airplane while playing their yard. Mark grabs the plane and takes off running at rate of 7.5 miles per hour. One minute after Mark starts running, David starts to chase him at rate of 9mph. How long will David to reach Mark and how far will they have run?
A coffee machine dispenses 8-ounce cups of coffee automatically. the amount of coffee may vary by 3%. what are the least and greatest number of ounces the coffee machine may dispense?
If a coffee machine dispenses 8-ounce cups of coffee automatically. and the amount of coffee may vary by 3% then the least and greatest number of ounces the coffee machine may dispense is 7.76 and 8.24 respectively.
The least and greatest number of ounces the coffee machine may dispense can be calculated by converting the percentage given.
As, 3% = 3 / 100
3% of 8 = 3 / 100 × 8 = 24 / 100 = 0.24
Now by adding and subtracting the calculated value to 8, the least and greatest number of ounces can be determined.
8 - 0.24 = 7.76
8 + 0.24 = 8.24
Hence, the least ounces the coffee machine may dispense is equal to 7.76 and the greatest number of ounces the coffee machine may dispense is calculated to be 8.24 ounces.
To learn more about percentages, click here:
https://brainly.com/question/24877689
#SPJ4
Using the number line above, select the number that would be the opposite of Point T.
Answer:-9
Step-by-step explanation:
Solve the equation for the specified variable.
S = BA-7, for B
Answer:
[tex]B= \frac{S + 7}{A}[/tex]
Step-by-step explanation:
We are given the following equation:
S = BA - 7
And we want to solve it for B.
This is a literal equation, and to solve these, we need to isolate the variable we are solving for (in this case, B) on one side.
Here's the equation again:
S = BA - 7
We can start by adding 7 to both sides (removes it from the right side).
S = BA - 7
+7 +7
________________
S + 7 = BA
Now, divide both sides by A to isolate B. Remember that we're dividing both S AND 7 by A.
(S + 7) = BA
÷A ÷A
[tex]\frac{S+7}{A} = B[/tex]
This can be rewritten to be: [tex]B = \frac{S + 7}{A}[/tex]
You can also write it as [tex]B = \frac{S}{A} +\frac{7}{A }[/tex] if you wish.
Kay is making beaded belts for her friends from 6.5 meters of cord. One belt uses 0.625 meter of cord. How many belts can she make? Show your work.
Answer:
10 belts
Step-by-step explanation:
6.5 meters of cord / 0.625 meters per belt = 10.4 belts
Because 0.4 meters of cord is not enough for a belt, the answer is 10.
4(3n-2)=what and explain by righting out. each step
Answer:
12n - 8
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyStep-by-step explanation:
Step 1: Define Expression
4(3n - 2)
Step 2: Expand
Distribute 4: 4(3n) - 4(2)Multiply: 12n - 8Answer:
4(3n-2)
=> 12n-8
=> 12n=8
=> n=8/12
=> n= 2/3
If 16^x = 1/64 find the value of x.
Answer:
x = - [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]16^{x}[/tex] = [tex]\frac{1}{64}[/tex] , that is
[tex](4^2)^{x}[/tex] = [tex]\frac{1}{4^3}[/tex]
[tex]4^{2x}[/tex] = [tex]4^{-3}[/tex]
since bases on both sides are equal , both 4 then equate exponents
2x = - 3 ( divide both sides by 2 )
x = - [tex]\frac{3}{2}[/tex]
In ΔSTU, s = 4.6 inches, t = 1.8 inches and ∠U=118°. Find the length of u, to the nearest 10th of an inch.
Answer:
5.7
Step-by-step explanation:
Delta math
In ΔSTU, s = 4.6 inches, t = 1.8 inches and ∠U=118°. Hence, the length of u is 5.54 inches.
What is a cosine law?Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.
u² = s² + t² - 2(s)(t)·cos U
Given that the ΔSTU, s = 4.6 inches, t = 1.8 inches and ∠U=118°.
We can find the length of u by using the Cosine rule
u² = s² + t² - 2(s)(t)·cos U
u² = 4.6² + 1.8² - 2(4.6)(1.8)·cos 118
u² = 19.78 + 3.24 - 16.56 x cos U
u² = 19.78 + 3.24 + 7.77
u² = 30.79
u = 5.54
Hence, the length of u is 5.54 inches.
Learn more about cosine law;
https://brainly.com/question/21718480
#SPJ2
There are 2 grams of sugar in 8 oz of a fruit drink. Which table shows this relationship. *
Answer:
c
Step-by-step explanation:
one full drink or 2 oz. is two grams so a half a drink or four oz. is 1 gram and a drink and a half or 12 oz. is 3 grams
In table C there are 2 grams of sugar in 8 oz of a fruit drink. Therefore, option C is the correct answer.
Given that, there are 2 grams of sugar in 8 oz of a fruit drink.
What is data table?A table is an arrangement of information or data, typically in rows and columns, or possibly in a more complex structure. Tables are widely used in communication, research, and data analysis.
In table C we can see corresponding to 2 grams of sugar 8 oz of fruit drink.
In table C there are 2 grams of sugar in 8 oz of a fruit drink. Therefore, option C is the correct answer.
Learn more about the data table here:
https://brainly.com/question/12918406.
#SPJ2
a certain corner of a room is selected as the origin of a rectangular coordinate system. if a fly is crawling on an adjacent wall at a point having coordinates (1.5, 1.3), where the units are meters, what is the distance of the fly from the corner of the room?
The distance formula to get the distance of the fly from the corner of the room in meters is 1.985 meter.
Distance formula -
The distance formula is given by the equation -
[tex]d=\sqrt{ (x2-x1)^{2} +(y2-y1)^{2} \\[/tex]
[tex]where , (x_1, x_2)[/tex] and [tex](y_1,y_2)[/tex] are two given points.
Apply the distance formula to get the distance of the fly from the corner of the room in meters.
Now,
[tex]x_1 ,y_1[/tex] are form the origin,
Given:
[tex](x_2,y_2) =(1.5,1.3)[/tex]
By using the equation ,
[tex]d=\sqrt{ (x2-x1)^{2} +(y2-y1)^{2} \\[/tex]
[tex]\\d = \sqrt[2]{(1.5^{2} -0^{2})+ (1.3^{2}-0^{2} ) }[/tex]
[tex]d=\sqrt{(2.25+1.69)\\\\d=\sqrt{\frac{225}{100} +\frac{169}{100} } \\d=\sqrt{\frac{394}{100} } \\d=\frac{\sqrt{394} }{10} \\\\[/tex]
Root value of 394,
[tex]\sqrt{394}[/tex] = 19.85
[tex]d= \frac{19.85}{10} \\\\d=1.985[/tex] metre.
Therefore, the distance formula to get the distance of the fly from the corner of the room in meters is 1.985
To learn more about distance formula :- brainly.com/question/8283882
#SPJ4
Help pls
im braindead still XD
Answer:
-2.5 , -1 , 15.03 , 15.32
-10 , -6 1/2 , -1 , 0
0.02 , 0.2 , 2.02 , 2.2
Step-by-step explanation:
Answer:
-2.5 , -1 , 15.03 , 15.32
-10 , -6 1/2 , -1 , 0
0.02 , 0.2 , 2.02 , 2.2
Step-by-step explanation:
Given m<1=83°, find m<2 so the <1 and <2 are supplementary:
m<2=1
(Please enter the number of degrees only with no words or symbols)
Answer:
m∠2= 97
Step-by-step explanation:
When 2 angles are supplementary, they add up to 180 degrees.
We are told that angle 1 is 83 and the angle 1 and 2 are supplementary
So, angle 1 and 2 add up to 180, let's subtract 83 from 180 to find measure of angle 2
180-83=97
hope this helps! feel free to ask any questions
Which is a unit rate?
1 Cookie/ 1/3 bag
1 Cookie/ 9 bags
2/3 cookies
3 cookies/bag
Answer:
3 cookies/bag
Step-by-step explanation:
First of all, let's define a unit rate. A unit rate is a ratio of the amount of one measurement to one unit of another measurement term. Unit rates can be expressed as fractions.
Now, here is something easier for you to remember: the second unit always have to be something with the quantity of 1.
In this case, "3 cookies/bag" shows how there are three cookies per, or in each bag--which means 1 bag. The second unit, which is bag, has the quantity of one.
Can someone please help me I have a few more also that I need help with.
Answer:
77
Step-by-step explanation:
Please mark as brainliest. I'm happy to help
what is z? -0.25z = -1.25
Answer:
z = 5
Step-by-step explanation:
-0.25z = -1.25
-1.25 ÷ -0.25 = 5
z = 5