Answers
a) Wayne's savings before he spent $28 is $30
b) Stef's savings after she spent $28 is $8
Step-by-step explanation:
step 1 :
let,
Wayne's savings = 5x
Stef's savings = 6x
step 2 :
After spending $28 each of them, The ratio becomes 1/4.
⇒ (28 - 5x) / (28 - 6x) = 1/4
⇒ 4(28 - 5x) = 1 (28 - 6x)
⇒ 112 - 20x = 28 - 6x
⇒ 112 - 28 = 20x - 6x
⇒ 84 = 14 x
x = 84/4 = 6
step 3 :
a) Wayne's savings before he spent $28 = 5x
substitute x=6,
Wayne's savings = 5(6) = $30
step 4 :
b) Stef's savings after she spent $28 = Total savings - $28
= 6x - 28
= 6(6) - 28
∴ Stef's savings after she spent $28 = 36 - 28 =$8
(a) Wayne's savings before he spent $28 is $30.
(b) Stef's savings after she spent $28 is $8.
Solution:
Ratio of Wayne's savings to Stef's savings = 5 : 6
Let x be the common amount they have.
After spending $28 each, the ratio becomes 1 : 4.
5x – 28 : 6x – 28 = 1 : 4
This can be written in a fraction form.
[tex]$\Rightarrow\frac{5x-28}{6x-28}=\frac{1}{4}[/tex]
Do cross multiplication.
[tex]$\Rightarrow 4(5x-28)}=1({6x-28})[/tex]
[tex]$\Rightarrow 20x-112=6x-28[/tex]
Arrange like term one side.
[tex]$\Rightarrow 20x-6x=112-28[/tex]
[tex]$\Rightarrow 14x=84[/tex]
⇒ x = 6
(a) Wayne's savings before he spent $28 = 5x = 5(6) = $30
(b) To find stef's savings after spent $28:
Stef's savings before she spent $28 = 6x = 6(6) = $36
Stef's savings after she spent $28 = $36 – $28 = $8
Hence Wayne's savings before he spent $28 is $30
Stef's savings after she spent $28 is $8.
Related Questions
Amelia need 1/2 stick of butter to make cornbread he also needs one fourths stick butter to make apple muffins what fraction of a stick of butter does he need in all
Answers
Amelia needs [tex]\frac{3}{4}[/tex] stick of butter to make cornbread and apple muffins.
Step-by-step explanation:
Given,
Stick of butter needed to make cornbread = [tex]\frac{1}{2}[/tex]
Stick of butter needed to make apple muffins = [tex]\frac{1}{4}[/tex]
Total stick of butter needed = Cornbread + Muffins
Total stick of butter needed = [tex]\frac{1}{2}+\frac{1}{4}[/tex]
Total stick of butter needed = [tex]\frac{2+1}{4}[/tex]
Total stick of butter needed = [tex]\frac{3}{4}[/tex]
Amelia needs [tex]\frac{3}{4}[/tex] stick of butter to make cornbread and apple muffins.
Keywords: fraction, addition
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The coordinates of the vertices if triangle ABC are A (1,-1) , B (1,4) , and C (8,4). What is the length in units of the line segment that connects vertex A and vertex B?
Answers
Length of the line segment is 5 units.
Step-by-step explanation:
Step 1: Length of the line segment that connects A and B is the distance between the points A (1, -1) and B(1, 4). x1 = 1, x2 = 1, y1 = -1, y2 = 4Step 2: Calculate the distance using distance formula √(x2 - x1)² + (y2 - y1)²⇒ Length = √(1 - 1)² + (4 - -1)² = √5² = 5 units
What is 8 4/7 divided by 15 equal
Answers
[tex]\(8 \frac{4}{7}\)[/tex] divided by 15 is equal to [tex]\(\frac{4}{7}\).[/tex]
To divide the mixed number [tex]\(8 \frac{4}{7}\)[/tex] by 15, we first need to convert the mixed number to an improper fraction and then perform the division.
Step 1: Convert [tex]\(8 \frac{4}{7}\)[/tex] to an improper fraction.
[tex]\[ 8 \frac{4}{7} = \frac{(8 \times 7) + 4}{7} = \frac{56 + 4}{7} = \frac{60}{7} \][/tex]
Step 2: Perform the division.
[tex]\[ \frac{60}{7} \div 15 = \frac{60}{7} \times \frac{1}{15} \][/tex]
Now, multiply the numerators and denominators:
[tex]\[ \frac{60 \times 1}{7 \times 15} = \frac{60}{105} \][/tex]
Next, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 15:
[tex]\[ \frac{60 \div 15}{105 \div 15} = \frac{4}{7} \][/tex]
Show the expression with one exponent (5^8)4
Answers
Answer:
5^32 mark as brainliest
Step-by-step explanation:
Which expressions are equivalent to 7 (negative three-fourths x minus 3)? Select two options.
Answers
The equivalent expressions are:
[tex]7(-\frac{3}{4}x - 3) = (7 \times \frac{-3}{4}x) + (7 \times -3)\\\\7(-\frac{3}{4}x - 3) = \frac{-21x}{4} - 21[/tex]
Solution:
Given expression is:
[tex]7(-\frac{3}{4}x - 3)[/tex]
We have to find the equivalent expressions
By distributive property,
a(b + c) = ab + ac
Therefore,
[tex]7(-\frac{3}{4}x - 3) = (7 \times \frac{-3}{4}x) + (7 \times -3)\\\\7(-\frac{3}{4}x - 3) = \frac{-21x}{4} - 21[/tex]
Thus equivalent expressions are found
Answer:
Im pretty sure its a and e
Step-by-step explanation:
lmk if im wrong or right
Find the x-coordinates of the points where the graph crosses the x-axis.
y = (x - 3)(x + 8)
Answers
To find the x-coordinates of the points where the graph crosses the x-axis, set y = 0 and solve for x. The x-coordinates are 3 and -8.
Explanation:The question asks for the x-coordinates of the points where the graph of the equation y = (x - 3)(x + 8) crosses the x-axis. To find these points, we need to determine the values of x that make y equal to zero. Setting y = 0, we get (x - 3)(x + 8) = 0. This equation will be true if either (x - 3) = 0 or (x + 8) = 0. Solving each equation gives us x = 3 and x = -8, respectively. These are the x-coordinates of the points where the graph crosses the x-axis.
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To find the x-coordinates where the graph of y = (x - 3)(x + 8) crosses the x-axis, set y to zero and solve for x, yielding the points (3, 0) and (-8, 0).
To find the x-coordinates where the graph crosses the x-axis, we need to set the y-value to zero and solve the equation. This is because when a graph crosses the x-axis, its y-coordinate is always zero. The equation given is y = (x - 3)(x + 8).
To find the x-coordinates, we set y to zero:
x = -8
Thus, the graph crosses the x-axis at the points (3, 0) and (-8, 0).
What percent of 140 is 50.4?
Answers
Answer:
36
Step-by-step explanation:
X/100% x 140 = 50.4
X x 140 = 50.4 x 100
X x 140 = 5040
X = 5040/140
X = 36
What is the slope intercept form of 6x+2y=8
Answers
Answer: y = -3x + 4
Step-by-step explanation:
subtract the 6x on both sides (2y = -6x + 8)
divide on both sides by 2 to isolate y ( y = -3x + 4)
Done :)
What is 83.9 rounded two decimal places
Answers
Astronomers sometimes use angle measures divided into degrees, minutes, and seconds. One degree is equal to 60 minutes, and one minute is equal to 60 seconds. Suppose that ∠J and ∠K are complementary and that the measure of ∠J is 41 degrees, 38 minutes, 9 seconds. What is the measure of ∠K?
Pleaseee answer now!!!
Answers
The measure of ∠K is 49 degrees 22 minutes 51 seconds.
Step-by-step explanation:
Given that ∠J and ∠K are complementary.
∠J = 41°38'9".
∠K = ?
When a sum of two angles result is 90°, then it is called as complementary angles.
Since ∠J and ∠K are complementary, then their sum is 90°.
∠J +∠K=90°.
∠K= 90° - ∠J.
=90°60'60" - 41°38'9".
=49°22'51".
∠K= 49 degrees 22 minutes 51 seconds.
How to write the improper fraction 15/5 as a mixed number
Answers
15/5 = 3 with remainder 0
So we could write it as [tex]\frac{15}{5} = 3\frac{0}{5}[/tex] which is a mixed number, but the 0/5 part isn't needed and we can simply say '3'.
Expressed as the product of prime factors,
198 = 2 x 32 x 11 and 90 = 2 x 32 x 5.
Use these results to find
(a) the smallest integer, k, such that 198k is a perfect
square,
Answers
Answer:
22
Step-by-step explanation:
198 = 2×3×3×11
For a perfect square, factors have to occur in pairs
198×2×11 (because 3 is already twice)
198×2×11
198×22
198k = 198×22
k = 22
The value of k as smallest integer is 22 if 198k is a perfect square.
What is prime factor?A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11,.....
The given numbers are 198 and 90.
The prime factor of 198 = 2 x 3 x 3 x 11
The prime factor of 90 = 2 x 5 x 9
(a)
to make 198 perfect square,
The prime factor must be in square,
198k = 2 x 2 x 3 x 3 x 11 x 11
k = 2 x 11
k = 22
The value of k is 22 if 198k is a perfect square.
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Find the missing side length, m.
Answers
Answer:
m=5
Step-by-step explanation:
Since we know that triangle ABC is similar to QRS, we know that the side lengths will be proportional to one another. As such, we should take a ratio to determine the side length of m.
Choose whole numbers to make the division easier
[tex]\frac{QR}{AB} = \frac{QS}{AC} \\\frac{10}{6} = \frac{m}{3} \\\frac{10*3}{6} =m\\m=10*3/6 = 5[/tex]
The missing side length, [tex]$m$[/tex], is [tex]$\boxed{5}$[/tex].
The missing side length, [tex]$m$[/tex], can be found using the fact that triangles [tex]$ABC$[/tex] and[tex]$QRS$[/tex] are similar. This means that their corresponding side lengths are proportional. We can set up a proportion like this:
(m)/(3)=(10)/(6)
Cross-multiplying, we get:
[tex]$$6m[/tex] =[tex]30$$[/tex]
Solving for [tex]$m$[/tex], we get:
[tex]$$m[/tex] =[tex]5$$[/tex]
Therefore, the missing side length, [tex]$m$[/tex], is [tex]$\boxed{5}$[/tex].
what is the measure of b if a=20 and c=29. using the pythagorean theorem
Answers
Since a^2+b^2=c^2 becomes 20^2+b^2=29^2, we solve for b:
400+b^2=841
b^2=441
b=21
So the length of b is 21 units.
Hope this helped!
Answer:
Step-by-step explanation:
b=21
a Leg
20
c Hypotenuse
29
combining like terms -3(5x+4)-(2x+2)-3x+6
Answers
Answer:
-20x -4
Step-by-step explanation:
3(5-2x)+9x=45 what is x
Answers
Answer:
10
Step-by-step explanation:
Let's solve your equation step-by-step.
3(5−2x)+9x=45
Step 1: Simplify both sides of the equation.
3(5−2x)+9x=45
(3)(5)+(3)(−2x)+9x=45 (Distribute)
15+−6x+9x=45
(-6x+9x)+(15)=45 (Combine Like Terms)
3x+15=45 3x+15= 45
Step 2: Subtract 15 from both sides.
3x+15−15=45−153x=30
Step 3: Divide both sides by 3.
3/3=30/3
x=10
Answer:
x=10
Answer:
Note that ( − 9 x − 45 ) = ( − 9 ) ( x + 5 ) and that ( x 3 + 5 x 2 ) = ( x 2 ) ( x + 5 ) We can write x 3 + 5 x 2 − 9 x − 45 XXX = ( x 2 − 9 ) ( x + 5 ) If we further note that ( x 2 − 9 ) is the difference of squares ( x + 3 ) ( x − 3 ) we can expand this to x 3 + 5 x − 9 x − 45 XXX = ( x + 3 ) ( x − 3 ) ( x + 5 )
Step-by-step explanation:
Write 80/100 as tenths in fraction form and decimal form
Answers
Answer:
0.8
Step-by-step explanation:
PLS HELP GIVING BRAINLIEST Turner Middle School has 525 boys, 625 girls, 58 teachers, and a supporting staff of 12 employees. The school uses an average of 1,267,760 gallons of water per month. Assuming that the water usage is proportional to the number of people in the school, about how much water do the students consume per week? a. 17,940 gal c. 316,940 gal b. 299,000 gal d. 1,196,000 gal
Answers
Answer:
d. 1,196,000 galStep-by-step explanation:
Number of students = 525+625=1 150
The number of people = 525+625+58+12=1 220
let x represent the amounot of water consumed by students
1220———————>1 267 760
1150———————> x
then
x = (1 150×1 267 760)÷1 220 = 1 195 019.67213115
:)
IF A LIQUID WEIGHS 2 POUNDS AND HAS A CApacity of 3 gallons. what is its density
Answers
Answer:
0.08 g/cm³
Step-by-step explanation:
We are given;
Mass of the liquid = 2 poundsBut; 1 pound = 453.592 g
Therefore, mass = 907.184 g
Volume of the liquid = 3 gallonsBut; 1 gallon = 3785.41 cm³
Thus, volume = 11356.23 cm³
We are required to determine the density of the liquid;
We need to know that;
Density = Mass ÷ Volume
Therefore;
density of the liquid = 907.184 g ÷ 11356.23 cm³
= 0.0799 g/cm³
= 0.08 g/cm³
Thus, the volume of the liquid is 0.08 g/cm³
Translate the following sentence to an equation.
The sum of five times a number and four is equal to negative eleven.
5n + 4 = -11
5n - 4 = -11
4n + 5 = -11
4n - 5 = -11
Answers
Answer:
5n+4=-11
Step-by-step explanation:
Write an equation of a line that passes through the x-intercept 4 and y-intercept -2
Answers
Answer:
[tex]y=\frac{1}{2} x-2[/tex]
Step-by-step explanation:
We have the two points (4,0) and (0,-2)
Find the slope
[tex]m=\frac{-2-0}{0-4} =\frac{-2}{-4} =\frac{1}{2}[/tex]
y-intercept is -2
[tex]y=\frac{1}{2} x-2[/tex]
18. You run along a path at a constant speed of 5.5 miles per hour. How far do you travel in 1.5 hours? in 3.8 hours?
Answers
Answer:
the travel of only 1.5 hours:8.25
The travel in 3.8 hours:20.9
Step-by-step explanation:
1.5(5.5)
1.5(3.8)
“An A grade will be given to students having at least 450 total test points. There are two more tests to take before the semester is over. Lesha wants to know what she needs to score in order to get an A. Write and solve an equation to determine what score she needs to average on the next two tests if each question is with 1 point. Explain your reasoning.”
Answers
The required average on next two tests are:
[tex]t\geq \frac{450-p}{2}[/tex]
Solution:
An A grade will be given to students having at least 450 total test points
Let p represent her present test point total, and t represent the necessary average on the next two tests
There are two more tests to take before the semester is over
Therefore,
[tex]p+2t\geq 450[/tex]
A grade is given to students having at least 450 total test points
"at least" means greater than or equal to
So we have used greater than or equal to symbol
Solve the inequality for "t"
[tex]p+2t\geq 450\\\\Subtract\ p\ from\ both\ sides\\\\2t\geq 450-p\\\\Divide\ both\ sides\ by\ 2\\\\t\geq \frac{450-p}{2}[/tex]
Thus the required average on next two tests are:
[tex]t\geq \frac{450-p}{2}[/tex]
Determine whether the statement is true of false and support your reasoning:
Mr. Flores has 100 pictures in a photo album. Of these pictures, 20 show his friends, 50 show his family, and 30 show his pet dachshund, Frou-Frou.
Based on this information, the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family.
Answers
Answer:
The statement that the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family is FALSE. We can clearly see that the probability of selecting a picture of his family is greater than the probability of selecting a picture of Frou Frou.
Step-by-step explanation:
the probability of randomly selecting a picture of Frou Frou is = 30/100 = 0.3
The probability of randomly selecting a picture of his family = 50/100 = 0.5
The statement that the probability of Mr. Flores randomly selecting a picture of Frou-Frou is greater than the probability of randomly selecting a picture of his family is FALSE. We can clearly see that the probability of selecting a picture of his family is greater than the probability of selecting a picture of Frou Frou.
An office remodeling project costs $15,880. If you pay $3,680
towards the project, how much do you finance?
Answers
Answer:
23.17%
Step-by-step explanation:
The project costs $15,880 of which you contributed $3,680. To know the percentage of how much you finance,
(amount paid / cost)*100%
= (3680/15880)*100%
= (0.231738035)*100%
= 23.1738035%
Thus the amount contributed is 23.17% of the cost.
What is ED?
I've been trying to solve this for a while and I just can't figure anything out.
Answers
Answer:
ED=12 units
Step-by-step explanation:
From the diagram triangle EAB is similar to triangle EDC.
The corresponding sides will be proportional.
EA/ED=AB/DC
This implies that:
[tex] \frac{2x + 4}{x + 4} = \frac{9}{6} [/tex]
We cross multiply to get:
[tex]6(2x + 4) = 9(x + 4)[/tex]
We expand to get:
[tex]12x + 24 = 9x + 36[/tex]
Group similar terms to get:
[tex]12x - 9x = 36 - 24[/tex]
Combine the similar terms to get:
[tex]3x = 12[/tex]
Divide through by 3 to get:
[tex]x = \frac{12}{3} [/tex]
This will simplify to:
[tex]x = 4[/tex]
Therefore ED=2*4+4=8+4=12
The president of a company creates a graph of the price of the company’s stock over one year. He describes the graph as follows: • The price of the stock rose to about $17 before falling to about $3. • There have only been two periods during which the price of the stock decreased. • The price of the stock is expected to increase in the long run. Which graph correctly shows the price of the stock?
Answers
Answer:
Option D
Just took test on ed2020 it is the last graph. Option D
Step-by-step explanation:
Answer: D
Step-by-step explanation:
A triangular pane of glass has a height of 30 inches and an area of 270 square inches.What is the length of the base of the pane
Answers
Answer: 18in
Step-by-step explanation: Since area of triangle is A = 1/2 x b x h 30×18 = 540 and 540 Divided by two = 270 square inches
What is the equation of the line that passes through the point (8,3) and has a slope
of - 1/2?
Answers
Determine the y-intercept:
We make the equation 3=-1/2(8)+b
3=-4+b
7=b
Since the y-intercept is b, we have our full equation: y=-1/2x+7
Hope this helped!
What does -8/3 simplify to ?
Answers
Answer:
exact form: -8/3
decimal form: -2.6666666
mixed number: -2 2/3
Step-by-step explanation: