Answer:
Step-by-step explanation:
2x+x+3(2x)=63
3x+6x=63
9x=63
9x/9=63/9
X=7
2x=14
3(2x)=42
Solve the inequality-x/2 ≤ 1
Answer:
Step-by-step explanation:
Solve the inequality -x/2 ≤ 1. Let's eliminate the fraction first, by multiplying both sides by 2:
-x ≤ 2
We want to solve for +x, not for -x.
Therefore, divide both sides of this latest inequality by -1, remembering to reverse the direction of the inequality sign:
-x ≤ 2 → x ≥ -2
A recipe calls for 2/3 cup of flour for every 4 teaspoons of vanilla. How much vanilla should be used for every 1 cups of flour?
A. 1/6
B. 2 2/3
C. 4 2/3
D. 6
Please help and explain everything! Thanks!
Answer: For 1 cup of flour, there should be 6 teaspoons of vanilla.
Step-by-step explanation:
What I did is that I found what 1 ÷ 2/3 equals. To find that, I used the reciprocal so the new equation would be 1 × 3/2 which equals 3/2. So since 2/3 × 3/2 equals 1, we have to do the same to 4 teaspoons. 4 × 3/2 equals 6. Therefore, there should be 6 teaspoons of vanilla for every one cup of flour.
Hope this helps! Don't hesitate to ask for clarification.
b) Are the black triangles above congruent or similar? Explain. (1 point)
Congruent because it contains the same angle measures and shape.
Answer:
congruent
Step-by-step explanation:
find the LCM of m^2 - 4m - 5 and m^2 + 8m + 7
Answer:
LCM=(m+1)(m-5)(m+7)
Step-by-step explanation:
Given expressions are [tex]m^2-4m-5[/tex] and [tex]m^2+8m+7[/tex].
To find the LCM, first we need to find factors of both expressions.
[tex]m^2-4m-5[/tex]
[tex]=m^2+1m-5m-5[/tex]
[tex]=m(m+1)-5(m+1)[/tex]
[tex]=(m+1)(m-5)[/tex]
Similarly factor other expression
[tex]m^2+8m+7[/tex]
[tex]=(m+1)(m+7)[/tex]
Common factor in both is (m+1)
bring down remaining non-common factors.
So LCM=(m+1)(m-5)(m+7)
A company produces and sells widgets and gizmos. In January the company sold 350 items for a total of $9,000. If each widget sold for $35, and each gizmo sold for $22, how many of each item did the company sell? Let x1 = the number of widgets sold and x2 = the number of gizmos sold.
Write an equation relating the number of each item sold to the total number sold: x1 + x2 =
Answer:
The company sold 100 widgets and 250 gizmos.
Step-by-step explanation:
Let [tex]x_1[/tex] be the number of widgets sold and [tex]x_2[/tex] be the number of gizmos sold.
We are told that the company sold 350 items. We can represent this information in an equation as:
[tex]x_1+x_2=350...(1)[/tex]
We have been given that a each widget sold for $35 and each gizmo sold for $22. The company sold 350 items for a total of $9,000.
We can represent this information in an equation as:
[tex]35x_1+22x_2=9,000...(2)[/tex]
From equation (1), we will get:
[tex]x_2=350-x_1[/tex]
Substitute this value in equation (2):
[tex]35x_1+22(350-x_1)=9,000[/tex]
[tex]35x_1+7,700-22x_1=9,000[/tex]
[tex]13x_1+7,700=9,000[/tex]
[tex]13x_1+7,700-7,700=9,000-7,700[/tex]
[tex]13x_1=1,300[/tex]
[tex]\frac{13x_1}{13}=\frac{1,300}{13}[/tex]
[tex]x_1=100[/tex]
Therefore, the company sold 100 widgets.
Substitute [tex]x_1=100[/tex] in equation (1):
[tex]100+x_2=350[/tex]
[tex]100-100+x_2=350-100[/tex]
[tex]x_2=250[/tex]
Therefore, the company sold 250 gizmos.
Answer:
x1 + x2 = 350
Step-by-step explanation:
The total number of items sold is the sum of the number of widgets sold and the number of gizmos sold:
(widgets sold) + (gizmos sold) = total items sold
We are supposed to represent widgets sold using x1, and gizmos sold using x2. The total number of items sold is given in the problem statement as 350. Substituting these values into the above equation, we get the equation you're looking for:
x1 + x2 = 350
A chef kept track of the number of apples people ate last week in his cafeteria. The results are shown here.
How many people ate fewer than 2 apples last week?
A) 3
B) 7
C) 10
D) 11
Number of people who ate fewer than two apples last week is 10.
The Correct option is (C)
What is data?Data are individual pieces of factual information recorded and used for the purpose of analysis.
It can be seen from the graph that,
0 apples eaten by 1 people
1 apples eaten by 9 people
2 apples eaten by 4 people
3 apples eaten by 5 people
4 apples eaten by 0 people
5 apples eaten by 7 people.
According to Condition,
people ate fewer than 2 apples last week= 1+9
=10
Thus, 10 people ate fewer than 2 apples last week.
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Find the surface area of the prism.
8 m
7 m
2 m
Answer:
the surface area of the rectangular prism is 172m
Evaluate (−481) power 0
Any number raised to the power of 0 equals 1.
(-481)^0 = 1
Answer:
1
Step-by-step explanation:
All numbers to the power of 0 is 1 with this reason:
x³
x² = x³/x
x¹ = x²/x
x⁰ = x/x
All numbers divided by itself is 1.
Write the following equation in slope intercept:
2x + 3y = 12
Y = mx + b
2x + 3y = 12
3y = -2x + 12
y = -2/3 + 4
Answer:
y = -2/3x +4
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
2x+3y = 12
We need to solve for y
Subtract 2x from each side
2x-2x+3y = -2x+12
3y = -2x+12
Divide by 3
3y/3 = -2/3 x +12/3
y = -2/3x +4
A train was traveling at a constant speed.the table below shows the distance,in miles the train traveled for the first 4 hours.Write an equation to represent the relationship between t,the time,and d,the total distance traveled by the train
Answer:
1 hour 95 min. 2 hour 190 min. third hour 285 min. fourth hour 380 min.
Step-by-step explanation:
How to solve for x/ extraneous solutions
Answer:
x = 8Step-by-step explanation:
[tex]\log_ab=c\iff a^c=b\\\\===================\\\\Domain:\ 8x>0\to x>0\\\\\log_4(8x)=3\iff4^3=8x\\\\8x=64\qquad\text{divide both sides by 8}\\\\x=8\in D[/tex]
write 9/5 as a sum of unit fractions
Answer:
4/5 + 5/5 = 9/5
Step-by-step explanation:
That's one of many ways you can do it
I think that he answer is 1 4/5
Find the area of the rhombus. Please need help
Answer:
20 i think
Step-by-step explanation:
because their is 2 parts of the rhombus and they are both equal sides so if the one side is 10ft. then the other side is 10ft. and if you add 10+10 you get 20.
What size picture will result when a 5 in. • 7 in. Picture is reduced using an 80% setting?
A 5" * 7" image reduced by 20% in scale to 80% of the original size will be 4" * 5.6". Roughly the size of a large flash card.
When a 5 inch by 7 inch picture is reduced using an 80% setting, the new dimensions will be 4 inches by 5.6 inches.
To calculate the new size of a 5 inch by 7 inch picture when reduced by 80%, we simply multiply both dimensions by the reduction percentage. Hence, the width and the height of the picture will be reduced to 80% of their original size.
Original width: 5 inches
Original height: 7 inches
Reduction setting: 80% (or 0.8)
New width: 5 inches × 0.8 = 4 inches
New height: 7 inches × 0.8 = 5.6 inches
Therefore, the new dimensions of the picture will be 4 inches by 5.6 inches after an 80% reduction.
How many floors does she travel?
Answer:
15 floors
Step-by-step explanation:
She parks on the third floor below ground +3
She goes up to the twelfth floor +12
3+12=15
Marilyn lives 3.5 block from the library. She leaves the library and walks 3.5
blocks before realizing she is walking in the opposite direction from her house.
After walking 3.5 blocks back, how far does Marilyn have to walk?
Answer:
3.5 blocks.
Step-by-step explanation:
After walking 3.5 blocks back she is back at her starting point.
Marilyn has walked 7 blocks in total, going the wrong direction and back to the library. She still needs to walk another 3.5 blocks to reach her house.
Explanation:Marilyn has already walked 7 blocks (3.5 blocks in the wrong direction and 3.5 blocks back to the library). As her house is 3.5 blocks from the library, she has another 3.5 blocks to walk.
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What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest form.
___ cm³
A rectangular prism with the width as five centimeters, the length as three and a half centimeters and the height as four and a half centimeters.
PLS HELP ASAP!!!
Answer:
78.75 cm³
Step-by-step explanation:
Volume = Width × Height × Length
V = 5 × 4.5 × 3.5
V = 78.75 cm³
Use the quadratic formula s to solve 2y^2-6y-8=0
{-4,-1}
{4,-1}
{-4,1}
{4,1}
Answer:
{4, - 1}
Step-by-step explanation:
Given
2y² - 6y - 8 = 0 ← in standard form
with a = 2, b = - 6, c = - 8
Using the quadratic formula to solve for y
y = ( - (- 6) ± [tex]\sqrt{(-6)^2-(4(2)(-8)}[/tex] ) / (2 × 2)
= ( 6 ± [tex]\sqrt{36+64}[/tex] ) / 4
= ( 6 ± [tex]\sqrt{100}[/tex] ) / 4
= ( 6 ± 10 ) / 4
x = [tex]\frac{6+10}{4}[/tex] = [tex]\frac{16}{4}[/tex] = 4
OR
x = [tex]\frac{6-10}{4}[/tex] = [tex]\frac{-4}{4}[/tex] = - 1
Solution is { 4, - 1 }
According to the rational root theorem which is a factor of the polynomial f(x)=3x^3-5x^2-12x+20
Answer:
[tex]f(x)=3(x+2)(x-2)(x-\frac{5}{3})[/tex]
Step-by-step explanation:
The rational roots theorem tells you that given a polynomial function with integer or whole number coefficients, a list of possible solutions can be found by listing the factors of the constant, or last term, over the factors of the coefficient of the leading term.
In your case, for the polynomial [tex]f(x)=3x^3-5x^2-12x+20:[/tex]
the last term is 20;the leading coeeficient is 3.So, possible rational roots can be among:
[tex]\pm1,\pm2,\pm4,\pm5,\pm10,\pm20,\pm\dfrac{1}{3},\pm\dfrac{2}{3},\pm\dfrac{4}{3},\pm\dfrac{5}{3},\pm\dfrac{10}{3},\pm\dfrac{20}{3}.[/tex]
Note that
[tex]f(-2)=3\cdot (-2)^3-5\cdot (-2)^2-12\cdot (-2)+20=-24-20+24+20=0.[/tex]
This means that [tex]x=-2[/tex] is a root of the polynomial and [tex]x-(-2)=x+2[/tex] is the factor. Also
[tex]f(2)=3\cdot 2^3-5\cdot 2^2-12\cdot 2+20=24-20-24+20=0.[/tex]
This means that [tex]x=2[/tex] is a root of the polynomial and [tex]x-2[/tex] is the factor. Also
[tex]f(\frac{5}{3})=3\cdot (\frac{5}{3})^3-5\cdot (\frac{5}{3})^2-12\cdot \frac{5}{3}+20=\frac{125}{9}-\frac{125}{9}-20+20=0.[/tex]
This means that [tex]x=\frac{5}{3}[/tex] is a root of the polynomial and [tex]x-\frac{5}{3}[/tex] is the factor.
Then
[tex]f(x)=3(x+2)(x-2)(x-\frac{5}{3}).[/tex]
Carl and Laura are reading different copies of the same book. Carl has already read 10 pages of his copy of the book when Laura begins reading her copy of the book. A system of equations can be used to compare the number of pages (y) each person has read x minutes after Laura begins reading her copy of the book. The solution to the system of equations is (40, 50). What does the solution (40, 50) represent in this situation?
a.)Carl and Laura have both read 50 pages after Laura has been reading for 40 minutes.
b.)Carl has read 50 pages and Laura has read 40 pages.
c.)Carl has read 40 pages and Laura has read 50 pages.
d.)Carl and Laura have both read 40 pages after Laura has been reading for 50 minutes.
Final answer:
The solution (40, 50) to the system of equations indicates that after 40 minutes, Laura has read 40 pages and Carl, with a head start, has read a total of 50 pages, option D.
Explanation:
The solution to the system of equations (40, 50) represents the amount of time Laura has spent reading and the number of pages both Carl and Laura have read. In this context, 'x' represents the number of minutes Laura has been reading her copy of the book, and 'y' represents the number of pages each person has read. Therefore, the solution (40, 50) means that after Laura has been reading for 40 minutes, Laura has read 40 pages, and Carl, who had a 10-page head start, has read a total of 50 pages.
what's 22 * 19 + area model
Answer:
(20+2)(10+9)
Step-by-step explanation:
The area model is written as (a+b)(c+d). To write a multiplication problem into an area model, split it into numbers which add to it. Multiples of 10 are most commonly used.
For example 22*19 becomes (20+2)(10+9).
which of the following represents the best way to calculate the area of the shaded region?
Errrrrrr what following. I know that you need to separate the parts into simple shapes eg:triangle and then find the area of all the shapes and add up. All the shapes should make up the shaded area.
Answer:
b
Step-by-step explanation:
Sally has a part-time job mowing lawns. She charges $5 per hour.
If she has $242 at the end of the month how long has she spent mowing lawns In hours AND minutes?
Answer:48 hours and 24 minutes
Step-by-step explanation:
Yuki picked strawberries and placed them in a basket. Yuki ate 12 of the 30 strawberries she picked. What percentage of the strwaberries she picked remain in her basket?
A: 12%
B: 30%
C: 60%
D: 100%
It's C that's correct!
Since there's a total of 30 strawberries and Yuki ate 12 strawberries, there will be 18 strawberries left.
To find the percentage of the amount that remained:
18/30 × 100 = 60%
Therefore the correct option is A
Answer:
Yuki picked strawberries and placed them in a basket. Yuki ate 12 of the 30 strawberries she picked. What percentage of the strwaberries she picked remain in her basket?
A: 12%
B: 30%
C: 60%
D: 100%
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
30 - 12 = 18
18 / 30 × 100 = 60
is paid an annual salary of $26,000. Find the Pat's weekly salary
Answer:500
Step-by-step explanation:26,000/52=500 i did $26,000 divided by 52 because there are 52 weeks in a year and it gave me 500 so that is how i got the answer
There are 52 weeks in a year, so the annual salary is 52 times the week salary.
So, we have
[tex]\dfrac{26000}{52} = 500[/tex]
which means that Pat makes 500$ a week
-10x < 40
What is the solution to this inequality?
Answer:
[tex]x>-4[/tex]
Step-by-step explanation:
Solve like a normal equation by isolating the variable and then dividing by the coefficient.
[tex]-10x<40 \\ \\ x>-4[/tex]
Answer:
x > - 4, or it can be written as (- 4, ∞)
Step-by-step explanation:
- 10x < 40
-10x/10 < 40/10
- x< 4
x > -4
You start driving north for 32 miles, turn right, and drive east for another 24 miles.
How many miles must you travel to return directly back to your starting point?
Answer:
40 miles
Step-by-step explanation:
You can recognize the right triangle as a 3-4-5 right triangle with a scale factor of 8. So the length of the hypotenuse is 8·5 = 40 miles.
___
Or, you can use the Pythagorean Theorem, which tells you that the sum of the squares of the leg distances will equal the square of the straight-line (hypotenuse) distance:
32² + 24² = h²
1024 +576 = h² = 1600
h = √1600 = 40 . . . . miles
Factor completely 3x3 − 6x2 − 24x. 3x(x − 4)(x + 2) 3x(x + 4)(x − 2) 3x(x − 3)(x − 2) 3x(x + 3)(x − 2)
Answer:
3x(x - 4)(x + 2)
Step-by-step explanation:
Given
3x³ - 6x² - 24x ← factor out common factor of 3x from each term
= 3x(x² - 2x - 8) ← factor the quadratic
Consider the factors of the constant term (- 8) which sum to give the coefficient of the x- term.
The factors are - 4 and + 2, since
- 4 × 2 = - 8 and - 4 + 2 = - 2, thus
x² - 2x - 8 = (x - 4)(x + 2) and
3x³ - 6x² - 24x = 3x(x - 4)(x + 2)
Answer:
3x(x - 4)(x + 2)
Step-by-step explanation:
Which of the following best represents the slope of the line? A. -3 B. - 1 3 C. 1 3 D. 3
Answer: - 1/3 I just saw the other answer and got it wrong so I decided to give u guys the right answer !! :)
Which quantity is proportional to 90⁄2? Check all that are true. 45⁄1 15⁄3 180⁄3 180⁄4 270⁄8
Answer:
45/1 and 180/4
Step-by-step explanation:
1. True
[tex]\dfrac{90}{2}=\dfrac{45\cdot 2}{1\cdot 2}=\dfrac{45}{1}[/tex]
2. False
[tex]\dfrac{15}{3}=\dfrac{3\cdot 5}{3\cdot 1}=\dfrac{5}{1}\neq \dfrac{45}{1}[/tex]
3. False
[tex]\dfrac{180}{3}=\dfrac{60\cdot 3}{3\cdot 1}=\dfrac{60}{1}\neq \dfrac{45}{1}[/tex]
4. True
[tex]\dfrac{180}{4}=\dfrac{45\cdot 4}{1\cdot 4}=\dfrac{45}{1}[/tex]
5. False
[tex]\dfrac{270}{8}=\dfrac{135\cdot 2}{4\cdot 2}=\dfrac{135}{4}\neq \dfrac{45}{1}[/tex]