Answer:
9 is the least common denominator for the given equationStep-by-step explanation:
Given equation is StartFraction 2 Over 9 EndFraction x + two-thirds x = 7.
It can be written as [tex]\frac{2}{9}x+\frac{2}{3}x=7[/tex]
To find the least common denominator for the given equation :That is to find the Least common Multiple of the denominators.
[tex]\frac{2}{9}x+\frac{2}{3}x=7[/tex]
[tex]\frac{2x+2x(3)}{9}=7[/tex] ( here LCM of 9 and 3 is 9 so we take 9 as LCM )
Therefore 9 is the least common denominator for the given equationAnswer: the answer is 9
Step-by-step explanation: I took the test and its right
attached is the problem, and possible answers, please solve and check
Answer:
Option B
Step-by-step explanation:
Using the law of logarithms
[tex]n log x= log x^{n}[/tex]
Therefore, since all the logs are to the same base, I will assume the base.
Also, when the bases are the same
log y+ log x= log (x+y)
[tex]\frac {1}{2}(log 4+ log 16)=log 4^{0.5}+log 16^{0.5}=log 2+log 4=log 6[/tex]
Now log 6-log 2= log (6-2)= log 4
Therefore, option B is correct
In the coordinate plane, what is the length of the line segment that connects points at (0,-1) and (-7, -2)?
Enter your answer to the nearest hundredth.
Answer:100cm
Step-by-step explanation:
compare. Write <,>,or=
2/6. 2/4
Answer:
2/6<2/4
Step-by-step explanation:
We can start by simplifying the two fractions. 2/6=1/3 and 2/4=1/2. 1/3<1/2 so 2/6 is smaller than 2/4.
The formula for the area of a triangle is A=12bh .
Find the area of a triangle with a base (b) of 7 feet and a height (h) of 12 feet.
The area of the triangle is _____ square feet
Answer: 42 square feet.
Step-by-step explanation:
1/2 times 12 times 7 is 42.
Answer:
42
Step-by-step explanation:
mike bought some t-shirts at a department store. Mike gave the cashier $100 and received $25 in change. The price of the T-shirt was $25, how many T-shirts did he buy
What is the unknown factor that makes each of the following statements true?
5-х = ? (х-5)
b-k= ? (k-b)
– 3х +7 = ? (3х – 7)
A. -1/2
B. 1
C. -2
D.-1
Answer:
-1 case D)
Step-by-step explanation:
5-x=-(x-5) so the unknown factor is -1
b-k=-(k-b), again, -1
Similar for third case.
What are the slope and y-intercept of the line 4y = –x – 32?
Answer: Slope: -1/4
Y-intercept: -8
Answer:Dante’s soccer team sells T-shirts to raise money for new equipment. For each T-shirt sold, the team raises $8. Parents also make a donation of $100 toward the equipment.
What is the equation that represents the total amount raised, y, if x T-shirts are sold?
Step-by-step explanation:
A soda can is the shape of a cylinder. It has a diameter of 8 centimeters and a volume of 653.12 cm³. What is the lateral surface area of the soda can? *
Answer:
326.56
youre welcome
Step-by-step explanation:
5y+1=1
Subtract 1 from both sides
Step-by-step explanation:
[tex]5y + 1 = 1 \\ subtracting \: 1 \: from \: both \: sides \\ \red{ \boxed{ \bold{ 5y + 1 - 1 = 1 - 1}}} \\ 5y = 0 \\ y = 0[/tex]
What is the slope of a line that is parrallel to the line y=3/4x+2 ?
Answer:
3/4
Step-by-step explanation:
Parallel lines will always have the same slope, but their y-intercepts can be any real number.
Jill is 18 years old. Her sister is 3 years old. How many times older is Jill than her sister?
Answer:
6
Step-by-step explanation:
18/3=6 You have to divide 18 by 3 in order to know how many times older Jill is than her sister.
Graph the quadratic inequality.
y>x2 - 6x + 11
Answer:
put the ^ when you do exponents!
Step-by-step explanation:
There are three parts to graphing an inequality.
1. determine if the line will be dashed or solid
2. determine where you will shade in
3 graph with the appropriate line and shade
1. it is just > and not ≥ so the line will be dashed, which means the line itself is not part of the answer.
2. it is y> so you shade in the area inside the parabola. if y was an actal number it might be more complicated
3. graph x^2 - 6x + 11. If that seems a bit hard, put it into vertex form by completing the square.
y = x^2 - 6x + 11
y = (x - 3)^2 +2
Since x^2 is positive it opens upward and then plug in 0 for x and y in y = (x - 3)^2 +2 to get the x and y intercepts and the -3 and +2 tells you the vertex (in this case the minimum) is at (3,2), then remember the points are mirrored on either side of the vertex. so if the y intercept is 2 to the left and one higher than the vertex, there will also be a point 2 to the RIGHT and 1 up. then just connect the dots. Keep in mind there may not be any x intercepts if it never goes below the x axis *hinthintwinkwink*
if all else fails just graph a handful of points to get the idea of the shape. Just remember you are shading inside of the parabola and using dashed lines.
Divide 275 into two parts which are in the ratio 4:7?
Answer:
100 : 175
Step-by-step explanation:
Divide 275 into two parts which are in the ratio 4:7?
To divide 275 into 4 :7, we will follow the steps below
First, We will add the ratio numbers together, that is; 4 + 7 = 11
4 : 7 of 275 will be;
4/11 × 275
=4 × 275 / 11
=1100/11
=100
Then we will now proceed to the second part;
7/11 × 275
= 7 × 275 / 11
=1925/11
=175
Therefore dividing 275 into 4 : 7 yields 100 : 175
A stocks value decreased the same amount each day for 4 days. If the total change in value was -2.5 what was the change each day?
Answer:
-0.625
Step-by-step explanation:
The stock's value decreased by -0.625 each day over a period of four days, calculated by dividing the total decrease of -2.5 by the number of days.
Explanation:The student's question pertains to finding the amount by which a stock's value decreased each day over four days, given that the total decrease was -2.5. To solve this problem, we use the concept of an arithmetic series, where each term changes by a constant difference. Since we know the total change in the stock's value was -2.5 over four days, we divide the total change by the number of days to find the daily change.
To calculate the change in stock value each day, we can use the formula:
Daily Change = Total Change / Number of Days
Plugging the values into the formula, we get:
Daily Change = -2.5 / 4 = -0.625
Therefore, the stock value decreased by -0.625 each day for the 4-day period.
Frank suspects a function he created to predict the population of bacteria is flawed. His data indicates the population began with 150 cells and grew by 20 percent every hour. His prediction function is "The population of bacteria is B(h) = 150(.2)h after h hours." What is Frank's error?
Frank's error is that his function suggests a linear growth model instead of an exponential one. The correct function should be B(h) = 150 * (1.2)^h to represent an exponential growth where the population increases by 20 percent every hour.
Explanation:Frank's error in his prediction function lies in the incorrect representation of the exponential growth of bacteria. His function reads B(h) = 150(.2)h, which implies a linear growth model, adding only 20% of the original amount, rather than a certain percentage of the current population. In reality, as the context describes the bacteria population growing by 20 percent every hour, the function should represent an exponential growth model accurate to the situation. Hence, the correct function should be B(h) = 150 * (1.2)^h, where 1.2, which signifies 120 percent (the original 100% plus the additional 20%), raised to the power h, accounts for the continuous multiplication or compounding of the bacteria every hour.
Learn more about Exponential Growth here:https://brainly.com/question/12490064
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Frank's error lies in the formulation of his prediction function. It should reflect exponential growth rather than linear growth. The population is 1.20 times what it was the previous hour, not 0.20 times.
The function he created, [tex]\( B(h) = 150(0.2)^h \),[/tex] incorrectly implies that the population increases by a factor of 0.2 each hour, which would represent a decrease since 0.2 is less than 1. Additionally, the initial population is multiplied by 0.2 instead of being increased by 20% each hour.
The correct way to model the population growth, assuming it grows by 20% each hour, is to use an exponential growth formula where the population is multiplied by [tex]\( 1 + \text{growth rate} \)[/tex] each hour that passes. Since the growth rate is 20%, or 0.20 in decimal form, the correct prediction function should be: [tex]\[ B(h) = 150(1 + 0.20)^h \][/tex]
This can be simplified to: [tex]\[ B(h) = 150(1.20)^h \][/tex]
This function correctly represents a 20% increase in the population each hour, starting with an initial population of 150 cells.
Frank's error was in the growth factor used in his function. It should have been [tex]\( 1 + \text{growth rate} \)[/tex] (which is 1.20 for a 20% increase) instead of just the growth rate (0.20). The correct function reflects that each hour, the population is 1.20 times what it was the previous hour, not 0.20 times.
simplify the quotient 3^1 divided by 3^4
Answer:
1/243 for edge
Step-by-step explanation:
The simplified form of the quotient 3⁻¹ divided by 3⁴ is 1/243.
What is the quotient?A quotient is defined as when dividing one number by another, the result is called the quotient.
To simplify the quotient 3⁻¹ divided by 3⁴, we can use the rule that says when we divide two exponential expressions with the same base, we can subtract their exponents.
So, we have:
3⁻¹ ÷ 3⁴
3⁻¹ divided by 3⁴ = 3⁻¹⁻⁴
Now, we can simplify the expression by subtracting the exponents:
3⁻¹⁻⁴ = 3⁻⁵ = 1/3⁵ = 1/243
So, the simplified form of the quotient 3⁻¹ divided by 3⁴ is 1/243.
Learn more about quotient here:
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Which eaquation would best help solve the following problem the height of a triangle is 6 meters more than its base The area of the triangle is 56 m^2
Answer:
X²+6X=112
Step-by-step explanation:
area=1/2 base x height
56=x(x=6)/2
Multiply each side by two to eliminate the denominator
112=x(x=6)
112=x²+6x
John earns a base pay of $275 per week plus an 8% commission on all of his sales. Write an inequality that represents the minimum amount of sales, s, that John must earn to make more than $560 per week. *
Answer:
8% is 0.08
275 + 0.08s > 560
0.08s > 285
s > 3562.5
A rectangular piece of paper is 6 inches wide and 8 inches long. A square with a side of 3/4 inch is cut out from each of the four corners. How much paper is left after the corners are removed?
Answer:
45 in.
Step-by-step explanation:
6 x 8 = 48
.75 x 4 = 3
48 - 3 = 45
45 inches left
After cutting out four square corners, each with a side length of 3/4 inch from a 6 by 8 inches rectangular piece of paper, 45.75 square inches of paper is left.
To solve how much paper is left after the corners are removed, we need to calculate the total area of the paper and subtract the total area of the corners that were cut out.
The original dimensions of the paper are 6 inches by 8 inches, so its total area is:
Area of rectangle = width times length = 6 inches times 8 inches = 48 square inches.
Each corner is a square with a side of 3/4 inch, so the area of one corner is:
Area of one square corner = (3/4 inch) times (3/4 inch) = 9/16 square inches.
Since there are four corners:
Total area removed = 4 inches (9/16 square inches) = 9/4 square inches = 2.25 square inches.
Finally, subtract the area removed from the total area to find the remaining area:
Remaining area = Total area of rectangle - Total area removed
Remaining area = 48 square inches - 2.25 square inches = 45.75 square inches.
Therefore, after cutting out the corners, 45.75 square inches of paper is left.
What is 30% of 120 is what number?
Answer:
36
Step-by-step explanation:
30% as a decimal is 0.30, take that and multiply it by 120 to find 30% of 120
120 × 0.30 = 36
Subtract (6a^2+3a) - (4a^2 + 2a)
Answer:
2a² + a ( or a(2a+1) )
Step-by-step explanation:
(6a²+3a) - (4a² + 2a) (expand parentheses)
= 6a²+3a - 4a² - 2a (group like terms)
= 6a²- 4a²+3a- 2a
= 2a² + a
= a(2a+1)
Answer:
2a^2+a
Step-by-step explanation:
This is an algebra. An algebra is an expression with no equality sign, and it will be expressed till the simplest form.
(6a^2+3a) - (4a^2 + 2a)
Remove the brackets
6a^2+3a-4a^2-2a
6a^2-4a^2+3a-2a
2a^2+a
Which number sentence is NOT an inequality?
A. X + 5.4 > 8
B. 1/4 (x - 5) = 13
C. 3x + 7.5<9
D. 1/2x - 19 > 24
Answer:
Option B, 1/4 (x - 5) = 13
Step-by-step explanation:
An inequality has a less than, greater than, less than or equal to, and greater than or equal to. But, there are no equal signs allowed in a inequality. That makes it an expression.
Answer: Option B, 1/4 (x - 5) = 13
Answer:
B
Step-by-step explanation:
When creating vases for the craft fair, Thomas used the proportion 3 pounds of clay is to 8 vases as 9 pounds of clay is to 24 vases. Which proportion can be used to represent the situation? StartFraction 3 over 8 EndFraction = StartFraction 24 over 9 EndFraction StartFraction 3 over 8 EndFraction = StartFraction 9 over 24 EndFraction StartFraction 3 over 9 EndFraction = StartFraction 24 over 8 EndFraction StartFraction 9 over 3 EndFraction = StartFraction 8 over 24 EndFraction
Answer:
The correct answer is B. 3/8 = 9/24
Six times a number plus three times a second number is 27. The second
number is one more than two times the first number. What is the second
number?
Answer:5 1/3
Step-by-step explanation:
number = n
second number = s
6n + 3s = 27
2n + 1 = s
6n + 3(2n + 1) = 27
6n + 6n + 1 = 27
12n = 26
n = 26/12
n = 2 1/6
2(2 1/6) + 1 = s
4 1/3 + 1 = s
5 1/3 = s
Final answer:
To find the second number, we create a system of linear equations using the given information and solve for the variables. The solution shows that the second number is 5.
Explanation:
The student's question involves setting up a system of two linear equations and solving them to find the values of two unknown numbers.
Let the first number be x and the second number be y. We are given the following equations based on the problem:
6x + 3y = 27
y = 2x + 1
First, we can substitute the second equation into the first to solve for x:
6x + 3(2x + 1) = 27
6x + 6x + 3 = 27
12x + 3 = 27
12x = 24
x = 2
Now, substitute x = 2 into the second equation to find y:
y = 2(2) + 1
y = 4 + 1
y = 5
Therefore, the second number, y, is 5.
on a triangle which segment appears to be perpendicular to segment bc? tirangle has abc.
Answer:
attatch a picture
line AB im assuming
Step-by-step explanation:
How many solutions are there to the equation n^2-13n=-40
Answer:
n = 5
n = 8
Step-by-step explanation:
n^2 - 13n = -40
Equate everything to zero
n^2 - 13n + 40 = 0
Factorise
(n - 5)(n - 8) = 0
Either
n - 5 = 0
Add 5 to both sides
n - 5 + 5 = 0 + 5
n = 5
Or
n - 8 = 0
Add 8 to both sides
n - 8 + 8 = 0 + 8
n = 8
n = 5 or
n = 8
It has two real solutions
1. Mike and Lisa Lerner had combined wages of $91,301 last year. They also had a bank interest of $792 and
$667. They received stock dividends of $287 and $530. During the year, Lisa won a $1,000 prize. Find the
total income from wages, bank interest, dividends, and the prize.
Answer:
The total income from wages, bank interest, dividends, and the prize = $ 94577
Step-by-step explanation:
Total wages of Mike and Lisa in last year = $ 91301
Total bank interest of Mike and Lisa = $ 792 + $ 667 = $ 1459
Total income from dividends = $ 287 + $ 530 = $ 817
Prize of Lisa won = $ 1000
Thus the total income from wages, bank interest, dividends, and the prize =
$ 91301 + $ 1459 + $ 817 + $ 1000 = $ 94577
Final answer:
The total income from wages, bank interest, dividends, and the prize is $94,577.
Explanation:
To find the total income from wages, bank interest, dividends, and the prize, we need to add up all the amounts mentioned.
First, we add Mike and Lisa's wages: $91,301. Then we add their bank interests: $792 + $667 = $1,459. Next, we add their stock dividends: $287 + $530 = $817.
Finally, we add Lisa's prize: $1,000. Adding all these amounts together, the total income from wages, bank interest, dividends, and the prize is $91,301 + $1,459 + $817 + $1,000 = $94,577.
solve the following: -7x + 5 = 8x - 25
Good morning ☕️
Answer:
2Step-by-step explanation:
-7x + 5 = 8x - 25
then
25 + 5 = 8x + 7x
then
15x = 30
then
x = 2
___________________
:)
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
Given equation:
[tex]-7x + 5 = 8x - 25[/tex]
To find the value of 'x', take the terms of 'x' to one side and the constants to the other side:
Subtracting '[tex]5[/tex]' to both side:
[tex]-7x+5-5=8x-25-5\\\\-7x=8x-30[/tex]
Subtracting '[tex]8x[/tex]' both side:
[tex]-7x-8x=8x-8x-30\\\\-15x=-30[/tex]
[tex]x=\frac{-30}{-15}[/tex]
[tex]x=2[/tex]
what is 6 2/3 x 2 1/2 if you answer you will get 35 poinst
mixed fraction [tex]16\frac{2}{3}[/tex]
Step-by-step explanation:
Decimal Form: 16.666667
What is the Approximate volume of the sphere below?
Answer:
16.75
Step-by-step explanation:
do pie times 4/3 times the radius and you will get your answer
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3} \\\\\\ V=\cfrac{256\pi }{3}\implies V\approx \stackrel{in^3}{268.08}[/tex]