Answers
area of a triangle is 1/2 x base x height
c would be the base and x is the height
so 1/2cx is the expression needed
Related Questions
What causes water molecules to stick together in liquid water?
A. Water vapor
B. Carbon dioxide
C. Sun's gravity
D. Hydrogen bonds
Answers
Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week. Part A: Create an equation that shows the amount of wages earned, W, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours. (3 points) Part C: Andrew earned $330 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)
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For Part A, all you need to do is write out an equation for how many dollars Andrew would make for x hours during regular hours (not overtime). Since he makes 6 dollars per hour, this will be 6x.
W = 6x
For Part B, create a similar equation for overtime hours. Overtime hours only apply after Andrew has worked 40 hours, so plug that into your first equation and add that to the second equation.
W = 6x
W = 6(40)
W = 240
S = 240 + 9y
For Part C, consider what we now know. If Andrew earns any money over 240 dollars (which is how much he earns after 40 hours), we know he worked overtime. So, we can just plug 330 into the second equation for S and solve for the number of additional hours he worked, y.
330 = 240 + 9y
– 240 – 240
90 = 9y
9 9
10 = y
Now, we can add up the initial 40 hours plus the additional 10 hours, which is 50 hours total.
Hope this helped you out! :-)
Your goal is to save at least $240.00 over the next 4 week. How much money must you save each week in order to meet that goal? Write and solve an inequality
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So at least $60/week (notice the = sign, because it at at least, and not 'more than')
The solution is x ≥ $ 60
The value of the inequality equation is x ≥ 60
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Let the minimum money per week to be saved be = x
The number of weeks = 4
The goal is to save at least $240.00 over the next 4 week
So , substituting the values in the equation , we get
x ≥ 240 / number of weeks
x ≥ 240 / 4
On simplifying the equation , we get
x ≥ 60
Therefore , the value of A is x ≥ 60 and should save a minimum of $ 60 per week
Hence , the inequality equation is x ≥ 60
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Double-checking my answer.. Given 3^2x = 9^6, what value of x satisfies this equation? (Use Laws of Exponents).
Thanks:)
Answers
Solve for X:
3^2x = 9^6
Simplify
9x=9^6
9x=531441
Divide both sides by 9.
(9x)/9=(531441)/9
x=59049
Hope this helps!
-Benjamin
Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earning the same interest. let m represent the balance in martin’s account and let c represent the amount of money in cary’s account. choose the pair of expressions that describe the accounts y years after martin opened his account. martin: 200(1.05)y cary: 200(1.05)y+4 martin: 200(1.05)y+4 cary: 200(1.05)y–4 martin: 200(0.05)y cary: 200(0.05)y–4 martin: 200(1.05)y cary: 200(1.05)y–4
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year interest balance
1 200 * 5% 200(1.05)
2 200(1.05) * 5% 200(1.05)^2
3 200(1.05)^2*5% 200(1.05)^3
y 200(1.05)^y
=> m = 200 (1.05)^y
four years later, cary deposits $200 in an account earning the same interest.
year interest balance
5 200 * 5% 200(1.05)
6 200(1.05) * 5% 200(1.05)^2
7 200(1.05)^2*5% 200(1.05)^3
y 200(1.05)^(y-4)
=> c = 200(1.05)^ (y-4)
Answer:
Martin: 200(1.05)^y
Cary: 200(1.05)^(y–4)
Answer:
d then d again
Step-by-step explanation:
Luisa knit a rectangular scarf that measures 4 feet by 1 foot. She wants to use the remaining 6 square feet of fabric to create a border around the scarf.
Which equation can she use to find the required width of the border x?
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To solve this problem, let us recall that the formula for Area of a rectangle is:
A = l * w
Where,
l = length of one side = 4 ft
w = width of one side = 1 ft
Therefore the original area is:
Ao = 4 ft * 1 ft
Ao = 4 ft^2
Since each border would be increased by x, therefore the new l and w would be:
l = 4 + 2x
w = 1 + 2x
The new area becomes:
A = (4 + 2x) (1 + 2x)
The difference of the two would be the area of the remaining scarf:
A – Ao = 6 square ft
(4 + 2x) (1 + 2x) – 4 = 6 ---> 1
(4 + 2x) (1 + 2x) = 10 ---> 2
The equation to use can be equation 1 or equation 2.
A choir has 3 spots open for altos, and 8 altos are interested in them. In how many ways can the open spots be filled?
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n!/(k!(n-k)!), n=number of elements to choose from, k=number of choices made
In this case:
8!/(3!(8-3)!)
56
So there are 56 unique threesomes possible with 8 members.
There are total 56 ways to fill the open spot .
What is combination?
A combination is a way for determining the number of possible arrangements in a collection of items where the order of selection does not matter.
Formula for combination[tex]C(n, r) =\frac{n!}{(n - r)!r!}[/tex]
where,
n is the number of items in set.
r is the number of items selected from the set.
According to the question we have,
Number of altos, n = 8
Number of open spots, r = 3
Therefore, the number of ways to fill open spots = C(8, r)
Number of ways = [tex]\frac{8!}{3!(8-3)!}[/tex]
Number of ways = [tex]\frac{8!}{5!3!}[/tex][tex]= \frac{(8)(7)(6)(5!)}{5!3!}[/tex] = [tex]\frac{(8)(7)(6)}{(3)(2)} =8(7) = 56[/tex]
Hence, there are total 56 ways to fill the open spot .
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Please, would somebody help me solve this math problem? I have no idea how to solve it.
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Plug in the values
(2x+2)(2x)/2
(4x^2+4x)/2
2x^2+2x
Final answer: B
Given a group of 8 women and 11 men, how many different ways are there of choosing one man and one woman for a committee?
Answers
Final answer:
There are 88 different ways of choosing one man and one woman for a committee.
Explanation:
In order to find the number of different ways of choosing one man and one woman for a committee, we can use the concept of combinations. The number of ways of choosing one item from a group of n items is denoted by n C 1, which is equal to n. So, the number of ways of choosing one man from a group of 11 men is 11, and the number of ways of choosing one woman from a group of 8 women is 8. To find the total number of ways, we multiply these two numbers:
Total number of ways = 11 * 8 = 88
Therefore, there are 88 different ways of choosing one man and one woman for a committee.
The function $f : \mathbb{r} \rightarrow \mathbb{r}$ satisfies $f(x) f(y) - f(xy) = x + y$ for all $x$, $y \in \mathbb{r}$. find $f(x)$.
Answers
(05.01 MC)
The table and the graph each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,210 and 4,280 and 5,350 and 6,420. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 550 in increments of 110 for each grid line. A line passing through the ordered pairs 2, 110 and 4, 220 and 6, 330 and 8, 440 is drawn.
How much more would the value of y be in the table than its value on the graph when x = 11?
100
165
395
440
Answers
The value of y in the table is 165 more than the value of y in the graph
The points on the table are represented as:
(3,210) and (4,280)So, the equation of the table is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{280 - 210}{4 - 3} (x - 3) + 210[/tex]
[tex]y = 70(x - 3) + 210[/tex]
Expand
[tex]y = 70x - 210 + 210[/tex]
[tex]y = 70x [/tex]
When x = 11,
We have:
[tex]y = 70 \times 11[/tex]
[tex]y = 770[/tex]
The points on the graph are represented as:
(2,110) and (4,220)So, the equation of the graph is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{220 - 110}{4 - 2} (x - 2) + 110[/tex]
[tex]y = 55 (x - 2) + 110[/tex]
Expand
[tex]y = 55x - 110 + 110[/tex]
[tex]y = 55x[/tex]
When x = 11,
We have:
[tex]y = 55 \times 11[/tex]
[tex]y = 605[/tex]
Calculate the difference between the y-values
[tex]y_2 - y_2 =770 - 605[/tex]
[tex]y_2 - y_2 =165[/tex]
Hence, the value of y in the table is 165 more than the value of y in the graph
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he time spent dancing (minutes) and the amount of calories burned can be modeled by the equation c = 5.5t. Which table of values matches the equation and includes only viable solutions? Image for option 1 Image for option 2 Image for option 3
Answers
Answer:
0 0
5 27.5
10 55
15 82.5
Step-by-step explanation:
Why is world population distribution uneven what factors contribute to this uneven distribution?
Answers
HELP If f(x)=15x+3, then f^-1(x)=?
Answers
PM me
The inverse of the function f(x) = 15x + 3 is found by swapping x and f(x) in the equation and solving for f^-1(x), which leads to f^-1(x) = (x - 3) / 15.
Explanation:To find the inverse of the function f(x) = 15x + 3, it is necessary to first swap x and f(x) in the function equation. This results in x = 15f^-1(x) + 3. Secondly, solving for f^-1(x) means isolating this on one side of the equation. That results in f^-1(x) = (x - 3) / 15.
So, the inverse function of f(x) = 15x + 3 is f^-1(x) = (x - 3) / 15.
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For each equation below find y if x=2
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B - would be 2 to the second - 1 = 3
What is the midpoint of (4,8) and (3,12)
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Please solve for c :3
3c - 2 = 5(c+2)
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First of all, solve 5(c+2) by applying the distributive property.
I mean, 5*c and 5*2
So rewrite:
3c - 2 = 5c + 10
Now, you have to solve for c and then move all the Cs to the left of equal and change them sign, same to all known terms but move them to the right instead!
3c - 5c = 10 + 2
-2c = 12
The c can't be negative so divide both terms for -1
2c = -12
divide both terms for 2
2c/2 = -12/2
c = -6
Find the difference.
Correct and best explained answer gets brainliest.
Answers
(-3x^4-9x^3-4x^2-4)-(5x^3-7x^2+6)
= -3x^4-9x^3-4x^2-4-(5x^3-7x^2+6)
= -3x^4-9x^3-4x^2-4-5x^3+7x^2-6
=-3x^4-14x^3+3x^2-10
hence, option D is the answer.
HOPE IT HELPED :D ☺☺
The product of the roots of 8x² - 2x = 1 is:
Answers
Answer:
[tex]\text{Product of its zeros = }\frac{-1}{8}[/tex]
Step-by-step explanation:
The quadratic equation is given to be : 8x² - 2x = 1
We need to find the product of its zeros
First finding the number of zeros :
⇒ 8x² - 2x - 1 = 0
⇒ 8x² - 4x + 2x - 1 = 0
⇒ (4x + 1)(2x - 1) = 0
[tex]\implies x = \frac{-1}{4}\:\:and\:\: x = \frac{1}{2}[/tex]
[tex]\text{Product of its zeros = }\frac{-1}{4}\times\frac{1}{2}=\frac{-1}{8}[/tex]
Which polynomial is a perfect square trinomial? (1 point) 49x2 − 28x + 16 4a2 − 20a + 25 25b2 − 20b − 16 16x2 − 24x − 9?
Answers
4a² − 20a + 25 =
(2a)² - 2*2a*5 + 5² =
(2a - 5)²
what is the x-intercept of the graph of the function f(x)=x2-16x+64?
Answers
Answer:
x-intercept: (8,0)
Step-by-step explanation:
Given: [tex]f(x)=x^2-16x+64[/tex]
For x-intercept, Put y=0 and solve for x.
x-intercept: It is a point where y-coordinate zero.
[tex]x^2-16x+64=0[/tex]
[tex]x^2-8x-8x+64=0[/tex]
[tex](x-8)(x-8)=0[/tex]
Equate each factor to 0 and solve for x
x-8 = 0 , x-8 = 0
x=8,8
x-intercept: (8,0)
Hence, The x-intercept is 8.
The x-intercept of the function is 8
The equation of the function is given as:
[tex]f(x) = x^2 - 16x + 64[/tex]
Expand the equation
[tex]f(x) = x^2 - 8x - 8x + 64[/tex]
Factorize the above equation
[tex]f(x) = x(x - 8) - 8(x -8)[/tex]
Factor out x - 8
[tex]f(x) = (x - 8) (x -8)[/tex]
Set f(x) to 0, to calculate the x-intercept
[tex](x - 8) (x -8)=0[/tex]
Rewrite as:
[tex](x - 8)^2=0[/tex]
Take the square roots of both sides
[tex]x - 8=0[/tex]
Solve for x
[tex]x = 8[/tex]
Hence, the x-intercept of the function is 8
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A circle has a center of (5,-5) and goes through (6,-2). What is the radius?
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The distance between points O and P, that is |OP|, is the radius of this circle,
We use the distance between 2 points formula:
|OP|=[tex] \sqrt{ (x_2-x_1)^{2} + (y_2-y_1)^{2} }= \sqrt{ (6-5)^{2} + (-2-(-5))^{2} }[/tex]
[tex]= \sqrt{ 1^{2}+ (-2+5)^{2}} = \sqrt{1+9}= \sqrt{10} [/tex] (units)
Answer: [tex]\sqrt{10} [/tex] units
Line segment
a.a series of points that extend in two directions without end plane
b.two lines that intersect at 90° angles perpendicular lines
c.lines that lie in the same plane and do not intersect line
d.a flat surface that extends infinitely and has no thickness parallel lines
e.part of a line that has two endpoints
Answers
Point A and Point B are two points on Line L
The line between point A and point B that is also a part of Line L is called line segment
The correct definition of a line segment is given by the option e)
Line segment is a part of a line that has two end points
There are 20 wild pigs on an island and the number of pigs doubled each year for the past 5 years. The independent variable is
Answers
The independent variable is time.
Answer:
The independent variable is time.
Step-by-step explanation:
Given,
The original number of pigs on the island = 20,
Also, the number of pigs doubled each year,
After 1 year the pigs = 20(2),
After 2 years = 20(2)²,
After 3 years = 20(2)³,
......................., so on...
Similarly, the number of pigs after t years would be,
[tex]y=20.2^t[/tex]
⇒ The value of y depends upon t,
⇒ The number of pigs depends upon the time ( in years ),
Since, the variable in which the other variable depends is called independent variable,
Hence, the independent variable must be time.
The relationship between feet and inches is described by the equation y = 12x, where x = a given length in feet and y = the equivalent length in inches. If a table is 7.25 feet long, what is its length in inches? A. 84 inches B. 87 inches C. 81 inches D. 90 inches
Answers
The length of the table in inches is 87 inches.
Explanation:To solve this problem, you can use the equation y = 12x to convert the length from feet to inches. Given that the table is 7.25 feet long, you can substitute x = 7.25 into the equation to find y.
y = 12(7.25) = 87
Therefore, the length of the table in inches is 87 inches.
A mother gives birth to a 9 pound baby. every 4 months, the baby gained 2 pounds. if x is the age of the baby in months, then y is the weight of the baby in pounds. find an equation of a line in the form y = mx + b that describes the baby's weight.
Answers
slope = (11 - 9) / ( 4 - 0) = 2/4 = 0.5
at x = 0, it is said that the weight of the baby is 9 lbs so the value of b would be 9.
The equation of the line would be y = 0.5x + 9
Final answer:
The equation of the line that represents the baby's weight as it grows is y = 0.5x + 9, where x is the age of the baby in months, and y is the weight of the baby in pounds.
Explanation:
The student is looking for an equation of a line that represents the weight of a baby as it grows. This situation can be described using a linear equation in the form of y = mx + b, where y represents the weight of the baby in pounds, x represents the age of the baby in months, m is the rate at which the baby gains weight, and b is the initial weight of the baby at birth.
Given that the baby weighs 9 pounds at birth, we have our b value as 9. It is also given that the baby gains 2 pounds every 4 months, which can be converted to a monthly weight gain of ½ pound per month (since 2 pounds ÷ 4 months = ½ pound per month). Consequently, the value of m is ½ or 0.5.
Using these values, the equation of the line that describes the baby's weight over time can be written as:
y = 0.5x + 9
This equation indicates that the baby's weight (y) is 9 pounds at birth (when x = 0) and increases by 0.5 pounds each month.
What 12 multiplied by 3
Answers
An __________ is used to indicate the repeating part of a repeating decimal.
Answers
What is the area of the polygon given below?
Answers
(4*7)+(13*9)+(6*6)=181
Answer:
181 square units
Step-by-step explanation:
What do the parallel lines shown on segment BD and segment DC represent? _____________________
Answers
the 2 parallel lines mean that the lines are equal
SO since BD = 18, DC is also 18
BD = 18 = DC
Thus, correctly assuming that the point D is the mid point of line segment BC.