Subtract 1/3 from both sides
x/12 = 5/6 - 1/3
Simplify 5/6 - 1/3 to 1/2
x/12 = 1/2
Multiply both sides by 12
x = 12 × 12
Simplify 1/2 × 12 to 12/2
x = 12/2
Simplify 12/2 to 6
x = 6
2/3m-4/5-3/5m need answer ASAP
Combine Like Terms:
2/3m+-4/5-3/5m
=(2/3m+-3/5m)+(-4/5)
=1/15m+-4/5
Answer:
-1/5m-4/5
Step-by-step explanation:
Is there an outlier in the data set? Explain your reasoning.
Answer:
no
Step-by-step explanation:
there is not one point that is very distant from all of the other ones
no there is not an outlier :)
Please help me out
Which of these inequalities are equivalent to r > -11? Check all that apply.
-r < 11
3r < -33
3r > -33
-3r < 33
-3r > 33
Step-by-step explanation:
[tex]r>-11\qquad\text{change the signs}\\\\\boxed{-r<11}\qquad\text{multiply both sides by 3}\\\\\boxed{-3r<33}\\\\r>-11\qquad\text{multiply both sides by 3}\\\\\boxed{3r>-33}[/tex]
Answer:
A
C
D
Step-by-step explanation:
four friends were born on consecutive years the sum of their ages is 62 what is the youngest friend
Answer:
The age of youngest friend = 14 years
Step-by-step explanation:
It is given that, four friends were born on consecutive years the sum of their ages is 62
Let 'x' be the age of youngest friend
age of other friends are (x + 1), (x + 2) and (x + 3)
To find the age of youngest friend
From the given information we can write,
x + (x + 1) + (x + 2) + (x + 3) = 62
4x + 6 = 62
4x = 62 - 6 = 56
x = 56/4 = 14
Therefore age of youngest friend = 14
Write the standard equation of a circle with the center (2,5) and a radius 16
(X-2)^2 +(y-5)^2 = 256
Find the circumference of a circle with an area of 254.47 square inches.
Answer:
56.5 inches
Step-by-step explanation:
We are given the area of a circle and we are to find the circumference of the same circle.
We know that the area of a circle is given by [tex]\pi r^2[/tex] so equating the given value to get.
[tex]\pi r^2=254.47[/tex]
[tex]r^2=\frac{254.47}{\pi }[/tex]
[tex]r=\sqrt{81.00}[/tex]
r = 9 inches
Since we now know the radius of the circle so we can find its circumference.
Circumference of circle = [tex]2\pi r[/tex] = [tex]2\pi (9)[/tex] = 56.5 inches
Answer: 56.54 in
Step-by-step explanation:
The area can be calculated with this formula:
[tex]A=\pi r^2[/tex]
Where r is the radius
And the circumference can be calculated with this formula:
[tex]C=2\pi r[/tex]
Where r is the radius
Solve for the radius from [tex]A=\pi r^2[/tex]. Then, tha radius is:
[tex]r=\sqrt{\frac{A}{\pi }}=\sqrt{\frac{254.47in^2}{\pi }} =9in[/tex]
Then, the circumference is:
[tex]C=2\pi (9in)=56.54in[/tex]
Sydney needs 70cm of fringe for each scarf she make how many scarves can she make if she has 6 meters if Fringe
Answer:
Sydney can she make 8 scarves
Step-by-step explanation:
Remember that
1 m=100 cm
so
6 m=6*100=600 cm
using proportion
70/1=600/x
x=600/70
x=8.6 scarves
therefore
Round down
Sydney can she make 8 scarves
5x - 2y = 3
-5x + 4y = 9
Solve the system of equations.
A) x = 6, y = 3
B) x = 6, y = 13
1
2
C) x = 3, y = 6
D) x = 1, y = 0
Answer: Your answer is c
Step-by-step explanation: The first thing you can do is add the two equations together to cancel out x
5x-2y=3
-5x+4y=9
added them together will get us 2y=12, from here divide 2 and get y=6
Plug 6 into the first equation and solve for x.
5x-2(6)=3
5x-12=3, add 13 to the other side
5x=15, divide 5 and get the answer
x=3
Which graph best represents the function f(x) = 3(1.5)x?
graph of increasing exponential function going through point 0, 2
graph of increasing exponential function going through point 0, 3
graph of increasing exponential function going through point 0, 1
graph of increasing exponential function going through point 0, 4
Answer:
B). graph of increasing exponential function going through point (0, 3)
Step-by-step explanation:
Given function is [tex]f\left(x\right)=3\left(1.5\right)^x[/tex]
Now we need to find about which of the given choices best describes the given function. Where given choices are:
A). graph of increasing exponential function going through point 0, 2
B). graph of increasing exponential function going through point 0, 3
C). graph of increasing exponential function going through point 0, 1
D). graph of increasing exponential function going through point 0, 4
plug x=0 into given function
[tex]f\left(x\right)=3\left(1.5\right)^x[/tex]
[tex]f\left(0\right)=3\left(1.5\right)^0=3(1)=3[/tex]
Hence graph passes through point (0,3).
growth factor 1.5 is greater than 1 so that means it is increasing function.
Hence correct choice is:
B). graph of increasing exponential function going through point (0, 3)
Express the polynomial as a product of linear factors. 3x^3+12x^2+3x-18
Answer:
f(x) = 3(x + 2)(x - 1)(x + 3)
Step-by-step explanation:
A logical first step would be to factor 3 out of all four terms:
f(x) = 3x^3+12x^2+3x-18 = 3(x^3 + 4x^2 + x - 6)
Roots of this x^3 + 4x^2 + x - 6 could be factors of 6: {±1, ±2, ±3, ±6}.
I would use synthetic division here to determine which, if any, of these possibilities are actually roots of x^3 + 4x^2 + x - 6. Let's try x = 1 and see whether the remainder of this synth. div. is 0, which would indicate that 1 is indeed a root of x^3 + 4x^2 + x - 6:
1 / 1 4 1 -6
1 5 6
------------------------
1 5 6 0
Yes, 1 is a root of x^3 + 4x^2 + x - 6, and so (x - 1) is a factor of x^3 + 4x^2 + x - 6.
Look at the coefficients of the quotient, which are 1, 5 and 6.
This represents the quadratic 1x² + 5x + 6, whose factors are (x + 2) and
(x + 3).
Thus, the given polynomial in factored form is:
f(x) = 3x^3+12x^2+3x-18 = 3(x + 2)(x - 1)(x + 3)
Answer:
3(x + 2)(x - 1)(x + 3)
Step-by-step explanation:
apex
Simplify the expression. Write your answer as a power.
2¹⁹×2⁵÷2¹²×2³
Answer:
32768^1
Step-by-step explanation:
Solved the equation and added the first power.
The Cooking Club made some pies to sell during lunch to raise money for an end-of-year banquet. The Cafeteria contributed pies to the club. Each pie was then cut into four pieces to the club. Each pie then cut into four pieces and sold. There were a total of 36 pieces to sell. How many pies did the club make?
Answer:pies 9 :p
Step-by-step explanation:
36÷4=9
which expression is equivalent to (2x-3) (x+5
2x^2+10x-3x-15= 2x^2+7x-15
Answer:
2x^2+10x-3x-15= 2x^2+7x-15
Step-by-step explanation:
Y+2=-3(x-4)
Find the missing value in the solution to the equation. ( , -2)
Answer:
(4,-2)
Step-by-step explanation:
plug in and simplify;
y+2=-3(x-4)
-2+2=-3(x-4)
0=-3x+12
3x=12
x=4
The missing value in the solution of the equation is ( 4 , -2)
What is an Equation ?An equation is a mathematical statement that consists of two algebraic expression equated by an equal sign.
The given equation is
y +2 = -3 (x-4)
The value of x at y = -2 ,
Substituting the value of y in the equation
-2 + 2 = -3 ( x -4)
0 = -3x +12
-12 = -3x
x = 4
The value of x is 4
Therefore the missing value in the solution of the equation is ( 4 , -2)
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Your friend can clap his hands 28 times in 12 seconds. How many times can your friend clap his hands in 1.75 minutes?
Answer:
Step-by-step explanation:
12 seconds for 28 claps
1 second for (28/12) claps
? claps for 1.75 mins?
1.75 minutes = 105 seconds (1.75×60 = 105)
105 seconds for (28/12)×105 claps
= 245 claps
Answer:
Your friends can clap their hands 245 times in 1.75 minutes.
Step-by-step explanation:
First of all, you should know how many seconds represents 1.75 minutes, because the amount of applause your friends can make is in that measure of time. In order to make this conversion, a simple rule of three is made, knowing that 1 minutes is 60 seconds:
If 1 minute is 60 seconds, how many seconds are 1.75 minutes?
[tex]\frac{1.75minutes*60seconds}{1minute} =105 seconds[/tex]
Knowing that your friend can clap his hands 28 times in 12 seconds and knowing that 1.75 minutes is 105 seconds, you can perform a rule of three again:
If they can clap their hands 28 times in 12 seconds, how many applause can they make in 105 seconds?
[tex]\frac{105seconds*28applause}{12} =245 applause[/tex]
Then your friends can clap their hands 245 times in 105 seconds, which is 1.75 minutes.
Four thousand students at a school were asked to name their favorite pizza topping. The results were 800 Pepperoni, 1,000 Sausage, 1,200 Mushrooms, 560 Peppers, 240 Onions, and 200 Other. Your friend expresses these results in this circle graph. Your friend made a mistake, however. What is wrong with his graph?
Answer:
The pepperoni and peppers are mixed up
Step-by-step explanation:
Answer:
The mistake my friend made was that pepperoni and peppers are mixed up, pepperoni is suppose to be 20% while peppers is supposed to be 14%
Step-by-step explanation:
Given that 4000 students
Pepperoni = 800
Sausage = 1,000
Mushrooms = 1,200
Peppers = 560
Onions = 240
Other = 200
To find the degree of each on the circle graph, we have:
Pepperoni = 800/4,000 * 100 = 20%
Sausage = 1,000/4,000 * 100 = 25%
Mushrooms = 1,200/4,000 * 100 = 30%
Peppers = 560/4,000 * 100 = 14%
Onions = 240/4,000 * 100 = 6%
Other = 200/4,000 * 100 = 5%
The mistake my friend made is that pepperoni and peppers are mixed up, pepperoni is suppose to be 20% while peppers is supposed to be 14%
equivalent 0f 2(2a-5)-(a-3)
Answer:
3a-7
Step-by-step explanation:
2(2a-5)-(a-3)
Distribute the 2
2*2a -2*5 - (a-3)
4a -10 - (a-3)
Distribute the minus sign
4a-10 -a +3
Combine like terms
4a-a -10+3
3a-7
plzzz help me with this question look at picture
ANSWER
B. 81
EXPLANATION
The given expression is:
[tex] {3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } [/tex]
Recall that:
[tex] {a}^{m} \div {a}^{n} = {a}^{m - n} [/tex]
We simplify the expression using the properties of exponents to obtain:
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{11}{5} - - \frac{9}{5} } [/tex]
We simplify the exponents to get;
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{11 + 9}{5}} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{ \frac{20}{5}} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = {3}^{4} [/tex]
[tex]{3}^{ \frac{11}{5} } \div {3}^{ - \frac{9}{5} } = 81[/tex]
The correct answer is B. 81
If the first of three consecutive integers is subtracted from 138, the result is the sum of the second and third. What are the integers?
Answer:
45, 46, 47Step-by-step explanation:
n, n + 1, n + 2 - three consecutive integers
The equation:
138 - n = (n + 1) + (n + 2)
138 - n = n + 1 + n + 2 combile like terms
138 - n = 2n + 3 subtract 138 from both sides
-n = 2n - 135 subtract 2n from both sides
-3n = -135 divide both sides by (-3)
n = 45
n + 1 = 46
n + 2 = 47
The three consecutive integers in question are 45, 46, and 47. This was solved by setting up and solving a simple algebraic equation.
Explanation:Solution:Let the three consecutive integers be x, x+1, and x+2. According to the problem, the sum of the second and third integers is equal to 138 minus the first one. This can be written mathematically as:
x + (x + 1) + (x + 2) = 138
Solving this equation gives:
3x + 3 = 138
3x = 135
x = 45
Hence, the three consecutive integers are 45, 46, 47.
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Which statement about the diagram are correct check all that apply
where is the picture for the problem?
Answer: here’s the possibile picture and answer
Step-by-step explanation:
(C & D)
can someone help me out please:(:(
Answer:
[tex]\large\boxed{\sqrt{20}-\sqrt{80}=-2\sqrt5}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{20}=\sqrt{4\cdot5}=\sqrt4\cdot\sqrt5=2\sqrt5\\\\\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5\\\\\sqrt{20}-\sqrt{80}=2\sqrt5-4\sqrt5=(2-4)\sqrt5=-2\sqrt5[/tex]
Henry works at a computer store. He is paid $14.00 per hour, plus 5% commission. He worked 8 hours and sold 6 computers today for a total of $5,790. Henry wants to determine how much he earned. To calculate his pay, Henry multiplies 14 × 8, then adds the product to 5,790, then multiplies the sum by 0.05. Is his calculation correct?
A) Yes, Henry's calculation is correct.
B) No, he should have multiplied $5,790 by 0.05.
C) No, he should have added $112 to $5,790.
D) No, he should have multiplied 112 by 0.05.
No he should have multiplied 5,700 by 0.05
Answer:
The correct option is B) No, he should have multiplied $5,790 by 0.05.
Step-by-step explanation:
Consider the provided information.
He is paid $14.00 per hour, plus 5% commission. He worked 8 hours and sold 6 computers today for a total of $5,790.
Now find his total earning as shown:
$14 × 8 = $112
It is given that he sold 6 computers for a total of $5,790 and he gets a commission of 5% of total sale.
5% = [tex]\frac{5}{100}=0.05[/tex]
Now multiply 0.05 with $5,790
$5,790 × 0.05 = $289.5
Hence, the total income is $112+$289.5=$401.5
To calculate his pay, Henry multiplies 14 × 8, then adds the product to 5,790, then multiplies the sum by 0.05.
Henry's calculation is incorrect as he needs to multiply 5,790 with 0.05 and then he need to add the product of 14 × 8
Therefore, the correct option is B) No, he should have multiplied $5,790 by 0.05.
each column of the matrix T=[0,0,3,0,3,0] represents a vertex of a triangle. if rosa scales the triangle by fining 3T what are the vertices of the scaled triangle?
Answer:
(0,0), (0,9), (9,0)
Step-by-step explanation:
The matrix corresponding vertices are:
(0,0)
(0,3)
(3,0)
Rosa scales by 3T, so we need to multiply each point by 3.
(3*0, 3*0)
(0*3, 3*3)
(3*3, 0*3)
=
(0,0)
(0,9)
(9,0)
last answer choice is right.
Answer:
[tex]\large\boxed{(0,\ 0),\ (0,\ 9),\ (9,\ 0)}[/tex]
Step-by-step explanation:
[tex]n\cdot\left[\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right] =\left[\begin{array}{ccc}(n)(a)&(n)(b)&(n)(c)\\(n)(d)&(n)(e)&(n)(f)\end{array}\right] \\\\============================[/tex]
[tex]\text{We have:}\\\\T=\left[\begin{array}{ccc}0&0&3\\0&3&0\end{array}\right] \Rightarrow\text{vertex}\ (0,\ 0),\ (0,\ 3),\ (3,\ 0)\\\\-----------------------------\\\\3T=\left[\begin{array}{ccc}(3)(0)&(3)(0)&(3)(3)\\(3)(0)&(3)(3)&(3)(0)\end{array}\right] =\left[\begin{array}{ccc}0&0&9\\0&9&0\end{array}\right] \\\\\text{new vertex:}\ (0,\ 0),\ (0,\ 9),\ (9,\ 0)[/tex]
Simplify (7x2 - 2x + 9) + (3x2 + 15x - 4)
Answer: 10x+13x+5
Step-by-step explanation:
Answer:
Step-by-step explanation:
7x^2 + 3x^2 = 10x^2
-2x + 15x = 13x
9 - 4 = 5
Put these together. Don't do any more than putting them together in a string.
Answer: 10x^2 + 13x + 5
A map is drawn using the scale 2 cm:100 mi. On the map, Town B is 3.5 centimeters from Town A, and Town C is 2 centimeters past Town B. How many miles apart are Town A and Town C?
A.) 275 miles
B.) 200 miles
C.) 550 miles
D.) 1,100 miles
Answer:
275 miles
Step-by-step explanation:
3.5 cm = 175 and 2 more centimeters past that is 100 so 175 +100=275
so your answer is a 275 miles
Drag each tile to the correct box.
Find the y-intercept of each exponential function and order the functions from least to greatest y-intercept.
Answer:
1) g(x) ----> y-intercept -3
2) h(x) ----> y-intercept -1
3) f(x) ----> y-intercept 2
Step-by-step explanation:
we know that
The y-intercept or initial value, is the value of y when the value of x is equal to zero
Calculate the y-intercept of each exponential function
case 1) A function g, has a growth factor of 2 and a value of 1, and passes through the point (1,-2)
The exponential function is equal to
[tex]g(x)=1(2)^{x}+c[/tex]
Find the value of c
For x=1, g(x)=-2
substitute
[tex]-2=(2)^{1}+c[/tex]
[tex]-2=2+c[/tex]
[tex]c=-4[/tex]
so
[tex]g(x)=(2)^{x}-4[/tex]
Find the y-intercept
For x=0
[tex]g(0)=(2)^{0}-4[/tex]
[tex]g(0)=-3[/tex]
case 2) Observing the table
For x=0
f(0)=2
therefore
The y-intercept of f(x) is 2
case 3) Observing the graph
For x=0
h(0)=-1
therefore
The y-intercept of h(x) is -1
Order the functions from least to greatest y-intercept
1) g(x) ----> y-intercept -3
2) h(x) ----> y-intercept -1
3) f(x) ----> y-intercept 2
Final answer:
To find the y-intercept of an exponential function, evaluate it at x = 0. The constant term in the function represents the y-intercept. Order the functions by comparing these constant terms from least to greatest.
Explanation:
To find the y-intercept of an exponential function, we need to evaluate the function when x is equal to zero. The exponential function is usually given in the form f(x) =[tex]ab^x[/tex], where a is the y-intercept. This is because any number (except zero) raised to the power of zero is 1, so[tex]b^0[/tex] will always be 1, leaving us with f(0) = a.
After finding the y-intercept for each function, order them from least to greatest to complete the task. For example, if we have functions such as f(x) = [tex]2(3)^x, g(x) = 5(2)^x[/tex], and h(x) = [tex]-1(4)^x,[/tex] their y-intercepts would be 2, 5, and -1 respectively. Ordered from least to greatest, the functions by their y-intercepts would be h(x), f(x), g(x).
look at picture and plzz help
Answer:
a= 3 b=6 c= 5
Step-by-step explanation:
For this case we have the following expression:
[tex]3 ^ {\frac {6} {5}}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [c] {a ^ b} = a ^ {\frac {b} {c}}[/tex]
Then according to the given expression we have the following:
[tex]a = 3\\b = 6\\c = 5[/tex]
Answer:
[tex]a = 3\\b = 6\\c = 5[/tex]
Solve log 60 - log 30
Answer:
log(2)
Step-by-step explanation:
property of logs says
Log(60) - Log(30) = Log(60/30) = Log (2)
Answer:
1.20
Step-by-step explanation:
properties of log
log x - log y = logx/logy
Emilee signed a finance agreement for her purchase what is the total amount she will pay back under this agreement
To calculate the total amount Emilee will pay back under a finance agreement, one needs to know the specifics of the loan. Joanna's example, with a known interest rate and term, shows how to use the present value of an annuity formula to find out the maximum loan and total amount paid over time.
Explanation:The question pertains to calculating the total amount that Emilee will pay back under a finance agreement for her purchase. To determine this amount, one must know the principal amount of the loan, the interest rate, and the term of the loan.
For instance, if Joanna can afford to pay $12,000 a year for a house loan at an annual interest rate of 4.2% for 30 years, one can use the formula for the present value of an annuity to calculate the maximum loan she can afford. The formula is PV = PMT [1 - (1 + i)^(-n)] / i, where PV is the present value (the maximum loan), PMT is the annual payment ($12,000), i is the interest rate per period (4.2% annually), and n is the number of periods (30 years).
By applying this formula, Joanna can afford a maximum loan of approximately $202,556.98. Over 30 years, she will end up paying $12,000 times 30, which equals $360,000 in total. Similarly, to determine the total amount Emilee will repay, the same types of calculations would apply based on the terms of her finance agreement.
Answer: $1308
Step-by-step explanation: APEX
12 monthly payments of $109 = $1308
Tonya bought gifts for her family that cost $25, $14, $33, and $19. She has to buy one more gift and wants her mean cost to be $25. What should she spend on the last gift?
____________________________________________________
Answer:
Your answer would be $34.
____________________________________________________
Step-by-step explanation:
In order to get the mean cost that she wants from the gift, we would need to get the numbers that we already had, and have another set of row with the amount of gifts she needs with the mean she wants.
Here is how it should look like:
$25 $14 $33 $19 x
$25 $25 $25 $25 $25
We are trying to find the number for "x"
Therefore, we would need to use the process of adding, then subtracting after.
Lets add:
[tex]25+14+33+19=91\\\\25+25+25+25+25=125[/tex]
What we would do now is subtract the numbers in order to get the price that Tonya wants from her gift, if she buys another gift.
[tex]125-91=34[/tex]
Tonya should spend $34 on her last gift.
$34 should be your FINAL answer
____________________________________________________