Answer:
x² + 2x + [3\x - 1]
Step-by-step explanation:
Since the divisor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, -c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
1| 1 1 -2 3
↓ 1 2 0
------------------
1 2 0 3 → x² + 2x + [3\x - 1]
You start by placing the c in the top left corner, then list all the coefficients of your dividend [x² + 5x - 36]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder, which in this case is a 3, so what you is set the divisor underneath the remainder of 3. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², 2 becomes 2x, and the remainder of 3 is set over the divisor, giving you the other factor of x² + 2x + [3\x - 1].
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Write the standard equation of a circle with the center (2,5) and a radius 16
(X-2)^2 +(y-5)^2 = 256
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
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 :)
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]
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:
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:
HELPPPP ASAP!!!!!!!!!!!! Using the distributive property, which of the following expressions is equivalent to 5(3 + 5y)?
A. 8 + 5y
B.15 + 5y
C.15 + 25y
D. 8 + 10y
Answer:
C.15+25y
Step-by-step explanation:
5(3+5y) solved via distribution is 15+25y
Happy to help :D
C. Because 5(3+5y) is the same as 5x3 plus 5x5y which is 15 + 25y
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]
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
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:
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
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)
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)
To know more about Equation
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Factor completely 49x^2-25
Answer:
(7x-5)(7x+5)
Step-by-step explanation:
Answer:
(7x + 5)(7x - 5)
Step-by-step explanation:
49x² - 25 ← is a difference of squares and factors in general as
a² - b² = (a + b)(a - b)
49x² = (7x)² ⇒ a = 7x
25 = 5² ⇒ b = 5
49x² - 25
= (7x)² - 5² = (7x + 5)(7x - 5)
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
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%
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).
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
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]
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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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
____________________________________________________
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.
what is 18.23 rounded to the nearest tenth?
Answer:
The answer is 18.2.
Hope this helps!
Answer: 18.2
Step-by-step explanation:
you would round to 18.2 because with 5 and above, you give it a shove, 4 and below let it go
What is the area of point O?
Answer:
28.26 cm²
Step-by-step explanation:
It's not the point O, but the circle O.
The area of a circle is given by the formula A = π r²
We already have r (3cm)... so we can plug it directly into the equation:
A = π r² = π 3² = 9π = 28.26 cm²
Answer:
A = 28.27
Step-by-step explanation:
A = π r^2
A = π 3^2
A= π (9)
A = 28.27433
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
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.
Suppose you need to choose a new combination for your combination lock. You have to choose 3 numbers, each different and between 0 and 40. How many combinations are there? Explain
Answer:
63,960 possibilities in total.
Step-by-step explanation:
For the first number, you can choose from 41 different numbers, so there are 41 possibilities.
For the second number, you cannot choose the same as the first one, so you are now limited to 40 possibilities.
For the third number, you are down to 39 possibilities since you cannot pick the same as the first two ones.
So, you have 41 * 40 * 39 = 63,960 possibilities in total.
Picking a new combination is easy... remembering it is the hard part :-)
If you want to calculate it from a formula standpoint, the base formula would be:
[tex]P(n,r) = \frac{n!}{(n-r)!} = \frac{41!}{(41-3)!} = 63960[/tex]
Where n is the total numbers possible and r is the quantity of numbers you have to pick.
math help uwu ,,, will reward tyvm. (─‿‿─)
Answer:
Step-by-step explanation:
Here's how I would do it (not necessarily the only way or best way).
Draw an imaginary line from A to C. This splits the kite into two triangles: ABC and ADC. Since AB ≅ AD, CB ≅ CD, and AC ≅ AC, the two triangles must be congruent by SSS. Therefore, ∠B ≅ ∠D.