The product of the polynomials (3x+2) and (-x^3-3) is:
(3x+2)*(-x^3-3) = (3x)*(-x^3) + (3x)*(-3) + 2*(-x^3) + 2*(-3) = -3x^4 - 2x^3 -9x - 6
Multiplying it by (3 + x), we got:
(3 + x)*(-3x^4 - 2x^3 -9x - 6) = 3*(-3x^4) + 3(-2x^3) + 3*(-9x) +3*(-6) + x*(-3x^4) + x*(-2x^3) + x*(-9x) + x*(-6) = -3x^5 -11x^4 -6x^3 -9x^2 - 33x - 18
Therefore, the coefficient of x^4 is -11.
While working at a bakery, you are responsible for decorating cakes. You would like to add a string of flowers to the border of a round cake you are decorating. The cake has a radius of 14 inches.
What is the length, to the nearest inch, of the string of flowers you will need?
Answer:
88 inches
Step-by-step explanation:
we need to find the circumference of the cake and the formula is 2rPi
The diameter is 28 and that times pi is about 88
Hopes this help please mark brainliest
The Hoffmans are planning their next family night. They always have dinner out somewhere and then do something fun together. There are 2 adults and 7 children in the family. Each family member is allowed 4 meal suggestions, and each child is allowed 4 activity suggestions. Assuming no family members choose the same thing, how many different family night possibilities are there?
Explanation
Number of children = 7
Number of adults = 2
Meal Suggestion per family member=4
Activity Suggestion per child = 4
Total number of family member = (7 + 2) = 9
Therefore, total meal suggestion
[tex]9\times4\text{ =36}[/tex]Total activity suggestions
[tex]7\times4=28[/tex]Hence the number of different possibilities
[tex]36+28=64[/tex]Answer
[tex]64[/tex]Arthur found that for every 200 peasants only 10 had seen a Dane. If there were 150,000 peasants in the kingdom how many had never seen a Dane?
We can solve this problem by applying the rule of 3.
If 10 out of 200 peasants had seen a Dane, x out of 150,000 had seen a Dane.
We can calculate x as:
[tex]\begin{gathered} 200\text{ peasants}\longrightarrow10\text{ seen Dane} \\ 150,000\text{ peasants}\longrightarrow x=\frac{10}{200}\cdot150,000=0.05\cdot150,000=7,500 \end{gathered}[/tex]Out of 150,000, 7,500 had seen a Dane. Then 150,000-7,500=142,500 peasants had never seen a Dane.
Answer: 142,500 peasants had never seen a Dane.
A cereal box says that now it contains 20% more. Originally, it came with 18.5 ounces of cereal. How much cereal does the box come with now? Explain your reasoning.
Percentages can be expressed as decimals. Percentage of something can be found by multiplying the number by the decimal.
20% = 0.20
20%(18.5)
0.20(18.5)
3.7
Since this is a 20% increase, we will add this to the original value.
18.5 + 3.7 = 22.2
Find the surface area of the prism. 10 m Not drawn to scale b 600 m2 150 m2 280 m2 d 42 m2
Here, we have a rectangular prism.
Given:
Length, L = 10 m
Width, w = 6 m
Height, h = 5 m
Let's find the surface area of the rectangular prism.
To find the surface area of the rectangular prism, apply the formula below:
[tex]SA=2(wl+hl+hw)[/tex]Input values into the formula:
[tex]\begin{gathered} SA=2(6\ast10+5\ast10+5\ast6) \\ \\ SA=2(60+50+30) \\ \\ SA=2(140) \\ \\ SA=280 \\ \\ SA=280m^2 \end{gathered}[/tex]Therefore, the Surface Area of the rectangular prism is 280 square meters
ANSWER:
c. 280 m²
How to solve -14+(-31)
Answer:
-45
Explanation:
-14 + (-31)
= -14 - 31
= -45
please help ill try to give brainiest
Answer:
4 cups of sugar require 14 cups of sugar
Step-by-step explanation:
Given 7/8 cup flour= 1/4 cup sugar
Required determine the cups of flour for 4 cups of sugar
Determine the cups of flour for 4 cups of sugar
First, we need to determine the unit rate for 1 cup of sugar.
This is done by multiplying both sides by 4
Next, we determine cup of flour for 4 cups of sugar.
This is done by multiplying both sides by 4
Hence;4 cups of sugar require 14 cups of sugar
I hope this helps! if it doesn't if you tell me what the options are I can try to help more.
If the average of 12, 7, 9, a, and b is 12, thenwhat is the average of a + b?
If the average of 12, 7, 9, a, and b is 12, then
what is the average of a + b?
we know that
the average is equal to
(12+7+9+a+b)/5=12
simplify
(28+a+b)/5=12
Multiply both sides by 5
28+a+b=60
isolate (a+b)
a+b=60-28
a+b=32average a+ba+b/2=32/2=16answer is 16The measure of the larger angle of an isosceles triangle is sixteen times the measure of each of the other two angles. Find the measure of the larger angle.
name the place value for each digit in the number 1,675,892
What is the solution to the equation below? A = 16 B. X2 CE 04
Here, we want to get the value of x
The first thing we have to do here is to isolate the root
We have this as;
[tex]\begin{gathered} \sqrt[]{x}\text{ = 12-8} \\ \sqrt[]{x}\text{ = 4} \\ (\sqrt[]{x})^2=4^2 \\ x\text{ = 16} \end{gathered}[/tex]The sum of two numbers is 12 4 times the smaller number is 1 less than 3 times the larger number
Answer: 5 and 7
Step-by-step explanation:
Let x be the smaller number and y be the larger number.
x + y = 12
4x = 3y - 1
I will solve for y by substituting for x from the first equation. (There are different ways to solve this, but for simplicity I am using the substitution method.)
x = 12 - y
4(12 - y) = 3y - 1
48 - 4y = 3y - 1
49 = 7y
y = 7
Now that I have found the larger number y, I will now plug it into the first equation and solve for x.
x + y = 12
x + 7 = 12
x = 5
a bag of the same size small balls contains 6 blue balls, 5 red balls, 5 yellow balls, and 4 green balls. What is the probability of selecting a blue or green ball on the first draw?
Please help me solve
Whoever answers correctly gets brainliest
For those who can't see the paper:
π²/♾️=9
Answer:
I think the answer will be the infinity sign=1 whole, 1/9
f(x)=x^2-2x+ 3; d(x) = X-4
Answer: A1:F-IF.A.1. A1:F-IF.A.2. A1:F-IF.A.3. A1:F-IF.B.4. A1:F-IF.B.5 ... Find all the zeros of the polynomial y = x 3 - 2x 2 - 3x. A. -3, 1.
Step-by-step explanation:
On a coordinate plane, how are the locations of the points (-3, 7) and (-3,-7) related?
The two points / coordinates are (-3, 7) and (-3 , -7).
The relationship that exists between two points.
it is a reflection across x-axis.
Solution:Reflection over x-axis: A reflection or flip over the x-axis in which the x-axis is the line of reflection. The formula is: (x , y) → (x,−y) ( x , y ) → ( x , − y ) .Simply multiply the output variable by -1 to represent an equation on the x-axis: y = f(x) → y = −f(x) y = f ( x ) → y = − f ( x ).When a point is reflected across the y-axis, the y-coordinate remains unchanged, but the x-coordinate is assumed to be the additive inverse.Simply multiply the input variable by -1 to reflect an equation over the y-axis: y=f(x)→y=f(−x) y = f ( x ) → y = f ( − x ) .Given 2 coordinates, (-3, 7) and (-3,-7)
It is clear from the given points (-3, 7) and (-3, -7), that the x-coordinates are the same but the sign of the y-coordinates is opposite.If we reflect a figure across the x-axis, we change the sign of the y-coordinate while keeping the x-coordinates the same, i.e.,So the given points (-3, 7) and (-3,-7) has a relation that is it is reflection about x-axis.
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which of the following statements have the same result? explain each step in solving each one. 1. f(3) when f(x)=2x+32. f^-1(3) when f(x)=2x-9/33. 5y+13=4y+4(10 points)
Let's find the inverse function:
1. replace f(x) with y
[tex]y=\frac{2x-9}{3}[/tex]2. Replace every x with a y and every y with an x:
[tex]x=\frac{2y-9}{3}[/tex]3. solve for y:
[tex]y=\frac{3x+9}{2}[/tex]4. replace y with f^-1(x)
[tex]f^{-1}(x)=\frac{3x+9}{2}[/tex]Now:
[tex]f^{-1}(3)=\frac{3(3)+9}{2}=\frac{9+9}{2}=\frac{18}{2}=9[/tex]since the functions are equal for x = 3 we can conclude that they have the same result
[tex]f(3)=f^{-1}(3)[/tex]A restraurant Buys 56 Pounds of Beef at $1.12/ Pound and 24 quarts of Milk at $.90 quart. how Much Money was spent?
Answer:
Step-by-step explanation:
1.12 * 56 = 62.72
.90 * 24 = 21.60
62.72 + 21.60 = $84.32
Jim has a total of 77 red and Blue marbles. The number of blue marbles is five more than twice the number of red marbles.A. Write a pair of linear equations to represent the information. Be sure to state what the variables represent.B. Explain the substitution method of solving this pair of equations. Solve the equations to find the number of red marbles.
A.
Jim has a total of red and blue marbles.
Let "r" represent the number of red marbles and "b" represent the number of blue marbles, to determine the total number of marbles he has, you have to add both, so that:
[tex]r+b=77[/tex]You know that the number of blue marbles "b" is five more than twice the number of red marbles "r"
Twice the number of red marbles means that r is multiplied by 2, you can express it as "2r", and he has five more than twice the number of red marbles, then you have to add 5 to 2r. You can express the number of blue marbles as follows:
[tex]b=2r+5[/tex]B.
Using both equations you can calculate the values of b and r using the substitution method.
We know that b=2r+5, and that r+b=77, the substitution method allows us to replace the known value of b, which is "2r+5" into the equation "r+b=77", this way we will determine one equation with only one variable "r":
[tex]\begin{gathered} r+b=77\to\text{if b=2r+5} \\ r+(2r+5)=77 \end{gathered}[/tex]From this expression, you can determine the value of r, first erase the parentheses, and simplify the like terms:
[tex]\begin{gathered} r+2r+5=77 \\ 3r+5=77 \end{gathered}[/tex]Second, pass 5 to the other side of the expression by applying the opposite operation to both sides of the equal sign:
[tex]\begin{gathered} 3r+5-5=77-5 \\ 3r=72 \end{gathered}[/tex]Third, divide both sides by 3 to reach the value of r:
[tex]\begin{gathered} \frac{3r}{3}=\frac{72}{3} \\ r=24 \end{gathered}[/tex]He has 24 red marbles
Estimate 93+ 31 by first rounding each number to the nearest ten.
Answer:
To estimate 93+31 by first rounding number to the nearest ten.
Solving 93+31, we get
[tex]93+31=124[/tex]Explanation:
Simply put, when you have a number and you want to round to the nearest tens, this means that you will need to find which 10 they are nearest to. For example, if you think about the number 53, you can easily say that it is near 50 than it is near 60. So the rounded number of 53 nearest to ten is 50.
Here, the number is 124
Rounding the number to the nearest ten.
[tex]124\approx120[/tex]Answer is: 120.
Solve for x by "Factoring". You MUST show every level of work (like you saw in the lesson) in order to receive full credit.
x^2-x-42
=(x^2+6)+(-7x-42)
=x(x+6)-7(x+6)
=(x+6)(x-7)
keep going to solve for x
The factorization of the quadratic expression 25x² - 4 gives us (x + 6)(x - 7) where; x = -6 or 7
How to factorize a quadratic equation?We are given the quadratic equation as;
x² - x - 42
Now, this quadratic equation can be written as;
x² + 6x - 7x - 42
We can group this using algebra properties to get;
(x² + 6x) - (7x + 42)
Collecting like terms gives us;
x(x + 6) - 7(x + 6)
Thus, the factorization is;
(x + 6)(x - 7)
Thus, the values of x would be;
x + 6 = 0
x = -6
x - 7 = 0
x = 7
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Tommy wishes to retire at the age of 67 with $95,000 in savings. Determine the monthly payment into an IRA if the APR is 6.8% and he begins making payments at:Step 1: 25 years oldThe next part is finding the answer for 35 years old
Step 1
State the annuity formula
[tex]A=\frac{P[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}[/tex]where;
[tex]\begin{gathered} P=? \\ r=6.8\text{\%=}\frac{6.8}{100}=0.068 \\ n=12 \\ t=67-25=42 \\ A=\text{ \$95000} \end{gathered}[/tex]Step 2
Find the monthly payment from 25 years old
[tex]95000=\frac{P[(1+\frac{0.068}{12})^{42\times12}-1]}{\frac{0.068}{12}}[/tex][tex]\begin{gathered} \frac{0.068P\left[\left(1+\frac{0.068}{12}\right)^{42\times \:12}-1\right]}{\frac{0.068}{12}}=95000\times \:0.068 \\ 195.02614P=6460 \\ \frac{195.02614P}{195.02614}=\frac{6460}{195.02614} \\ P=33.1237639 \\ P\approx\text{ \$}33.12 \end{gathered}[/tex]Step 3
Find the monthly payment from 35 years old
[tex]\begin{gathered} 95000=\frac{P[(1+\frac{0.068}{12})^{32\times12}-1]}{\frac{0.068}{12}} \\ n=67-35=32 \\ \frac{P\left[\left(1+\frac{0.068}{12}\right)^{32\times \:12}-1\right]}{\frac{0.068}{12}}=95000 \\ \frac{0.068P\left[\left(1+\frac{0.068}{12}\right)^{32\times \:12}-1\right]}{\frac{0.068}{12}}=95000\times \:0.068 \\ 93.08447P=6460 \\ P=69.39933 \\ P=\text{\$69.40} \end{gathered}[/tex]Answer;
[tex]\text{ \$69.40}[/tex]there is a stack of cards, each given a different number 1-10, suppose we select a card randomly from the stack, replace it, then randomly select a card. what is the probability that the 1st card is an ODD number and the second card is Less then 5?
Given that:
- A stack of different cards numbered from 1 to 10.
- A card is randomly selected and then replaced. Then another card is randomly selected.
• You need to find the probability that the first card is an odd number.
By definition, Odd Numbers are those numbers that cannot be divided by 2. In this case, these are:
[tex]1,3,5,7,9[/tex]Knowing that the total number of cars is:
[tex]10[/tex]You can set up:
[tex]P(X=ODD)=\frac{5}{10}[/tex]Then:
[tex]P(X=ODD)=\frac{1}{2}[/tex]• You need to find the probability that the second card is less than 5.
Notice that the numbers cards from the stack that are less than 5 are:
[tex]1,2,3,4[/tex]Therefore, you can set up that:
[tex]\begin{gathered} P(X<5)=\frac{4}{10} \\ \\ P(X<5)=\frac{2}{5} \end{gathered}[/tex]• Now you can set up:
[tex]P=\frac{1}{2}\cdot\frac{2}{5}[/tex]Solving the Multiplication, you get:
[tex]\begin{gathered} P=\frac{1\cdot2}{2\cdot5} \\ \\ P=\frac{2}{10} \\ \\ P=\frac{1}{5} \end{gathered}[/tex]Hence, the answer is:
[tex]P=\frac{1}{5}[/tex]if g(x)=(x + 1), for what value of x will g(x)=3?A) 1B) 2C) 3D) 4
Given
[tex]g(x)=x+1[/tex]You need to calculate the value of x for g(x)=3, replace it in the equation as follows:
[tex]3=x+1[/tex]And calculate for x, to do so, you can pass the "+1" to the other side of the equal sign by performin the oposite operation "-1" to both sides:
[tex]\begin{gathered} 3-1=x+1-1 \\ 2=x \end{gathered}[/tex]For x=2 g(x)=3
Hey help me out pls I would love if you did
Firstly, we would find the fractional part of the circle and then express it as a percentage.
The circle has 4 sub-divisions and a part of it is shaded. Thus, the fractional part of the shaded area is:
[tex]\frac{1}{4}[/tex]Expressing this as percentage, we have:
[tex]\frac{1}{4}\times100=25\text{\%}[/tex]Hence, the percentage represented by the shaded area is 25%
Solve the system using a matrix.
-2x - 3y = -26
3x + 4y = 36
([? ],[_])
Help
Answer:
-2x-3y=-26
3x+4y=36
using matrix method
(-2 -3(x = (-26
3 4) y ) 36)
AB=C
multiplying A^-1 on both sides
A^-1AB=A^-1C
IB=A^-1C ........(¡) (AA^-1=I)
determined of A |A|=-8-(-9)=-8+9=1
adjoint of A= (4 3
-3 -2)
now
IB=A-^1C
B=adjoint A/determined of A.C
B=(4 3
-3 -2)/1 .C
B=(4 3 (-26
-3 -2). 36)
B=(-104+108
78-72)
( x (4
y) = 6)
Equating the corresponding elements of equal matrices
:.x=4
:.y=6
so the required value of x and y is 4and6.
In the expression 5^2, the 2 represents the _________________.
A: product
B :sum
C: base
D: exponent
In the expression 5^2, the 2 represents the D. exponent.
What is exponent?Exponentiation is a mathematical process that involves the base b and the exponent or power n. An exponent is the result of multiplying a certain number or variable (such as x, y, or z) by itself.
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6⁴ is multiplied by itself four times,
In this case, 5² will be 5 × 5 = 25.
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29.95 per gallon * 12.25 gallons long division
First, we can multiply each number by 100 to eliminate the decimal part:
29.95 * 100 = 2995
12.25 * 100 = 1225
We can do it because 100/100 = 1 and the division is not altered.
Then, we have the following division:
1. Find a value that you can multiply by 1225 that is near or exactly 2995. After this, multiply the value by 1225 and subtract the result from 2995 (dividend).
Try with 2:
Then 2 x 1225 = 2450
_2____
1225 | 2995
- 2450
----------
545
Now the rest 545 is less than the divisor (1225). We can also see that we do not have more numbers besides the last digit of the dividend (2995). In this case, we can add a zero beside 545 to get the decimal part of the division.
We can also have to add a dot at the quotient.
That is:
_2.____
1225 | 2995
- 2450
----------
5450
We need, again, to find a number that multip
The measure of <1 is greater than 97° and at most 115°. Graph the possible values of x.
Answer:
The possible values of x are 10, 11, and 12
Step-by-step explanation:
9(10) + 7 = 97
9(11) + 7 = 106
9(12) + 7 = 115
Express your answer as a polynomial in standard form.f(x) = x² - 7x + 14 g(x) = 4x - 9 Find: (gof)(x)
