Omar will buy at least 5 pounds of candy. To find this, divide his minimum spending ($40) by the cost per pound of candy ($8). The inequality solved for p is p \geq 5, meaning Omar can buy 5 or more pounds of candy.
Explanation:To find out the possible number of pounds of candy Omar will buy, we can set up an inequality using the given information. We know the cost per pound of candy is $8, and Omar is going to spend at least $40 on candy. Therefore, the inequality representing the situation can be written as:
8 imes p \\(cost per pound \\ times number of pounds)\\ \geq 40 (Omar's minimum spending)
To solve for p, the number of pounds, we divide both sides of the inequality by 8:
p \geq \frac{40}{8} \Rightarrow p \geq 5
So, Omar will buy at least 5 pounds of candy. This means that the possible numbers of pounds he may buy are 5 or more.
Use what you know about decimals or fractions to explain why (0.2)⋅(0.002)=0.0004.
Answer:
you take 0.002 and multiply this by 0.2, to then get your answer of 0.0004
Step-by-step explanation:
distributive property to simplify 64-16
Final answer:
The expression 64-16 simplifies to 48, and does not need the distributive property for simplification as it is a straightforward subtraction.
Explanation:
The question is asking to use the distributive property to simplify the expression 64-16. While this expression doesn't necessarily require the distributive property as it's a simple subtraction, sometimes in mathematics we leverage distributive properties or other algebraic rules to simplify or reorganize expressions. However, if we have a closer look at the provided reference information, none of it relates directly to the expression 64-16, which simplifies to 48. Therefore, there's no need to apply the distributive property here; the expression is already in its simplest form.
What
percent of 150 is 225?
To determine what percent 225 is of 150, the calculation (225 / 150) × 100% is used, resulting in 225 being 150% of 150.
Explanation:To find what percent of 150 is 225, we can use the formula for calculating percents:
Percentage = (Part / Whole) × 100%
Where 'Part' is 225 and 'Whole' is 150. Now, let's calculate:
Percentage = (225 / 150) × 100%
Percentage = 1.5 × 100%
Percentage = 150%. So, 225 is 150% of 150.
helpppppppppppppppppp
Answer:
[tex]13 \frac{1}{8} + 21 \frac{3}{4} = 13 \frac{1}{8} + 21 \frac{6}{8} = 34 \frac{7}{8} [/tex]
[tex]35 \frac{1}{2} - 34 \frac{7}{8} = 35 \frac{4}{8} - 34 \frac{7}{8} = 34 \frac{12}{8} - 34 \frac{7}{8} = \frac{5}{8} [/tex]
The correct answer is C.
A person invests 7500 dollars in a bank. The bank pays 4% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 12800 dollars?
Answer:
13.6 years
Step-by-step explanation:
From the question;
Money invested (Principal) is 7500 dollars Rate of interest is 4% compounded annually Amount, (money accrued ) is 12800 dollarsWe are needed to determine the time it took for the money to reach the given amount;
To solve the question we need to know the compound interest formula, that is;[tex]A=P(1-\frac{r}{100})^n[/tex]
Where n is the interest periods;
Therefore, substituting the variables with the corresponding values, we can determine n.Therefore;
[tex]12800=7500(1-\frac{4}{100})^n[/tex]
Dividing both sides by 7500, we get;
[tex]1.7067=(1-\frac{4}{100})^n[/tex]
[tex]1.7067=(1.04)^n[/tex]
Introducing logarithms on both sides;
[tex]log1.7067=log(1.04)^n\\nlog1.04=log1.7067\\n=\frac{log1.7067}{log1.04} \\n=13.63[/tex]
Thus, n=13.6 years
Thus, it would take 13.6 years for the invested money to accumulate to 12800 dollars
NEED ANSWER ASAP!!!!!!!
in the system: {y=28+0.05x}
{y=25+0.07x}
what is the substitute for x where y is the same on both equations?
Hi there (◕‿-)
Since both equations are equal to y, they must equal each other. So set them to equal each other.
28 + 0.05x = 25 + 0.07x (✿ ♥‿♥)
Let's start by subtracting 25 from both sides!
3 + 0.05x = 0.07x (28-25=3, 25-25=0)
Now let's subtract 0.05 from both sides Ｏ(≧▽≦)Ｏ
3 = 0.02x
We need this x by itself, so let's get rid of it. Do this by divide both sides by 0.02 （ ´_⊃｀）
150 = x
So x = 150. Let's test this. Substitute 150 in for x in both equations! ＼（＾○＾）人（＾○＾）／
28+0.05(150) = 25+0.07(150)
28 + 7.5 = 25 + 10.5 (0.05*150=7.5, 0.07*150 = 10.5)
35.5 = 35.5
It works! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
So x = 150
Enzo is making a scale drawing of the rectangle below. A rectangle has a length of 8 centimeters and width of 5 centimeters. Enzo says that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters. Which explains whether Enzo is correct? Enzo is correct because he used a factor of 2 to enlarge the rectangle. Enzo is correct because he doubled one dimension and added the two lengths to get the other dimension. Enzo is not correct because the enlarged rectangle should be 16 centimeters by 5 centimeters. Enzo is not correct because he did not multiply the length and width by the same factor.
Answer:
Enzo is not correct bc he did not multiply the length and width by the same factor
Hopes that helped:P
Answer:
the answer is d
Step-by-step explanation:
like this if you like anime
20 POINTS!!
What is the GCF of 24 a^3b and 36 ab^2?
a. 2 ab
b. 4 a^3b
c. 12 ab
d. 72 a^3b^2
Answer:
option c - 12 ab
Step-by-step explanation:
Two numbers are , 24 a³b and 36 a b².
The meaning of G C F between two number is that greatest number which divide both the number.
We will factorize , 24 a³b and 36 a b² and take out the common factors to determine their G CF.
24 a³ b= 2×2×2×3×a×a×a×b
36 a b²=2×2×3×3×a×b×b
G C F(Greatest common factor)=2×2×3×a×b
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If 5n = 0,then what does 6n equal
Answer:0
Step-by-step explanation:
Because any multiples by 0 is 0
Answer:
0
Step-by-step explanation:
Since 5 x n = 0, n has to be 0 since you can’t multiply anything but 0 to get the result of 0. Hope this helped!
What is the value of x in the equation 4 and StartFraction 3 Over 10 EndFraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)?
The value of x is –3.
Solution:
Given statement:
4 and Start Fraction 3 Over 10 End Fraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)
Let's convert this into algebraic expression.
[tex]$4\frac{3}{10} -\left(2\frac{2}{5}x+5\frac{1}{2}\right)=\frac{1}{2}\left(-3\frac{3}{5}x+1\frac{1}{5}\right)[/tex]
First convert mixed fraction into improper fraction.
[tex]$\frac{43}{10} -\left(\frac{12}{5}x+\frac{11}{2}\right)=\frac{1}{2}\left(-\frac{18}{5}x+\frac{6}{5}\right)[/tex]
[tex]$\frac{43}{10} -\frac{12}{5}x-\frac{11}{2}=-\frac{18}{10}x+\frac{6}{10}[/tex]
Now, take LCM and make the denominators same.
LCM of 2, 5, 10 = 10
[tex]$\frac{43}{10} -\frac{12\times2}{5\times2}x-\frac{11\times5}{2\times5}=-\frac{18}{10}x+\frac{6}{10}[/tex]
[tex]$\frac{43}{10} -\frac{24}{10}x-\frac{55}{10}=-\frac{18}{10}x+\frac{6}{10}[/tex]
Arrange like terms one side of the equation.
[tex]$\frac{18}{10}x -\frac{24}{10}x=\frac{6}{10}-\frac{43}{10}+\frac{55}{10}[/tex]
[tex]$\frac{18x-24x}{10} =\frac{6-43+55}{10}[/tex]
[tex]$\frac{-6x}{10} =\frac{18}{10}[/tex]
[tex]$-6x=\frac{18\times10}{10}[/tex]
[tex]$-6x=18[/tex]
Divide both sides of the expression by –6, we get
⇒ x = –3
Hence the value of x is –3.
Answer:
-3
Step-by-step explanation:
if I work 4 days a week and get 8 dollars a day. How much will I make in 2months
Answer:
$256
Step-by-step explanation:
Alright so,
There are 7 days in a week and you're only working 4 of those days. In one week you would make $32 since 4*8=32. (4 being the days you work and 8 being the amount you get a day)
There are about 4 weeks in one month and 4*2=8, therefore there are 8 weeks in 2 months.
Remember, in one week you make $32. What you can do now is multiply, it's easy work and you'll get it fast:)
32x8=$265
Hope it helps!
Answer:
256
Step-by-step explanation:
A tank is 5/8 filled with water. When the metal cube is placed in the tank, it is 3/4 full. Use the guess, check, revise strategy to find the dimensions of the cube.
The cube has the dimensions of:
[tex]1.26m \ by \ 1.26m \ by \ 1.26m[/tex]
Explanation:A cube is a prism whose sides all have the same length. So the dimension of this cube will be given by one of its sides. For any object that is submerged in water, the volume of the displacement liquid equals the volume of the object.
[tex]For \ any \ cube \ the \ volume \ in \ terms \ of \ one \ side \ (s) \ is: \\ \\ V=s^3[/tex]
Suppose the volume of the tank when full is [tex]16m^3[/tex], so if it is 5/8 filled with water, then:
[tex]V_{5/8}=\frac{5}{8}(16) \\ \\ V_{5/8}=10m^3[/tex]
When the metal cube is placed in the tank, it is 3/4 full:
[tex]V_{3/4}=\frac{3}{4}(16) \\ \\ V_{3/4}=12m^3[/tex]
So the difference between these two volumes is the displacement volumen that equals the volume of the cube:
[tex]V=V_{3/4}-V_{5/8} \\ \\ V=12-10 \\ \\ V=2m^3[/tex]
So, the side of the cube is:
[tex]s=\sqrt[3]{2} \\ \\ \boxed{s\approx 1.26m}[/tex]
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two friends are taking an English class that has a monthly reading list once a student chooses a book from the list no other student can choose that book if there are three mystery and four romance books left what is the probability that both friend randomly selected romance book one after the other?
Answer:
To find the probability that both friends randomly select a romance book one after the other, we can use the concept of conditional probability.
Let's denote the events:
- Event A: First friend selects a romance book.
- Event B: Second friend selects a romance book.
Given that there are 4 romance books left and a total of 7 books left (3 mystery + 4 romance), the probability of Event A happening for the first friend is:
\[ P(A) = \frac{4}{7} \]
After the first friend selects a romance book, there are now 3 romance books left out of a total of 6 books remaining (since one book has been chosen). So, the probability of Event B happening for the second friend, given that the first friend selected a romance book, is:
\[ P(B|A) = \frac{3}{6} = \frac{1}{2} \]
Now, to find the probability of both events happening, we multiply their probabilities:
\[ P(A \text{ and } B) = P(A) \times P(B|A) \]
\[ P(A \text{ and } B) = \frac{4}{7} \times \frac{1}{2} \]
\[ P(A \text{ and } B) = \frac{4}{14} \]
\[ P(A \text{ and } B) = \frac{2}{7} \]
So, the probability that both friends randomly select a romance book one after the other is \( \frac{2}{7} \).
Circle assignment! THANKS so much its worth so much of my grade
Answer:
1. B) Figure B.
2. C) Figure C.
3. D) Figure D.
4. C) Figure C.
Step-by-step explanation:
Given: Radius of Circle A= 4
Radius of Circle B= 5
Radius of circle C= 6
Radius of circle D= 7
Now, finding circumference and area of all the circle.
We know, circumference of circle= [tex]2\pi r[/tex]
Area of circle= [tex]\pi r^{2}[/tex]
Where, r= radius of circle and π = 3.14
First, solving for figure A
Circumference= [tex]2\times 3.14\times 4= 25.12\ cm[/tex]
Area= [tex]3.14\times 4^{2} = 50.24\ cm^{2}[/tex]
Solving for Figure B
Circumference= [tex]2\times 3.14\times 6= 31.4\ cm[/tex]
Area= [tex]3.14\times 5^{2} = 78.5\ cm^{2}[/tex]
Solving for Figure C
Circumference= [tex]2\times 3.14\times 6= 37.68\ cm[/tex]
Area= [tex]3.14\times 6^{2} = 113.04\ cm^{2}[/tex]
Solving for Figure D
Circumference= [tex]2\times 3.14\times 7= 43.96\ cm[/tex]
Area= [tex]3.14\times 7^{2} = 153.86\ cm^{2}[/tex]
∴ 1. Answer is Figure B.
2. Answer is figure C.
3. Answer is Figure D
4. Answer is Figure C.
What would 20-(2+1)-6÷3 be
Answer:
15
Step-by-step explanation:
2+1=3
6 divided by 3= 2
20-3-2=15
what is the first step when dividing two fractions
Answer:
Completely factor both the numerators and denominators of all fractions.
Step-by-step explanation:
Jared deposits $2 into his savings account every day for six weeks. Using the associate
Answer:
(2*7)*6 or 2*(7*6) = $84
Step-by-step explanation:
The associative property would always give the same value as an answer no matter the way of expression, once the expressions are right. So in this case,
Since has saves $2 every day and there are 7 days in a week,
2*7
and save this continously for 6 weeks.
(2*7)*6
This equals $84
OR
7 days in a week for 6 weeks
7*6
and saved $2 per day
2*(7*6)
This equals $84
What is 0.5p - 3.45 = -1.2
Andre had lots of Halloween cand. He ate the same amount of candy each day. After 10 days he had 115
pieces. After 18 days he had 43 pieces. How many will he have after 22 days?
Answer:
he had 343 pieces of candy after 22 days
Step-by-step explanation:
You can find this by first divide 10/ 115 this is equal to 15.5 to find how many candies he eats per day. Then you multiply 15.5 by 22(days) to find this answer .
Andre eats 9 pieces of candy per day. After 18 days, he had 43 pieces. By calculating his daily consumption, we can deduce that after 22 days, Andre will have 7 pieces of candy left.
The question asks us to determine how many pieces of candy Andre will have after 22 days, given the information on how many he had after 10 and 18 days.
First, let's find out how much candy Andre eats each day. After 10 days, he had 115 pieces, and after 18 days, he had 43 pieces.
Calculate the difference in the number of days: 18 - 10 = 8 days.Calculate the difference in the amount of candy: 115 - 43 = 72 pieces.Divide the candy difference by the days' difference to find out how much candy he eats daily: 72 pieces / 8 days = 9 pieces/day.Find out how many days are between day 18 and day 22: 22 - 18 = 4 days.Calculate the amount of candy Andre will eat in 4 days: 9 pieces/dayTherefore, Andre will have 7 pieces of candy left after 22 days.
What is 1 2/4 x 3 5/6
Answer:
5.75
Step-by-step explanation:
We can first off make them improper fractions. They're easier to deal with.
1 2/4 = 6/4.
3 5/6 = 23/6
6/4 * 23/6.
Multiply numerators: 23 * 6 = 138.
Multiply denominators: 4 * 6 = 24.
138/24.
Simplify: 23/4
Reid and Maria both play soccer. This season Reid scores 4 less than twice the number of goals that Maria scored the difference in the number of goals they scored was 6 how many goals did each of them score.
Answer: Reid scored 1 and Maria scored 5.
Step-by-step explanation:
5 x 2 = 10
10-4= 6
5 + 1 = 6
What is the result when 4x2 + 7x − 5 is subtracted from 9x2 − 2x + 3?
Answer:
-10 + 9x - 8
Step-by-step explanation:
4x2 + 7x - 5 subtracted from
9x2 -2x + 3
8 + 7x - 5
18 - 2x + 3
(8-18) (+7x - -2x) (-5 - +3)
-10 ( +7x +2x) (-5-3)
-10 + 9x -8
The result when 4x2 + 7x − 5 is subtracted from 9x2 − 2x + 3 is found by adding the additive inverse of each term in the polynomial being subtracted. Result is: 5x2 - 9x + 8.
Explanation:Subtraction of Polynomials:
To find the result when 4x2 + 7x − 5 is subtracted from 9x2 − 2x + 3, first remember that subtraction of polynomials is equivalent to adding the additive inverse of each term in the polynomial being subtracted.
The inverse of 4x2 is -4x2The inverse of 7x is -7x and,The inverse of -5 is +5So, 4x2 + 7x − 5 becomes -4x2 - 7x + 5. We then add this to 9x2 − 2x + 3 term by term.
The final result is: (9x2 + -4x2) + (-2x - 7x) + (3 + 5) = 5x2 - 9x + 8
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10.6666666667 as a fraction
The fraction form of the number 10.666666667 is,
⇒ 32/3
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction.
Given that,
A number is,
⇒ 10.6666666667
For the fraction form,
Let us assume that,
⇒ x = 10.666666667 .. (i)
Multiply by 10 on both sides,
⇒ 10x = 106.666666667 .. (ii)
Subtract (ii) from (i);
⇒ 10x - x = 106.666666667 - 10.66666667
⇒ 9x = 96
Divide 9 on both sides,
⇒ x = 96/9
Or, it can be written as,
⇒ x = 32/3
So, the fraction form is, 32/3
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Final answer:
To convert the decimal 10.6666666667 to a fraction, we write it as the sum of 10 and the repeating decimal 0.6666666667. The repeating decimal equates to 2/3 after simplification, leading to the mixed number 10 2/3 or the improper fraction 32/3.
Explanation:
To convert the decimal 10.6666666667 to a fraction, we need to express it as the sum of its whole number part and its fractional part. The whole number part is 10, and the fractional part is 0.6666666667.
First, let's focus only on the fractional part. To turn 0.6666666667 into a fraction, notice that it's a repeating decimal. If we denote the repeating part by 'x', the equation will be:
x = 0.6666666667
Multiplying by 10 gives:
10x = 6.6666666667
Subtracting the original equation from this new equation:
9x = 6
Now, we solve for 'x':
x = 6/9
However, this fraction can be simplified to:
x = 2/3
Therefore, the fraction form of 10.6666666667 is 10 2/3, which can also be written as an improper fraction:
(10 × 3/3) + 2/3=(30/3) + 2/3=32/3Ralph’s shirt company sells t-shirts for $7.50 each with a flat rate of $10 for shipping. Frank’s t-shirt company sells t-shirts for $10 each with free shipping.
Answer:
I assume your asking who's is better and why?
Step-by-step explanation:
Ralph has stated that for 1 shirt it will cost
$7.50 + $10 shipping= $17.50
Frank says it's $10 a shirt no shipping
if you work out the cost of Ralph's up to 5 shirts using the equation
($7.50 x number of shirts ) + $10 shipping
with each equation replace number of shirts with the number 1,2,3,4 and 5
1 shirt will cost you $17.50
2 shirts will cost you $25.00
3 shirts will cost you $32.50
4 shirts will cost you $40.00
5 shirts will cost you $47.50
at Frank's shop
1 shirt will cost you $10
2 shirts will cost you $20
3 shirts will cost you $30
4 shirts will cost you $40
5 shirts will cost you $50
Frank's is better to buy no more than 4 shirts from as he's cheaper up to 4 shirts.
Ralph is cheaper for bigger orders with 5 or more shirts in them
The question deals with the comparison of the costs of buying T-shirts from Ralph’s company versus Frank’s company. The cost differs based on the number of T-shirts purchased and the associated shipping fees.
Explanation:The question is asking for a comparison between the two companies selling T-shirts and the associated costs. Ralph's company sells T-shirts for $7.50 each with an additional flat rate of $10 for shipping. In contrast, Frank's company sells T-shirts at a slightly higher price of $10 each but does not charge any shipping fees.
For example: If a customer wants to buy one T-shirt from each company, from Ralph’s company it would cost $7.50 (T-shirt price) + $10 (shipping fee) = $17.50. From Frank’s, it would cost $10 (T-shirt price) since shipping is free. So the cost would be different in both cases. However, if the customer opts to buy multiple t-shirts, the total cost might change depending on the number of t-shirts they decide to buy because of the fixed shipping cost on Ralph's side.
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Which of the following is an even function?
f(x) = |x|
f(x) = x3 – 1
f(x) = –3x
f (x) = RootIndex 3 StartRoot x EndRoot
Answer: f(x) = |x|
Step-by-step explanation:
A function is even if for every real N, f(N) = f(-N)
As you know, the module of a function always returns the positive value of a number, so I-3I = 3 = I3I (and that for every number)
So the function f(x) = IxI is an even function.
Functions with odd powers can not be even functions, so the second and tird options are discarded.
the fourth functions seems to be:
f(x) =∛x = (x)1/3 which is not even, because if x = 1, f(1) = 1, and if x=-1, f(-1) = -1
In the given functions, an even function is [tex]f(x)=|x|[/tex]. Therefore, the correct answer is option A.
A function's even, odd, or neither properties can be expressed algebraically or graphically in a variety of ways. If a function's graph remains unchanged when reflected in the y-axis, it is said to be an even function. Consider a function f(x) that is considered an even function if f(-x) equals f(x).
1) [tex]f(x)=|x|[/tex]
Let [tex]x = -3[/tex], we get
[tex]f(-3)=|-3|[/tex]
[tex]f(-3)=3[/tex]
[tex]f(-x)= f(x)[/tex]
2) [tex]f(x)=x^3-1[/tex]
Let [tex]x = -1[/tex], we get
[tex]f(-1)=(-1)^3-1[/tex]
[tex]f(-1)=-1-1[/tex]
[tex]f(-1)=-2[/tex]
[tex]f(-x)\neq f(x)[/tex]
3) [tex]f(x)=-3x[/tex]
Let [tex]x = -1[/tex], we get
[tex]f(-1)=-3(-1)[/tex]
[tex]f(-1)=3[/tex]
[tex]f(-x)\neq f(x)[/tex]
4) [tex]f(x)=\sqrt[3]{x}[/tex]
Let [tex]x = -1[/tex], we get
[tex]f(-1)=\sqrt[3]{(-1)}[/tex]
[tex]f(-x)\neq f(x)[/tex]
Therefore, the correct answer is option A.
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PLZ HELP!!! I need the answer by tomorrow. I will give points cuz I don't know how to mark the brainliest.
Answer:
U'(-5, -2), V'(-3, -1), W'(-3, 3), Z'(-5, 6).
Plot these points. Then connect them to form trapezoid U'V'W'Z'.
Give a real world example for a system of equations! Max points!!!
Answer:
likewise your friend is two times older than u and u r two times younger than him then assume the given sum as 120 so your friend"s age will be 2x and ur age will be y so the sum obtained Is 2x+y=120
Answer: Alex had 8 apples to share Amon him and three of his friends. What is 8 / 4 ? It is 2
Step-by-step explanation:
Hans spent three days baking 224 cookies. On the second day, he baked twice as many as he did on the first day. On the third day, he baked half as many as he did on the first day.
How many cookies did he bake on the second day?
Final answer:
To find the number of cookies Hans baked on the second day, we solve the equation x + 2x + x/2 = 224, where x is the number of cookies baked on the first day. Solving this, we find x=64, meaning he baked 128 cookies on the second day.
Explanation:
The question involves solving a problem about Hans, who spent three days baking a total of 224 cookies. On the second day, he baked twice as many cookies as on the first day, and on the third day, he baked half as many as on the first day. To find how many cookies he baked on the second day, let's denote the number of cookies baked on the first day as x.
On the second day, he baked 2x cookies.
On the third day, he baked x/2 cookies.
Adding these together: x + 2x + x/2 = 224.
Combining like terms, we get 3.5x = 224.
Dividing both sides by 3.5 gives x = 64.
Therefore, he baked 2x = 2*64 = 128 cookies on the second day.
1/3+1/4 I really don’t get this so can someone please help me with this problem
Answer:
7/12
Step-by-step explanation:
You have to find a common denominator, so you would multiply 3 from the 1/3 by 4 which gets you twelve. And bc you multiplied the 3 you have to multiple the 1 so 1/3 would be 4/12. You would then multiply 4 by 3 and get 12. Then do the same to the one on top. So 1/4 would be 3/12. You then add 3 and 4 and get 7. That’s the numerator, the denominator stays 12. So it would be 7/12
Write the expression in complete factored form. 4a(x-9)-7(x-9)=
Answer:
[tex]4a(x-9)-7(x-9)=(x-9)[4a-7][/tex]
Step-by-step explanation:
we have the expression
[tex]4a(x-9)-7(x-9)[/tex]
Factor the term (x-9)
so
[tex](x-9)[4a-7][/tex]
therefore
[tex]4a(x-9)-7(x-9)=(x-9)[4a-7][/tex]