You can write an equivalent fraction with a smaller numerator and denominator
Fractions
This is the ratio of two integers:
Let the odd numerator be 5 Let the odd denominator be 15We are to determine if you can write an equivalent fraction with a smaller numerator and denominator.
Ratio = 5/15
Simplify
Ratio = (5*1)/(5*3)
Ratio = 1/3
This shows that you can write an equivalent fraction with a smaller numerator and denominator
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How do I simplify 3x (2y + 8)
Answer:
Step-by-step explanation:
5. Find the midpoint of AB given A(-7, 4) and B(3,-4).
Answer:
The answer is (-2,0)
Step-by-step explanation:
When you put both points on the graph. Draw a line through them.
See where the line hits a point from in between the points.
Heres an easy question...
What's 2+2+6+7+9???
Whoever answers it first gets 76pts!!!! :)
Answer: 26
Step-by-step explanation: I think so...
Answer:
26
Step-by-step explanation:
Divide using polynomial long division
(x^2+x-17)/(x-4)
The solution for (x^2+x-17) / (x-4) is (x + 5) + 3/(x-4)
Step-by-step explanation:
The given polynomial is (x^2+x-17) divided by (x-4)
Steps for long division method :
check the polynomial is written in descending order of power (x^3, x^2, and so on).To make the first term zero, multiply the divisor with one power lesser than the first term. For eg. To divide x^2, multiply the divisor with x.Subtract and bring down the next term.The above two steps are repeated until the last term gets divided.The term remaining after the last subtract step is the remainder. The final answer must be written in quotient and remainder as a fraction with the divisor.Using long division method :
x + 5
x-4 | x^2 + x - 17
(-)(x^2 - 4x)
5x - 17
(-)(5x -20)
3
The quotient is (x+5).
The remainder is 3.
The solution is written in the form of quotient + remainder/ divisor
∴ The final answer is (x^2+x-17) / (x-4) = (x + 5) + 3/(x-4)
Final answer:
To divide (x²+x-17) by (x-4) using polynomial long division, divide the highest order term of the dividend by the highest order term of the divisor, multiply the divisor by the result, subtract the result from the dividend, and repeat until there are no more terms or the remainder has lower degree. The quotient is x+5 and the remainder is -3.
Explanation:
To divide (x²+x-17) by (x-4) using polynomial long division:
Write the dividend (x²+x-17) and the divisor (x-4) in the division format.
Divide the highest order term of the dividend (x²) by the highest order term of the divisor (x). The result is x.
Multiply the entire divisor (x-4) by the result from step 2 (x) and write the result below the dividend.
Subtract the result from step 3 from the dividend.
Repeat steps 2-4 until there are no more terms to bring down or the degree of the remainder is less than the degree of the divisor.
The final quotient is x+5 and the remainder is -3.
Jim is 2 years older than 3 times his little brother Tommy. Together their ages add up to 18. How old is each?
Final answer:
By setting up an equation based on the given information that Jim is 2 years older than 3 times Tommy's age and their combined ages are 18, we find that Tommy is 4 years old and Jim is 14 years old.
Explanation:
The question is about finding the ages of Jim and his younger brother Tommy given that Jim is 2 years older than 3 times Tommy's age and together their ages add up to 18. Let's denote Tommy's age as T years. Therefore, Jim's age would be 3T + 2 years. According to the problem, if we add both ages, the sum is 18. So, we can set up the following equation to find their ages:
T + (3T + 2) = 18
Simplifying this equation gives:
4T + 2 = 18
4T = 16
T = 4
Thus, Tommy is 4 years old. To find Jim's age, we substitute Tommy's age back into the equation for Jim's age:
Jim's age = 3(4) + 2 = 12 + 2 = 14
Therefore, Tommy is 4 years old, and Jim is 14 years old.
Mackin Investing charges its customers a 1% commission. The Ross Group, a discount broker, charges $25 per trade. For what amount of stock would both brokers charge the same commission?
Answer:
The amount of stock for which both brokers would charge the same commission is $2500.
Step-by-step explanation:
i) Let the amount of stock to be traded be worth $x
ii) therefore for both the brokers to charge the same commission we can write
1% of x = $25 [tex]\RIghtarrow[/tex][tex]\Rightarrow[/tex] 0.01 [tex]\times[/tex] x = 25 [tex]\therefore[/tex] x = [tex]\frac{25}{0.01} = 2500[/tex]
The amount of stock for which both brokers would charge the same commission is $2500.
- Write the linear function for the line that passes through the point (3, 7) and has a slope of 2.
Answer:
lool at the picture shown
Find the cube root of 3357
I need to determine sin B.
Answer:
SinB = Sin30 = 0.5
Step-by-step explanation:
Ok lets use sine rule
a/SinA = b/SinB = c/SinC
a/Sin60 = b/SinB = 12/Sin90
b/Sin30 = 12/Sin90
b = (12 × Sin30) ÷ Sin90
b = (12 × 0.5) ÷ 1
b = 6cm
SinB = Sin30 = 0.5
Find the solution of the system of equations -6x+3y=-15 4x-3y=13
Write a function rule that relates y to x
The function rule that relates y (circumference) to x (diameter) is y = π x [pi × x]
Explanation:Since x represents the diameter of the circle and y represents the circumference.
For a circle with radius r, circumference of the circle (y)equals,
y = 2πr ................................(1)
Diameter of a circle is twice the radius of the circle.
Assuming x as the diameter
[tex]x = 2\times r = 2r[/tex] ...........................(2)
Substituting (2) in (1), we get
y = π(2r) = πx ..............................................(3)
A function rule is an equation that determines the relation between a dependent variable and an independent variable. The relation between diameter of a circle and its circumference can be given as
Circumference = Pi × Diameter of circle
y = π × x
where π = 3.142
Patty spent 3.5 times as much as Sandy
on their shopping trip. If Sandy spent
$20.50, how much did Patty spend?
Answer:
Patty spent $71.75
Step-by-step explanation:
20.50 x 3.5 = 71.75
Answer: 71.75
3.5* 20.50
and then you have to graph it but im stuck on graphing f(2) so please help
[tex](-1, 9), \ (0, 6), \ (1, 4), \ (2, 2\frac{2}{3} ), \ (1, \frac{7}{9} )[/tex]
Solution:
Given [tex]f(x)=6\left(\frac{2}{3}\right)^{x}[/tex]
Domain = {–1, 0, 1, 2, 3}
Substitute the given values in the function.
At x = –1,
[tex]f(-1)=6\left(\frac{2}{3}\right)^{-1}[/tex]
[tex]=6 \times \frac{3}{2}[/tex]
= 9
[tex](x, f(x))=(-1, 9)[/tex]
At x = –0,
[tex]f(0)=6\left(\frac{2}{3}\right)^{0}=6[/tex]
[tex](x, f(x))=(0,6)[/tex]
At x = 1,
[tex]f(1)=6\left(\frac{2}{3}\right)^{1}=4[/tex]
[tex](x, f(x))=(1,4)[/tex]
At x = 2,
[tex]f(2)=6\left(\frac{2}{3}\right)^{2}[/tex]
[tex]=\frac{24}{9}[/tex]
[tex]=2\frac{6}{9}[/tex] (Cancel the common terms)
[tex]=2\frac{2}{3}[/tex]
[tex](x, f(x))=(2, 2\frac{2}{3} )[/tex]
At x = 3,
[tex]f(3)=6\left(\frac{2}{3}\right)^{3}[/tex]
[tex]=\frac{48}{27}[/tex] (Cancel the common terms)
[tex]=\frac{16}{9}[/tex]
[tex]=1\frac{7}{9}[/tex]
[tex](x, f(x))=(3, 1\frac{7}{9} )[/tex]
Plot the points in the graph.
The image of the graph is attached below.
The centroid of a triangle is at (8, 7). One vertex of the triangle is at (0, 1). What is the midpoint of the side opposite this vertex?
Answer:
(12,10)
Step-by-step explanation:
Let the midpoint of the side opposite this vertex have coordinates B(a,b)
We have the centroid at C(8,7) and the vertex of the triangle at A(0,1).
The centroid divides AB internally in the ratio 2:1
We use the formula:
[tex](\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]
where m:n=2:1 is the ratio of internal division.
We substitute the coordinates of A and B and the ratio to get:
[tex](\frac{2a+1*0}{2+1},\frac{2b+1*1}{2+1})[/tex]
This should simplify and give us the centroid.
[tex](\frac{2a}{3},\frac{2b+1}{3})=(8,7)[/tex]
This implies that:
[tex]\frac{2a}{3}=8,\frac{2b+1}{3}=7[/tex]
We solve for a and b
[tex]2a=24,2b+1=21[/tex]
[tex]a=12,b=10[/tex]
Therefore the midpoint of the side opposite this vertex is (12,10)
3x^3 - 2y^-6x^2y^2+xy for x=2/3 and y=1/2
To evaluate the expression[tex]\(3x^3 - \frac{2}{y^6}x^2y^2 + xy\) for \(x = \frac{2}{3}\) and \(y = \frac{1}{2}\),[/tex]let's substitute these values into the expression:
[tex]\[3\left(\frac{2}{3}\right)^3 - \frac{2}{{\left(\frac{1}{2}\right)}^6}\left(\frac{2}{3}\right)^2\left(\frac{1}{2}\right)^2 + \frac{2}{3} \times \frac{1}{2}\][/tex]
Let's simplify this step by step.
1. [tex]\(3\left(\frac{2}{3}\right)^3 = 3 \times \frac{8}{27} = \frac{24}{27} = \frac{8}{9}\)[/tex]
2. [tex]\(- \frac{2}{{\left(\frac{1}{2}\right)}^6}\left(\frac{2}{3}\right)^2\left(\frac{1}{2}\right)^2 = - 2 \times 2^6 \times \frac{1}{3^2} \times \frac{1}{2^2} = - 2 \times 64 \times \frac{1}{9} \times \frac{1}{4} = - \frac{128}{9}\)[/tex]
3 .[tex]\(\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}\)[/tex]
Now, let's add these results together:
[tex]\[\frac{8}{9} - \frac{128}{9} + \frac{1}{3} = \frac{8 - 128 + 3}{9} = \frac{-117}{9} = -\frac{13}{3}\][/tex]
So, [tex]\(3x^3 - \frac{2}{y^6}x^2y^2 + xy\) evaluated at \(x = \frac{2}{3}\) and \(y = \frac{1}{2}\) is \(-\frac{13}{3}\).[/tex]
The square of m reduced by 49
Square of m reduced by 49 = m²- 49
Step-by-step explanation:
Let us consider the variable as m.
Square of m is given as m².
Reduction factor is 49.
So the expression for the square of m reduced by 49 is given as m²- 49.
how many times more is 21.25 than 1.7 answers?
Answer:
19.55
Step-by-step explanation:
21.25
- 1.7
_____
19.55
You can buy popcorn at the village theater in small, medium, or large sizes. The popcorn can be buttered or plain. If all of the choices are equally likely, what is the probability that a customer chooses a medium size with butter?Explain how you got your answer.
Answer:
1/6
Step-by-step explanation:
Steps to solve 4.3x+19.35=8.11+4.0x
Answer:
x = -37 7/15
Step-by-step explanation:
1. Find the terms with the variable. They are 4.3x on the left and 4.0x on the right.
2. Identify the term with the least coefficient*. It is 4.0x on the right.
3. Subtract that term from both sides of the equation.
4.3x -4.0x +19.35 = 8.11 +4.0x -4.0x
0.3x +19.35 = 8.11 . . . . . . simplify
4. Identify any constant term on the side of the equation with the variable. It is 19.35 on the left.
5. Subtract that constant from both sides of the equation.
0.3x +19.35 -19.35 = 8.11 -19.35
0.3x = -11.24 . . . . . . . simplify
6. Divide both sides of the equation by the coefficient of the variable. That coefficient is 0.3 in this equation.
(0.3x)/0.3 = (-11.24)/0.3
x = -37.466666... (repeating decimal)
__
If you like, you can express the solution as a mixed number:
x = -11.24/0.30 = -1124/30 = -562/15
x = -37 7/15
_____
You are expected to be able to do the math using the numbers in any form they might appear: integers, mixed numbers, fractions, decimals, scientific notation. You can convert the problem here to an integer problem by multiplying both sides by 100:
430x +1935 = 811 +400x
The answer still has a fraction in it: x= -1124/30 = -37 7/15.
_____
* You subtract the term with the least coefficient so the variable term in the result has a positive coefficient. That may be desirable, but is not necessary. You can subtract either variable term to get the variable on one side of the equal sign. You have to pay attention to the resulting sign when you divide by the variable's coefficient.
Mrs.Lohens made curtains for her children’s bedrooms. She used 4 3/4 yards of fabric for Nickys room and 6 5/8 yards for Linda’s room. How much fabric did she use in all?
Answer:
[tex]11\frac{3}{8}\ yd[/tex]
Step-by-step explanation:
we know that
To find out the total yards of fabric used, add up the yards of fabric used for Nickys' room and the yards of fabric used for Linda's room
so
[tex]4\frac{3}{4}+6\frac{5}{8}[/tex]
Convert mixed number to an improper fraction
[tex]4\frac{3}{4}\ yd=4+\frac{3}{4}=\frac{4*4+3}{4}=\frac{19}{4}\ yd[/tex]
[tex]6\frac{5}{8}\ yd=6+\frac{5}{8}=\frac{6*8+5}{8}=\frac{53}{8}\ yd[/tex]
Adds the fractions
[tex]\frac{19}{4}+\frac{53}{8}=\frac{2*19+53}{8}= \frac{91}{8}\ yd[/tex]
Convert to mixed number
[tex]\frac{91}{8}\ yd= \frac{88}{8}+ \frac{3}{8}= 11\frac{3}{8}\ yd[/tex]
Payton plays 15 games of fortnight in 15 minutes. If he maintains this rate, how many games will he play in 3 hours
Payton will play 180 games in 3 hours.
Step-by-step explanation:
Given,
Games played in 15 minutes = 15 games
We will find unit rate;
15 minutes = 15 games
Dividing both sides by 15
[tex]\frac{15}{15}\ minutes=\frac{15}{15}\ games\\\\1\ minute = 1\ game[/tex]
Time = 3 hours = 3*60 = 180 minutes
180 minutes = 180*games per minute
180 minutes = 180*1 games
180 minutes = 180 games
Payton will play 180 games in 3 hours.
Keywords: unit rate, multiplication
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Solve for x. Show your work. -1/2 x < -12
-1/2x < -12
Divide both sides by -1/2
Also because you are dividing by a negative number you need to reverse the inequality sign.
X > 24
10 times a number, then add 20
Answer:
10x+20
Step-by-step explanation:
Answer: The equation is 10x+20
(x is a variable, not a multiplication symbol)
Step-by-step explanation:
10 times a number, that is unknown, plus 20.
x is the unknown number.
10x plus 20.
10x+20
The graph of the equation x = y2 + 4 is symmetric with respect to which of the following?
a. the 3-axis
c. the line y = -x+ 4
b. the x-axis
d. the line y = x
Answer:
the graph of the equation will be symmetric about option b.) x axis
Step-by-step explanation:
i) the given equation is x = [tex]y^2[/tex] + 4
ii) therefore [tex]y^{2}[/tex] = x - 4
iii) the equation is that of a parabola with vertex at (4,0)
iv) the graph of the equation will be symmetric about option b.) x axis
A family on vacation drove the first 200 miles in 4 hours and the second 200 miles in 5 hours. Which expression below gives their average speed for the entire trip?
A.200+2004+5
B.(2004+2005)÷2
C.2004+2005
D.4004+4005
Answer:
(2004+2005) divided by 2
Step-by-step explanation:
1. What is the extraneous solution of √x−3 + x = 9?
2. If the volume of a cube is 108 ft^3, what is the side length? Keep your answer in radical form.
Can someone help with either of them? Thanks!
Answer:
1. x = 12
2. 3∛4 feet.
Step-by-step explanation:
1. We are given the equation of x as [tex]\sqrt{x - 3} + x = 9[/tex] and we have to find the extraneous solution of the equation.
Now, [tex]\sqrt{x - 3} + x = 9[/tex] ............. (1)
⇒ [tex]\sqrt{x - 3} = 9 - x[/tex]
Squaring both sides we get,
⇒ x - 3 = 81 - 18x + x²
⇒ x² - 19x + 84 = 0
⇒ x² - 12x - 7x + 84 = 0
⇒ (x - 12)(x - 7) = 0
⇒ x = 12 or 7.
Now, putting x = 12 in the equation (1) we get,
[tex]\sqrt{12 - 3} + 12 \neq 9[/tex]
Again, putting x = 7 in the equation (1) we get,
[tex]\sqrt{7 - 3} + 7 = 9[/tex]
Therefore, x = 12 is an extraneous solution of this equation. (Answer)
2. The volume of a cube with side lengths a ft. is given to be 108 ft³.
So, a³ = 108
⇒ a = 3∛4 feet.
Therefore, the length of the sides of the cube are each 3∛4 feet. (Answer)
Suppose that f(x) = x2 and g(x) = 2/5 x2 Which statement best compares the
graph of g(x) with the graph of f(x)?
O
A. The graph of g(x) is the graph of f(x) compressed vertically.
O
B. The graph of g(x) is the graph of f(x) compressed vertically and
flipped over the x-axis.
O
C. The graph of g(x) is the graph of f(x) stretched vertically and
flipped over the x-axis.
O
D. The graph of g(x) is the graph of f(x) stretched vertically.
The function g(x) is the function f(x) scaled down by a factor of 2/5, resulting in a vertical compression of the graph. Thus, the correct answer is A. The graph of g(x) is f(x)'s graph vertically compressed.
Explanation:The function g(x) = 2/5 x2 is f(x) = x2 multiplied by a scalar factor of 2/5. This means that every y-coordinate in the graph of f(x) is scaled down by a factor of 2/5 to produce the corresponding y-coordinate in the graph of g(x). It does not flip the graph over the x-axis. Therefore, the graph of g(x) is simply the graph of f(x) compressed vertically. So, the correct answer is A. The graph of g(x) is the graph of f(x) compressed vertically.
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What is the perimeter, P, of a rectangle that has a length of x + 5 and a width of y - 1?
Answer:
P = 2x + 2y + 8, Answer is A
Step-by-step explanation:
I got it right on the test so yea.
The sum of two numbers is 60. If twice the smaller number is subtracted from the large number, the result is 9. Find the two numbers
Answer:Therefore the two numbers are -20 and -40
Step-by-step explanation:
Let the two numbers be a and b,
It is given that their sum is 60, so a + b = -60,
It is also given that their difference is 20, so a - b = 20,
Since we don’t know yet which one out of a and b is greater, assume any one of them to be larger than the other (a in my case),
Add the above two equations, you get,
2a = -40 or a = -20,
Substitute this value of a in any of the formed equations,
a + b = -60,
-20 + b = -60 or b = -40,
Let the two numbers be a and b,
It is given that their sum is 60, so a + b = -60,
It is also given that their difference is 20, so a - b = 20,
Since we don’t know yet which one out of a and b is greater, assume any one of them to be larger than the other (a in my case),
Add the above two equations, you get,
2a = -40 or a = -20,
Substitute this value of a in any of the formed equations,
a + b = -60,
-20 + b = -60 or b = -40,
Therefore the two numbers are -20 and -40
The smaller number is 17, and the larger number is 43. The two equations formed from the given information are solved simultaneously to find these numbers.
To solve this problem, we need to set up two equations based on the given information. Let's denote the smaller number by s and the larger number by l.
The sum of the two numbers is 60: s + l = 60.
If twice the smaller number is subtracted from the large number, the result is 9: l - 2s = 9.
We can solve these equations simultaneously. First, rearrange the second equation to express l in terms of s: l = 2s + 9. Next, substitute this expression into the first equation:
s + (2s + 9) = 60
3s + 9 = 60
3s = 51
s = 17
Now we have found the smaller number is 17. To find the larger number, we substitute s back into the equation for l:
l = 2(17) + 9
l = 34 + 9
l = 43
So the two numbers are 17 and 43
Find the value of 49/50 divided by 7/6