Answers
Answer
x = 15Step-by-step explanation:
[tex] \sf{ \frac{40}{x + 1} = \frac{15}{6} }[/tex]
Do cross multiplication
[tex] \dashrightarrow{ \sf{15(x + 1) = 40 \times 6}}[/tex]
Distribute 15 through the parentheses
[tex] \dashrightarrow \sf \: 15x + 15 = 40 \times 6[/tex]
Multiply the numbers : 40 and 6
[tex] \dashrightarrow{ \sf{15x + 15 = 240}}[/tex]
Move 15 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{15x = 240 - 15}}[/tex]
Subtract 15 from 240
[tex] \dashrightarrow \: \sf{15x = 225}[/tex]
Divide both sides by 15
[tex] \dashrightarrow{ \sf{ \frac{15x}{15} = \frac{225}{15} }}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{x = 15}}[/tex]
Hope I helped!
Best regards! :D
Related Questions
3(x-1)-2(2x+1)=8(x-1)
Answers
Answer:
x = 1/3
Step-by-step explanation:
3(x-1)-2(2x+1)=8(x-1)
Distribute
3x -3 -4x-2 = 8x -8
Combine like terms
-x -5 = 8x -8
Add x to each side
-x-5+x = 8x-8+x
-5 = 9x-8
Add 8 to each side
-5+8 = 9x-8+8
3 = 9x
Divide by 9
3/9 = 9x/8
1/3 =x
3(x-1)-2(2x+1)=8(x-1)
Use distributive property:
3x-3 -4x-2 = 8x-8
Combine like terms:
-x -5 = 8x -8
Add 8 to both sides:
-x +3 = 8x
Add x to both sides:
3 = 9x
Divide both sides by 9:
x = 3/9
x = 1/3
Find f(-5) and f(12) for each piecewise function f(x){-4x+3 if x<3
{-x^3 If 3<_x<_8
{3x^2+1 If x>8
The lines go under the inequality lol but please help !
Answers
==================================================
Explanation:
The given piecewise function is
[tex]f(x) = \begin{cases}-4x+3 \ \text{ if } \ x < 3\\-x^3 \ \text{ if } \ 3 \le x \le 8\\3x^2+1 \ \text{ if } \ x > 8\end{cases}[/tex]
At first piecewise functions may be strange confusing things, but they aren't so bad. I like to think of it like this: f(x) is a function that changes its identity based on what the input x is. We have three situations
f(x) = -4x+3 when x < 3f(x) = -x^3 when [tex]3 \le x \le 8[/tex]f(x) = 3x^2+1 when x > 8In a sense, we have three different functions but they are combined somehow.
If x is smaller than 3, then we go for the first definition. Or if x is between 3 and 8, then we go for the second definition. Or if x is larger than 8, then we go for the third definition.
-----------------------
f(-5) means f(x) when x = -5. We see that -5 is smaller than 3, so x = -5 makes x < 3 true. We'll use the first definition
f(x) = -4x+3
f(-5) = -4(-5)+3
f(-5) = 20+3
f(-5) = 23
------------------------
Now the input is x = 12. This is larger than 8. In other words, x = 12 makes x > 8 true. We'll use the third definition
f(x) = 3x^2+1
f(12) = 3(12)^2+1
f(12) = 3(144)+1
f(12) = 432+1
f(12) = 433
------------------------
Side notes:
We won't use the second definition since we don't have any x inputs between 3 and 8To say "less than or equal to" on a keyboard, you can write "<=" without quotes. For example, [tex]x \le 5[/tex] is the same as x<=5Determine whether the source given below has the potential to create a bias in a statistical study. Washington University obtained word counts from the most popular novels of the past five years. Choose the correct answer below.A. There does not appear to be a potential to create a bias. The organization is reputable and has many professional and credible members.B. There does not appear to be a potential to create a bias. The organization would not gain from putting a spin on the results.C. There does appear to be a potential to create a bias. There is an incentive to produce results that are in line with theorganization's creed and that of its funders.D. There does appear to be a potential to create a bias. There is an incentive to make the results statistically insignificant.
Answers
Answer:
B
Step-by-step explanation:
How do I solve 3.24 x 1.2? I have tried and I always get the same answer! Please help! The answer is supposed to be 3.888 but I have gotten 6.47 each time. I'm good at math but I really need help!
Answers
Answer:
3.888
Step-by-step explanation:
3.24 × 1.2
Using Multiplication method multiply through like normal multiplication, don't
put your decimal yet
= 3.24
× 1.20
_______
000
6480
+32400
_______
38880
_________
Counting the number of decimal places to knowing where to properly place your decimal sign
3.24 = 2 decimal place
1.20 = 2 decimal place
Total = 4 decimal places
3.8880
Therefore, 3.24 × 1.20 = 3.8880 or 3.888
Which number is rational ?
Answers
Answer:
d) Root 16 is rational
Step-by-step explanation:
Root 16=4
4 is rational
Therefore root 16 is rational
Point B lies between points A and C on Line segment A C . Let x represent the length of segment AB in inches. The length of line A C is 20 inches. The space between points A and B is labeled x. The space between points B and C is labeled 3 x. Use the segment to complete the statements. The value of x is . The length of Line segment A B in inches is . The length of Line segment B C in inches is
Answers
Part 1) The value of x is 5
Part 2) The length of line AB is 5 inches
Part 3) The length of BC is 15 inches
Answer:
5
5
15
Step-by-step explanation:
find the area of the shape
Answers
Answer:
546
Step-by-step explanation:
Formula: 0.5*[sum of parallel sides] *height
Answer:
636 in.²
Step-by-step explanation:
First divide the shape into three pieces, you will get a triangle and two rectangles, the base of the triangle is 30 in. The height is 8 in. Multiply 30×8 to get 240 and then divide by two to get 120. Next the rectangle on top has sides that are 24 in. and 8 in. You will get 192. Lastly the rectangle on the bottom has sides of 54 in. and 6 in. For this you will get 324. Finally you add up 120+192+324 to get 636 in.²
Suppose y varies directly with x, and y = 6 when x =10. What is the value of x when y = 15?
Answers
Answer:
x=19
Step-by-step explanation:
because if you add 6 by 9 and you get 15 and if you plus 9 with 10 uoi get 19
The list below shows the number of medals that one nation's team won at the Olympics. What is the ratio of gold medals to the total number of medals that the team won? Gold 34 Silver 30 Bronze 39
Answers
Answer:
34:103
Step-by-step explanation:
Add up all the numbers and then put gold then : then the numbers added up
A proportion exists an equation that sets two ratios at the same value.
34 : 103 exists the ratio of gold medals to the total number of medals that the team won 103.
What is the difference between ratio and proportions?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. A ratio is a comparison between two values. A ratio is created when two ratios are equal.
If a ratio depicts the same relationship, it is proportionate. Two ratios can be written as fractions and then reduced to determine if they are proportionate to one another. You have proportionate ratios if the reduced fractions are equal.
Use ratios to compare two things.
The formula for the ratio of any two quantities is expressed as
a : b ⇒ a/b.
On the other hand, the proportional formula is
a : b :: c : d ⟶ ab = cd
a : b :: c : d ⟶ ab = cd
Types of proportion
Direct proportionReverse proportioncompound proportionContinued proportion34 : 103 exists the ratio of gold medals to the total number of medals that the team won 34 + 30 + 39 = 103
Add up all the numbers and then put gold then : then the numbers added up
To learn more about ratio and proportions, refer to:
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If 10 chips are 130 cals how much is just one chip?
Answers
1. On which road would there be a larger standard deviation in speed: a backroad or an interstate? Justify your answer
Answers
Answer:
Your answers may vary slightly. 5.2 Normal Distributions: Finding Probabilities If you are given that a random variable Xhas a normal distribution, nding probabilities corresponds to nding the area between the standard normal curve and the x-axis, using the table of z-scores. The mean (expected value) and standard deviation ˙should be given
Step-by-step explanation:
Find the missing side
length of the right
triangle. Remember
a² + b² = c²
12 ft
5 ft
?
Answers
Hey guys i was wondering if i could get some help
Answers
==================================================
Explanation:
The given piecewise function basically means we have h(x) defined in two different ways based on what x is
If x is less than 2, then h(x) = 4 - x^3 which is what the first row says
Or
If x = 2 or larger, then h(x) = 2x-3 which is what the second row says.
---------
We want to find h(0). We want to find h(x) when x = 0. We'll use the first definition since x = 0 is less than 2.
h(x) = 4 - x^3
h(0) = 4 - (0)^3
h(0) = 4 - 0
h(0) = 4
Choose the expression equivalent to 6x+8+2x+15
Answers
Answer:
Step-by-step explanation:
8x + 23
is -2 a solution for 7x+3=-17-3x ?
Answers
Answer:
yes -2 is the correct answer
Step-by-step explanation:
7x+3=-17-3x
7x+3x=-17-3
10x=-20
x=-20/10
x=-2
Answer:
[tex]\boxed{\bold{\huge{\boxed{\sf Yes.}}}}[/tex]
Step-by-step explanation:
=> [tex]\sf 7x+ 3 = -17-3x[/tex]
Combining like terms
=> [tex]\sf 7x+ 3x = -17-3[/tex]
=> [tex]\sf 10x = -20[/tex]
Dividing both sides by 10
=> [tex]\sf x = -2[/tex]
So, -2 is a solution of the given equation.
what is the answer to the equation 8n + 10 = 50 solve for n
Answers
Answer: [tex]n=5[/tex]
Add -10 to each side of the equation
[tex]10 + -10 + 8n = 50 + -10[/tex]
Combine like terms
[tex]0 + 8n = 50 + -10\\8n = 50 + -10\\8n = 40[/tex]
Divide each side by 8
[tex]8n/8=40/8\\n=5[/tex]
Answer:
n = 5
Step-by-step explanation:
8n +10 = 50
-10 -10
8n = 40
8 8
n = 5
Standard Form to Scientific Notation:
5.8 x 107 =
Answers
Answer:
just move the decimal a 107 times and add 0's
Step-by-step explanation:
The perimeter of a rectangle is P = 2w + 2L, where w is the width of the rectangle and L is the length of the rectangle. Rearrange this formula to find the width of the rectangle
Answers
Answer:
P-2L/2= w
P subtract 2L divided by 2 will give u the width
Step-by-step explanation:
Answer:
p
Step-by-step explanation:
p=2w+2l
p -2w=2l
2l=p -2w
divide both sides by 2
l=1/2p-w
Six girls share 5 1/3 pounds of pretzel each one receive the same amount. However, Sue only eats half of her pretzels and leaves the uneaten on the plate . How many pounds does sue leave on her plate?
Answers
Answer:
4/9 pounds
Step-by-step explanation:
5 1/3 pounds of pretzels divided equally for 6 girls would mean that each girl gets 8/9 pounds of pretzel.
If Sue ate half of the 8/9 pounds, that would equal to 4/9 pounds of pretzel.
Write an equation of the line passing through the point (6,-2) that is parallel to the line y=4x-11
Answers
Answer:
y=4x-26
Step-by-step explanation:
First, a parallel equation, ALWAYS has the same slope. Just plug in your x value into 4(x) , then find a number that adds or subtracts to get your y value, and that number you added or subtracted is your y-intercept.
The equation of the line passing through the point (6,-2) that is parallel to the line y=4x-11 is y = 4x - 26
The equation of the linear passes through the point (6, -2) and is parallel to the line y = 4x - 11
Parallel lines have the same slope.
Therefore,
y = 4x - 11
using
y = mx + b
where
m = slope
b= y-intercept
Therefore, the slope of y = 4x - 11 is 4.
And the slope of the other line will be 4 because they are parallel.
Therefore,
y = mx + b
y = 4x + b
it passes through (6, -2)
-2 = 6(4) + b
-2 - 24 = b
b = -26
The equation will be y = 4x - 26
learn more on linear equation here: https://brainly.com/question/19954463
Given the graphs of y = f(x) and y = g(x),
g(x) = f(x)
expresses g(x) in terms of f(x).
Answers
Step-by-step explanation:
g(x) = f(x) + 4.
This is because g(x) is a translation of f(x) that has been moved up by 4 units. (-2 to 2 when x = 0)
Given the graphs of y = f(x) and y = g(x),
g(x) = f(x) + 3
expresses g(x) in terms of f(x).
The Answer is 3.
Simplify 3(у- 1) +7 completely.
А. Зу+6
В. Зу+ 4
С. 3y+10
D. Зу- 3
Answers
Answer:
B. 3y + 4
Step-by-step explanation:
Step 1:
3 (y - 1) + 7
Step 2:
3y - 3 + 7
Answer:
3y + 4
Hope This Helps :)
so the answer is 3y-3+7. you combine like terms and get B. 3y+4
Please I need help with this question!!
Answers
[15 + 1/2 ] - [ 2 + 3/4 ] - [6 + 2/3 ]......convertng these to improper fractions, we have
[31 /2 ] - [11 / 4 ] - [ 20 / 3 ] getting a common denominator (12), we have
[186 / 12] - [33 / 12 ] - [ 80 / 12 ] = 73 / 12 inches = about 6.0833 inches left
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{6 \frac{1}{12} \: \: \: inches}}}}} [/tex]
Step-by-step explanation:
Total inches of a green ribbon = [tex] \sf{15 \frac{1}{2} }[/tex]
Finding the total inches of ribbon that she cut off
[tex] \sf{2 \frac{3}{4} + 6 \frac{2}{3} }[/tex]
Convert the mixed number into an improper fraction
[tex] \dashrightarrow{ \sf{ \frac{2 \times 4 + 3}{4} + \frac{3 \times 6 + 2}{3}}} [/tex]
[tex] \dashrightarrow{ \sf{ \frac{8 + 3}{4} + \frac{18 + 2}{3} }}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{11}{4} + \frac{20}{3} }}[/tex]
Take the L.C.M ( Least Common Multiple ) of 4 and 3
L.C.M = 4 and 3 = 12
[tex] \dashrightarrow{ \sf{ \frac{11 \times 3 + 20 \times 4}{12} }}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{33 + 80}{12}}} [/tex]
[tex] \dashrightarrow{ \sf{ \frac{113}{12} }}[/tex]
Total inches of ribbon that she cut off = 113/12
Now, finding the left inches of ribbon
[tex] \sf{15 \frac{1}{2} - \frac{113}{12} }[/tex]
Convert mixed number into improper fraction
[tex] \dashrightarrow{ \sf{ \frac{15 \times 2 + 1}{2} - \frac{113}{12} }}[/tex]
[tex] \dashrightarrow {\sf{ \frac{31}{2} - \frac{113}{12} }}[/tex]
Take the L.C.M of 2 and 12 , you will get 12
[tex] \dashrightarrow{ \sf{ \frac{31 \times 6 - 113}{2} }}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{186 - 113}{12}}} [/tex]
[tex] \dashrightarrow{ \sf{ \frac{73}{12} }}[/tex]
Convert the improper fraction into mixed number
[tex] \dashrightarrow{ \sf{6 \frac{1}{12} }}[/tex] inches
Hope I helped!
Best regards! :D
if Rx) = 2x - x-6 and g(x) = x - 4, find f(x) = g(x).
Answers
Answer:
i have the same question on my worksheet Step-by-step explanation: i need help this is the hardest one
2x - 3 = 1 and -3x + 6 = 12
Answers
Answer:
I am confused by the question no CAPPPPPP
Step-by-step explanation:
the solution to 5/2 x-7 =3/4 x +14
Answers
Answer:
x = 12.
Step-by-step explanation:
5/2x - 7 = 3/4x + 14.
put the like terms together keeping in mind that when a number crosses the equal sign it changes its sign and it acquires the opposite sign.
5/2x - 3/4x = 14 + 7
7/4x = 21.
divide both sides by the reciprocal of 7/4, the number next to the unknown
so x = 21 ×4/7
x = 12.
I need help on this one , I keep getting the same answered but says it’s wrongg
Answers
Answer:
Step-by-step explanation:
p(x)= -3+4x
p(-2)=-3+4(-2)
p(-2)=-3-8=-11p(0)=-3p(5)=-3+4(5)
p(5)=-3+20
p(5)=17Solve for x.
-6x - 29 = 5x - 7
Answers
Answer:
x = -2
Step-by-step explanation:
-6x - 29 = 5x - 7
Add -6x to both sides
-29 = 11x - 7
Add 7 on both sides
-22 = 11x
Divide
[tex]\frac{-22}{11}[/tex] = [tex]\frac{11x}{11}[/tex]
x = -2
Answer:
x = -2
Step-by-step explanation:
move the terms
-6x -5x = -7 + 29collect like terms
-11x = 22
divide both sides of the equation by -11
x = -2Point U is on line segment TV. Given UV = 4 and TU = 13, determine
the length TV.
Answers
Answer:
17 units
Step-by-step explanation:
In the figure below, Y is between X and Z
and XZ = 40
Please help ASAPPPP!!!
Answers
Answer:
32
Step-by-step explanation:
The value of a is 8.
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
XZ = XY + YZ
40 = 3a + 8 + a
40 = 4a + 8
40 - 8 = 4a
32 = 4a
a = 32/4
a = 8
Thus,
a is 8.
Learn more about expressions here:
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