Answer:
4x - 5
Step-by-step explanation:
To make this 2 terms, we'll have to first identify if we have to distribute anything.
Since 10 - 4x is inside a parenthesis and [tex]\frac{1}{2}[/tex] is beside that, we know that we'll have to distribute the expression.
[tex]-\frac{1}{2}[/tex] (10 - 4x) = [tex]-\frac{10}{2}[/tex] + [tex]\frac{4}{2}[/tex]x = -5 + 2x.
Then, combine like terms:
2x - 5 + 2x = 4x - 5.
Remember, the coefficient always goes before the constant.
Your answer should be 4x - 5.
Which expression is equivalent to √3+5/√3-5
The simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]
How to rationalize surd functions?
Given the surd function expressed as:
[tex]\frac{\sqrt{3} +5}{\sqrt{3} - 5 }[/tex]
Multiply by the conjugate of the denominator to have:
[tex]= \frac{\sqrt{3} +5}{\sqrt{3} - 5 } \times \frac{\sqrt{3} +5}{\sqrt{3} + 5 } \\=\frac{\sqrt{9}+5\sqrt{3}+5\sqrt{3}+25 }{3-25}[/tex]
Simplify the resulting expression
[tex]\\=\frac{3+10\sqrt{3}+25 }{-22}\\=\frac{28+10\sqrt{3}}{-22} \\= \frac{14+5\sqrt{3}}{11}[/tex]
Hence the simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]
Learn more on rationalization here: https://brainly.com/question/14261303
5 people are evenly sharing 12 kilograms of apples.
How many kilograms of apples should each person get?
Choose 1 answer:
A. 5/12 kilograms of apples
B. 2 10/5 kilograms of apples
C. 12/5 kilograms of apples
D. 1 2/5 kilograms of apples
Answer:
C. 12/5 kilograms of apples
Step-by-step explanation:
If 5ppl =12kg of apples
then 1 person= ?kg of apples
If more less divides and if less more divides
Therefore
1×12
5
= 12
5
Here are the first five terms of a quadratic sequence. 9 24 47 78 117 Find an expression, in terms of n, for the nth term of this sequence.
Answer:
4n^2+3n+2
Step-by-step explanation:
9 24 47 78 117
15 23
8
8/2 = 4
=4n^2
9-4 = 5 (the minus value come from 4n^2 where n is the position where 9 lays)
24-16 = 8
47-36 = 11
so plus 3 every time so 3n
4n^2+3n for the first value is 7 so you need an extra 2
4n^2+3n+2
The quadratic sequence is 4n² + 3n + 2.
What is a quadratic sequence?The difference between words always varies by the same amount, which is a characteristic of quadratic number sequences. The "difference between the differences between the words in the sequence is always the same" as a result. The second difference is referred to as constant.
As per the given data:
The given sequence is a quadratic sequence.
The given terms are: 9 24 47 78 117
The difference between the first three consecutive terms:
9 24 47
15 23
Difference of difference:
8
and 8/2 = 4
∴ The first term is 4n²
9-4 = 5 (the minus value come from 4n² where n is the position where 9 lays)
24-16 = 8
47-36 = 11
so plus 3 every time
∴ The second term to add is 3n
4n² + 3n for the first value is 7, so you need an extra 2
∴ The third term to add is 2
4n² + 3n + 2
Hence, the quadratic sequence is 4n² + 3n + 2
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Find the length of the third side. If necessary, round to the nearest tenth.
Answer:
Step-by-step explanation:
Is FGH ~ JKL? If so, identify the similarity postulate or theorem that applies.
Answer:
It is similar by AA
Step-by-step explanation:
AA stands for angle-angle. In similar figures, angles are congruent, and the sides are proportional. the corresponding angles are the same. Hope this helps!
Divide. enter your solution as a mixed number.
6,132 ÷ 203 =
(enter all mixed numbers as x y/z.)
Answer: 30 6/29
Step-by-step explanation: 6132 \ 203 is 30 and 42/203. 42/203 simplified is 6/29
Pls help pls help !!!!!!!
the equation A = bh is used to calculate the area, A , of a parallelogram with base, b , and height, h . Calculate the area of a parallelogram with a base of 15 inches and a height of 9 inches
Answer:
135
Step-by-step explanation:
A = bh
A = 15 x 9
A = 135
Chapter 9: Volumes of Pyramids > Section Exercises 9.5 > Exercise 21
For the given angle measure, find the measure of a supplementary angle and the measure of a complementary angle, it possible. If not possible, type the word none in lowercase
letters in the box
27
The supplementary angle is:
The complementary angle is:
Answer:
The complementary angle is 63 degrees and
The supplementary angle is 153 degrees.
Step-by-step explanation:
A complementary Angle has a total of 90 if you subtract 27 from 90 you will get 63
A supplementary adds up to 180 degrees so subtract 27 and you will get 153.
Hope that helps.
Answer:
Supplementary angle = 153°
Complementary angle = 63°
Step-by-step explanation:
Supplementary angles: Two angles that sum to 180°
Complementary angles: Two angles that sum to 90°
Given angle = 27°
⇒ Supplementary angle = 180° - 27° = 153°
⇒ Complementary angle = 90° - 27° = 63°
ted collected 22 pounds of aluminum cans, how many ounces of aluminum cans did he collect?
Answer:
352 oz
Step-by-step explanation:
1 lb = 16 oz
22 * 16 = 352
Jimmy is playing a game at a state fair, where he is throwing a dart at a target. For each throw, Jimmy can choose to throw the dart at a rectangular target or at a circular target. To score a point during the game, Jimmy must hit the bulls-eye of the target that he chooses. So far, Jimmy has thrown the dart at the rectangular target 9 times, and he has thrown the dart at the circular target 11 times.
When Jimmy has thrown the dart at the rectangular target, he has missed the bulls-eye 6 times. When Jimmy has thrown the dart at the circular target, he has missed the bulls-eye 9 times.
Based on the information above, if Jimmy's goal is to score a point on his next throw, which target should he choose?
Using proportions, it is found that Jimmy should target the rectangular target, as he has hit a higher proportion of throws there.
What is a proportion?A proportion is a fraction of a total amount.
In the rectangular target, he has hit it 3 out of 9 times, hence the proportion is:
pR = 3/9 = 0.3333.
In the circular target, he has hit it 2 out of 11 times, hence the proportion is:
pC = 2/11 = 0.1818.
Due to the higher proportion of hits, he should throw at the rectangular target.
More can be learned about proportions at https://brainly.com/question/24372153
What is the slope of the line whose equation is -2y = -4x + 5
Answer:
2
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-2*y-(-4*x+5)=0
STEP 1:
Pulling out like terms
1.1 Pull out like factors :
-2y + 4x - 5 = -1 • (2y - 4x + 5)
Equation at the end of step 1:
STEP 2:
Equation of a Straight Line
2.1 Solve -2y+4x-5 = 0
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line -2y+4x-5 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 5/-2 so this line "cuts" the y axis at y=-2.50000
y-intercept = 5/-2 = -2.50000
Calculate the X-Intercept :
When y = 0 the value of x is 5/4 Our line therefore "cuts" the x axis at x= 1.25000
x-intercept = 5/4 = 1.25000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.500 and for x=2.000, the value of y is 1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.500 - (-2.500) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 2
Geometric figure: Straight Line
Slope = 2
x-intercept = 5/4 = 1.25000
y-intercept = 5/-2 = -2.50000
Answer:
2
Step-by-step explanation:
y=mx+b where m is the slope
to get y by itself you divide both sides by -2 resulting in
y= 2x+(-5/2)
2=m
PLEASE HELP I NEED IT NOW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
what is the problem ? you teacher gave you even the conversion rates in the question.
so, when 1 gallon = 3.79 liters, then how much is 4 gallons ?
4 gallons is 4 times 1 gallon. so, of course, we need to apply the same factor to the other side too.
4 gallons = 4×3.79 = 15.16 ≈ 15 liters
and e do the same for all the other table elements :
8 liters = 8×0.26 = 2.08 ≈ 2 gallons
12.5 liters = 12.5×0.26 = 3.25 ≈ 3 gallons
6 gallons = 6×3.79 = 22.74 liters ≈ 23 liters
Given P(A) = 0.55, P(B) = 0.42 and P(AUB) = 0.639, find the value of
P(An B), rounding to the nearest thousandth, if necessary.
Answer:
The probability of A and B, denoted as P(A ∩ B) is equal to 0.331.
Step-by-step explanation:
Recall our formula for the probability of A or B:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)We are given are variables already, which we can once again define:
P(A) = 0.55P(B) = 0.42P(A ∪ B) = 0.639To find P(A ∩ B), we start by plugging in the values into our formula:
0.639 = 0.55 + 0.42 - P(A ∩ B)We can add the RHS of the equation:
0.639 = 0.97 - P(A ∩ B)Subtracting 0.97 on both sides, we get closer to our answer:
-0.331 = -P(A ∩ B)To obtain our final answer, we can simply just divide both sides by -1:
0.331 = P(A ∩ B)P(A ∩ B) = 0.331Therefore, the probability of A and B is equal to 0.331.
Create equations to solve for f and g
Answer:
Step-by-step explanation:
Please help me with this please and thank you
Answer:
Nnnnnnnnnnnn
Step-by-step explanation:
L bozo
Please help me on this question
Answer:
V = £21,012.50
Step-by-step explanation:
Compound interest formula
[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = final amountP = principalr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of times periods elapsedGiven:
A = VP = £20,000r = 2.5% = 0.025n = 1t = 2Substituting given values into the formula:
[tex]\sf \implies V=20000(1+\frac{0.025}{1})^{(1 \times 2)}[/tex]
[tex]\sf \implies V=21012.5[/tex]
Write each expression without the absolute value symbol.|14-(6-x)|
what is the value of the expression 4y²-7y-6 when y=5
Soft drinks sell for P8.50 and fruit juice sells for P11.00 each. On a certain day, the number of soft drinks sold was four times the number of fruit juice sold. How many soft drinks were sold if the total income was P900.00?
The number of soft drinks sold was 4 times the number of fruit juice -> On average, every 4 soft drinks sold, 1 fruit juice is.
-> Every P34.00 of soft drinks sold, P11.00 of fruit juice is.
So, the income is P45.00 everytime.
Since the total income is P900.00, the amount of 4 soft drinks and 1 fruit juice sold is 900 : 45 = 20 times
So, there were 20 x 4 = 80 soft drinks sold.
Recheck : 80 x 8.5 + 20 x 11 = 680 + 220 = 900.
Can someone help? I don’t get this one
Answer:1.4*10^-9
Step-by-step explanation:
Answer:
1.4×10−x^-{9}
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10.
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Hopefully this helps you!
- Matthew
Which statement about the graph of y = 1/4(2/3)^x is true?
The graph crosses the y-axis at (0, 1/6)
The graph decreases from left to right.
The graph includes point (1, 1/4)
The graph has an asymptote at y = 1/4
Answer:
The graph decreases from left to right.
Step-by-step explanation:
A taxi hurries 63 miles in 2 hours
5 minutes. What is its average speed in
miles per hour?
Answer:
30 .24 m/hr
Step-by-step explanation:
2 hours and 5 minutes = 2 + 5/60 hours = 2 5/60 hrs
63 miles / (2 5/60) = 30.24 m/hr
Step-by-step explanation:
To find the average speed, we must know this formula :
[tex] \\ {\longrightarrow\sf \qquad{Average \: speed = \dfrac{Distance \: Travelled}{Total \: Time \: Taken}}} \\ \\ [/tex]
Also we know that, 2 hr 5 min = 2.083 hrs approximately so,Now, substituting the given values in the formula :
[tex] \\ {\longrightarrow\sf \qquad{Average \: speed = \dfrac{63 \: miles}{2.083 \: hr}}} \\ \\ [/tex]
[tex] \\ {\longrightarrow\sf \qquad{Average \: speed = 30.24 \: mph}} \\ \\[/tex]
Therefore,
The average speed of the taxi is 30.24 mph
CALCULATE THE SIDE LENGTHS USING THE GIVEN SCALE.
Answer:
x = 4 mm
y = 15 mm
Step-by-step explanation:
x = 12 mm / 3 = 4 mm
y = 3 × 5 mm = 15 mm
there were 150 people in a parade last year. This year there are 20 people in the parade. What is the percent change of people in the parade from last year to this year?
Answer:
7.5
Step-by-step explanation:
How many solutions does the equation 4x 8 = − 2 − 2 5x have? two one zero infinitely many
The equation 4x + 8 = -2 - 2 + 5x has one solution
How to determine the number of solutions?The equation is given as:
4x + 8 = -2 - 2 + 5x
Collect like terms
4x - 5x = -2 - 2 - 8
Evaluate the like terms
-x = -12
Divide both sides by -1
x = 12
The above means that the equation 4x + 8 = -2 - 2 + 5x has one solution
Read more about equation solutions at:
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Answer:
it does have one solution
Step-by-step explanation:
A spinner has 12 equal-sized sections. Nine of the sections are red. a. What is the probability that the spinner will land on red? b. Use words to describe the probability. a. out of 12, or /4 or _% .
Answer:
9out of 12, 3/4, 75%
Step-by-step explanation:
Red makes up 3 quarters of the spinner, or 9 parts out of 12.
Graph y=|x-2|
ASAP I really need this please
Step-by-step explanation:
move the parent function to the right 2 times.
Answer:
see image
Step-by-step explanation:
An absolute value graph is a V-shaped graph(in yellow, see image) You can use "transformations of parent functions" to graph it (high school/college) OR use a table of values (middleschool/hs). The - 2 that's in the parenthesis with the x causes the graph to slide to the RIGHT 2 units. (shown in green) The green graph is what you are asking for.
If you aren't learning about translations (which means shift or slide and is a type of transformation) then you can just make a table of values. Pick several x's and put them in the equation and find out what y's go with them. Plot the points on the graph and connect. See image.
Solve this inequality
2x2 – 15x < 27
Use the functions and the scenario to solve the problem.
f(x)=1/2x+6
g(x)=x−3
Shiloh and Leanne are asked to evaluate f(x)−g(x).
Shiloh suggests f(x)−g(x)=(x−3)−(1/2x+6)=1/2x−9.
Leanne suggests f(x)−g(x)=(1/2x+6)−(x−3)=−1/2x+9.
Evaluate each student's answer.
Select two answers. Select the correct evaluation of Shiloh's work and the correct evaluation of Leanne's work
Answer:
Leanne is correct. It is important that g(x) is subtracted from f(x).
Shiloh is incorrect. She subtracted f(x) from g(x), and subtraction isn't commutative.
*Just took the test, got the answer correct!! Hope this helps!