Given f(x) = -2 ang g(x) = 4x - 8, find h(x) = f(x) + g(x)
h(x) = 4x - 10
Step-by-step explanation:
The given is:
f(x) = -2g(x) = 4x - 8We need to find h(x) = f(x) + g(x)
∵ f(x) = -2
∵ g(x) = 4x - 8
∵ h(x) = f(x) + g(x)
- Substitute f(x) and g(x) in h(x), and then add the like terms
∴ h(x) = (-2) + (4x - 8)
- Simplify the right hand side
∴ h(x) = -2 + 4x - 8
- Add like terms in the right hand side
∴ h(x) = 4x + (-2 - 8)
∵ -2 - 8 = -10
∴ h(x) = 4x + (-10)
∴ h(x) = 4x - 10
h(x) = 4x - 10
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*Picture attached* NUMERICAL REASONING If someone can please help me answer this one. I’m lost.
Answer:
57
Step-by-step explanation:
Write and solve a proportion.
47 / 289 = x / 350
x ≈ 57
Please help!!!! I’ll mark you as brainliest if you get it correct
Answer: $37.45(to the nearest hundredths)
Step-by-step explanation:
% increase in last year living cost =5%
% increase in last year income =5%
This year income = $39.420
To calculate last year income implies
5% decrease of this year income; thus:
5/100 * $39.420 = $1.971
Last year income = $39.420 - $1.971 = $37.449 = $37.45 (to the nearest hundredths)
Answer:
37.4490 (rounded to the nearest hundredth) = 37.45
Step-by-step explanation:
ok so her bills or wateva went up 5% right and she gets a lil 5% raise or sumn from her job which made her money got up to $39.42. so if you think about it all you do is multiply 39.42 and (5%) which = 0.05 in decimal form and then after you multiply you should get 1.9710 and once you get that you gone take her money she getting now which is 39.42 - her 5% raise she got and once you subtract you gone get 37.4490 or 37.45 rounded
what grade is a 259 out of 360 plz help
Answer:
Convert fraction (ratio) 259 / 300 Answer:86.3%
Factor using the distributive property using the GCF
10x-35
Answer:
5(2x-7)
Step-by-step explanation:
One serving of yogurt has 95 calories.
What is the reasonable
estimate for the number of calories in 2.5 servings of
yogurt ?
Answer:
About 300 calories
The drawing will help
in the function f(x)=x^2 has the domain of {-2,4,8,9} what is the range
For the function f(x) = x^2 range will be { 4 , 16 , 68 , 81 }
Solution:Given that:
[tex]\text {Function is } f(x)=x^{2}[/tex]
Domain of the function is {-2, 4, 8, 9}
Need to determine range of the function.
Domain of the function is possible input of the function that is x and range of the function is possible output of the function that is f(x)
As there are only four input values for x that are -2,4,8,9 we can determine the range by calculating value of f(x) for each of the x
[tex]\begin{array}{l}{\text {At } x=-2:} \\\\ {f(x)=f(-2)=-2^{2}=4}\end{array}[/tex]
[tex]\begin{array}{l}{\text {At } x=4:} \\\\ {f(x)=f(4)=4^{2}=16}\end{array}[/tex]
[tex]\begin{array}{l}{\text {At } x=8:} \\\\ {f(x)=f(8)=8^{2}=64} \\\\ {\text {At } x=9:} \\\\ {f(x)=f(9)=9^{2}=81}\end{array}[/tex]
Thus the range of given function is { 4 , 16 , 68 , 81 }
1.since it is a ratio of two integers 2 over 3 is irrational... true or false.
2.since it is a terminating decimal 8.32 is rational..true or false
Answer:
1. false
2. true
Step-by-step explanation:
1. false because fractions are rational
2. true because it can be turned into a fraction
Which algebraic expression is equivalent to this expression? 3(2x − 8) – 11x A. -5x – 8 B. -5x – 24 C. -17x – 24 D. -17x – 24
Answer:
B
Step-by-step explanation:
Given
3(2x - 8) - 11x ← distribute parenthesis
= 6x - 24 - 11x ← collect like terms
= - 5x - 24 → B
5 3⁄10 hectometers = meters
Answer:
[tex]\large\boxed{5\dfrac{3}{10}\ hectometers=530\ meters}[/tex]
Step-by-step explanation:
[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]
[tex]5\dfrac{3}{10}=5.3\\\\1\ hectometers=100\ meters\qquad(1\ hm=100m)\\\\5\dfrac{3}{10}\ hm=5.3\ hm=5.3\cdot100\ m=530\ m[/tex]
What is 0.46% of 80?
The 0.46 percentage of the number 80 is 0.368 .
Given data:
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %.
The percentage value is represented as p.
The value of p = 0.46%
So, p = 0.0046
The number is represented as q.
The value of q = 80
Now, A = p * q
On simplifying the equation:
A = 0.0046 * 80
A = 0.368
Hence, the percentage value is 0.368
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if a= -0.5 and b=5, find the value of 4a+b
When [tex]\(a = -0.5\) and \(b = 5\), the value of \(4a + b\) is \(3\).[/tex]
To find the value of [tex]\(4a + b\) when \(a = -0.5\) and \(b = 5\)[/tex], we simply substitute the values of a and b into the expression 4a+b and then perform the arithmetic.
Given that [tex]\(a = -0.5\) and \(b = 5\)[/tex], we have:
[tex]\[4a + b = 4(-0.5) + 5\][/tex]
Now, let's calculate:
[tex]\[4a + b = -2 + 5\]\[4a + b = 3\][/tex]
The population of a rural city follows the exponential growth model P(t)=2900e^0.039t where t is the number of years after 1990. What was the population in the year 1990?
Answer:
2900
Step-by-step explanation:
Very easy. Evaluate P(0).
P(0) = 2900e^0.039(0) = 2900e^0 = 2900(1) = 2900
Which of the following are roots of the polynomial function?
Check all that apply.
(x) = x2 - 6x + 7x-2
Answer:
x=1, -2
Step-by-step explanation:
x^2-6x+7x-2
x^2+x-2
factor out the trinomial,
(x-1)(x+2)
zero property
x-1=0, x+2=0,
x=0+1=1
x=0-2=-2
If 8 cases of merchandise cost 60$, what would a dozen cases cost?
Answer: $90
Step-by-step explanation: First, we can change "one dozen" to 12 since it represents the same value.
To find out how much 12 cases of merchandise will cost, we will need to find the unit price per case of merchandise.
Unit price means the cost per unit in this case, the cost per case of merchandise.
Since we know that it costs $60 for 8 cases of merchandise, to find the cost for 1 case of merchandise, we need to divide 8 into $60 or $60 ÷ 8.
60 ÷ 8 = 7.50
Now, we know that it costs $7.50 for 1 case of merchandise.
To find the cost for 12 cases of merchandise, we will multiply the cost for 1 case of merchandise by the number of cases of merchandise we have.
In this case, we will multiply 7.50 by 12 which gives us 90.
Therefore, a dozen cases of merchandise will cost $90.
A ball is thrown and it follows a parabolic path. At each horizontal distance (x) the following equation models the ball’s height (y).
Y=-0.02x^2+0.8x+3
What will the height of the ball be at a distance of 10 feet?
A. 6
B. 7
C. 8
D. 9
Answer D). 9 ft is correct
Height of the ball at a horizontal distance of 10 feet is 9 ft
Step-by-step explanation:
A ball is thrown and it follows a parabolic path. At each horizontal distance (x) the following equation models the ball’s height (y).
Y(x) = [tex]-0.02x^{2} +0.8x+3[/tex]
Question asked is " What will be height (Y) of the ball when X=10 ft "
Simply putting value of X in given equation
we get,
Y(x) = [tex]-0.02x^{2} +0.8x+3[/tex]
Y(x) = [tex]-0.02(10)^{2} +0.8(10)+3[/tex]
Y(x) = [tex]-0.02(100)} +8+3[/tex]
Y(x) = [tex]-2 +8+3[/tex]
Y(x) = [tex]9[/tex]
Therefore, Height of the ball at a horizontal distance of 10 feet is 9 ft
Answer D. 9 ft is correct
The height of the ball at a distance of 10 feet according to the given equation is 9 feet (option D). This was achieved by substituting the value of 10 into the equation.
Explanation:To find the height of the ball at a distance of 10 feet, you need to substitute the value for the horizontal distance (x) in the given equation. The equation modeling the ball's height is: Y=-0.02x^2+0.8x+3. So, we replace x with 10 in this equation, as follows:
Y=-0.02(10)^2+0.8(10)+3 Y=-0.02(100)+8+3 Y=-2+8+3 Y=9
Therefore, the height of the ball at a distance of 10 feet is 9 feet, so option D is correct.
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Find an equation of the line containing the given pair of points.
(4.6, -8) and (6.6, 2.2)
The equation of the line containing the given pair of points (4.6 , -8) and (6.6 , 2.2) is y = 5.1 x - 31.46
Step-by-step explanation:
The equation of a line is y = m x + b, where
m is the slope of the line, [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are 2 points lie on the lineb is the y-intercept, to get it substitute x and y in the equation by the coordinates of one of the 2 given points∵ The line contains the points (4.6 , -8) and (6.6 , 2.2)
∴ [tex]x_{1}[/tex] = 4.6 and [tex]x_{2}[/tex] = 6.6
∴ [tex]y_{1}[/tex] = -8 and [tex]y_{2}[/tex] = 2.2
∵ [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- Substitute the values above in the rule of m
∴ [tex]m=\frac{2.2-(-8)}{6.6-4.6}=\frac{2.2+8}{2}=\frac{10.2}{2}=5.1[/tex]
∴ The slope of the line is 5.1
∵ The equation of a line is y = m x + b
Substitute m by 5.1
∴ y = 5.1 x + b
To find b substitute x and y by the coordinates of point (4.6 , -8) OR point (6.6 , 2.2)
∵ x = 6.6 and y = 2.2
∴ 2.2 = 5.1(6.6) + b
∴ 2.2 = 33.66 + b
- Subtract 33.66 from both sides
∴ -31.46 = b
∴ y = 5.1 x + (-31.46)
∴ y = 5.1 x - 31.46
The equation of the line containing the given pair of points (4.6 , -8) and (6.6 , 2.2) is y = 5.1 x - 31.46
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What does control for eximerment mean
.
Answer:
The definition of a control experiment is a test where the person conducting the test only changes one variable at a time in order to isolate the results. An experiment where all subjects involved in the experiment are treated exactly the same except for one deviation is an example of a control experiment.
Step-by-step explanation:
Answer/Explanation:
You need a control to show how 1 changed variable will change to result.
I’m thinking of three consecutive odd integers. When I add the larger two the result is nine less than three times the smallest of them. What are the three consecutive odd integers?
To find the three consecutive odd integers, we can solve an equation representing the given information.
Explanation:Let the smallest odd integer be x. The next consecutive odd integer will be x + 2, and the largest odd integer will be x + 4.
The problem states that when the larger two integers are added, the result is nine less than three times the smallest integer:
(x + 2) + (x + 4) = 3x - 9
Simplifying the equation, we have:
2x + 6 = 3x - 9
Adding 9 to both sides:
2x + 15 = 3x
Subtracting 2x from both sides:
15 = x
So the smallest odd integer is 15. The consecutive odd integers are 15, 17, and 19.
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A restaurant sold 350 less hotdogs than hamburgers. Altogether the restaurant sold 700 hotdogs and hamburgers. How many of each did they sell?
Answer:
The restaurant sold 175 hotdogs and 525 hamburgers.
Step-by-step explanation:
Let the restaurant sold x hotdogs and y hamburgers.
Given the restaurant sold 350 more hamburgers than hotdogs.
So, we can write x + 350 = y ....... (1)
Again given that the number of total hotdogs and hamburgers sold in the restaurant is 700.
So, x + y = 700 ........ (2)
Solving equations (1) and (2) we get
2x + 350 =700
⇒ 2x = 350
⇒ x = 175
Then from equation (1) we get,
y = 350 + 175 = 525
Therefore, the restaurant sold 175 hotdogs and 525 hamburgers. (Answer)
2 FUIILS
A clothing store sells T-shirts, t, for $8 a shirt, and shorts, s, for $12 each. The
store earned $180 revenue last month. The store sold three times as many T-
shirts as shorts. Which system of equations represents this scenario?
8t+12s=180 and t=3s is the system of equations that represents the given scenario.
Step-by-step explanation:
Given,
Cost of a t-shirt = $8
Cost of a shorts = $12
t-shirt = t
shorts = s
Revenue earned = $180
According to given statement;
8t+12s=180
The store sold three times as many T- shirts as shorts.
t = 3s
8t+12s=180 and t=3s is the system of equations that represents the given scenario.
Keywords: linear equation, revenue
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Answer: 8t+12s=180;t=3s APEX
Hello! Can someone please help me solve this? its very hard for me.
Answer:
16990.616 $ you can expect to have in your account after five years.
Step-by-step explanation:
Given that,
Amount invested is principal amount (p) = $ 15000
Annual rate of interest (r) = 2.5% = 0.025
Compounded quarterly (n) = 4
Sum of the amount after 5 years (t)
We know that from compound interest formula,
[tex]\text { Final amount }(\mathrm{A})=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
To find the final amount substitute the given values in the above formula,
[tex]\text { Final amount }(\mathrm{A})=15000\left(1+\frac{0.025}{4}\right)^{4 \times 5}[/tex]
[tex]\text { Final amount }(\mathrm{A})=15000\left(1+6.25 \times 10^{-3}\right)^{20}[/tex]
[tex]\text { Final amount }(\mathrm{A})=15000(1.00625)^{20}[/tex]
[tex]\text { Final amount }(\mathrm{A})=15000 \times 1.132707738[/tex]
Final amount (A) = 16990.62
The final amount that he can expect is $ 16990.62.
Leon’s older brother is 4 3/4 feet tall . Leon is 1/3 foot shorter than his brother . How tall is Leon ?
Answer:
4 5/12
Step-by-step explanation:
4 3/4 = 19/4
19/4 = 57/12
1/3 = 4/12
57/12 - 4/12 = 53/12 = 4 5/12
The seventh grade class supplied bags of snacks and beverages for the school dance They supplied19 more beverages than bags of snacks The dance was supplied with a total of 371 items.
Answer:
14 bags of snacks.
Step-by-step explanation:
x = the first number
y = the second number
x minus y = 3
x plus y = 13
x - y = 3
x + y = 13
3 x = 8 x + y = 13 8 + y = 13 y = 5 x - y = 3 x +y = 13 2x = 16
The first number = 8
The second number = 5
2x = 16
Difference of the numbers is 3
x = 8
8 – 5 = 3
Sum of the numbers is 13
x + y = 13
8 + 5 = 13
8 + y = 13
y = 5
4 snacks plus beverages = 371 beverages = snacks plus 19
The 8th grade class supplied bags of snacks and beverages for the school dance. They supplied 19 more beverages than bags of snacks. The dance was supplied with a total of 371 items.
x = the number of snacks
y = the number of beverages
snacks plus beverages = 371
beverages = snacks plus 19
x + y = 371
y = x + 19
5 x + y = 371
y = x + 19
Number of snacks = 176
Number of beverages = 195
x + x + 19 = 371
2x = 371
total number of snacks = 371
2x = 352
= 371?
371 = 371
x = 176
19 more beverages than snacks
y = x + 19
= 195
y =
195 = 195
y = 195
6 The seventh and eighth grade bands held a joint concert
The seventh and eighth grade bands held a joint concert. Together there were 188 band members. If the eighth grade band is 3 times as big as the seventh grade band, how big is the eighth grade band?
x = size of the 7th grade band
y = size of 8th grade band
7th grade and 8th grade together = 188 8th grade is 3 x 7th grade
x + y = 188
y = 3x
7 x + 3x = 188 x = 47 y = 3(47) y = 141 x + y = 188 y = 3x 4x = 188
7th grade band = 47 students
8th grade band = 141 students
x + 3x = 188
4x = 188
7th and 8th grade together = 188
= 188?
x = 47
188 = 188
y = 3x
8th grade is 3 times as big as 7th grade
y = 3(47)
141 = 3(47)
141 = 141
y = 141
8 x + y = 81 x = 2y earrings plus necklaces = 81
Amy has 81 pieces of jewelry. She has twice as many earrings as she has necklaces
x = number of earrings
y = number of necklaces
earrings plus necklaces = 81
earrings = 2 x necklaces
x + y = 81
x = 2y
9 2y + y = 81 y = 27 x = 2(27) x = 54 x + y = 81 x = 2y 3y = 81 x = 2y
Number of earrings = 54
Number of necklaces = 27
2y + y = 81
3y = 81
81 pieces of jewelry total
= 81?
y = 27
81 = 81
x = 2y
Twice as many earrings as necklaces
x = 2(27)
2(27) = 54
54 = 54
x = 54
10 9x + 6y = 48 6x + 12y = 72 9 rose plus 6 lily = 48
Julia is making candles. In the morning, she made 9 rose candle plates and 6 lily candle plates. They had a total of 48 candles. In evening, she made 6 rose candle plates and 12 lily candle plates. They had a total of 72 candles. How many candles did each plate have?
x = candles on rose plates
y = candles on lily plates
9 rose plus 6 lily = 48
6 rose plus 12 lilly = 72
9x + 6y = 48
6x + 12y = 72
11 x = 2 6(2) + 12y = 72 12y = 60 y = 5 [9x + 6y = 48] (-2) 6x + 12y = 72
Candles on the rose plates = 2
Candles on the lilly plates = 5
-18x - 12y = -96
6x +12y = 72
9 rose and 6 lilly is 48 plates
9(2) + 6(5) = 48
-12x = -24
= 48
x = 2
6 rose and 12 lilly is 72 plates
6(2) + 12y = 72
6(2) + 12(5) = 72?
y = 72
= 72
12y = 60
y = 5
12 3 adults plus 12 children = 162 3 adults plus 8 children = 122
The cost of admission to a popular music concert was $162 for 12 children and 3 adults. Admission for another group was $122 for 8 children and 3 adults. How much was the admission for each child and adult?
x = the cost of one adult ticket
y = the cost of one child ticket
3 adults plus 12 children = 162
3 adults plus 8 children = 122
3x + 12y = 162
3x + 8y = 122
13 3x + 12y = 162
[3x + 8y = 122] (-1)
The cost of one adult ticket = $14
The cost of one child ticket = $10
3x + 12y = 162
-3x + -8y = -122
12 children and 3 adults spent $162
12 at $10 and 3 at $14 = $162?
4y = 40
$120 + $42 = $162
y = 10
8 children and 3 adults spent $122
3x + 12(10) = 162
8 at $10 and 3 at $14 = $122?
3x = 162
$80 + $42 = $122
3x = 42
x = 14
Answer:
14
Step-by-step explanation:
What do both shapes have in common ?
Answer:
1 right angle
Step-by-step explanation:
The sides are not in common
Answer:
1 right angle
Step-by-step explanation:
They dont have the same number of sides
1 15/100 +1/50 +1.175
To solve the expression, rewrite each term with the same denominator and then add them together. The final answer is 2.345.
Explanation:To solve the expression 1 15/100 +1/50 +1.175, we need to rewrite all the terms with the same denominator. The least common denominator (LCD) of 100 and 50 is 100. Therefore, we can rewrite the expression as follows:
1 15/100 is equivalent to 1.15
1/50 is equivalent to 0.02
Now, we can add the three terms together:
1.15 + 0.02 + 1.175 = 2.345
Therefore, the final answer is "2.345."
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Simplify 4 squared plus 25
45.6379 rounded to the nearest hundread
Answer:
45.64
Step-by-step explanation:
thats the answer
To round 45.6379 to the nearest hundred, we increase the digit in the tenths place by 1 and change all the numbers to the right of it to zeros.
Explanation:To round 45.6379 to the nearest hundred, we look at the digit in the hundredth place, which is 5. Since 5 is greater than or equal to 5, we round up. Therefore, we increase the digit in the tenths place by 1 and change all the numbers to the right of it to zeros. The rounded number to the nearest hundred is 45.6400.
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Write and solve 7 less than the product of 4 and 6
Answer:
7<24
Step-by-step explanation:
I'm bad at explaining but I hope this helps if I'm actually right
7<4×6
7<24
The required inequality for 7 less than the product of 4 and 6 is 7 < 24.
Equality is determined for statement 7 less than the product of 4 and 6.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
The statement states that 7 is less than the product of 6 and 4
Now,
the product of 6 and 4 = 6 * 4 = 24, Implies
7 < 24
Thus, the required inequality for 7 less than the product of 4 and 6 is 7 < 24.
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Given that 2/3a = 16, which of the following illustrates how the multiplicative inverse
property can be used to find the value of a?
Since the multiplicative inverse of a fraction p/q is the fraction that swaps its numerator and denominator, i.e. q/p, we have that the inverse of 2/3 is 3/2.
So, if we multiply both sides of the equation by 3/2, we have
[tex]\dfrac{3}{2}\cdot\dfrac{2}{3}a=16\cdot\dfrac{3}{2}[/tex]
3/2 and 2/3 are multiplicative inverse of each other, and by definition this means that they give 1 when multiplied:
[tex]\dfrac{3}{2}\cdot\dfrac{2}{3}a=1\cdot a=a=16\cdot\dfrac{3}{2}[/tex]
On the right hand side, we have
[tex]16\cdot\dfrac{3}{2}=8\cdot 3=24[/tex]
And so the solution is [tex]a=24[/tex]