Answer:
See below, please
Step-by-step explanation:
We know
\(f(x) = {x}^{2} + 3x - 7\)
\(g(x) = 3x + 5\)
\(h(x) = 2 {x}^{2} - 4\)
Hence
\(f(g(x))\)
\( = {(3x + 5)}^{2} + 3 \times (3x + 5) - 7\)
\( = (9 {x}^{2} + 30x + 25) + (9x + 15) - 7\)
\( = 9 {x}^{2} + 39x + 33\)
\(h(g(x))\)
\( = 2 \times {(3x + 5)}^{2} - 4\)
\(2 \times (9 {x}^{2} + 30x + 25) - 4\)
\( = 18 {x}^{2} + 60x + 50 - 4\)
\( = 18 {x}^{2} + 60x + 46\)
\((h - f)(x)\)
\( = h(x) - f(x)\)
\( = (2 {x}^{2} - 4) - ( {x}^{2} + 3x - 7)\)
\( = {x}^{2} - 3x + 3\)
\((f + g)(x)\)
\( = f(x) + g(x)\)
\( = ( {x}^{2} + 3x - 7) + (3x + 5)\)
\( = {x}^{2} + 6x - 2\)
What is the volume of this shape
Answer: 2304
Step-by-step explanation: 18 x 16 x 8
Work out the equation of the line which passes throught the point (-1,2) and is parallel to the line y=x+4
Answer:
y = x + 3
Step-by-step explanation:
In point slope form, the equation of line is,
\(y - b = m(x - a)\)
where a and b correspond to the x and y coordinates of the given point and m is the slope
Since the line is parallel to y = x+4, it has the same slope so m = 1 since the slope of y = x+4 is 1
and putting the values of the point (-1,2), we get,
y - 2 = x - (-1)
y-2 = x + 1
y = x + 3
guys pls helpppppp me I need help
Answer:what grade is this?
Step-by-step explanation:
A store sells 3 different sizes of the same juice. The 8 ounce bottle costs $2.96, the 16 ounce bottle costs $5.44, and the 24 ounce bottle costs $9.36. Which size bottle is the better buy?
Answer:
24 ounce bottle.
Step-by-step explanation:
8 Ounce bottle=2.7 for each ounce
16 ounce bottle=2.9 for each ounce
24 ounce bottle=2.6 for each ounce
If possible, can anyone help with these two? --sorry, im dumb ;-;-- THANKS!
Answer:
1) 3^2 or 9
2)5^18
Step-by-step explanation:
Ok but you have to hit that crown :D
Simplify: 3^8x3^4 = 3^12
3^2x3^8=3^10
3^12/3^10 = 3^2 or 9
5^3^6=5^18
Hope this helps :D
Find the component form of the vector that translates P(-3,6) to P'(-4,8) .
Vector is the quantity that has magnitude as well as direction. The component form of the vector that translates P(-3,6) to P'(-4,8) is -i + 2j.
What is vector?A vector quantity has both magnitude and direction. It is added using parallelogram law of addition.
The sum of two vector quantities is always a vector quantity.
The sum of two vector quantities can vary from their scalar difference to their scalar addition.
The given points are P(-3,6) to P'(-4,8) .
The vector component form of two points (x₁,y₁) and (x₂,y₂) is given by ,
(x₂-x₁)i + (y₂-y₁)j
Therefore, The vector component form of given points are,
(-4-(-3))i + (8-6)j
-i + 2j.
Hence "The component form of the vector that translates P(-3,6) to P'(-4,8) -i + 2j.
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What is a place value chart in maths?
In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.
The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.
A place value chart can be used to understand the value of a digit in a number.
Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.
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Exactly one of terry, chris, and kim will attend a party. The probability terry attends is 0.31 and the probability chris attends is 0.5. What is the probability that kim attends? 0.33 0.5 0.81 0.19
D) 0.19 is the probability that Kim will attend the party.
Given:
The probability terry attends is 0.31 and the probability chris attends is 0.5.
To find: Probability of kim attending the party
Concept :
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
The question here talks about exactly one of them attending the party so the sum of probability is equal to 1.
P(Terry) + P(Chris)+ P(Kim) = 1
0.31+0.5 + P(Kim) =1
P(Kim) = 0.19
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
For inequality –3(2x – 5) < 5(2 – x) the correct option is (–6x + 15 < 10 – 5x).
What is inequality?
An inequality is a mathematical statement that describes a relationship between two values or expressions, indicating that they are not equal.
To solve the inequality –3(2x – 5) < 5(2 – x), we need to simplify the expression first.
Starting with the left-hand side, we can distribute the –3 to get:
–3(2x – 5) = –6x + 15
For the right-hand side, we can distribute the 5 to get:
5(2 – x) = 10 – 5x
Substituting these back into the original inequality, we get:
–6x + 15 < 10 – 5x
To solve for x, we can first move all the x terms to one side by adding 5x to both sides:
–x + 15 < 10
Then, we can move the constant term to the other side by subtracting 15 from both sides:
–x < –5
Finally, we can divide both sides by –1 (remembering to flip the inequality sign since we're dividing by a negative number) to get:
x > 5
So the first correct representation of the inequality is x > 5.
To get the second correct representation, we can also start with the inequality –6x + 15 < 10 – 5x, and move all the x terms to one side:
–6x + 5x < 10 – 15
So second option (–6x + 15 < 10 – 5x) are correct representations of the inequality.
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A square has an area of 1369 square inches. What is the length of its side
Answer:
37 inches
Step-by-step explanation:
1369 = l^2
The square root of 1369 is 37.
calculate the gradient: a stream has 100 feet of elevation change in 2 miles. note: if doing this during an exam, show your calculator to the camera so your instructor understands what you are doing. question 9 options: a) 50 feet/mile b) 2 feet/mile c) .02 feet/mile d) 100 ft/mile
Every mile traveled along the stream, the elevation changes by 50 feet/mile.
The gradient of the stream can be calculated by dividing the elevation change by the distance traveled. In this case, the stream has an elevation change of 100 feet over a distance of 2 miles. Thus, the gradient can be calculated as:
Gradient = Elevation change / Distance traveled
= 100 feet / 2 miles
= 50 feet/mile
The gradient is an important concept in many fields, including geology, hydrology, and civil engineering. It represents the rate at which a physical quantity, such as elevation or temperature, changes with distance. A steep gradient indicates a rapid change, while a gentle gradient indicates a slow change.
Therefore, the answer is option (a) 50 feet/mile. This means that for every mile traveled along the stream, the elevation changes by 50 feet.
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an electrician charges a set fee of $150 for every house call and then charges an additional $70 per hour. write an equation for c, in terms of t, representing the total cost of the electricians services if the electrician spends t hours at the house working.
Answer:
y = 70x + 150
Step-by-step explanation:
y-intercept: 150
slope: 70x
Let x represent the amount of hours the electrician spent in the house.
Answer:
C=150+70t
Step-by-step explanation:
In this equation, C stands for the total cost, and t stands for the number of hours worked. Since 150 is a set fee it must be a constant in the equation and to must be added to the hourly cost. 70 must be multiplied by t because the electrician charges 70 dollars for every hour he works. Then, both the set fee plus the hourly fee together equal the total cost.
HELP ME FAST PLEASE!!!!!
Answer:
the first one
Step-by-step explanation:
kkrkrkrkrkrk
Answer:
(-4,1)
Step-by-step explanation:
Pls help I can't even under stand it
Answer:
$17.50
Step-by-step explanation:
first you multiply the price of the books by three to get the total price of 22.50. since she already has 5.00 you can subtract that from the total to get 17.50. 17.50 is the amount she needs to make the purchase.
Hope this helps.
The decimal 132.64 written in expanded form is ______.
What’s a number between 10 and 11?
I NEED HELP. DON’T TROLL
Answer:
You start with the decimals place since you can't go any further than another whole number.
10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9 and so on, in the tenths hundredths and thousandths place.
There can be only rational numbers or decimals
For example
10.210.710.310.23310.89Cover the entire area except for today's date and year April, 1st, Monday
Answer:
It's friday for me so here u go
Step-by-step explanation:
The store plans to purchase the uniforms and hand out 5 uniforms to every employee, one for each day of the week uniforms come in packs of 8, and the store plans to purchase 56 packs of uniforms. How many employees can store give uniforms to? Will the store have any uniforms left over?
Answer:
89 employees
3 uniforms left
Step-by-step explanation:
Number of Uniforms per employee = 5
Uniform per pack = 8
Number of packs = 56
Total number of uniforms :
56 * 8 = 448 uniforms
Number of employees who can get uniform :
1 employee = 5 uniforms
Number of employees = 448 / 5 = 89.6
Hence, 89 employees
Yes, (448 - (89*5)
= 448 - 445
= 3 uniforms left
80 divided by 192.0!!!!!!!!!!!!!!!
Answer: .416666667
Step-by-step explanation: Take 80 and divide it by 192.0= .416666667
answer ,, true or false ?
Answer:
true
Step-by-step explanation:
(1 point) Find the distance from the point (-3, -2, -2) to the plane 4x + 3y + 4z = 1.
The distance from the point (-3, -2, -2) to the plane 4x + 3y + 4z = 1 is 27 / √41.
To find the distance from a point to a plane, we can use the formula:
Distance = |Ax + By + Cz + D| / √(A² + B² + C²)
The equation of the plane is 4x + 3y + 4z = 1, which can be rewritten as:
Ax + By + Cz + D = 0
where A = 4, B = 3, C = 4, and D = -1.
Let's calculate the distance from the point (-3, -2, -2) to the plane:
Distance = |(4 × -3) + (3 × -2) + (4 × -2) + (-1)| / √(4² + 3²+ 4²)
= |-12 - 6 - 8 - 1| / √(16 + 9 + 16)
= |-27| / √41
= 27 / √41
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The first three terms of an arithmetic sequence are as follows.
30, 26, 22
Find the next two terms of this sequence.
The picture needs to be answered.
Answer:
if 3 children go to the water park, 4 adults can go: TRUE
if 6 children go to the water park 3 adjults can go: FALSE
no adults, 6 children: TRUE (even 9 children can go)
no children, 6 adults: TRUE
10x is indeed the cost of the children
15y is indeed the cost of the adults
jar contains 6 quarters, 3 dimes, 4 nickels, and 10 pennies. if a coin is randomly selected from the jar, what is the probability that it will not be a dime or a penny?
Probability that a coin pulled at random from the jar will not be a dime or penny is 20 or 13.
Given that,
6 quarters, 3 dimes, 4 nickels, and 10 pennies are included in the jar.
We have to find what is the probability that a coin pulled at random from the jar won't be a dime or a penny.
We know that,
6 quarters, 3 dimes, 4 nickels, and 10 pennies are included in the jar.
6+3+4+10 =23
Probability that a coin pulled at random from the jar will not be a dime is 23-3=20
Probability that a coin pulled at random from the jar will not be a penny is 23-10=13
Therefore, Probability that a coin pulled at random from the jar will not be a dime or penny is 20 or 13.
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In triangle LMN, LM = 6, MN = 9, and LN = 7. Find m∠M to the nearest tenth of a degree. A. 50.0 degrees B. 41.8 degrees C. 45.5 degrees D. 87.3 degrees Please help I need it as soon as possible! Thank you
Answer:
A. 50.0 degreesStep-by-step explanation:
In a triangle LMN, we are given te following;
LM = 6
MN = 9
LN = 7
To get the angle m<M, we will use the cosine rule
LN² = LM²+MN² - 2(LM)(MN)cosm<M
7² = 6²+9²-2(6)(9)cosm<M
49 = 36+81-108cosm<M
49 = 117-108cosm<M
49 - 117 = -108cosm<M
-68 = -108cosm<M
cosm<M = -68/-108
cosm<M = 17/27
cosm<M = 0.6296
m<M = cos^-1(0.6296)
m<M = 50.97
Hence the required angle to nearest tenth is 50.0 degrees
for the following diagram, angles 3 and 6 are:
Answer:
alternate
is this an exam or test?
A PE teacher divides the class evenly for
game of kickball. If the likelihood of being on
Team Eagles and Team Jaguars is the same,
then describe a simulation that could represent
the team assignment for next 10 students in PE
class.
PLEASE HELP QUICKLY
Answer:
it would be 5
Step-by-step explanation:
(—5t^3+4t^2—t)—(8t^2+t)
Answer:
Step-by-step explanation:
suppose that f(0)=−3 and f′(x)≤8 for all values of x. use the mean value theorem to determine how large f(4) can possibly be. answer: f(4)≤
The largest value that f(4) can possibly be is 29.
The mean value theorem states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in the open interval (a, b) such that:
f(b) - f(a) = f'(c)(b - a)
In this case, we are given that f(0) = -3 and that f'(x) ≤ 8 for all values of x. To determine how large f(4) can possibly be, we can use the mean value theorem with a = 0 and b = 4:
f(4) - f(0) = f'(c)(4 - 0)
Substituting the given values:
f(4) - (-3) = f'(c)(4)
f(4) + 3 = 4f'(c)
Since f'(x) ≤ 8 for all values of x, we can say that f'(c) ≤ 8. Therefore:
f(4) + 3 ≤ 4f'(c) ≤ 4(8) = 32
Therefore, we have:
f(4) ≤ 32 - 3 = 29
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5 multiply by c 24-47-48 divide 24
Answer:
70
Step-by-step explanation:
nk