Given the definitions of f(x) and g(x) below, find the value of (gof)(3).
f(x) = 2x² - x - 15
g(x) = -5x +9
Answer:
[tex] \huge{ \boxed{gof(3) = 9}}[/tex]
Step-by-step explanation:
In order to find gof(3), we first have to find gof(x). To find gof(x) substitute the f(x) into g(x). That is, for every x found in g(x) substitute it by f(x).
From the question
[tex]f(x) = 2 {x}^{2} - x - 15 \\ g(x) = - 5x + 9 \\ \\ gof(x) = - 5(2 {x}^{2} - x - 15) + 9 \\ gof(x) = - {10x}^{2} + 5x + 75 + 9 \\ \\ gof(x) = - {10x}^{2} + 5x + 84[/tex]
To find gof(3), substitute the value of x that is 3 into gof(x). For every x found in gof(x), replace it by 3 and solve.
[tex]gof(3) = - 10( {3})^{2} + 5(3) + 84 \\ \quad \: \: \: \: \: = - 10(9) + 15 + 84 \\ \: \: \: = - 90 + 15 + 84 \\ = 9[/tex]
We have the final answer as
gof(3) = 9helpp me fast thank u pleasee
The value of x from the given equations is 0.6.
The given equations are y=4x and y=-x+3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Here, 4x=-x+3
⇒ 4x+x=3
⇒ 5x=3
⇒ x=3/5
⇒ x=0.6
Hence, the value of x from the given equations is 0.6.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ1
Need help with homework
we have the expression
[tex]10-4+2(4)^2[/tex]step 1
squared 4 before multiplying
[tex]\begin{gathered} 10-4+2(16) \\ 10-4+32 \end{gathered}[/tex]therefore
step 1 is incorrect
Justine's work is incorrect
the answer is option N 1How far can a family travelin 4 days if they travel 620 milesin two days? (at the same rateof speed)
Let x be the number of miles the family travel in 4 days
620 miles = 2 days
x = 4 days
cross-multiply
2x = 2480
Divide both-side of the equation by 2
x = 1240 miles
Determine whether the given numbers represent the lengths of sides of a right triangle.15,11,4Do the given numbers represent the lengths of the sides of a right triangle?No or Yes
Answer:
No
Explanation:
To determine if the lengths form the side of a right triangle, use the Pythagorean Theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ Where\; c\text{ is the hypotenuse, the longest side} \end{gathered}[/tex]Substitute 15,11 and 4 into the formula:
[tex]\begin{gathered} 15^2=225 \\ 11^2+4^2=121+16=137 \\ \text{Therefore:} \\ 15^2\ne11^2+4^2 \end{gathered}[/tex]Since the Pythagorean Theorem does not hold, the side lengths(15,11,4) do not represent the lengths of the sides of a right triangle.
Rita started playing a video game at 9:10 A.M. It took her 1 hour and 45 minutes to beat the first level and 1 hour and 25 minutes to beat the second level. Rita played the final level for 1 hour and 10 minutes and finished the game. What time was it when Rita stopped playing the game?
Answer: it would be about 1:30pm
Step-by-step explanation:
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
what 82 x 82 x 82 x 82
Answer:45212176
Step-by-step explanation:calculator
Answer:
82x82x82x82, or 82 squared to the 4th power, is 45212176.
−1,51.27,−1,0,12,57,7677,√2,√8,5
Given the following question:
[tex]-1,5,\frac{1}{2},\frac{5}{7},0,\sqrt[]{2},\sqrt[]{8},-1.27,\frac{76}{77}[/tex]Natural numbers are positive integers.
5 is a natural number
Whole numbers are integers, neither fraction or decimals just integers.
5, and 0 are whole numbers
Integers are a set of numbers that can be expressed without being a fraction/decimal.
-1, 5, and 0 are integers.
Rational numbers are a set of numbers that can be written as fractions.
-1, 5, 1/2, 5/7, 0, 76/77, 1.27 are all rational numbers they can all be expressed as a fraction.
(zero is also rational)
Irrational numbers cannot be expressed as a fraction
√2, √8,
Real numbers are numbers that include rational and irrational numbers.
-1, 5, 1/2, 5/7, 0, 76/77, -1.27, √2, √8
can yall help me with this
In solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.There are three main categories of fractions in mathematics. 'Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.So, the wrong step will be:
(4/7) ÷ (-1/2)Then, the next step should be:
(4/7) × (-2/1)But, the steps it is given as:
(4/7) × (-2/-1)Which makes the error.
Therefore, in solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).
Know more about fractions here:
https://brainly.com/question/28933207
#SPJ1
For which inequality is x= 5 a solutionx < 2x > 9x < 18x > 42
Let's check each inequality if the value x = 5 is part of the solution:
a. x < 2
5 is a value greater than 2, so it isn't part of the solution of this inequation.
b. x > 9
5 is lesser than 9, so it isn't part of the solution of this inequation.
c. x < 18
5 is lesser than
Addison drove 162 miles in 8 hours. What was her speed in miles per hour?
[tex]\fbox{20.25}[/tex]
To find her miles per hour, we need to divide the total miles by the total hours to find how many miles she drives in each hour.
[tex]162\div8[/tex]
[tex]=20.25[/tex]
• 100%XIsabel is thinking of two numbers. Their greatest common factor is 14. Their least common multiple is 168. One of the numbers is 56.What is the other number?O A. 84Ο Ο ΟOB. 42C. 28O D. 8O E. 7
GCF = 14
LCM = 168
let x and y be the numbers
if X = 56
The other number (y) can be obtained using the formula:
=> (GCF x LCM) / X
=> (14 X 168)/ 56
=> 2352/56
=>42
Option B is correct
It takes 5 workers 12 hours to unload one truck. How long would it take 6 workers to unload the truck?
Mr Kennedy raised beef cattle. The stock tank near the windmill has a diameter of 3 meters. When it is full, the water is 1.5 meters deep. How many cubic meters of water are in the stock tank when it is full use 3.14 for pi.A 7.1 B 10.6 C 42.4 D 14.1
Answer: B 10.6
Explanation:
We would assume that the stock tank is cylindrical. We would calculate the volume by applying the formula,
Volume = πr^h
where
π = 3.14
r is the radius of the cylinder
h is the height of the cylinder
From the information given,
diameter = 3
radius = diameter/2 = 3/2
r = 1.5
h = 1.5
Volume = 3.14 x 1.5^2 x 1.5 = 10.5975 cubic meters
By rounding to the nearest tenth,
Volume = 10.6 cubic meters
17. a = -3: Yes/No?
4a + 3 = -9
Math
T.28 Write an equation for a parallel or perpendicular line 5SH
Recommendations
alo
Learn with an example
Submit
Watch a video
Line q has an equation of y = -x+ 2. Line r includes the point (9, -3) and is parallel to
line q. What is the equation of line r?
Skill plans
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answer:
y = - x + 6===========================
GivenLine q with equation of y = - x + 2,Line r with the point (9, - 3) and parallel to line q.To find Equation of line r.SolutionWe know parallel lines have equal slopes, so line r has the slope of - 1.
Line r is:
y = - x + b, where b- the y-interceptSubstitute the coordinates of the point into this equation and find the value of b:
- 3 = - 9 + bb = - 3 + 9b = 6The equation of line r is:
y = - x + 6A car can travel 100 km on five liters of gas. How many liters will be needed to travel 40 km?
Answer:
2
Step-by-step explanation:
40 x 5 ÷ 100
2 x 5 ÷ 5 = 2
Hi please help me in this onei don't know how to solve itfind the value of x
EXPLANATION
If the measure of ∠2= x+78 and the other ∠=40 degrees, by definition we know that sum of interior angles of a triangle is equal to 180 degrees.
Furthermore, we have two congruent legs, so this is an Isosceles triangle with two congruent angles (with the same measure).
Thus,
180 = 40 + 2* m∠2
Substituting m∠2 by the equation as follows:
180 = 40 + 2(x + 78)
Subtracting -40 to both sides:
180 - 40 = 2(x+78)
Simplifying:
140 = 2(x+78)
Dividing both sides by 2:
140/2 = x + 78
Simplifying:
70 = x + 78
Subtracting -78 to both sides:
70 - 78 = x
Simplifying:
-8 = x
Switching:
x = -8
Answer: The value of x is -8.
5.2=
5.2=
\,\,620(0.5)^{\frac{x}{10}}
620(0.5)
10
x
Answer:
D
Step-by-step explanation:
A) (18,-2)
B) (18,2)
C) (15,-2)
D) (15,2)
Answer: Location of T' on the coordinate axis will be (16,7).
T (6,4) → T' (16,7).
Step-by-step explanation:
coordinate vertices of points in rectangle JKLM are:
J (-8,-8)
K (-4,-8)
L (-4,-5)
M (-8,-5)
and coordinate vertices of points in rectangle J'K'L'M' are:
J' (2,-5)
K' (6,-5)
L' (6,-2)
M' (2,-2)
coordinate vertices of points in Quadrilateral STUV are:
S (1,4)
T (6,4)
U (4,6)
V (2,6)
transformation in coordinate vertices from rectangle JKLM to rectangle J'K'L'M' is:
J (-8,-8) → J' (2,-5)
⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.
and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.
similarly for
K (-4,-8) → K' (6,-5)
⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.
and along y axis -8 → -5 which means that the rectangle is shifting upwards by 3 units.
L (-4,-5) → L' (6,-2)
⇒ along x axis -4 → 6 which means that rectangle is shifting towards right by 10 units.
and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.
M (-8,-5) → M' (2,-2)
⇒ along x axis -8 → 2 which means that rectangle is shifting towards right by 10 units.
and along y axis -5 → -2 which means that the rectangle is shifting upwards by 3 units.
So, the location of T' of the Quadrilateral S'T'U'V' on the coordinate plane will be:
along x axis the Quadrilateral will shift towards right by 10 units
So, 6 → 6+10=16
and along y axis the Quadrilateral will shift upwards by 3 units
So, 4 → 4+3=7
⇒ T (6,4) → T' (16,7).
Step-by-step explanation:
can anyone help???????
Answer:
The sum of the angles is 180°.
We already know that one angle is 90°, and the other one is 38.
so: 180-(90+38)=52°
the exterior angle+52°= 180° (beacuse the form a flat angle)
so x=180-52
so: x=128°.
Answer:
128°
Step-by-step explanation:
We know that,
the exterior angle of a triangle is equal to the sum of the interior opposite angles of a triangle.
Accordingly,
38 + 90 = x
128° = x
your textbook authors suggest that if your population has fewer than 100 people you should group of answer choices use a stratified sampling method. use simple random selection. find a larger population test everyone in the population.
The proper sampling technique used when the number of samples is less than 100 is saturated sampling where the entire population will be the research sample.
What is saturated sampling ?
According to Arikunto if the population is less than 100 people so the researcher need to take all the samples namely saturated sampling.
What is stratified sampling ?
Stratified sampling is a sampling technique which used when we do a research on a heterogenous population. How to use this technique is to divide the population into several stratum and then take random samples from each stratum an then all the samples that have been taken are collected into one sample.
In conclusion, if the population has fewer than 100 people , the expert suggested to use saturated sampling.
Learn more about sampling at :
https://brainly.com/question/27829028
#SPJ4
22 more than a number divided by 4
Answer:
X / 4 + 22
Step-by-step explanation:
22 more means we add 22. Then, we take x as our variable, in this case, it is "a number". We divide x by 4, and then we add 22. x / 4 + 22.
3. Which expressions are equivalent to the given one?
Select each that apply.
20/-4
a. 20 x
b. 20 x-1
c. 5
d. -5
Answer:
b, d
Step-by-step explanation:
20/-4 = -5
20 x (-1/4) = -5
Which points define the solution set of this linear-quadratic system of equations?
A. point A and point B
B. point D and point F
C. point C and point E
D. point B and point D
Answer:
C. C and E
Step-by-step explanation:
The solutions for a system of equations is the point of intersection of the two graphs of those equations. Here, there are two points of intersection, that is, two points where the graphs cross. The graphs cross at point C and point E.
C and E are the solutions to this system.
If four people equally share a 1/2 page to 3/4page.what fraction of the page in the photograph
Step-by-step explanation:
fraction of page of photograph is 3/32
(1/2÷4)*3/4
1/2*1/4*3/4
1/8*3/4
=3/32
Mr. Peasley wrote an expression that is equivalent to
20 ÷ 1 + 4 on the board. Which expression could be the one Mr. Peasley wrote?
Responses
A 3 • 12 – 3 • 43 • 12 – 3 • 4
B 36 ÷ 3 • 2 + 1 36 ÷ 3 • 2 + 1
C 5 • 6 + 2 • 3 ÷ 2 • (1 + 5)5 • 6 + 2 • 3 ÷ 2 • (1 + 5)
D 6 + 6 • (10 + 2)
20 ÷ 1 + 4 on the board is 36 ÷ 3 • 2 + 1 36 ÷ 3 • 2 + 1.According to the order of operations, you should execute addition and subtraction last and multiply and division first, proceeding from left to right
How can addition, subtraction, multiplication, and division be calculated?According to the order of operations, you should execute addition and subtraction last and multiply and division first, proceeding from left to right. Divide and multiply from left to right as you continue. After that, add and subtract starting from the left.Remind them, if necessary, that addition and subtraction occur after multiplication and division in the order of operations.Mathematics has created standards (agreements) for how we interpret mathematical expressions in order to avoid these and other potential ambiguities. A writer who intended the contrary interpretation would have to write the sentence differently: 10 (5 2). One of these conventions stipulates that when all of the operations are the same, we go left to right. Therefore, 10 5 3 = 2.To learn more about mathematical expressions refer to:
https://brainly.com/question/1859113
#SPJ1
Use the table below to answer question 9.
x -3 0 1 3
f(x) 12 0 0 6
g(x) 39 3 7 39
h(x) -14 1 -2 -20
2*f(3)-3*g(1)+h(3)=
answer:
-29
step-by-step explanation:
you need a graphing calculator.
so, let's start by setting up a table (for my sake because that text is confusing)
x f(x) g(x) h(x)
-3 12 39 -14
0 0 3 1
1 0 7 -2
3 6 39 -20
okay, that's out of the way. now, your equation is 2 * f(3) - 3 * g(1) + h(3).
for f(3), we look at the chart to see which f(x) value matches x=3.
f(3) = 6
same with g(1) and h(3)
g(1) = 7
h(3) = -20
now, replacing the functions(x) with their numbers is the next step.
2 * 6 - 3 *7 + (-20)
(2*6) - (3*7) - 20
(12) - (21) - 20 = -29
Three friends go grocery shopping together, and each buys the same kind of oranges. LaMar buys 2 pounds (lb) and pays $7.00. Enrico buys 5 pounds and pays $17.50. Anna buys 3 pounds and pays $10.50. Identify the graph and unit price that represent the orange costs.
The unit price of the oranges bought by the three friends is $3.50 per pound.
Lamar bought 2 pounds for $7 , unit price = 7 / 2 = $ 3.5 per pound
Enrico bought 5 pounds for $17.50 , unit price = 17.50 / 5 = $ 3.5 per pound
Anna bought 3 pounds for $10.50 , unit price = 10.5/ 2 = $3.5 per pound
Hence we can see that the unit price rate for the oranges is $3.50 .
The average price of a product is calculated by dividing the total sales income by the number of units sold. Managers must supply "similar" units when a single product is given in many variations, such as different bottle sizes.
By weighting different unit selling prices higher by unit sales mix (%) for each single variant, the determination of average pricing is made practicable. We obtain pricing per statistical unit when we employ a standard rather than a genuine range of sizes and product types.
To learn more about unit price visit:
https://brainly.com/question/16037164
#SPJ9