Answer:
( f - g)(2) = 14Step-by-step explanation:
f(x) = 3x² + 1
g(x) = 1 - x
To find (f - g)(2) first find (f - g)(x)
To find (f - g)(x) subtract g(x) from f(x)
That's
(f - g)(x) = 3x² + 1 - ( 1 - x)
(f - g)(x) = 3x² + 1 - 1 + x
(f - g)(x) = 3x² + x
To find ( f - g)(2) substitute 2 into (f - g(x)
That's
( f - g)(2) = 3(2)² + 2
( f - g)(2) = 3(4) + 2
( f - g)(2) = 12 + 2
We have the final answer as
( f - g)(2) = 14Hope this helps you
What is the solution to this system of equations? 2x + 3y = 7 and -4x - 6y = -2
Answer:
No Solution
Step-by-step explanation:
I used a graphing tool to graph the lines. When graphed, the lines are parallel, and they do not intercept at a point.
There is no solution to the system.
Answer:
Step-by-step explanation:
We will use the graphing method.
Graph the both equations. The intersection point coordinates are the solution of the system.
● 2x + 3y = 7
● -4x -6y = -2
The two lines are parallel. So the system has no real solution. If we tried solve it with calculations we will find an impossible result ( 12 = 0)
14. A plane traveled from California and back. It took one hour longer on the way out than it did on the way back. The plane's average
speed out was 300 mph. The average speed on the way back was 350 mph. How many hours did the trip out take?
A. 13 hours
B. 8 hours
C. 7 hours
D. 6 hours
Answer:
C. 7 hours
Step-by-step explanation:
Let the time for the trip out be represented by t. Then the time for the return trip is t-1. The distance was the same for both trips, so we have ...
distance = speed × time
300t = 350(t -1)
300t = 350t -350 . . . . eliminate parentheses
350 = 50t . . . . . . . . . . add 350-300t
7 = t . . . . . . divide by 50
The trip out took 7 hours.
Nathan, a tutor, buys 5 calculators for $7.50 each at a store, planning to provide one to each of his clients. However, the next day, he discovers that the same calculators has gone on sale for $5.00 and also discovers that he will only have three tutoring clients instead of five. He returns the five calculators and purchases three calculators at the new sale price. He uses the following expression to determine the amount he should receive back from the store. (5 x $7.50) - (3 x $5.00) Which of the following expressions could Nathan have used. 5 ($7.50 - $5.00). $7.50 - $5.00. (5 x $7.50) - $5.00. (5 x $7.50) - $5.00. 3 ($7.50 - $5.00) +2 x $7.50
Answer: 5 (7.50-3 )
Step-by-step explanation:
Given: Previous price of calculator = $7.50
Number of client =5
Total price = (Number of calculators) x (Price for each calculator)
Total price of 5 calculators = (5 x $7.50)
New price of calculator = $5.00
Number of client =3
Total price of 3 calculators = (3 x $5)
Price will receive = (Total price of 5 calculators) -(Total price of 3 calculators )
= (5 x $7.50) - (3 x $5)
= 5 (7.50-3 )
Required expression: 5 (7.50-3 )
The points shown on the graph represent the numbers in a geometric sequence.What is the initial value of the sequence? 1 2 3 8
Answer:
1
Step-by-step explanation:
It starts with number one, so one must be the initial value of the sequence.
1
Step-by-step explanation:
The number of students at a school decreased 20% from 2010 to 2011. If the number of
students enrolled in 2011 was k, which of the following expresses the number of students enrolled in 2010
in terms of k?
A) 0.75k
B) 1.20%
C) 1.25K
D) 1.5k
Answer:
C
Step-by-step explanation:
Okay, here we have a reduction in the number of students by 20% from 2010 to 2011.
In 2011, we had k students, so we want to calculate the number of students we had in 2010.
Let the number of students present in 2010 be x
So mathematically;
x - 20% of x = k
x - 0.2(x) = k
0.8x = k
x = k/0.8
x = k * 1/0.8
x = k * 1.25
x = 1.25k
A laptop battery has 81% power after 1 hour of use and 24% after 4 hours use. What is the slope?
Answer:
Step-by-step explanation:
If A laptop battery has 81% power after 1 hour of use
It looses 19 % of its energy in one hour.
The difference between 81% and 24% is 57%
The slope of the line of rate of decrease of battery percentage is 19% per hour.
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is
y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is it's graph or the rate of change is large.
We know slope(m) of a line = (y₂ - y₁)/(x₂ - x₁).
The problem can be constructed as having two points (1, 81) and (4, 24).
∴ Slope(m) = (24 - 81)/(4 - 1).
Slope(m) = - 57/3.
Slope(m) = - 19.
learn more about slope here :
https://brainly.com/question/3605446
#SPJ2
Multiply negative 1 over 3 multiplied by 1 over 4. Which of the following is correct? negative 1 over 3 negative 1 over 4 negative 1 over 7 negative 1 over 12
Answer:
-1/12
Step-by-step explanation:
-1/3 * 1/4
Multiply the numerators
-1 *1 = -1
Multiply the denominators
3 *4 =12
numerator over denominator
-1/12
Answer:
the answer is [tex]\frac{-1}{12} \\[/tex]
Step-by-step explanation:
[tex]\frac{1}{3} x \frac{1}{4}[/tex]
3x4= 12 is now the denominator
and
the numerator stays the same because -1x1=-1
so there for the answer is [tex]\frac{-1}{12}[/tex]
hope this helped you ^.^ happy holiday
Before an algebraic fraction is selected as a final answer what should you always check?
That the power of the numerator is greater than the denominator.
That the coefficients of the denominator are greater than those in the numerator.
That the variables are all written in alphabetical order.
That the fractions are reduced with all common factors canceled.
Answer:
That the fractions are reduced with all common factors canceled.
Step-by-step explanation:
Hello,
Before an algebraic fraction is selected I should that the fractions are reduced with all common factors cancelled so that I got the irreducible fraction.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
find the area of quadrilateral ABCD.
Answer:
14.89 units²Step-by-step explanation:
[tex]P_{ABCD}=P_{ACD}+P_{ABD}[/tex]
We can use Heron's formula to calculate area of triangles:
[tex]P_\triangle=\sqrt{s(s-a)(s-b)(s-c)}[/tex] where:
a, b, c - sides of triangle
s - semi-perimetr of triangle {(a+b+c):2}
ΔACD:
a = 4.39 , b = 3.42 , c = 4.57
s = (4.39 + 3.42 + 4.57)÷2 = 12.38÷2 = 6.19
[tex]P_{ACD}=\sqrt{6.19(6.19-4.39)(6.19-3.42)(6.19-4.57)}\\\\P_{ACD}=\sqrt{6.19\cdot1.8\cdot2.77\cdot1.62}=\sqrt{49.9986108}=7.070969579...\\\\P_{ACD}\approx7.071[/tex]
ΔACD:
a = 5.44 , b = 7.84 , c = 3.42
s = (5.44 + 7.84 + 3.42)÷2 = 16.7÷2 = [tex]P_{ACD}=\sqrt{8.35(8.35-5.44)(8.35-7.84)(8.35-3.42)}\\\\P_{ACD}=\sqrt{8.35\cdot2.91\cdot0.51\cdot4,93}=\sqrt{61.09371855}=7.81624708...\\\\P_{ACD}\approx7.816[/tex]
[tex]P_{ABCD}=P_{ACD}+P_{ABD}\\\\P_{ABCD}\approx7.071+7.816 = 14.887\\\\P_{ABCD}\approx 14.89[/tex]
Someone please help me ASAP
Answer:
the percentage share for BBC2 remained almost the same at about 11 % each year
if you look at the chart the BBC2 almost remains stable between 10 and 12 %
1980 ( between 39 and 51)
1985 ( between 37 and 49 ) and so on
( these numbers are not exactly the same , it is about or approximately)
Help a friend out I don’t understand it
Answer:
THEY ARE COMPLIMENTARY BUT NOT NECESSARILY CONGRUENT.
Step-by-step explanation:
This is so because their lines don't meet.
help plz I think the first one is correct but I'm not sure
The left side 10x+25 is the cost expression for Black Diamond, while the right hand side 5x+50 is for Bunny Hill. The x is the number of hours.
How to solve this pythagoras theorem
Answer:
see explanation
Step-by-step explanation:
The hypotenuse is the longest side thus is (4x + 1)
The legs are 2x and (4x - 1)
Using Pythagoras' theorem, then
(4x + 1)² = (2x)² + (4x - 1)² ← expanding factors
16x² + 8x + 1 = 4x² + 16x² - 8x + 1 , that is
16x² + 8x + 1 = 20x² - 8x + 1 ( subtract 20x² - 8x + 1 from both sides )
- 4x² + 16x = 0 ( multiply through by - 1 )
4x² - 16x = 0 ← factor out 4x from each term
4x(x - 4) = 0
Equate each factor to zero and solve for x
4x = 0 ⇒ x = 0
x - 4 = 0 ⇒ x = 4
Now x > 0, thus x = 4
2x = 2(4) = 8
4x - 1 = 4(4) - 1 = 16 - 1 = 15
4x + 1 = 4(4) + 1 = 16 + 1 = 17
Thus
perimeter = 8 + 15 + 17 = 40 cm
the length of a rectangle is three times its width .if the perimeter is 72cm,calculate the width of the rectangle.
Answer:
Width = 9
Step-by-step explanation:
According to the problem...
3x = length
x = width
2(3x + x) = 72
3x+x = 36
4x = 36
x = 9 = width
Hope that helped!!! k
The solutions to (x + 3)^2- 4=0 are x = -1 and x = -5
True or false
Answer:
THE ANSWER WOULD BE TRUE MY FRIEND
Please help!! Two birds sit at the top of two different trees. The distance between the first bird and a birdwatcher on the ground is 32 feet. The distance between the birdwatcher and the second bird is 45 feet. What is the angle measure, or angle of depression, between this bird and the birdwatcher? Round your answer to the nearest tenth. 35.4° 44.7° 45.3° 54.6°
Answer:
45.3°
Step-by-step explanation:
A right triangle is formed given the information above.
Angle of depression = x°
Distance between first bird and birdwatcher = opposite to angle x° = 32 ft
Distance between second bird and birdwatcher = hypotenuse of the right triangle formed = 45 ft
The trigonometric ratio formula to use is:
[tex] sin(x) = \frac{opp}{hypo} [/tex]
[tex] sin(x) = \frac{32}{45} [/tex]
[tex] sin(x) = 0.7111 [/tex]
[tex] x = sin^{-1}(0.7111) [/tex]
[tex] x = 45.3 [/tex] (nearest tenth)
Angle of depression = 45.3°
Answer:
45.3°
Step-by-step explanation:
Hope this helps :)
Exponential form of 81/625
Step-by-step explanation:
Hey, there!!
you number is: 81/625
We know that,
81=9×9
and
625=25×25
and............................................................
9×9 means 9^2
and 25×25 means 25^2
so, the exponential form of the question is,
=[tex] \frac{ {9}^{2} }{ {25}^{2} } [/tex]
{we simply find exponential form by finding their fraction}
Hope it helps...
What value of n makes the equation true 2/3 n= -12
Answer:
The answer is - 18
Step-by-step explanation:
[tex] \frac{2}{3} n = - 12[/tex]
To solve the equation multiply both sides of the equation by 3
That's
[tex]3 \times \frac{2}{3} n = - 12 \times 3[/tex]Simplify
[tex]2n = - 36[/tex]Divide both sides of the equation by 2
[tex] \frac{2n}{2} = \frac{ - 36}{2} [/tex]We have the final answer as
n = - 18The value of n that makes the equation true is - 18
Hope this helps you
In a right triangle, the length of one leg is 36 in. The length of the other leg is 10 in. What is
the length of the hypotenuse?
A.) 162
B.) 72
C.) 1296
D.) 1396
Answer:
Hey there!
Pythagorean Theorem
a^2+b^2=c^2
10^2+36^2=c^2
100+1296=c^2
1396=37.4.
Um... did you make a typo?
Let me know if you did, because then I can edit my answer.
What is the distance between the points (2, 10) and (-6,4) on the coordinate
plane?
Answer:
10
Step-by-step explanation:
the distance is given by
[tex] \sqrt{ {(2 - ( - 6))}^{2} + {(10 - 4)}^{2} } [/tex]
=
[tex] \sqrt{100} [/tex]
= 10
PLEASE HELP ASAP! Alayna is hanging a picture frame in the center of a wall that is 8 feet wide. If the picture frame is 22 1/4 inches wide, how far will each side of the picture frame be from the edge of the wall (in inches)? First, estimate the amount and then find the exact measurement. In two or more complete sentences, explain how you solved the problem. You may include a diagram in your explanation if you wish.
Answer:
See below.
Step-by-step explanation:
Approximation:
The wall is 8 ft wide.
The frame is 22 1/4 inches wide. 22 1/4 inches is close to 2 ft since 2 ft = 24 inches.
8 ft - 2 ft = 6 ft
There will be approximately 6 ft of space tot he sides of the frame.
6 ft/2 = 3 ft
3 ft * 12 in./ft = 36 in.
There will be approximately 36 in. on each side of the frame.
Exact:
8 ft - 22 1/4 in. = 8 * 12 in. - 22 1/4 in. =
= 96 in. - 22 1/4 in.
= 95 4/4 in. - 22 1/4 in.
= 73 3/4 in.
The total amount of width of the wall not occupied by the frame is 73 3/4 in.
Half of that amount is on each side of the frame.
(73 3/4 in.)/2 = (73 3/4 in.) * 1/2 = (73 * 1/2 + 3/4 * 1/2) in. =
= 36 1/2 in. + 3/8 in.
= 36 4/8 in. + 3/8 in.
= 36 + 7/8 in.
= 36 7/8 in.
2.) Which expression has a value of -4?
A. (4) B. 1-41
C. 141
D.-141
3.) Which list of integers is in order from least to greatest?
A. -4,-7,0, 2
B. 0, 2, -4,-7
C-7, -4,0,2
D 2,0, -7,-4
I
4.) What is the value ofthe expression?
A -45 B. 19 C. 19
11+-24 + (-32)
D. 67
5.) Find the difference.
A. -47 B. -17
-32-(-15)
C. 17 D. 47
P
What is the solution to 7 × p = -56? A. -49 B. -8 C. 8 D. 49
Answer:
-8
Step-by-step explanation:
Hello!
What we do to one side of the equation we do to the other side
7 * p = -56
Divide both sides by 7
p = -8
The answer is -8
Hope this helps!
Which of the following options have the same value as 75\%75%75, percent of 969696?
Answer:
90
Step-by-step explanation:
What is the product? Two-thirds times eight-ninths
10/27
16/27
Two-thirds
Five-sixths
Answer:
16/27
[tex]\frac{2}{3}[/tex] × [tex]\frac{8}{9}[/tex] = [tex]\frac{16}{27}[/tex]
what is the value of 600.79-40.0032+5.01 to the nearest Hundredths
Answer:
565.80
Step-by-step explanation:
600.79-40.0032+5.01 = 565.7968
565.7968 to the nearest Hundredths =
565.80
Answer:
565.80
Step-by-step explanation:
600.79 - 40.0032 + 5.01
600.79 - 40.0032 = 560.7868
560.7868 + 5.01 = 565.7968
565.7968 to the nearest hundredth = 565.80
Howard earns $46 for every 2 hours of work. What is the constant of proportionality in the scenario?
Answer:
23
Step-by-step explanation:
Take the amount of money and divide by the hour
46/2 = 23
23 dollars for every hour
The constant of proportionality is 23
Solve five and six eighths plus four and four fifths.
Answer:
Two and three fourtieths.
Step-by-step explanation:
5 6/8 + 4 4/5
= 46/8 + 24/5
= 83/40
= 2 3/40
Two and three fourtieths(2 3/40) is the answer.
Answer: 9 22/40
Step-by-step explanation:
Show that 12.34343434………………can be expressed in the form p/q
Answer:
1222/99
Step-by-step explanation:
12.343434.. =
= 12.(34)
= 12 34/99
= (12*99+34)/99
= (1188+34)/99
= 1222/99
what is the lcm of 7÷25 and 3÷25
Answer:
LCM of 7/25 and 3/25 is 25
Step-by-step explanation:
The full meaning of LCM is Lowest (Least) Common Multiple
Lowest (Least)Common Multiple can be defined as the lowest or least number that is the multiple of two or more number. Note that this least number is not zero
Lowest(Least) common Multiple when applied to fractions is the least number that is the multiple of the denominators of the fraction.
In the above question, we are asked stop find the LCM of 7÷25 and 3÷25
= LCM of 7/25 and 3/25
The two denominators are the same, hence, the LCM is 25.
