Answer:
Attached please find answer
Step-by-step explanation:
= (x² + x - 42) / (x - 6)
= [x² + (7x - 6x) - 42] / (x - 6)
= [x² + 7x - 6x - 42] / (x - 6)
= [(x² + 7x) - (6x + 42)] / (x - 6)
= [x(x + 7) - 6(x + 7)] / (x - 6)
= [(x + 7)(x - 6)] / (x - 6)
= x + 7 → when x approches 6
= 6 + 7
= 13
Other method:
Lim (x² + x - 42) / (x - 6)
x→ 6
When x → 6, there is an indeterminate expression because: 6 - 6 = 0
Do you know the l'Hôpital's rule, when x → a:
Lim [ f(x) / g(x) ] = Lim [ f'(x) / g'(x) ]
f(x) = x² + x - 42
f'(x) = 2x + 1
g(x) = x - 6
g'(x) = 1
= f'(x) / g'(x)
= (2x + 1)/1
= 2x + 1 → when x approches 6
= 12 + 1
= 13
Which equation represents the function shown on the graph? y = x y = x y = 2x y = 4x
Answer:
The correct answer is y=4x
Step-by-step explanation:
Find the point slope equation of the line through (10, -4) with a slope of -6.
Answer:
y=-6x+56
Step-by-step explanation:
The point-slope equation of a line is given as
y=mx+c where m is slope and c is y-intercept of a line.
We are given m=-6 and a point (10,-4) which can be put into y=mx+c to find the only unknown c. Thus,
c=-4+6x10=56.
Now we can easily form the point-slope equation of the line
y=-6x+56.
Tomas collected 139 cans for recycling on Monday, and twice that number on Tuesday. How many cams did he collect on Tuesday
Answer:
278
Step-by-step explanation:
139x2=278
On a map of North Carolina, the distance between Charlotte and Wilmington is 14.75 inches. If 2 inches
equals 24 miles, what is the approximate distance between the two cities?
Answer:
12
Step-by-step explanation:
I don't really know but good luck I hope it right
Ben also bought a package of 3 T-shirts for $14.25. What is the unit price, per T-shirt
Answer:
4.75 per T-shirt
Step-by-step explanation:
Divide 14.25 by 3
12 POINTS PLEASE HELP ME
Answer:
11,44,83
Step-by-step explanation:
4y+7y+6=116(exterior angle is equal to sum of two opposite interior angle in traingle)
11y=116-6
y=110÷11=11
4y=4×11=44
7y+6=7×11+6=83
3 points) A fence is to be built to enclose a rectangular area of 240 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 13 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
Answer:
For the rectangular area, we will have a length L, and a width W, such that the two sides with measure L and one with measure W will be made with the material of $4 per ft, and the other side with measure W will be made with the material that costs $13 per ft.
Then the total cost will be:
C = (L + L + W)*$4 + W*$13.
And we know that the area is equal to 240 ft^2, then:
240ft^2 = L*W
To solve this, the first step is to isolate one of the variables in the second equation. I will isolate L:
L = (240ft^2)/W
Now we can replace this in the first equation to get:
C = ( 2*(240ft^2)/W + W)*$4 + W*$13.
C = $4*480ft^2/W + W*$17
Now we want to find the minimum of this function, then we need to look at the zero of the first derivative of C:
C' = - ($4*480 ft^2)/W + W*$17 = 0
- ($4*480 ft^2) + $17*W^2 = 0
Let's solve this for W:
$17*W^2 = ($4*480 ft^2)
W^2 = ($4*480 ft^2)/$17 = 112.94ft^2
W = √(112.94 ft^2) = 10.63 ft.
Then the width must be 10.64 ft, and the length can be obtained with the equation:
L*W = 240 ft^2
L*10.64 ft = 240 ft^2
L = (240 ft^2)/10.64ft = 22.56 ft
The width is 10.64 ft, and the length is 22.56 ft
Identify and locate the symmetry elements in each of the following objects(ignore labeling or writing). Identify the point group for each object.a) A wine bottle (without labels)b) A tennis racquet (without labels)c) A tennis ball with the seams.d) An American footballe) One shoe and a pair of shoes, one on your left foot the other on your rightfoot.
Answer:
hello your question is incomplete attached below is the complete question
answer: attached below
Step-by-step explanation:
1) attached below
2)
a) wine bottle ( without labels ) :
Linear structure with no center of inversion its point group is c ∞ v
b) A tennis racquet ( without labels )
1 C2 axis , 2 бv planes , point group ---- C2v
c) A tennis ball with the seams
3 perpendicular c2 axis , one through the narrow portions of each segment, others through the seams
d)
Moe puts $1500 in a bank certificate that pays an annual rate of 4.5% compounded annually. No withdrawals or deposits are made. How much will the certificate be worth (to the nearest dollar) at the end of 7 years?
Answer:
FV= $2,041.29
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $1,500
Number of periods (n)= 7 years
Interest rate (i)= 4.5% = 0.045
To calculate the future value, we need to use the following formula:
FV= PV*(1+i)^n
FV= 1,500*(1.045^7)
FV= $2,041.29
i23
= i20+3
Use the example as a model. Simplify the
expressions.
= i20 x 1
737
x ;3
= 15 x ;
= 1x is
Answer:
- I^20+1 i= /2 i^2= -1 i^3= -i i^4= 1 for every four it repeat itself. 4, 8, 12, 16, 20. therefore i^20=1 1+1=2.
Sorry if I'm wrong!
According the a University Center for Logistics Management, 7% of all merchandise sold in the United States gets returned. A Seattle department store samples 89 items sold in January and found that 10 of the items were returned. H0: p = 0.07 H1: p < 0.07 Calculate the test statistic: Group of answer choices 1.31 2.33 0.99 1.15 1.57
Answer:
The test statistic is 1.57.
Step-by-step explanation:
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
A Seattle department store samples 89 items sold in January and found that 10 of the items were returned.
This means that [tex]n = 89, X = \frac{10}{89} = 0.1124[/tex]
7% of all merchandise sold in the United States gets returned.
This means that [tex]\mu = 0.07[/tex]
For a proportion, the standard deviation is [tex]\sigma = \sqrt{p(1-p)} = \sqrt{0.07*(1-0.07)} = 0.2551[/tex]
Test statistic:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{0.1124 - 0.07}{\frac{0.2551}{\sqrt{89}}}[/tex]
[tex]t = 1.57[/tex]
The test statistic is 1.57.
a knife is three times the cost of a spoon. 9 spoons and 12 knives cost £82.80. Work out the cost of one knife.
3/4 into a percent and a decimal
Answer:
75% and .75
Step-by-step explanation:
Which classification best describes the relationship between <2 and <4?
Answer:
c) because 2*2 =4 and 4 -2 =2
Step-by-step explanation:
Select all that apply. Which of the following name an angle in the drawing? ACB CDE ECB BDA
Answer:
ecb and acb
Step-by-step explanation:
negative 50 divided by positive 10
What happens to the mode of the data set shown below if
the number 16 is added to the data set?
18
19
26
24
18
25
19
20
19
OA) The mode is increased by 1.
OB) The mode does not change.
Oc) The mode is increased by 2.
OD) The mode is increased by 7.
Answer:
OB) The mode does not change
( I will give brainlist) Mrs. Perkey solved the problem below. Oh no! It looks like she made a mistake! -3/5 + -2/5 = -1/5 What did she do wrong? Please explain how to solve this problem the correct way for full points.
Answer:
It is actually -1.
Step-by-step explanation:
((-3) / 5) + ((-2) / 5) her problem should be set up like this. She just plain out did -3/5+-2/5 and that is not what your supposed to do.
pls mark me brainliest
Answer:
-5/5= -1
Step-by-step explanation:
-3/5 + -2/5 = -5/5
when u have to add 2 minus values it shuld not be subtracted by each other but added instead and put the (-) sign infront of the final value as given above.
Marco sells and ships oranges from the trees in his orange grove for $1.25 per pound plus a shipping fee. One package has a shipping fee of $4.95 and a total cost of $11.20. Write and solve an equation to find the number of pounds of oranges in the package. Show your work.
(Please help )
Answer:
Let x = the number of pounds of oranges in the packet.
The equation: 11.20 = 1.25x + 4.95
11.20 = 1.25x+4.95
6.25 = 1.25x
x = 5
There are 5 pounds of oranges in the packet.
Let me know if this helps!
Solve 1/2 x 3/4 *
A. 3/8
B. 4/6
C. 5/4
D. 4/8
Answer:
A
Step-by-step explanation:
Multiply the numerators together, then multiply the denominators together.
Solve the Equation p - 15 = 30.
Answer:
45
Step-by-step explanation:
add 15 on both sides
what is x=9 z=2 times?
Answer:
x=9
z=2
Step-by-step explanation:
the measures of the angles of a triangle are shown in the figure below solve for x 46° 2x+20° 72°
Answer:
x = 21
Step-by-step explanation:
Add all the angles to get 138 + 2x = 180. Subtract 138 to get 2x = 42. x = 21
Answer:
x = 21
Step-by-step explanation:
Can I have brainliest?
The owner of a ballroom dance studio has 8 locations in the Houston area. Each studio is a 30 foot by 30 ft. room. If each couple requires 72 inch by 72 inch area, what is a reasonable estimate for the total number of people the dance company can accommodate in the city of Houston for all of it's locations?
Answer: 400
Step-by-step explanation:
Area required by each couple = 72 inch by 72 inch
= 6 feet by 6 feet [ 1 feet = 12 inches and [tex]72\text{ inches}=\dfrac{72}{12}\text{ feet}=6 \text{ feet}[/tex]]
= 36 square feet
Area in each studio = 30 ft by 30 ft = 900 square feet
Then, Area of 8 studios in Houstan = 8 x (900 feet) = 7200feet
Total couple the dance company can accommodate in the city of Houston for all of it's locations = [tex]\dfrac{7200}{36}=200[/tex]
Total people = 2 x (Total couples)= 2 x 200=400
Hence, a reasonable estimate for the total number of people the dance company can accommodate in the city of Houston for all of it's locations = 400
What is 2y+4x =10 in y=mx+b
Answer:
The answer should be y = -2x + 5
Step-by-step explanation:
Subtract 4x to move it to the other side.
(2y = -4x + 10)
Then you divide both sides by 2 to get y by itself.
a bird bath that is 3 ft talk casts a shadow that is 2 ft long.Find the height of a tent that casts a 6 ft shadow.
Answer:
is it 5ft
Step-by-step explanation:
if the bird bath had a foot taken off in the shadow then wouldn't a foot be taken off for the tent as well
1. Aubrey is driving on a long road trip. She currently has 14 gallons of gas in her car. Each hour that she drives, her car uses up 0.75 gallons of gas. How much gas would be in the tank after driving for 6 hours? How much gas would be left after tt hours?
2. Find the sum of -8x^2+3 and -9x^2+3x-3−
3.Simplify the expression to a polynomial in standard form:
(-3x-5)(-x^2+x-5)
Answer:
See solutions below
Step-by-step explanation:
1) Total amount of gallons = 14 gallons
If she uses up 0.75 gallons of gas each hour then;
1 hour = 0.75gallons
after driving 6 hours, amount of gallons used will be;
6 hours = x
Divide both expressions
1/6 = 0.75/x
x = 6 * 0.75
x = 4.5gallons
Amount of gas left = 14 - 4.5 = 9.5 gallons of gas
Hence 9.5 gallons of gas will be left after 6 hrs
Similarly;
1 hour = 0.75gallons
after driving t hours, amount of gallons used will be;
t hours = x
x = 0.75t
Amount of gas left after t hours = (14 - 0.75t) gallons of gas
2) We are to find the sum of -8x^2+3 and -9x^2+3x-3
-8x^2+3 + (-9x^2+3x-3)
= 8x^2+3 -9x^2+3x-3
Collect like terms
= 8x^2 -9x^2+3x + 3-3
= -x^2 + 3x
Hence the sum is -x²+3x
3) Expressing in standard form;
(-3x-5)(-x^2+x-5)
Expand
= 3x³-3x²+15x+5x²-5x+25
Collect like terms
= 3x³-3x²+5x²+15x-5x+25
= 3x³+2x² + 10x + 25
Hence the product in polynomial form is 3x³+2x² + 10x + 25
what is the least whole number that has the remainders 10,12, and 15 when divided by 16, 18. and 21, respectively
Answer:
[tex]1002[/tex]
Step-by-step explanation:
First find difference between the divisors and remainders.
[tex]16-10=6\\18-12=6\\21-15=6[/tex]
Here, the difference between the divisors and remainders is equal.
So, the required number is equal to LCM of [tex](16,18,21)-6[/tex]
[tex]16=2^4\\18=2(3^2)\\21=3(7)[/tex]
LCM of [tex](16,18,21)=2^4(3^2)(7)=1008[/tex]
Required Number [tex]=1008-6=1002[/tex]
Members of a softball team raised $2039.50 to go to a tournament. They rented a bus for $1157.50 and budgeted $49 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.
Answer:
18 = number of players
Step-by-step explanation:
Giving the following information:
Members of a softball team raised $2039.50 to go to a tournament. They rented a bus for $1157.50 and budgeted $49 per player for meals.
To calculate the total number of players they can bring, we need to use the following formula:
Total amount of money= fixed cost + unitary variable cost*number of players
2,039.5= 1,157.5 + 49*number of players
882/49= number of players
18 = number of players
Answer:
49x+1157.50=2039.50
x=18
A circle's circumference is 600 m.
What is a good approximation of the circle's area?
A. 300 m2
B. 3,000 m2
C. 30,000 m2
D. 300,000 m2
Answer:
i think its a but im not sure