All polynomials are continuous, so the limit can be evaluated by direct substitution:
[tex]\displaystyle \lim_{x\to-3} (x^3+3x^2+4x-12) = (-3)^3+3(-3)^2+4(-3)-12 = \boxed{-24}[/tex]
The Limit of (x cubed + 3 x squared + 4 x minus 12) as x approaches negative 3 is -24.
What are polynomials?Polynomials are those algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.
All polynomials are continuous, so the limit can be evaluated by direct substitution:
[tex]\lim_{x \to {-3}} x^3 + 3 x ^2+ 4 x - 12\\\\= (-3)^3 + 3 (-3)^2+ 4 (-3)- 12\\\\= -24[/tex]
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If the slope of a line is 0, does the line rise (from left to right), fall (from left to right), horizontal or vertical?
When the slope is 0
it is in a horizontal positionthe rise is zero, same from left to right; right to leftThis picture below shows some examples of equation with slope as 0
Answer:
horizontal
rise remains conserved
Step-by-step explanation:
Slope is 0
means
[tex]\\ \rm\dashrightarrow tan\theta=0[/tex]
[tex]\\ \rm\dashrightarrow \theta=tan^{-1}(0)[/tex]
[tex]\\ \rm\dashrightarrow \theta=0°[/tex]
Line will be parallel to x axis
Factor the following expression using the greatest common factor 18a+24c
Step-by-step explanation:
divide each by six
3a+4c
Answer:
6(3a+4c)
Step-by-step explanation:
GCF = 6
18a/6+24c/6
= 6(3a+4c)
A ladder 15 feet long leans against a house and makes an angle
of 60° with the ground. Find the distance from the house to the
foot of the ladder.
A 13 feet
)
B 7.5 feet
C 10 feet
D
8.2 feet
Answer:
B
Step-by-step explanation:
assume a right angle between the house and the ground.
then the ladder is the hypotenuse and distance from ladder to house is d
using the cosine ratio in the right triangle and the exact value
cos60° = [tex]\frac{1}{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{d}{15}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 15 ( divide both sides by 2 )
x = 7.5
distance from house to foot of ladder is 7.5 feet
What life cycle adaptation allows a seahorse to make lots of babies in a short amount of time? (2 points)
a seahorse
Group of answer choices
The female hatches the eggs in the sand while the male gets rid of predators.
The female hatches the eggs in the sand while the male protects them.
The male carries the babies while the female makes more eggs.
The male makes more eggs while the female carries the babies
The seahorse make a lot of babies because the male carries the babies while the female makes more eggs.
What is mating?Mating is the process in which opposite or hermaphroditic organisms pair for reproduction.
During mating between the male and female seahorse mates, the female seahorse puts her eggs in the male pouch and the male fertilises the egg in his pouch. The eggs develop into baby seahorse in the father pouch.
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Look at the equation.
X-3 = 12
Which value of x makes this equation true?
4
(b9
с
15
d) 36
Answer:
c) 15
Step-by-step explanation:
Plugging in the value of x as 15 in the equation,
15-3 which is equal to 12
The graph and the table below show the relationship between y, the total cost, and x, the number of loads washed, at two laundromats.
A cyclist is training for a big race. One day she biked 33. 25 miles in 1 hour and 45 mins. At that rate how long wil it take for her to complete the 47. 5 mile race? How fast was the biker traveling?
Answer: 2.5hr
Step-by-step explanation:
33.25miles in 1¾ hr
Speed = 33.25 ÷ 7/4 hr
Speed = 33.25 × 4/7 = 19miles/hr
Time to travel 47.5miles = 47.5/19
2. 5 kg of potatoes cost £1. 40
workout the cost of 4. 25 kg of potatoes
Is it possible that a packet of candies does not divide into 9 equal parts, but rather divides into 3 equal parts? Give an example with your answer.
Answer:
Yes, if there are 6 candies it can be divided equally by 3 and not 9.
Step-by-step explanation:
Find the median of the data.
24,74,61,29,38,27,68,54
Answer:
The median is 46
Step-by-step explanation:
To find the median, you must first order the numbers, from left to right, lowest to highest:
24, 27, 29, 38, 54, 61, 68, 74
Next, we have to find the number in the middle. We can do this by counting inwards one and crossing out each of the lowest and highest each time we get closer to the middle/center.
24, 27, 29, 38, 54, 61, 68, 74
, 27, 29, 38, 54, 61, 68,
, , 29, 38, 54, 61, ,
, , , 38, 54, , ,
Now, if there is no exact middle, we would add them add divide by 2. If there was an exact middle, that would be the answer. But there isn't.
38 + 54 = 92
92 / 2 = 46
The median is 46
Four more than three times a number x is 48
A retailer agreed to take 5000 ball point pen. However he found that 12 persent are faulty. What was the percentage decrement
Answer:
88%
Step-by-step explanation:
The correct answer is 88% because 12% of the pens are defective.
As a result, 12% ÷ 5000 = 12 ÷ 100 x 5000
= 600
There are 600 defective pens.
The pens that are left are 5000 - 600 = 4400.
4400 pens are in good working order.
This means that 88 percent = 4400 ÷ 5000 x 100
I hope this helps! ^-^
What is the approximate area of the hexagon? 24 in.2 42 in.2 48 in.2 84 in.2
Answer: 42 in²
Step-by-step explanation: right on edge
Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.
4
4(1.4)
2
N(2.0)
14
-2
x
(Pl-1, -2)
M(4,0)
The perimeter is about
units.
Check the picture below, now the distance from 2,0 to 4,0 there's no need to do much calculation since that's just 2 units, as you see there.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{4}) ~\hfill d1=\sqrt{[ 1- 2]^2 + [ 4- 0]^2} \\\\\\ d1=\sqrt{(-1)^2+4^2}\implies \boxed{d1=\sqrt{17}} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{-2}) ~\hfill d2=\sqrt{[ -1- 1]^2 + [ -2- 4]^2} \\\\\\ d2=\sqrt{(-2)^2+(-6)^2}\implies \boxed{d2=\sqrt{40}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{0}) ~\hfill d3=\sqrt{[ 4- (-1)]^2 + [ 0- (-2)]^2} \\\\\\ d3=\sqrt{(4+1)^2+(0+2)^2}\implies \boxed{d3=\sqrt{29}}[/tex]
[tex]~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{2~~ + ~~\sqrt{17}~~ + ~~\sqrt{40}~~ + ~~\sqrt{29}~~\approx~~17.83}[/tex]
The perimeter of the polygon with the vertices L = (1, 4), P = (-1, -2),
N = (2, 0) and M = (4, 0) is approximately 17.93 units.
We have,
The polygon has the following sides:
LP, PN, NM, and ML.
The coordinates for each point are:
L = (1, 4)
P = (-1, -2)
N = (2, 0)
M = (4, 0)
The perimeter of the polygons.
= LP + PN + NM + ML
Using the distance formula for the distance between two points (a, b) and (c, d):
Distance = √((c - a)² + (d - b)²)
Let's calculate the distances between the points:
LP:
Distance(LP)
= √((-1 - 1)² + (-2 - 4)²)
= √((-2)² + (-6)²)
= √(4 + 36)
= √40
= 6.32
PN:
Distance(PN)
= √((2 - (-1))² + (0 - (-2))²)
= √((2 + 1)² + (0 + 2)²)
= √(3² + 2²)
= √(9 + 4)
= √13
≈ 3.61
NM:
Distance(NM)
= √((4 - 2)² + (0 - 0)²)
= √(2² + 0²)
= √4
= 2
ML:
Distance(ML)
= √((4 - 1)² + (0 - 4)²)
= √((4 - 1)² + (-4)²)
= √(3² + 16)
= √(9 + 16)
= √25
= 5
Now,
Perimeter = LP + PN + NM + ML
Perimeter ≈ 6.32 + 3.61 + 2 + 5 ≈ 16.93
Thus,
The perimeter of the polygon is approximately 17.93 units.
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How do you find the measure of angle A?
Answer:
m∠A = 18
Step-by-step explanation:
Formula:
the sum of the interior angles of a triangle is 180.
____________________
According to the formula :
[tex]m\angle A\ +\ m\angle B\ +\ m\angle C=180[/tex]
⇔ x - 22 + 3x + 19 + x - 17 = 180
⇔ 5x + (19 - 17 - 22) = 180
⇔ 5x + (2 - 22) = 180
⇔ 5x - 20 = 180
⇔ 5x = 180 + 20
⇔ 5x = 200
[tex]\Leftrightarrow x = \frac{200}{5} \\\Leftrightarrow x = 40[/tex]
Conclusion:
m∠A = x - 22 = 40 - 22 = 18
Aaron was plotting the shape of his garden on grid paper. While it was an irregular shape, it was perfect for his yard. each square on the grid represents 1 square meter. What is the area of the garden?
pls, add an explanation as well as an answer, i wont open any links, thanks :)
Answer:
44 [tex]m^{2}[/tex]
Step-by-step explanation:
As the shape contain triangle ,rectangle and square so we calculate the area of all these and then add up.
As one box = 1 [tex]m^{2}[/tex]
Area of Triangle= [tex]\frac{1}{2}*b*h[/tex]
b= 8, h=2
Area of Triangle= [tex]\frac{1}{2}*8*2[/tex]
Area of Triangle= [tex]8 m^{2}[/tex]
Area of Rectangle= [tex]l*w[/tex]
l=8,w=4
Area of Rectangle= [tex]8*4\\[/tex]
Area of Rectangle= [tex]32m^{2}[/tex]
Area of Square=[tex]a^{2}[/tex]
a=2
Area of Square=[tex]2^{2}[/tex]
Area of Square=[tex]4m^{2}[/tex]
Total Area=[tex]8 m^{2}[/tex]+[tex]32m^{2}[/tex]+[tex]4m^{2}[/tex]=44[tex]m^{2}[/tex]
Can someone please explain 3 and 4 to me? I don’t understand how to solve them
Answer:
see explanation
Step-by-step explanation:
3) line l and m are perpendicular so they intersect at 90 degrees
I labelled the angles that are the same measure.
2x + 23 = 90 subtract 23
2x = 67 divide by 2
x = 23.5 degrees
4) 2m + 66 = 120 subtract 66
2m = 54 divide by 2
m = 27 degrees
ANSWER ASAPP PLSSS
There are 7 options on the dessert menu at a restaurant. Ellen and Connie like all of the choices equally, so they each choose a dessert at random from the menu. What is the probability that Ellen will choose apple pie and Connie will choose strawberry cheesecake for dessert? Express your answer as a decimal. If necessary, round your answer to the nearest thousandth.
Answer:
1/7 * 1/7 = 0.02040816326
Step-by-step explanation:
Probability of selecting 1 of the 7 menu items is P(1 item) = 1/7
Thus, probability that they select the items from menu written in the question is; P(both select 1 item) = 1/7 * 1/7 = 0.02040816326
Estimate the value Square Root 49 to your best judgement and explain why
V49 = 7 because 7²=49?
.........
What is the missing term?
Answer:
-2x
filler filler filler
What is the answer
5 3/5 - 3 14/16
Answer:
138/80
Step-by-step explanation:
5×5+3/5-3×16+14/16
28/5-62/16
28×16/5×16-62×5/16×5
448/80-310/80
448-310/80
138/80
Which statement about 6x2 7x – 10 is true? one of the factors is (x 2). one of the factors is (3x – 2). one of the factors is (2x 5). one of the factors is (x – 5).
One of the factors of the given quadratic expression is (x+2).
The given quadratic expression is:
[tex]6x^{2} +7x-10[/tex]
What is a quadratic expression?Any expression of the form [tex]ax^{2} +bx+c[/tex] is called a quadratic expression where a≠0.
Splitting the middle term of the given expression
[tex]6x^{2} +12x-5x-10[/tex]
[tex]6x(x+2)-5(x+2)[/tex]
[tex](x+2)(6x-5)[/tex]
Hence, one of the factors of the given quadratic expression is (x+2).
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Express -48 by 60 as a rational number with denominator 25 pura Karen
Answer:
-20/25
Step-by-step explanation:
To change a fraction to one with a different denominator, common factors can be removed or added to numerator and denominator as required.
__
-48/60 can be reduced to lowest terms by removing the common factor of 12. It can be made to have a denominator of 25 by adding a common factor of 5.
[tex]-\dfrac{48}{60}=-\dfrac{4\cdot12}{5\cdot12}=-\dfrac{4}{5}\\\\=-\dfrac{4\cdot5}{5\cdot5}=\boxed{-\dfrac{20}{25}}[/tex]
__
Alternatively, the numerator of the desired fraction can be found by multiplying the given fraction by the desired denominator.
numerator = 25×(-48/60) = -1200/60 = -20
new fraction = -20/25
A carpenter has to cut four lengths of wood, each 128cm long. What is the total length of wood that he needs?
Answer:
512cm
Step-by-step explanation:
same length of 128 4 times. 512
A company sells cocoa powder in a cylindrical container that is 5 inches long with a circular base of diameter 4 inches. The company is planning to sell a family-size product that will use similar packaging scaled by a factor of 2.
The circumference of the original container is (62.8, 15.7, 12.57, 6.28)
inches. This is (18.84, 9.42, 37.68, 12.57)
inches less than the circumference of the new container.
The circumference of the original container is 12.57 inches.
The cirucmference of the original container is 12.57 inches less than the circumference of the new container.
What is the circumference of the cylinder?The circumference of a cylinder is the distance round the cylinder. It is the perimeter of the cylinder.
The circumference of a cylinder = πD
Where:
π = 22/7D = diameterThe circumference of the original container = 22/7 x 4 = 12.57 inches
The circumference of the family sized container 12.57 x 2 = 25.14 inches
Difference in the circumference = 25.14 - 12.57 = 12.57 inches
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Answer: 12.57 for both
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
What is the value of y??
Answer:
3
Step-by-step explanation:
The opposite sides are equal
2y+ 4 = 10
2y = 6
y = 3
A standard number cube is tossed. Find P(2 or even)
Answer:
1/2
Step-by-step explanation:
there are 3 even numbers including 2. there are 6 possible outcomes. 3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
6-8x=7x-9x-36 i really need help
Answer:
Simplifying
6 + -8x = 7x + -9x + -36
Reorder the terms:
6 + -8x = -36 + 7x + -9x
Combine like terms: 7x + -9x = -2x
6 + -8x = -36 + -2x
Solving
6 + -8x = -36 + -2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2x' to each side of the equation.
6 + -8x + 2x = -36 + -2x + 2x
Combine like terms: -8x + 2x = -6x
6 + -6x = -36 + -2x + 2x
Combine like terms: -2x + 2x = 0
6 + -6x = -36 + 0
6 + -6x = -36
Add '-6' to each side of the equation.
6 + -6 + -6x = -36 + -6
Combine like terms: 6 + -6 = 0
0 + -6x = -36 + -6
-6x = -36 + -6
Combine like terms: -36 + -6 = -42
-6x = -42
Divide each side by '-6'.
x = 7
Simplifying
x = 7
Answer:
x = 7
Hope This Helps! :) Please Give brainliest if you can!
anyone know the answer??
Answer:
the second option
Step-by-step explanation:
in ax²+bx+c = 0:
[tex]x = \frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
subtract both sides by 6 to get to this form, as the right side will be left with 0
6x² + 8x - 6 = 0
here, the coefficient for x² (a) is 6, the coefficient for x (b) is 8, and the remaining number added on (c) is -6
plugging our numbers into the formula, we get
[tex]x = \frac{-8+-\sqrt{(-8)^2-4(6)(-6)} }{2(6)}\\= \frac{-8+-\sqrt{64-(-144)} }{12} \\= \frac{-8+-\sqrt{208} }{12} \\ = \frac{-8+\sqrt{208} }{12} or \frac{-8-\sqrt{208} }{12}\\= 0.53518375848 or -1.86851709182\\= approximately -1.87, 0.54[/tex]
In triangle ABC, m∠ A = 45˚ and a = c. Which best describes triangle ABC? *