If the -8 is under the square root, then...
[tex]\displaystyle L = \lim_{x\to -3} \sqrt{x^2-8}\\\\L = \sqrt{(-3)^2-8}\\\\L = \sqrt{9-8}\\\\L = \sqrt{1}\\\\L = 1\\\\[/tex]
OR
If the -8 is not under the square root, then...
[tex]\displaystyle L = \lim_{x\to -3} \sqrt{x^2}-8\\\\L = \sqrt{(-3)^2}-8\\\\L = \sqrt{9}-8\\\\L = 3-8\\\\L = -5[/tex]
Either way, we replace x with -3 and simplify.
For more information, refer to the direct substitution rule for limits.
The limit of [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex] is one.
What is Limits?A limit is the value that a function approaches as the input approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity.
The given limit is [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex]
Now replace x with -3 as limit value is -3
√(-3)²-8
Square root over minus three square minus eight
The three square is nine
√9-8
When eight is subtracted from nine we get one.
√1
The square root of one is always one
[tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex]=1
Hence, [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex] is one.
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What is the surface area in square inches of a basketball that has a diameter of 9 inches
if its diameter is 9, that means its radius is half that, or 4.5.
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4.5 \end{cases}\implies \begin{array}{llll} SA=4\pi (4.5)^2\implies SA=81\pi \\\\\\ SA\approx 254.47~in^2 \end{array}[/tex]
The surface area of the basketball with diameter of 9 in will be 254.34 in².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given that, a basketball has a diameter of 9 inches we need to find its surface area,
Since, the basketball is in the shape of the sphere and the surface area of the sphere = 4π×radius²
Therefore, the surface area of the basketball =
= 4×3.14×(9/2)²
= 4×3.14×4.5×4.5
= 254.34 in²
Hence the surface area of the basketball with diameter of 9 in will be 254.34 in².
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Write each of the following products in standard form. Show the work that
leads to your final answers.
(a) (x+8)(2x-3)
(b) (x-5)²
[tex]\textbf{a)}\\\\~~~(x+8)(2x-3)\\\\=2x^2 -3x + 16x - 24\\\\=2x^2 +13x -24\\\\\textbf{b)}\\\\~~~(x-5)^2\\\\=(x-5)(x-5)\\\\=x^2 -5x -5x+25\\\\=x^2 -10x +25[/tex]
2. What is the volume of this prism?
5
5
1.7
2
2
17 cubic units
28 cubic units
1.7
5
2
1.7
The volume of the rectangular prism is 17 cubic units
How to determine the volume?The given parameters are:
Length = 5 unitsWidth = 2 unitsHeight = 1.7 unitsThe volume is calculated as:
Volume = Length * Width * Height
Substitute known values
Volume = 5 * 2 * 1.7
Evaluate
Volume = 17
Hence, the volume of the prism is 17 cubic units
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Montraie has a coin collection. He keeps 10 of the coins in his box, which is 20% of the collection. How many total coins are in his collection?
By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.
How to calculate the quantity of coins in a collection
In this question we know the quantity of coins in a box and such coins are part of the coin collection. By definition of percentage we have the total quantity of coins in the collection:
x = 10*(100/20)
x = 50
By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.
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David's phone battery level drops 6 percentage points each hour when he is not playing a game on it. When David does play a game on his phone, the phone battery level drops 18 percentage points each hour. On a particular day, the phone battery level was at 100 percentage points at 12:00 noon and at 22 percentage points at 6:00 P.M. If David did not charge his phone during this time, how many hours did he spend playing the game between 12:00 noon and 6:00 P.M. on that day
The number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be 3.5 hours.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
David's phone battery level drops 6 percentage points each hour when he is not playing a game on it.
When David does play a game on his phone, the phone battery level drops 18 percentage points each hour.
On a particular day, the phone battery level was at 100 percentage points at 12:00 noon and at 22 percentage points at 6:00 P.M.
If David did not charge his phone during this time.
Then the number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be
Let x be the number of no gaming hours and y be the number of gaming hours.
Then the equation will be
6x + 18y = 100 - 22
6x + 18y = 78
x + 3y = 13 ...1
x + y = 6 ...2
By solving the equations 1 and 2, we have
x = 2.5 hours and y = 3.5 hours
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Please help studying for finals
Answer:
C angle H = 75.4
Step-by-step explanation:
In order to find the measure of angle H we must first find the value of x
Firstly it's good to know that the sum of the angles in a quadrilateral always add up to 360 degrees
Knowing this we can create an equation.
Since the angle measures must add up to 360 degrees we know that angle F + angle E + angle H + angle G = 360
Plugging in the given expressions for each angle we acquire
14x - 11 + 5x + 21 + 6x + 16 + 8x - 7
We can now solve for x
==> combine like terms
33x + 19 = 360
==> subtract 19 from both sides
33x = 341
==> divide both sides by 33
x = 10 1/3
Now that we have identified the value of x and we can plug in x = 10 1/3 into the given expression of angle H and evaluate to get the measure
Angle H = 8x - 7
==> plug in x = 10 1/3
Angle H = 8(10 1/3) - 7
==> multiply 8 and 10 1/3
Angle H = 82.7 - 7
==> subtract 7 from 82.7
Angle H = 75.6
C is the closest answer
Answer:
C. m∠H = 75.4°
Step-by-step explanation:
all sides of a quadrilateral add up to 360°
So, (5x + 21) + (14 - 11) + (6x + 16) + (8x - 7) = 360
Add like terms:
33x + 19 = 360
33x = 360 - 19
33x = 341
x = 341/33
x = 10.33...
Substitute:
∠H = 8x - 7
∠H = 8(10.3) - 7
∠H = 75.4°
so what? idc abt ur feelings just awnser me
The measure of center that will be used to emphasize the average height of the students is frequency of the numbers.
Average height of the students
The average height of the students is calculated as follows;
Average = total height/number of students
total height = 135 + 130 + 170 + 170 + 160 + 90 = 855
Average = (855)/(6)
Average = 142.5 cm
From the given heights of the students, 170 cm has the highest frequency and will influence the average height more.
Thus, the measure of center that will be used to emphasize the average height of the students is frequency of the numbers.
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What is the equation of the line that passes through the point (5,3) and has a slope of -1/5 ?
Answer: y=-1/5x+4
Step-by-step explanation: use the equation y=mx+b (x,y)->(5,3) 5 is an x value and 3 is a y value so you want to plug in these values into the equation. 3=-1/5(5)+b. We already know our slope so just plug it into m. Now multiply -1/5 and 5 which is -1. 3=-1+b you want to isolate b so you can find the intercept. Add one to both sides so it cancels out. 4=b we found our y-intercept so we can write the equation now. y=-1/5x+4
What is the theoretical probability of drawing a blue marble from a bag containing 6 Green marbles, 9 yellow marbles and 5 blue marbles?
Answer:
1/20
Step-by-step explanation:
number of favourable outcomes/number of outcomes
what is the minimum and maximum mass of 1.5 kg
The minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.
Minimum and Maximum mass measurement
The minimum and maximum mass measurement is determined from the uncertainty in the measurement.
For a given uncertainty of 2.2%, the minimum and maximum mass measurement is calculated as follows;
2.2% of 1.5 kg = 0.022 x 1.5 kg = 0.033 kg
minimum mass = 1.5 kg - 0.033 kg = 1.467 kg
maximum mass = 1.5 kg + 0.033 kg = 1.533 kg
Thus, the minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.
The complete question is below:
what is the minimum and maximum mass of 1.5 kg if the uncertainty in measurement is 2.2%?
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Product of square of x and cube of y
Since the square root of
x=√x
and the cube root of
x=3√x
and their product
=√x × 3√x
= x1/2 × x1/3 [Since, n√a =a 1/n]
=x1/2+1/3 [Since, a^m ×a^n =a^m+n]
=x^3+2 /6
= x 5/6
Therefore, required product is
=√6x5
Answer:
[tex]x^2y^3[/tex]
Step-by-step explanation:
[tex]\text{Square of}~ x =x^2\\\\\text{Cube of}~ y = y^3\\\\\text{Product} = x^2y^3[/tex]
evaluate f(x) = 3/6x+6 when x = -1
a) undefined
b) 0
c) 3
d) 3/36
Answer:
a) Undefined.
Step-by-step explanation:
[tex]f(x) = \dfrac 3{6x+6} = \dfrac{3}{6(x+1)} = \dfrac{1}{2(x+1)}\\\\\\f(-1) =\dfrac{1}{2(-1+1)}= \dfrac{1}{0}[/tex]
what is the awnser to this The Hernandez family orders 3 large pizzas. They cut the pizzas so that each pizza has the same number of slices, giving them a total of 24 slices.
The Wilson family also orders several large pizzas from the same pizza restaurant. They also cut the pizzas so that all their pizzas have the same number of slices. For the Wilson family, the equation y = 10x represents the relationship, where x represents the number of pizzas and y represents the number of total slices.
Which statements best describe the pizzas bought by the Hernandez and Wilson families? Select two options.
For the Hernandez family, the equation y = 3x represents the relationship between the number of slices and number of pizzas, where x represents the number of pizzas and y represents the number of total slices.
For each family, a graph of the relationship between number of pizzas, x, and number of slices, y, goes through the point (0, 0) and is a straight line.
The Hernandez family’s slices are smaller than the Wilson family’s slices.
If the Wilson family ordered 3 large pizzas from the same restaurant as the Hernandez family, they would have more slices than the Hernandez family after each family cut their pizzas into slices.
The constant of proportionality is 10 for the Wilson family, but cannot be determined for the Hernandez family.
The two true statements are the second statement (both lines contain the point (0,0)) and the fourth statement (If the Wilson family buys 3 pizzas, they will get more slices than the Hernandez family).
Which is the correct statement?
First, we know that the Hernandez family orders 3 large pizzas, such that they cut each pizza in the same number of slices, getting a total of 24 slices.
Then the number of slices that they get for each pizza is:
24/3 = 8
So from each large pizza, they get 8 slices.
So the relation between the number of pizzas bought (x) and the number of slices (y) is:
y = 8*x
In the other hand for the Wilson family we have the relation:
y = 10*x
Where y and x are the same ones as the defined above.
Then the true statements are:
"If the Wilson family ordered 3 large pizzas from the same restaurant as the Hernandez family, they would have more slices than the Hernandez family after each family cut their pizzas into slices."
This is true because Wilson family cuts each pizza in 10 slices, while the Hernandez family cuts each pizza in 8 slices.
"For each family, a graph of the relationship between number of pizzas, x, and number of slices, y, goes through the point (0, 0) and is a straight line."
The point (0, 0) means that if they buy 0 pizzas, they get 0 slices, which is true, so both relations contain this point.
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justify whether the solution makes sense.
a. Are the two triangles similar?
b. How do you know? Justify.
Answer:
They are identical triangles.
Step-by-step explanation:
Angles in a triangle add up to 180 degrees.
The triangle with 39 and 90 has a missing angle of 51 degrees, and the triangle with 51 and 90 vice versa.
✎ let's answer it
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
it's ↓
( identical triangle)
by #galadohannadivine29True or false: f(x) represents a function.
A. True
B. False
Answer:
A.) True
Step-by-step explanation:
A set of outputs and inputs becomes a function when there is only one output per input. In this case, each "x" value only has one "y" value, making it a function.
A triangular prism. The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet. The 2 triangular sides have a base of 2 feet and height of 1.5 feet.
Trenton is building a skateboarding ramp in the shape of a triangular prism. According to his plan, the ramp would have a base of 2 feet, a height of 1.5 feet, and a length of 3 feet. The riding surface would measure 2.5 feet.
If Trenton wants to cover all faces of the ramp with plywood, how much plywood will he need to buy?
Trenton will need
square feet of plywood.
The amount of plywood that he needs to buy will be 21 square feet.
What is the surface area of the triangular prism?Let the prism with a length of L of the rectangular surface.
And the dimension of the triangle is A, B, and C. Then we have
SA = 2(area of triangle) + 3(area of rectangle surface)
A triangular prism.
The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet.
The 2 triangular sides have a base of 2 feet and a height of 1.5 feet.
Then the area of the triangle will be
⇒ 1/2 x 2 x 1.5
⇒ 1.5 square feet
The area of the rectangles will be
⇒ 3 x 2 + 3 x 2.5 + 3 x 1.5
⇒ 18 square feet
Then the surface area of the triangular prism will be
Surface area = 2 x 1.5 + 18
Surface arae = 3 + 18
Surface area = 21 square feet
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which of the following is a statement of the triangle inequality theorem
Answer:
A
Step-by-step explanation:
Pick any two sides....their sum must be greater than the third side....
a+b > c
a+c > b
c + b > a
The following group of values was entered into the TVM solver on a graphing calculator
N=108; I%= 6.6 PV =; PMT=-620 FV =0; P/Y = 12; C/Y=12; PMT:END which of theses expressions with return the same value for PV
Based on the entries into the TVM solver, the expression that will return the same value for PV is [tex]\frac{(620) (( 1 + 0.066)^{108} - 1) }{(0.066) (1 + (0.066))^{108}}[/tex].
Which formula will give the same Present Value?The formula for present value for this series of cashflows is:
= [tex]\frac{(Payment) (( 1 + Interest rate)^{Number of years} - 1) }{(Periodic interest) (1 + (Periodic interest))^{Number of years}}[/tex]
Based on the P/Y and the C/Y being 12, the number of periods given in the graphing calculator will be the same in the formula, which is 108 periods.
The interest rate of 6.6% will also be the same in the formula.
The best option is therefore option B which has all these figures and so will give the same present value.
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Answer: 0.0055 and 108
aka ($620) ((1+0.0055)^108 -1 / (0.0055) (1+0.0055)^108
Step-by-step explanation: Just did it, Good luck! :)
In 9th grade Jade started a college fund with
$15,000 at a rate of 6.3% compounded bi-
annually. How much money will she have in 4
years?
Answer:
this is the answer I got hope it helps
Please help me this is very hard the first person to help me get's marked as brainly but i need the correct answer
Josh wants to pour 70.83 grams of salt into a container. So far, he has poured 39.1 grams. How much more salt should Josh pour?
Answer:
31.73 grams
Step-by-step explanation:
70.83 g - 39.1 g = 31.73 g
8 9/10 x 1 4/5 = ? please answer soon and thanks
Answer:
16 1/50
Step-by-step explanation:
First, turn the fractions into improper fractions.
8 9/10 can be 89/10 and 1 4/5 can be 9/5.
Then you multiply them together:
89/10 * 9/5= 801/50
Now, since 801/50 is 16.02 turn that into a mixed fraction. It becomes 16 1/50.
That's your answer.
Can you help me solve this equation I been trying to search a video explaining this but nothing and I gaved up studying for six days and now I am trying to get back to track anyways ... The equation is a linear equation : f(x)=-x-11 with the following
1.4f(-2)+5f(1)
2.-5f(12)-2f(-9)
3. 3f(5)x f(2)
4.f(9)/f(-6)
Answer:
4 I promise
jhjhhhhjjj bug check txt TC gym c rectify txt
Find the margin of error if p = 71% and n = 100. round to four decimal places.
0.2204
0.0041
0.0848
0.0908
Using the z-distribution, it is found that the margin of error for the 95% confidence interval is of 0.0889.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The estimate and the sample size are given as follows:
[tex]\pi = 0.71, n = 100[/tex]
Hence, the margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.71(0.29)}{100}}[/tex]
M = 0.0889.
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For a two-tailed test with a sample size of 20 and a. 20 level of significance, the t value is _____.
Using a t-distribution calculator, it is found that the critical value for the hypothesis test is of t = 1.3277.
How to find the critical value of the t-distribution?The critical value is found considering three inputs:
The tail.The significance level.The amount of degrees of freedom, which is one less than the sample size.Hence, for a two-tailed test, with a 0.2 significance level and 19 df, the critical value is of t = 1.3277.
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If f(x) = 3x² - 4 and g(x) = x+2, find (f - g)(x).
Answer:
for the x values: -2,-1,0,1,2
y-values: 13, 6, 5, 4, -3
Step-by-step explanation:
Please help!!! answer the following questions, thanks:)
(you don't need to draw the venn diagram, I just need the questions below answered)
Answer:
hope you can understand
What is the area of the parallelogram?
A parallelogram has a base of 3 feet and height of 2 and one-half feet.
7 and one-half feet squared
9 feet squared
10 and one-half feet squared
12 feet squared
Answer:
7 and one-half feet squared
Step-by-step explanation:
3 x 2.5 = 7.5
When a number is halfway between two multiples of one hundred, round to _____.
A. zero
B. the smaller multiple
C. the nearest fifty
D. the larger multiple
Answer:
D. The larger multiple
Step-by-step explanation:
n7nj7j
Write the equation for the graph of the line
shown.
My answer is y= 2x-1 but I’m not sure if it’s right
Answer: Hope this explains everything for you!
y= -2x+3
Step-by-step explanation:
y= 2x-1 is wrong
First, we will start by identifying the y-int, the y-int is when x is zero. The y-int is 3 since when x is 0, y is 3, (0,3).
y= 2x+3 (So that means -1 is actually 3)
Plus even if your slope is 2, since from the 2 points you go up 2 and run by 1, if you're not going to calculate it with 2 points, you need to see if its uphill, downhill, etc. (More info in the image below) The slope is actually negative meaning it is -2.
So the equation of the line is actually y= -2x+3