The solutions to the equation 4(x² − 5) − 1 = 3 are ±√6
How to determine the solutions to the equation?From the question, we have the following parameters that can be used in our computation:
4(x 2−5)−1=3
Express properly
This gives
4(x² − 5) − 1 = 3
Subtract -1 from both sides of the equation
So, we have the following representation
4(x² − 5) = 4
Divide both sides by 4
This gives
x² − 5 = 1
Subtract -5 from both sides of the equation
So, we have the following representation
x² = 6
Take the square root of both sides
x = ±√6
Hence, the solution is ±√6
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Odin is recording the depreciation of his car. The table displays the number of years and the car's depreciated value for each year.
What will be the value of his car in year 10?
PLEASE GIVE ME THE ANSWER!!
Answer:
$1,158.08
Step-by-step explanation:
The value of the car in year 10 is $1158.08
How to determine the car value in year 10?From the table, we have the following points
(x, y) = (1,5000) and (2,4250)
Start by calculating the rate of depreciation using:
r = y2/y1
So, we have:
r = 4250/5000
Evaluate
r = 0.85
The value of the car in nth year is calculated using:
y = y1 * r^(n - 1)
For the 10th year, we have:
y = 5000 * 0.85^(10 - 1)
Evaluate the product
y = 1158.08
Hence, the value of the car in year 10 is $1158.08
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Could someone help answer this? Thanks!
The limit of a function y=f(x) at x=a is sometimes best understood as the approximate height of the function around x=a based on the values around x=a whereas the value of the function f at x=a is the exact height of the function at that point. Consider two functions 1) f(x)=x+1 and g(x)=(x^2-1)/(x-1). Answer the following questions. (a) Discuss the process of finding the limit x->1 f(x). (b) How does it differ from f(1)?
a) The process to find the limit is given as follows:
f(x): simply replace x by 1.g(x): factor and then replacing.b) When a function does not have any discontinuity at x = 1, the procedure is the same as calculating f(1), however in the case of a discontinuity, such as for f(x), the discontinuity first has to be removed, if possible.
How to calculate the limit of a function?The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.
Hence:
lim x -> 1 f(x) = 1 + 1 = 2.lim x -> 1 g(x) = (1² - 1)/(1 - 1) = 0/0.For the case of g(x), there is a discontinuity, meaning that the function has to be factored to remove the discontinuity.
Applying the subtraction of perfect squares, we have that:
x² - 1 = (x - 1)(x + 1).
Then:
g(x) = (x - 1)(x + 1)/(x - 1) = x + 1.
Meaning that the limit is then calculated as follows:
lim x -> 1 g(x) = lim x->1 x + 1 = 1 + 1 = 2.
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Pls pls help I’ll mark u brainliesttt
Answer:
89.44
Step-by-step explanation:
[tex]120^2-80^2=8000[/tex]
[tex]\sqrt{8000} = 89.44[/tex]
80 POINTS This is a picture of Joseph Stalin, Franklin Roosevelt, and Winston Churchill at the Tehran Conference in 1943. They were the leaders of the Soviet Union, the United States, and the United Kingdom. During World War II, these men were known as the "Big Three" because they led
A.
the most powerful of the Allied countries.
B.
countries that had declared war on each other.
C.
the countries that suffered the most casualties in the war.
D.
the only countries fighting against Nazi Germany.
Option A. They led the most powerful of the Allied countries.
find each angle measure to the nearest degree
4) Find m.
10 cm
15 cm
'R
will mark brainliest if correct
Answer: QP=11.18cm;
QP=11.18cm;
m<Q=42;m<R=48*
Step-by-step explanation:
Hope this helps and the 48 degree
tell me all the questions of this
Answer:
To find the radius..just divide them by two
For the diameter multiply by two
Circumference formula is
[tex]2\pi \: r[/tex]
Find the measure of KM in the circle.
Answer:
KM = 180° - 133° = 47°
KM = 47°
A student believes that the average grade on the statistics final examination was 87. A sample of 36 final examinations was taken. The average grade in the sample was 83.96 with a standard deviation of 12. The student wants to test whether the average is different from 87 at 90% level of confidence. Compute the p-value for this test.
Answer:
The p-value for this test is 0.1375.
Step-by-step explanation:
A student believes that the average grade on the statistics final examination was 87. The student wants to test whether the average is different from 87 at 90% level of confidence.
At the null hypothesis, we test if the average is 87, that is:
[tex]H_0: \mu = 87[/tex]
At the alternate hypothesis, we test if the average is different from 87, that is:
[tex]H_a: \mu \neq 87[/tex]
The test statistic is:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]s[/tex] is the standard deviation of the sample and n is the size of the sample.
87 is tested at the null hypothesis:
This means that [tex]\mu = 87[/tex]
The average grade in the sample was 83.96 with a standard deviation of 12. Sample of 36
This means that [tex]X = 83.96, s = 12, n = 36[/tex]
Value of the test-statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{83.96 - 87}{\frac{12}{\sqrt{36}}}[/tex]
[tex]t = -1.52[/tex]
Pvalue:
Probability of the sample mean differing of 87, which means that we have a two-tailed test, with t = -1.52 and 36 - 1 = 35 degrees of freedom.
With the help of a calculator, the pvalue is of 0.1375.
The p-value for this test is 0.1375.
What is the total area of the figure?
Plz help its my last grade
Answer:
D
Step-by-step explanation:
i think i do am not si sure
Answer:
A, the first option
Step-by-step explanation:
1. Add 15 to both sides to cancel out the 15 from the left. (5x < -50)
2. Divide both sides by 5 to cancel out the 5 from the left. ( x < -10)
This inequality does not include the -10 because it's less than -10 not less than or equal to. So, the point at -10 should not be filled in.
x has to be LESS than, so the graph should include numbers that are less than -10 which leads us to our answer, A.
The function graphed above is:
Increasing on the interval(s)
Х
Decreasing on the interval(s)
Х
Step-by-step explanation:
When the slope of the function is positive, it is increasing
when the slope of the function is negative, it is decreasing
just like with the line function y = mx + b
so if you put a line tangent to the function at every point the slope of the line will indicate a increasing or decreasing point of the function
also beware where the slope is zero it is not increasing or decreasing
there are two intervals of increasing, one interval of decreasing and two point of zero slope or neither increasing or decreasing
increasing interval 1) x < -2 2) x > 1.5
decreasing interval 1) -2 < x < 1.5
at -2 and 1.5 the slope is zero
If the slope of a function is positive at all the points of the curve in a interval, function will be increasing.
f'(x) > 0
If the slope of a function is negative at all the points of the curve in a interval,
function will be decreasing.
f'(x) < 0
As we can see from the graph slope of the curve is positive in the intervals (-∞, -2) and (1.5, ∞) and decreasing in the interval (-2, 1.5).
Therefore, function is increasing in the intervals → (-∞, -2) and (1.5, ∞).
And the function is decreasing in the interval → (-2, 1.5)
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Juan has 40 pieces of paper and it has seven times as many pieces of paper as Juan
Answer:
280
Step-by-step explanation:
I need help in this with explanation
Step-by-step explanation:
The figure is made up of an 8x8 square and 4 identical triangles with 8-ft bases and 4 ft in height. Each triangle has an area = (1/2)bh = (1/2)(8)(4) = 16 ft^2. The square part has an area of 8x8 = 64 ft^2. Therefore, the total area of the figure is
A = (area of square) + 4×(area of triangle)
= 64 ft^2 + 4(16ft^2)
= 128 sq ft
You are walking near a river. While standing at A, you measure an angle of 90° between B and C, as shown. You then walk to B and measure
an angle of 61° between A and C. The distance between A and B is about 1 mile. How wide (in miles) is the river between A and C? Round your
answer to the nearest tenth.
61
B Im
A
The width is about
miles.
Answer:
3.6
Step-by-step explanation:
tan61=x/2
2(tan61)=x
3.6=x
The water depth in a harbor rises and falls over time. The function f(t) = 4.1 sine (StartFraction pi Over 6 EndFraction t minus StartFraction pi over 3 EndFraction) + 19.7 models the water depth, in feet, after t hours.
During the first 24 hours, at what times does the water depth reach a maximum?
Answer:
Below
Step-by-step explanation:
f(t) = 4.1 (sin pi/6 t - pi/3) + 19.7 <===will be a maximum when the sin portion is equal to 1
so sin ( pi/6 t - pi/3) = 1 given that sin is equal to one at 0 and pi and 2 pi and 3 pi and 4 pi etc
pi/6 t - pi/3 = 0 or pi , 2 pi, 3 pi , 4 pi
then t = 2 and 8 and 14 and 20 hrs ( every 6 hrs starting with t = 2)
A study conducted on 40,000 words in the English language found that about 6,670 words started with the letter T, which Is the most common
letter to start a word. If we randomly pick of 20 unique words, which of these lists of words will come closest to the theoretical probability of getting
a word beginning with T?
Answer:
To answer this problem, first let us calculate for the theoretical probability obtained from the study conducted:
Theoretical Probability = 6,670 / 40,000
Theoretical Probability = 0.16675 = 0.17
From the given choices, the list of words which can give this similar amount of probability is:
“to, sarcastic, epithet, for, less, corruptible, than, the, offspring, open, any, primary, loyalty, table, out, whom, example, who, mention, say”
In this set of words, the number of words starting with letter T is 4. Calculating for the probability of getting a word starting with T in this set is:
Sample probability = 4 / 20
Sample probability = 0.20
Step-by-step explanation:
B) If one gallon of paint covers 0.5 square meters, how many gallons of black paint wil they
need to paint the house?
Show your work
1
Answer:
depends on the size of the house
let's say the house is 10 square meter then you would need 5 gallons
let's the house is 60 square meter then you would need 30 gallons
Step-by-step explanation:
whatever the square meter just divide it with 2 and that should be your answer
Which graph represents a function?
Answer:
The fourth graph since it passes the vertical line test.
Each input has one output.
Hope this helps :)
I WILL GIVE U BRAINLIEST AND THANKS AND 5 STARS
-------------------------------------------------------------------------------------
please help this is very important
Answer:
a, d, f
Step-by-step explanation:
3 - 3= 0
6 = 2(3)
3^2 = 9
Answer and Step-by-step explanation:
To find all equations where x = 3 is a solution, solve all equations for x and see if it is equal to 3.
A. x - 3 = 0
x = 3
B. 1 + x = 2
x = 1
C. 9 - x = 3
x = 6
D. 6 = 2x
x = 3
E. [tex]\frac{1}{5} x = 3[/tex]
x = 15
F. [tex]x^2 = 9[/tex]
x = 3
A, D, and F are the answers.
#teamtrees #PAW (Plant And Water)
the square root of 11.737476 has ____ decimal place
Answer:
3 decimal places
Step-by-step explanation:
square root of 11.737476 is 3.426
Answer:
3•426
having 3 decimal places
y = x2 - 6x-16
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answer:
it's C
Step-by-step explanation:
-16 means where the line crosses y axis
I need this please quick
No links
16 points!
Solve each equation for both variables help please 15 points
Answer:
x = 12 and y = 11
Step-by-step explanation:
4x+3y=-15 -----equation 1st
4x-y = -27 ____equation 2nd
then,
Multiple equation second by 3 and slove it with equation first
4X +3Y = -15
12X -3Y = -81 (Multiples it with 3)
-8x = -96 (subtracted)
x=-96/-8
therefore, x=12
again,
from equation first
4x+3y = -15
or 4 × 12 + 3y = -15
or 3y = -15+48
or 3y= 33
or y=33/3
therefore, y =11
I hope this helps. If you have any doubt feel free to ask!!
Answer:
x = -6, y = 3
Step-by-step explanation:
1) 4x + 3y = -15
2) 4x - y = -27
0 + 4y = 12 subtract equation (2) from equation (1)
4y = 12
y = 12/4 = 3 substitute y = 3 into either equation 1 or 2 and solve for x
4x + 3(3) = -15
4x = -24
x = -6
Check your answers by plugging x = -6, y = 3 into the equations:
4(-6) + 3(3) = -15 correct!
4(-6) - 3 = -27 correct!
What is the measure of c?
Answer:
45 degrees
Step-by-step explanation:
PLEASE HURRY I WILL GIVE BRAINLY PLEASE HURRY
In triangle LMN, m∠L = (4c + 53)°. If the exterior angle to ∠L measures 87°, determine the value of c.
c = 87
c = 8.5
c = 35
c = 10
Answer:c=35
Step-by-step explanation:
i just did this
find a number such that 30% of it is 1260
well, that number is "x", which oddly enough is the 100%, now, we also know that 30% of that is 1260, so hmmmm
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 1260& 30 \end{array} \implies \cfrac{x}{1260}~~=~~\cfrac{100}{30} \\\\\\ \cfrac{ x }{ 1260 } ~~=~~ \cfrac{ 10 }{ 3 }\implies 3x=12600\implies x=\cfrac{12600}{3}\implies x=4200[/tex]
find the area of the polygon.
Answer:
174 ft²
Step-by-step explanation:
The polygon cam be decomposed into two rectangles.
The area of the polygon = rectangle A + rectangle B
Area of rectangle A = L* W
L = 18 ft
W = 9 ft
Area of rectangle A = 18*9 = 162 ft²
Area of rectangle B = L* W
L = 20 - 18 = 2 ft
W = 6 ft
Area of rectangle A = 2*6 = 12 ft²
✔️Area of the polygon = 162 + 12 = 174 ft²
To the nearest tenth, find the volume of a sphere with a radius of 4.8 cm. Use 3.14 for π.
Answer:
463 rounded
Step-by-step explanation:
4/3 times pi times r times r times r.
4.8 x 4.8 x 4.8 = 110.592 x 3.14 x 4/3 = 463
Volume of sphere is 463.01 [tex]cm^{3}[/tex].
What is the volume of sphere?The volume of sphere is the measure of space that can be occupied by a sphere. If we draw a circle on a sheet of paper, take a circular disc, paste a string along its diameter and rotate it along the string. This gives us the shape of a sphere.
Volume of sphere = [tex]\frac{4}{3}\pi r^{3}[/tex]
Given
Radius of sphere r = 4.8 cm
Volume of sphere
V = [tex]\frac{4}{3}\pi r^{3}[/tex]
V = [tex]\frac{4}{3} \pi (4.8)^{3}[/tex]
V = 463.01 [tex]cm^{3}[/tex]
Volume of sphere is 463.01 [tex]cm^{3}[/tex].
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Find the area of the trapezoid
Answer:
20 is the answer
Step-by-step explanation:
I did the math.hope it helps :)
Card 7 * Caleb can ride his bike 30 miles in 2 hours. At this rate, how long will it take him to ride 75 miles?
Answer:
5 Hours
Step-by-step explanation:
2 : 30 = 1 : 15
75 ÷ 15 = 5
Answer:
5 hours
Step-by-step explanation:
30/2 = 15 miles per hour
75/15 = 5 hours