The equation for the translated function is:
g(x) = |x + 4|
How to find g(x)?
For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left.if N < 0, the translation is to the right.Here we have:
f(x) = |x|
And the translation is of 4 units to the left, so the translated function is:
g(x) = f(x + 4) = |x + 4|
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m(x)=-x^2+4x+21. prove the zeros and determine the extreme value algebraically
The zeros of the function are:
[tex]\begin{gathered} -(x+3)(x-7)=0 \\ x=-3 \\ or \\ x=7 \end{gathered}[/tex]The vertex is a point V(h,k) on the function. It's either at the base or the top of the function, depending upon wether it opens, upward or downward respectively.
For a function of the form:
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{The vertex(extreme value) is:} \\ h=\frac{-b}{2a} \\ k=y(h) \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} m(x)=-x^2+4x+21 \\ a=-1 \\ b=4 \\ c=21 \\ h=\frac{-4}{2(-1)}=\frac{-4}{-2}=2 \\ k=m(h)=-(2)^2+4(2)+21=-4+8+21=25 \end{gathered}[/tex]Hence, the extreme value is 25 at x = 2
That's it, do you have any question?
Benjamin & Associates, a real estate developer, recently built 185 condominiums in McCall,Idaho. The condos were either three-bedroom units or four-bedroom units. If the total numberof bedrooms in the entire complex is 657, how many three-bedroom units are there? How manyfour-bedroom units are there?
we have the following:
x = number of three bedroom
y = number of four bedroom
therefore,
[tex]\begin{gathered} x+y=185 \\ 3x+4y=657 \end{gathered}[/tex]A toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 32 feet
per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function
h(t)=1612 +32t+5. How long will it take the rocket to reach its maximum height? What is the maximum height?
Learn with an example v Sharon has a red ribbon and an indigo ribbon. The red ribbon is 6 1/4 inches long. The indigo ribbon is 6 1/4 inches longer than the red ribbon. How long is the indigo ribbon?
Let R be the length of the red ribon and let I be the length of the indigo ribbon. We have that the red ribbon is 6 1/4 inches long, then:
[tex]R=6\frac{1}{4}=\frac{25}{4}[/tex]Then, the indigo ribbon is 6 1/4 inches longer than the red ribbon. Then we have:
[tex]I=R+6\frac{1}{4}[/tex]therefore:
[tex]I=\frac{25}{4}+\frac{25}{4}=\frac{50}{4}=\frac{25}{2}=12\frac{1}{2}[/tex]finally, we have that the indigo ribbon is 12 1/2 inches long
O is the center of the regular hexagon below. Find its perimeter. Round to the nearest tenth if necessary.
To solve this problem, we have to find the side length and multiply it by the number of sides of the figure.
To find the length side we will use the following formula:
[tex]ap=\sqrt[]{I^2-(\frac{I^{}}{2})^2}\text{.}[/tex]Where ap is the length of the apothem, and I is the side length.
Substituting the given values, we get:
[tex]10=\sqrt[]{I^2-(\frac{I}{2})^2}.[/tex]Solving the equation for I, we get:
[tex]\begin{gathered} \\ I=\frac{2\times10}{\sqrt[]{3}}. \end{gathered}[/tex]Therefore, the perimeter of the hexagon is:
[tex]6I=6\times\frac{2\times10}{\sqrt[]{3}}\approx69.3\text{ units.}[/tex]Answer:
[tex]69.3\text{ units.}[/tex]= Homework: Module 17If r(x) =find r(a) and write the answer as one fraction.X-29r(a) =(Simplify your answer. Do not factor.)
As given by the question
There are given that function
[tex]r(x)=\frac{7}{x-2}[/tex]Now,
To find the value of r(a^2), put x = a^2 into the function
Then,
[tex]\begin{gathered} r(x)=\frac{7}{x-2} \\ r(a^2)=\frac{7}{a^2-2} \end{gathered}[/tex]Hence, the function is shown below:
[tex]r(a^2)=\frac{7}{a^2-2}[/tex]How far apart, in inches, would the same two cities be on a map that has a scale of 1 inch to 40 miles?
Using scales, the distance of the two cities on the map would be of:
distance on the map = actual distance/40
What is the scale of a map?A scale on the map represents the ratio between the actual length of a segment and the length of drawn segment, hence:
Scale = actual length/drawn length
In this problem, the scale is of 1 inch to 40 miles, meaning that:
Each inch drawn on the map represents 40 miles.
Then the distance of the two cities on the map, in inches, would be given as follows:
distance on the map = actual distance/40.
If the distance was of 200 miles, for example, the distance on the map would be of 5 inches.
The problem is incomplete, hence the answer was given in terms of the actual distance of the two cities. You just have to replace the actual distance into the equation to find the distance on the map.
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so I've been using the formula for the volume of a cylinder but I'm still not getting anything even remotely close to my answer choices. the volume is 438.08π mL and the radius is 3.7 cm. I'm solving for the height
Answer:
H = 32 cm
Explanation:
The area of a cylinder is given by
[tex]V=\pi r^2h[/tex]Now solving for h gives
[tex]h=\frac{V}{\pi r^2}[/tex]Now V = 438.08 π and r = 3.7 cm. Putting these values in the above equations gives
[tex]h=\frac{438.08\pi\operatorname{cm}^3}{\pi(3.7cm)^2}[/tex][tex]\boxed{h=32\operatorname{cm}\text{.}}[/tex]which is our answer!
Clark and Lindsay Banks have agreed to purchase a home for $225,000. They made a down payment of 15%. They have obtained a mortgage loan at a 6.5% annual interest rate for 25 years. What is the mortgage total if they finance the closing costs?
SOLUTION
We will be using the annual compound interest formula to solve this question.
[tex]\begin{gathered} A=P(1+\frac{R}{100})^{mn} \\ \text{where m=1, n=25years, R=6.5,} \end{gathered}[/tex]After a down payment of 0.15 x $225,000 = $33750
The principal value will be $225,000 - $33750 = $191250
Put all these values into the compound interest formula above,
we will have:
[tex]\begin{gathered} A=191250(1+\frac{6.5}{100})^{1\times25} \\ A=191250(1+0.065)^{25} \end{gathered}[/tex][tex]\begin{gathered} A=191250(1.065)^{25} \\ \text{ = 191250}\times4.8277 \\ \text{ =923,297.63} \end{gathered}[/tex]The mortgage total if they finance the closing costs will be:
$923,297.63
- 32 + 2Determine for each 2-value whether it is in the domain of f or not.In domainNot in domain203
f(x) = x-3 / x+2
To be in the domain, we have to avoid 0 on the bottom of the fraction.
So, the bottom of the fraction is x+2.
x=-2
(-2)+2= 0
-2 is not in the domain
x= 0
(0)+2= 2
0 is in the domain
x=2
(2)+2=4
Divide 8 1/8 by 7 1/12 simplify the answer and write as a mixed number
The division of 8 1/8 by 7 1/12 is 91/136.
What is division?Division simply has to do with reduction of a number into different parts. On the other hand, a mixed number is the number that's made up of whole number and fraction.
Dividing 8 1/8 by 7 1/12 will go thus:
8 1/8 ÷ 7 1/12
Change to improper fraction
65/8 ÷ 85/7
= 65/8 × 7/85
= 91/136
The division will give a value of 91/136.
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Parallelogram ABCD was transformed to form parallelogram A'B'C'D'.У.101864D2-10-8-616 8 10a245-6881-101Which rule describes the transformation that was used to form parallelogram A'B'C'D'?O (x + 10, y + 3)0 (-x, y-3)O (x - 10.y-3)(x + 10. y-3)
Explanation
Step 1
to find the transformation, count the units moved in each axis
for x, (red line)
for y( green line)
[tex]\begin{gathered} \text{for x}\Rightarrow horizontal\Rightarrow from\text{ 2 to -8=-8-(2)=-}10 \\ \text{for y }\Rightarrow vertical\text{ }\Rightarrow\text{from 5 to 2, =2-5=-3} \\ so,\text{ the transformation is} \\ (x-10,y-3) \end{gathered}[/tex]Prove the Question according to the theorem of a Circle
Given -
P,Q,R and S are 4 points on the circle and PQRS is a cyclic quadrilateral
Prove -
[tex]\angle PQR\text{ + }\angle PSR\text{ = 180}[/tex]Explanation -
[tex]\angle1\text{ = }\angle6\text{ ------\lparen1\rparen \lparen Angles in same segment\rparen}[/tex][tex]\angle5\text{ = }\angle8\text{ ------\lparen2\rparen \lparen Angles in the same segment\rparen}[/tex][tex]\angle2\text{ = }\angle8\text{ ------\lparen3\rparen \lparen Angles in the same segment\rparen}[/tex][tex]\angle7\text{ = }\angle3\text{ -------\lparen4\rparen\lparen Angles in the same segment\rparen}[/tex]By using angle sum property of quadrilateral
[tex]\angle P\text{ + }\angle Q\text{ + }\angle R\text{ + }\angle S\text{ = 360}[/tex][tex]\angle1\text{ + }\angle2\text{ + }\angle3\text{ + }\angle4\text{ + }\angle5\text{ + }\angle6\text{ + }\angle7\text{ + }\angle8\text{ = 360}[/tex][tex](\angle1+\angle2+\angle7+\angle8)+(\angle3+\angle4+\angle5+\angle6)=360[/tex]By using equation 1,2,3 and 4
[tex]2(\angle3+\angle4+\angle5+\angle6)\text{ = 360}[/tex][tex]\angle3+\angle4+\angle5+\angle6\text{ = 180}[/tex][tex](\angle3+\angle4)+(\angle5+\angle6)\text{ = 180}[/tex][tex]\angle PQR\text{ + }\angle PSR\text{ = 180}[/tex]Hence Proved
you get a student loan from the educational assistance Foundation to pay for your educational expenses as you earn your associate's degree you will be allowed 10 years to pay the loan back find the simple interest on the loan if you borrow $3,600 at 8 percent
Simple interest = PRT/100
where p = $3600
R=8
T=10
Substituting into the formula;
S.I = $3600 x 8 x 10 /100
=$36 x 8 x 10
=$2880
The average American man consumes 9.6 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. What is the distribution of X? X - NO b. Find the probability that this American man consumes between 9.7 and 10.6 grams of sodium per day. C. The middle 10% of American men consume between what two weights of sodium? Low: High:
The variable of interest is
X: sodium consumption of an American male.
a) This variable is known to be normally distributed and has a mean value of μ=9.6grams with a standard deviation of δ=0.8gr
Any normal distribution has a mean = μ and the variance is δ², symbolically:
X~N(μ ,δ²)
For this distribution, we have established that the mean is μ=9.6grams and the variance is the square of the standard deviation so that: δ² =(0.8gr)²=0.64gr²
Then the distribution for this variable can be symbolized as:
X~N(9.6,0.64)
b. You have to find the probability that one American man chosen at random consumes between 9.7 and 10.6gr of sodium per day, symbolically:
[tex]P(9.7\leq X\leq10.6)[/tex]The probabilities under the normal distribution are accumulated probabilities. To determine the probability inside this interval you have to subtract the accumulated probability until X≤9.7 from the probability accumulated probability until X≤10.6:
[tex]P(X\leq10.6)-P(x\leq9.7)[/tex]Now to determine these probabilities, we have to work under the standard normal distribution. This distribution is derived from the normal distribution. If you consider a random variable X with normal distribution, mean μ and variance δ², and you calculate the difference between the variable and ist means and divide the result by the standard deviation, the variable Z =(X-μ)/δ ~N(0;1) is determined.
The standard normal distribution is tabulated. Any value of any random variable X with normal distribution can be "converted" by subtracting the variable from its mean and dividing it by its standard deviation.
So to calculate each of the asked probabilities, you have to first, "transform" the value of the variable to a value of the standard normal distribution Z, then you use the standard normal tables to reach the corresponding probability.
[tex]P(X\leq10.6)=P(Z\leq\frac{10.6-9.6}{0.8})=P(Z\leq1.25)[/tex][tex]P(X\leq9.7)=P(Z\leq\frac{9.7-9.6}{0.8})P(Z\leq0.125)[/tex]So we have to find the probability between the Z-values 1.25 and 0.125
[tex]P(Z\leq1.25)-P(Z\leq0.125)[/tex]Using the table of the standard normal tables, or Z-tables, you can determine the accumulated probabilities:
[tex]P(Z\leq1.25)=0.894[/tex][tex]P(Z\leq0.125)=0.550[/tex]And calculate their difference as follows:
[tex]0.894-0.550=0.344[/tex]The probability that an American man selected at random consumes between 10.6 and 9.7 grams of sodium per day is 0.344
c. You have to determine the two sodium intake values between which the middle 10% of American men fall. If "a" and "b" represent the values we have to determine, between them you will find 10% of the distribution. The fact that is the middle 10% indicates that the distance between both values to the center of the distribution is equal, so 10% of the distribution will be between both values and the rest 90% will be equally distributed in two tails "outside" the interval [a;b]
Under the standard normal distribution, the probability accumulated until the first value "a" is 0.45, so that:
[tex]P(Z\leq a)=0.45[/tex]And the accumulated probability until "b" is 0.45+0.10=0.55, symbolically:
[tex]P(Z\leq b)=0.55[/tex]The next step is to determine the values under the standard normal distribution that accumulate 0.45 and 0.55 of probability. You have to use the Z-tables to determine both values:
The value that accumulates 0.45 of probability is Z=-0.126
To translate this value to its corresponding value of the variable of interest you have to use the standard normal formula:
[tex]a=\frac{X-\mu}{\sigma}[/tex]You have to write this expression for X
[tex]\begin{gathered} a\cdot\sigma=X-\mu \\ (a\cdot\sigma)+\mu=X \end{gathered}[/tex]Replace the expression with a=-0.126, μ=9.6gr, and δ=0.8gr
[tex]\begin{gathered} X=(a\cdot\sigma)+\mu \\ X=(-0.126\cdot0.8)+9.6 \\ X=-0.1008+9.6 \\ X=9.499 \\ X\approx9.5gr \end{gathered}[/tex]The value of Z that accumulates 0.55 of probability is 0.126, as before, you have to translate this Z-value into a value of the variable of interest, to do so you have to use the formula of the standard normal distribution and "reverse" the standardization to reach the corresponding value of x:
[tex]\begin{gathered} b=\frac{X-\mu}{\sigma} \\ b\cdot\sigma=X-\mu \\ (b\cdot\sigma)+\mu=X \end{gathered}[/tex]Replace the expression with b=0.126, μ=9.6gr, and δ=0.8gr and calculate the value of X:
[tex]\begin{gathered} X=(b\cdot\sigma)+\mu \\ X=(0.126\cdot0.8)+9.6 \\ X=0.1008+9.6 \\ X=9.7008 \\ X\approx9.7gr \end{gathered}[/tex]The values of sodium intake between which the middle 10% of American men fall are 9.5 and 9.7gr.
At a college basketball game, the ratio of the number of freshmen who attended to the number of juniors who attended is 3:4. The ratio of the number of juniors who attended to the number of seniors who attended is 7:6. What is the ratio of the number of freshmen to the number of seniors who attended the basketball game?
A) 7:8
B) 3:4
C) 2:3
D) 1:2
The ratio of the number of freshmen to the number of seniors who attended the basketball game is 7 : 8.
What is the ratio?Ratio is used to show the relationship between two or more numbers. Ratio provides information on the frequency of one value within other values. The sign that is used to represent ratio is :.
The ratio of freshmen to juniors is 3 : 4.
The ratio of juniors to seniors is 7 : 6.
In order to determine the required values, let us make some assumptions.
The number of freshmen is 21
The number of juniors is 28.
Given the two above assumption, the number of seniors = (28 x 6) / 7 = 24
The ratio of freshmen to seniors = number of freshmen : number of seniors
21 : 24
Express the ratio in its simplest form - 7 : 8.
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1) What is the surface area of this Cylinder: height of 9cm and a radius of 7cm. 1) Use 3.14 and round your a 9 cm
EXPLANATION
This is a cylinder with a height of 9 cm and a radius of 7cm.
The Area of a cylinder is given by the following expression:
Area= 2xπxr ² + 2xπxrxh
As r=7cm and h=9cm, replacing terms:
Area = 2xπx(7) ² + 2xπx7x9
Multiplying numbers:
Area = 98xπ + 126xπ
Simplifying:
Area= 224xπ
Representing π as a number:
Area= 224 x 3.14= 703.36 cm^2
Which representation does not show y as a function of x?1.II.€9> 10III.x 1 3 5 7y -6 -18 -30 -42IV. {(-2,3), (-1,4), (0,4), (3, 2)}a) I and IIb) I, II, and IIIc) I and IVd) All of the above are functions
We can say that I is not a function because inputs can only have one output.
II it's not a function since if you draw an horizontal line through the function intersect in two points, then it's not a function.
The answer is A.
Write an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x|.
h(x)=?
an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x| is y = |x|/4
What is vertical stretch/vertical compression ?
• A vertical stretch is derived if the constant is greater than one while the vertical compression is derived if the constant is between 0 and 1.
• Vertical stretch means that the function is taller as a result of it being stretched while vertical compress is shorter due to it being compressed and is therefore the most appropriate answer.
The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.
The function g(x) is defined as |x|.
To vertically shrink the graph of g(x) by a factor of 1/4, divide the function by 4.
g(x) = f(x)/3
f(x) is equal to (|x|)/4.
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determin wether true or false. (2 points) True False The functions f(x) = x – 5 and g(x) = -3x + 15 intersect at x = 5. The functions f (x) = 3 and g(x) = 11 – 2. intersect at x = 3. O The functions f (x) = x + 3 and g(x) = -x + 7 intersect at x = 2. The functions f (x) = {x – 3 and g(x) = -2x + 2 intersect at x = -2.
To find the intersection point between f(x) and g(x) we will equate their right sides
[tex]\begin{gathered} f(x)=x-5 \\ g(x)=-3x+15 \end{gathered}[/tex]Equate x - 5 by -3x + 15 to find x
[tex]x-5=-3x+15[/tex]add 3x to both sides
[tex]\begin{gathered} x+3x-5=-3x+3x+15 \\ 4x-5=15 \end{gathered}[/tex]Add 5 to both sides
[tex]\begin{gathered} 4x-5+5=15+5 \\ 4x=20 \end{gathered}[/tex]Divide both sides by 4 to get x
[tex]\begin{gathered} \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Then the first one is TRUE
For the 2nd one
f(x) = 3, and g(x) = 11 - 2x
If x = 3, then substitute x by 3 in g(x)
[tex]\begin{gathered} g(3)=11-2(3) \\ g(3)=11-6 \\ g(3)=5 \end{gathered}[/tex]Since f(3) = 3 because it is a constant function and g(x) = 5 at x = 3
That means they do not intersect at x = 3 because f(3), not equal g(3)
[tex]f(3)\ne g(3)[/tex]Then the second one is FALSE
For the third one
f(x) = x + 3
at x = 2
[tex]\begin{gathered} f(2)=2+3 \\ f(2)=5 \end{gathered}[/tex]g(x) = -x + 7
at x = 2
[tex]\begin{gathered} g(2)=-2+7 \\ g(2)=5 \end{gathered}[/tex]Since f(2) = g(2), then
f(x) intersects g(x) at x = 2
The third one is TRUE
For the fourth one
[tex]f(x)=\frac{1}{2}x-3[/tex]At x = -2
[tex]\begin{gathered} f(-2)=\frac{1}{2}(-2)-3 \\ f(-2)=-1-3 \\ f(-2)=-4 \end{gathered}[/tex]g(x) = -2x + 2
At x = -2
[tex]\begin{gathered} g(-2)=-2(-2)+2 \\ g(-2)=4+2 \\ g(-2)=6 \end{gathered}[/tex]Hence f(-2) do not equal g(-2), then
[tex]f(-2)\ne g(-2)[/tex]f(x) does not intersect g(x) at x = -2
The fourth one is FALSE
Use dimensional analysis to determine which rate is greater. The pitcher for the Robins throws a baseball at 90.0 miles per hour. The pitcher on the Bluebirds throws a baseball 125.4 feet per second. Which pitcher throws a baseball faster? Complete the explanation:When I convert the Bluebirds pitcher's speed to the same units as the Robins pitcher's speed the speed is __ mi/h. Since the Bluebirds pitcher's speed is ____ the Robins pitcher's speed, the pitcher on the ____ throws a faster ball.
ANSWER and EXPLANATION
We want to solve the problem by using dimensional analysis.
To do this, let us convert the speed of the Bluebirds baseball to miles per hour.
We have that:
1 feet per second = 0.6818 miles per hour
125.4 feet per second = 85.50 miles per hour
As we can see the baseball of the Bluebirds is slower than the Robins (90 miles per hour)
Now, to complete the explanation:
When I convert the Bluebirds pitcher's speed to the same units as the Robins pitcher's speed, the speed is _85.50_ mi/h.
Since the Bluebirds pitcher's speed is _less than_ the Robins pitcher's speed, the pitcher on the __Robins_ throws a faster ball.
simplest form , 7/6 ÷ 4
[tex]\text{ }\frac{7}{6}\text{ / 4 = }\frac{\frac{7}{6}}{\frac{4}{1}}\text{ = }\frac{7}{24}[/tex]
The answer is 7/24
Which of the following IS a function?
Answer:
The ans C hope it helps u
have a good day
Which statement best reflects the solution(s) of the equation? X/ x-1 - 1/ x-2 = 2x-5/x^2-3x+2 There is only one solution: x=4. The solution x=1 is an extraneous solution. There are two solutions: x=2 and x=3. There is only one solution: x=3. The solution x=2 is an extraneous solution. There is only one solution: x=3. The solution x=1 is an extraneous solution.
The best reflects solution of the equation is, There is only one solution: x = 3. The solution x = 2 is an extraneous solution.
What is extraneous solution?
An extraneous solution is a root of a converted equation that is not a root of the original equation because it was left out of the original equation's domain is referred to as a superfluous solution.
We are given the following equation,
(x / x - 1) - (1 / x - 2) = (2x - 5)/(x^2 - 3x + 2)
Solving the given equation we have,
(x^2 - 3x + 1) / (x^2 - 3x + 2) = (2x - 5) / (x^2 - 3x + 2)
x^2 - 3x + 1 = 2x - 5
x^2 - 5x + 6 = 0
x^2 - 3x - 2x + 6 = 0
x(x - 3) - 2(x - 3) = 0
(x - 3)(x - 2) = 0
(x - 3) = 0, (x - 2) = 0
x = 3, x = 2
At x = 2 the denominator of the equation will be 0. So solution of the equation is not valid at x = 2.
Therefore, x = 3 is the only one solution. The solution x = 2 is an extraneous solution.
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2.) Part A: complete the following table for the functions
Complete the following table for the functions:
[tex]\begin{gathered} f(x)=x^2+1 \\ g(x)=f(x-5) \\ h(x)=f(x+3) \end{gathered}[/tex]The below function represents the transformation of the independent variables:
[tex]\begin{gathered} f(x)=x^2+1 \\ g(x)=f(x-5)\ldots\ldots\text{.f(x) will decrease by 5 units} \\ h(x)=f(x+3)\ldots\ldots.f(x)\text{ will increase by 3 units} \end{gathered}[/tex]need help with excerise step by step been 20 year's
Given:
Standard deviation
[tex]\sigma=5.18[/tex]Mean
[tex]\mu=129[/tex]Required:
Find the longest braking distance one of these cars could have and still in the bottom.
Explanation:
The z-score formula is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the given values and find the value of z.
[tex]z=\frac{x-129}{5.18}[/tex]This is the first percentile which is X when Z has a p-value of 0.01, so z = -2.327.
[tex]\begin{gathered} -2.327=\frac{x-129}{5.18} \\ x-129=-2.327(5.18) \\ x-129=-12.054 \\ x=129+12.054 \\ x=116.946\text{ ft} \end{gathered}[/tex]Final answer:
The longest braking distance one of these cars could have and still in the bottom 1% is 116.946 ft.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
√70 = 8.3 is between 8 and 9
-√5 = -2.2 is between -3 and -2
√81 = 9 (exactly 9)
-2√4 = -2 × 2 = -4 (exactly -4)
4√8 = 8√2 = 11.3 is between 11 and 12
Find (fog)(x) and (gof)(-1) for the functions f(x) = 3x² + 5 and g(x) = -x + 1
Answer:
Step-by-step explanation:
fog(x)=3(-x+1)^2+5
=3(x^2+2x+1)+5
=3x^2+6x+3+5
fog(x) =3x^2+6x+8
gof(x)=-(3x^2+5)+1
=-3x^2-5+1
gof(x)=-3x^2-4
gof(-1)=-3(-1)^2-4
=-3-4
gof(-1) =-7
3.615 x 4 regrouping
In a student council election there are 2 people running for treasure 3 people running for secretary 4 running for vice president and 2 people running for class president How many possible outcomes are there?
Given:
There are given that the 2 people running for treasure, 3 people running for secretary, 4 running for vice president, and 2 people running for class president.
Explanation:
According to the concept of outcomes:
The outcomes are defined for the possible results of an experiment.
Then,
In the given question, the outcomes are:
[tex]\text{Outcomes}=2+3+4+2=11[/tex]Final answer:
Hence, the total number of outcomes is 11.
