The form of linear equation that describes line is:
[tex]y=sx+n[/tex]
First we must calculate the slope.
[tex]s=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}[/tex]
Now it looks a bit more like this:
[tex]y=\dfrac{5}{2}x+n[/tex]
All we need now is to put in y and x from one point doesn't matter which. I'll pick A.
The equation now looks like this:
[tex]-3=\dfrac{5}{2}\cdot2+n[/tex]
Solve for n.
[tex]
-3=5+n \\
n=-8
[/tex]
And finally write the equation.
[tex]f(x)=\dfrac{5}{2}x-8[/tex]
Hope this helps.
r3t40
HELP SOS IMMEDIATELY THANK YOUUUUU!!!!
Answer: b) 18.37
Step-by-step explanation:
Since the intial t-value is 1960 and the final t-value is 1990, then t = 30
[tex]P(30)=\dfrac{100}{1+400\cdot e^{-0.15(30)}}\\\\\\.\quad =\dfrac{100}{1+400\cdot e^{-4.5}}\\\\\\.\quad =\dfrac{100}{1+400(0.0111)}}\\\\\\.\quad =\dfrac{100}{1+4.4436}}\\\\\\.\quad =\dfrac{100}{5.4436}}\\\\\\.\quad =\boxed{18.37}[/tex]
Starting at home, Emily traveled uphill to the hardware store for 606060 minutes at just 666 mph. She then traveled back home along the same path downhill at a speed of 121212 mph.
What is her average speed for the entire trip from home to the hardware store and back?
Answer:
about 1325 mph
Step-by-step explanation:
average speed = total distance / total time= (distance uphill + distance downhill) / (time uphill + time downhill)
time uphill = 606060 minutes / 60 = 10101 hours
path = 666 mph * 10101 hours = 6727266 m
time downhill = 6727266 m / 10101 hours = 55.5 h
average speed = (6727266 m + 6727266 m) / (10101 hours + 55.5 h) = about 1325 mph
Answer:
8
Step-by-step explanation:
which term best describes the set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant?
Answer:
ellipse
Step-by-step explanation:
Yea that's pretty much the definition of an ellipse. The points in this case would be the "foci"
The term that best describes the set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant is an ellipse. This can be obtained by understanding what an ellipse is.
What is an Ellipse?A set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant.
Equation of an ellipse, [tex](\frac{x}{a})^{2} +(\frac{y}{b})^{2}=1[/tex] Two focal points Major axis = 2a, Minor axis = 2b Distance between foci= 2c a²=b²+c² d₁ and d₂ be distances from any point to foci, then d₁+d₂= constantHence the term that best describes the set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant is an ellipse.
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Can somebody pls answer this ASAP plsssssssssssssssssssssssssss
Answer: D
Dependent variable is Distance.
Answer:
The answer is Distance
hence option d is correct
PLEASE HELP 12 POINTS
Answer:
Step-by-step explanation:
She has a total of 3 + 3 + 2 choices which is 8
She chooses the first one that has 3 members in it.
3/8 is the probability of that fact.
She chooses the second one from a group that also has 3 members only now there are only 7 choices total. That fact is
3/7
So your total probability is
3/8 * 3/7 = 9/56
Those two numbers are prime to one another.
Please help me with this !
Answer:
-8 is the solution
Step-by-step explanation:
[tex]-32\frac{3}{5}=-8[/tex]
[tex]((-32)^{\frac{1}{5}})^{3}\\\\-2^{3}=-8[/tex]
For this case we must simplify the following expression:
[tex]-32 ^ {\frac {3} {5}}[/tex]
We can rewrite the 32 as [tex]2 ^ 5 = 2 * 2 * 2 * 2 * 2[/tex]
So:
[tex]- (2 ^ 5) ^ {\frac {3} {5}}[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So:
[tex]- (2 ^ 5) ^ {\frac {3} {5}} = - 2 ^ {\frac {15} {5}} = - 2 ^ 3 = -2 * -2 * -2 = -8[/tex]
Answer:
-8
Which of the following is the result of expanding the series
12
22
6x + 8
6x + 12
For this case we evaluate the series for each value of "n" from 0 to 3:
So:
[tex](0x + 2) + (1x + 2) + (2x + 2) + (3x + 2) =\\(0 + 2) + (x + 2) + (2x + 2) + (3x + 2) =\\2 + x + 2 + 2x + 2 + 3x + 2 =[/tex]
We add similar terms and we have the result of expanding the series is:
[tex]8 + 6x[/tex]
ANswer:
Option C
[tex]6x + 8[/tex]
Answer: Third option.
Step-by-step explanation:
Given [tex]3\\\sum(nx+2)\\n=0[/tex], We know that indicates that we need to start with [tex]n=0[/tex] and finish with [tex]n=3[/tex],
In order to expand the series, the procedure is the following:
[tex]3\\\sum(nx+2)=(0x+2)+(1x+2)+(2x+2)+(3x+2)\\n=0\\\\3\\\sum(nx+2)=2+x+2+2x+2+3x+2\\n=0\\\\3\\\sum(nx+2)=6x+8\\n=0[/tex]
This result matches with the third option.
What is the quotient (2x^4-3x^3-3x^2+7x-3) divided by (x^2-2x+1)
Answer:
You can find the quotient of the expression in the images below, together with more information and a full analysis
(2x^4-3x^3-3x^2+7x-3)/(x^2-2x+1)
Answer:
The quotient is: 2x^2+x-3
Step-by-step explanation:
we need to divide (2x^4-3x^3-3x^2+7x-3) by (x^2-2x+1)
The division is attached in the figure below.
The quotient is: 2x^2+x-3
The remainder is: 0
What is the domain of the function shown below? f(x)=-24/x^2+8
Answer:
D
Step-by-step explanation:
d/dx(8 - 24/x^2) = 48/x^3
Open code
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Indefinite integral assuming all variables are real:
integral(-24/x^2 + 8) dx = 8 x + 24/x + constant
Open code
Limit:
lim_(x-> ± ∞) (8 - 24/x^2) = 8
Please mark brainliest and have a great day!
Answer:
D, All real numbers
Step-by-step explanation:
How do I round 13,870 to the nearest ten-thousand.
Answer: 10,000
Step-by-step explanation:
If you round to the nearest ten thousand, you round the number that makes it ten thousand in the first place.
Answer: From the right, you count 1 number, 0, then 2 numbers, 7, then 3 numbers, 8, then 4 numbers, and you get rid of those to make it 10,000.
Step-by-step explanation: Because 3, next to the 1 there rounds down, it makes 3,870 be rounded down overall.
What property is used in the second step of solving the inequality below?
5x-9<91
5x<100
x<20
Answer:
The Multiplication property
Step-by-step explanation:
The Multiplication property by a constant was used
For real numbers a and b, and c different from zero:
If c is positive and [tex]a <b[/tex] then [tex]a*\frac{1}{c} <b*\frac{1}{c}[/tex].
If c is negative and [tex]a <b[/tex] then [tex]a*\frac{1}{c} >b*\frac{1}{c}[/tex].
In this case we have
[tex]5x<100[/tex] Then [tex]\frac{5}{5}x<\frac{100}{5}[/tex]
Finally
[tex]x<20[/tex]
Solve for y in terms of x: 3y-2x=7 Show work!
Answer:
y = (2/3)x + 7/3
Step-by-step explanation:
First we want to isolate 3y on the left side. To accomplish this, add 2x to both sides. The result will be 3y = 2x + 7.
Next we divide all three terms by 3 to complete the isolation of y on the left side:
y = (2/3)x + 7/3
Answer:
y = ⅓(2x + 7)
Step-by-step explanation:
3y - 2x = 7
3y = 2x + 7
y = ⅓(2x + 7)
What is the factor form of x^2-9x+14
[tex]x^2-9x+14 =x^2-2x-7x+14=x(x-2)-7(x-2)=(x-7)(x-2)[/tex]
Answer:
(x - 7)(x - 2)
Step-by-step explanation:
Consider the factors of the constant term (+ 14) which sum to give the coefficient of the x- term (- 9)
The factors are - 7 and - 2, since
- 7 × - 2 = + 14 and - 7 - 2 = - 9, hence
x² - 9x + 14 = (x - 7)(x - 2) ← in factored form
At school there are 526 students and 263 are girls about how likely is it that a randomly chosen student will be a boy
Answer: 50% chance that a randomly chosen student will be a boy
Answer:
Step-by-step explanation
total number of student= 526
total number of girl= 263
total number of boy= 526 - 263 = 263
Probability that chosen student will be boy = number of favorable items/ total number of possible outcome= 263/526 = 1/2
The surface area of this rectangular prism is 1,414 square meters. What is the volume?
Answer:
2940
Step-by-step explanation:
Surface Area of a rectangular prism is 2(LW)+2(HW)+2(LH)
We have that the surface area is 1414 where L=c , H=20, W=7
Let's plug all of this in to solve for c:
2(LW)+2(HW)+2(LH)=1414
2(c*7)+2(20*7)+2(c*20)=1414
14c+280+40c=1414
54c+280=1414
54c=1414-280
54c=1134
c=1134/54
c=21
Now the volume of a rectangular prism is V=L*W*H
So plug in our values L=21, H=20, W=7
V=21*20*7=2940
Two cars leave Phoenix and travel along roads 90 degrees apart. If Car 1 leaves 60 minutes earlier than Car 2 and averages 40 mph and if Car 2 averages 50 mph, how far apart will they be after Car 1 has traveled 3.5 hours?
Answer:
The two cars will be almost 188 miles far from each other.
Step-by-step explanation:
Travel Time for Car 1 = t = 3.5 hours
Travel time for Car 2 = t-1 = 3.5 - 1 = 2.5 hours
Average speed of car 1 = 40 mph
Average speed of car 2 = 50 mph
Distance traveled by Car 1 = 40*3.5 = 140 miles
Distance Traveled by Car 2 = 50*2.5 = 125 miles
As both the roads are at a 90 degree angle. The path of the two cars and the joining line of their final position forms a right angle triangle where:
altitude = a = 140
base = b = 125
Distance of cars after 3.5 hours = c = ?
According to Pythagoras theorem:
c^2 = a^2 + b^2
c^2 = 140² + 125²
c² = 19600+15625
c = √35225
c = 187.68
Almost 188 miles.
Which of the following is the expansion of (2x – y) 2?
Answer:
4x² - 4xy + y²
Step-by-step explanation:
For clarity it is essential that you use (2x - y)^2 or (2x – y)² to indicate the square of (2x - y).
Since we're squaring (2x - y), we expect 3 terms in the expansion.
(2x - y)(2x - y) = 4x^2 - 4xy + y^2, or 4x² - 4xy + y²
Next time you see "the following," please share the answer choices. Thank you.
The revenue each season from tickets at the theme park is represented by t(c)=5x. The cost to pay the employees each season is represented by r(x)=(1.5)^x. Examine the graph of the combined function for total profit and estimate the profit after four seasons
Answer:
The profit after 4 seasons is 14.938 units
Step-by-step explanation:
To quickly solve this problem, we can use a calculator or any graphing tool
to examine both graphs
Revenue
t(x)=5x
Cost
r(x)=(1.5)^x
Profit
P = Revenue - costs = t(x) -r(x)
P = 5x - (1.5)^x
The profit after 4 seasons is 14.938 units
Answer:
14.9
Step-by-step explanation:
x= -2y
x-y=9
Solve using substitutio
Answer:
y = -3; x = 6
Step-by-step explanation:
-2y - y = 9
-3y = 9
y = -3
Solutions of the linear equations given are x = 6 and y = -3.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given are two linear equations.
x = -2y
x - y = 9
We have to solve this by substitution method.
Substituting x = -2y in x - y = 9, we get,
-2y - y = 9
-3y = 9
y = -3
Substituting y = -3 in x = -2y,
x = -2 × -3 = 6
Hence the values of x and y are 6 and -3 respectively.
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Is 24 squared between 5 and 6
[tex]\bf \sqrt{24}\qquad \approx \qquad 4.899~\hfill \underset{\textit{nope, is outside}}{~\hfill \stackrel{\sqrt{24}}{4.899}}\rule[0.35em]{2em}{0.25pt}\boxed{5}\rule[0.35em]{10em}{0.25pt}\boxed{6}[/tex]
Which function has an inverse function?
A.f(x)= |x+3|/5
B. f(x)= x^5-3
C. f(x)= x^4/7+27
D. f(x)= 1/x²
Answer: Option B
Step-by-step explanation:
By definition, only those functions that are one to one have an inverse function.
A function is one by one if there are not two different input values, [tex]x_1[/tex] and [tex]x_2[/tex], that have the same output value y
Note that the function [tex]f(x)= \frac{|x+3|}{5}[/tex] is not a one-to-one function
When x=2 [tex]f(x)= \frac{|2+3|}{5}=1\ ,\ \ y=1[/tex]
When x=8 [tex]f(x)= \frac{|-8+3|}{5}=1\ \ ,\ y=1[/tex]
Note that the function [tex]f(x)= \frac{x^4}{7}+ 27[/tex] is not a one-to-one function
When x=1 [tex]f(x)= \frac{(1)^4}{7}+27\ ,\ \ y=\frac{190}{7}[/tex]
When x=-1 [tex]f(x)= \frac{(-1)^4}{7}+27\ ,\ \ y=\frac{190}{7}[/tex]
Note that the function [tex]f(x)= \frac{1}{x^2}[/tex] is not a one-to-one function
When x=1 [tex]f(x)= \frac{1}{(1)^2}\ ,\ \ y=1[/tex]
When x=-1 [tex]f(x)= \frac{1}{(-1)^2}\ ,\ \ y=1[/tex]
Then the answer is the option B.
You can verify that The function [tex]f (x) = x ^ 5-3[/tex] is a one-to-one function and therefore its inverse is a function
What is the product? a-3/15a × 5/a-3
Answer:
[tex]\frac{1}{3a}[/tex]
Step-by-step explanation:
Given
[tex]\frac{a-3}{15a}[/tex] × [tex]\frac{5}{a-3}[/tex]
Cancel the factor (a - 3) on the numerator and denominator
Cancel the 5 and 15 by dividing both by 5, leaving
[tex]\frac{1}{3a}[/tex]
Answer: The required answer is [tex]\dfrac{1}{3a},~a\neq 3.[/tex]
Step-by-step explanation: We are given to find the following product :
[tex]P=\dfrac{a-3}{15a}\times\dfrac{5}{a-3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Since (a - 3) is present in both numerator and denominator, so we can divide them if
[tex]a-3\neq 0\\\\\Rightarrow a\neq 3.[/tex]
Then, we get from (i) that
[tex]P\\\\\\=\dfrac{(a-3)}{15a}\times\dfrac{5}{(a-3)}\\\\\\=\dfrac{5}{15a}\\\\\\=\dfrac{1}{3a}.[/tex]
Thus, the required answer is [tex]\dfrac{1}{3a},~a\neq 3[/tex]
Find the inverse function of F(x) = 2arccosx. F-1(x) = ____
a.) 1/2 cos(x)
b.) 2 cos(x)
c.) cos (1/2 x)
d.) cos (2x)
ANSWER
C.
[tex]{f}^{ - 1} (x) = \cos( \frac{x}{2} ) [/tex]
EXPLANATION
The given function is
[tex]f(x) = 2 \arccos(x)[/tex]
Let
[tex]y= 2 \arccos(x)[/tex]
Interchange x and y.
[tex]x= 2 \arccos(y)[/tex]
Divide both sides by 2.
[tex] \frac{x}{2} = \arccos(y)[/tex]
We take cosines to get,
[tex] \cos( \frac{x}{2} ) = y[/tex]
[tex] {f}^{ - 1} (x) = \cos( \frac{x}{2} ) [/tex]
Anita Alvarez sells clothing for Toddler’s Shop. Baby blankets sell for $29.99 after a markup rate based on cost of 109%. Find the markup.
Answer:
$2.48
Step-by-step explanation:
Let cost be c
So we can say 109% of the cost is the selling price.
109% means 1.09. Thus we can setup an equation to find the cost, c.
1.09c = 29.99
c = 29.99/1.09
c = 27.51
The markup is selling price - cost, hence,
29.99 - 27.51 = $2.48
Which of the following statements is false? (N = natural numbers)
OCNE
a-Nasa
Mais
(O) CN
{1} CN
Answer:
{O c N}
Step-by-step explanation:
A bowl contains 25 balls numbered 1 to 25. A ball is drawn and its number is noted. Without replacing the first ball, another ball is drawn.
The probability that the numbers on both balls are odd numbers is (blank)
13/50 is the probability
1st step: 13/25 times 1/2 = 0.26
2nd step: 0.26 as a fraction is 13/50
The graph of relation r is shown. Which of the following graphs represents the relation and it’s inverse
Answer:
I attach the missing image from your question.
To easily solve this question, we must realize that the graph of the relation is very similar to that of the expression
y = √(x-a) , where a>0
If we take a look at the image attached, we have plotted the graph of
y = √(x-1) , and its correspondent inverse function.
This means that the answer is the first option
Complete the steps to factor 2x^2 + 6x + 5x + 15 by grouping.
What is there greatest common factor of Group 1?
A)2 B)x C)2x
Answer:
answers in pictures
Step-by-step explanation:
The greatest common factor of group 1 will be 2x so option C is correct.
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
The solution of the given equation will be as follows:-
= 2x² + 6x + 5x + 15
= 2x ( x + 3 ) + 5 ( x + 3 )
= ( x + 3 ) ( 2x + 5 )
We can see in the second step the first group have a common factor of 2x.
Therefore greatest common factor of group 1 will be 2x so option C is correct.
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Given that (-4,2) is on the graph of f(x) find the corresponding point for the function -1/2f(x)
Answer:
The corresponding point is (-4.-1)
Step-by-step explanation:
we know that
The point (-4,2) is on the graph of f(x)
so
For x=-4
f(x)=2
therefore
For x=-4
-(1/2)f(x)=-(1/2)*2=-1
The corresponding point is (-4.-1)
WILL GIVE 20 POINTS
The steps below are used to solve for the unknown angle, X, but are not arranged in the correct order.
1: x=15
2: 75+15= 90
3: 75+x=90
4: 75-75+x=90-75
Which sequence shows the correct order of the steps Virginia should follow to find the measure of the unknown angle.
A) 1,2,3,4
B) 3,4,1,2
C) 4,2,1,3
D) 2,3,1,4
Answer:
The answer is B
Step-by-step explanation:
75 + x = 90
First, Virginia had to write an equation to solve for x.
75 - 75 + x = 90 - 75
Second, Virginia used the subtraction property of equality to isolate x.
x = 15
Third, "x = 15" was the answer Virginia got after subtracting 90 and 75.
75 + 15 = 90
Finally, she had to verify her answer