Answer:
[tex]x=-\frac{6}{7}[/tex]
[tex]y=-17\frac{6}{7}[/tex]
Step-by-step explanation:
We are given the following system of equations that we are to solve:
[tex] y = 8 x - 1 1 [/tex] - (1)
[tex] y = x - 1 7 [/tex] - (2)
Since the left hand side of both the equations is the same so we will equate the right hand sides of both the equations to get:
[tex]8x-11=x-17[/tex]
[tex]8x-x=-17+11[/tex]
[tex]7x=-6[/tex]
[tex]x=-\frac{6}{7}[/tex]
Substituting this value of [tex]x[/tex] in (1) to find [tex]y[/tex]:
[tex]y=8(-\frac{6}{7})-11[/tex]
[tex]y=-17\frac{6}{7}[/tex]
Final answer:
The solution to the system of equations y = 8x - 11 and y = x - 17 is found by setting the equations equal to each other and solving for x, then substituting back to find y. The solution is x = -6/7 and y = -125/7.
Explanation:
To solve the system of equations, you want to find a single value for x and y that satisfies both equations simultaneously. The given equations are:
y = 8x - 11
y = x - 17
Since both equations are equal to y, we can set them equal to each other and solve for x:
8x - 11 = x - 17
Now, let's get all the x terms on one side and the numbers on the other:
8x - x = -17 + 11
7x = -6
Dividing both sides by 7 gives us:
x = -6/7
Now that we have x, we can substitute it back into one of the equations to find y:
y = 8(-6/7) - 11
y = -48/7 - 11
Convert -11 to a fraction,
y = -48/7 - 77/7
y = -125/7
The solution to the system of equations is x = -6/7 and y = -125/7.
A square base of a pyramid has the dimensions 5 yards by 5 yards. The height of one of the triangular faces is 12 yards. How can you find the surface area of the pyramid?
Answer:
145 yards squared
Step-by-step explanation:
So the area of the base is area of a square with side length of 5 yards [tex]5*5=25[/tex]
The area of one triangular face base times height divided by two and then simply multiplied by 4 because there are 4 triangular faces.
[tex](\frac{5*12}{2} )*4 = 120[/tex]
So the total surface area is [tex]25+120=145[/tex] yards squared
Answer:
First, draw and label a net of the pyramid. The triangular faces have a base of 5 yards and a height of 12 yards. Find the area of each of the faces. The square base has an area of 25 yd2. Each of the triangular faces has an area of 30 yd2. Add the areas together to find the surface area: 25 + 30 + 30 + 30 + 30 = 145 yd2.
Step-by-step explanation:
What is the inverse of the function f(x) = 2x + 1?
Answer:
The inverse f-1(x) = ( x - 2) / 2.
Step-by-step explanation:
Let 2x + 1 = y
Now find x in terms of y:
2x = y - 1
x = (y - 1) / 2
Replace the x by the inverse f-1(x) and the y by x, so we have:
f-1(x) = ( x - 2) / 2.
[tex]f(x)=2x+1\\\\y=2x+1\\2x=y-1\\x=\dfrac{y-1}{2}\\\\f^{-1}(x)=\dfrac{x-1}{2}[/tex]
the length of a rectangle is 5 centimeters less than twice its width. It’s area is 28 square centimeters. Find the dimensions of the rectangle
Answer:
It didn't saying anything about rounding but the the dimensions in there exact form are:
[tex]L=\frac{-5+\sqrt{249}}{2} \text{ cm}[/tex]
and
[tex]W=\frac{5 + \sqrt{249}}{4} \text{ cm }[/tex].
Now if they said to round to the nearest hundredths the dimensions in this rounded form would be:
L=5.39 cm and W=5.19 cm
(Check your question again and see if you meant what you have)
Step-by-step explanation:
L is 5 less than twice W
L = 2W-5
Area of rectangle=L*W
Area is 28 means L*W=28.
I'm going to insert L=2W-5 into L*W=28 giving me
(2W-5)*W=28
Distribute
2W^2-5W=28
Subtract 28 on both sides
2W^2-5W-28=0
a=2
b=-5
c=-28
We are going to use the quadratic formula.
Plug in...
[tex]W=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\W=\frac{5 \pm \sqrt{(-5)^2-4(2)(-28)}}{2(2)}\\\\W=\frac{5 \pm \sqrt{25+224}}{4}\\\\W=\frac{5 \pm \sqrt{249}}{4}[/tex]
W needs to be positive so [tex]W=\frac{5 + \sqrt{249}}{4}[/tex]
And [tex]L=2W-5=2(\frac{5 + \sqrt{249}}{4})-5[/tex]
[tex]L=\frac{5+\sqrt{249}}{2}-5[/tex]
[tex]L=\frac{5+\sqrt{249}}{2}-\frac{10}{2}[/tex]
[tex]L=\frac{-5+\sqrt{249}}{2}[/tex]
Does L*W=28?
Let's check.
[tex]L \cdot W=\frac{-5+\sqrt{249}}{2} \cdot \frac{5 + \sqrt{249}}{4}[/tex]
[tex]L \cdot W=\frac{249-25}{8}[/tex]
In the last step, I was able to do a quick multiplication because I was multiplying conjugates. (a+b)(a-b)=a^2-b^2.
[tex]L \cdot W=\frac{ 224}{8}[/tex]
[tex]L \cdot W=28[/tex]
how many possible outcomes are there when you roll four dice
Answer:
24
Step-by-step explanation:
I think you would do 6 sides on the dice times 4 dice.
Answer:
There is 1,296 possible outcomes
Step-by-step explanation:
You are rolling a die which has 6 faces 4 times.
Each of those rolls has 6 outcomes. That other outcome has 6 other outcomes, which goes on for 4 rolls.
SO you multiply 6*6*6*6=1296 possible outcomes
PLZ VOTE ME FOR BRAINLEST
Todd is playing a board game and rolls two number cubes. Let A={the sum of the number cubes is even} and let B={the sum of the number cubes is divisible by 2}. List the outcomes A n B A)3,6,9,12 B) 2,4,6,8,10,12 c) 2,3,4,5,6,7,8,9,10 or D) 0,2,4,6,8,12
Answer:
The correct option is B
Step-by-step explanation:
Todd rolls two number cubes.
Let A={the sum of the number cubes is even}
A={2,4,6,8,10,12}
Let B={the sum of the number cubes is divisible by 2}
B = {2,4,6,8,10,12}
Now we have to find A∩B
Intersection refers to the values which are common in both the sets. The sums in both sets are even and divisible by 2.
So,
A={2,4,6,8,10,12} B = {2,4,6,8,10,12}
A∩B = {2,4,6,8,10,12}
Thus the outcomes A∩B = {2,4,6,8,10,12}
The correct option is B....
Answer:
B
Step-by-step explanation:
[tex]3a - 2 - b - a[/tex]
Answer:
2a -b -2
Step-by-step explanation:
3a -2 - b- a
Combine like terms
3a -a -b -2
2a -b -2
Help ASAP pls !!!!!!!!!!!!!
Answer:
I think it's B.
Step-by-step explanation:
They are asking for integers greater than -3 and less than 5.
For this case we have to:
[tex]x <-3[/tex]: Represents the solution of all strict minor numbers to -3.
[tex]x> 5[/tex]: Represents the solution of all strict major numbers to 5.
The global solution is given by the intersection of both sets.
If we represent the solution in a straight line, it gives us empty. do not intersect.
Answeer:
Option C
The function f(x) = 4(2) ^x represents the number of people who share a cat
video x hours after it first appears on a website. How does the number of
people sharing the video change each hour?
Answer:
It will double every hour.
Step-by-step explanation:
f(x) = 4(2)^x
This is an exponential function so the number of people will increase at a faster rate each hour. It will accelerate.
Lets try entering a few values:
After 1 hour, people = 4*2 = 8
After 2 hours , people =4*2^2 = 16
After 3 hours, people = 4(2)^3 = 32
After 4 hours, people = 4(2)^4 = 64.
It is doubling every hour.
.
Les tried to evaluate 600 x 4 step by step.
600 X 4
Step 1
= 10 x 6 x 4
Step 2
= 10 x 24
Step 3
= 240
Find Les's mistake.
Choose 1 answer:
@ Step 1
B Step 2
C Step 3
DLes did not make a mistake.
Answer:
A Step 1
Step-by-step explanation:
600 X 4
6*100 *4
The mistake is in the first line
600 = 6*100 not 6*10
Which fact helps you prove the isosceles triangle theorem, which states that the base angles of any isoceles triangle have equal measure?
Answer:
If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.
Step-by-step explanation:
The fact that one angle of a triangle is larger than the other angle and the side that is opposite the larger angle is longer than the side which is opposite the smaller angle proves the isosceles triangle theorem.
This theorem proves that the base angles of any isosceles triangle have equal measure.
If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.
e2020
this is a question from MathXL Pearson Statistics. please help
Answer:
Event A has 13/52 outcomes.
Step-by-step explanation:
Total no of cards in a deck = 52
No of clubs in a deck = 13
Event A has outcomes = No of clubs in a deck/Total no of cards in a deck
= 13/52
So, Event A has 13/52 outcomes.
Dan took a train to his vacation spot. His train travels 75 miles each hour before making a stop. He left the station at 10:00. Phil is taking a vacation to the same spot, except his train travels 60 miles each hour before making a stop. Phil’s train left the station at 8:00. What time will they be in the same place?
Answer:
6pm
Step-by-step explanation:
Assumption: Both Dan and Phil both depart from the same station and arrive at the same station. (i.e they both travel the same distance)
Dan's travel speed is 75mph and Phil's travel speed is 60mph
Let Dan's travel time be [tex]t_{Dan}[/tex] and Phil's travel time be [tex]t_{Phil}[/tex]
Use Formula Distance travelled = speed x time, hence
Dan's Distance Travelled =75 [tex]t_{Dan}[/tex]
Phil's Distance Travelled =60 [tex]t_{Phil}[/tex]
Because they travel the same distance, we can equate the 2
75 [tex]t_{Dan}[/tex] = 60 [tex]t_{Phil}[/tex]
or [tex]t_{Dan}[/tex] = (60/75) [tex]t_{Phil}[/tex]
[tex]t_{Dan}[/tex] = 0.8 [tex]t_{Phil}[/tex] -------> eq 1
We also know that Dan left at 10:00 and Phil left at 8:00. If they end up being at the same place, this means that Phil's journey will be 2 hours longer than Dan, or
[tex]t_{Phil}[/tex] = [tex]t_{Dan}[/tex] + 2------> eq2
we can solve the system of 2 equations to get
[tex]t_{Phil}[/tex] = 10 hrs
[tex]t_{Dan}[/tex] = 8 hrs
If Phil left at 8:00 am, he will be in the same place as Dan at 8:00 + 10 hrs = 6 pm.
Double Check:
If Dan left at 10:00, he will be in the same place as Phill at 10:00 + 8 hrs = 6 pm.
What is the volume of the cylinder shown below? I WILL MARK BRAINLIEST
Answer:
[tex] H.~~ 138.16~ft^3 [/tex]
Step-by-step explanation:
Start with the volume formula for a cylinder.
[tex] V = \pi r^2h [/tex]
Now use the given information.
r = 2 ft
h = 11 ft
Use 3.14 for pi.
[tex] V = 3.14 \times (2~ft)^2 \times 11 ft [/tex]
[tex] V = 3.14 \times 4~ft^2 \times 11 ft [/tex]
[tex] V = 3.14 \times 44~ft^3 [/tex]
[tex] V = 138.16~ft^3 [/tex]
One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 40 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer:
84°
Step-by-step explanation:
smallest angle=x
3x=2nd angle
x+40=3rd angle
angles in a triangle add up to 180 degrees so
5x+40=180
5x=140
x=28
largest angle = 3x
so 3 x 28 = 84 degrees
The largest angle is 84 degrees
Answer:
Largest angle = 84°
Step-by-step explanation:
According to the given information, we are assuming the smallest angle of the triangle to be [tex]x[/tex] degrees, next angle to be [tex]3x[/tex] degrees and the last angle to be [tex]x+40[/tex] degrees.
We know that all three angles of a triangle add up to 180 degrees so:
[tex]x+3x+x+40=180[/tex]
[tex]5x=140[/tex]
[tex]x=28[/tex]
Smallest angle = 28°
Next angle = [tex]3(28)[/tex] = 84°
Last angle = [tex]28+40[/tex] = 68°
Therefore, the largest angle = 84°
There are 321 visitors at the library. Each library table seats 12 people. How many tables are needed to seat all of the visitors?
(Explain the process of how you got your answers)
Hello.
The answer is: 27
To get this answer you can divide 321 and 12. But that will give you an uneven number such as 26.75. And because you cant have 26.7 tables you will wound it up to be 27 tables.
Answer:
321÷12=26.75
answer: 27
Step-by-step explanation:
since you know that each table can only seat 12 people and there is 321 visitors you divide 321 by 12 which you get 26.75, but u cant have 26.75 tables so you round up to 27 so you can seat all the visitors because if you round down to 26, 9 people won't have a seat.
True or False? The circumcenter of a triangle is the center of the only circle
that can be inscribed about it.
Answer:
The statement is False
Step-by-step explanation:
we know that
An inscribed circle is the largest circle contained within the triangle. The center of the circle inscribed in a triangle is the incenter of the triangle.
The incenter is the point where the angle bisectors of the triangle intersect.
The circumscribed circle is the circle that passes through all three vertices of the triangle. The center of the circumscribed circle is called the circumcenter of the triangle
The circumcenter is the point where the perpendicular bisectors of the sides intersect.
therefore
The circumcenter of a triangle is the center of the only circle
that can be circumscribed about it.
The statement is false
The circumcenter of a triangle is the center of the only circle that can be inscribed about it. True or false?
Answer: False
17
Find the x-intercepts of the parabola with vertex (1,-9) and y-intercept at (0,-6).
A. (-1,0), (3,0)
B. (-0.73,0), (2.73,0)
C. (-1.48,0), (2.48,0)
D. (-4.67,0), (1.67,0)
let's firstly find the equation of the parabola, bearing in mind that x-intercepts or solutions/zeros/roots means y = 0.
[tex]\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=1\\ k=-9 \end{cases}\implies y=a(x-1)^2-9 \\\\\\ \textit{we also know that } \begin{cases} x=0\\ y=-6 \end{cases}\implies -6=a(0-1)^2-9\implies 3=a(-1)^2[/tex]
[tex]\bf 3=a\qquad \qquad \textit{therefore}\qquad \qquad \boxed{y=3(x-1)^2-9} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{y}{0}=3(x-1)^2-9\implies 9=3(x-1)^2\implies \cfrac{9}{3}=(x-1)^2\implies 3=(x-1)^2 \\\\\\ \pm\sqrt{3}=x-1\implies \pm\sqrt{3}+1=x\implies x= \begin{cases} \sqrt{3}+1\\ -\sqrt{3}+1 \end{cases}\implies x\approx \begin{cases} 2.73\\ -0.73 \end{cases}[/tex]
Which is a possible turning point for the continuous function f(x)? (–3, –4) (–2, –1) (0, –5) (1, –8)
Answer:
That would be the point(-2, -1)
Step-by-step explanation:
The graph rises between (-3, -4) and (-2, -1) then falls as it passes through the last 2 points ( y = -1 goes to y= -5 and then to y = -8 as x values move to the right).
Answer: (–2, 1)
Step-by-step explanation:
just did this
F(x)=x^2 What is F(x)+f(x)+f(x)
Answer:
Step-by-step explanation:
F(x)=x^2 What is F(x)+F(x)+F(x) =3F(x) =3x²
Answer:
[tex]F(x)+F(x)+F(x)[/tex] = [tex]3x^{2}[/tex]
Step-by-step explanation:
Given is :
[tex]F(x)=x^{2}[/tex]
We have to find: [tex]F(x)+F(x)+F(x)[/tex]
This means we have to find [tex]x^{2} +x^{2} +x^{2}[/tex]
This becomes [tex]3x^{2}[/tex]
Hence, [tex]F(x)+F(x)+F(x)[/tex] = [tex]3x^{2}[/tex]
Solve the following system of equations by graphing and select the correct answer below:
4x + 3y = 29
2x − 3y = 1
a) x = 3, y = 5
b) x = −3, y = 5
c)x = 5, y = 3
d) x = 5, y = −3
Answer: option c
Step-by-step explanation:
Find the x-intercept and y-intercept of each line.
To find the x-intercept, substitute [tex]y=0[/tex] into the equation and solve for "x".
To find the y-intercept, substitute [tex]x=0[/tex] into the equation and solve for "y".
- For the first equation:
x-intercept
[tex]4x + 3y = 29\\\\4x + 3(0)= 29\\\\4x=29\\\\x=\frac{29}{4}\\\\x=7.25[/tex]
y-intercept
[tex]4x + 3y = 29\\\\4(0) + 3y = 29\\\\3y=29\\\\y=\frac{29}{3}\\\\y=9.66[/tex]
Graph a line that passes through the points (7.25, 0) and (0, 9.66)
- For the second equation:
x-intercept
[tex]2x - 3y = 1 \\\\2x - 3(0) = 1 \\\\2x=1\\\\x=0.5[/tex]
y-intercept
[tex]2x - 3y = 1\\\\2(0) - 3y = 1\\\\-3y=1\\\\y=-0.33[/tex]
Graph a line that passes through the points (0.5, 0) and (0, -0.33)
Observe the graph attached. You can see that point of intersection of the lines is (5,3); then this is the solution of the system. Therefore:
[tex]x=5\\y=3[/tex]
ANSWER
c)x = 5, y = 3
EXPLANATION
The given system has equations:
[tex]4x + 3y = 29[/tex]
and
[tex]2x - 3y = 1[/tex]
We graph the above equations using a graphing software to obtain the graph shown in the attachment.
The solution to the given system is the point of intersection of the two straight lines.
From the graph, the two straight lines intersected at (5,3).
This implies that the solution to the system is:
[tex]x = 5 \: and \: y = 3[/tex]
The correct answer is option is C
Select the correct answer from each drop-down menu.
consider the equation
-22 + 3x
___________ = 2
3x + 7
How do you begin isolating the variable x to one side of the equation?
A) Multiply both sides by 3x + 7.
Reset
B) Divide both sides by 3x + 7.
C) Multiply both sides by -22 + 3x.
D) Divide both sides by -22 + 3x.
The solution of the equation is
A) -12
B) -9
C) -6
D) -3
Answer:
A)Multiply both sides by 3x + 7.
Reset
A)the solution of the equation is x=-12
Step-by-step explanation:
Hello
let
to begin isolating we must multiply both sides by 3x + 7.
Reset
this way
[tex]\frac{-22+3x}{3x+7}=2\\\frac{-22+3x}{3x+7}*(3x+7)=2*(3x+7)\\-22+3x=2*(3x+7)[/tex]
let´s continue to find x
[tex]\\-22+3x=2*(3x+7)\\-22+3x=6x+14\\-22-14=6x-3x\\-36=3x\\x=\frac{-36}{3}\\ x=-12[/tex]
the solution of the equation is x=-12
have a great day
Could anyone answer and also provide explanation.
Answer:
b
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
2x + 3y = 1 ( subtract 2x from both sides )
3y = - 2x + 1 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{1}{3}[/tex] ← in slope- intercept form
with y- intercept c = [tex]\frac{1}{3}[/tex] ← does not pass through the origin
(b)
2x + 3y = 0 ( subtract 2x from both sides )
3y = - 2x + 0 ( dividing all sides by 3 ), gives
y = - [tex]\frac{2}{3}[/tex] x + 0 ← in slope- intercept form
with y- intercept c = 0 ← passes through the origin
(c)
2x + 3y = 6 ( subtract 2x from both sides )
3y = - 2x + 6 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + 2
with y- intercept c = 2 ← does not pass through the origin
what is the value of x?
Answer:
x = 130
Step-by-step explanation:
The sum of the exterior angles of a polygon is always 360
140 + x + 56+ 34 = 360
Combine like terms
230 +x = 360
Subtract 230 from each side
230+x-230 = 360-230
x =130
A, B, and C are polynomials, where A = n, B = 2n + 6, and C = n2 – 1. What is AB – C in simplest form?
Answer:
B=n2 + 6n + 1
Step-by-step explanation:
A = n
B = 2n + 6
C = n^2 - 1
AB - C = n * (2n + 6) - (n^2 - 1) = 2n^2 + 6n - n^2 + 1 = n^2 + 6n + 1
Answer:
The simplest form of the expression AB-C is [tex]n^2+6n+1[/tex].
Step-by-step explanation:
In this exercise we only need to use the properties of arithmetic operations and a minimal knowledge of algebraic notation. We have the expressions
[tex]A = n[/tex],[tex]B=2n+6[/tex],[tex]C=n^2-1[/tex].Now we make the indicated operations, beginning by AB:
[tex]AB=n\cdot(2n+6) = 2n^2+6n[/tex] using the distributive property of multiplication.
Then, we make AB-C:
[tex]AB-C = 2n^2+6n - (n^2-1) = 2n^2+6n-n^2+1 = n^2+6n+1[/tex].
In the last step we must be vary careful with the change of signs in the expression inside parenthesis.
HELPPPPPP!!
Leila, Larry, and Cindy are running for 12th grade class offices. They will be named to the positions of president, vice-president, and secretary according to the number of votes each receives. The person with the most votes will be president, the person with the second-highest number of votes will be vice-president, and so on. In how many different ways can the three students form a set of class officers?
Answer:
In 6 different ways can the three students form a set of class officers.
Step-by-step explanation:
There are 3 people Leila, Larry, and Cindy and 3 positions president, vice-president, and secretary.
We need to find In how many different ways can the three students form a set of class officers.
This problem can be solved using Permutation.
nPr = n!/(n-r)! is the formula.
Here n = 3 and r =3
So, 3P3 = 3!/(3-3)!
3P3 = 3!/1
3P3 = 3*2*1/1
3P3 = 6
So, in 6 different ways can the three students form a set of class officers.
Solve the following equation. Then place the correct number in the box provided. 2x - 20 = 32
Answer:
x=26
Step-by-step explanation:
Given:
2x - 20 = 32
2x=32+20
2x=52
2x/2=52/2
x=26!
Find RS in the picture please
Answer:
D 5
Step-by-step explanation:
PQ + QR + RS = PS
Substituting what we know
2x-6 + 1 + x-4 = 18
Combine like terms
3x-9 = 18
Add 9 to each side
3x-9+9 =18+9
3x= 27
Divide each side by 3
3x/3 =27/3
x=9
We want to find RS
RS = x-4
= 9-4
=5
If f = {(4, 2), (6, 1), (8, 4), (10, 2), (12,5)}, what is the range?
Range means all the y values included on the function/relation on the graph. In this case the y values/range is:
{1, 2, 4, 5}
^^^Remember to order them from smallest to largest and to a number only once if there are more then one of that number included in the range.
Hope this helped!
~Just a girl in love with Shawn Mendes
Which formula gives the area of a parallelogram? (3)
Answer:
A = bh (the last one)
Step-by-step explanation:
To find the area of a parallelogram, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply. The base and height of a parallelogram must be perpendicular.
Answer:
A=bh
Step-by-step explanation:
Need help in number 9. Thanks for helping
Answer:
B.
Step-by-step explanation:
The range is just the list of y-coordinates while the domain is just a list of the x-coordinates when it comes to a list of points.
So anyways all your y-coordinates are -2,-1,0,1,2. So that is your range.
Answer:
B.
Step-by-step explanation: