Answer:
[tex]\huge\boxed{b.\ x=6;\ y=3}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x=2y&(1)\\2x+3y=21&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\2(2y)+3y=21\\4y+3y=21\qquad\text{combine like terms}\\7y=21\qquad\text{divide both sides by 7}\\\dfrac{7y}{7}=\dfrac{21}{7}\\\boxed{y=3}\\\\\text{Substitute it to (1):}\\x=2(3)\\\boxed{x=6}[/tex]
Answer: (6, 3)
Explanation: Our first equation tells us that x means the same thing as 2y so we can replace the x in the second equation with a 2y.
Our second equation then becomes 2(2y) + 3y = 21.
If we simplify on the left side we get
4y + 3y = 21 which simplifies to 7y = 21.
Solving from here, we find that y = 3.
To find x, plug 3 back in for y in the first equation
to get x = 2(3) which simplifies to x = 6.
So our answer is (6, 3).
The solution set for 7q2 − 28 = 0 is
Answer:
2 and -2
Step-by-step explanation:
● 7q^2 -28 = 0
Add 28 to both sides
● 7q^2-28+28 = 28
● 7q^2 = 28
Divide both sides by 7
●7q^2/7 = 28/7
● q^2 = 4
You can write directly q= 2 or q= -2
To understand it use the absolute value.
● |q| = 2
● q = 2 or q = -2
The solutions are {2, -2}
Which expressions are linear factors of the polynomial? Choose all that apply.
x3 + 2x2.5x-6
ox-2
O X+3
Ox-1
Ox+1
Answer:
The linear factors are:
[tex]x - 2[/tex]
[tex]x + 3[/tex]
[tex]x + 1[/tex]
Step-by-step explanation:
Given
[tex]x^3 + 2x^2 - 5x - 6[/tex]
Required
Select all linear factors of the polynomial
Solving for x - 2;
Equate x - 2 to 0 and solve for x
[tex]x - 2 = 0[/tex]
[tex]x = 2[/tex]
Substitute 2 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]
[tex]2^3 + 2(2^2) - 5(2) - 6[/tex]
[tex]= 8 + 8 - 10 - 6[/tex]
[tex]= 0[/tex]
Because, we arrived at 0, then x - 2 is a factor
Solving for x + 3;
Equate x + 3 to 0 and solve for x
[tex]x + 3 = 0[/tex]
[tex]x = -3[/tex]
Substitute -3 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]
[tex](-3)^3 + 2(-3^2) - 5(-3) - 6[/tex]
[tex]= -27 + 2(9) + 15 - 6[/tex]
[tex]= -27 + 18 + 15 - 6[/tex]
[tex]= 0[/tex]
Because, we arrived at 0, then x + 3 is a factor
Solving for x - 1;
Equate x - 1 to 0 and solve for x
[tex]x - 1 = 0[/tex]
[tex]x = 1[/tex]
Substitute 1 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]
[tex](1)^3 + 2(1^2) - 5(1) - 6[/tex]
[tex]= 1 + 2(1) - 5 - 6[/tex]
[tex]= 1 + 2 - 5 - 6[/tex]
[tex]= -8[/tex]
Because, we did not arrived at 0, then x - 1 is not a factor
Solving for x + 1;
Equate x + 1 to 0 and solve for x
[tex]x + 1 = 0[/tex]
[tex]x = -1[/tex]
Substitute -1 for x in [tex]x^3 + 2x^2 - 5x - 6[/tex]
[tex](-1)^3 + 2(-1^2) - 5(-1) - 6[/tex]
[tex]= -1 + 2(1) + 5 - 6[/tex]
[tex]= -1 + 2 + 5 - 6[/tex]
[tex]= 0[/tex]
Because, we arrived at 0, then x + 1 is a factor
Which of the following functions represent exponential growth? f(x)=.0001(1.77)^x f(x)=2(1.5)^x/2 f(x)=5(0.5)^-x f(t)=5e^-t
Answer:
Hello There. ☆~\《`°---_●£●__---`°》\~☆
An exponential growth function is represented by
f(x)=a(b)^{x},a>0,b>1.
The given functions can be written as,
A)f(x)=.001(1.77)^x,0.001>0,1.77>1
B)f(x)=2(1.5)^{x/2}=2(\sqrt{1.5} )^x,2>0,\sqrt{1.5} >1
C)f(x)=5(0.5)^{-x}=5(2)^x,5>0,2>1
D) f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e.
So the function f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e violates the conditions for an exponential growth function. It is an exponential decay function.
The correct choices are (A), (B), (C).
Hope It Helps!~ ♡
ItsNobody~ ☆
The functions that represent exponential growth are choices (A), (B), and (C). The correct option is A, B, and C.
What is exponential growth?Exponential growth is the process of gradual increase of quantity over time.
An exponential growth function is represented by
[tex]\rm f(x)=a(b)^{x}[/tex], a>0,b>1
The given functions can be written as,
A)[tex]f(x) = .001(1.77)^x[/tex], 0.001>0,1.77>1
B) [tex]f(x) = 2(1.5)^{x/2} = 2(\sqrt{1.5} )^x,[/tex] 2>0, [tex]\sqrt{1.5}[/tex] >1
C)[tex]f(x) = 5(0.5)^{-x}=5(2)^x[/tex], 5>0, 2>1
D) [tex]f(t) = 5e^{-t}=5(\frac{1}{e} )^x[/tex], 5>0, 1/e.
So, the function [tex]f(t)=5e^{-t}=5(\frac{1}{e} )^x,5 > 0,1/e[/tex] violates the conditions for an exponential growth function. It is an exponential decay function.
The correct choices are (A), (B), and (C).
Learn more about exponential growth;
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What is the number of possible outcomes for the tree diagram below?
Answer: A. 9
Step-by-step explanation:
In the given tree diagram , there are 3 branches , to each branch there are 3 leaf nodes.
By using Fundamental counting principal ,
Number of possible outcomes for the tree diagram = (Number of branches) x (Number of leaf nodes)
[tex]=3 \times 3\\\\=9[/tex]
Hence, the number of possible outcomes for the tree diagram = 9
So, the correct option is A. 9.
Can anyone plz help me
Answer:
vertex (-4,-1)
2nd point ( 0,31)
Step-by-step explanation:
f(x) = 2x^2 + 16x + 31
First find the vertex
The x coordinate of the vertex is -b/2a where ax^2 +bx +c
-16/ 2(2) = -16/4 = -4
Substitute into the function
f(-4) = 2 ( -4)^2 +16(-4) +31
= 2 *16-64 + 31
= 31 -64 +31
= -1
The vertex is at ( -4,-1)
Another point can be x=0
f(0) = 0+16(0)+31
= 31
( 0,31)
PLEASE HELP ME QUICK !!!!!!!! -8 x 10^7/-4 x 10^6
Answer:
20
Step-by-step explanation:
Ava is buying paint from Amazon. Ava needs 3⁄4 cup of blue paint for every 1 cup of white paint. Ava has 28 ounces of white paint. How many cups of blue paint does he need?
Answer:
21
Step-by-step explanation:
So we know the ratio is 3/4:1
So if she has 28 ounces of white pain, we can do 28*3/4=21. You could also do 28/4 (find out how much 1/4 of the value is) which is 7 and then multiply that by 3. What your basically doing is your putting it into 4 equal parts and then just multiplying by 3 since that's the amount of parts you need/have.
How is everyone doing today? Here is a problem for the day! Problem - 10 + 8 x 119
Answer:
..
-10 + 8× 119
= -10 + 952
= 942. .....
Answer:
236 (i think)
Step-by-step explanation:
cuz 0-10= -10+8= -2 X 119=236 (sorry if you cant read this my keyboard sucks
Identify an equation in point-slope form for the line perpendicular to
y=-2x+ 8 that passes through (-3,9).
O A. y - 9 = -2(x+3)
O B. y+3 - 3(x-9)
O C. y-9-(x + 2)
O D.y +9 = 2(x – 3)
The correct option is A. The equation in point-slope form for the line perpendicular to y = -2x + 8 and passing through (-3, 9) is: y - 9 = 1/2(x + 3).
To find the equation of a line perpendicular to y = -2x + 8 that passes through the point (-3, 9), we need to determine the slope of the perpendicular line.
The given equation is in slope-intercept form, y = mx + b, where m represents the slope. In this case, the slope of the given line is -2.
Since the perpendicular line has a slope that is the negative reciprocal of -2, we can determine its slope as 1/2.
Now that we have the slope (1/2) and a point (-3, 9) on the line, we can use the point-slope form of a line to write the equation:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
Plugging in the values, we get:
y - 9 = 1/2(x - (-3))
Simplifying:
y - 9 = 1/2(x + 3)
Rearranging to match the given options:
y - 9 = 1/2(x) + 3/2
The equation in point-slope form for the line perpendicular to y = -2x + 8 and passing through (-3, 9) is:
y - 9 = 1/2(x + 3)
Therefore, the correct option is A.
Learn more about equation here
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Complete question is below
Identify an equation in point-slope form for the line perpendicular to
y=-2x+ 8 that passes through (-3,9).
A. y - 9 = 1/2(x+3)
B. y+3 = 3(x-9)
C. y - 9 = (x + 2)
D. y + 9 = 1/2(x – 3)
Quadrilaterals L M N O and Q R S T are shown. Given that LMNO ≅ QRST, complete the statements. Side LM is congruent to side . Angle MNO is congruent to angle .
When you have two congruent figures, the vertices are listed in the same order. This means that
Side LM ≅ Side QR, Side MN ≅ Side RS, etc. The same applies for the angles.
Therefore, Side LM ≅ Side QR and Angle MNO ≅ Angle RST.
The complete statements are Side LM is congruent to the side QR and angle ∠MNO is congruent to angle ∠RST.
What is congruent quadrilateral?The two quadrilaterals whose angles and sides of one quadrilateral are the same as the corresponding angles and sides of another quadrilateral then two quadrilaterals are congruent to each other.
The order of the lettering for congruent parts should place the lettering for corresponding parts in the same order.
Given in the question that the quadrilateral LMNO and QRST are congruent.
LMNO ≅ QRST
As we know Congruent Parts of the congruent Figures are also congruent, we have;
side LM is congruent to side QR.
side MN is congruent to side RS.
side NO is congruent to side ST.
side OL is congruent to side TQ.
Similarly, for the corresponding angles of the quadrilaterals, we have;
angle ∠MNO is congruent to angle ∠RST.
angle ∠NOL is congruent to angle ∠STQ.
angle ∠OLM is congruent to angle ∠TQR.
angle ∠LMN is congruent to angle ∠QRS.
Therefore, Side LM is congruent to the side QR and angle ∠MNO is congruent to angle ∠RST.
Learn more about Congruent quadrilateral
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What is the mass in grams of 1.00 gal of water? The density of water is 1.00 g/ml.
The mass of water will be - 3785.41 grams.
We have density of water is 1.00 g/ml.
We have to determine the mass in grams of 1.00 gal of water.
Describe the relation between Mass (m) and Density (ρ).The relation between Mass (m) and Density (ρ) is -
m = ρV
where - V is the volume of object.
According to the question -
Density of water - 1.00 g/ml
Volume of water - 1 gallon = 3785.41 ml
m = ρV
m = 1 x 3785.41 = 3785.41 grams.
Hence, the mass of water will be - 3785.41 grams.
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FIRST GETS BRAINLLEST If each 12 feet on the scale drawing below equals 3 cm, what is the actual length of the green line?
12cm
14cm
15cm
16.5 cm
Answer:
12 cm
Step-by-step explanation:
You would only have to focus on the green line and then you just have to divide it by 12 and you get 4 and than you multiply 3 cm by 4 and the answer for the actual length of the green line will be 12 cm.
Answer:
12 cm
Step-by-step explanation:
The ratio of feet to cm is 12:3. Set up a ratio to find the length of the green line in cm.
12 feet ÷ 3 cm = 48 ft ÷ x
Cross multiply and divide.
3 x 48 = 12 × x
144 = 12x
x = 12
The actual length of the green line is 12 cm.
Hope that helps.
30 POINTS! Arrange the steps to solve this problem. 9 steps.
Answer:
1. Multiply the first equation by 3
3(x + y ) = 3(-2)
3x + 3y - 6
2. Add 3x + 3y = - 6 ( obtained in step 1) to
2x - 3y = - 9 (given) and solve for x
3. x = - 3
4. Substitute the value of x in the first equation
( x + y = - 2) to get y = - 1
5. The solution for the linear system of equations is ( - 3 , 1)
Hope this helps you
(30 POINTS!!!) One press can run the day’s newspapers in 6 hours, while another can do the same job in 8 hours. After running together for 2 hours to complete the job, the faster one breaks. How much longer must the slower press run to finish the newspapers?
Amount of the job done after 2 hours:
2(1/6 + 1/8)
2(4/24 + 3/24)
2(7/24)
7/12 (amount of job finished)
.
amount of job left to do:
1 - 7/12
12/12 - 7/12
5/12 (remaining)
.
Let x = time (hours) slower press takes to finish job
then
x(1/6) = 5/12
multiplying both sides by 6:
x = 5/12 *6
x = 5/2 hours
or
x = 2 hours and 30 minutes
The slower press (8-hour press), will take h 3 hours, 20 minutes to complete the job
Aaron covers 300 miles in 6 hours, what's his average speed?
Answer:
50mph
Step-by-step explanation:
Speed=v
time=t
distance=s
v=s/t
v=300m/6h
v=50mph
Let me know if my answer is wrong.
Hope this helps :) ❤❤❤
Answer:
[tex]\boxed{Speed = 50 miles/hr}[/tex]
Step-by-step explanation:
Given:
Distance = S = 300 miles
Time = t = 6 hours
Required:
Average Speed = v = ?
Formula:
Average Speed = Total Distance Covered / Total Time Taken
Solution:
v = S/t
v = 300 miles / 6 hours
v = 50 miles/hr
Brett is making chocolate bars. He wants to make 35 bars from Monday to Friday. One cocoa pod makes ⅚ of bar. If he harvests the same number of cocoa pods each day, how many cocoa pods should he harvest each day to reach his goal of making 35 bars total from Monday to Friday?
Answer:
one cocoa pod makes 5/6 bar
to make 35 bars, he needs
35 / (5/6) = 35 * 6/5 = 42 pods
Monday - Friday is 5 days
42/5 = 8.4
helpppp me now plz help
Answer:
0.53 is the right answer
The ratio of boys and girls in the school
chorus is 4 to 5. There are a total of 20
boys in the chorus. How many students are
in the chorus?
Answer:
45
Step-by-step explanation:
20 boys= 5 times the ratio
So, 5x5=25
25 girls and 20 boys= 45 students
Answer:
45 students
Step-by-step explanation:
to make sure there are 20 boys you need to multiply 4 by 5
so multiply the 5 by 5 as well
then add what you get!!
Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2).
Answer:
(-6,6), (0,12), (4,8)
Step-by-step explanation:
To dilate an object, we need to multiply the x and y values by the given scale factor.
In this case the scale factor is 2 --> 2(x, y)
Before-> After dilation
2(-3,3) = (-6,6)
2(0,6) = (0,12)
2(2,4) = (4,8)
Please leave a 'thanks' if this helps!
The linear combination method gives a solution of (–4, 2) for which of these systems of linear equations? 3 x + 13 y = 14. 6 x + 11 y = negative 2. 4 x + 5 y = 12. 8 x + 3 y = negative 4. 5 x + 4 y = 12. 7 x + 8 y = 12. 10 x + 3 y = 8. 17 x + 6 y = 10.
Answer:choice one
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I did the test
how is this question solved?
Answer:
[tex]\large \boxed{\sf \ \ 35.805 \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all we need to find the intersection points of y = 12 and
[tex]y=f(x)=e^x+e^{-x}[/tex]
We need to solve the following equation.
[tex]e^x+e^{-x}=12\\\\\text{*** We multiply by }e^x\text{ both side ***}\\\\\left(e^x\right)^2+1=12e^x\\\\\text{*** Let's note } X =e^x\text{, it comes *** }\\\\X^2-12X+1=0[/tex]
[tex]\Delta=b^2-4ac=12^2-4=140=2^2\cdot 35\\\\X_1=\dfrac{12-2\sqrt{35}}{2}=6-\sqrt{35}\\\\X_2=\dfrac{12+2\sqrt{35}}{2}=6+\sqrt{35}\\[/tex]
And, we take the greater solution to solve:
[tex]X=e^x=6+\sqrt{35}<=>\boxed{x=ln(6+\sqrt{5})}[/tex]
Let's note it a.
Let's compute the integral.
We need to compute the following (because 12-f(x) is pair the integral that we are looking for is)
[tex]\displaystyle 2\int\limits^a_{0} {\left(12-(e^x+e^{-x})\right)} \, dx =12*(2a)-2\int\limits^a_{0} {(e^x+e^{-x})} \, dx \\\\=24a-2[e^x-e^{-x}]_{0}^a=24a-2(e^a-e^{-a})[/tex]
We can replace a by the value we already found.
[tex]24\cdot ln(6+\sqrt{35})-2\left( 6+\sqrt{35}-\dfrac{1}{6+\sqrt{35}}\right)\\\\=24\cdot ln(6+\sqrt{35})-2\left(6+\sqrt{35}-\dfrac{\sqrt{35}-6}{(\sqrt{35}-6)(\sqrt{35}+6)}\right)\\\\=24\cdot ln(6+\sqrt{35})-2\left(\dfrac{29*6+29*\sqrt{35}-\sqrt{35}+6}{29}\right)\\\\\\=24\cdot ln(6+\sqrt{35})-2\left(\dfrac{180+28\sqrt{35}}{29}\right)\\\\[/tex]
= 59.46933...-26.66432...=35.8050...
So the answer is [tex]\boxed{\sf \ \ 35.805 \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the output. y. when the input. r. is 7.
Answer:
When x = 7, y = 4
Step-by-step explanation:
We are simply looking for the y-value for when the graph input x equals 7. When we look at the graph when x = 7, we see that our y-value y equals 4.
Answer:
x=7 y=4
Step-by-step explanation:
One student ate 3/20 of all candies and another 1.2 lb. The second student ate 3/5 of the candies and the remaining 0.3 lb. What weight of candies did they each eat?
Answer:
First person ate 2.1 pounds and second person ate 4.8 pounds
Step-by-step explanation:
First we find the common denominator. So 3/5=12/20. 12/20+3/20+15/20. That means that 5/20=1.5 lb. So 1/20=.3 pounds. So person number one ate .9+1.2=2.1 pounds of candy and person number two ate 4.5+.3=4.8
AD= 36 cm. Points C, B∈AD, such that AB:BC:CD=2:3:4. Find the distance of midpoints of the segments AB and CD.
Answer:
The distance of the midpoint of AB = 4 cm
The distance of the midpoint of CD = 28 cm
Step-by-step explanation:
The given information are;
Segment AD = 36
Point C and point B are points on AD such that AB:BC:CD = 2:3:4
Which gives;
The proportion of AB in AD = 2/(2+3+4) = 2/9
The length of AB = 2/9×36 = 8 cm
The proportion of BC in AD = 3/(2+3+4) = 3/9
The length of AD = 3/9×36 = 12 cm
The proportion of CD in AD = 3/(2+3+4) = 4/9
The length of AD = 4/9×36 = 16 cm
The coordinate of the midpoint of AB = 8/2 = 4 cm from A
The distance of the midpoint of AB = 4 cm
The coordinate of the midpoint of CD = 8 + 12 + 16/2 = 28 cm from A
The distance of the midpoint of CD = 28 cm.
PLEASE HELP!!!! QUESTION IS BELOW
Answer:
[tex]\boxed{70\°}[/tex]
Step-by-step explanation:
Angle ABP and angle MAB are corresponding angles.
Corresponding angles are equal.
Angle ABP = 50 degrees
Angle CBP and angle BCQ are corresponding angles.
Corresponding angles are equal.
Angle CBP = 20 degrees
Angle ABC is the sum of angles CBP and ABP.
[tex]50+20=70[/tex]
10 POINTS IDENTIFY THE SLOPE, Y-INTERCEPT AND GRAPH.
1. Y = 2x + 3
2. Y = 3/4x - 2
Answer for problem 1: slope = 2, y intercept = 3
Answer for problem 2: slope = 3/4, y intercept = -2
Explanation:
Both equations are in the form y = mx+b. This is known as slope intercept form. This is because we can read off the values of the slope and y intercept very quickly. We have y = 2x+3 match up with y = mx+b. The m is the slope and b is the y intercept. So m = 2 and b = 3 for this equation. A similar situation happens with the other equation as well. It might help to rewrite the second equation into y = (3/4)x + (-2).
Answer:
slope: 1.) 2 ,,, 2.) 3/4
y-int: 1.) (0,3) ,,, 2.) (0,-2)
graph: attached in pictures/ blue line represents y=2x+3 ,,, red line represents y=3/4-2
Step-by-step explanation:
Find the.equation of the line through point (-4,1) and parallel to y=-1/2x -2
Answer: y = -1/2x -1
Step-by-step explanation: since the new line is parallel to the given line the slope of both the lines world be same. Therefore putting the new values in the equation
y-y1=m(x-x1)
y-1=-1/2(x+4)
y-1=-1/2x -2
y=-1/2x-1
Can someone help with this please thanks!
Answer:
150 I believe but don't quote me on that
8. After a certain transformation is applied to point (x,y) is moved to (y,-x).
Name the transformation.
Rotation
Translation
Reflection
Dilation
Answer:
Rotation
Step-by-step explanation:
when you rotate a point it swaps the numarical values x⇄y as well as in some cases it changes its the symbol from negative to positive depending on the quadrant, in this case, it started in quadrant one and ended in quadrant three.
please help attachment
Answer:
v = 7
Step-by-step explanation:
a. v = 5x + 2y
= 5 × 3 + 2 × -4
= 15 + -8
= 7
Sorry I know only the A one anyways , hope this helps :)
Answer:
Step-by-step explanation:
a v = 5x+ 2y = 5*3 + 2*-4 = 7
b 3p(p+5) = 3p^2 =15p
c 4k = 44
k=44/4 =11
i hope the person who had deleted my answer this much explanation is only required if not please say so that I can correct myself by ellaborating ...