There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)
There's no solution to this particular system because the two lines are parallel.
How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.
The line on the left passes through the points (-1, 0) and (0, -2), so it has slope
(-2 - 0)/(0 - (-1)) = -2/1 = -2
The line on the right passes through (0, 2) and (1, 0), so its slope is
(0 - 2)/(1 - 0) = -2/1 = -2
The slopes are equal, so the lines are parallel.
Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.
Sorin hits a cricket ball straight up into the air. After 1.5s, the ball is falling straight down with a speed of 6.5 m/s. We want to find the initial vertical velocity of the ball. We can ignore air resistance. Which kinematic formula would be most useful to solve for the target unknown?
Step-by-step explanation:
We have, Sorin hits a cricket ball straight up into the air. After 1.5 s, the ball is falling straight down with a speed of 6.5 m/s.
We want to find the initial vertical velocity of the ball.
The relation between initial speed, final speed, acceleration and time is given by using first equation of kinematics. Let v₀ is the initial speed. So,
[tex]v=v_o +at[/tex]
Here, v = -6.5 m/s, t = 1.5 s and a = -g
[tex]v_o=v-at\\\\v_o=v+gt\\\\v_o=-6.5+9.8\times 1.5\\\\v_o=8.2\ m/s[/tex]
So, the initial velocity of the ball is 8.2 m/s and the formula used is (1).
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A. y = 3x
B. y = x
C. y = 2x
D. y = -1/3x
E. y = -3x
F. y = 1/3x
If angle AOC = 40 degrees, how many degrees is angle ABC?
80........................
i think of a number multiply it by 3 and subract 2 . The result is 14
Answer:
5.3
Step-by-step explanation:
Answer:
The answer is 5.3
Step-by-step explanation:
5.3x3-2= 13.9 but when you round its 14
how many times does 6 go into 29
Answer:
4 times
Step-by-step explanation:
Answer:
4.8333333 or 4 5/6 times
Step-by-step explanation:
29/6 = 4.83333333
Molly wants to put a fence around an area. The fence will follow the diagram of the triangle shown below. (Look at picture) About how much fencing does Molly need?
Answer:
Step-by-step explanation:
43feet
hi!! <3 i attached a picture of a easy trigonometry question can you please help if you don’t mind <33
Answer:
Side AB has a length of 4, and side BC has a length of 11.7
Select the expressions that are equivalent to 6(x + 7).
(7 + x) 6
6x + 42
(x + 7)6
42x + 6
Answer:
[tex]6x + 42[/tex]
Step-by-step explanation:
Apply the distributive property:
[tex]6x + 6 \times 7[/tex]
Multiply 6 by 7
[tex]6x + 42[/tex]
Thank you so very much for helping
Answer:
Angle 2
Step-by-step explanation:
They are 90 degrees when added together
Answer:
<2
Step-by-step explanation:
Complementary angles add to 90 degrees ( form right angles)
<1 and <2 add to 90 degrees so they are complementary angles
If a right triangle is rotated around one of its legs for 360 degrees, what three dimensional shape is produced?
Answer:
The shape of a cone
Step-by-step explanation:
If we rotate the right triangle for 360 degrees around one leg, we will have a shape of a cone (a conical shape).
the leg we choose to rotate around will be the height of the cone.
The other leg will be the radius of the cone's base.
And the hypotenusa of the right triangle will be the slant height of the cone.
Evaluate the expression 3 x
{10 +1} +5.
Answer:
38
Step-by-step explanation:
3 x {10 +1} +5.
PEMDAS
Parentheses first
3 x {11} +5.
Then multiply and divide
33+5
38
Answer:
38
Step-by-step explanation:
3 x {10 +1} +5 Following PEMDAS, solve in the parentheses
3 x 11 + 5 Multiply 3 x 11
33 + 5 Add
38
What is the answer? Plz need help
30x and 12 have a common factor of 6. So yes, this might have been the result of distributing the 6 in
6(5x - 2)
Answer:
30x - 12 = 2(15x - 6)
30x - 12 = 3(10x - 4)
30x - 12 = 6(5x - 2)
Step-by-step explanation:
30 and 12 have these factors in common: 2, 3, 6
There are three possible answers.
30x - 12 = 2(15x - 6)
30x - 12 = 3(10x - 4)
30x - 12 = 6(5x - 2)
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing!
Answer:
the right answer is : A
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
im smort
What is the range of the function y= e^4x
Answer:
The answer would be {y|y>0}
Step-by-step explanation:
hope this helps
which point is an x-intercept of the quadratic function
f(x)=(x-8)(x+9) ?
Answer:
(0, 8)
Step-by-step explanation:
i just got this question
Answer:
(-9,0)
Step-by-step explanation:
To find the x intercept, set y=0 and solve for x
f(x) = (x-8) (x+9)
0 = (x-8) (x+9)
Using the zero product property
x-8 =0 x+9=0
x=8 x=-9
(8,0) (-9,0) are the x intercepts
Find two numbers, if their sum is 49 and their difference is 1/2 .
This question is for my little sister who needs help with her Math.
I'm too busy to help.
Answer: 49.5 and -0.5
Step-by-step explanation:
a + b =49
a - b = 0.5
a= 49.5
b= -0.5
The two numbers are approximately 24.25 and 24.75.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
Let's call the two numbers x and y.
According to the problem, we have two equations:
x + y = 49 (since their sum is 49)
x - y = 1/2 (since their difference is 1/2)
We can solve this system of equations using the method of substitution.
First, we can rearrange the second equation to solve for one of the variables in terms of the other:
x - y = 1/2
x = y + 1/2
Now we can substitute this expression for x into the first equation:
(y + 1/2) + y = 49
2y + 1/2 = 49
2y = 48.5
y = 24.25
Now we can use this value of y to solve for x:
x = y + 1/2 = 24.25 + 1/2 = 24.75
Therefore, the two numbers are approximately 24.25 and 24.75.
Learn more about algebra here:
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a rectangle has an area of 24m². its length is 5m longer than the width.
write an expression for the rectangle's length
Answer:
2x+2(x+5)) = 24
Step-by-step explanation:
2x+ 2(x+5) = 24
x is represented by the shorter side. Multiply by 2 because of the 2 sides. For the longer side, since it is 5m longer than the shorter side, you have to write (x+5). Multiply by 2 because of the 2 sides. Finally, add them both together since it is the area and set it equal to 24.
pls help it will mean alot!!
due rn!!
Answer:
f(x) = 4^x
f(4) = 4^4 = 256
Hope this helps!
:)
the answer is 256 but i am not sure
hope this helps and be safe :)
Find the surface area.
Any help will be appreciated thank you
Answer:
Find the area of the shape
First the two triangles
3 x 4 = 12 so the area of both triangles is twelve
Now it is only 1 big rectangle left
The side lengths can be added 3 + 4 + 5 = 12
12 x 11 = 132
132+12=144
144 is the surface area/area
If you have any questions please ask
Step-by-step explanation:
what is m equal to.
4(m − 13) − 8 = 8
Answer:
m = 17
Step-by-step explanation:
[tex]4(m - 13) - 8 = 8 \\ 4(m - 13) = 8 + 8 \\ 4(m - 13) = 16 \\ (m - 13) = \frac{16}{4} \\ m - 13 = 4 \\ m = 4 + 13 \\ \huge \red { \boxed{m = 17}}[/tex]
(4x2 - 10x + 9) + (6x - 2) =
A) 4x2 - 4x + 7
B) 4x2 - 4x + 11
C) 4x2 - 16x - 7
D) 4x2 - 16x + 11
Answer:
4x^2−4x+7
Step-by-step explanation:
Let's simplify step-by-step.
4x^2−10x+9+6x−2
=4x^2+−10x+9+6x+−2
Combine Like Terms:
=4x^2+−10x+9+6x+−2
=(4x^2)+(−10x+6x)+(9+−2)
=4x^2+−4x+7
Answer:
=4x^2−4x+7
Answer:
A
Step-by-step explanation:
Solve the equation for x, and enter your answer below.
10x - 15x + 5= -45 + 40
Answer: x = 2
Step-by-step explanation:
[tex]10x - 15x + 5= -45 + 40[/tex]
subtract 5
[tex]10x - 15x= -45 + 40-5[/tex]
Combine like terms;
[tex]-5x=-10[/tex]
Divide by -5
[tex]x=\frac{-10}{-5}\\ x=2[/tex]
Answer:
[tex]x = 2[/tex]
Step-by-step explanation:
[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]
Caleb’s puppy weighs 2,250 grams. If the puppy weighed 600 grams at his last visit to the veterinarian’s office, what is the percent increase in the puppy’s weight rounded to the nearest whole number? Enter your answer in the box.
Answer:
[tex]73\%[/tex]
Step-by-step explanation:
Given: Present weight of Caleb’s puppy = 2,250 grams
Puppy weighed 600 grams at his last visit to the veterinarian’s office.
To find: percent increase in the puppy’s weight rounded to the nearest whole number
Solution:
Increase in puppy's weight = 2250 - 600 = 1650 grams
Percent increase in the puppy’s weight =( Increase in puppy's weight/Present weight of Caleb’s puppy) × 100 = [tex]\frac{1650}{2250}(100)=73.33 \%[/tex]
[tex]73.33\%[/tex] is rounded to [tex]73\%[/tex]
Please help I will give Brainliest please. Just tell what I need to do or solve I need help ASAP *image*
Answer:
Step-by-step explanation:
Hard to figure out huh
Find the area of the shaded regions:
The pink is the shaded region.
40π
You dont need paper hw since we're in quarantine
Answer:40
Step-by-step explanation:
a1 = 92 cm
b1 = 66.7 cm
a2 = 38 cm
b2 = 53.42 cm
h = 52 cm
Answer:
area=250.12. perimeter=3380
Step-by-step explanation:
In parallelogram WXYZ, what is CY?
Answer:
The correct answer is 11 ft.
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. This means that the portion marked x+4 is the same length as the portion marked 2x-7; this gives us the equation x+4=2x-7.
Subtract x from each side:
x+4-x=2x-7-x
4=x-7.
Add 7 to both sides:
4+7=x-7+7
11=x
Answer:
11
Step-by-step explanation:
On edge
A rectangular prism has a length of 12in, a height of 5in, and a width of 8in. What is its volume, in cubic in?
Answer: The volume is 480 in^3
Step-by-step explanation:
v= lwh
v= 12 * 5 * 8
v= 480 in^3
Answer:
Volume of the rectangular prism = [tex]480in.^{3}[/tex]
Step-by-step explanation:
Formula for the volume of a rectangular prism= Ah, where A= base area
& h= height
Base area(A)= Length×Width
= 12in.×8in.
= [tex]96in.^{2}[/tex]
Since height=5in.,
Volume= [tex]96in.^{2}[/tex]×5in.
= [tex]480in.^{3}[/tex]
Hope this helps!!!
Pls mark as brainliest
So do i divide by 2 each time?
There is a unique positive real number x such that the three numbers
log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.
The number x can be written as m/n, where m and n are relatively prime positive integers.
Find m+n.
Step-by-step explanation:
If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.
Let a = log82x, b = log4x and c = log2x
If a = log8 2x; 8^a = 2x... (1)
If b = log4 x; 4^b = x ... (2)
If c = log2 x; 2^c = x...(3)
Since a, b c are in GP, then b/a = c/b
Cross multiplying:
b² = ac ...(4)
From eqn 1, x = 8^a/2
x = 2^3a/2
x = 2^(3a-1)
From eqn 2; x = 4^b
x = 2^2b
From eqn 3: x = 2^c
Equating all the values of x, we have;
2^(3a-1) = 2^2b = 2^c
3a-1 = 2b = c
3a-1 = c and 2b = c
a = c+1/3 and b = c/2
Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;
(c/2)² = c+1/3×c
c²/4 = c(c+1)/3
c/4 = c+1/3
Cross multiplying;
3c = 4(c+1)
3c = 4c+4
3c-4c = 4
-c = 4
c = -4
Substituting c = -4 into equation 3 to get the value of x we have;
2^c = x
2^-4 = x
x = 1/2^4
x = 1/16
Since the number x can be written as m/n, then x = 1/16 = m/n
This shows that m = 1, n = 16
m+n = 1+16
m+n = 17
The required answer is 17.
The value of m+n in which m and n are relatively prime positive integers is 17.
What is geometric sequence?Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,
[tex]\log_82 x,\log_4x, \log_2x[/tex]
The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,
[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]
Using the base rule of logarithmic function,
[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]
Using the Power rule of logarithmic function,
[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]
The number x can be written as
[tex]\dfrac{m}{n}[/tex]
Here, m and n are relatively prime positive integers. Thus, the value of m+n is,
[tex]m+n=1+16=17[/tex]
Hence, the value of m+n in which m and n are relatively prime positive integers is 17.
Learn more about the geometric sequence here;
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