To graph the equation y = 3x + 1 - 2, find the slope and y-intercept. Plot the y-intercept and use the slope to find additional points. Connect the points to get the graph.
Explanation:To graph the equation y = 3x + 1 - 2, we need to find the slope and the y-intercept. The slope, represented by m, is 3 in this equation. The y-intercept, represented by b, is -1. We can plot the y-intercept on the graph first, which is the point (0, -1). From there, we can use the slope to plot additional points and draw a line through them. Since the slope is 3, we can move up 3 units on the y-axis and 1 unit to the right on the x-axis to find another point. By connecting these points, we will have the graph of y = 3x + 1 - 2.
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How many solutions exist for given equation 12x + 1 = 3(4x + 1
Answer:
no solutions
Step-by-step explanation:
12x + 1 = 3(4x + 1)
Distribute the 3
12x + 1 = 12x + 3
Subtract 12x from each side
12x-12x +1 = 12x-12x+3
1 =3
This is never true, so there are no solutions
Answer:
There are no solution
Step-by-step explanation:
A(B+C)=ab+ac
3(4x+1)=12x+1
12x+1=12x+3
Subtract by 1 both sides of equation.
12x+1-1=12x+3-1
Simplify.
3-1=2
12x=12x+2
Then subtract by 12x both sides of equation.
12x-12=12x+2-12x
Simplify, to find the answer.
0=2
The sides are not equal.
It's should be no solution.
No solution is the correct answer.
solution set of 2x + y < 4
Step-by-step explanation:
Subtract
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Subtract
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y
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Multiply each term in
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y
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y
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Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.
(
2
,
0
)
ANSWER
See attachment
EXPLANATION
The given inequality is
[tex]2x + y \: < \: 4[/tex]
To solve we need to graph this inequality.
To do that we graph the corresponding linear equation
[tex]y = - 2x + 4[/tex]
This is a straight line with slope
[tex]m = - 4[/tex]
and y-intercept (0,4)
The graph of this function is to the right of the origin.
The solution set of the corresponding inequality is the half plane that is shaded.
We plot the point (0,0) into the given inequality to determine which half plane must be shaded
[tex]2(0) + 0 \: < \: 4[/tex]
[tex]0 < 2[/tex]
This is true so we shade the lower half plane. The solution set is the lower half plane shaded in the attachment.
Note that the boundary line must be a dashed line because the inequality does not involve equal sign.
Choose the function whose graph is given by:
A. y=3sin(x-2)+1
B. y=3cos(x-3)+1
C. y=6sin(x-2)-2
D. y=3sin(x-2)+2
Answer:
A
Step-by-step explanation:
a site called desmos, its a graphing calculator and you should use it :)
The function whose graph is given below is:
A) [tex]y=3\sin (x-2)+1[/tex]
Step-by-step explanation:From the graph that is provided to us we observe that,
when x=2
then f(x)=1
Hence, we will check which function satisfies this point.
B)
[tex]y=3\cos(x-3)+1[/tex]
At x=2 we have:
[tex]y=3\cos (3-2)+1\\\\i.e.\\\\y=3\cos(1)+1\\\\y>1[/tex]
Hence, option: B is incorrect.
C)
[tex]y=6\sin (x-2)-2[/tex]
when x=2 we have:
[tex]y=6\sin (2-2)-2\\\\i.e.\\\\y=6\sin 0-2\\\\i.e.\\\\y=-2\neq 1[/tex]
Hence, option: C is incorrect.
D)
[tex]y=3\sin (x-2)+2[/tex]
when x=2 we have:
[tex]y=3\sin (2-2)+2\\\\i.e.\\\\y=3\sin 0+2\\\\i.e.\\\\y=2\neq 1[/tex]
Hence, option: D is incorrect.
So, we are left with option: A
A)
[tex]y=3\sin (x-2)+1[/tex]
when x=2
we get: y=1
Similarly all the other points are satisfied.
Also, the graph of this function matches the given graph.
Complete the square for 2x2 - 4x = 14.
Answer:
2x^2-4x=14
x^2-2x=7
x^2-2x+1=8
(x-1)^2=8
Simplify 24÷(-2)(3)+7
a. -29
b. 3
c. 11
Answer:
a. -29
Step-by-step explanation:
The expression is:
24÷(-2)(3)+7
We can see that there is division, multiplication and addition involved. We will use the mathematical DMAS rule to solve the problem. So, division will be done first,
Division will give us:
24÷(-2)*(3)+7
= -12 * 3 + 7
After division, multiplication will be done:
Multiplication will give us:
= -36 +7
which equals to -29
So, option a is the correct answer ..
Find the difference 7/8 - 3/10
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The radius is 14 and CD = 22. Find EB.
Answer:
14 - [tex]\sqrt{23}[/tex]
Step-by-step explanation:
CD=22 => ED=11
AD=14 (radius). With Pythagorean theorem, [tex]AE^{2}[/tex]=[tex]AD^{2}[/tex]-[tex]ED^{2}[/tex] => AE = [tex]\sqrt{23}[/tex]
EB= AB-AE = 14 - [tex]\sqrt{23}[/tex]
The measure of EB from the expression is 5.34
The given diagram is A circle with the following sides
radius AB = 14
CD = 22
From the diagram, AB = AE + EB
Determine the measure of AE using Pythagoras theorem
AD² =AE² + ED²
14² = AE² + 11²
AE² = 14² - 11²
AE² = 196 - 121
AE² = 75
AE = √75
AE = 8.66
EB = AB - AB
EB = 14 - 8.66
EB = 5.34
Hence the measure of EB from the expression is 5.34
What is 510° expressed in radian measure?
Answer: π/180
Step-by-step explanation:
510 Degree (°) =. 8.90118 Radian (rad) Degree : A degree, a degree of arc or arc degree is a measurement of plane angle, on behalf of 1/360 of a full rotation. The symbol for degree is °. It is not an SI unit, however, it is accepted for use with SI. One degree is equal to π/180 radians.
Answer:
17pi/6 rad
Step-by-step explanation:
2 pi radians = 360 degrees
Divide both sides by 2.
pi radians = 180 degrees
From the statement above, you get the conversion factors:
(pi rad)/(180 deg) = (180 deg)/(pi rad) = 1
Both fractions above equal 1. Since multiplying by 1 does not change the number, multiply 510 deg by the fraction above that will cancel out degrees and will leave you with radians.
510 deg * (pi rad)/(180 deg) = 510pi/180 rad = 17pi/6 rad
Adam has some candy to give to his three children. He first took seven pieces for himself and then evenly divided the rest among his children. If Adam started with 13 pieces, how many did each child receive
A taxi cab costs $1.50 for the first mile and $0.75 for each additional mile. Which equation could be solved to find how many miles you can travel in a taxi for $10 given that x is the number of additional miles?
A. 1.5x - 0.75= 10
B.0.75x + 1.5= 10
C. 0.75x - 1.5=10
D. 1.5x + 0.75=10
Answer:
B.0.75x + 1.5= 10
Step-by-step explanation:
Answer:
B. 0.75(x)+1.50 = 10
and 11.333333333....
Step-by-step explanation:
Which expression is equivalent to?...
Answer:
B x^9 ∛ y
Step-by-step explanation:
(x^27 y) ^ (1/3)
x^27^(1/3) y^(1/3)
We can distribute the exponent a^b ^c = a^(b*c)
x^(27*1/3) y^(1/3)
x^9 y^(1/3)
Evaluate e1/2 to one decimal place.
1.6
13.6
3.7
7.4
I believe its 1.6
For this case we have the following expression:
[tex]e ^ {\frac {1} {2}}[/tex]
We must evaluate the expression, then:
[tex]e ^ {0.5} =[/tex]
If we enter the expression in a calculator we have that the decimal form is given by:
[tex]1.64872127[/tex]
If we round the expression we have to:
[tex]e ^ {\frac {1} {2}} = 1.7[/tex]
The option that is closest is option A.
Answer:
Option A
A stereo system is being installed in a room with a rectangular floor measuring 14 feet by 9 feet and a 7- foot ceiling. The stereo amplifier is on the floor in one corner of the room. A speaker is at the ceiling in the opposite corner of the room. What is the shortest connection
Answer:
Approximately 24 feet.
Step-by-step explanation:
Refer to the two diagrams attached (created with Geogebra.)
The wire between the speaker and the amplifier shall be routed along the wall. The length of the connection depends on the height of the point P at which the wire turns. Point P is shown in green in both diagrams.
To find the optimal position of that turning point, imagine that the two adjacent walls of the room are unfolded into two rectangles in the same plane (diagram 2.) Consider the claim: the shortest connection shall be a straight line that links the two devices when the two walls are unfolded. This explanation will show why this claim is true using the triangle inequality theorem.
Assume this claim is false: the connection will be even shorter if the wire turns at P', which is a point other than P. The length of the connection is now the sum of the two segments:
the distance between the amplifier and P', and the distance between P' and the speaker.In contrast, if the wire is routed through point P, the length of the connection will simply be
the length of the segment between the amplifier and the speaker.Point P is on the line that connects the amplifier and the speaker in diagram 2. However, P' is a point other than P, meaning that P' is off the line between the speaker and the amplifier. It is thus possible for the following three points to form a triangle:
The amplifier,The speaker, andPoint P'.By the triangle inequality theorem, the sum of any two sides of a triangle is greater than the length of the third side. To make full use of this theorem, consider the length of the three sides in this triangle:
[tex]\left\{\begin{array}{ll}\left.\begin{aligned}&\text{distance between amplifier and P}'\text{.}\\&\text{distance between P}' \text{ and speaker.}\end{aligned}\right\}&\text{Length of the second connection}\\\text{distance between amplifier and speaker}\end{array}\right.[/tex].
The sum of the first two distances shall be greater than the third. In other words, the length of the connection through P' will be greater than the length of the connection through P. This fact contradicts the assumption that the original claim is false. In other words, the claim that P gives the shortest connection is true.
Find the length of the shortest connection using the Pythagorean Theorem. Refer to the second diagram, the connection is the hypotenuse of a right triangle with
a leg of length [tex]14 + 9 = 23[/tex] feet, andanother leg of length [tex]7[/tex] feet.The length of the connection (the hypotenuse) will be:
[tex]\sqrt{23^{2} + 7^{2}}\approx 24[/tex] feet.
Which is the solution the equation 3.5(2h + 4.5)
[tex]\text{Hey there!}[/tex]
[tex]\text{In order for you to solve this equation, you need to DISTRIBUTE!}[/tex]
[tex]\text{The algebraic formula for distribution is: a(b+c) = a(b)+a(c) = ab + ac}[/tex]
[tex]\text{Now, that we have that portion solved, we can answer your question!}[/tex]
[tex]\text{3.5(2h) + 3.5(4.5)}[/tex]
[tex]\text{3.5(2h) = 7h}[/tex]
[tex]\text{3.5(4.5) = 15.75}[/tex]
[tex]\text{= 7h + 15.75}[/tex]
[tex]\boxed{\boxed{\bf{Answer:7h+15.75}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
According to the synthetic division below, which of the following statements are true
Answer:
B and D
Step-by-step explanation:
The polynomial x² + 6x - 8 ( from values in first row )
is being evaluated at x = - 5 thus the factor is (x + 5)
If (x + 5) is a factor the remainder = 0
Hence (x + 5) is not a factor since remainder = 12 ≠ 0
When the polynomial is evaluated at x = 5 it's value is 12
The remainder theorem states that f(h) = remainder, hence
f(- 5) = 12 ← remainder
calculate the scale factor for thr dilation. What is AB?
6 units
7.6 units
9.5 units
12 units
Answer:
AB is 6 units
Hope this helps
Step-by-step explanation:
The scale factor of the dilation is: 2.5.
The length of AB is: 6 units.
What is the Scale Factor of a Dilation?The scale factor of a dilation (reduction or enlargement) = dimension of new figure / corresponding dimension of original figure.
The scale factor of the image given = B'C'/BC
Scale factor = 9.5/3.8 = 2.5
To find the length of AB, divide the length of A'B' by the scale factor of the dilation.
AB = 15/2.5
AB = 6 units. (option A)
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A number is 5 more than 3 times another number. The sum of the two numbers is 33. As an equation, this is written x + 3x + 5 = 33, where x represents the smaller number. Plug in the numbers from the set {3, 5, 7, 9} to find the value of x.
The value of x that holds true for the equation is blank . So, the smaller number is blank and the larger number is blank .
Answer:
x=7
Step-by-step explanation:
Solve for x:
3 x + x + 5 = 33
x + 3 x = 4 x:
4 x + 5 = 33
Subtract 5 from both sides:
4 x + (5 - 5) = 33 - 5
5 - 5 = 0:
4 x = 33 - 5
33 - 5 = 28:
4 x = 28
Divide both sides of 4 x = 28 by 4:
(4 x)/4 = 28/4
4/4 = 1:
x = 28/4
The gcd of 28 and 4 is 4, so 28/4 = (4×7)/(4×1) = 4/4×7 = 7:
Answer: x = 7
The larger number is 26 and the smaller number is 7.
What are the numbers?To determine the solution, take the following steps:
The given equation is x + 3x + 5 = 33
Combine similar terms: x + 3x =33 - 5
Add similar terms: 4x = 28
Divide both sides by 4 : 7
The larger number = 33 - 7 = 26
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Miles paid $5824, including 4% sales tax, for an out-of-state purchase of a car. In order to calculate the amount of sales tax he owes in his state, he must first determine the price of the car without sales tax. How much did the car cost before sales tax?
Answer: $5,591
Step-by-step explanation:
4% = .04
5824 x .04 = 232.96
5824 - 232.96 = 5591
Before sales tax, the car cost $5591
What is the value of K?
Answer:
2
Step-by-step explanation:
m² = 4² + 8²
m² = 16 + 64
m² = 80
l² = k² + 4²
l² = k² + 16
m² + l² = (k + 8)² m² = 80, (b)
80 + k² + 16 = k² + 16k + 64
k² - k² - 16k = 64 - 80 -16
-16k = -32
k = -32/-16
k = 2
Which expression best estima
18-3
0 -18-3
-18+(-3)
18+(-3)
Answer:
18 + -3
Step-by-step explanation:
It is not really an estimate because it is obviously seen that +- = -.
-2(7a+4b)-6c=
Simplify
Answer:
Because of the minus sign
2 becomes - 2
The answer is -2
Multiply a and 7
Multiply a and 1
The a just gets copied along.
The answer is a
a
7*a evaluates to 7a
Multiply b and 4
Multiply b and 1
The b just gets copied along.
The answer is b
b
4*b evaluates to 4b
7*a+4*b evaluates to 7a+4b
Multiply -2 by 7a+4b
we multiply -2 by each term in 7a+4b term by term.
This is the distributive property of multiplication.
Multiply -2 and 7a
Multiply 1 and a
The a just gets copied along.
a
-2 × 7a = -14a
Multiply -2 and 4b
Multiply 1 and b
The b just gets copied along.
b
-2 × 4b = -8b
-2*(7*a+4*b) evaluates to -14a-8b
Multiply c and 6
Multiply c and 1
The c just gets copied along.
The answer is c
c
6*c evaluates to 6c
The answer is -14a-8b-6c
-2*(7*a+4*b)-6*c evaluates to -14a-8b-6c
The final answer is
-14a-8b-6c
Step-by-step explanation:
Please mark brainliest and have a great day!
I need help please?!!!!):
Answer:
4
Step-by-step explanation:
The mean of a set of data: (n₁ + n₂ + n₃...)/n, where n₁,₂,₃... are numbers in the set, and n is the number of numbers.
Plug in: (1 + 5 + 5 + 7 + 3 + 3 + 4)/7
Add: 28/7
Divide: 4
Answer:
4
Step-by-step explanation:
When finding the mean of a data set you add up all the numbers and divide it my how many numbers there is
1+5+5+7+3+3+4= 28
28 divided by 7 = 4
Mean of the set of data is 4
Hope this helps :)
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- A. Hazle <3
(1/(x-1))-(3/(x^2+2x-3))
[tex] \frac{1}{x - 1} - \frac{3}{x {}^{2} + 2x - 3 } [/tex]
[tex]
\dfrac{1}{x-1}-\dfrac{3}{x^2+2x-3} \\
\dfrac{1}{x-1}-\dfrac{3}{(x+3)(x-1)} \\
\dfrac{1\cdot(x+3)-3}{(x+3)(x-1)} \\
\dfrac{x+3-3}{(x+3)(x-1)} \\
\dfrac{x}{(x+3)(x-1)}
[/tex]
Hope this helps.
r3t40
The graph for the equation y=x-4 is shown below.
Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
A. y - x = -4
B. y - x = -2
C. y - 4 = x
D. y + 4x = 1
Answer:
A. y - x = -4
Step-by-step explanation:
y=x-4
To get infinite equations, the equation must be equal to y=x-4
We will solve each of these for y to see if they are identical
A. y - x = -4
Add x to each side
y-x+x = x-4
y = x-4
This is the same
It will give infinite solutions
B. y - x = -2
y-x+x = x-2
y =x-2
This is not the same.
It is parallel and will give no solutions
C. y - 4 = x
y-4+4 = x+4
y = x+4
This is parallel and will give no solutions
D. y + 4x = 1
y +4x-4x = -4x+1
This will intersect at a point
Answer: The correct answer is c.
Step-by-step explanation:
I just answered the question for school
Factor completely 2x5 + 10x4 - 22x3.
Answer: 2x³(x² + 5x - 11)
Step-by-step explanation:
2x⁵ + 10x⁴ - 22x³
Factor out the GCF (2x³)
2x³(x² + 5x - 11)
Since there are no values whose product is -11 and sum is +5, this cannot be factored further.
How many square inches are in 60 square feet?
Answer:
8640 in ^2
Step-by-step explanation:
1 ft = 12 in
60ft^2 * 12 inches * 12 inches
-------------- -------------- = 8640 in ^2
1 ft 1 ft
Answer:8640
Step-by-step explanation:
Convert 15/9 to a decimal
Answer:
15/9 =1.7
if u divide 3 by both of them you will have 5/3 .5/ 3 with give you 1.666666667 aproximately to 1.7 that is in one decimal plave
Step-by-step explanation:
What is the smallest angle of rotational symmetry for a square
Answer:
90°
Step-by-step explanation:
a full rotation is 360° but since there are 4 angles, then divide the 360 by 4 and you'll get 90°
Find the difference.
(-5ab+a+3) - (ab+2)
Enter the correct answer.
Need help ASAP !!!!
Answer:
-6ab+a+1
Step-by-step explanation:
add or subtract like terms.
The difference between (-5ab+a+3) and (ab+2) is calculated by combining like terms and performing the subtraction, resulting in -6ab + a + 1.
To find the difference between the two expressions (-5ab+a+3) and (ab+2), we need to subtract the second expression from the first. Applying the distributive property of subtraction over addition (i.e., a - (b + c) = a - b - c), we get:
-5ab - ab: Combine like terms by subtracting ab from -5ab which gives us -6ab.+ a: There's no like term to combine with a in the second expression, so it remains as is.+ 3 - 2: Subtract 2 from 3 which gives us +1.Putting it all together, the difference of the two expressions is -6ab + a + 1.
I to the exponent of 65
Answer:
Step-by-step explanation:
A= 1 * 1 = 2
A2 = 1 * (1 * 1)
A2 = 1 * 1
A2 = 1
a3 = 1 * 1 * (1 * 1)
a3 = 1 *1 * 1
a3 = 1 * (1*1)
a3 = 1* 1
a3 = 1
You keep on going in this manner until you hit 1^65 = 1
The only thing you have to accept is that (1 * 1) = 1