Answer:
61728394.5
Step-by-step explanation:
Using order of operations, you can either perform the multiplication first or the division first.
123,456,789 × 2 / 4 =
123,456,789 / 2 =
61728394.5
Answer:
61,728,394.5
Step-by-step explanation:
Remember to follow PEMDAS & left->right rule.
In this case, they are multiply & divide, so you can solve through left - > right rule:
123,456,789 x 2 = 246,913,578
246,913,578/4 = 61,728,394.5
61,728,394.5 is your answer.
~
which table represents vaiable solution for y=5x, where x is the number of tickets sold for the school play and y is the amount of money collected for the tickets?
Answer:
The answer is the first table: (0, 0), (10, 50), (51, 255), (400, 2000)
Step-by-step explanation:
Let's check all of the tables:
Table 1:
x = 0, y = 0 ⇒ 0 = 5 · 0 ⇒ 0 = 0
x = 10, y = 50 ⇒ 50 = 5 · 10 ⇒ 50 = 50
x = 51, y = 255 ⇒ 255 = 5 · 51 ⇒ 255 = 255
x = 400, y = 2000 ⇒ 2000 = 5 · 400 ⇒ 2000 = 2000
Multiply the polynomials. (x – 5)(x2 + 4x – 2)
the cheap answer is simply
(x-5)(x²+4x-2)
we can simply multiply the terms on one by the terms of the other and then add like-terms and simplify.
[tex]\bf (x-5)(x^2+4x-2)\implies \begin{array}{cllll} x^2+4x-2\\ \times x\\ \cline{1-1}\\ x^3+4x^2-2x \end{array}+ \begin{array}{cllll} x^2+4x-2\\ \times -5\\ \cline{1-1}\\ -5x^2-20x+10 \end{array} \\\\\\ x^3+4x^2-2x-5x^2-20x+10\implies x^3+4x^2-5x^2-2x-20x+10 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x^3-x^2-22x+10~\hfill[/tex]
Answer:
51x
Step-by-step explanation:
Write an exponential function whose graph contains the points (1, 6) and (0, 2).
Answer:
y = 2 [tex](3)^{x}[/tex]
Step-by-step explanation:
The exponential function is of the form
y = a [tex](b)^{x}[/tex]
To find a and b substitute the given points into the equation
Using (0, 2), then
2 = a [tex](b)^{0}[/tex] ⇒ a = 2
Using (1, 6), then
6 = 2 [tex](b)^{1}[/tex] ⇒ b = 3
Equation is y = 2 [tex](3)^{x}[/tex]
Evaluate 3(a + b + c) 2 for a = 2, b = 3, and c = 4.
Answer:
54
Step-by-step explanation:
Given:
[tex]3(a + b + c) 2[/tex]
Input the numbers provided into the equation
3(2 + 3 + 4)2
Add all of the numbers inside the parentheses
3(9)2
Multiply
3 * 2 = 6
6 * 9 = 54
Hey there! :)
3(a + b + c)2 ; when a = 2, b = 3, c = 4
In order to evaluate this, we simply need to plug everything in then simplify/
3(2 + 3 + 4)2
Simplify everything inside the parenthesis first.
3(9)2
Simplify.
27 × 2
Simplify.
54 is our final answer.
Hope this helped! :)
choose the equation that represents a line that represents a line that passes through points -3, 2 and 2,1 A. 5x+y=-13 B. 5x-y=17 C. x-5y=13 D. x+5y=7
bearing in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{2-(-3)}\implies \cfrac{-1}{2+3}\implies -\cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=-\cfrac{1}{5}[x-(-3)]\implies y-2=-\cfrac{1}{5}(x+3)[/tex]
[tex]\bf y-2=-\cfrac{1}{5}x-\cfrac{3}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5\left(y-2 \right)=5\left( -\cfrac{1}{5}x-\cfrac{3}{5} \right)}\implies 5y-10=-x-3 \\\\\\ 5y=-x+7\implies x+5y=7[/tex]
what is the factorization of 3x^2-8x+5
Final answer:
The quadratic expression 3x²-8x+5 is factored by finding two numbers that multiply to 15 and sum to -8, resulting in the factorization (3x-5)(x-1).
Explanation:
The factorization of the quadratic expression 3x²-8x+5 can be found by looking for two numbers that multiply to give the product of the coefficient of x² (which is 3) and the constant term (which is 5), and also sum to give the coefficient of x (which is -8). These numbers are -5 and -3, as (-5) × (-3) = 15 (which is 3 × 5) and (-5) + (-3) = -8. Therefore, the expression can be factored as (3x-5)(x-1).
Kenji and Antwan have jobs that pay differently. Antwan gets paid an hourly wage of $20. Kenji gets paid an hourly
wage of $15 and receives $35 a day in tips.
Both men worked h hours on Tuesday and earned the same amount of money.
if the equation 20h = 15h + 35 models this situation, how many hours did each man work?
Each worked 7 hours
Each worked 1 hour
Each worked 1 day.
Each earned $7.
Answer:
The answer is 7 hours
Step-by-step explanation:
20 times 7 is 140 and 15 times 7 is 105 so 105 plus 35 is 140 hence the answer is 7 hours.
The number of hours that each man works will be 7 hours. Then the correct option is A.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Kenji and Antwan have jobs that pay differently. Antwan gets paid an hourly wage of $20. Kenji gets paid an hourly wage of $15 and receives $35 a day in tips.
Both men worked h hours on Tuesday and earned the same amount of money. If the equation 20h = 15h + 35 models this situation.
Then the solution to the equation will be
20h = 15h + 35
5h = 35
h = 7 hours
The number of hours that each man works will be 7 hours. Then the correct option is A.
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Evaluate
2a + 3b for a = -1 and b = 0.
1. -1
2.-2
3. 1 1/2
4. 1/2
ANSWER ASAP PLEASE!
Answer:
So it's B.
Step-by-step explanation:
Because 2a+3b, a= -1 and b = 0
so, 2(-1) + 3(0)
-2 + 0 = -2
Hope my answer has helped you and if not i'm sorry.
Solve 4(1-x) + 3x = -2(x + 1)
Answer:
-2 = x
Step-by-step explanation:
4(1-x)+3x = -2(x+1) Distribute
4 - 4x + 3x = -2x -2 Combine Like Terms (On the same sides of the equal sign)
4 -x = -2x -2 Combine Like Terms (On different sides of the equal sign)
4 = -3x - 2 Solve
6 = -3x
-2 = x
Final answer:
The solution to the equation 4(1-x) + 3x = -2(x + 1) is found to be x = -6, after simplifying and checking by substitution back into the original equation, which confirms the solution by resulting in an identity.
Explanation:
To solve the equation 4(1-x) + 3x = -2(x + 1), we need to expand and simplify our equation:
4 - 4x + 3x = -2x - 2
4 - x = -2x - 2
Adding 2x to both sides we get:
4 + x = -2
Now subtracting 4 from both sides, we obtain:
x = -6
We then check this solution by plugging it back into the original equation, confirming that it simplifies to an identity. Therefore, x = -6 is the correct solution.
What is the equation of the line represented by the table below?
There are two ways to solve this question:
1. The quickest way to solve this question is perhaps to try substitute an x-value from the table into each of the possible answer equations and seeing if it returns the same y-value as in the table.
Let us use point (0, 2) from the table:
A. y = 12x - 5
if x = 0: y = -5
The value we wanted is 2, therefor A is not correct
B. y = -5x + 2
if x = 0, y = 2
This is correct, however to check if it really is this equation we should substitute a few more points in.
if x = -2: y = -5(-2) + 2 = 12 (correct)
if x = -1: y = -5(-1) + 2 = 7 (correct)
Given that the first three values are correct, we can say that the answer is B. y = -5x + 2.
To make sure even further however we may also substitute x = 0 into C. and D.
C. y = 10x - 5
if x = 0: y = -5 (not correct)
D. y = -2x + 2
if x = 0: y = 2 (this is correct so we must try substituting another value from the table)
if x = -2: y = -2(-2) + 2 = 6 (the value from the table for x = -2 is y = 12, therefor this is not correct)
Thus the answer is B. y = -5x + 2
2. The second method is to find the equation of the line itself without testing points. The first step is to find the gradient. We can do this using any two points, (x1, y1) and (x2, y2), and the formula for the gradient of a straight line:
m = (y2 - y1)/(x2 - x1)
Let's use the first two points from the table (-2, 12) and (-1, 7). Thus:
m = (7 - 12)/(-1 - (-2))
m = (-5)/1
m = -5
Now we can substitute this and one point (let's take (0, 2) into the formula for a straight line y - y1 = m(x - x1), where (x1, y1) is our point. Thus:
y - 2 = -5(x - 0)
y - 2 = -5x
y = -5x + 2
Therefor, looking at the possible answers, we can see that this matches answer B.
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 )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 12) and (x₂, y₂ ) = (- 1, 7) ← 2 ordered pairs from table
m = [tex]\frac{7-12}{-1+2}[/tex] = - 5
note that (0, 2) is where the graph crosses the y- axis ⇒ c = 2
y = - 5x + 2 → B
A chemical company makes two brands of antifreeze. The first brand is 65% pure antifreeze, and the second brand is 90% pure antifreeze. In order to obtain 40 gallons of a mixture that contains 80% pure antifreeze, how many gallons of each brand of antifreeze must be used?
[tex]\bf \begin{array}{lcccl} &\stackrel{solution}{gallons}&\stackrel{\textit{\% of }}{antifreeze}&\stackrel{\textit{gallons of }}{antifreeze}\\ \cline{2-4}&\\ \textit{1st brand}&x&0.65&0.65x\\ \textit{2nd brand}&y&0.90&0.9y\\ \cline{2-4}&\\ mixture&40&0.8&32 \end{array}~\hfill \to \begin{cases} x+y&=40\\ \boxed{x}=40-y\\ \cline{1-2} 0.65x+0.9y&=32 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{substituting in the 2nd equation}}{0.65\left( \boxed{40-y} \right)+0.9y=32}\implies 26-0.65y+0.9y=32 \\\\\\ 26+0.25y=32\implies 0.25y=6\implies y=\cfrac{6}{0.25}\implies \blacktriangleright y=24 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{x=40-y\implies }x=40-24\implies \blacktriangleright x=16 \blacktriangleleft[/tex]
Answer:
it should be used 16 gallons of 65% pue antifreeze and 24 gallons of 80% antifreeze.
Step-by-step explanation:
Let 'x' = amount of 65% antifreeze.
Let 'y' = amount of 90% antifreeze.
We need to obtain 40 gallons of mixture, then:
x + y = 40 gallons [1]
Also we know that the mixture should contain 80% pure antifreeze, then:
0.65x + 0.9y = 0.80(x+y) → 0.15x = 0.1y → y = 1.5x [2]
Now, subtituting the value of 'y' into [1]:
x + y = 40 gallons → x + 1.5x = 40 gallons → 2.5x = 40 gallons
⇒ x = 16 gallons.
Then: y = 40 - 16 = 24 gallons.
Now, it should be used 16 gallons of 65% pue antifreeze and 24 gallons of 80% antifreeze.
Factor completely.
-2k - k 3 - 3k 2
a.) k(-k + 1)(k - 2)
b.) -k(k - 1)(k - 2)
c.) -k(k + 1)(k + 2)
Answer:
-k (k+1) (k+2)
Step-by-step explanation:
-2k - k³ - 3k² (factor-k out)
-k (2 + k² + 3k) (rearrange to standard quadratic form)
-k (k² + 3k + 2) (factor expression inside parentheses using your favorite method)
-k (k+1) (k+2)
Answer:
Option c.
Step-by-step explanation:
The given expression is
[tex]-2k-k^3-3k^2[/tex]
We need to find the factor form of the given expression.
Taking out HCF.
[tex]-k(2+k^2+3k)[/tex]
Arrange the terms according to there degree.
[tex]-k(k^2+3k+2)[/tex]
Splitting the middle terms we get
[tex]-k(k^2+2k+k+2)[/tex]
[tex]-k((k^2+2k)+(k+2))[/tex]
[tex]-k(k(k+2)+(k+2))[/tex]
[tex]-k(k+1)(k+2)[/tex]
The factor form of given expression is -k(k+1)(k+2). Therefore, the correct option is c.
the length of a flower garden is 9 meters. the width of the garden, w, is unknown. if the area of the garden is greater than 45 square meters, what are the possible values of w, its width, in meters?
Answer:
The width should be more than 5 m. So it can be 6,7 ...
Step-by-step explanation:
The length of a flower garden is = 9 m
The width of a flower garden is = w
The area of a flower garden > 45 sq. m
The area of a flower garden = l * b
l * b > 45
9 * b > 45
the width should be more than 5 m. So it can be 6,7 ...
Answer:
w > 36
Step-by-step explanation:
i got it right on edgeinuity
Which of the following is true about the function below? 1/sqrt x+10
Answer:
what are the questions about it? cant answer if there are no questions
Step-by-step explanation:
Answer:
its domain isn (-10,∞) and its range is (0,∞)
Step-by-step explanation:
if this is the a.pex question regarding what is true about the function below, here you go
What transformation were applied to ABCD to obtain A’B’C’D?
Answer:
Rotation 90 degree counterclockwise then 2 units up.
Step-by-step explanation:
Given : Quadrilateral ABCD and A'B'C'D'.
To find: What transformation were applied to ABCD to obtain A’B’C’D.
Solution: We have given
A (3,6) →→ A'(-6,5)
B( 3,9)→→ B'(-9 ,5)
C(7,9)→→C'(-9 ,9)
D(7,6)→→D'(-6,9)
By the 90 degree rotational rule : (x ,y) →→(-y ,x) and unit 2 unit up
A (3,6) →→ A'(-6,3) →→ A'(-6,3+2)
B( 3,9)→→ B'(-9 ,3)→→ B'(-9 ,3+2)
C(7,9)→→C'(-9 ,7) →→C'(-9 ,7+2)
D(7,6)→→D'(-6,7)→→D'(-6,7+2)
Therefore, Rotation 90 degree counterclockwise then 2 units up.
The transformation applied is Rotation 90 degree counterclockwise then 2 units up.
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
The transformation which was applied to ABCD to obtain A’B’C’D be found by finding the change in the coordinates of the quadrilateral. Therefore,
A (3,6) ⇒ A'(-6,5)B( 3,9) ⇒ B'(-9 ,5)C(7,9) ⇒ C'(-9 ,9)D(7,6) ⇒ D'(-6,9)As it is observed that the change in the coordinate is 90 degrees counterclockwise then 2 units up. Therefore, the transform of the coordinates can be done as (x ,y)⇒(-y ,x)⇒(-y, x+2).
A (3,6) ⇒ A'(-6,3+2)B( 3,9) ⇒ B'(-9 ,3+2)C(7,9) ⇒ C'(-9 ,7+2)D(7,6) ⇒ D'(-6,7+2)Since the condition holds true, it can be concluded that the transformation applied is Rotation 90 degree counterclockwise then 2 units up.
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Two pools are being filled with water. Pool A
is filled at a rate of 3 gallons every hour. Pool
B is filled at a rate of 4 gallons every 1 hour.
Which expression is correct for the pool that is
filling faster?
I need help
Answer:Pool B is being filled quicker
Step-by-step explanation: It is being filled quicker because 4 is a bigger number than 3 so there is your answer
156
364
Question 4 (5 points)
In a survey, 60% of those questioned chose winter as their favorite season. If 48 people chose
winter, then how many people were surveyed?
29
32.
80
128
Question 5 (5 points)
Answer:
Third option: 80 people.
Step-by-step explanation:
Let be "x" the number of people that were surveyed.
You know that 48 people chose winter as their favorite season and these amount of people are the 60% of those questioned.
Knowing this, you can calculate the number of people that were surveyed with this procedure:
[tex]x=\frac{(48\ people)(100\%)}{60\%}\\\\x=(48\ people)(\frac{5}{3})\\\\x=80\ people[/tex]
Therefore, 80 people were surveyed. This matches with the third option.
what are the roots of the equation
[tex] {x}^{2} - 16x + 89 = 0[/tex]
in simplest a+bi form?
By completing the square,
[tex]x^2-16x+89=x^2-16x+64+25=(x-8)^2+25=0[/tex]
[tex](x-8)^2=-25[/tex]
[tex]x-8=\pm\sqrt{-25}[/tex]
[tex]x=8\pm5i[/tex]
Find the image of (1, 2) after a reflection about x= 3 followed by a reflection about x= 7.
Please Help!!!
Answer:
(9,2)
Step-by-step explanation:
(1,2) is reflected over vertical line x=3 which means since (1,2) is 2 units over from x=3 that the reflection is going to be 2 units over in the other direction from x=3 so the first image is (5,2)
Now the last image is processed by a reflection through vertical line x=7
(5,2) is 2 units from x=7 so the reflection will also be 2 units from the vertical line x=7 so the final image is (9,2).
Answer (9,2)
Answer:
(9, 2 )
Step-by-step explanation:
Under a double reflection in 2 parallel vertical lines
The y- coordinate remains unchanged
The x- coordinate is twice the difference of the parallel lines added to the original x- coordinate, that is
image = (1 + 2(7 - 3), 2 ) = (1 + 8, 2) = (9, 2 )
For which function is f(x) equal to f'(x)?
Answer:
f(x) = [tex]e^{x}[/tex]
Step-by-step explanation:
The only function that has it;s derivative equal to the function is the exponential function.
That is f(x) = f'(x) = [tex]e^{x}[/tex]
Which parent function is represented by the table?
Can someone please help?
Answer:
A. f(x) = x²
Step-by-step explanation:
Observing the values
when x= -2..............f(x)= 4..................this is x²............-2²= 4
when x= -1..............f(x)= 1......................this is x²............ -1² = 1
when x= 0..............f(x)=0.....................this is x².......... 0²= 0
when x= 1.............f(x)= 1........................this is x²........ 1²= 1
When x=2........... f(x) = 2...................... this is x²........ 2² = 4
⇒The first option is correct.
ANSWER
The correct answer is A.
EXPLANATION
We can see from the table that:
[tex]f( - 2) = {( - 2)}^{2} = 4[/tex]
[tex]f( - 1) = {( - 1)}^{2} = 1[/tex]
[tex]f(0) = {(0)}^{2} = 0[/tex]
[tex]f(1) = {( 1)}^{2} = 1[/tex]
[tex]f(2) = {(2)}^{2} =4[/tex]
In general we can conclude that,
[tex]f(x) = {( x)}^{2} = {x}^{2} [/tex]
Therefore the parent function represented by the table is
[tex]f(x) = {x}^{2} [/tex]
When you shift a function you are
Answer:
translating it
Step-by-step explanation:
Shifting a function, in mathematics and economics, refers to the process through which the entire graph or model of a function is moved either up, down, left or right. A phase shift, commonly noted by φ, is an example of this, seen when aligning a cosine or sine function with initial conditions of data. In economics, factors like income, household preferences and taxes cause shifts in the consumption function.
Explanation:When you shift a function in mathematics, you are essentially moving the entire graph of the function either up, down, left, or right. This is done by altering the function equation. For instance, the position of a block on a spring, modeled by a periodic function like a cosine function, can be shifted to the right. This rightward shift is termed a phase shift, typically denoted by the Greek letter phi (φ). The equation for the position as a function of time for the block becomes x(t) = Acos(wt + φ), where φ reflects the phase shift.
A shift in a function can also occur under economic contexts. Factors besides income can trigger the entire consumption function to shift, either parallelly up or down or make the slope of the consumption function steeper or flatter.
Shifting of functions is a crucial concept, whether we're handling a cosine or sine function to align the function with data's initial conditions or in economical situations where changes in income, taxes, or household preferences could cause significant shifts in the consumption function.
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Naomi made a triangular pyramid from cardboard. The triangular base has a height of 4 inches and a base length of 15 inches. The height of the pyramid is 6 inches. If Naomi wants to double the volume of the pyramid, which method can she use? She can double the base length of the base so that the new volume is 120 cubic inches. She can double the base length of the base so that the new volume is 360 cubic inches. She can double both the base length and height of the base so that the new volume is 240 cubic inches. She can double both the base length and height of the base so that the new volume is 720 cubic inches.
Answer:
She can double the base length of the base so that the new volume is 120 cubic inches
Step-by-step explanation:
The method she can use to double the volume of triangular pyramid is she can double the base length of the base so that the new volume is 120 cubic inches.
What is triangular pyramid?A tetrahedron, also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedral and the only one that has fewer than 5 faces.
Volume of triangular pyramid :
Volume of triangular pyramid = 1/3 × Base Area × Height
According to the question
Naomi made a triangular pyramid from cardboard.
The triangular base has a height = 4 inches
The triangular base has a base length = 15 inches
The height of the pyramid = 6 inches
Therefore,
Base area of triangular pyramid
= [tex]\frac{1}{2} * Base\ of\ triangle * Height\ of\ triangle[/tex]
= [tex]\frac{1}{2} * 15 * 4[/tex]
= 30 [tex]inches ^{2}[/tex]
So,
Volume of triangular pyramid = 1/3 × Base Area × Height
= [tex]\frac{1}{3}[/tex] × 30 × 6
= 60 [tex]inches ^{3}[/tex]
Now,
Naomi wants to double the volume of the triangular pyramid
i.e
New Volume of triangular pyramid = 120 [tex]inches ^{3}[/tex]
Which can be obtain if she can double the base length of the base
Hence, the method she can use to double the volume of triangular pyramid is she can double the base length of the base so that the new volume is 120 cubic inches.
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Given the frequency table, what percentage of the students in grades 9–10 like rap music? Round to the nearest whole percent. Band Preference for School Dance Rap Rock Country Row totals Grades 9–10 40 30 55 125 Grades 11–12 65 20 35 120 Column totals 105 50 90 245
Answer:
32%
Step-by-step explanation:
The given table in the correct format is attached in the image below. We need to tell what percentage of students from the grades 9 - 10 like rap music.
Total number of students in grades 9 - 10 = 125
Number of students in grades 9 - 10 who like rap music = 40
Percentage of students in grades 9 - 10 who like the rap music will be calculated as:
[tex]\frac{\text{Number of students in grades 9-10 who like rap music}}{\text{Total number of students in grades 9-10}} \times 100 \%[/tex]
Using the given values in above expression we get:
[tex]\frac{40}{125} \times 100\%\\\\= 32\%[/tex]
This means 32% of the students in grades 9 - 10 like rap music
Answer:
B: 32% I got it Correct on my test.
Step-by-step explanation:
Hope this helps :)
Indicate in standard form the equation of the line through K(6,4) L(-6,4)
[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-4}{-6-6}\implies \cfrac{0}{-12}\implies 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=0(x-6)\implies y-4=0\implies y=4[/tex]
Answer: [tex]y-4=0[/tex]
Step-by-step explanation:
The equation of line passing through two points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
The standard form of equation of a line is given by :-
[tex]Ax+By+C=0[/tex], where A , B , and C are integers.
Then , the equation of line passing through two points K(6,4) and L(-6,4) is given by :-
[tex](y-4)=\dfrac{4-4}{-6-6}(x-6)\\\\\Rightarrow\ y-4=(0)(x-6)\\\\\Rightarrow\ y-4=0[/tex]
Select all functions that have a y-intercept of (0,5).
f(x)=7(b)^x-2
f(x)=-3(b)^x-5
f(x)=5(b)^x-1
f(x)=-5(b)^x+10
f(x)=2(b)^x+5
Answer:
[tex]f(x)=7(b)^{x}-2[/tex]
[tex]f(x)=-5(b)^{x}+10[/tex]
Step-by-step explanation:
we know that
The y-intercept is the value of y when the value of x is equal to zero
Verify each case
case 1) we have
[tex]f(x)=7(b)^{x}-2[/tex]
so
For x=0
[tex]f(0)=7(b)^{0}-2[/tex]
[tex]f(0)=7(1)-2=5[/tex]
therefore
The function has a y-intercept of (0,5)
case 2) we have
[tex]f(x)=3(b)^{x}-5[/tex]
so
For x=0
[tex]f(0)=3(b)^{0}-5[/tex]
[tex]f(0)=3(1)-5=-2[/tex]
therefore
The function does not have a y-intercept of (0,5)
case 3) we have
[tex]f(x)=5(b)^{x}-1[/tex]
so
For x=0
[tex]f(0)=5(b)^{0}-1[/tex]
[tex]f(0)=5(1)-1=4[/tex]
therefore
The function does not have a y-intercept of (0,5)
case 4) we have
[tex]f(x)=-5(b)^{x}+10[/tex]
so
For x=0
[tex]f(0)=-5(b)^{0}+10[/tex]
[tex]f(0)=-5(1)+10=5[/tex]
therefore
The function has a y-intercept of (0,5)
case 5) we have
[tex]f(x)=2(b)^{x}+5[/tex]
so
For x=0
[tex]f(0)=2(b)^{0}+5[/tex]
[tex]f(0)=2(1)+5=7[/tex]
therefore
The function does not have a y-intercept of (0,5)
Given triangle ABC, (1,8), (-5, 13) and (7, 13) what type of triangle do these points make
Check the picture below.
so the vertex at the bottom is exactly half-way of the opposite side, and equidistant from the other two vertices, meaning the two slanted sides are twins, and thus this is an isosceles triangle.
hich is the lowest common denominator that would be used to add these four fractions?
3⁄8, 5⁄16, 2⁄3, 1⁄2
A. 48
B. 96
C. 32
D. 128
Step-by-step explanation:
To find the LCM, we must check and find the value that all four denominators can divide without a remainder.
Let's take 48
Therefore: 48/8= 6
48/16= 3
48/3= 16
48/2= 24
So, we can see that clearly 48 is our LCM
Therefore; 6(3/8)+3(5/16)+16(2/3)+24(1/2)
=18/48+15/48+32/48+24/48
=(18+15+32+24)/48
=89/48
Answer:
Its 48 to clarifiy instead of a long paragraph
Step-by-step explanation:
Which are factors of x2 – 4x – 5? Check all that apply.
1.) (x – 5)
2.) (x – 4)
3.) (x – 2)
4.) (x + 1)
5.) (x + 5)
Ask: Which two numbers add up to -4 and multiply to -5?
-5 and 1
Rewrite the expression using the above
= (x - 5) and (x + 1)
mac is 5 feet tall and cast a 4 foot 6 inch shadow. at the same time a nearby tree casts a 20 foot shadow what’s the closest high to the tree
By using the principles of similar triangles and setting up a ratio based on the given information, we can determine that the tree is approximately 22.22 feet tall.
Explanation:We can solve this problem using similar triangles. In this case, the person (Mac) and his shadow form one triangle, while the tree and its shadow form another triangle. It's given that Mac is 5 feet tall and casts a 4 foot 6 inch (or 4.5 feet) shadow. At the same time, a nearby tree casts a 20 foot long shadow. The question asks, how tall is the tree?
What we need to do here is simple: set up a proportion using the ratios of the lengths of the sides of these two triangles. The ratio is height to shadow. So, let's use the information given:
Ratio for Mac and his shadow: 5 feet/4.5 feet.Ratio for tree and its shadow: let's represent the unknown height of the tree as 'T' in feet. So, the ratio for the tree and its shadow becomes T feet/20 feet.Equating both ratios gives us: 5/4.5 = T/20. Solving this equation for 'T' will give us the height of the tree in feet.
Therefore, to compute 'T', cross multiply to get: T = (5*20)/4.5 = 22.22 feet approximately.
So, the tree is approximately 22.22 feet tall.
Learn more about Similar Triangles here:https://brainly.com/question/32489731
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