A line 'a' and line 'b' are perpendicular to each other.
We know that the formula for the slope of line passing through two points (x1, y1) and (x2, y2) is,
m = (y2 - y1)/(x2 - x1)
A line 'a' passes through points (-3,5) and (0,0)
Let m1 be the slope of line 'a'
m1 = (0 - 5)/(0 - (-3))
m1 = -5/3
A line 'b' passes through points (3,5) and (0,0).
Let m2 be the slope of line 'b'
m2 = (0 - 5)/(0 - 3)
m2 = (-5)/(-3)
m2 = 5/3
We can observe that, m1 * m2 = -1
Since the product of slopes of the lines is -1, the lines a and b are perpendicular.
Therefore, the lines are perpendicular.
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Select ALL equations that have no solution.
A 6x – 2 – 3x = 3x – 2
B 6x – (3x + 8) = 16x
C 10 + 6x = 15 + 9x – 3x
D 11 + 3x – 7 = 6x + 5 – 3x
E 12x + 2 = 2 + 12x
The equations have no solution.
6x – 2 – 3x = 3x – 2
10 + 6x = 15 + 9x – 3x
11 + 3x – 7 = 6x + 5 – 3x.
We have determine from the given option which option has no solution.
When an equation has a solution?
An equation with no solution will be an equation when simplified, which will be a false statement.
The equation, 6x – 2 – 3x = 3x – 2
add like terms,
3x-2=3x-2
So we get,This equation has no solution
10 + 6x = 15 + 9x – 3x
10+6x=15+6x
add like terms we cannot find the value of x.
Therefore the given equation has no solution.
11 + 3x – 7 = 6x + 5 – 3x.
add like terms,
4+3x=3x-5
we cannot find the value of x.
So this equation has no solution.
Therefore, The equations 6x – 2 – 3x = 3x – 2,10 + 6x = 15 + 9x – 3x and 11 + 3x – 7 = 6x + 5 – 3x have no solution.
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The equation, 687.5 = 550(1 + 0.05t), represents the amount of money earned on a simple interest savings account. What does the value 550 represent?
The value 550 represents the initial balance in the account, which means the account started with $550.
The value 550 represents the final balance in the account, which means the account balance ended with $550.
The value 550 represents the final balance in the account, which means the account balance started with $550.
The value 550 represents the amount of interest earned, which means $550 was added to the initial balance.
Answer: The value 550 represents the initial balance in the account, which means the account started with $550.
Step-by-step explanation:
The 550 represents the start balance that was put into the account. The (1+0.05t0 is the interest being added every t years/months.
Write at least four more addition or multiplication equations for 2 in which all
the fractions have a denominator of 8.
Answer:
Step-by-step explanation:
2 + 3/8 = 7/8
2 x 7/8 = 7/4
2 + 5/8 = 9/8
2 x 9/8 = 9/4
2 + 6/8 = 8/8
2 x 8/8 = 16/8
2 + 7/8 = 15/8
2 x 15/8 = 15/4
Could Someone Help Me with this rewrite dis equation into y=mx+b
y< -3/4x+2
The equation in the form of y=mx+b will be y= -3/4x+2
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that the inequality is y< -3/4x+2,
We have to write the inequality in the form of y=mx+b
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the equation in the form of y=mx+b will be y= -3/4x+2
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Identify a value of k that transforms finto g, where g(x) = f(x) + k.
7 is a value of k that transforms f into g, where g(x) = f(x) + k. Using the concept of x and y-axis:
What is x-axis and y-axis?A two-dimensional number line, like two perpendicular axes, can be used as a coordinate system. This coordinate system is typical: The x-axis and y-axis are the names of the horizontal and vertical axes, respectively. The origin is the point at which all lines in a coordinate system intersect.
The coordinates that are shown on the x and y axes give rise to their respective names. The vertical y-axis is aligned with the horizontal x-axis. They are referred to as axes because they are perpendicular to one another.
From the graph it is observe that,
Graph of Function f(x) cut at y axis in the point 3
graph of function g(x) cut y axis in the point 4
So, the difference between the cut of y axis is k
Thus, {g(x)-f(x)=k}
Hence, k = [4 - (-3)] = 7
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Please Help Me ASAP!!!!!!!!!
Answer: 6,3
Step-by-step explanation:
Answer:
6,3
Step-by-step explanation:
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for the length of the room are
(b) y²-5y=750 , (c) 750-y(y-5)=0 and (e) (y+25)(y-30)=0
Given that:
The area of rectangular room is 750 square feet.
Let the length of the rectangular room be y feet.
Since the width of the rectangular 5 less than the length of the room.
Then the width of the given rectangular room is (y-5) feet.
We know the area of a rectangular plot is = Length×width.
Thus , the area of the rectangular room is = y(y-5) square feet
According to problem,
area of the rectangular room = 750 square feet
⇒ y(y-5) =750.........(1)
⇒ y²-5y=750 .......(2)
⇒ y²-5y-750=0
⇒ y²-30y+25y-750=0
⇒ y(y-30)+25(y-30)=0
⇒ (y-30)(y+25)=0 ......(3)
⇒ y-30=0 or, y+25=0
⇒ y= 30, -25
∵ the length of a rectangle can't be negative.
So, y=30.
We can rewrite the equation (1) in form of
(i)
y(y-5) =750
⇒750= y(y-5)
⇒750-y(y-5)=0.......(4)
(ii)
y(y-5) =750
⇒y(y-5) -750=0.......(5)
Hence , the equations that can be used to solve for the length of the room are
(b) y²-5y=750 , (c) 750-y(y-5)=0 and (e) (y+25)(y-30)=0
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in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time. group of answer choices true false
in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time is a True statement.
In a simple linear regression equation, the independent variable is the one that is used to predict the dependent variable. In this case, time would be the independent variable and sales would be the dependent variable. Therefore, it is true that in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time.A linear regression equation is used to describe the relationship between two variables, where one is the independent variable and the other is the dependent variable. The independent variable is the one that is used to predict the dependent variable. In this case, time series data is being used to forecast the trend in sales, so time would be the independent variable and sales would be the dependent variable. Therefore, it is true that in forecasting the trend in sales from time series data with a simple linear regression equation, the independent variable would be time.
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Which equation can be used to find d, the number of dollar coins Giuliana has?
The equation of the number of dollar cins giuliana has, is found to be
0.25(22 – d) + d = 10.75.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Giuliana has 22, quarters and dollar coins worth a total of $10.75.
Let the number of dollar coins be represented by d, while the number of quarter coins be represented by (22-d). Therefore, the sum of the total amount that is with Giuliana can be written as,
(1 x d) + (0.25 x (22-d)) = 10.75
d + 0.25(22-d) = 10.75
Hence, the equation can be used to find d, the number of dollar coins Giuliana has is 0.25d + 22 – d = 10.75.
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what is the slope of a line that is perpendicular to y = 2x + 3
a. 2
b. -2
c. 1/2
d. -1/2
Answer: The answer is: a
Consider the relation below
Is it a function?
Is the relation a one to one function?
Is the inverse of the relation below itself of function ?
Answer:
it may be not
take an example x=(1) y={123) and define a relation of R as the set of pairs (1,1) (1,2)(1,3) so this not a function
Simplify (28x102)-(69x10 Write the final answer in scientific notation
6.62x10-9
6.62x10-8
41x10
41x10
Please help find the value of x!!
Answer:31
Step-by-step explanation: solve it
Gabe is the human resources manager for the Advanced Scientific Research Lab. He has to record the heights (in centimeters) and weights (in pounds) for each of the scientists in the lab. Height distribution (cm) 178 163 174 186 154 167 167 181 159 165 177 191 158 Weight distribution (lbs) 157 163 190 187 183 173 184 189 193 192 177 173 168 13 Select the correct answer. What is the shape of the height and weight distribution? A. The height and weight distribution exhibit a negative and a positive skew, respectively. B. Both the height and weight distribution exhibit a positive skew. C. Both the height and weight distribution exhibit a negative skew. D. Both the height and weight distribution are symmetric about the mean. E. The height and weight distribution exhibit a positive and a negative skew, respectively.
Last option: The height and weight distributions, respectively, show positive and negative skews.
What is bar graph?Graphs are used to represent information in bar charts. To depict values, it makes use of bars that reach various heights. Vertical bars, horizontal bars, clustered bars (multiple bars that compare values within a category), and stacked bars are all possible options for bar charts.
There isn't a lot of data, but it shows that the weights have a negative skew and the heights have a positive skew, with the long tails pointing in opposite directions.
[tex]\frac{change}{strating point } X 100%[/tex]
2.5 millions of books were sold in 1991.
Millions of books sold in 1992 equaled 3.4.
Change = 0.9 (in millions).
[tex]\frac{0.9}{2.5} X 100 = 36[/tex]%
The height and weight distributions, respectively, show positive and negative skews.
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A company's minimum cost of $1000 occurs when operating for 16 hours per day. The cost of operating 8 hours per day would be $2600. Write a quadratic equation that models the company's costs.
The quadratic equation that models the company's costs is y = 25(x - 16)² + 1000
How to determine the quadratic equation that models the company's costs.From the question, we have the following parameters that can be used in our computation:
Minimum cost of $1000 at 16 hours
Operating cost of $2600 at 8 hours
A quadratic equation is represented as
y = a(x - h)² + k
The minimum point is the vertex
So, we have
(h, k) = (16, 1000)
Substitute (h, k) = (16, 1000) in y = a(x - h)² + k
y = a(x - 16)² + 1000
The cost of $2600 at 8 hours means
(x, y) = (8, 2600)
So, we have
2600 = a(8 - 16)² + 1000
Evaluate the difference
1600 = a(8 - 16)²
So, we have
64a = 1600
Divide by 64
a = 25
Substitute a = 25 in y = a(x - 16)² + 1000
y = 25(x - 16)² + 1000
Hence, the equation is y = 25(x - 16)² + 1000
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5. Two burgers and one hotdog cost $4.82. At the
same price, one
burger and two hotdogs cost $3.70.
How much does a hotdog cost?
Hello!
Let's use 'x' to represent the cost of the burger, and 'y' to represent the cost of the hotdog.
2x + y = 482
× + 2y = 370
2x + 47 = 740
-3y = -258
y = 86 cents
2x + 86 = 482
2x = 396
x = 198
A burger costs $1.98 and a hot dog costs $.86
I hope this didn't confuse you, I'm not very good at explaining!
Margot is studying the yield of bushels of wheat in comparison to the amount of rainfall, in inches, that occurs. She finds the linear regression equation to be y = 47.3 +0.78x. What does 47.3 mean in the context of the problem?
Responses
A For every inch of rain that falls 47.3 bushels of wheat are produced .For every inch of rain that falls 47.3 bushels of wheat are produced.
B If no bushels of wheat were produced, 47.3 inches of rain fell.If no bushels of wheat were produced, 47.3 inches of rain fell.
C For every bushel of wheat that is produced, 47.3 inches of rain fell.For every bushel of wheat that is produced, 47.3 inches of rain fell.
D If no rain fell, 47.3 bushels of wheat would be produced.
The thing that 47.3 mean in the context of the problem is D. If no rain fell, 47.3 bushels of wheat would be produced.
What does 47.3 mean in the context of the problem?It is important to note that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this situation, Margot is studying the yield of bushels of wheat in comparison to the amount of rainfall, in inches, that occurs. She finds the linear regression equation to be y = 47.3 +0.78x.
It should be noted that when no rain fell, 47.3 bushels of wheat would be produced. This is the constant value.
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Please answer quickly
1) The length of AC is 14.
2) The length of AB is 8.
3) The length of BC is 17.
4) The length of AB is 29.1.
5) The length of BC 53.
6) The measure m∠C is 53.8°
What is sine rule of a triangle?
AB/sin C = BC/ sin A = AC / sin B
1)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
22° + 118° + ∠C = 180°
∠C = 40°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AB = 24, ∠C = 40°, and ∠B = 22°:
AB/sinC=AC/sin B
24/sin 40° = AC/ sin 22°
AC = 13.98
AC ≈ 14
2)
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 7, ∠B = 44°, and ∠C = 53°:
AC/sin B=AB/sin C
7/sin 44° = AB/ sin 53°
AB = 8.047
AC ≈ 8
3)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
39° + ∠B + 51°= 180°
∠B = 90°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 27, ∠B = 90°, and ∠A = 39°:
BC/sinA=AC/sin B
BC/sin 39° = 27/ sin 90°
BC = 16.99
BC ≈ 17
4)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
∠A + 101° + 63°= 180°
∠A = 16°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting CB = 9, ∠A = 16°, and ∠C = 63°:
AB/sinC=BC/sinA
AB/sin 63° = 9/ sin 16°
AB = 29.09
AB ≈ 29.1
5)
Applying sum rule of interior angle
∠A + ∠B + ∠C = 180°
93° + ∠B + 58° = 180°
∠B = 29°
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AC = 16, ∠B = 29°, and ∠A = 93°:
AC/sinB=BC/sin A
16/sin 29° = BC/ sin 93°
BC = 32.95
BC ≈ 33
6)
Applying sine law in △ABC:
AB/sinC=BC/sinA=AC/sin B
Putting AB = 21, ∠A = 88°, and BC= 26:
AB/sinC=BC/sinA
21/sin C = 26/ sin 88°
sin C/21 = sin 88°/26
C = 53.82
C ≈ 53.8
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Are the lines A and B parallel? (The figure may not be drawn to scale). Please help!! Giving brainliest for whoever has the right answer
Answer:
Yes, they are parallel.
Step-by-step explanation:
61 + 119 = 180
One line is 180 degrees.
How long is the hypotenuse of a right triangle 24 square inches in area and with one leg 6 inches long? A. 24 inches B. 18 inches C. 12 inches D. 10 inches
Answer:
D
Step-by-step explanation:
area of triangle = 1/2*B*H
Assuming its one leg we write
24 = 1/2*6*h
h= 8
With this info we can use Pythagoras Theorum
[tex]a^{2} = b^{2} + c^{2}[/tex]
[tex]x^{2} = 8^{2} + 6^{2}[/tex]
[tex]x^{2} = 100[/tex]
[tex]\sqrt{100}[/tex]
[tex]x = 10[/tex]
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Step-by-step explanation:
part (a) - you plug 25 into the given function they give you and that'll be your answer
part (b) - 200 is your original amount given by the function so what is half of 200? 100. So set 100 on the right side of your function and solve for t to find the year
Apply the 30°-60°-90° Triangle Theorem to find the length of the longer leg of a triangle if the length of the shorter leg is 5√3 inches.
Answer:
15 inches
Step-by-step explanation:
The shortcut for finding the side lengths on a 30°-60°-90° triangle is that the long leg is
the short leg × √3.
So for your question:
5√3 × √3
= 5 × √3 × √3
= 5 × 3
= 15
Just in case it comes up next, the other shortcut is that the hypotenuse is double the short leg. Hypotenuse =
2 × 5√3 = 10√3
What is an equation of the line that passes through the point ( 2 , − 3 ) (2,−3) and is perpendicular to the line 2 x + 5 y = 10 2x+5y=10?
Answer: y=-[tex]\frac{5}{2}[/tex]x+2 or 5x+2y=4
Step-by-step explanation:
let’s make l1: 2x+5y=10,
then 5y=-2x+10
then y=-[tex]\frac{2}{5}[/tex]x+2
So k1=-[tex]\frac{2}{5}[/tex]let’s make the unknown line equals l2: y=k2*x + bBecause l2 is perpendicular to l1, so k2*k1=-1then who can calculate k2=-[tex]\frac{5}{2}[/tex]Because l2 passes the point (2,-3),so when x=2, we can know y=-3we can get an equation is -3=-[tex]\frac{5}{2}[/tex]*2 +bSo b=2l2: y=-[tex]\frac{5}{2}[/tex]x +2 or 5x+2y=4Which relation is also a function?
Answer:
Step-by-step explanation:
I am not 100% positive but I am 75% positive it is B.
Which expression is equivalent to (m^−2 n^−3)−3?
m6n9
m−6n−9
m−5n−6
1 over the quantity m raised to the fifth power times n raised to the sixth power end quantity
Answer:
(a) m^6·n^9
Step-by-step explanation:
You want to know an expression equivalent to (m^-2·n^-3)^-3.
Rules of exponents(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
Application[tex](m^{-2}n^{-3})^{-3}=m^{(-2)(-3)}n^{(-3)(-3)}=\boxed{m^6n^9}[/tex]
(5x+1)(3x-5)-(x-3)(5x+1)
Answer:
is 2(x minus 1)(5x + 1)
Step-by-step explanation:
2. Compare the weather on two different days using an inequality. Then see if their comparisons change by finding the absolute value of each.
Day 1:
Day 2:
Comparison of Day 1 and Day 2: _-4___ ___5____
Comparison of days with absolute value: __ _______
Inequalities are used to compare unequal expressions.
The actual comparison is: -3.5F < 5F or 5F > -3.5F
Given,
In the question:
Compare the weather on two different days using an inequality. Then see if their comparisons change by finding the absolute value of each.
Now, According to the question:
The temperatures are given as:
Temperature: -3.5F, 5F, 1.5F, -0.5F, -2F, 2.5F, -4F
From the above list, we have:
Day 1 : -3.5F
Day 2 :- 5F
By comparison,
-3.5F < 5F or 5F > -3.5F
Using absolute values, the inequalities are:
|-3.5F| < |5F| or |5F| > |-3.5F|
Hence, the actual comparison is:
-3.5F < 5F or 5F > -3.5F
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A specialty shop procures several grandfather clocks for $200 apiece and offers them to customers
or $568 each. What percentage is the mark-up?
Use the picture equation
I'm stuck I need help :(
Is this a function? Explain, why or why not!
Answer:
No
Step-by-step explanation:
A function can have only output for each input. The input 3 has two outputs 3 and 5.
The input 4 has two outputs 4 and 6.