Line k contains the points (-9,4) and (9,-8) in the xy-coordinate plane. What are the two other points that lie on line k?
Answers
Answer
D. (-3, 0) and (3, -4)
Explanation
Let the coordinate of the points be A(-9, 4) and B(9, -8).
We shall look for the gradient m of line using
m = (y₂ - y₁)/(x₂ - x₁)
Substitute for x₁ = -9, y₁ = 4, x₂ = 9 and y₂ = -8
m = (-8 - 4)/(9 - -9) = -12/18 = -2/3
From option A - D given, only C and D would have the same gradient of -2/3 as line AB
To know the correct option, we shall look for the equation of the line AB, that is,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
(y - 4)/(x - -9) = (-8 - 4)/(9 - -9)
(y -4)/(x + 9) = -12/18
(y - 4)/(x + 9) = -2/3 -----------*
Between option C and D, only D satisfies the equation *
That is, using (-3, 0), we have (0 - 4)/(-3 + 9) = -4/6 = -2/3
Also, using (3, -4), we have (-4 - 4)/(3 + 9) = -8/12 = -2/3
Related Questions
On a circle of radius 9 feet, what angle would subtend an arc of length 7 feet?
_____ degrees
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The angle subtend an arc length of 7 feet is 44.56°
Given,
Radius of a circle = 9 feet
Arc length of a circle = 7 feet
Arc length :
The distance between two places along a segment of a curve is known as the arc length.
Formula for arc length:
AL = 2πr (C/360)
Where,
r is the radius of the circle
C is the central angle in degrees
Now,
AL = 2πr (C/360)
7 = 2 × π × 9 (C/360)
7 = 18 π (C/360)
7/18π = C/360
C = (7 × 360) / (18 × π)
C = (7 × 20) / π
C = 140 / π
C = 44.56°
That is,
The angle subtend an arc length of 7 feet is 44.56°
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Using solving systems using elimination addition method3x-7y=5-3x+7y=-9help
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In the elimination method, we need to eliminate one of the variables using addition or subtraction.
In this case, if we add both equations, we have that:
Since we obtained a FALSE result, we can say that this system of linear equations has NO SOLUTIONS.
In summary, using the elimination method, we add both equations. The result for that was a false r
If the snow is falling at a rate of 1 inches per hour, how many hours will it take to snow 12 inches?
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Imagine the following, we will place a tube under the snow. So we have the following
After one hour, the tube will be filled with 1 inch of snow.
After 2 hours, we will have one inch more
So, one way to calculate the amount of snow after a specific amount of hours, is simply multiplying the hours by the rate at which the height of the snow changes. IN here, the height changes 1 inch per hour. So after x hours the height of the snow would be
[tex]1\cdot\text{ x }[/tex]We want to find x, such that the height of the snow is 12.
So we have the equation
[tex]1\cdot x\text{ = 12}[/tex]which gives us that in 12 hours we will have 12 inches of snow.
There are two points (-7,6) and (7,2) the upper part is a shaded circle the ordered pairs that are solutions to the inequality on the graph.This is the line -- - - - - - - -- - -- - - - - - - -- - - - - - --- - - - - - -You can use DESMOS(6,3)(-6,6)(5,0)(2,4)
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SOLUTION
Incomplete question
PLEASE HELP
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, the team observes that the angle of elevation to the top of the mountain is 25o. From a point 1,000 feet closer to the mountain along the plain, the team finds that the angle of elevation is 29o. How tall (in feet) is the mountain? Round to two decimal places.
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The height of the mountain is 2936.39 feet.
Given,
In the question:
The angle of elevation to the top of the mountain is 25°.
To find the height of the mountain, we can draw triangles as in the image attached.
Now, According to the question:
Let's call the height of the mountain 'h', and the distance from the first point (25degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(29) = h/x
tan(25) = h/(x+1000)
tan(25) is equal to 0.4663, and tan(29) is equal to 0.5543, so:
h/x = 0.5543 -> x = h/0.5543
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.5543 + 1000) = 0.4663
h = 0.4663 * (h/0.5543 + 1000)
h = 0.8412h + 466.3
0.1588h = 466.3
h = 466.3 / 0.1588 = 2936.39 feet
Hence, the height of the mountain is 2936.39 feet.
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14. Construction workers are laying out the rectangular foundation for a new building.They want to check that the corner is 90°. They measure the diagonal as shown to be 9.5 m. Is the angle 90° Explain your reasoning.
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Explanation: We can see on the image that the two sides and the diagonal represent a triangle. We also know that this triangle to have a 90 degrees angle is will be called a right triangle. Finally, all right triangles obey the Pythagorean equation
[tex]h^2=a^2+b^2[/tex]NOTE:
h = hypotenuse
a and b = other sides
Step 1: Once we know the length of the two sides we can use the Pythagorean equation to find the length of the hypotenuse for the triangle to be a right triangle and consequently have an angle that measures 90 degrees.
Step 2: Let's calculate as follows
[tex]\begin{gathered} h^2=a^2+b^2 \\ h=\sqrt[]{8^2+6^2} \\ h=10 \end{gathered}[/tex]Step 3: We can see above, that to have an angle that measures 90 degrees (right triangle) the triangle have to have a hypotenuse = 10 which is different from 9.5.
Final answer: So the angle does not measure 90°.
in a 30 60 90° triangle giving the short leg equals 5 find a hypotenuse of the triangle
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To answer this question we need to remember that the longest and shortest side in any triangle are always opposite to the largest and smallest angle, respectively.
With this in mind we can draw the triangle:
Now, we need to find the hypotenuse. To do this we can use the cosine function for the angle 60. Remember that the cosine function is given as:
[tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex]In this case we have that:
[tex]\begin{gathered} \cos 60=\frac{5}{\text{hyp}} \\ \text{hyp}=\frac{5}{\cos 60} \\ \text{hyp}=10 \end{gathered}[/tex]Therefore the hypotenuse is 10.
hi, can you help me answer this question please, thank you!
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The correct option is B
Explanation:The given statement shows that there is a 95% chance that the mean of a sample of 29 gadgets will be between 12.8 and 34.9
Mrs. Smith stores water in different size bottles. she has 4 containers that are 2 1/2 quarts each and 3 containers that are 425 cups each. how many fluid ounces of water does she have?
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Answer:
The total volume of fluid ounces of water she have is;
[tex]422\text{ ounces}[/tex]Explanation:
Given that she has 4 containers that are 2 1/2 quarts each
[tex]\begin{gathered} V_1=4\times2\frac{1}{2}\text{ quarts} \\ V_1=10\text{ quarts} \end{gathered}[/tex]Recall that to convert quarts to ounce;
[tex]1\text{ quart }=32\text{ ounces}[/tex][tex]\begin{gathered} V_1=10\text{ quarts }=10\times32\text{ ounces} \\ V_1=320\text{ ounces} \end{gathered}[/tex]Also, she has 3 containers that are 4.25 cups each;
[tex]\begin{gathered} V_2=3\times4.25\text{ cups} \\ V_2=12.75\text{ cups} \end{gathered}[/tex]To convert cups to ounces;
[tex]1\text{ cup}=8\text{ ounces}[/tex]So;
[tex]\begin{gathered} V_2=12.75\text{ cups }=12.75\times8\text{ ounces} \\ V_2=102\text{ ounces} \end{gathered}[/tex]The total volume of fluid ounces of water she have is;
[tex]V=V_1+V_2[/tex]substituting the values;
[tex]\begin{gathered} V=320+102\text{ ounces} \\ V=422\text{ ounces} \end{gathered}[/tex]Therefore, the total volume of fluid ounces of water she have is;
[tex]422\text{ ounces}[/tex]Please help this is due tomorrow!!
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The expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The given polynomial expression below is:
⇒ 10x⁵y⁷/5x⁵y · 3x⁴y⁸/3x⁻³y¹⁰
Apply the division operation in the constant terms
⇒ 2x⁵y⁷/x⁵y · x⁴y⁸/x⁻³y¹⁰
Apply the arithmetic operation in the Exponents of the same base variables
⇒ 2y⁶ · x⁷y⁻²
⇒ 2y⁶⁻² · x⁷
⇒ 2y⁴ · x⁷
⇒ 2x⁷· y⁴
Therefore, the expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
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Order the numbers from least (1) to greatest (10).ITEM BANK-Move to Battom3.564.034.212V12mor
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To order these numbers, we begin with the whole part of each number. In the case of having two numbers with equal whole part, we look for the greatest tenth. So, the order would be
[tex]3.56;4.03;4.2;12[/tex]Notice that, 4.03 is less than 4.2, because its tenth is less.
CRITICAL THINKING Describe two different sequences of transformations in which the blue figure is the image of the red figi 1 1 2 B I y ET
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1) rotation 90° clockwise over the origin and a reflection over the x-axis
2) rotation 90° counter clockwise over the origin and reflection over y-axis
Find the slope of the line defined by each pair of points.:( points :(-1,4). Points. (-1,-5)
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Notice that the x coordinate of both points is the same, therefore the line is a vertical line.
Answer: The slope is undefined.
8x +1312x + 7X == [?]Enter
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The two angles given in the problem lie the opposite of each other with respect to the transversal line. This means that these two angles are supplementary angles. The sum of the two angles will be equal to 180 degrees, hence, we can set up an equation solving for x. We have
[tex]8x+13+12x+7=180[/tex]Solve for x, we have
[tex]\begin{gathered} 20x+20=180 \\ 20x=180-20 \\ \frac{20x}{20}=\frac{160}{20} \\ x=8 \end{gathered}[/tex]The value of x
Finding Slope
HELP ME PLS
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The slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
The first point = (-5,6)
The second point = (-9,-6)
The slope of the line defined as the change in y coordinates with respect to the change in x coordinates.
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = [tex]\frac{-6-6}{-9-(-5)}[/tex]
= -12/-4
= 3
Hence, the slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
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Question 8 of 10What is the slope of the line described by the equation below?y=-x+ 8A. 8B. 1OOOC. -8O D.-1SUBMIT
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We have the following equation
y = -x + 8
this equation is writen in slope intercept form
y = mx + b
where m is the slope
From the above, we can see that the slope is m = -1
Solve the following compound inequalities. Use both a line graph and interval notation to write each solution set.
t+1-5 ort+1> 5
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The value of the inequality expression given as t + 1 < -5 or t + 1 > 5 is (-oo, -6) u (4, oo)
How to determine the solution to the inequality?The inequality expression is given as
t + 1 < -5 or t + 1 > 5
Collect the like terms in the above expressions
So, we have
t < -5 - 1 or t > 5 - 1
Evaluate the like terms in the above expressions
So, we have
t < -6 or t > 4
Hence, the solution to the inequality is t < -6 or t > 4
Rewrite as an interval notation
(-oo, -6) u (4, oo)
See attachment of the number line
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Find the equation of the linear function represented by the table below in slope-intercept form.xy1-82-123-164-20
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Given :
The table for y and x is given as
Explanation :
The slope-intercept form is determined as
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]First find the slope of the equation using the coordinates from the table.
[tex]m=\frac{-12-(-8)}{2-1}=\frac{-12+8}{1}=-4[/tex]Now substitute the values in the slope-intercept form.
[tex]\begin{gathered} y-(-8)=-4(x-1) \\ y+8=-4(x-1) \\ y=-4x+4-8 \\ y=-4x-4 \end{gathered}[/tex]Answer:
Hence the equation of line is determined as
[tex]y=-4x-4[/tex]If f (x) = 4x^3 - 25x^2 – 154x+ 40 and (x - 10) is a factor, what are the remaining factors?
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Parking spaces in a parking lot are parallel to each other. Find the measure of the two
unknown angles and explain your reasoning.
measure of angle m:
measure of angle n:
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Answer:
m = 70° , n = 110°
Step-by-step explanation:
m and 110° are same- side interior angles and sum to 180°
m + 110° = 180° ( subtract 110° from both sides )
m = 70°
n and 110° are corresponding angles and are congruent , then
n = 110°
Lne segment AC and BD are parallel, what are the new endpoints of the line segments AC and BD if the parallel lines are reflected across the y-axis?
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Given a point P = (x, y) a reflection P' alongside the y axis of that point follows the rule:
[tex]P=(x,y)\Rightarrow P^{\prime}=(-x,y)[/tex]We need to multiply the x coordinates of the points by (-1)
The cordinates of the points in the problem are:
A = (2, 5)
B = (2, 4)
C = (-5, 1)
D = (-5, 0)
Then the endpoints of the reflection over the y axis are:
A' = (-2, 5)
B' = (-2, 4)
C' = (5, 1)
D' = (5, 0)
Which is the second option.
Hooke's Law says that the force exerted by the spring in a spring scale varies directly with the distance that the spring is stretched. If a 20 pound mass suspended on a spring scale stretches the spring 20 inches, how far will a 29 pound mass stretch the spring? Round your answer to one decimal place if necessary.
Answers
The Hooke's law is given by:
F = k*x
Where:
F = force
k = constant factor
x = distance
If F = 20 and x = 20
20 = k*20
Solving for k:
20/20 = k
k = 1
So: how far will a 29 pound mass stretch the spring?
29 = 1* x
Solving for x:
29/1 = x
x = 29 in
A grocer mixed grape juice which costs $1.50 per gallon with cranberry juice whichcosts $2.00 per gallon. How many gallons of each should be used to make 200 gallons of cranberry/grape juice which will cost $1.75 per gallon?
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Let x be the amount of gallons of grape juice we are using to get the mixture we want. Let y be the amount of gallons of cranberry juice used to get the desired mixture.
Since we are told that we want a total of 200 gallons of the new mixture, this amount would be the sum of gallons of each liquid. So we have this equation
[tex]x+y=200[/tex]To find the values of x and y, we need another equation relating this variables. Note that since we have 200 gallons of the new mixture and the cost per gallon of the new mixture is 1.75, the total cost of the new mixture would be
[tex]1.75\cdot200=350[/tex]As with quantities, the total cost of the new mixture would be the cost of each liquid. In the case of the grape juice, since we have x gallons and a cost of 1.50 per gallon, the total cost of x gallons of grape juice is
[tex]1.50\cdot x[/tex]In the same manner, the total cost of the cranberry juice would be
[tex]2\cdot y[/tex]So, the sum of this two quantites should be the total cost of the new mixture. Then, we get the following equation
[tex]1.50x+2y=350[/tex]If we multiply this second equation by 2 on both sides, we get
[tex]3x+4y=700[/tex]Using the first equation, we get
[tex]x=200\text{ -y}[/tex]Replacing this value in the second equation, we get
[tex]3\cdot(200\text{ -y)+4y=700}[/tex]Distributing on the left side we get
[tex]600\text{ -3y+4y=700}[/tex]operating on the left side, we get
[tex]600+y=700[/tex]Subtracting 600 on both sides, we get
[tex]y=700\text{ -600=100}[/tex]Now, if we replace this value of y in the equation for x, we get
[tex]x=200\text{ -100=100}[/tex]Thus we need 100 gallons of each juice to produce the desired mixture.
Simplify using the laws of exponents. Use the box to the right of the variable as it’s simplified exponent.
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Given:
[tex](15m^8)\placeholder{⬚}^3[/tex]To find:
to simplify using laws of exponents
First, we need to expand the expression:
[tex]\begin{gathered} In\text{ exponent laws, a}^3\text{ = a }\times\text{ a }\times\text{ }a \\ \\ Applying\text{ same rule:} \\ (15m^8)\placeholder{⬚}^3\text{ = \lparen15m}^8)\times(15m^8)\text{ }\times(15m^8) \\ =\text{ 15 }\times\text{ }m^8\times\text{15 }\times\text{ }m^8\times\text{15 }\times\text{ }m^8\text{ } \\ \\ collect\text{ like terms:} \\ =\text{ 15 }\times\text{ 15 }\times15\text{ }\times m^8\times\text{ }m^8\times\text{ }m^8\text{ } \end{gathered}[/tex][tex]\begin{gathered} Simpify: \\ 15\times15\times15\text{ = 3375} \\ \\ m^8\text{ }\times\text{ m}^8\text{ }\times\text{ m}^8 \\ when\text{ multiplying exponents with same base, } \\ \text{we will pick one of the base and add the exponents together } \\ m^8\text{ }\times\text{ m}^8\text{ }\times\text{ m}^8\text{ = m}^{8+8+8} \\ =\text{ m}^{24} \end{gathered}[/tex][tex]\begin{gathered} 15\times15\times15\times m^8\times m^8\times m^8\text{ = 3375 }\times\text{ m}^{24} \\ \\ =\text{ 3375m}^{24} \end{gathered}[/tex]Determine the prime factorization of 350
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define Prime factorization.
Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself. Examples of prime numbers are 2,3,5,7...etc.
STEP 2: Find the prime factors of the given number
Prime factorization of any number means to represent that number as a product of prime numbers.
We start by dividing the number by the lowest possible prime numbers.
STEP 3: Express 350 as a product of its prime factors
[tex]\begin{gathered} \text{Prime factors}=2,5,5,7 \\ \text{Product of prime factors=}2\times5\times5\times7 \\ =2\times5^2\times7 \end{gathered}[/tex]Hence, the prime factorization of 350 is given as:
[tex]2\times5^2\times7[/tex]Solve the quadratic equation by completing the square.x^2+18x+75=0First choose the appropriate form and fill in the blanks with the with the correct numbers. Then solve the equation. If there is more than one solution, separate them with commas.
Answers
we have the quadratic equation
x^2+18x+75=0
complete the square
x^2+18x=-75
x^2+18x+81=-75+81
x^2+18x+81=6
rewrite as perfect squares
(x+9)^2=6
Find out the solutions
square root both sides
[tex]x+9=\pm\sqrt[\square]{6}[/tex][tex]x=-9\pm\sqrt[\square]{6}[/tex]The first solution is
[tex]x=-9+\sqrt[\square]{6}[/tex]The second solution is
[tex]x=-9-\sqrt[\square]{6}[/tex]Question 3 (9 points)Find Pred then green)What is the probability that you select a red marble, then a green marbleP (red) -P (then Green) - (Total of marbles will be 1 less)P (red then green) = *Hint: Multiply
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Solution
Step 1
Write out an expression for the probability
[tex]\text{The probaility of an event occurring= }\frac{\text{Number of required events}}{\text{Total number of events}}[/tex]Step 2
Define terms
Total number of events = 8 marbles
Number of required events = red then marble
Number of red = 2 marbles2
Number of green = 2 marbles
Note: The question is without replacement.
Step 3
Get the required probabilities and the answer
[tex]\begin{gathered} Pr(\text{red marble) = }\frac{2}{8} \\ Pr(\text{green marble without replacement) =}\frac{2}{7} \end{gathered}[/tex]Hence the Pr(of red then green) is given as
[tex]\begin{gathered} =Pr(\text{red) }\times Pr(green\text{ without replacement)} \\ =\frac{2}{8}\times\frac{2}{7}=\frac{1}{14} \end{gathered}[/tex]Hence the probability of picking a red marble then a green marble = 1/14
assume the rate of inflation is 7% per year for the next 2 years. what will be the cost of goods 2 years from now adjusted for inflation if the goods cost $330.00 today? round to the nearest cent
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To find the cost of the goods after two years we are going to use the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where P is the cost now, r is the inglation rate in decimal form, n is the number of times the interest is taken per year and t is the time.
In this case we have P=$300.00, r=0.07, n=1 (once per year) and t=2 (two years). Plugging this values we have:
[tex]A=330(1+\frac{0.07}{1})^{1\cdot2}=377.82[/tex]Therefore after two years the cost will be $377.82
O EQUATIONS AND INEQUALITIESSolving a decimal word problem using a linear equation with th.
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Given:
[tex]PlanA=0.16\text{ for each minutes of calls}[/tex][tex]PlanB=25\text{ monthly fee plus 0.12 for each minute of calls}[/tex]To Determine: The numbers of calls for the which the two plans are equal
Solution
Let x be the number of minutes of calls for which the two plans are equal
The cost of plan A is
[tex]C_{ost\text{ of plan A}}=0.16x[/tex]The cost of plan B
[tex]C_{ost\text{ of plan B}}=25+0.12x[/tex]If the cost for the two plans are equal, then
[tex]0.16x=25+0.12x[/tex]Solve for x
[tex]\begin{gathered} 0.16x-0.12x=25 \\ 0.04x=25 \\ x=\frac{25}{0.04} \\ x=625 \end{gathered}[/tex]Hence, the number of minutes of calls for which two plans are equal is 625 minutes
[tex]6x - 9y - 7x + - 6y[/tex]simplify please
Answers
6x - 9y - 7x + -6y
To simplify the expression add the like terms
The like terms are the terms which have the same variable and same degree
6x, -7x are like terms
-9y, -6y are like terms
So let us add them
(6x + -7x) + (-9y + -6y)
6 + -7 = -1
6x + -7x = -x
-9 + - 6 = -15
-9y + -6y = -15y
(6x + -7x) + (-9y + -6y) = -x + -15y
Remember (+)
