Answers
- do we need to be on the left or the right side of the line to find points that satisfy the equation?
- is the line itself included or not
To start with the second question, since y has to be greater than and not equal, the line itself is NOT included in the solution area. This means the correct answer has to have a dashed line.
The general way to know on which side of the line you have to be, is to fill in one easy point and see if the equation holds. Let's fill in (0,0), (but any point will do).
you get: 0 > 1 - 3*0, which is NOT true. So (0,0) is in an area that is not our solution. The top-right picture is therefore not the answer.
What remains is the bottom-right picture, that is the correct shaded area. All points in the shaded area satisfy the equation.
Related Questions
Write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 .
Answers
an equation of the line passing through point P(0, 0) that is perpendicular to the given line is
[tex]y=\frac{1}{9} x[/tex]
Given :
the line passing through point P(0, 0) that is perpendicular to the line
y = −9x−1
The given equation is in the form of y=mx+b
where m is the slope and b is the y intercept
Find out slope from the given equation y=-9x-1
Slope of the given equation is -9
Slope of perpendicular lines are negative reciprocal of one another
slope of perpendicular line is negative reciprocal of -9 is [tex]\frac{1}{9}[/tex]
slope of perpendicular line m=[tex]\frac{1}{9}[/tex]
The line passes through the point (0,0) that means y intercept is 0
the value of b=0
[tex]m=\frac{1}{9} , b=0\\y=mx+b\\y=\frac{1}{9} x+b\\y=\frac{1}{9} x[/tex]
an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 is
[tex]y=\frac{1}{9} x[/tex]
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The equation of the line passing through point P(0, 0) and perpendicular to the line y = -9x-1 is y = (1/9)x, with the slope of the line being the negative reciprocal of -9.
Explanation:To write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1, we first identify the slope of the given line. The slope of the line y = −9x−1 is −9, so the slope of a line perpendicular to it will be the negative reciprocal. Therefore, the perpendicular slope is 1/9.
Since the point P(0, 0) is also the y-intercept, we can directly write the equation of the perpendicular line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Thus, the equation of the line we are looking for is y = (1/9)x.
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Perpendicular bisector of MU. Find the values of m.
Answers
Suppose a random sample of 36 is selected from a population with a standard deviation of 12. if the sample mean is 98, the 95% confidence interval for the population mean is ______________.
Answers
Answer:
36%
Step-by-step explanation:
If the typical balance on Lucy's credit card is $750 and the interest rate (APR) on her credit card is 16%, how much in interest would you expect Lucy to be charged in a typical month?
Answers
[tex]i= \frac{(1+ \frac{0.16}{12} )^{12}-1}{12} \\ \\ =\frac{(1+0.0133 )^{12}-1}{12} \\ \\ =\frac{(1.0133 )^{12}-1}{12}= \frac{1.172-1}{12} \\ \\ = \frac{0.1723}{12} =0.01436=1.436\%[/tex]
Therefore, the amount of interest Lucy will be charged in a typical month is given by 0.01436 x $750 = $10.77
In two days, 48,000 gallons of oil gushed out of a well. At what rate did the oil flow from the well?
gallons per hour
Answers
24 000 gallons / 24 hours = 1 000 gallons per hour
1 000 gallons / 60 minutes = 16.(6) gallons per minute
You are paid $8.25/hour. You work 35 hours/week for 3 weeks. Your involuntary deductions are FICA (7.65%), federal withholding (13%), and state withholding (9%). How much is your realized income?
Answers
The answer is:
$609.39
Which of the following statements is true?
The interquartile range of weights of both apples is the same.
The upper quartiles of each group are within 2 grams of each other.
There were more Red Delicious apples weighed than Granny Smith apples.
The median weight of Granny Smith apples is less than the median weight of Red Delicious apples.
Answers
Ana is driving from her home in Miami to her grandmothers house in New York. On the first day she will travel 240 miles to Orlando Florida to pick up her cousin. Then they will travel 350 miles each day write an equation for the total number of miles m that Ana has traveled after d days
Answers
The equation for the total number of miles m that Ana has traveled after d days is m = 240 + 350d.
What is an equation?
An equation is an equality relationship between two expressions written on both sides of the equal to sign.
Ana travels 240 miles on the first day.
Her cousin and she travel 350 miles everyday.
If d is the number of days, then to find the equation for the total number of miles covered m,
m = 240 + 350d miles in d days.
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The equation d = m/v can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an equivalent equation solved for V.
Answers
Answer:
The equivalent equation of [tex]d=\frac{m}{V}[/tex] is [tex]V=\frac{m}{d}[/tex].
Step-by-step explanation:
The given equation is
[tex]d=\frac{m}{V}[/tex]
Where d is density, m is mass and V is volume.
We have to solve this equation for V. To separate the variable V on one side multiply both sides by V.
[tex]d\times V=\frac{m}{V}\times V[/tex]
[tex]dV=m[/tex]
Diven both sides by d.
[tex]\frac{dV}{d}=\frac{m}{d}[/tex]
[tex]V=\frac{m}{d}[/tex]
Therefore the equivalent equation of the given equation is [tex]V=\frac{m}{d}[/tex].
Find JL if JK = 17 - x, KL = 2x - 7, and K is the midpoint of JL
Answers
JK + KL = JL
(17-x) + (2x-7) = JL
Simplify.
10-x = JL
Final answer:
By setting up an equation where JK equals KL since K is the midpoint, solving for x, and substituting back to find the length of JL, we find that JL is 18 units long.
Explanation:
To find the length of JL when given that JK = 17 - x and KL = 2x - 7, and knowing that K is the midpoint of JL, we can form an equation recognizing that JL is the sum of JK and KL. Because K is the midpoint, we know that JK and KL are actually equal in length, so we can set them equal to each other and solve for x:
17 - x = 2x - 7
Combining like terms by adding x to both sides and adding 7 to both sides gives us:
24 = 3x
Dividing both sides by 3:
x = 8
Since JK and KL are equal and K is the midpoint, JL will be twice the length of either segment. Substituting x into either expression, JK or KL:
JL = 2 * JK = 2 * (17 - x) = 2 * (17 - 8) = 2 * 9 = 18
or
JL = 2 * KL = 2 * (2x - 7) = 2 * (2*8 - 7) = 2 * (16 - 7) = 2 * 9 = 18
Therefore, JL = 18.
Complete the point-slope equation of the line through (1,3) and (5,1)
Answers
Formula for slope: [tex] \frac{y2-y1}{x2-x1} [/tex]
Plug in values: [tex] \frac{1-3}{5-1}= -\frac{2}{4} = -\frac{1}{2} [/tex]
Slope: [tex]- \frac{1}{2} [/tex]
Second, we must plug into point-slope form.
Formula for point-slope: [tex]y - y1 = m(x-x1) [/tex]
Plug in the values: [tex]y - 3 = - \frac{1}{2}(x-1)[/tex]
And there you have your answer in point-slope form.
The point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1), where the slope m= -0.5 was calculated using the formula m = (y2 - y1) / (x2 - x1).
Explanation:To complete the point-slope equation of the line through points (1,3) and (5,1), we first need to find the slope of the line, which can be calculated using the formula: m = (y2 - y1) / (x2 - x1), here (x1,y1) and (x2,y2) are the coordinates of two points on the line.
Substituting in the given coordinate values gives us m = (1 - 3) / (5 - 1), which simplifies to m = -0.5, indicating a downward slope.
The point-slope form of the equation of a line is y - y1 = m(x - x1). So, substituting one of the given points (1, 3) and the calculated slope into the point-slope form gives us y - 3 = -0.5(x - 1).
Therefore, the point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1).
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Simplify. Express your answer as a single term, without a denominator. t0u/tu
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Sawyer has triple the number of Hot Wheels cars as Fisher. If Fisher has x number of cars, how many does Sawyer have?
A) x + 3
B) 3x
C) 3/x
D) 2x
Answers
True or false the product of a complex number and its conjugate is a real number
Answers
It is true that the product of a complex number and its conjugate is a real number and this can be determined by using arithmetic operations.
Let the complex number be (a + bi). Therefore, its conjugate is given by (a - bi).
The following calculation can be used to determine the product of a complex number and its conjugate:
= (a + bi).(a - bi)
Multiply (a) by (a - bi) and then multiply (bi) by (a - bi) in the above expression.
[tex]\rm =a^2-abi+abi-b^2i^2[/tex]
Simplify the above expression.
[tex]\rm =a^2-b^2i^2[/tex]
Remember the value of ([tex]\rm i^2 = -1[/tex]). So substitute the value of [tex]\rm i^2[/tex] in the above expression.
[tex]\rm = a^2+b^2[/tex]
From the above calculation, it can be concluded that it is true that the product of a complex number and its conjugate is a real number.
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The measures of two complementary angles are 3x+1 and 5x-y. Find x
A: 8
B: 12
C: 14
D: 23
Answers
David and his family went out to eat in the bill was $80 and he gave the waiter 30% how much was did he give the waiter
Answers
w = 80(0.30)
w = 24
David gave the waiter $24.
That equals 8
Then multiply by 3
That equals 24
Final answer: $24
△ABC△ABC is similar to △XYZ△XYZ. Also, angle A measures 45° and angle C measures 60°.
What is the measure of angle Y?
Answers
C & Z= 60 degrees
There is 180 degrees in a triangle.
A+C=105 degrees
180-105=75
B = Y
Y=75 degrees
Answer: The value of angle Y is 75 ° .
Step-by-step explanation:
Given Δ ABC ≈ Δ XYZ
∠ A = 45°
∠ C = 60°
To find =
∠Y =? in ΔXYZ
Solution:
In Δ ABC
∠ A = 45 °
∠ C = 60 °
∠ B = ?
∠ A + ∠ C +∠ B = 180 ° (angle sum property of triangle)
∠ B = 75 °
Since, given that Δ ABC ≈ Δ XYZ and in similar triangles ,angles of respective vertices are equal. As shown in the image attached
∠ A = 45 ° = ∠ X
∠ B = 75 ° = ∠ Y
∠ C = 60 ° = ∠ Z
So, the value of angle Y is 75 ° .
A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $504. What was the simple interest rate of the bonds? Do NOT round off a decimal answer.
Answers
Alan bowls one game, which consists of 10 frames. The number of pins he knocked down in each frame is 5, 6, 7, 5, 7, 9, 2, 4, 8, and 7. Which measure should Alan use to learn the difference of the greatest and the least number of pins he knocked down?
Answers
Answer:
Range.
Step-by-step explanation:
Alan must use the measure called Range, which indicates the dispersion between the extreme values of a variable. It is calculated as the difference between the highest and the lowest value of the variable. It is denoted as R. First the data is sorted, then it is calculated as:
R = x (n) - x (1) where,
x (n): It is the largest value of the variable.
x (1): It is the smallest value of the variable.
In the given case (5, 6, 7, 5, 7, 9, 2, 4, 8, and 7), we sort the data, and get,
2, 4, 5, 5, 6, 7, 7, 7, 8, 9
x (n) = 9
X (1) = 2
R = 9 - 2 = 7
Hope this helps!
The graphs of the equations 2x+5y=3 and 2x+5y=7 are parallel lines. Find the equation of the line that is parallel to both lines and lies midway between them.
Answers
y = mx + b
1) 2x + 5y = 3
5y = -2x + 3
Divide all terms by 5.
y = [tex] -\frac{2}{5}x [/tex] + [tex] \frac{3}{5} [/tex]
2) 2x+5y=7
5y = -2x + 7
y = [tex]- \frac{2}{5}x [/tex] + [tex] \frac{7}{5} [/tex]
Now that both equations are in standard form, we know that the equation of the line that is parallel to both lines must have the same slope as the two lines which is -2/5.
In order to find the y-intercept of the line, we have to add up the y-intercepts of the two lines and divide them by 2.
[tex] \frac{3}{5} [/tex] + [tex] \frac{7}{5} [/tex]
= [tex] \frac{10}{5} [/tex] ÷ 2
= 2 ÷ 2
= 1
The y-intercept of the equation is 1.
The equation of the line that is parallel to both lines and lies midway between them will have the slope of [tex] -\frac{2}{5}x [/tex] and a y-intercept of 1.
Solution: y = [tex] -\frac{2}{5}x [/tex] + 1
What is the midpoint of the line segment whose endpoints are (-8, 12) and (-13, -2)?
(-10.5, 5)
(-10.5, 7)
(-2.5, 7)
Answers
The midpoint of the line segment is [tex](\frac{-21}{2} ,5)[/tex].
What is midpoint of a line segment?
Midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Formula for finding the midpoints of a line segment[tex](x,y)=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2} }{2} )[/tex]
Where,
[tex](x, y)[/tex] is the midpoint of the line segment.
[tex](x_{1},y_{1}) and (x_{2} ,y_{2} )[/tex] are the endpoints of the line segment.
Let (x, y) be the midpoint of the line segment.
According to the given question
We have
(-8, 12) and (-13, -2) are the endpoints of the line segment.
Therefore, the midpoint of the line segment is given by
[tex](x,y)=(\frac{-8-13}{2} ,\frac{12-2}{2} )[/tex]
⇒[tex](x, y) = (\frac{-21}{2} ,\frac{10}{2})[/tex]
⇒[tex](x,y)=(\frac{-21}{2} ,5)[/tex]
Hence, the midpoint of the line segment is [tex](\frac{-21}{2} ,5)[/tex].
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How many distinct triangles can be formed for which m∠X = 51°, x = 5, and y = 2? zero one two
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[tex] \displaystyle{ \frac{\sin \angle X}{x}= \frac{\sin \angle Y}{y}[/tex],
where x and y are the sides opposite to angles X and Y, respectively.
Substituting the known values, we have:
[tex] \displaystyle{ \frac{51^{\circ}}{5}= \frac{\sin \angle Y}{2}[/tex], thus
[tex]\displaystyle{ \sin \angle Y=\frac{\sin 51^{\circ}}{5}\cdot2\approx \frac{0.777}{5}\cdot2=0.31[/tex].
Using a calculator, we can find that arcsin(0.31)=18 degrees, approximately.
We know that sine of (180-18)=162 degrees is also 0.31. But 162 and 51 degrees add up to more than 180 degrees.
Thus, there is only one triangle that can be formed under these conditions.
Answer: B: One
Step-by-step explanation:
f(x)=24x+7 What is the domain of f
Answers
hope this helps, God bless!
What is the simplified form of each expression? (1 point)
1.) -(10)^-1
-1/10
-1/1^10
1/10
10
2.) 1/c^-5 (1 point)
c^5
5c
-c^5
-5/c
3.) What is the value of y^-5/x^-3 for x = 2 and y = -4? (1 point)
10/3
128
-1/128
-128
4.) Is the number written in scientific notation if not, explain. 5.1 x 10^8 (1 point)
Yes; the number is written in scientific notation.
No; the first factor is not a number between 1 and 10.
No; it is not written as a number times a power of 10.
5.) What is the number written in a standard notation? (1 point)
5.71 x 10^-3
-171.3
0.0571
0.000571
0.00571
6.) Suppose that the diameters of different types of hairs are 1.7 x 10^-4 cm, 1.4 x 10^-3 cm, 1.2 x 10^-5 cm, and 1.9 x 10^-4 cm? what is the order of the hairs from least to greatest diameter? (1 point)
Who ever is good at math please ''Try'' to help me out here?! :D And Thank you so much if ya do! :P
Answers
-(10)⁻¹ = -1/10
Answer: - 1/10
2.
1/c⁻⁵ = c⁵
Answer: c⁵
3.
[tex] \frac{y^{-5}}{x^{-3}} = \frac{x^{3}}{y^{5}} [/tex]
When x = 2 and y = -4, obtain
2³/(-4)⁵ = 8/-1024 = -1/128
Answer: -1/128
4.
5.1 x 10⁸ is written in scientific notation.
Answer: Yes; the number is written in scientific notation.
5.
5.71 x 10⁻³ = 0.00571 (in standard notation)
Answer: 0.00571
6.
The given diameters are
1.7 x 10⁻⁴, 1.4 x 10⁻³, 1.2 x 10⁻⁵, 1.9 x 10⁻⁴ cm
In ascending order, they are
1.2 x 10⁻⁵, 1.7 x 10⁻⁴, 1.9 x 10⁻⁴, 1.4 x 10⁻³ cm
Answer: 1.2 x 10⁻⁵, 1.7 x 10⁻⁴, 1.9 x 10⁻⁴, 1.4 x 10⁻³
Answer:
a
b
a
d
a
a
Step-by-step explanation:
What is the best first step in solving the equation 3 + = 5? Subtract 3 from both sides. Find the cube of . Cube both sides of the equation. Subtract 5 from both sides.
Answers
What is
Write
52 over 6
as a mixed number.
Give your answer in its simplest form.
Answers
True or false if a function y = f(x) satisfies dy/dx = y, then y = e^x
Answers
If y = f(x) = e^x
Then dy/dx = f’(x) = e^x
Therefore y = dy/dx
In ΔABC, m∠B = m∠C. The angle bisector of ∠B meets
AC at point H and the angle bisector of ∠C meets AB at point K. Prove that BH = CK.
Answers
Statement Reason
m∠B = m∠C Given
AB = AC Isosceles Triangle Definition
AK=KB=AH=HC Angle Bisector Postulate
ΔBKC = ΔHBC Line BC is common side
BH = CK Corresponding parts of congruent triangles are congruent
To prove that BH = CK in triangle ABC, we can use the angle bisector theorem. The theorem states that the angle bisector of an angle in a triangle divides the opposite side into two segments proportional to the other two sides. By applying this theorem and representing BH as x and CK as y, we can show that x = y, thus proving that BH = CK.
Explanation:In triangle ABC, to prove that BH = CK, we can use the angle bisector theorem. Since m∠B = m∠C, the angle bisector of ∠B will divide the side AC into two segments proportional to the other two sides. Let's denote BH as x and CK as y. According to the angle bisector theorem, we have:
AB / BC = AH / HCAC / BC = AK / BKSince AB = AC (isosceles triangle), we can rewrite the first equation as:
x / BC = AH / HC
And the second equation as:
AC / BC = AK / y
Since AB = AC, we can substitute AC with AB:
x / BC = AK / y
Now, we can cross-multiply and solve for x and y:
x * BC = AK * HC
y * BC = x * HK
Simplifying, we get:
x = AK * HC / BC
y = x * HK / BC
Since HK = HC, we have:
x = AK
y = x
Therefore, BH = x = CK = y.
Kelly reads x hours a week. tim reads two times more than kelly and jim reads five hours more than tim. which expression represents the amount of time jim reads?
Answers
Jim= add 5
x times 2 plus add 5
Answer:
2x+ 5 expression represents the amount of time jim reads
Step-by-step explanation:
As per the statement:
Kelly reads x hours a week.
⇒Kelly read in a week = x hours
Also, tim reads two times more than kelly
⇒tim read in a week= 2x
It is also given that:
jim reads five hours more than tim.
⇒Jim = tim read + 5
⇒Jim read in a week = 2x +5
Therefore, expression represents the amount of time jim reads is, 2x+ 5
in the graph below, point D is reflected across the y axis. what are the coordinates of its image ?
Answers
Generally, whenever a point (x,y) is reflected across the y axis, the y coordinate stays the same and the sign of x coordinate changes.
So [tex](x,y)[/tex] changes to [tex](-x,y)[/tex].
Point D in the diagram shown has coordinates [tex](3,-1)[/tex]. According to the rule, the x-coordinate, 3, will change to -3 and the y-coordinate, -1, would stay the same.
Hence, our image of D after the reflection about y-axis would have coordinates [tex](-3,-1)[/tex].
ANSWER: [tex](-3,-1)[/tex]
Answer:
(-3, -1)
Step-by-step explanation: