The standard form of a line passing through the points (-1, -3) and (2, 1) is 4x - 3y = 5.
The slope of the given line, m = (1 - (-3))/(2 - (-1)) = (1 + 3)/(2 + 1) = 4/3.
Computed using the formula for the slope of a line, m = (y₂ - y₁)/(x₂ - x₁), when a line passes through the points (x₁, y₁) and (x₂, y₂).
The point intercept form of a line is y - y₁ = m(x - x₁) when the line passes through the point (x₁, y₁) and has the slope m.
Thus, the given line in the point intercept form can be written as:
y - 1 = (4/3)(x - 2).
The standard form of a line is ax + by = c.
To convert the point intercept form to the standard form, we do as follows:
y - 1 = (4/3)(x - 2),
or, 3(y - 1) = 3(4/3)(x - 2) {Multiplying both sides by 3},
or, 3y - 3 = 4x - 8 {Simplifying},
or, 8 - 3 = 4x - 3y {Rearranging},
or, 4x - 3y = 5 {Rearranging and simplifying}.
Thus, the standard form of a line passing through the points (-1, -3) and (2, 1) is 4x - 3y = 5.
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9 times 2/3=
SIMPIFIED
Answer:
6
Step-by-step explanation:
9 x 2/3
9/1 x 2/3 = 18 / 3 = 6
PLEASE HELP!!!!!!!!!!!!I BEG YOU
For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: y = negative 4 x squared
The values of a, b, and c are -4,0 and 0 and the parabola opens downward with y-intercept (0,0).
we have
y=-4x^2
What is the standard form of the quadratic equation?The quadratic equation in standard form is equal to
ax^2+bx+c=0
So,In this problem
a=-4, b=0 and c=0
The y-intercept is the value of y when the value of x is equal to zero
y=-4(0)^2=0
The y-intercept is the point (0,0)
The coefficient a is negative, therefore the parabola opens down.
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if you anwser the question i give you brainly
The graph is in a reciprocal relationship with Option C
What is a Function ?A function is a mathematical statement used to relate a dependent and n independent variable.
The function is represented by the graph
The nature of the graph is exponential
and the equation is determined by the points on the graph
( 1,1) ( 2,4) '
The equation is
y = ( 1/4) 4ˣ
The inverse of the function will be found by replacing the y variable with x and vice versa and then solving to bring the function into the form of x.
x = ( 1/4) [tex]\rm 4^y[/tex]
Plotting this gives the answer as Option C
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According to a report in USA Today, more and more parents are helping their young adult children get homes. Suppose eight persons in a random sample of 60 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion
The margin of error for a 95% confidence interval for the population proportion is 0.0815.
Given sample size=60 and confidence interval of 95%.
We have to calculate margin of error for a confidence interval of 95%.
Margin of error is the difference between actual values and calculated values. Margin of error is a part of z test.
We have been given sample size=60.
8 people have received help from their parents from the sample.
p=8/60=0.13
which is sample proportion.
z=1-0.13
=0.87
To calculate standard error=[tex]\sqrt{p*z/n}[/tex]
=[tex]\sqrt{0.13*0.8/60}[/tex]
=0.0416
at 95% confidence interval
z(α/2)=1.96
therefore margin of error=1.96*0.0416
=0.081536
=0.0815
Hence the margin of error for 95% confidence interval is 0.0815
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A searchlight uses a parabolic mirror to cast a beam of light in parallel rays where the light bulb is located at the focus of the parabola in order to give the best illumination. The mirror is modeled by y^2=36(x-10), where the measurements are in cm. What is the location of the light bulb?
Answer:
the third option
Step-by-step explanation:
Our equation is
[tex] {y}^{2} = 36(x - 10)[/tex]
Equation of a vertical parabola is
[tex]( {y - k)}^{2} = 4p(x - h)[/tex]
where (h,k) is the center
The focus is
(h+p, k)
Equation of directrix is
x= h-p,
Here the center is (10,0)
Next, we factor out 4 in the original equation
[tex]4(9)[/tex]
So we have
[tex] {y}^{2} = 4(9)(x - 10)[/tex]
So our p=9,
So our focus is
(10+9,0) or (19,0)
The third option is the answer
The location of the light bulb is at point A. (10, 0).
Option A is the correct answer.
We have,
To find the location of the light bulb, we need to identify the coordinates (x, y) at which the light bulb is located.
In the given parabolic mirror equation, y² = 36(x - 10), the vertex form of the equation for a parabola with a vertical axis is (h, k), where h is the
x-coordinate of the vertex and k is the y-coordinate of the vertex.
Comparing the given equation with the standard form
(y - k)² = 4a(x - h),
we can see that h = 10 and k = 0.
So, the location of the light bulb is at the point (10, 0).
Therefore,
The location of the light bulb is at point A. (10, 0).
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A searchlight uses a parabolic mirror to cast a beam of light in parallel rays where the light bulb is located at the focus of the parabola in order to give the best illumination.
The mirror is modeled by y² = 36 (x-10), where the measurements are in cm.
What is the location of the light bulb?
A. (10, 0)
B. (14, 0)
C. (19, 0)
D. (36, 0)
find f(-1) and find one value of x for which f(x)=0
[tex]f( - 1) = - 3[/tex]
[tex]f(x) = 0 \\ for \: x = 2 \: or \: x = - 2[/tex]
look at image.................
Answer:
-1/3
Step-by-step explanation:
When x is 1, y is 5
When x is 4, y is 4
5-4=1
1-4=-3
1/-3=-1/3
Which equation represents the line that is perpendicular to and passes through (-40,20)?
The equation of the perpendicular line to the given line is: y = -5/4x - 30.
What is the Equation of Perpendicular Lines?The slope values of two perpendicular lines are negative reciprocal of each other.
Given that the line is perpendicular to y = 4/5x+23, the slope of y = 4/5x+23 is 4/5. Negative reciprocal of 4/5 is -5/4.
Therefore, the line that is perpendicular to it would have a slope (m) of -5/4.
Plug in m = -5/4 and (x, y) = (-40, 20) into y = mx + b to find b:
20 = -5/4(-40) + b
20 = 50 + b
20 - 50 = b
b = -30
Substitute m = -5/4 and b = -30 into y = mx + b:
y = -5/4x - 30
The equation of the perpendicular line is: y = -5/4x - 30.
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Can you please find the value of x
Answer:
14
Step-by-step explanation:
when two lines intersect, the opposite angles are equal: vertical angles rule
this means that 88 and 6x + 4 are the same, therefore we get the equation 6x+4 = 88.
subtracting 4 from both sides, we find that 6x = 84
we get our final answer by dividing each side of the equation by 6:
x = 14
omg help me please!!!!
help me i give you brainly
Answer:
False
Step-by-step explanation:
I'm not a 100 percent though
Pleased help asp
Please help asp
Please help asp
b.HELPPPP MEEEE PLSSSS AND THANK YOUU
Answer:
A. (3, 8) and [tex]2\sqrt{2}[/tex]
B. (2, 4) and [tex]2\sqrt{10}[/tex]
Step-by-step explanation:
Midpoint formula: [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2})[/tex]
Distance formula: [tex]\sqrt{(x_{2}-x_{1}) ^2+(y_{2}-y_{1}) ^2 }[/tex]
A. plug in the points in the formulas
(4, 7) and (2, 9)
Midpoint:
[tex](\frac{4 + 2}{2} , \frac{7+9}{2} )=6/2, 16/2 = (3,8)[/tex]
Length:
[tex]\sqrt{(2-4)^2+(9-7)^2}=\sqrt{4+4} =\sqrt{8} =2\sqrt{2}[/tex]
B.
(5, 5) and (-1, 3)
Midpoint:
[tex](\frac{5-1}{2} , \frac{5+3}{2} )=4/2,8/2=(2,4)[/tex]
Length:
[tex]\sqrt{(-1-5)^2+(3-5)^2} =\sqrt{-6^2+-2^2} =\sqrt{36+4} =\sqrt{40} = 2\sqrt{10}[/tex]
Can you consider marking my answers as brainliest lol it would mean a lot. Hope this helped.
Please answer with everything needed i appreciate everyones help:))
Answer:
[tex]a = (h)(2h - 5)[/tex]
Answer:
Area of the rectangle = 2h² - 5
Step-by-step explanation:
• base length l = 5 less than twice the height h
= 2h - 5
• height = h
Area of rectangle = base × height
⇒ l × h
⇒ (2h - 5)(h)
⇒ 2h² - 5
Each statement describes a transformation of the graph of . Which statement correctly describes the graph of y = f(x − 7) + 3?
A.
It is the graph of f translated 3 units up and 7 units to the left.
B.
It is the graph of f translated 7 units down and 3 units to the right.
C.
It is the graph of f translated 7 units up and 3 units to the right.
D.
It is the graph of f translated 3 units up and 7 units to the right.
Answer: D. It is the graph of f translated 3 units up and 7 units to the right
Step-by-step explanation:
the +3 part of the equation makes the function translated vertical 3 units
then the x - 7 part makes it translate horizontal to the right 7 units (always the opposite of the sign)
because when
x-7=0,
x=7
The value of an investment portfolio decreased by 8 % in 2010. In 2011, its value increased by 5% of
its value in 2010. Given that the value of the portfolio at the end of 2011 was $ 61 824, find its
original value.
Answer:
$63422.42
Step-by-step explanation:
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the tens digit of a two digit number is 5 greater than the units digit. if you subtract the reversed number from the original number you will get 1/4 of the original number
what is the original number
From the given information, the original number is 180. 02
How to determine the original numberLet the unit digit be x
The unit in tens is x+ 5
The original number = 10(x+5) + x = 11x + 50
The reversed number = 10x+ (x+5) = 11x+5
From the information given, we have that
(11x + 50) - (11x + 5) = 1/4 (11x + 50)
Expand the expression
11x + 50 - 11x - 5 = 1/ 4(11x + 50)
Collect like terms
11x - 11x + 50 - 5 = 1/ 4 (11x + 50)
45 = [tex]\frac{11x + 50}{4}[/tex]
Cross multiply
45 * 4 = 11x + 50
180 = 11x + 50
11x = 180 -50
11x = 130
x = 130/11
x = 11. 82
To find the original number, we have
Original number = 11x + 50
Substitute the value of x
Original number = 11(11.82) + 50
Original number = 130. 02 + 50
Original number = 180. 02
Therefore, the original number is 180. 02
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The question "How many servers will be needed to reduce the waiting time of restaurant customers to less than 9 minutes?" is a type of
The question posed in the task content is a goal seeking analysis type of question.
How many servers will be needed to reduce the waiting time of restaurant customers to less than 9 minutes is a goal seeking analysis question.
Goal seeking analysisA goal seeking analysis question is a type of question which helps to determine the efficient and effective measure of achieving a goal either individually or in a group.
The question will help the manager of the restaurant to determine how many servers is needed in order to reduce the waiting time of customers.
Complete question:
The question "How many servers will be needed to reduce the waiting time of restaurant customers to less than 9 minutes?" is a type of
a. goal-seeking analysis.
b. what-if analysis.
c. sensitivity analysis.
d. utility modeling.
a. goal-seeking analysis.
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A pillar 80 m tall casts a shadow 39 m long. Find the distance between the top of the pillar and the foot of the shadow
Answer:
89
Step-by-step explanation:
[tex] \sqrt{ {80}^{2} + {39}^{2} } = 89[/tex]
The distance between the top of the pillar and the foot of the shadow is 80 meters.
How to find the distanceLet's call the distance we want to find "x".
In particular, set up the following proportion:
pillar height / shadow length = distance / shadow length
Plugin the given values
80 / 39 = x / 39
Simplifying and solving for x
x = (80 / 39) * 39
x ≈ 80
Therefore, the distance between the top of the pillar and the foot of the shadow is 80 meters.
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math!!
PLEASE HELP!!
what is the angle indicated in the triangle below??
a) 46 degrees
b) 65°
c) 44°
d) 35°
e) 55°
f) 90°
Answer:
e) 55°
Step-by-step explanation:
use the tangente ratio
[tex]tan\alpha =\frac{10}{7} =1.42857[/tex]
[tex]angle(?)=tan^{-1} (1.42857)=55^{0}[/tex]
Hope this helps
Answer:
55 degrees (e)
Step-by-step explanation:
This is a trigonometry problem. We are given a right triangle with an unknown angle in which the opposite and adjacent sides of the angle are known (10 and 7). We also know that the tangent of any angle is the length of the opposite divided by the length of the adjacent. If we let the unknown angle be Ф, we can say that tan(Ф) = 10/7. To isolate Ф, all we have to do is take the inverse. In other words, Ф = arctan(10/7). Using a graphing calculator, we find that arctan(10/7) is approximately 55 degrees.
I will give Brainliest.
Answer:
m=months
clark= 10000-105m
lois= 7500-50m
10000-105m=7500-50m
+50m
10,000-55m=7500
-10000
-55m=-2500
simplify
55m=2500
divide by 55
m=45.45
so i would say b
Hope This Helps!!!
4.Find three consecutive integers such that the difference of double the largest number and triple the smallest number is -44. Find the three numbers by setting up an equation. Make sure to define your variables
Solving a linear equation, we will see that the 3 numbers are:
48, 49, and 50.
How to find the 3 numbers?
3 consecutive integers can be written as:
x, x + 1, x + 2
Here we know that 2 times the largest number minus 3 times the smallest one is -44, then:
2*(x + 2) - 3x = -44
We can solve that linear equation for x:
2x + 4 - 3x = -44
(2 - 3)x = -44 - 4
-x = -48
x = 48
Then the 3 numbers are:
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Jamie has a restaurant bill of $70.70. About how much money should she leave for a 10% tip?
$7.00
$0.70
$1.00
$7.70
Area =
Help me please :)
Answer:
24 unit²
Step-by-step explanation:
use Pythagoras to calculate the height of triangle
which gives you 6 √100-64
then half hight x base
Classify the following triangle. Check all that apply.
Caraline is planting flowers in her garden she plants 7 flowers in 4 minutes after 12 minutes she has planted 21 different flowers
Answer:
A.28 minutes
B.40 minutes
C.56 minutes
D.70 minutes
Step-by-step explanation:
Find the missing angles. will give brainliest if done correctly.
Answer:
x = 69 v = 103
Step-by-step explanation:
Angles in a triangle add up to 180 degrees:
34 + 77 + x = 180
x = 69
Angles on a straight line add up to 180:
77 + v = 180
v = 103
Answer:
x = 69°V = 103°Step-by-step explanation:
the sum of the interior angles in a triangles is 180°, take away from 180 the know angles (34° and 77°) and you will have your answer
180 - 34 - 77 = 69°
Now we find angle V
The angle V and the angle of 77 ° are on a straight line, so the sum is 180°, from 180° you subtract 77 ° and you have the value of V
180 - 77 = 103 °
Find a in degrees.
a
6
√11
5
? ]°
Round to the nearest hundredth.
Answer:
33.55
Step-by-step explanation:
[tex]sin \alpha = \sqrt{11} \div 6 \\ [/tex][tex] \alpha = {sin}^{ - 1} 0.5527[/tex][tex] \alpha = 33.55[/tex]Answer:
α = 33.56° (nearest hundredth)
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta=\alpha[/tex]O = [tex]\sf \sqrt{11}[/tex]A = 5H = 6As all sides of the right triangle have been given, any of the trigonometric ratios can be used to find α.
Sine Ratio
[tex]\begin{aligned}\sf \sin(\alpha) & = \sf \dfrac{\sqrt{11}}{6}\\\implies \alpha & = \sf \sin^{-1}\left(\dfrac{\sqrt{11}}{6}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]
Cosine Ratio
[tex]\begin{aligned}\sf \cos(\alpha) & =\sf \dfrac{5}{6}\\\implies \alpha & = \sf \cos^{-1}\left(\dfrac{5}{6}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]
Tangent Ratio
[tex]\begin{aligned}\sf \tan(\alpha) & =\sf \dfrac{\sqrt{11}}{5}\\\implies \alpha & = \sf \tan^{-1}\left(\dfrac{\sqrt{11}}{5}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]
Therefore, α = 33.56° (nearest hundredth)
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Can someone help me with these 4 geometry questions? Pls it’s urgent, So ASAP!!!!
Question 4
1) [tex]\overline{BD}[/tex] bisects [tex]\angle ABC[/tex], [tex]\overline{EF} \perp \overline{AB}[/tex], and [tex]\overline{EG} \perp \overline{BC}[/tex] (given)
2) [tex]\angle FBE \cong \angle GBE[/tex] (an angle bisector splits an angle into two congruent parts)
3) [tex]\angle BFE[/tex] and [tex]\angle BGE[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle BFE[/tex] and [tex]\triangle BGE[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\overline{BE} \cong \overline{BE}[/tex] (reflexive property)
6) [tex]\triangle BFE \cong \triangle BGE[/tex] (HA)
Question 5
1) [tex]\angle AXO[/tex] and [tex]\angle BYO[/tex] are right angles, [tex]\angle A \cong \angle B[/tex], [tex]O[/tex] is the midpoint of [tex]\overline{AB}[/tex] (given)
2) [tex]\triangle AXO[/tex] and [tex]\triangle BYO[/tex] are right triangles (a triangle with a right angle is a right triangle)
3) [tex]\overline{AO} \cong \overline{OB}[/tex] (a midpoint splits a segment into two congruent parts)
4) [tex]\triangle AXO \cong \triangle BYO[/tex] (HA)
5) [tex]\overline{OX} \cong \overline{OY}[/tex] (CPCTC)
Question 6
1) [tex]\angle B[/tex] and [tex]\angle D[/tex] are right angles, [tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex] (given)
2) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)
3) [tex]\angle BAC \cong \angle CAD[/tex] (an angle bisector splits an angle into two congruent parts)
4) [tex]\triangle BAC[/tex] and [tex]\triangle CAD[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle BAC \cong \triangle DCA[/tex] (HA)
6) [tex]\angle BCA \cong \angle DCA[/tex] (CPCTC)
7) [tex]\overline{CA}[/tex] bisects [tex]\angle ACD[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)
Question 7
1) [tex]\angle B[/tex] and [tex]\angle C[/tex] are right angles, [tex]\angle 4 \cong \angle 1[/tex] (given)
2) [tex]\triangle BAD[/tex] and [tex]\triangle CAD[/tex] are right triangles (definition of a right triangle)
3) [tex]\angle 1 \cong \angle 3[/tex] (vertical angles are congruent)
4) [tex]\angle 4 \cong \angle 3[/tex] (transitive property of congruence)
5) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)
6) [tex]\therefore \triangle BAD \cong \triangle CAD[/tex] (HA theorem)
7) [tex]\angle BDA \cong \angle CDA[/tex] (CPCTC)
8) [tex]\therefore \vec{DA}[/tex] bisects [tex]\angle BDC[/tex] (definition of bisector of an angle)