Use y = mx + b to determine the equation of a line that passes through the point A(-1, 4) and is
parallel to the line:
4x – 2y + 8 = 0
Answer:
Step-by-step explanation:
If we are looking for a line parallel to the given line, we need to find the slope of the given line, since parallel lines have the exact same slope. That means that we need to solve this equation for y, which naturally puts the line into slope-intercept form. Solving for y:
-2y = -4x - 8 and
2y = 4x + 8 so
y = 2x + 4 and the slope, we see here, is 2. Use that slope and the given point of (-1, 4) to write the new equation we need.
In point-slope form, the line will be
y - 4 = 2(x - (-1)) which simplifies a bit to
y - 4 = 2(x + 1). That's point-slope form. Putting it into slope-intercept just requires that we solve this equation for y:
y - 4 = 2x + 2 and
y = 2x + 6. That's slope-intercept form of the same line. The last form is standard, which looks like this:
-2x + y = 6 or, if you don't like to lead with a negative,
2x - y = -6
A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 101.8 pounds and a standard deviation of 3.76 pounds. a) What is the probability that a drum meets the guarantee
Answer:
0.6844 = 68.44% probability that a drum meets the guarantee.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 101.8 pounds and a standard deviation of 3.76 pounds.
This means that [tex]\mu = 101.8, \sigma = 3.76[/tex]
What is the probability that a drum meets the guarantee?
Probability of at least 100 lbs of solvent, which is 1 subtracted by the p-value of Z when X = 100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 101.8}{3.76}[/tex]
[tex]Z = -0.48[/tex]
[tex]Z = -0.48[/tex] has a p-value of 0.3156.
1 - 0.3156 = 0.6844
0.6844 = 68.44% probability that a drum meets the guarantee.
1. Which equation should be used to find the area of the triangle below? *
1 point
5 inches
-5 inches
2 inches
Answer:
See Explanation
Step-by-step explanation:
Required
Expression for area of triangle
This is calculated using
[tex]Area = \frac{1}{2} * base * height[/tex]
Assume that:
[tex]base = 5cm; height = 2cm[/tex]
The equation becomes
[tex]Area = \frac{1}{2} * 5* 2[/tex]
The ratio of the numbers of students in Mr. Moore’s class compared to the number of students in Miss Henry’s class is 5:4. The ratio of the number of students in Miss Henry’s class compared to the number of students in Mr. Wilson’s class is 8:9. What is the ratio of number of students in Mr. Moore’s class to Mr. Wilson’s class.
Answer:
10:9
Step-by-step explanation:
First ratio is 5:4. 4 is equal to Henry class
If you múltiply the ratio by 2 you get
10:8, This ratio can be compared because now Henry class has 8
2(5:4)
10:8
8:9
Meaning that the answer is 10:9
Find the perimeter of the
polygon if ZB = ZD.
6.5 cm
B
7.5 cm
D
8.5 cm
с
P = [?] cm
Enter
Answer:60
Step-by-step explanation:
The Perimeter of the polygon is 60 cm.
A polygon is a closed figure made up of three or more line segments connected end to end.
To solve this question we will use the property of the tangents drawn from a point to a circle.
"Length of tangents drawn from a point to a circle are equal in measure."
With this property,
Therefore, BG ≅ FB ≅ 7.5 cm
AG ≅ AH ≅ 6.5 cm
CF ≅ EC ≅ 8.5 cm
Since m∠B ≅ m∠D
Therefore, length of tangents FB ≅ GB ≅ DE ≅ DH ≅ 7.5 cm
Since, Perimeter of ABCD = AB + BC + CD + DA
AB = 7.5 + 6.5
AB = 14 cm
BC = 7.5 + 8.5
BC = 16 cm
CD = 8.5 + 7.5
CD = 16 cm
DA = 7.5 + 6.5
DA = 14 cm
Now Perimeter = 16 + 16 + 14 + 14
= 60 cm
Therefore, P = 60 cm will be the answer.
Learn more about polygons;
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Find the perimeter of this quarter circle with radius,
r
= 2mm.
Give your answer as an expression in terms of
π
.
Answer:
pi
Step-by-step explanation:
First find the circumference of the circle
C = 2 * pi*r
C = 2 * pi *2
C = 4pi
A quarter circle is 1/4 of a circle
1/4 C = 1/4 (4pi)
1/4C = pi
Please answer ai i pray toyou ai brainly 5+5f-6=7
Answer:
f = 1.6
Step-by-step explanation:
Answer:
f = 8/5
Step-by-step explanation:
[tex]5 + 5f - 6 = 7\\5f - 1 = 7\\5f = 7 + 1 \\5f = 8\\\\f = \frac{8}{5}[/tex]
find the values of x and y
Answer:
y = 60°
x = 12
Step-by-step explanation:
Because all sets of opposite sides are parallel, opposite angles are equal, and opposite sides have the same length.
Which expression is equivalent to 5^6?
The patio at the back of the house is to be extended into the backyard in a semi-circle. What will be the area of the yard
after the patio is done?
Answer:
A = 413 sq feet
Step-by-step explanation:
The area of the yard = area of rectangle - area of semicircle
The radius of the semicircle, r = 10 feet
The length of the rectangle = 38.5 - 10 = 28.5 feet
So,
The area of the yard = lb - (πr²/2)
[tex]=20\times 28.5-(\dfrac{3.14\times 10^2}{2})\\\\A=413\ ft^2[/tex]
So, the required area is equal to 413 sq feet.
Which word describes the slope of the line?
positive
negative
zero
undefined
Answer: zero
Step-by-step explanation: For any horizontal or flat line, the slope is always zero
80ft
18ft
what is the length of the hypotenuse in feet?
Answer:
Solution given:
perpendicular [P]=80ft
base[B]=18ft
hypotenuse [H]=?
By using Pythagoras law
H²=P²+B²
H²=80²+18²
H=[tex]\sqrt{6724}=82[/tex]
the length of the hypotenuse in feet is 82ft.
PLS HELP ASAP! THANK YOU.
Answer: 16m
Step-by-step explanation: no problem.
I need help ASAP Please
Answer:
49
Step-by-step explanation:
working is attached
if its wrong don't flame me im just a random girl on this app
a graph of a non-vertical straight line is a?
a) nonlinear function
b) exponential function graph
c) non-function
d) linear function
Answer:
The correct answer is d
Step-by-step explanation:
A graph of a non-vertical straight line is a linear function
Activity 1
Instructions: Fill in the table with the missing information.
Experiment
Sample Space
Sample Point
Event
Dutcome
Number of
Possible
Outcome/s
3
Rolling a die
1,2,3,4,5,6
5
2, 4, 6
Getting an
even
number
Getting two
heads
1. Flipping two
coins
HH, HT, TH, TT
2. Choosing a
day in a
week
Choosing a
day that
starts with
letters
Choosing a
month that
ends with
letter R
3. Choosing a
month in a
coin and a
dle together
5. Letter in the
word
PENCIL
6. Numbers
from 1 to 10
P.E.N.C.IL
e,
Getting an
odd number
5
Plss Help Asap
44:59
The graph of y = ? - 1 is shown.
Which statement about the graph is accurate?
TX
6-
5
O The x-intercept of the graph is (2, 1).
The graph has no y-intercepts.
O The y-intercept of the graph is (2,0).
O The graph has no x-intercepts.
4
3
2
1
3
2
1
2
X
1
-2-
-3
4
5
Save and Exit
Next
Submit
Mark this and return
Answer:
The graph has no y intercepts
Step-by-step explanation:
Given
[tex]y = \frac{2}{x} - 1[/tex]
Required
True about the graph
The graph has no y intercepts because this would mean:
[tex]y = \frac{2}{0}-1[/tex]
2/0 is undefined. Hence, the graph has no y intercept.
Point: (1,1) Line: y=1/5x+4/5
Answer:
True.
Step-by-step explanation:
Let x = 1
y = 1/5(1) + 4/5
= 1/5 + 4/5
y = 5/5 = 1
Therefore, this statement is true.
1/4 + 3/8 Reduce your Answer to the lowest term?
Answer:
5/8
Step-by-step explanation:
math
The height of a cylinder is 10 centimeters. The diameter of this cylinder is 2.5 centimeters longer than the height. Which
is closest to the volume of the cylinder?
The volume of the cylinder is 391π cubic meter which is correct option(D).
What is the volume of the cylinder?The volume of the cylinder is defined as the product of circular base area and its height.
Volume of the Cylinder as : V = π r² h
Given data as :
The height of a cylinder is 10 centimeters,
And that the diameter of this cylinder is 2 centimeters longer than the height,
Thus, the diameter of the cylinder is 10 + 2.5 = 12.5 cm
The radius of the cylinder = diameter / 2 = 12.5 / 2 = 6.25 cm.
The volume of the cylinder is given by
Formula : Volume of the Cylinder = V = π r² h
Substitute the values, we have
V = π × (6.25)² × 10
V = 390.625π cubic meter
V ≈ 391π cubic meter
Hence, the volume of the cylinder is 391π cubic meter.
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Please help is for now 6
Answer:
-2g-11
Step-by-step explanation:
2(3g-4)-(8g+3)
6g-8-8g-3
-2g-11
Can someone answer this for me (in the picture)
Find the area of the regular polygon. Round to the nearest tenth.
Answer:
3462.8 squared unit
Step-by-step explanation:
Applying,
A = nh²tan(360/n)......... equation 1
Where A = area of the regular polygon, n = number of sides of the polygon, h = length of the apothem.
From the question,
Give; n = 5 sides, h = 15
Substitute these values into equation 1
A = 5×15²×tan(360/5)
A = 1125×tan72
A = 1125×3.078
A = 3462.75
A = 3462.8 squared unit
please help. Thank you
Answer:
30.8 degrees
Step-by-step explanation:
cosx = [tex]\frac{8.5}{9.9}[/tex]
x= [tex]cos^{-1}[/tex][tex]\frac{8.5}{9.9}[/tex]
= 30.8 degrees (nearest tenth of a degree)
Which expression is equivalent to -3(y-5)
A. -3y-4
B -3y+4
C. -3y-12
D -3y+12
Answer:
neither when you multiply them you get -3y+15 not 12
hope this helps
have a good day :)
Step-by-step explanation:
which number is not equal to one of the following expressions? 1,400 x 10
140,000÷100 1,400 x 100
1,400
140
140,000
14,000
Melissa got 18 out of 20 on a math quiz. Tom got 85% on the quiz. Whose mark was greater?
Answer:
[tex]tom = \frac{85}{100} \times 20 \\ = 17 \: questions[/tex]
Melissa had a greater mark.
Answer:
Melissa
Step-by-step explanation:
Melissa: 18/20
Tom: 85/100
You need a common denomenater so multiply 18 and 20 by 5:
90/100>85/100
Melissa has the greater mark by 5%
IN OPQ, the measure of Q= 90, OQ=12, PO= 13, and QP=5. What ratio represents the cosine of O?
Answer:
12/13
Step-by-step explanation:
The cosine of O
= QO / PO
= 12 / 13
Mata soccer practice on May 4 he will practice every fourth day after that tent begins baseball practice on May 3 and continuous practice every day day after that what will be the first date on which they both have practice
Answer:
May 4th
The pattern goes like this
May 4th, May 8th, May 12th, May 16th, ...
The equation of a linear function in point-slope form is y-y1=m(x-x1). Harold correctly wrote the equation y=3(x-7) using a point and the slope. Which point did Harold use ?
Answer:
(7, 0).
Step-by-step explanation:
We have y = 3(x - 7)
y = 3x - 21
Point-slope form is
y - y1 = 3(x - x1)
y - y1 = 3x - 3x1
Comparing this to the equation y = 4x - 21 we see that y1 = 0 and x1 = 7.
Answer:
(7,0)
Step-by-step explanation:
correct on edge
