If you multiply the slopes of two perpendicular lines, the product is -1.
(As long as neither line is vertical.)
w
(0,4)
Use that fact and the graph to complete the statements below.
CLEAR
CHECK
The slope of line g is - 1/2.
= -1/2 • ____= - 1
So, the slope of line h is ___
The equation for line h is
y = ___x + _____ .
Answers
[tex]$-\frac{1}{2}\cdot2=-1[/tex]
Slope of the line h is 2.
The equation for line h is y = 2x + 4.
Solution:
General equation of a line is y = mx + c,
where m is the slope of the line and c is the y-intercept.
In the given image, line g and line h are intersecting lines and perpendicular to each other.
Equation of line g is [tex]y=-\frac{1}{2} x+2[/tex].
Slope of the line g ([tex]m_1[/tex]) = [tex]-\frac{1}{2}[/tex]
If two lines are perpendicular, then the product of the slopes is –1.
⇒ [tex]m_1 \cdot m_2=-1[/tex]
To find the slope of the line h:
[tex]$\Rightarrow-\frac{1}{2} \cdot m_2=-1[/tex]
[tex]$\Rightarrow m_2=-1 \times(-2)[/tex]
[tex]$\Rightarrow m_2=2[/tex]
Slope of the line h is 2.
To find the equation of a line h:
Line h passing through the point (0, 4) and slope 2.
Point-slope formula:
[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex]
[tex]\left(y-4)=2\left(x-0\right)[/tex]
[tex]y-4=2x[/tex]
[tex]y=2x+4[/tex]
The equation for line h is y = 2x + 4.
Related Questions
Worth 20 points PLZ HELP ASAP
An F note has a frequncy of 689.46Hz calculate the wavelegnth in meters
Answers
Answer:
434822.11875961m
Step-by-step explanation:
this is because the formula is λ = C/f
Where,
λ (Lambda) = Wavelength in meters
c = Speed of Light (299,792,458 m/s)
f = Frequency
Which summation formula represents the series below? 1 + 2 + 6 + 24
Answers
Question:
Which summation formula represents the series below? 1 + 2 + 6 + 24
(a) [tex]\sum_{n=2}^{5}(n-1) ![/tex]
(b) [tex]\sum_{n=0}^{3} n ![/tex]
(c) [tex]\sum_{n=1}^{4}(n+1) ![/tex]
(d) [tex]\sum_{n=2}^{5} n ![/tex]
Answer:
Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex] is the correct answer.
Explanation:
Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex](2-1) !+(3-1) !+(4-1) !+(5-1) ![/tex]
Subtracting, we have,
[tex]1 !+2!+3 !+4 ![/tex]
Expanding the factorial,
[tex]1+(2*1)+(3*2*1)+(4*3*2*1)[/tex]
Simplifying, we get,
[tex]1+2+6+24[/tex]
Thus, the summation [tex]\sum_{n=2}^{5}(n-1) ![/tex] represents the series [tex]1+2+6+24[/tex]
Hence, Option a is the correct answer.
Option b: [tex]\sum_{n=0}^{3} n ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex]0!+1!+2!+3![/tex]
Expanding the factorial,
[tex]0+1+(2*1)+(3*2*1)[/tex]
Simplifying, we get,
[tex]0+1+2+6[/tex]
Thus, the summation [tex]\sum_{n=0}^{3} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option b is not the correct answer.
Option c: [tex]\sum_{n=1}^{4}(n+1) ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex](1+1) !+(2+1) !+(3+1) !+(4+1) ![/tex]
Adding, we have,
[tex]2!+3!+4!+5![/tex]
Expanding the factorial,
[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]
Simplifying, we get,
[tex]2+6+24+120[/tex]
Thus, the summation [tex]\sum_{n=1}^{4}(n+1) ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option c is not the correct answer.
Option d: [tex]\sum_{n=2}^{5} n ![/tex]
By substituting the values of n and expanding the summation, we have,
[tex]2!+3!+4!+5![/tex]
Expanding the factorial,
[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]
Simplifying, we get,
[tex]2+6+24+120[/tex]
Thus, the summation [tex]\sum_{n=2}^{5} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]
Hence, Option d is not the correct answer.
Hence, the correct answer is Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]
Answer: A
Step-by-step explanation:
Which transformation of the red triangle on the graph maps it onto the missing piece of the square? A. a translation 16 units right
B. a reflection across the y-axis
C. a 90° counterclockwise rotation about the origin
D. a 90° clockwise rotation about the origin
E. a 180° rotation about the origin
Answers
Answer:
D.) A 90 degree clockwise rotation about the origin
Step-by-step explanation:
The red triangle should have a 90° clockwise rotation about the origin. Option C is correct.
Given that,
A graph of figures is shown in the pictures,
Which transformation of the red triangle on the graph maps it onto the missing piece of the square is to be determined.
The translation is defined as the change of position through linear distance and angle.
What is simplification?The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.
In order to occupy the required space on the green figure by red triangle, it should be rotated to 90° clockwise about the origin.
Thus, the red triangle should have a 90° clockwise rotation about the origin. Option C is correct.
Learn more about translation here:
brainly.com/question/11914505
#SPJ2
Which expression is equivalent to 4√147
A. 28√3
B. 12√7
C. 3√7
Answers
Answer:
A) 28*sqrt(3)
Step-by-step explanation:
Answer:
28√3 is your answer
Step-by-step explanation:
Find the slope of the line
y=-6x+\frac{1}{4}[/tex]
Answers
The equation given is the equation of a line in slope-intercept form.
The slope of the line is the numerical value associated with the variable X.
The number in front of X is -6, so the slope of the line would be -6
Answer: To find an equation that is parallel to
y
=
−
6
x
+
1
, the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.
(
6
,
0
)
m
=
−
6
So the answer would be -6
Step-by-step explanation:
The figure on the right is made up of 5 squares.
Each side of the square is 7 cm.
What is the area of the figure?
Answers
Answer: [tex]245cm^{2}[/tex]
Step-by-step explanation:
The formula for calculating the area of a square is given by :
Area = [tex]l^{2}[/tex]
where [tex]l[/tex] is the length of a side .
Therefore , the area of one of the square given implies :
Area = [tex]7^{2}[/tex]
Area [tex]= 49[/tex]
And since there are 5 squares in all , the area will therefore be :
Area = [tex]5[/tex] x[tex]49[/tex]
Area = [tex]245cm^{2}[/tex]
Therefore: the area of the shape is [tex]245cm^{2}[/tex]
If the total surface area of a cube is 302.46ft2 what best describes the length of the side of the cube?
Answers
Answer:
7.1ft
Step-by-step explanation:
The formula for calculating the total surface area of a cube is 2(L²+L²+L²)
=2(3L²)
= 6L²
Where L is the length of the cube
If the total surface area of a cube is 302.46ft², then
302.46 = 6L²
L² = 302.46/6
L² = 50.41
L =√50.41
L = 7.1ft
The length of the side of the cube is 7.1ft
The length of the side of the cube is approximately [tex]\( 7.1 \, \text{ft} \).[/tex]
To find the length of the side of a cube given its total surface area, we need to use the formula for the surface area of a cube.
The formula for the surface area of a cube is:
[tex]\[ \text{Surface Area} = 6s^2 \][/tex]
where s is the length of a side of the cube.
Given the total surface area is [tex]\( 302.46 \, \text{ft}^2 \)[/tex], we can set up the equation:
[tex]\[ 6s^2 = 302.46 \][/tex]
To solve for s we first divide both sides by 6:
[tex]\[ s^2 = \frac{302.46}{6} \][/tex]
[tex]\[ s^2 = 50.41 \][/tex]
Next, we take the square root of both sides to find s
[tex]\[ s = \sqrt{50.41} \][/tex]
[tex]\[ s \approx 7.1 \, \text{ft} \][/tex]
Thus, the length of the side of the cube is approximately [tex]\( 7.1 \, \text{ft} \).[/tex]
Can u solve 7-12 and 14 please
Answers
Answer:
1. 19
Step-by-step explanation:
Anusha needs to find a rectangular container large enough to hold a volume of 130 in.3. Which container should she use?
A. a container with the dimensions 2 by 5 by 10 inches
B. a container with the dimensions 3 by 4 by 10 inches
C. a container with the dimensions 3 by 5 by 10 inches
D. a container with the dimensions 4 by 2 by 10 inches
PLEASE HELP!!
Answers
Option C
Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches
Solution:
Anusha needs to find a rectangular container large enough to hold a volume of 130 cubic inches
The volume of rectangular container is:
[tex]volume = length \times width \times height[/tex]
Option A
Container with the dimensions 2 by 5 by 10 inches
Therefore, volume is given as:
[tex]Volume = 2 \times 5 \times 10 = 100[/tex]
Thus volume is 100 cubic inches
Option B
Container with the dimensions 3 by 4 by 10 inches
Therefore, volume is given as:
[tex]Volume = 3 \times 4 \times 10 = 120[/tex]
Thus volume is 120 cubic inches
Option C
Container with the dimensions 3 by 5 by 10 inches
Therefore, volume is given as:
[tex]Volume = 3 \times 5 \times 10 = 150[/tex]
Thus volume is 150 cubic inches
Option D
Container with the dimensions 4 by 2 by 10 inches
Therefore, volume is given as:
[tex]Volume= 4 \times 2 \times 10 = 80[/tex]
Thus volume is 80 cubic inches
Thus Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches
Answer:C. a container with the dimensions by 5 by 10 inches
If a chessboard were to have pennies placed on each square such that 1 penny was placed on the first square, 2 on the second, 4 on the third, and so on (doubling the number of pennies on each subsequent square), how many pennies would be on the chessboard when finished?
How many squares are on the chessboard?
Answers
This is just like the rice chessboard problem! To quickly get the answer, we can simply do (2^64)-1.
Take a look at the following:
1+2+4+8=15=2^4-1
1+2+4+8+16=31=2^5-1
There's that rule involved, and we can simply use 2^64-1 instead of adding too many numbers.
Hope this helped!
Total number of pennies on the chessboard is equals to [tex]2^{64} -1[/tex].
Total number of squares on the chessboard = 64
What is pattern?" Pattern is defined as the numbers are arranged in such a way that it follow certain rule or formula."
According to the question,
Number of pennies in first square = 1
Number of pennies in second square = 2
Number of pennies in third square = 4
Condition given,
Doubling the number of pennies on each subsequent square.
Calculate pattern follow as per given condition we have,
Total Number of pennies in first square = 1
= [tex]2^{1} -1[/tex]
Total Number of pennies till second square = 1 + 2
= [tex]2^{2} -1[/tex]
Total Number of pennies till third square = 1+ 2 + 4
= [tex]2^{3} -1[/tex]
Total Number of pennies till fourth square = 1+ 2 + 4 +8
= [tex]2^{4} -1[/tex]
Total number of squares on the chessboard = 64
Therefore, as per the pattern follow on each subsequent square we get,
Total number of pennies till 64th squares chessboard = [tex]2^{64} -1[/tex]
Hence, total number of pennies on the chessboard is equals to [tex]2^{64} -1[/tex].
Total number of squares on the chessboard = 64.
Learn more about pattern here
https://brainly.com/question/14720576
#SPJ3
Over the past 6 days you’ve spent $8, $14, $12, $11, $5 and $13 dollars on food . On average, how much per day are you spending on food?
A)$10.50
B)$11
C)$11.5
D)$12
E)$11.25
Answers
Answer:
The answer is A)$10.50
Step-by-step explanation:
In order to solve the average amount, you have to add the total amount of money spent and divide it by the total number of times you spent money on food. The total sum of money spent was $63. If you divide that by how many times you ate (6 times) you'll get the dividend/answer of 10.5.
Hope this helps :)
You are spending, on average, A) $10.50 per day on food.
The correct answer is A) $10.50.
To find the average amount spent per day on food, you need to add up the total amount spent over the 6 days and then divide it by the number of days (6).
Total amount spent on food = $8 + $14 + $12 + $11 + $5 + $13
= $63
Average amount spent per day = Total amount spent / Number of days
= $63 / 6
= $10.50
So, you are spending, on average, $10.50 per day on food.
for such more question on average
https://brainly.com/question/130657
#SPJ2
A rectangle has a height of 4cm and a width of 8cm what is the area
Answers
Answer: 32
Step-by-step explanation:
4cm × 8cm = 32cm
What is the measurement of angle R
Answers
Can someone help me with the question shown above. It is a 7th grade math problem
Answers
-
-
22*15 = 330
-
-
330-125 = 205.
What is 77 divided by 13690
Answers
Answer: 0.00562454
Step-by-step explanation:
Did I save you a lot of time? Lol hope I helped
Answer:
the answer would be 0.00562454346 or if u want it as a fraction it would be 281227173/50000000000
Step-by-step explanation:
What’s 36x^2 + 24xy + 4y^2?
Explain the steps.
Answers
Answer:
4(3x+y)^2
Step-by-step explanation:
36x^2+24xy+4y^2
=9*4x^2+6*4xy+4y^2
=4(9x^2+6xy+y^2)
=4(3x+y)*(3x+y)
=4(3x+y)^2
What is the slope of the line that contains the
coordinate points (8, -3) and (-2, 7)?
220x219
Answers
Answer:
-1
Step-by-step explanation:
Slope = (y2 - y1)/(x2 - x1)
= (7 - (-3))/(-2 - 8)
= (7+3)/(-10)
= 10/(-10) = -1
5 1/2 of 2 1/3 is what number?
Answers
Answer:
19 1/4
Step-by-step explanation:
5 1/2 of 2 1/3
Change mixed fraction to improper fraction
11/2 of 7/2
Of means multiplication
11/2 x 7/2
77/4
19 1/4
Round the number to the nearest hundred. 281
Answers
Answer:
300
Step-by-step explanation:
because you said nearest hunderd and 281 would be 200 if it was 149 but since its 281 its further to 300
your welcome
lex <3
Answer:
300
You first look to the right of the hundred and if it is 5 and above u add 1 to the hundreds place. If its 4 and below u keep it the same. You just have to remember that all the place values after the one rounded would have a value of 0
If the radius of the smaller sphere is 3 inches and the radius of the larger sphere is 6 inches how many times greater is the volume of the larger sphere
Answers
Answer:
8
Step-by-step explanation:
The formula of volume is 4/3 × π × radius3.
volume of smaller sphere = 4/3 x 3.14 x 3*3*3
v = 113.04
volume of larger sphere = 4/3 x 3.14 x 6*6*6
v = 904.32
904.32 / 113.04 = 8
The Answer Is 8 times
A building has the shape of a pyramid within a square base. The mid segment parallel to the ground of each triangular face of the pyramid has a length of 58 feet. Find the length of the base the pyramid.
Answers
Answer:
The length of the base the pyramid is 116 feet.
Step-by-step explanation:
See the diagram attached to this answer.
Let Δ OAB is the side triangle of the square pyramid, and A'B' is the mid segment parallel to the ground with length of 58 feet.
Now, Δ OAB and Δ OA'B' are similar triangle and the length of sides of the triangle Δ OA'B' are in the same ratio with the corresponding sides of Δ OAB.
Hence, [tex]\frac{OA'}{OA} = \frac{OB'}{OB} = \frac{A'B'}{AB} = \frac{1}{2}[/tex]
⇒ AB = 2 × 58 = 116 feet.
The length of the base the pyramid is 116 feet. (Answer)
Final answer:
The length of the base of the pyramid in question, referenced as the Great Pyramid of Cheops, is historically known to be 230 meters on each side.
Explanation:
The student's question relates to finding the length of the base of a pyramid with a known mid-segment length in one of the triangular faces.
Based on the information provided, which references the Great Pyramid of Cheops (or the Great Pyramid of Giza), the original square base length of the pyramid was 230 meters on each side.
This measurement is crucial for answering questions related to the geometry and scale of pyramids in mathematical problems.
Solve the quadratic:
2X^2-64=0
Answers
Answer:
do you mean x=7
Step-by-step explanation:
this aint a quadratic function a qaudratic function is ax^2+bx+c=c
Frankie and Marcel are picking apples. Frankie has 18 apples, which is 4 times plus 2 more apples than Marcel has.
How many apples does Marcel pick?
Enter the correct answer in the box.
Answers
Answer:
marcel picked 4 apples
Step-by-step explanation:
18 = 4x + 2
solve for x
subtract 2 from each side
16 = 4x
divided by 4
16/4 = 4
Answer: 4 apples
Step-by-step explanation:
Joe tracked the height of his Dalmatian puppy from age 13 weeks to 25 weeks. He graphed the data and determined the line of best fit is y = 1.12x + 28.78 where x is the age in weeks and y is the height in centimeters. How old was the puppy when he was 54 centimeters tall? Round to the nearest tenth.
a. 22.5 weeks
b. 28.2
c. 73.9
d. 89.3
Answers
Answer:
22.5 weeks
Step-by-step explanation:
y = 1.12x + 28.78 represents the height of the puppy. Here that height is 54 cm:
Then 54 = y = 1.12x + 28.78
Combining the constants, we get 1.12x = 25.22. Dividing both sides by 1.12, x turns out to be 22.5 weeks.
Find the measure of θ. (to the nearest tenth)
A) 16.2°
B) 16.8°
C) 17.1°
D) 17.9°
Answers
Answer: D
Step-by-step explanation:
On USA test prep the answer is D.
Answer:
They are incorrect. The answer is actually 36.9
Step-by-step explanation:
Translate this phrase into an algebraic expression. 17 more than twice Craig's height. Use the variable c to represent craig's height
Answers
Answer:
C2+17
Step-by-step explanation:
Algebraic expression is 2c + 17
Given phrase;17 more than twice Craig's height
Find:Algebraic expression
Computation:We know that;
c = craig's height
So,
twice Craig's height
⇒ 2c
17 more than twice Craig's height
⇒ 2c + 17
Learn more:https://brainly.com/question/8868200?referrer=searchResults
Darius uses the shadow method to estimate the height of the flagpole. He finds that a 5-foot stick casts a 4-foot shadow. At the same time , he finds that the flagpole casts a 20-foot shadow . What is the height of the flagpole. Sketch a diagram.
Answers
Answer:
The height of the flagpole is 25 foot.
Step-by-step explanation:
Given:
Height of the stick = 5 foot
Shadow of the stick = 4 foot
Another one:
Height of the flagpole = 'x'
Shadow of the flagpole = 20 foot
Note:The shadows are formed at the same time of the day so the Sun makes an equal angle with both the situation.
Here from both ends it forms two similar triangles.
So,
We can say that:
⇒ [tex]\frac{Height\ of\ the\ flagpole}{Shadow\ of\ the\ flagpole}=\frac{Height\ of\ the\ stick}{Shadow\ of\ the\ stick}[/tex]
⇒ [tex]\frac{x}{20}=\frac{5}{4}[/tex]
⇒ [tex]\frac{x}{20}\times 20=\frac{5}{4}\times 20[/tex]
⇒ [tex]x=25[/tex] foot
So Darius estimated height of the flagpole = 25 foot.
Write this decimal in number, thirty-nine thousandths
Answers
Answer:
0.039
Step-by-step explanation:
Which equation represents a proportional relationship?
y=2x2
y = 4x - 2
y= 1/2x +3
y=5x
Answers
Answer:
D: y = 5x
Step-by-step explanation:
According to Google, a proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if: y=kx. for some constant k , called the constant of proportionality. So the only one in that form would be the y = kx.
The constant k = 5
Solve the equation for 3y-4=6-2y
Answers
To solve the equation, you need to isolate/get "y" by itself in the equation:
3y - 4 = 6 - 2y Add 2y on both sides
3y + 2y - 4 = 6 - 2y + 2y
5y - 4 = 6 Add 4 on both sides
5y - 4 + 4 = 6 + 4
5y = 10 Divide 5 on both sides
[tex]\frac{5y}{5} =\frac{10}{5}[/tex]
y = 2
PROOF
3y - 4 = 6 - 2y Substitute/plug in 2 for y
3(2) - 4 = 6 - 2(2)
6 - 4 = 6 - 4
2 = 2
After Solving the equation for 3y-4=6-2y, we get y = 2. We must isolate the variable y on one side of the equation in order to get the solution to the equation 3y - 4 = 6 - 2y. Here's a step-by-step procedure:
Start by solving 3y - 4 = 6 - 2y, which is the provided problem.
Add 2y to both sides of similar phrases to combine them: 3y + 2y - 4 = 6 - 2y + 2y.
Simply put, this is: 5y - 4 = 6.
Add 4 to both sides of the variable word to isolate it: 5y - 4 + 4 = 6 + 4.
This may be summarised as 5y = 10.
To find y, multiply both sides of the equation by 5. (5y) / 5 = 10 / 5.
This may be condensed to: y = 2.
Consequently, y = 2 is the answer to the equation 3y - 4 = 6 - 2y.
To know more about variable :
https://brainly.com/question/15078630
#SPJ6.