Answer:
[tex]y = -\frac{1}{3}x + 4[/tex]
Step-by-step explanation:
Required
Equation of line
passes through [tex](6,2)[/tex]
In an equation of the form [tex]y =mx + b[/tex]; the slope is [tex]m[/tex]
So, by comparison;
The slope of [tex]y = 3x + 1[/tex] is: [tex]m =3[/tex]
From the question, we understand that the required equation is perpendicular to [tex]y = 3x + 1[/tex]
This means that its slope is:
[tex]m_2 =-\frac{1}{m}[/tex]
So, we have:
[tex]m_2 =-\frac{1}{3}[/tex]
The line equation is:
[tex]y = m_2(x - x_1) + y_1[/tex]
Where:
[tex](x_1,y_1) = (6,2)[/tex]
So, we have:
[tex]y = -\frac{1}{3}(x - 6) + 2[/tex]
[tex]y = -\frac{1}{3}x + 2 + 2[/tex]
[tex]y = -\frac{1}{3}x + 4[/tex]
Please answer this, its one of my homework questions
Answer:
4^4=4^3*4=64*4=256
4^6=4^5*4=1024*4=4096
Step-by-step explanation:
Answer:
4^4 = 256
4^6 = 4,096
4 x^2+ 4x-14 x=0
Solve this please, you will get brainLiest. Thank you :)
Answer:
x could be 0 or it could be 5/2
Step-by-step explanation:
Answer:
x= 5/2
Step-by-step explanation:
4x^2 + 4x - 14x = 0
subtract 4x from 14x because they are like terms
4x^2 - 10x=0
4x^2 = 0 + 10x
4x^2 = 10x
x^2/x = 10/4
x=10/4
x=5/2
find the value of 3mm(m+y)
Answer:
Step-by-step explanation:
3mn (m+y)
= 3[tex]m^{2}[/tex]n + 3mny
Please help me solve this question and steps.Thank you.
9514 1404 393
Answer:
no
Step-by-step explanation:
The first step is to understand that the question is asking about the future value of series of payments. An appropriate formula is ...
P = A(n/r)((1 +r/n)^(nt) -1)
where P is the future value, A is the periodic payment made n times per year for t years. r is the annual interest rate.
The next step is to substitute the given values and do the arithmetic. Using the given values, we have ...
P = 250(12/0.056)((1 +0.056/12)^(12×2.5) -1) ≈ 8030.32
Shen will have accumulated about $8,030.32, which is not enough to meet his goal.
If 81 is added to a number the result is 39 less than three times the number
let x =the number
Step-by-step explanation:
81+x=3x-39
group like terms
81+39=3x-x
120=2x
120/2=2x/2
60=x
therefore x =60
Answer:
60
Step-by-step explanation:
number is represented as x.
81 is added to a number is
81 + x
39 less than three times the number
3x - 39
So
81 + x = 3x - 39
Solve for x.
81 + x = 3x - 39 Add 39 to each side so 39 cancels on the right.
81 + x + 39 = 3x - 39 + 39
81 + x + 39 = 3x
81 + 39 + x = 3x
120 + x = 3x Subtract x from each side.
120 + x - x = 3x - x
120 = 3x - x
120 = 2x Divide each side by 2
120/2 = 2x/2
120/2 = x
60 = x
An open tank is to be constructed with a square base of side x metres with four rectangular sides. The tank is to have a capacity of 108m^3. Determine the least amount of sheet metal from which the tank can be made?
Answer: roughly 151.81788 square meters of metal
=====================================================
Explanation:
The base is a square with side lengths x, so its area is x*x = x^2
Let h be the height of the tank. We have four identical wall panels that have area of xh square meters. The four walls lead to a lateral surface area of 4xh. Overall, the entire tank requires x^2+4xh square meters of metal. We're ignoring the top since the tank is open.
-----------
Let's set up a volume equation and then isolate h.
volume = length*width*height
108 = x*x*h
108 = x^2*h
x^2*h = 108
h = 108/(x^2)
-----------
Plug that into the expression we found at the end of the first section.
x^2+4xh
x^2+4x(180/(x^2))
x^2+(720/x)
------------
Depending on what class you're in, the next step here will vary. If you are in calculus, then use the derivative to determine that the local min happens at approximately (7.11379, 151.81788)
If you're not in calculus, then use your graphing calculator's "min" feature to locate the lowest point on the f(x) = x^2+(720/x) curve.
This lowest point tells us what x must be to make x^2+(720/x) to be as small as possible, where x > 0.
In this context, it means that if the square base has sides approximately 7.11379 meters, then you'll need roughly 151.81788 square meters of metal to form the open tank. This is the least amount of metal required to build such a tank, and that will have a volume of 108 cubic meters.
Given: In this figure, `/_AED` and `/_BEC` form a pair of vertical angles. Prove: `/_AED ~= /_ BEC `. Match each statement to its corresponding reason. Drag the items on the left to the correct location on the right.
Answer:
Step-by-step explanation:
The matched statement to its corresponding reason for the given alternate interior angles as:
Given: Let points A, B, and C form a triangle.
definition: Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.
Congruent angles: m∠1=m∠4, m∠3 = m∠5
Linear pair theorem: m∠4+m∠2+m∠5 = 180°
As per the shown figure,
Given:
Let points A, B, and C form a triangle.
Defining a parallel line and labeling angles:
Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.
Alternate Interior Angles Theorem:
∠1=∠4
∠3 = ∠5
Congruent angles have equal measures:
m∠1=m∠4
m∠3 = m∠5
Definition of a straight angle and angle addition:
m∠4+m∠2+m∠5 = 180°
Substitution:
m∠1 + m∠2 +m ∠3 = 180°
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36 and 60 as ratio //////// do not mind what I'm going to type on this sidehdshhdsdhdshjhsjdhsdhjd
36:60
= 18:30
= 9:15
= 3:5
PLS HELP!! WILL GIVE BRAINLIEST!!! >.<
Write one function for each house to describe the value of the house f(x), in dollars, after x years.
straightAnswer:
Step-by-step explanation:
The strategy would be to look for the equations of lines that passes for the points. it can be done but it's a hard work. I prefer to use a calc sheet . You can se that house 2 has a perfect fit to data because it has a [tex]R^2=1[/tex], however house 1 does not have a perfect fit, [tex]r^2=0.99..[/tex] altough it is a very good fit, in the image you can see the corresponding equations
Suppose that y varies directly with x and inversely with z; y = 27 when
x = 21, and z = 7. Write the equation that models the relationship. Then
find y when x = 25 and z = = 5.
The value of y is 45 when x = 25, z = 5 and the value of constant of proportionality is 9, and equation is y = 9x/z
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
We have:
y varies directly with x and inversely with z.
y ∝ x/z
Removing the proportional sign.
y = kx/z
k is the constant of proportionality.
Plug y = 27, x = 21, and z = 7 to get the value of k
27 = 21k/7
k = 9
y = 9x/z
Plug x = 25, and z = 5
y = 9(25)/5
y = 45
Thus, the value of y is 45 when x = 25, z = 5 and the value of constant of proportionality is 9, and equation is y = 9x/z
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the perimeter of a rectangular painting is 304 CM. If the width of the paint is 63 cm what is the length
Answer:
The PERIMETER P is the distance around the rectangle.
Let's call the width of the rectangle W and the length of the rectangle L.
As you go around the edge there two equal lengths and two equal widths.
The formula for the perimeter of a rectangle is P=2*L+2*W.
P=2L%2B2W
Substitute 290 for P and 62 for the width.
290=2L%2B2%2862%29
Solve for L.
290=2L%2B2%2862%29
290=2L%2B124
290-124=2L
2L=166
L=83
The equation L=83 means that the length is 83 cm.
CHECK your work.
2(62)+2(83) = 124+166 = 290cm.
The length of the rectangle is 83cm.
HELP!!! PLEASE!!!!!!!!!!
HELPPPP MEEE
5x-7+3x and 3x-7+5x
equivalent or not equivalent
4y+9+3y and 3y+9+4y
equivalent or not equivalent
6z-2z+4 and 4+2z-6z
equivalent or not equivalent
Answer: See explanation
Step-by-step explanation:
1. 5x-7+3x and 3x-7+5x
5x - 7 + 3x
Collect like terms
5x + 3x - 7 = 8x - 7
3x-7+5x
Collect like terms
3x + 5x - 7 = 8x - 7
They're equivalent
2. 4y+9+3y and 3y+9+4y
4y + 9 + 3y
Collect like terms
4y + 3y + 9 = 7y + 9
3y + 9 + 4y
Collect like terms
3y + 4y + 9 = 7y + 9
They're equivalent
3. 6z-2z+4 and 4+2z-6z
6z - 2z + 4 = 4z + 4
4 + 2z - 6z = 4 - 4z
They're not equivalent
Work out the value of 8³
Answer:
512
Step-by-step explanation:
pls help me do this question but pls don't get it wrong this is my attempt
Answer: (c)
Step-by-step explanation:
Given
The function is [tex]y=-x^2+6x-4[/tex]
Range of a function describes the values y can take
from the graph it is clear that the maximum value of y is 5
[tex]\therefore y\leq5[/tex]
Hence. option (c) is correct.
How many centimeters are there in 3 meters?
A. 100 cm
B. 200 cm
C. 300 cm
D. 400 cm
Answer:
Step-by-step explanation:
c
Answer this as soon as possible please!!!!!
16
The ideal width of a safety belt strap for a certain automobile is4 cm. An actual width can vary by at most 0.3
cm. Write an absolute value inequality for the range of acceptable widths, in centimeters.
IW - 41 303
0214
Answer:
|x - 4| ≤ 0.3
Step-by-step explanation:
The actual width = 4
Maximum variation, x = 0.3
Hence, the lowest width position based on actual width and possible variation is :
4 - 0.3 ≤ x ≤ 4 + 0.3
3.7 ≤ x ≤ 4.3
bcore: 9/ 120 5/17 answered Question 7 You deposit $4000 in an account earning 7% interest compounded monthly. How much will you have in th account in 10 years? Submit Question
Answer:
8038.65
Step-by-step explanation:
[tex]4000(1+\frac{.07}{12})^{12*10}=8038.65[/tex]
A field is a rectangle with a perimeter of 1100 feet. The length is 300 feet more than the width. Find the width and length of the rectangular field
Answer:
Step-by-step explanation:
perimeter of rectangle = 1100
let breadth be x
length = 300 + x
perimeter of rectangle = 2(l + b)
1100 = 2(300 + x + x)
1100 = 2(300 + 2x)
1100 = 600 + 4x
1100 - 600 = 4x
500 = 4x
500/4 = x
125 = x
therefore breadth is 125 feet
length = 300 + 125
=425 feet
Answer:
The rectangular field is 425 feet by 125 feet.
Step-by-step explanation:
Let w represent the width of the rectangular field.
Since the length is 300 feet more than the width, the length can be modeled by the expression (w + 300).
The perimeter of a rectangle is given by the formula:
[tex]P=2(w+\ell)[/tex]
Where P is the perimeter and w and l are the width and length, respectively.
We are given that the perimeter is 1,100 feet. Substitute:
[tex]1100=2(w+\ell)[/tex]
Divide both sides by two:
[tex]550=w+\ell[/tex]
We know that l = (w + 300). So:
[tex]550=w+(w+300)[/tex]
Simplify:
[tex]2w=250[/tex]
Divide both sides by two. So, the width is:
[tex]w=125\text{ feet}[/tex]
Since the length is 300 feet more than the width, that means the length is 425 feet.
The rectangular field is 425 feet by 125 feet.
An earthquake with a rating of 6.5 is
considered a major earthquake that can
cause damage over a large area.
Answer:
it is not considered a major earthquake, for it to be considered a major earthquake it has to have a rating of 8.0 or higher
Find the missing length indicated. Hey can someone help me out?
Answer:
C) 6
by-step explanation:
Which of the following is not equal to a ratio of 5 to 2?
A. 25: 10 C.35: 15
B. 35: 14 D. 40:16
Answer:
C 35:15
Step-by-step explanation:
because 35:15 =5:3 so it is not equal to a ratio of 5 is to 2
Answer:
C
Step-by-step explanation:
If you simplify all the ratios, then you get the following:
A. 25/5 : 10/5 = 5:2
B. 35/7 : 14/7 = 5:2
C. 35/5 : 15/5 = 7:3
D. 40/8 : 16/8 = 5:2
A books storevhad 30816 exercise books which were packed in cartons, each carton contains 24exercise books.The mass of an empty carton was 2kg and full was 12kg."what was the total mass of each empty carton, what was the total mass of the books alone?"
Step-by-step explanation:
the total mass of each empty carton
1284×2568kg
the total mass of books alone
30816×10=12840kg
A railway station measures 200 meters in length. How long is it?
A. 10,000 cm
B. 12,000 cm
C. 15,000 cm
D. 20,000 cm
Please help I need help with my hw
Answer:
a) 2.5 pounds of candy
b) 2.5 pounds of candy
[tex]\frac{0.5}{1} :\frac{y}{5}[/tex]
y × 1 = 0.5 × 5
y = 2.5
Step-by-step explanation:
1 = 5
1/2 = y or 0.5 = y
[tex]\frac{0.5}{1} :\frac{y}{5}[/tex]
y × 1 = 0.5 × 5
y = 2.5
The running back for the Bulldogs football team carried the ball 7 times for a total loss of 8 3/4 yards. Find
the average change in field position on each run. Enter the average change as a simplified mixed number.
The average change in field position on each run was
yards.
Answer:
-1 1/4 yards
Step-by-step explanation:
7 carries
-8.75 yards total yardage
-.8.75 / 7 = -1.25 yards average per carry
In mixed number ? -1 1/4 yards
Given that ABCD is a rectangle, find the total area of the figure below. Round your answer to the nearest tenth.
Options
18 ft²
20.25 ft²
21.5 ft²
22.5 ft²
Answer:
C
Step-by-step explanation:
Can y’all help me on question 20?!
Answer:
yes I can help you but ???
Triangle D E F is shown. Angle E F D is a right angle. The length of E F is 24 and the length of D F is 7.
Which trigonometric ratios are correct for triangle DEF? Select three options.
sin(D) = StartFraction 24 Over 25 EndFraction
cos(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 24 Over 7 EndFraction
sin(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 7 Over 24 EndFraction
Answer:
Sin(E) = 7/25
Sin(D) = 24/25
Tan(D)= 24/7
Step-by-step explanation:
Sin=opp/hyp
Tan=opp/adj
Cos=adj/hyp
The trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
How to determine the trigonometric ratios?The given parameters are:
EF = 24
DF = 7
Start by calculating the length DE using:
DE²= EF² + DF²
So, we have:
DE²= 24² + 7²
Take the square root of both sides
DE= 25
The sine of the angles is calculated using:
sin(Ф) = opp/hyp
So, we have:
sin(E) = 7/25
sin(D) = 24/25
The tangent of the angles is calculated using:
tan(Ф) = opp/adj
So, we have:
tan(D)= 24/7
Hence, the trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
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