Answer:
[tex]y=-\frac{2}{3}x + 6[/tex]
Step-by-step explanation:
We are given that a line has a slope of -2/3 and passes through the point (0,6)
We want to write the equation of this line; there are 3 forms of the line that we can use:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y interceptStandard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negativeSlope-point form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a pointAll though while writing the equation of the line in any of these ways is acceptable, the most common way is to write it in slope-intercept form, so let's do it that way.
As we are already given the slope, we can immediately substitute m with that value.
Replace m with -2/3:
y = -2/3x + b
Now we need to find b.
As the equation passes through the point (0, 6), we can use it to help solve for b.
Substitute 0 as x and 6 as y.
6 = -2/3(0) + b
Multiply
6 = 0 + b
Add
6 = b
Substitute 6 as b.
y = -2/3x + 6
Topic: finding the equation of the line
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The bases of a right prism are rhombii, each with area A = 44cm2. The height of the prism is h = 2.3dm. Find the volume, V, of the prism.
Step-by-step explanation:
did you make a typo, or do you actually mean dm ?
1 dm = 10 cm
in any case, in a right prism object it does not matter what shape the bases are.
the volume is always
base area × height
so, if you did not make a typo, then
height = 2.3 dm = 23 cm
and the volume of the prism is
44 × 23 = 1012 cm³
but if you did make a typo and
height = 2.3 cm,
then the volume of the prism is
44 × 2.3 = 101.2 cm³
Answer:
1012 centimeters cubed
Step-by-step explanation:
Volume=base x length x width
height = 2.3 dm, which is 23 cm, so the volume of the prism would be 44 × 23 = 1012 cm cubed
isaac has a balance of $28.17 in his utilities budget at the end of march. he budgets 16% of his $1,854.14 monthly net income each month. how much are the available funds for april?
The available fund for April is $324.83 if the Isaac has a balance of $28.17 in his utilities budget at the end of March.
What is expenses?It is defined as the money spends on the utility, the amount of money is required to buy something in other words it is the outflow of money from the solely earners income or the money incurred by any organization.
We have:
Current balance = $28.17
16% of his $1,854.14
= (1854.14×16)/100
= $296.66
The available fund for April = 296.66 + 28.17 = $324.83
Thus, the available fund for April is $324.83 if the Isaac has a balance of $28.17 in his utilities budget at the end of March.
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165
The distances between some planets are given below.
Planet Q
Planet Q is 3.5 10 km from planet P.
Planet R is 1.2 x 10 km from planet P.
Planet R
Planet P
Work out the shortest distance between
planet Q and planet R.
Give your answer in standard form.
four times the quotient of 3 divided by 4
Step-by-step explanation:
Step 1: Convert words into an expression
Four times the quotient of 3 divide by 4
We know that we are going to be multiplying 4 by something because in the statement we have four times. Reading further we also know that we are going to be dividing 4 from 3 which means that we will have 3/4. Finally, we see that we multiply our 3/4 by 4 which gives us our final solution.
[tex]4 * (3 / 4)[/tex]
If we want to solve it the 4's would just cancel and we would be left with 3.
3
Explanation:
You would start by dividing 3 by 4. Then multiply [tex]\frac{3}{4}[/tex] and 4. The 4s would cancel out leaving you with 3.
[tex]\frac{3}{4}[/tex] × [tex]4=3[/tex]
What is the range for this set of data?
7, 15, 12
3
5
8
1
Answer:
The range is (D) or '12'
Step-by-step explanation:
find the distance between the two points～
A ( 7 , 4 ) and B ( 3 , 2 )
thankyou!
Answer:
AB = [tex]\sqrt{20}[/tex]
Step-by-step explanation:
calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = B (3, 2 ) and (x₂, y₂ ) = A (7, 4 )
AB = [tex]\sqrt{(7-3)^2+(4-2)^2}[/tex]
= [tex]\sqrt{4^2+2^2}[/tex]
= [tex]\sqrt{16+4}[/tex]
= [tex]\sqrt{20}[/tex]
≈ 4.47 ( to 2 dec. places )
Answer:
[tex]distance = \sqrt{(3 - 7) ^{2} } + (2 - 4) ^{2} \\ = \: \: \sqrt{16} + 4 \\ \\ = \: \: \: \: 2 \sqrt{5} [/tex]
What is the area, measured in square centimeters, of the green shape
pictured below? Do not include units in your answer.
The answer is 6
In order to find the area, we need to use L x W
given that:
3(L) x 2(W) = 6 square centimeters
A function is given. h(t) = −t + 6/5 ; t = −3, t = 1
Answer:
h(-3) = 4.2 or 21/5
h(1) = 0.2 or 1/5
Step-by-step explanation:
Plug in -3 for t.
-(-3) + 6/5 = 4.2 or 21/5
Plug in 1 for t.
-(1) + 6/5 = 0.2 or 1/5
Ramesh invests rs12800 for three years at the rate of 10% per annum compound interest Find (I) the sum due to Ramesh at the end of the first year (ii) the interest he earns for the second year (iii) the total amount due to him at the end of three year
Answer:
1) 14080
2) 1408
3) 17036.80
Step-by-step explanation:
It is given that
Principal= 12800
Rate of interest =10% p.a
(i) We know that Interest for the first year=
(12800×10×1)/100
= 1280
So the sum due at the end of first year= 12800+1280
= 14080
(ii) Principal for second year = 14080
So the interest for the second year
=(14080×10×1)/100
=1408
iii) We know that Sum due at the end of second year
= 14080+1408
=15488
Here
Principal for third year= 15488
Interest for the third year= (15488×10×1)/100
=1548.80
So the total amount due to him at the end of third year= 15488+1548.80
= 17036.80
PLEASE HELP ME ANSWER THIS FAST
Answer:
65 square yards
Step-by-step explanation:
5x5=25
5x4=20
5x4=20
20+20+25= 65
I need help with question 10
Answer:
C
Step-by-step explanation:
pythagorean theorem: a²+b² = c²
area of square = length²
c = side opposite right angle = length of square Z
thus, area of square Z = c²
area of square X = a² (or b², it doesn't matter)
area of square Y = b² (or a²)
a² + b² = c²
region x + region y = region z
Side AB is opposite which angle in triangle ABC?
Answer:
∠ACB
Step-by-step explanation:
we have three options for angles in triangle ABC:
- ∠CAB
- ∠ABC
- ∠ACB
∠ACB is the only angle out of the three given that doesn't directly touch side AB, so this must be our answer
Donna borrowed $3000 from a bank for 2 years and was charged simple interest. The total interest that she paid on the loan was $120 . As a percentage, what was the annual interest rate of her loan?
Answer:
I = PRT / 100
P=3000R=?T = 2I = 120R = 100I/PT
R = 12000/6000
R = 2%
the formula for the circumference of a circl is c = 2 nr determine the circumference when the radius r is 10 cm
Answer:
20π cm or approximately 62.8 cm
Step-by-step explanation:
» Concepts
The circumference of a circle is the distance, or perimeter, around a circle in a certain unit such as centimeters. The formula to find the circumference, as stated, it 2πr, where r = radius.
» Application
In this case, we're asked to find the circumference of the circle using the formula 2πr. We're also given the radius as 10 cm.
» Solving
[tex]2(10)\pi[/tex] [tex]20\pi[/tex] 20π cmor
[tex]2(3.14)(10)[/tex] [tex](6.28)(10)[/tex] [tex]62.8[/tex] 62.8 cmAnswer:
c=2nr
but r=10 and n=3,14
c=2(3,14)(10)
c=62,8
55. The sum of an infinite geometric series is five times the value of the first term. What is the common ratio of the series?
Answer:
r = 4/5
Step-by-step explanation:
Formula
Sum of an infinite geometric series = a / (1 - r)
Givens
Sum = 5*a
a = a
r = ?
Solution
5a = a/(1 - r) Divide both sides by a
5a/a = a / (a * (1 - r) The a's on the right cancel
5 = 1 / (1 - r) Multiply both sides by 1 - r
5*(1 - r) = 1*(1 - r)/(1 - r) The 1 - r s on the right cancel
5*(1 - r) = 1 Remove the brackets.
5 - 5r = 1 Subtract 5 from both sides
5-5 - 5r = 1 - 5 Combine
-5r = - 4 Divide by - 5
r = 4/5
W over 5 =3 what does w equal
Answer:
1.667
Step-by-step explanation. Step by Step SolutionRearrange:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 5/w-(3)=0 Step by step solution :STEP 1: 5
Simplify —
w
Equation at the end of step 1: 5
— - 3 = 0
w
STEP 2:Rewriting the whole as an Equivalent Fraction 2.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using w as the denominator : 3 3 • w
3 = — = —————
1 w
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominatorAdding fractions that have a common denominator : 2.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible: 5 - (3 • w) 5 - 3w
——————————— = ——————
w w
Equation at the end of step 2: 5 - 3w
—————— = 0
w
STEP 3:When a fraction equals zero : 3.1 When a fraction equals zero ...Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.Here's how: 5-3w
———— • w = 0 • w
w
Now, on the left hand side, the w cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape : 5-3w = 0Solving a Single Variable Equation: 3.2 Solve : -3w+5 = 0 Subtract 5 from both sides of the equation : -3w = -5 Multiply both sides of the equation by (-1) : 3w = 5 Divide both sides of the equation by 3: w = 5/3 = 1.667 One solution was found : w = 5/3 = 1.667
What is the surface area?
5 m
7 m
4 m
140 m squared
16 m squared
166 m squared
156 m squared
Answer:
c. 166
Step-by-step explanation:
area = l x w
surface area = area
A person who searches for natural resources is a
A. prospector
B. detector
C. surveyor
D. researcher
A coin is tossed three times. The probability of getting two heads and a tail is
_.
Give answer as a fraction in lowest terms.
The coin is an illustration of probability, and the probability of getting two heads and a tail is 3/8
How to determine the probability?The sample space of tossing a coin three times is:
S = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
On the sample space, we have:
Two heads and a tail = 3
Sample size = 8
The required probability is then calculated using:
P = 3/8
Hence, the probability of getting two heads and a tail is 3/8
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How much time will have elapsed from 2:37 to 3:19
Answer:
42min would have elapsed
Step-by-step explanation:
2:37-2:40 (3 min)
2:40-3:00 (20 min)
3:00-3:19 (19 min)
if the ratio of nonfiction to fiction books on a bookshelf is 2 to 3. If the total number of books is 30, how many of them were nonfiction
Answer: 20
Step-by-step explanation: imagine the books in 10's cuz 30/3=10 and 2 of those tens out of the group of three are nonfiction, so that makes 20 out of 30
Can someone please help me with 6-10! I will give 100 points!!
Explanation:
6. A Linear function can be written in the form of f(x) = mx + b
7. In the form of f(x) = mx + b, the y intercept is b
8. The graph x = c is a vertical line with x intercept (c,0)
9. The graph y = c is a horizontal line with y intercept (0, c)
10. To find x intercept, let the y = 0, and solve for x
Answer:
See below ~
Step-by-step explanation:
Solutions :
===============================================================
6. A(n) linear function can be written in the form f(x) = mx + b.
===============================================================
7. In the form f(x) = mx + b, the y-intercept is b.
===============================================================
8. The graph of x = c is a vertical line with x-intercept (c, 0).
===============================================================
9. The graph of y = c is a horizontal line with y-intercept (0, c).
===============================================================
10. To find an x-intercept, let y = 0 and solve for x.
Eric, Kim, and Ed are trading downloaded songs. First, Eric gives Kim half of his songs. Then Kim gives one-third of her songs, which is 6 songs, to Ed. Finally, Ed gives Eric 2 songs. Because everyone end up with 12 songs, how many songs did Kim start with? How many songs did Eric start with?
The number of songs Kim started with are 18songs while the number of songs Eric started with are 36 songs.
Calculation of total songs owned by each traderFirstly, Kim = 1/2 of Eric's
Ed = 1/3 of Kim= 6 songs
Eric = 2 songs
Total songs by the whole traders is = 12 ×3 = 36songs
To find the total songs for Kim,If Kim gave Ed, 1/3 of her songs =6 , then her whole song is 6×3 = 18songs.
But she gave out 6 to Ed so 12 songs will remain.
To find total songs by Eric,If 18 songs received by Kim is half of Eric songs therefore, 18×2 = 36
But half was given to Kim therefore 18 songs is remaining for Eric
To find total songs by Ed,Ed received 6songs from kim and gave out 2, there, 4 songs is remaining for Ed.
Therefore the number of songs Kim started with are 18songs while the number of songs Eric started with are 36 songs.
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A cereal box is 9 1 2 inches long, 5 1 2 inches wide, and 12 inches high. What is the volume of the box?
Answer
5603328
Step by step explanation:
Hey! Rmemeber length x width x height!
Multiply: 9 1 2 x 5 1 2 x 12
Answer= 5603328
And thats it! If it is wrong you must have put the wrong numbers in, I dont get why their spaces though....
Have a good day!!
-3x° (2x7 - 4x + 1) multiply through polynomial
Answer:
-6x⁷ + 12x − 3
Step-by-step explanation:
Method 1 :
[tex]-3x^0\ (2x^7-4x+1)[/tex]
[tex]= (-3x^0)\times 2x^7-(-3x^0)\times4x+(-3x^0)\times1[/tex]
[tex]= (-3x^0)\times 2x^7+(3x^0)\times4x+(-3x^0)\times1[/tex]
[tex]=-6x^{0+7}+12x^{0+1}-3x^0[/tex]
[tex]=-6x^{7}+12x^{1}-3x^0[/tex]
[tex]=-6x^{7}+12x-3[/tex]
Method 2 :
Note : x⁰ = 1
[tex]-3x^0\ (2x^7-4x+1)[/tex]
[tex]=-3\ (2x^7-4x+1)[/tex]
[tex]=-3\times2x^7-(-3)\times4x+(-3)\times1[/tex]
[tex]=-6x^7+12x-3[/tex]
Which of the following represents the diameter of the circle below?
Answer:
xy represents the diameter
Circle p has radius 8. Points Q and R lie on circle P, and the length of arc QR is 4pie. What is measure angle QPR in radians?
In the circle the measure of angle QPR in radians is π/4.
What is a circle?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
The length of the arc QR is 4π, which is 1/2 of the circumference of the circle P.
Therefore, the circumference of the circle is -
2πr = 2π(8) = 16π
The angle subtended by the arc QR at the center of the circle is therefore -
θ = arc length / radius
θ = (4π) / 8
θ = π/2
Now, consider the triangle QPR.
The angle QPR at the center of the circle is equal to twice the angle subtended by the arc QR at any point on the circumference of the circle.
Therefore -
2∠QPR = θ = π/2
Solving for ∠QPR, we get -
∠QPR = (π/2) / 2
∠QPR = π/4
Therefore, the measure QPR is π/4.
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Concord Corporation sells its product for $7600 per unit. Unit variable cost are: manufacturing, $4400, and selling and administrative, $50. Fixed costs are: $14000 manufacturing overhead and $20000 selling and administrative. There was no beginning inventory at 1/1/21. Production was 20 units per year in 2021–2023. Sales were 20 units in 2021, 16 units in 2022, and 24 units in 2023. Net income under variable costing for 2023 is
The income under variable costing for 2023 for Concord Corporation is $73600.
How to calculate the net income?The formula to calculate the net income will be:
= Total sales - Total variable cost - Total fixed cost
= (7600 × 24) - (4400 + 50 × 24) - 2000
= 182400 - 106800 - 2000
= 73600
Therefore, the income under variable costing for 2023 for Concord Corporation is $73600.
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Supposea triangle has sides 3, 4, and5. Which of the following must be true? OA The triangle in question is not a right triangle. OB. The triangle in question is a right triangle. Oc.The triangle in question may or may not be a right triangle.
Answer: B. The triangle in question is a right triangle.
Reason:
The sides are
a = 3b = 4c = 5Plug them into the equation below and simplify both sides
[tex]a^2+b^2 = c^2\\\\3^2+4^2 = 5^2\\\\9+16 = 25\\\\25 = 25\\\\[/tex]
Therefore, we have a right triangle. For more information, check out the converse of the pythagorean theorem.
Hello
Please what’s the explanation to get the answer (2+2) ² (2+3)³
Answer:
141Step-by-step explanation:
Hello
Please what’s the explanation to get the answer (2+2) ² (2+3)³
we use PEMDAS
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
(2 + 2)² + (2 + 3)³ =
4² + 5³ =
16 + 125 =
141