Answer:
y = x + 2
Step-by-step explanation:
4x - 4y = -8 can be rearranged to slope-intercept form by isolating y.
[tex]4x - 4y = -8\\-4y = -8 - 4x\\y =\frac{-8-4x}{-4} \\y = 2 + x\\y = x + 2[/tex]
Willa is building birdhouses. Each side of the birdhouse will need 9 nails. How many nails does Willa need for each birdhouse? There are 7 sides on the birdhouse. If Willa uses only 7 nails on each side, how will the total number of nails she uses change?
The total number of nails will decrease by 14 nails when Willa will use 7 nails on each side.
Step-by-step explanation:
Sides of one birdhouse = 7
Nails used on each side = 9
Nails used on one birdhouse = Nails per side * Sides of birdhouse
Nails used on one birdhouse = 9*7 = 63 nails
If she uses 7 nails on each side, then the number of nails used on one birdhouse;
No. of nails = 7 * 7 = 49 nails
Change = Nails used on one birdhouse - No. of nails
Change = 63 - 49 = 14
The total number of nails will decrease by 14 nails when Willa will use 7 nails on each side.
Keywords: multiplication, subtraction
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Each birdhouse needs 63 nails. If Willa uses only 7 nails on each side, she will need a total of 49 nails.
Explanation:Each side of the birdhouse requires 9 nails, and there are 7 sides on the birdhouse. To find the total number of nails needed for each birdhouse, we can multiply the number of nails per side by the number of sides:
9 nails/side x 7 sides = 63 nails needed for each birdhouse.
If Willa only uses 7 nails on each side, the total number of nails she uses will change. The new total number of nails can be found by multiplying the new number of nails per side (7 nails) by the number of sides (7 sides):
7 nails/side x 7 sides = 49 nails in total.
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If cos theta = 3/5 and theta is in the first quadrant, what is sin 2 theta
Final answer:
To find sin 2θ when cos θ = 3/5, we first find sin θ using the Pythagorean identity and then apply the double angle formula, yielding sin 2θ = 24/25.
Explanation:
To find sin 2θ when given cos θ = 3/5 and θ is in the first quadrant, we can use the double angle formula for sine, which is sin 2θ = 2 sin θ cos θ. First, we need to find sin θ. Given that θ is in the first quadrant, all trigonometric functions are positive, and we can use the Pythagorean identity sin²θ + cos²θ = 1 to find sin θ. Since we know cos θ, cos²θ = (3/5)² = 9/25, which means sin²θ = 1 - 9/25 = 16/25. Taking the positive square root, since θ is in the first quadrant, sin θ = 4/5.
Now, we apply the double angle formula: sin 2θ = 2 × (4/5) × (3/5), which simplifies to sin 2θ = 24/25.
Chad made a snack by combining 1/3 of a bowl of granola with ¼ of a bowl of
chopped banana and ½ of a bowl of yogurt. Did one bowl hold all of the
ingredients at one time? Explain
Answer: No
Step-by-step explanation: because
1/2 +1/4 +1/3 is larger than one bowl.
6+3+4/12 = 13/12
;. 1 ¹/12.
Therefore, 1 bowl can not carry it
No, One bowl can not carry all of the ingredients at one time.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Chad made a snack by combining 1/3 of a bowl of granola with ¼ of a bowl of chopped banana and ½ of a bowl of yogurt.
The total amount 1/2 +1/4 +1/3 is larger than one bowl.
6 + 3 + 4/12 = 13/12
also 1 ¹/12.
Therefore, No 1 bowl can not carry it.
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Write an equation in point slope form (-7, 4) m=-¾
Answer:
y=-3/4x-5/4
Step-by-step explanation:
use the formula y-y1=m(x-x1)
y-4=-3/4(x-(-7))
Erica and Amy started biking in the opposite directions at the same time from the same place. Erica biked at a speed of 6 meters per second and Amy biked at a speed of 4 meters per second. How soon were they exactly 1 km apart?
Answer:
100 seconds
Erica and Amy are at distance of 1 km in 100 seconds
Step-by-step explanation:
They both are travelling in opposite directions so the sum of the distances they travel is the distance between them.
Let's take t as the total time taken to achieve a seperation of 1km
Distance traveled by Erica , (Speed of Erica - v1)
x1 = v1 * t
Distance travelled by Amy , (Speed of Amy - v2)
x2 = v2*t
Therefore sum of the distances they traveled is x1+x2 = x
x = v1*t + v2*t
x = t*(v1 + v2)
Here it is given that final seperation between Amy and Erica is 1km or 1000 m
Therefore x = 1000 m
Thus t = [tex]\frac{x}{v1+v2}[/tex]
Substituting given values v1 = 6 m/s v2 = 4 m/s
Therefore,
They are apart by exactly 1km in a time of 100 sec
List the steps that should be used to solve the equation f(x) = g(x) by graphing when f(x) = (1/2)² - 3 and g(x) = 3x + 5?
* So far I got to f(x) = (1/2)² - 3x - 8 = 0 (what is the next step and does this problem require the use of logarithms?)
value of x is: [tex]x=\frac{-31}{12}[/tex]
Step-by-step explanation:
We need to solve the equation f(x)=g(x)
where [tex]f(x)=(\frac{1}{2})^2-3[/tex]
and [tex]g(x) = 3x + 5[/tex]
Solving to find f(x)=g(x)
Putting values of f(x) and g(x)
[tex]f(x)=g(x)\\(\frac{1}{2})^2-3=3x + 5\\\frac{1}{4}-3=3x + 5\\Subtarct\,\,5\,\,on\,\,both\,\,sides:\\\frac{1}{4}-3-5=3x + 5-5\\\frac{1}{4}-8=3x\\Taking\,\,LCm\,\,on\,\,left\,\,side\\\frac{1-8*4}{4}=3x\\\frac{-31}{4}=3x\\Divide\,\,both\,\,sides\,\,by\,\,3\\x=\frac{-31}{4*3}\\x=\frac{-31}{12}[/tex]
So, value of x is: [tex]x=\frac{-31}{12}[/tex]
The graph will be a straight line x= -2.58 or x = -31/12
Keywords: Composition of Functions
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A radio telescope's shape can be approximated with the equation y=0.011x^2. Is the relationship between x and y linear? Is it proportional?
In 2015, nearly three out of every ten autos sold in a country was a crossover utility vehicle. If an auto dealership sold 4800 vehicles in total that year, how many of these sales would be expected to involve a cuv? Simplify your answer.
Answer:
about 160
Step-by-step explanation:
Answer:
1440 CUVs, approx. Actual number would be slightly lower.
Step-by-step explanation:
To answer this question, multiply 4800 vehicles by (3/10) for an approximation of the number of CUVs sold:
4800 3
---------- * ------- = 1440 CUVs
1 10
What fraction of an hour is 8 minutes in simplest form
8 minutes is 2/15 of an hour when simplified, which is obtained by dividing both the numerator and denominator of the fraction 8/60 by the greatest common divisor of 8 and 60, which is 4.
To convert 8 minutes into a fraction of an hour, first understand that 1 hour is equivalent to 60 minutes. Therefore, to find what fraction 8 minutes is of an hour, you can create the ratio of 8 minutes to 60 minutes, which simplifies to:
8 minutes / 60 minutes = 8/60
This fraction can then be simplified by dividing both the numerator and the denominator by the greatest common divisor (GCD) of 8 and 60, which is 4, to obtain:
8/60 ÷ 4/4 = 2/15
Thus, 8 minutes is 2/15 of an hour in simplest form.
What is the answer to the photo
Answer:
96 is the answer maybe of it
2(x-1)-y=-8
y=2x+8
substitution method
Answer:
No Solution.
Step-by-step explanation:
2(x-1)-y=-8
y=2x+8
----------------
2x-2-(2x+8)=-8
2x-2-2x-8=-8
2x-2x-2-8=-8
0-2-8=-8
-2-8=-8
-10=-8
no solution
At 6:00 AM the temperature was 35 degrees Celsius. At 5:00 PM the temperature was 28 degrees Celsius. Was it warmer or cooler at 5:00 PM?
Answer:
I think it was warmer
What is the value for x?
Answer: X = 4.33
Step-by-step explanation:
cos angle = hypotenuse / opposite side
cos 30° = X/5
0.866 = X/5
X = 4.33
2.4x-9.1x+12.5=-39.44
Answer:
I think the simplified answer is 7.69
Please help on question c
Answer: 240 km
Step-by-step explanation:
From the graph :
50 miles = 80km
1 miles = 80/50 km
Therefore :
150 miles = 80/50 x 150
150 miles = 240 km
1/4 of a rod was painted red. 2/5 was painted orange and 2/7 of the remainder was painted yellow. The yellow section was 20cm long how long was the rod
Answer: 200cm long
Step-by-step explanation:
Let the length of the rod be x
red = 1/4 of the rod , which means 1/4 of x
orange = 2/5 of x
The remainder = x - ([tex]\frac{x}{4}[/tex] +[tex]\frac{2x}{5}[/tex])
= x - ([tex]\frac{13x}{20}[/tex])
= [tex]\frac{7x}{20}[/tex]
yellow = 2/7 of the remainder , that is
yellow = 2/7 of [tex]\frac{7x}{20}[/tex]
yellow = [tex]\frac{x}{10}[/tex]
and it was given that the yellow section was 20cm long , that is
[tex]\frac{x}{10}[/tex] = 20cm
x = 20 x10
x = 200
Therefore the rod was 200cm long
To determine the length of a rod based on fractions of it being painted different colors, with the yellow section known to be 20cm, we set up a proportion based on the fractions of the rod painted and use this to solve for the total length of the rod, which is 200cm.
Explanation:The subject of this question is Mathematics, and it is typically encountered at the Middle School level. To find the length of the entire rod when 1/4 is painted red, 2/5 is painted orange, and 2/7 of the remainder is painted yellow with the yellow section being 20cm, we need to set up an equation and solve for the total length of the rod.
First, we determine the fraction of the rod that remains after painting 1/4 red and 2/5 orange:
Calculate the total fraction painted already (red and orange combined): (1/4) + (2/5).Subtract that from 1 to find the remaining fraction.Of that remaining fraction, 2/7 is painted yellow.Since 2/7 of the remainder is 20cm, we can set up the proportion (2/7 of remainder) = 20cm to find the remainder.Once we find the remainder, we use it to calculate the full length of the rod.Let's start the calculations:
1. (1/4) + (2/5) = 5/20 + 8/20 = 13/20.
2. The remaining fraction = 1 - 13/20 = 7/20.
3. Let x be the total length of the rod. Since 2/7 of the remainder is 20cm, we can write the equation (2/7) * (7/20) * x = 20cm.
4. Simplify and solve for x:
(2/7) * (7/20) * x = 20cm,
(1/10) * x = 20cm,
x = 20cm * 10,
x = 200cm.
Therefore, the total length of the rod is 200cm.
A bag contains 8 blue marbles 6 red marbles and 4 green marbles what is the probability of selecting a blue marble replaced it in the bag and then selecting a red marble
Answer:
[tex]\dfrac{4}{27}[/tex]
Step-by-step explanation:
A bag contains 8 blue marbles 6 red marbles and 4 green marbles, 8 + 6 + 4 = 18 marbles in total.
The probability of selecting a blue marble is
[tex]P(\text{blue marble})=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}=\dfrac{8}{18}=\dfrac{4}{9}[/tex]
Then the blue marble was replaced in the bag.
The probability of selecting a red marble is
[tex]P(\text{red marble})=\dfrac{\text{Number of red marbles}}{\text{Total number of marbles}}=\dfrac{6}{18}=\dfrac{1}{3}[/tex]
The probability of selecting a blue marble replaced it in the bag and then selecting a red marble is
[tex]P=\dfrac{4}{9}\cdot \dfrac{1}{3}=\dfrac{4}{27}[/tex]
what is the Y intercept of Y equals 4x +15 ?
Answer: 15
Step-by-step explanation: Linear equations can be written in the form
y = mx + b where the base "b" represents the y-intercept of the line.
So in this case, the y-intercept of the line would positive 15.
The equation can written as y = 4x + 15.
This equation is written in slope-intercept. y = mx + b
m = slope
b = y-intercept
In this equation the y-intercept (b) is 15.
_______
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A pair of dice is rolled. Find the probability that the sum of the two dice is less than 2
Answer:
0/36
Step-by-step explanation:
Answer:
0/36
Step-by-step explanation:
It is impossible to roll two dice and get a sum less than 2.
(I'm assuming this is a 6 sided die, but either way if you have more than one die this is impossible.
The lowest you can roll would be 1+1 therefore adding up to a 2.
9/16 = x/12
x-3/18 = 12/9
7/11 = 18/x+1
3x-4/14 = 9/10
Simplify
Answer:
Step-by-step explanation:
9/16=x/12
cross product
16x=9*12
16x=108
x=108/16
simplify
x=27/4
---------------
x-3/18=12/9
x=12/9+3/18
x=24/18+3/18
x=27/18
x=3/2
--------------------
7/11=18/x+1
18/x=7/11-1
18/x=7/11-11/11
18/x=-4/11
x=18/(-4/11)=(18/1)(-11/4)=-198/4=-99/2
x=-99/2
A line passes through (10,5) and (13,-4). Write the equation in standard form
Answer:
Standard Form : 3x+1y=35
Step-by-step explanation:
The equation of the line will be 3x+y-35=0
What is the equation of the line written in standard form?The equation of the line in standard form will be expressed by using the coefficient of x and coeficient of y which is given
ax+by+c=0
How to determine the equation of the line in standard form from two point passing through it?The equation of line which passes through two points will be
(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)
So according to asked question,
x₁=10,y₁=5
x₂=13,y₂=-4
the equation of line will be
(y-5)/(x-10)=(-4-5)/(13-10)
⇒(y-5)/(x-10)=-9/3
⇒(y-5)/(x-10)=-3
⇒y-5=-3(x-10)
⇒y-5=-3x+30
⇒y+3x-5-30=0
⇒3x+y-35=0
Therefore the equation of the line will be 3x+y-35=0
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87 1/2% of what number is 105?
Answer:
120
Step-by-step explanation:
87.5% of what number is 105?
87.5%=0.875
105/0.875=120
There are 16 ounces in 1 pound.juan is mailing a packet that weigth 10 pound he want to know the weight of the package in once’s
Answer:
160 ounces
Step-by-step explanation:
1 pound=16 ounces
so,
10 pounds=16 multiplied by 10= 160 ounces
Fun fact u spelled ounces at the very last.
pls can I have five star
The weight of the 10-pound package is 160 ounces.
Explanation:There are 16 ounces in 1 pound. Juan is mailing a packet that weighs 10 pounds. To find the weight of the package in ounces, multiply the number of pounds (10) by the unit equivalence (16).
10 pounds x 16 ounces/pound = 160 ouncesTherefore, the weight of the package is 160 ounces.
10. A nursery owner buys 5 panes of glass to
some damage to her greenhouse. The S Danes
cost $14.25. Unfortunately, she breaks 2 more
panes while repairing the damage What is the
cost of another 2 panes of glass?
if x varies directly as y, find x when y=8. x=11 when y=-3
Answer:
[tex]x=-\frac{88}{3}[/tex]
Step-by-step explanation:
When a quantity "A" varies DIRECTLY with another quantity "B", we can write the proportionality equation as:
A = kB
Where k is the proportionality constant (to be found)
In this problem, it is given x varies DIRECTLY with y, so we can write:
x = ky
Also, given, x = 11, y = -3, so we plug these into the equation and first find k:
x = ky
11 = k(-3)
k = -11/3
Now, we need to find x when y = 8, so we substitute and find x:
[tex]x=ky\\x=(-\frac{11}{3})(8)\\x=-\frac{88}{3}[/tex]
To find x for a given value of y when x varies directly as y, determine the constant of proportionality using the provided pair of values. Then use this constant to calculate x for the new value of y.
Explanation:Since x varies directly as y, we can write this as x = ky, where k is the constant of proportionality. To find the value of k, we use the given values: x=11 when y=-3. Substituting these values into the equation gives us 11 = k(-3), or k = -11/3.
To find x when y=8, we substitute y=8 and the value of k into the direct variation equation: x = (-11/3)(8) = -88/3 = -29.33. Therefore, x is approximately -29.33 when y=8.
sarah dvd collection. is stored in a cabinet that holds 6 dvds on each self. jow many shelves will she need to hold her collection of 89 dvds?
Answer:
15 shelves
Step-by-step explanation:
6 dvds = 1 shelf
89/6= 14.8333333333 shelves
But you cannot have 0.8333333333 shelves so you would round 0.8333333333 to 1
solve these absolute value equations step by step
Answer:
16 is x<3
Step-by-step explanation:
4x-10<2
Add 10 to both sides
4x<12
Divide 4 from both sides and you get x<3
Jiang purchased a moving truck for the business. He paid $40,000 for the truck. Its salvage value is $8,500. Select the correct answer from the drop-down menu.
The depreciation expense of the moving truck for a useful life of 10 years is (blank space). If the truck’s useful life where 15 years, the depreciation expense would come to(blank space).
Answer:
A. $3,150
B. $2,100
Step-by-step explanation:
A. Given,
Trucks cost price = $40,000
Salvage Value = $8,500
Useful life = 10 years
Since there is no requirement, I am using straight-line depreciation method to calculate the depreciation expense.
We Know,
Depreciation Expenses = (Cost price - Salvage Value) / Useful Life
Therefore,
Depreciation expense = ($40,000 - $8,500)/10
Depreciation Expense = $31,500/10
Depreciation Expense = $3,150
Therefore, under the straight-line method, the depreciation expense will be = $3,150.
B. Given, (When the useful year is 15)
Trucks cost price = $40,000
Salvage Value = $8,500
Useful life = 15 years
Since there is no requirement, I am using straight-line depreciation method to calculate the depreciation expense.
We Know,
Depreciation Expenses = (Cost price - Salvage Value) / Useful Life
Therefore,
Depreciation expense = ($40,000 - $8,500)/15
Depreciation Expense = $31,500/15
Depreciation Expense = $2,100
Therefore, under the straight-line method, the depreciation expense will be = $2,100
how many pencils measure 6 inches
Answer:
11
Step-by-step explanation:
because that are 11 pencils that are 6 inches or longer, that's what the picture says.
Answer:
Helpful piece of information - each x = 1 pencil
Step-by-step explanation:
If each x = 1 pencil, and their are 6 x's over the 6 inch mark, 2 x's over the 7 inch mark, and 3 x's over the 8 inch mark, how many pencils measure 6 inches or more?
11 pencils measure 6, 7, and 8 inches.
I hope this helps!
Which expression has a negative value? a)−1×−2 b)−1×2×−3×4×−5 C) 1×−2×−3×−4×−5 d)1×−2×3×−4×5
Answer:
b)−1×2×−3×4×−5 has a negative value.
Step-by-step explanation:
Given expressions are a)−1×−2 b)−1×2×−3×4×−5 C) 1×−2×−3×−4×−5 d)1×−2×3×−4×5
Firstly we have to multiply the digits with digit then after minus sign.
So for a)−1×−2
Solution, [tex]1\times2\ =2[/tex]
When two negative signs are multiplied with each other it gives a positive sign.
Both digits have a negative sign that means it gives a positive sign.
So the solution for 1st expression is [tex]2.[/tex]
b)−1×2×−3×4×−5
Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]
Here three digits have negative sign, two negative gives positive and then multiplied by negative gives negative.
So the solution for 2nd expression is [tex]-120[/tex].
C) 1×−2×−3×−4×−5
Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]
Here four digits have negative sign, two negative gives positive and again two negative gives positive means positive multiplied with positive gives positive.
So the solution for 3rd expression is [tex]120[/tex].
d)1×−2×3×−4×5
Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]
Two digits have a negative sign that means it gives a positive sign.
So the solution for 4th expression is [tex]120[/tex].
Hence the correct option is b.
Answer:
B
Step-by-step explanation: