[tex]3x+5y=50[/tex] is the equation of the line through point (10,4) and parallel to 3x+5y=8.
How to solve equation of the line through point and parallel to a given line?We can write the equation of a line parallel to a given line if we know a point on the line and an equation of the given line. y=2x+3 . Parallel lines have the same slope. The slope of the line with equation y=2x+3 is 2 .
Given
Equation of the line is 3x + 5y = 8.
Point = (10, 4)
First we find the slope of the line 3x + 5y = 8 by replacing it into slope intercept form:
[tex]3x + 5y = 8[/tex]
⇒ [tex]5y = -3x + 8[/tex]
⇒ [tex]y = \frac{-3}{5} x + \frac{8}{5}[/tex]
Therefore, the slope of the line is m = [tex]\frac{-3}{5}[/tex].
Now since the equation of the line with slope m passing through a point [tex](y-y_{1} )=m(x-x_{1})[/tex]
⇒ [tex]y - 4=\frac{-3}{5} (x-10)[/tex]
⇒ [tex]5(y-4)=-3(x-10)[/tex]
⇒ [tex]5y-20=-3x+30[/tex]
⇒ [tex]3x+5y=30+20[/tex]
⇒ [tex]3x+5y=50[/tex]
Hence, [tex]3x+5y=50[/tex] is the equation of the line through point (10,4) and parallel to 3x+5y=8.
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A rectangular piece of metal is 9 in. longer than it is wide. Squares with sides 3 in. long are cut from the four corners, and the flaps are folded upward to form an open box. Which equation indicates that the volume of the box is 80 in. cubed?
Step-by-step explanation:
Let the width be = w
The length will be = w+9
And height h = 3 inches ( side of square =3 in)
Volume = l x w x h
According to question
[tex]80 = w(w+9)3\\3w^2+27w-80=0[/tex]
So, this equation indicates that the volume of the box is 80 in.
Help please...........bad
Answer: 0,5, and -4 is the zeros
Step-by-step explanation:
Question: There are 60% of students currently taking AP Biology who have taken previous AP courses. Carver High School has 9 of 15 students who have taken previous AP courses. Design a simulation to determine the probability of getting this number of students, who have taken previous AP courses, in a group this size. Which of the following assignments of the digits 0 through 9 would be appropriate for modeling this situation? (2 points)
Options:
A. Assign 0, 1, and 2 as having taken previous AP courses and 4, 5, 6, 7, 8, and 9 as not having taken previous AP courses.
B. Assign 0, 1, 2, 3, 4, and 5 as having taken previous AP courses and 6, 7, 8, and 9 as not having taken previous AP courses.
C. Assign 0 and 1 as having taken previous AP courses and 2, 3, 4, 5, 6, 7, 8, and 9 as not having taken previous AP courses.
D.Assign 0, 1, 2, and 3 as having taken previous AP courses and 4, 5, 6, 7, 8, and 9 as not having taken previous AP courses.
E. Assign 7, 8, and 9 as having taken previous AP courses and 0, 1, 2, 3, 4, 5, and 6 as not having taken previous AP courses.
Answer:
B: Assign 0, 1, 2, 3, 4, and 5 as having taken previous AP courses and 6, 7, 8, and 9 as not having taken previous AP courses.
Step-by-step explanation:
Got it right on the quiz
The simulation of this probability is (b) assign 0, 1, 2, 3, 4, and 5 as having taken previous AP courses and 6, 7, 8, and 9 as not having taken previous AP courses.
How to design the simulation?The proportion of students taking AP biology is given as:
p = 60%
Express as fraction
p = 6/10
This means that for every 10 students, 6 of them are taking AP Biology.
To simulate this, we can make use of 10 numbers (say 0 to 9)
Of this 10 numbers, numbers 0 to 5 (i.e. 6 numbers) can be assigned to students taking AP Biology.
While the other number can be assigned to other students
Hence, the simulation of this probability is (b)
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I need help
Y=2x+7
X=4
Y=
Answer:
Y=15
Step-by-step explanation:
2(4)+7
8+7
15
Answer:
Y=15
Step-by-step explanation:
Use the lesser than sign in the greater than sign to fill in the middle blanks , between the two numbers given? < , >
Answer:
-67>-76
|-24|<|-42|
|45|<|-54|
Step-by-step explanation:
The first question is easy, when you're comparing negatives, the number that looks lower is actually greater. The second and third ones are a bit trickier. This --> || means the opposite of. Like |5| means -5. so just swap the numbers around and you have your answer.
Find the prime factorization of 32. Write in exponential form.
thank you !!!
Answer:
2 exponent is 5
Step-by-step explanation:
5
so 2
For what value of x does 3^2x-9^3x-4
Answer:
jdjndbncjjsnnxjjxjnxjnsnnx.
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I don't understand algebra 2!!! at all idk why
break it down please help
Answer:
1/5... 1 on top 5 on bottom
Step-by-step explanation:
sub in the values:
[tex]\frac{5+y}{6x}[/tex] will now be [tex]\frac{5+7}{6(10)}[/tex]
now add:
[tex]\frac{12}{60}[/tex]
simplify:
1/5
All the fudge machines at a chocolate factory work at the same rate. Six machines working simultaneously can complete a big order in 22 hours. How many hours would it take to fill the order if the number of working machines decreased by factor of 4?
Answer:
88 hours
Step-by-step explanation:
Since we are decreasing the number of machines by a factor of four and all the machines work at the same rate, we are simply going to increase the work hours by a factor of 4
Increasing the work hours by a factor of 4 will yield 22 * 4 = 88 hours
So it will take 88 hours to fill the order if the number of machines is deceased by a factor of 4
Jorge drank 500 liters of coke.How many milliliters of coke did he drink?
Pretty sure its 500000 milliliters.
hope this helps
Answer:
500,000 liters
Step-by-step explanation:
mulitply the volume of the liters value by 1000
1/2 of the sum of a number and 10
Answer:
1/2(x+10)
Step-by-step explanation:
What is the solution to this equation
-4x + 2 = 26
Answer:
x=-6
Step-by-step explanation:
Move all terms that don't contain x to the right and solve using the elimination process.
A scientist poured 1.6 x 103 milliliters of water into a container that already had 2.8 x 104 milliliters of salt water and 9.4 x 103 milliliters of sugar water.
This question is incomplete
Complete Question
A scientist poured 1.6 x 10³ milliliters of water into a container that already had 2.8 x 10⁴ milliliters of salt water and 9.4 x 10³ milliliters of sugar water. How many milliliters of liquid were in the container?
A.1.7 x 10⁴ milliliters
B.3.58 x 10⁴ milliliters
C.3.74 x 10⁴ milliliters
D.3.9 x 10⁴ milliliters
Answer:
C. 3.74 x 10⁴ milliliters
Step-by-step explanation:
The milliliters of liquid that WERE in the container = The milliliters of liquid that were in the container before adding 1.6 x 10³ milliliters of water
This equals to:
2.8 x 10⁴ milliliters of salt water and 9.4 x 10³ milliliters of sugar water.
Hence:
2.8 x 10⁴ milliliters of salt water + 9.4 x 10³ milliliters of sugar water
= (2.8 × 10⁴) + (9.4 × 10³)
= 37400
= 3.74 x 10⁴ milliliters
Therefore, option C is correct
Evaluate 1/6t+1/12 when t=1/2
Answer:
1/6
Step-by-step explanation:
You're welcome :)
7TH GRADE MATH ASAP. Liam is setting up folding chairs for a meeting. If he arranges the chairs in 8 rows of the same length, he has 11 chairs left over. If he arranges the chairs in 6 rows of that same length, he has 13 left over. How many chairs does Liam have?
Answer:
19 chairs
Step-by-step explanation:
you can make two equations
1. y = 8x + 11
2. y = 6x + 13
Y is the number of total chairs and x is the length
so 8x + 11 = 6x + 13
2x = 2
x = 1
so the length is one
To find the total number of chairs just plug in one as x
y = 8 + 11
y = 6 + 13
y = 19
so 19 chairs is the number of chairs Liam has.
What is the equation of the line that passes through the point (-6,1) and has a slope of 1/6?
Answer:
y - 1 = 1/6x + 1 <<< Point slope form
y = 1/6x + 2 <<< slope intercept form
Either one works unless the question specifies the form of the equation
Step-by-step explanation:
Point slope form: (y - y1) = m(x - x1)
Given: (-6,1) ; m = 1/6
(y - 1) = 1/6(x - (-6))
y - 1 = 1/6x + 1 <<< Point slope form
y = 1/6x + 2 <<< slope intercept form: y = mx + b
What is the sum of the rational expression below? 3x/x+2 + x/x+4
A. 4x^2 +14x/x^2 + 6x + 8
B. 4x/2x + 6
C. 3x^2/x^2 + 8
D. 4x^2 + 4x +8/x^2 + 6x +8
The sum of the rational expression is (4x²+14x)/ (x²+6x+8)
How to find the sum of the rational expression?
A rational expression is an expression that is the ratio of two polynomials. For example, the expression (x^2 + 2x + 1) / (x + 1) is a rational expression. The numerator and denominator can have different degrees and the expression can be simplified if there is a common factor.
To find the sum of the rational expression 3x/(x+2) + x/(x+4). First, find the LCM of (x+2) and (x+4), which is (x+2)(x+4):
3x/(x+2) + x/(x+4) = [3x(x+4) + x(x+2)] / (x+2)(x+4)
= [3x²+12x + x²+2x] / (x²+4x+2x+8)
= (4x²+14x)/ (x²+6x+8)
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Help me please
Make x the subject of the formula
X – 7r = bc
Answer:
x = bc + 7r
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesStep-by-step explanation:
Step 1: Define equation
x - 7r = bc
Step 2: Solve for x
Add 7r to both sides: x = bc + 7rNathan measured a line to be 7.4 inches long. If the actual length of the line is 7.2 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
2.8%
Step-by-step explanation:
(7.4 - 7.2) / 7.2 =
0.2 / 7.2 =
2.7777777777778%
If correct will mark brainliest !!!!!
Answer:
equilateral triangle, isosceles triangle, scalene triangle
(Left to Right)
Step-by-step explanation:
Answer:
1-equilateral triangle 2- isosceles triangle 3- scalene triangle
Step-by-step explanation:
Help me pleaseeee I need to finish
Molly walked 3.45 miles on a hike. Her sister walked 1.23 miles. Her brother walked How much farther did Molly walk than her brother and sister combined? 0.85 miles
Answer:
1.4
Step-by-step explanation:
If 3x + 6 = 213x plus 6 equals 21, what does x + 2x plus 2 equal?
Answer:
17
Step-by-step explanation:
PLS GIVE BRAINLIEST
Repost your question. Separate your words, variables and numbers correctly. Otherwise, it makes no sense.
What is the answer please.... need help
Answer:
[tex]f\left(x\right)=x^3-6x^2+3x+10[/tex] is the function of the least degree has the real coefficients and the leading coefficients of 1 and with the zeros -1, 5, and 2.
Step-by-step explanation:
Given the function
[tex]f\left(x\right)=x^3-6x^2+3x+10[/tex]
As the highest power of the x-variable is 3 with the leading coefficients of 1.
So, it is clear that the polynomial function of the least degree has the real coefficients and the leading coefficients of 1.solving to get the zeros
[tex]f\left(x\right)=x^3-6x^2+3x+10[/tex]
[tex]0=x^3-6x^2+3x+10[/tex] ∵ [tex]f(x)=0[/tex]
as
[tex]Factor\:x^3-6x^2+3x+10\::\:\left(x+1\right)\left(x-2\right)\left(x-5\right)=0[/tex]
so
[tex]\left(x+1\right)\left(x-2\right)\left(x-5\right)=0[/tex]
Using the zero factor principle
if [tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]x+1=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0[/tex]
[tex]x=-1,\:x=2,\:x=5[/tex]
Therefore, the zeros of the function are:
[tex]x=-1,\:x=2,\:x=5[/tex]
[tex]f\left(x\right)=x^3-6x^2+3x+10[/tex] is the function of the least degree has the real coefficients and the leading coefficients of 1 and with the zeros -1, 5, and 2.
Therefore, the last option is true.
64°
70°
to
Find the value of x.
x=134°
Step-by-step explanation:
180-(64+70)=46
x=180-46
x=134°
Answer:
134*
Step-by-step explanation:
64 + 70 should equal x but to make sure:
180-64-70= 46 then 180 - 46= 134 so yes
What is the unit rate? $101.25 earned in 9 hours
Answer:
$11.25
Step-by-step explanation:
Answer:
$11.25
Step-by-step explanation:
Divide $101.25 by 9
11.25
So $11.25 were earned each hour.
Hope this helps :)
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At Gary's car wash 49 cars can be washed in 4 hours. At this rate, how many cars can be washed in 8 hours?
Answer:
98
Step-by-step explanation:
49 + 49 = 98
I really need help
Solve for x
[tex]\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}[/tex]
1. Both are corresponding angles, hence they both are equal, so,
[tex]44x + 2 = 45x \\ = > 2 = 45x - 44x \\ = > 2 = x \\ = > x = 2[/tex]
Ans. C) 2
2. They both are in interior corressponding, hence their sum is equal to 180°, so,
[tex]10x + 6 + 104 = 180 \\ = > 10x + 110 = 180 \\ = > 10x = 180 - 110 \\ = > 10x = 70 \\ = > x = \frac{70}{10} \\ = > x = 7[/tex]
Ans. D) 7
3. They both are in interior corressponding, hence their sum is equal to 180°, so,
[tex]x + 75 + x + 125 = 180 \\ = > 2x + 200 = 180 \\ = > 2x = 180 - 200 \\ = > 2 x = - 20 \\ = > x = \frac{ - 20}{2} \\ = > x = - 10[/tex]
Ans. A) -10
4. Both are corresponding angles, hence they both are equal, so,
[tex]12x + 3 = 11x + 9 \\ = > 12x - 11x = 9 - 3 \\ = > x = 6[/tex]
Ans. A) 6
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Nikes cost $75.
They were reduced to $60. What is the percent of change?
Answer:
15%
75-60= 15
hope this helps
Express the following ratios in simplest form: 20:40
Answer:
1:2
Step-by-step explanation:
By dividing both sides by 20 you will get 1:2 which is the same thing as 20:40 if you multiply 1:2 on both sides by 20
Answer:
1 : 2
Step-by-step explanation:
20 : 40
20/10 : 4/10
2 : 4
2/2 : 4/2
1 : 2