Answer:
A. x = 6
Step-by-step explanation:
2x+3(x+10)=60
Use the distributive property to multiply 3 by x+10.
2x+3x+30=60
Combine 2x and 3x to get 5x.
5x+30=60
Subtract 30 from both sides.
5x=60−30
Subtract 30 from 60 to get 30.
5x=30
Divide both sides by 5.
x=
5
30
Divide 30 by 5 to get 6.
x=6
A factory produces bolts at a constant rate. After 4 hours, 3,200 bolts have been produced. Which graph models a relationship with the same rate?
The graph that models the relationship between the factory production and the time is the graph in option D
The number of bolts produced within four hours is 3200
The rate of production is the ratio of the change in the number of bolts produced to the the change in time
Change in the number of bolts produced, ∆y = 3200 bolts
Change in time, ∆t = 4 hours
Rate of change = ∆y / ∆t
Rate of change = 3200/4
Rate of change = 800 bolts per hour
The only graph that models this relationship is the graph in option D because it also have a rate of change of 800 bolts per hour
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Sandy worked extremely hard at her job and earned a large bonus at the end of the year. She decided to give her children 2/5 of the money and her grandchildren 1/4 of her bonus. How much of her bonus did she keep for herself?
Answer:
7/20 of her bonus
Step-by-step explanation:
Solution:
She gives her children 2/5 of her bonus and grandchildren 1/4 of her bonus.
= 1 - 2/5 - 1/4
= 1 - 8/20 - 5/20
= 1 -13/20
= 7/20
I hope it helps.
100 POINTS! Select the correct answer.
Which system of equations is represented by this graph?
Answer:
A
Step-by-step explanation:
Remember, the equation of slope-intercept is y=mx+b
We see that for A, that the first equation's slope is -2/3. That means we are going to move down two and left five. The reason why we are going down is that the slope is negative. We also know that our y-intercept is -4. So we first plot the point (0,-4). Then we move down two and left five. We apply the same knowledge with the second equation. When we plot both equations, we get the same exact graph as the picture.
Find the slope of the line
A seat for all games,events,concerts,and performances cost $900 there are 48 events in total but Alex only attended 14 how much did he pay.
3.find the measure of each missing angle
Answer:
Angle 1= 69
Angle 2= 37
Angle 3= 106
Angle 4= 21
Step-by-step explanation:
(Angle 2) The box in the corner is a 90-degree angle. So, 90-53=37
(Angle 1) Now that you have angle 2, add 37+74. You get 111. Subtract 180 and 111.
The answer for angle one is 69.
(Angle 3) Since it is a line, the two angles combined are 180 degrees. 180-74= 106.
(Angle 4) Now that you have angle 3, add 106 and 53. You will get 159. 180-159= 21
Find the range of the graphed function.
- 10
10
-10
O A. yis all real numbers.
B. y: 0
OC. -6 sys 9
OD. -10 sys
Answer:
The answer is C
Step-by-step explanation:
The range of the function plotted on the graph is [-6, 9].
What is function?A function is a relation between a dependent and independent variable. We can write the examples of function as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is the graph of a function shown in the image.
Range of a function is the set of {y} - values that exist for the values in the domain of the function. We can see from the graph that the values of {y} range from {y} = - 6 to {y} = 9 over the entire domain. See the black dots, that black dots mean that the both the numbers -6 and 9 are included in the range. So, in the set form, we can write the range of the function as -Range : [-6, 9].
Therefore, the range of the function plotted on the graph is [-6, 9].
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Which option shows the equation for the line in the graph
Answer:
y=-3x-10
Step-by-step explanation:
The y-intercept is -10 and the line is going in a negative direction. Meaning the slope will be negative.
Looking at the options, you can tell that the answer will in fact, be y=-3x-10
Or to solve, -2,-4 and -5,5
5--4 to get 9
-5--2 to get -3
9/-3 gets you -3. The slope of the line is -3. And you can notice that the intercept is -10.
This gets you y=-3x-10
Unit 4 linear equations homework 9 parallel and perpendicular lines (day1) activity
Directions if segments AB and CD are parallel,perpendicular, or neither
The lines that are parallel continuously have equal distances from each
other and perpendicular lines form 90° angle at their intersection.
The correct responses are;
Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular, ⊥Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel. ║Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neitherSegment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular, ⊥Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular, ⊥Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neitherThe equations are parallel, ║The equations are perpendicular, ⊥The equations are perpendicular, ⊥The equations are neither parallel or perpendicularReasons:
Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular
[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel where; Slope of [tex]\overline{AB}[/tex] = Slope of [tex]\overline{CD}[/tex]
[tex]\displaystyle \overline{AB} \ and \ \overline{CD} \ are \ perpendicular\ where; \ Slope \ of \ \overline{AB} = -\frac{1}{Slope \ of \ \overline{CD}}[/tex]
[tex]1. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{\frac{13 - 3}{-2 - 0}} = \frac{10}{-2} = -5[/tex]
[tex]\geq \displaystyle Slope \ of \ \overline{CD} = \frac{3 - 0}{10 - (-5)} = \frac{1}{5}[/tex]
[tex]\displaystyle \mathbf{Slope \ of \ \overline{AB}} = -\frac{1}{Slope \ of \ \overline{CD}}[/tex], [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular
[tex]2. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{\frac{7- 1}{3 - (-6)}} = \frac{6}{9} =\frac{2}{3}[/tex]
[tex]\geq \displaystyle Slope \ of \ \overline{CD} = \frac{-5 - (-1)}{-6 - 0} = \frac{-4}{-6}=\frac{2}{3}[/tex]
Slope of [tex]\mathbf{\overline{AB}}[/tex] = Slope of [tex]\overline{CD}[/tex] , [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel
[tex]3. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{ \frac{2- 4}{-6 - (-2)} = \frac{-2}{-4}} =\frac{1}{2}[/tex]
[tex]\displaystyle Slope \ of \ \overline{CD} = \frac{11 - (-7)}{-1 - 5} = \frac{18}{-6}=-3[/tex]
[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular
[tex]4. \ \displaystyle Slope \ of \ \overline{AB} = \frac{8- 3}{-3 - 2} = \frac{5}{-5} =-1[/tex]
[tex]\displaystyle Slope \ of \ \overline{CD} = \frac{6 - 2}{-4 - (-8)} = \frac{4}{4}=1[/tex]
[tex]\displaystyle Slope \ of \ \overline{AB} = \mathbf{-\frac{1}{Slope \ of \ \overline{CD}}}[/tex], [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular
[tex]5. \ \displaystyle Slope \ of \ \overline{AB} = \frac{-1 - 2}{-8 - (-4)} = \frac{-3}{-4} =\frac{3}{4}[/tex]
[tex]\displaystyle Slope \ of \ \overline{CD} = \mathbf{\frac{-3 - 6}{0 - 12}} = \frac{-9}{-12}=\frac{3}{4}[/tex]
Slope of [tex]\overline{AB}[/tex] = Slope of [tex]\overline{CD}[/tex] , [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel
[tex]6. \ \displaystyle Slope \ of \ \overline{AB} = \frac{5 - (-1)}{6 - 3} = \frac{6}{3} =2[/tex]
[tex]\displaystyle Slope \ of \ \overline{CD} = \mathbf{\frac{-5 - 7}{2 - (-4)}} = \frac{-12}{6}=-2[/tex]
[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular
Directions: To determine if the equations are parallel or perpendicular
Solution:
The equations are parallel if when expressed in the form, y = m·x + c, the value of m are equal
The equations are perpendicular, when we have;
[tex]\displaystyle The \ value \ of \ \mathbf{m} \ in \ one \ equation = -\frac{1}{The \ value \ of \ \mathbf{m} \ in \ the \ other\ equation }[/tex]
7. First equation
3·x + 2·y = 6
Therefore; [tex]\displaystyle y = -\frac{3}{2} \cdot x + 3[/tex]
Second equation; [tex]\displaystyle y = \mathbf{-\frac{3}{2} \cdot x + 5}[/tex]
The value of m which is the coefficient of x are both equal to [tex]\displaystyle -\frac{3}{2}[/tex]
Therefore, the equations are parallel
8. Equation 1; 3·y = 4·x + 15
Therefore;
[tex]\displaystyle y = \frac{4}{3} \cdot x + 5[/tex]
Equation 2; 9·x + 12·y = 12
[tex]\displaystyle y = -\frac{9}{12} \cdot x + 1 = 1 - \frac{3}{4} \cdot x[/tex]
The slope of the equation 2 is the negative inverse of the slope of equation 1, therefore, the equations are perpendicular
9. Equation 1: 8·x - 2·y = 4
Therefore;
y = 4·x - 2
Equation 2: x + 4·y = -12
Therefore;
[tex]\displaystyle y = -\frac{1}{4} \cdot x - 3[/tex]
The slope of the equation 2 is the negative inverse of the slope of equation 1, therefore, the equations are perpendicular.
10. Equation 1: 3·x + 2·y = 10
Therefore;
[tex]\displaystyle y = -\frac{3}{2} \cdot x - 5[/tex]
Equation 2: 2·x + 3·y = -3
[tex]\displaystyle y = -\frac{2}{3} \cdot x -1[/tex]
The slopes of the equation 1 and 2 are not equal, and are not the negative inverse of each other, therefore, the equations are neither parallel nor perpendicular.
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Lucy has ridden 45 miles of a bike course. The course is 60 miles long. What percentage of the course has Lucy ridden so far?
Answer:
a
Step-by-step explanation:
can someone help me peaseeeee
Paying 13 mortgage payments instead of 12 per year can save to you thousands in interest cost. If you had a $175,000 mortgage at 6% for 30 years, how much extra would you have to pay per year to make 13 instead of a 12 mortgage mortgage payments per year? How much would you pay if you paid 1/12 of it per month?
You would pay $14,583.33 per month if you divided the mortgage amount into equal monthly payments.
To calculate the additional amount you would have to pay per year to make 13 mortgage payments instead of 12, we need to determine the monthly mortgage payment first.
Using the formula for a fixed-rate mortgage:
[tex]M = \dfrac{P(r(1 + r)^n)} { ((1 + r)^n - 1)}[/tex]
M = P(r(1 + r)^n) / ((1 + r)^n - 1)
Here:
M = Monthly mortgage payment
P = Principal amount (mortgage amount)
r = Monthly interest rate (annual interest rate / 12)
n = Total number of payments (number of years × 12)
Let's calculate the monthly mortgage payment first:
P = $175,000
r = 6% / 12 = 0.005
n = 30 × 12 = 360
[tex]M = 175,000 \times\dfrac{ (0.005(1 + 0.005)^{360})}{ ((1 + 0.005)^{360} - 1)}[/tex]
M = $1,049.91
With a monthly mortgage payment of $1,049.91, we can calculate the additional amount you would need to pay per year to make 13 payments instead of 12.
Additional payment per year = Monthly payment × 12 - Monthly payment
Additional payment per year = $1,049.91 × 12 - $1,049.91
Additional payment per year = $12,599.92 - $1,049.91
Additional payment per year = $11,550.01
Therefore, you would need to pay $11,550.01 extra per year to make 13 mortgage payments instead of 12.
Now, let's calculate the amount you would pay if you made equal monthly payments throughout the year (1/12 of the mortgage amount per month).
Amount paid per month = Mortgage amount / 12
Amount paid per month = $175,000 / 12
Amount paid per month ≈ $14,583.33
Thus, you would pay $14,583.33 per month if you divided the mortgage amount into equal monthly payments.
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Find the indicated probability.
The following table show the results of a clinical trial for an allergy drug.
the product of 32.7 and 0.9 is?
Answer:
pruduct means multiply so 32.7x0.9=29.43
The angles in a triangle are
such that one angle is twice the
smallest angle, while the third
angle is three times as large as the
smallest angle. Find the measures
of all three angles.
Answer:
30, 60, and 90
Step-by-step explanation:
Let x be the Angle 1
2x is Angle 2
3x is Angle 3
x + 2x + 3x = 180
6x = 180
x = 30 degrees
2x = 60 degrees
3x = 90 degrees
Consider the ratio of boys to girls of 4:5.
a) What is the total number of parts?
b) What fraction of the total are boys?
c) What fraction of the total are girls?
d)If there were 18 students in total,how many of them are boys?
e)If there were 18 students in total, how many of them are girls?
Step-by-step explanation:
[tex]a)[/tex]
[tex]4+5=9 (parts)[/tex]
[tex]b)[/tex] our total is [tex]9[/tex] our boys are [tex]4\\[/tex]
our fraction is [tex]^4/_9[/tex]
[tex]c)[/tex] [tex]^5/_9[/tex]
[tex]d)[/tex] our whole used to be [tex]9[/tex] but we doubled it so it is [tex]18[/tex]
so we double [tex]4[/tex] which equals [tex]8[/tex]
[tex]^8/_{18}[/tex]
[tex]e)[/tex] [tex]^{10}/_{18}[/tex]
Brainliest please
14. Explain why a step in solving the equation 4n = -36 is to divide both sides by 4. Then
solve the equation.
Answer:
Because you cant combine unlike terms. And the goal is to get X by itself.
-9 is the answer
Step-by-step explanation:
When air is pumped into an automobile
tire, the pressure is inversely proportional to
the volume. If the pressure is 35 pounds
when the volume is 120 cubic inches, what
is the pressure when the volume is 140
cubic inches?
Answer:
I think it is 68.5714285714 cubic inches
Step-by-step explanation:
evaluate the function h(x) = |-2x|-9 for the given values of x a) h(4)=. b) h(-5)=. c) h(0) =
Answer:
h(4) = -1 ; h(-5) = 1 h(0) = -9
Step-by-step explanation:
a) h(x) = |-2x| - 9 Substitute x = 4
h(4) = | -2 · 4| - 9
h(x) = | -8| - 9
h(4) = 8 - 9
h(4) = -1
b) h(x) = |-2x| - 9 Substitute x = -5
h(-5) = |-2 · -5| - 9
h(-5) = |-10| - 9
h(-5) = 10 - 9
h(-5) = 1
c) h(x) = |-2x| - 9 Substitute x = 0
h(0) = |-2 · 0| - 9
h(0) = |0| - 9
h(0) = 0 - 9
h(0) = -9
Find the X- and Y-intercepts of the given equation: 3x + 5y = 15
Answer:
Using the slope-intercept form, the y-intercept is 3 Since the equation '3x + 5y = 15' is transformed to slope-intercept form 'y = (-3/5)x + 3' the slope is (-3/5).
Find the missing value given the points and slope.
(9,7) and (x,4)
m=3/7
Answer:
Step-by-step explanation:
5^-15 rewritten using a positive exponent.
Answer: 1/5 to the power of 15
HELP! ILL TIVE BRAINLIST IF RIGHT!! Joe earns a percentage of his monthly sales. If his commission rate stays the same each month, how much does he need to sell in March to earn $200 more than he did in February? (Picture below)
$3000
$76
$3800
$900
Answer:
$3800
Step-by-step explanation:
If the ratio between sales and commission is 5:1, we can find that commission for February was 560. 560+200 is 760 and 760*5=3800
The product of six minus a number and five equals 60÷2 which equation relates the sentence
Answer:
Step-by-step explanation:
You are organizing books on the shelf. Each book has a width of 3/4 inches. write and solve an equality for the numbers of books b can fit on the shelf
3/4 = 0.75 inches
24 inches / 0.75 inches
= 32 books
Make m the subject of the formula L = m + n
Help plzz
Tap the word that "they" refers to.
Answer:Frogs
I think so…If it’s wrong and you can tell me and I’ll try correct it
Hope its correct!
;)
Have a great day!
pls solve Solve. 3/4(x−8) =−1/2
x=−26/3
x = 10
x=22/3
Answer:
i think its the 3rd option
Step-by-step explanation:
i'd'k what it is but you can read it over and over again
(p.s Brainleist?)
Answer:
x=22/3
Step-by-step explanation:
what is a expression representing the product of 17 and c
Answer:
17c
Step-by-step explanation:
17 × c = 17c
solve pls brainliest
Answer:
C.
Step-by-step explanation:
It multiplies by 2
Hope I could help!