Answer:
a = -2, b = -2Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}-5a+b=8&\text{add}\ 5a\ \text{to both sides}\\7a+9b=-32\end{array}\right\\\\\left\{\begin{array}{ccc}b=5a+8&(1)\\7a+9b=-32&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\7a+9(5a+8)=-32\qquad\text{use the distributive property}\\\\7a+(9)(5a)+(9)(8)=-32\\\\7a+45a+72=-32\qquad\text{subtract 72 from both sides}\\\\52a=-104\qquad\text{divide both sides by 52}\\\\\boxed{a=-2}\\\\\text{Put the value of}\ a\ \text{to (1):}\\\\b=5(-2)+8\\\\b=-10+8\\\\\boxed{b=-2}[/tex]
Every time Liliana bakes a batch of brownies,
she uses 3/4 cup of chocolate. If she has 12/8
cup(s) of chocolate remaining, how many
batches of brownies can Liliana make? Input
your answer as a whole number.
Answer:
2
Step-by-step explanation:
12/8 is equal to 6/4.
6 divided by 3 is 2.
Answer:
2 batches of brownies
Step-by-step explanation:
3/4 = (3x2)/(4x2) = 6/8
(12/8) / (6/8) =
(12/8) x (8/6) =
12/6 =
2
Four more than twice a number is less than negative twelve. Find all numbers that make this statement true.
Answer:
x<-8
Step-by-step explanation:
four more than twice a number = 4+2X
is less than negative twelve = <-12
4+2X<-12
(4-4)+2X< -12-4
2x<-16
X<-8
To find the numbers that make the statement true, we need to solve the equation 2x + 4 < -12 for x. Any number less than -8 will make the statement true.
Explanation:To find the numbers that make the statement true, we need to translate the given sentence into a mathematical equation. Let's denote the unknown number as 'x'. The sentence 'Four more than twice a number is less than negative twelve' can be written as 2x + 4 < -12. Now, we can solve this equation for x:
Subtracting 4 from both sides, we get 2x < -16.
Dividing both sides by 2, we have x < -8.
Therefore, any number less than -8 will make the statement true.
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Noah started to solve the equation –4.6p – 6.3p + 3.9 = –9.18 below.
Combine like terms: –10.9p + 3.9 = –9.18
Apply the next steps to solve the equation. What is the solution?
Answer: p = 1.2
Step-by-step explanation:
Answer: p=1.2
Step-by-step explanation:
A class is going on a trip to a museum. It costs $750 to rent a bus. Each ticket to the museum costs $12 Write an algebraic expression that represents the cost of the trip for people. Then evaluate this expression for 37
people
The total cost of trip for 37 people will be $1194.
Step-by-step explanation:
Given,
Rent of bus = $750
Cost of one ticket = $12
Let,
x be the number of people.
T be the total cost of the trip for people.
According to given statement;
Total cost = Rent of bus + (Cost of one ticket * number of people)
[tex]T=750+12x[/tex]
For 37 people, x=37
[tex]T=750+12(37)\\T=750+444\\T=\$1194[/tex]
The total cost of trip for 37 people will be $1194.
Keywords: linear expression, addition
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Problem Solving
Solve each problem by looking for a pattern.
1. Harold has 4 classes each school moming. Each dass
is 1 hour long, and there are 10 minutes between
classes. The first class starts at 8:00 AM. What time
does the fourth class end?
Answer:
12:30PM
Step-by-step explanation:
Known information:
There are 4 classes.
Each class is 1 hour.
There are 10 minutes between classes, like a break.
Draw a diagram:
start-CLASS1, break, CLASS2, break, CLASS3, break, CLASS4-end
There are 3 breaks because there are no breaks before and after the first and last classes.
Multiply the number of classes by the time length for class.
Multiply the number of breaks by the time length for breaks.
Add the two numbers together to get the total school time:
Classes: 4*1h = 4h
Breaks: 3*10min = 30min
4h + 30min = 4h 30min
Calculate 4h and 30min after 8:00 AM.
Add 4 hours and 30 minutes to 8.
. 8:00
+ 4:30
. 12:30
In the AM/PM clock (not 24 hour clock) there are 12 hours. After 12:59, it becomes 1:00, not 13:00.
Since "12:30" is possible on the AM/PM, we do not need to fix it.
The AM/PM clock changes at 12:00.
This means that after 11:59PM it becomes 12:00AM.
After 11:59AM it becomes 12:00PM. (Usually lunch)
Since 12:30 passed 11:59, the AM/PM sign changes.
The fourth class ends at 12:30PM.
An item is regularly priced at $50.It is now priced at a discount of 80% off the regular price. What is the price now?
If the item is 80% off than the sale price is only 20% of the original price.
So, 20% x $50 = $10
Out loud. Find the solution to the expression in the easiest way:
2 14/49 - (7 3/85- 3 35/49)
Answer:
-88/85
Step-by-step explanation:
2 14/49=112/49
7 3/85=598/85
3 35/49=182/49
------------------------
112/49-(598/85-182/49)
112/49-1976/595
-88/85
1 5/8÷(−1 3/5) please help
Answer:
-65/64
Step-by-step explanation:
1 5/8/(-1 3/5)
1 5/8=13/8
-1 3/5=-8/5
(13/8)/(-8/5)
(13/8)(-5/8)
-65/64
A 12 pound turkey takes about 180 minutes to cook. How many hours would it take to cook a 20 pound turkey?
These are ratios, which are technically equal to each other. So, you can set up the problem like this:
12/180=20/x
180*20=3600
3600/12=300
So, it would take 300 minutes.
The required time consumed to cook 20 pounds of turkey is 300 minutes.
Given that,
A 12-pound turkey takes about 180 minutes to cook.
To determine how many hours would it take to cook a 20-pound turkey.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is the rate of change?The rate of change is defined as the change in value with the rest of the time is called rate of change.
A 12-pound turkey takes about 180 minutes to cook.
rate of cooking = 180 / 12 = 15 minute per pound of turkey
Time consumed to cook 20 pounds of turkey = 20 * 15 = 300 minutes
Thus, the required time consumed to cook 20 pounds of turkey is 300 minutes.
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The center of a circle lies on the line y = 3x + 1 and is tangent to the x-axis at (−2,0) .
What is the equation of the circle in standard form?
You don't have to give me the answer, but at least please help me understand what it is that I need to be looking for in order to solve this problem (step-by-step if it's possible), I'm stuck.
Answer:
(x + 2)² + (y + 5)² = 25
Step-by-step explanation:
The circle is tangent to the x-axis at (-2, 0). This means the center of the circle must be directly above or below this point. So the x-coordinate of the center is -2.
Since the center of the circle is on the line y = 3x + 1, we can find the y-coordinate:
y = 3(-2) + 1
y = -5
The center of the circle is (-2, -5). The distance between the center and the point (-2, 0) is 5 units. This is the radius of the circle.
We can now write the equation of the circle:
(x − h)² + (y − k)² = r²
(x + 2)² + (y + 5)² = 25
Graph:
desmos.com/calculator/wzionolfli
Th equation of the circle will be (x + 2)² + (y + 5)² = 25.
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
At, the circle is perpendicular to the x-axis (-2, 0). Therefore, the circle's centre must be located directly above or below this point. Therefore, the centre's x-coordinate is -2.
We can determine the y-coordinate because the circle's centre lies on the line y = 3x + 1:
y = 3(-2) + 1
y = -5
The circle's nucleus is (-2, -5). The centre is located 5 units away from the point (-2, 0). This is the circle's radius.
We can now write the equation of the circle:
(x − h)² + (y − k)² = r²
(x + 2)² + (y + 5)² = 25
Therefore, the equation of the circle will be (x + 2)² + (y + 5)² = 25.
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The scatterplot shows the highway miles per gallon and city miles per gallon for 8 different car models.
Based on the scatterplot, what is the best prediction for city MPG if the highway MPG is 40?
A) 20
B) 35
C) 45
D) 50
Answer:
The best prediction will be B) 35
Step-by-step explanation:
By looking at the scatterplot ,
we can see that it the City MPG vs Highway MPG approximately falls on a straight line.
we can either find the slope of it ( which might be a little out of syllabus ) or we can extend the line connecting the maximum number of points.
When we do so, We get a line as attached in the diagram.
And we extend it.
From the graph attached we find that the value of City MPG falls somewhere in between the lines of 30 and 35 ( though this is just and approximation).
thus the more appropriate answer would be : 35
In triangle ABC mzA -45, mzB = 40", and a = 7. Which equation should you
solve to find b?
Answer:
Option A. [tex]\frac{sin(45\°)}{7}=\frac{sin(40\°)}{b}[/tex]
Step-by-step explanation:
we know that
Applying the law of sines in the triangle ABC
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}[/tex]
substitute the given values
[tex]\frac{sin(45\°)}{7}=\frac{sin(40\°)}{b}[/tex]
[tex]b=\frac{7}{sin(45\°)}sin(40\°)\\\\b=6.4\ units[/tex]
A motorboat leaves a harbor and travels at an average speed of 15 mph
toward an island. The average speed on the return trip was 10 mph. How far was the
island from the harbor if the total trip took 5 hours?
Answer:
30 miles
Step-by-step explanation:
We know
D = RT
Where
D is the distance
R is the rate
T is the time
Towards Island:
R = 15
Let time be x
So, we can write:
D = 15x
Return from Island:
R = 10
Let time be y
So, we can write:
D = 10y
Also, total time is 5 hours, so we can write:
x + y = 5 [equation 2]
Now, since the distance for both legs of the journey is equal, we can write:
Distance 1 = Distance 2
15x = 10y
Now we replace this equation with equation 2, so we get:
Equation 2: x + y = 5 or x = 5 - y
15x = 10y
15(5 - y) = 10y
75 - 15y = 10y
75 = 25y
y = 75/25
y = 3
Distance 2 = D = 10y
Replacing y with 3, we get:
D = 10y
D = 10(3)
D = 30
So, the distance to island is 30 miles
in a group of 84 kids 3/7 brought their lunches of those who bought their lunches 9 got a slice of pizza. what fraction of the students who bought their lunches got a slice of pizza?
Answer:
3/16
Step-by-step explanation:
4/7 of 84 = 48 kids
9/48 = 3/16
Answer:
9/36=1/4
Step-by-step explanation:
3/7x84=36
Ans: 9/36=1/4
Number 31 please help
===============================================
Explanation:
Going from design 1 to design 2, we add on 3 triangles. This is because the triangle in design 1 has 3 exterior sides to form its perimeter.
Going from design 2 to design 3, we add on 6 triangles
Going from design 3 to design 4, we add on 9 triangles
------------
Note the pattern of triangles we add on each round: 3, 6, 9
This is the set of multiples of 3. Each number is increased by 3. The next design will have us add 12 triangles to the exterior of design 4. Then the next round has us add on 15 triangles to the outside.
-------------
Going from design 4 to design 5, we add on 12 triangles
Going from design 5 to design 6, we add on 15 triangles
--------------
Check out the attached image below for what designs 5 and 6 will look like. Note the use of color coding to help see how the figures build up from step to step. There are 15 orange triangles along the outside in design 6.
Which of the following statement are false?
A) 5/9 can be shown as equivalent to an improper fraction.
B) 8/2 can be simplified as a whole number.
C) 1 1/3 can be shown as equivalent to an improper fraction.
D) 6/7 can be shown as equivalent to a proper fraction.
Answer:
A
Step-by-step explanation:
Because 5/9 is an example of a proper fraction. In order to be an improper fraction, the numerator needs to be larger than the denominator. 8/2 can be simplified as 4 and 4 is a whole number. 11/3=3 2/3 is an example of improper fraction. 6/7, again, this is another example of a proper fraction.
If stanley bought a sandwich, that cost $3 with 50% off. what was the original price?
Answer:
The answer is 6$. Half of 6$ is 3$
Answer:
$6
Step-by-step explanation:
Let the original price be =Y,
50% of the original = Y×50/100 = 0.5Y
∴ 50% off =Y - 0.5Y = 3
0.5Y=3
divide both side by the co-efficient 0f Y i.e 0.5
⇒0.5Y/0.5=3/0.5
⇒Y= $6
Solve each system of equations algebraically. y=x+5, y=6
Answer:
x = 1
Step-by-step explanation:
y = 6
Substitute this into y = x + 5
6 = x + 5
1 = x
Answer:
x=1, y=6. (1, 6).
Step-by-step explanation:
y=x+5
y=6
---------
x+5=6
x=6-5
x=1
What is the number of the terms of geometrical sequence if its first, fourth and the last term is equal to 2, 54 and 486 respectively.
Answer:
The number of terms of the G.P. is 6
Step-by-step explanation:
Let the G.P. has first term a, common ratio r and the number of terms n.
The G.P. has first term 2, so a = 2.
Now, the fourth term is 54 i.e. ar³ = 54
⇒ 2r³ = 54
⇒ r³ = 27
⇒ r = 3
Now, the last term i.e. the nth term is= [tex]ar^{n - 1} = 486[/tex]
⇒ [tex]2 \times 3^{n - 1} = 486[/tex]
⇒ [tex]3^{n - 1} = 243 = 3^{5}[/tex]
Hence, (n - 1) = 5
⇒ n = 6
So the number of terms of the G.P. is 6 (Answer)
Alicia already spent $8.25 of her paycheck. If this was 15% of her paycheck, how much was she paid?
Answer:
She was paid $55.
Step-by-step explanation:
15%=0.15
8.25/0.15=55
Answer:
She was paid $55.
Step-by-step explanation:
15%=0.15
8.25/0.15=55
EFGH is a parallelogram. Find the measure of FG.
Answer:
FG = 47
Step-by-step explanation:
The opposite sides of a parallelogram are parallel and congruent, thus
EH = FG, that is
5z - 18 = 3z + 8 ( subtract 3z from both sides )
2z - 18 = 8 ( add 18 to both sides )
2z = 26 ( divide both sides by 2 )
z = 13
Hence
FG = 3z + 8 = (3 × 13) + 8 = 39 + 8 = 47
Based on the property of a parallelogram, the measure of FG is: 47.
Opposite Sides of a ParallelogramBased on the properties of a parallelogram, the opposite sides of a parallelogram are equal in length.
Therefore:
EH = FG
Substitute5z - 18 = 3z + 8
Combine like terms5z - 3z = 18 + 8
2z = 26
Divide both sides by 2z = 13
FG = 3z + 8
Plug in the value of zFG = 3(13) + 8
FG = 47
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Explain how the distributive property can be used to solve the equation 3(x+4)=36
Answer:
3(x+4)=36 is the same as 3x+12=36
If 3x+12=36, that means x=8
36-12= 24
24/3=8
Answer: Explain how the distributive property can be used to solve the equation 3(x+4)=36 For this question it says to explain how the distributive property can be used to solve the equation. So instead of putting the answer to the equation 3(x+4)=36. You explain how the distributive property gets you the answer... They're not asking for the answer to the equation 3(x+4)=36
Step-by-step explanation: So to the guy that answered this question you are wrong...
Help me with A and B. And gave me the answer and how you got to the answer.
Answer:
the answer is 12m + 4
Step-by-step explanation:
you do the distributive property which is 3*2m and then 3*4 and you get 6m+12 and then you do it again which you do 2*3m and then 2*-4 and you get 6m-8 and then you get 6m+12+6m-8 and you just add your like terms to get 12+4
hope this helped
In the xy coordinate plane, the slope of a line is 4 and it passes through the point (1, 3). Find the equation of a line that is parallel to the given line and passes through the point (3, 1)
Answer: Y=-1 or Y=-1+4
Step-by-step explanation:
Use the formula y2- y1 over x2-x1 so it should look like this 1-3 over 3-1 which is -2 over 2 then you divide that which is -1 and if you have to find one all you have to do is use one point label which is x and y so I pick (1,3) so you put 3=-1(1) once you have that you multipy so -1 times 1 is -1 so your gonna add 1 to the -1 and the three the -1 cancel out because it is a zero pair 3+1 is 4 so B=4To find the equation of a line parallel to the given line and passing through a specific point, we can use the point-slope form of a linear equation.
Explanation:To find the equation of a line that is parallel to the given line and passes through the point (3, 1), we need to use the fact that parallel lines have the same slope. Since the given line has a slope of 4, the parallel line will also have a slope of 4. Using the point-slope form of a linear equation, we can write the equation as:
y - y1 = m(x - x1)
Plugging in the values from the given point (3, 1) and the slope (4), we get:
y - 1 = 4(x - 3)
Simplifying the equation, we have:
y - 1 = 4x - 12
y = 4x - 11
Therefore, the equation of the line that is parallel to the given line and passes through the point (3, 1) is y = 4x - 11.
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Point D (-1,5) is reflected across the x-axis which statements about D are true
Answer:
When a point is reflected across the x axis, it has the same x axis but the y axis is multiplied by -1. Think about the x axis as a mirror and the point is projected across the x axis.
Hence the x coordinate is -1 and the y coordinate is -5.
Step-by-step explanation:
Answer:
the first option
Step-by-step explanation:
the x coordinate is -1
How do we do y=mxtb?
Answer:
Step-by-step explanation:
y=mx+b is the formula that we use in Algebra I for determining the slope intercept equation so we can graph the function.
An 8-ft-by-10-ft rug leaves 1 ft of the bedroom floor exposed an all four sides. Find the perimeter of the bedroom floor.
To find the perimeter of the bedroom floor, subtract the rug's length and width from the floor's length and width. Then, use the formula 2(length + width) to calculate the perimeter. The perimeter of the bedroom floor is 64 ft.
Explanation:To find the perimeter of the bedroom floor, we need to subtract the length and width of the rug from the length and width of the floor. The length of the floor is 10 ft and the rug leaves 1 ft exposed on each side, so the length of the rug is 8 ft. Similarly, the width of the floor is 8 ft and the rug leaves 1 ft exposed on each side, so the width of the rug is 6 ft. Therefore, the perimeter of the bedroom floor is 2(10 ft + 8 ft) + 2(8 ft + 6 ft) = 2(18 ft) + 2(14 ft) = 36 ft + 28 ft = 64 ft.
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If the radius of a circle with an area of 11.5 inches squared is multiplied by 6, what is the area of the new circle?
69 in squared
207 in squared
216.66 in squared
414 in squared
Answer:
The correct answer is D. 414 in squared.
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
Area of the first circle = 11.5 inches ²
2. Let's calculate the area of the new circle, given that the radius of the first circle is multiplied by 6.
Area of the first circle = 11.5 inches ²
Let's find the radius:
π * r² = 11.5
r² = 11.5 / 3.1416
r² = 3.66055513
r = 1.91 inches
The first circle has a radius of 1.91 inches
So, the radius of the second circle is 1.91 * 6 = 11.48 inches
Area of the second circle = π * r²
Area of the second circle = 3.1416 * 11.48²
Area of the second circle = 3.1416 * 131.79
Area of the second circle = 414.03 inches ²
Area of the second circle = 414 inches ² (Rounded to the nearest whole number)
The correct answer is D. 414 in squared.
calculate the Ek of a car which has a mass of 1000 kg and is moving at the rate of 20 m/s
The kinetic energy (Ek) of the car with a mass of 1000 kg moving at a speed of 20 m/s is calculated using the formula Ek = 0.5 * m * v². Substituting the given values, we find the kinetic energy to be 2.00 x 10⁵ Joules.
Explanation:To calculate the kinetic energy (Ek) of a car with a given mass and speed, you can use the formula Ek = 0.5 * m * v², where m is the mass, and v is the speed. In this case, the mass (m) of the car is 1000 kg, and the velocity (v) is 20 m/s.
Substituting the given values into the formula, we have Ek = 0.5 * (1000 kg) * (20 m/s)². This simplifies to Ek = 2.00 x 10⁵ J (Joules), which is the kinetic energy of the car.
It's important to note that kinetic energy always has units of Joules in the International System (or SI), and it represents the energy that an object has due to its motion.
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The Scatter plot below shows the linear trend of the number of golf carts a company sold the month of February and a line of best fit representing this trend. A. Write a function that models the number of golf carts sold as a function of the number of days in the month of February B. What is the meaning of the slope as a rate of change for this line of best fit.
Answer:a. Write a function that models the number of golf carts repaired as a function of the number of days in the month of February:
y=(1/3)x
b. What is the meaning of the slope as a rate of change for this line of best fit?
For each three days of the month of february the number of golf carts repaired was 1; that means each three days of the month of february was repaired one golf cart.
Step-by-step explanation:
a. Write a function that models the number of golf carts repaired as a function of the number of days in the month of February:
y=(1/3)x
b. What is the meaning of the slope as a rate of change for this line of best fit?
For each three days of the month of february the number of golf carts repaired was 1; that means each three days of the month of february was repaired one golf cart.
Let:
x: Day of the month
y: Number of golf carts repaired
a. Write a function that models the number of golf carts repaired as a function of the number of days in the month of February.
Taking two points of the right line, for example:
P1=(0,0)=(x1,y1)→x1=0, y1=0
P2=(3,1)=(x2,y2)→x2=3, y2=1
Slope: m=(y2-y1)/(x2-x1)
Replacing the known values:
m=(1-0)/(3-0)
m=1/3
Equation of the right line, using the form point-slope:
y-y1=m(x-x1)
Replacing the known values:
y-0=(1/3)(x-0)
y=(1/3)x
Answer:
A). f(x) = (-5)x + 90
Step-by-step explanation:
A). As shown in the graph, line of best fit is passing through two points (0, 90) and (18, 0).
Equation of this line will be in the form of y = mx + b.
Here m = slope of the line
b = y-intercept
Since slope of a line passing through two points (x, y) and (x', y') is represented by,
m = [tex]\frac{y-y'}{x-x'}[/tex]
So slope of the line of best fit from the given graph,
'm' = [tex]\frac{90-0}{0-18}[/tex]
m = (-5)
y-intercept 'b' = 90
When we plug in these values in the equation,
y = (-5)x + 90
Function representing this situation,
f(x) = -5x + 90
B). Slope of the line of best fit shows the change in sales per day in the month of Feb that is "5 golf carts per day".
Negative notation of the slope shows the decrease in the sales day by day.