Kevin and Randy Muise have a jar containing 85 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $ 14.25. How many of each type of coin do they have?
Which ordered pair (a, b) is a solution to the given system of linear equations?
A (1, 7)
B (3, 1)
C (11, –23)
D (23, –11)
Answer:
C. (11,-23)
Step-by-step explanation:
The given equations are
[tex]3a+b=10[/tex].....................equation 1
[tex]-4a-2b=2[/tex]...................equation 2
Multiply first equation by 2
[tex]6a+2b=20[/tex]
Now add this new equation to 2nd equation
[tex]6a-4a +2b-2b = 20+2[/tex]
[tex]2a = 22[/tex]
Divide both sides by 2
[tex]a=11[/tex]
We got a=11 , plug this value in anyone equation
3(11)+b=10[tex][/tex]
[tex]33+b=10[/tex]
Subtract 33 from both sides
[tex]b=-23[/tex]
So solution is (a,b) = ( 11,-23)
What is the area of this figure?
Enter your answer in the box.
Answer:
[tex]\text {Area of figure is }44 units^2[/tex]
Step-by-step explanation:
Given the figure and we have to find the area of given figure.
Area of figure=ar(ABC)+ar(CDE)+ar(AEFH)+ar(GHF)
From the figure, dimensions according to square boxes can be written as
AE=HF=8 units, EF=3 units, BI=3 units, GH=2 units, AC=CE=4 units.
[tex]ar(ABC)=ar(CDE)=\frac{1}{2}\timesAC\times BI=\frac{1}{2}\times4\times3=6 units^2[/tex]
[tex]ar(AEFH)=HF\times EF=8\times 3=24 units^2[/tex]
[tex]ar(GHF)=\frac{1}{2}\timesHF\timesGH=\frac{1}{2}\times8\times 2=8units^2[/tex]
∴ [tex]\text {Area of figure is }44 units^2[/tex]
What is the graph of y = x - 3 (shown below) translated up 2 units?
Answer:
The graph is that one which corresponds to the equation y = x-1. The graph is shown in the image below.
Step-by-step explanation:
Translate a linear curve means to move the whole curve up or down, where the final line will be in parallel to the original curve.
For translate the graph up to 2 unit, it must to be summed 2 unit in the right member of the original equation:
[tex] y = (x-3) + 2 [/tex]
[tex] y = x-3 + 2 [/tex]
[tex] y = x-1 [/tex]
Find the equatio of the line tht contains the point (5,6) and is perpendicualr to the line 4x+2y=2
Final answer:
The equation of the line that passes through the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.
Explanation:
The question asks us to find the equation of a line that passes through a given point and is perpendicular to a given line. To solve this, we first need to determine the slope of the given line, then find the perpendicular slope, and finally, use the point-slope form of a line to write the equation for our new line.
Here are the steps:
Find the slope of the given line. For the equation 4x + 2y = 2, we rearrange it to slope-intercept form (y=mx+b), which gives us y = -2x + 1. The slope is -2.
Since we want a line that is perpendicular to the given line, we need the negative reciprocal of -2, which is 1/2.
Now we use the point-slope form of a line, y-y1 = m(x-x1), with point (5,6) and slope 1/2. This gives us y - 6 = 1/2(x - 5).
Solving for y to get the slope-intercept form, we multiply both sides by 2 to get rid of the fraction: 2y - 12 = x - 5, and then solve for y: y = 1/2x + 7/2.
The equation of the line that contains the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.
The graph below shows a line segment MN: Which of the following equations best represents the line segment MN?
y = −3x + 2
y = −2x + 1
y = −3x − 2
y = −2x − 1
Answer:
D. [tex]y=-2x-1[/tex]
Step-by-step explanation:
We have been given a line on coordinate plane. We are asked to find the equation of our given line.
First of all, we will find slope of our given line using points [tex](-2,3)[/tex] and [tex](0,-1)[/tex] in slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where,
[tex]y_2-y_1[/tex] = Difference between two y-coordinates,
[tex]x_2-x_1[/tex] = Difference between two x-coordinates of same y-coordinates.
Upon substituting our given values in slope formula, we will get:
[tex]m=\frac{-1-3}{0--2}[/tex]
[tex]m=\frac{-4}{0+2}[/tex]
[tex]m=\frac{-4}{2}[/tex]
[tex]m=-2[/tex]
Now, we will use slope-intercept form of equation [tex]y=mx+b[/tex], where,
m = Slope of line,
b = The y-intercept.
Upon looking at our given graph, we can see that y-intercept is [tex]-1[/tex].
Therefore our required equation would be [tex]y=-2x-1[/tex] and option D is the correct choice.
A rectangular piece of sheet metal has a length that is 6 in. less than twice the width. a square piece 3 in. on a side is cut from each corner. the sides are then turned up to form an uncovered box of volume 1014 in. cubed find the length and width of the original piece of metal.
Determine the dimensions of the metal sheet by setting up and solving equations based on the given volume of the box and the relationship between its length and width.
Explanation:This problem can be tackled by using a bit of algebra and understanding volume calculations. We can use the equation for the volume of a box which is V=length*width*height. The problem gave us the volume of 1014 cu in. When a 3 in. square is cut from each corner of the rectangular piece of metal, the sides fold up to form the box, the height of the box becomes 3 in. This means we're missing the length and width of the box to solve for volume.
Since the length equals to twice the width minus 6 in., we can express the length as 2W - 6. Substituting these into the volume equation we get: 1014 = (2W - 6)(W)(3) which when simplified gives W, the width of the metal piece. Then substitute W into the length formula 2W - 6 to solve for the length.
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#SPJ3
A rectangle basin is being filled with water. The basin is 7 feet long, 12 feet wide, and 4 feet high. How much water is going to be needed to fill the basin.
Explain how to tell 100/105 is not in simplest form without finding all the factors
Liam works at a zoo. He was looking at some data showing the masses of their 5 African elephants. The mean mass of the elephants was 3,800 kilograms and the median mass was 3,600 kilograms. The heaviest elephant, named Omar, was recorded as 6,000 kilograms. Liam then found out that Omar's mass was written down incorrectly, and that Omar actually has a mass of 7,000 kilograms. How will increasing Omar's mass affect the mean and median?
The increase of Omar's mass from 6000kg to 7000kg will raise the mean mass of the elephants because the mean involves all values. However, it won't affect the median mass because the position of the middle value in the set won't change.
Explanation:The correction of Omar's mass from 6,000 kilograms to 7,000 kilograms will affect both the mean and the median mass of the elephants. However, the effect on each measure of central tendency will be different.
The mean is the average, calculated by adding up all values and then dividing by the number of values. If Omar's weight is increased, the total mass of the elephants will increase, leading to an increase in the mean mass of the elephants.
However, the median, which is the middle value when all values are arranged in ascending order, will not change because it only depends on the arrangement of values, not their actual size. Since Omar's mass is already the largest value, an increase in his mass will not change the position of the middle value.
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A radius is a0 the diameter
Answer:
Hence, A radius is half the diameter.
Step-by-step explanation:
The question is asked as:
A radius is [tex]a_0[/tex] the diameter.
i.e. what is the value of the constant [tex]a_0[/tex] such that the radius and the diameter are related to each other.
We know that:
The Radius is the length of the line through the center that touches a point on the edge of the circle.
The diameter is the length of the line through the center that touches two points on the edge of the circle.
Hence Radius is half the diameter.
so the value of [tex]a_0=\dfrac{1}{2}[/tex]
( Or we can say Diameter is twice the radius of the circle.
[tex]d=2r\\\\r=\dfrac{1}{2}d[/tex]
where d denotes the diameter of the circle and r denotes the radius of the circle ).
PLEASE HELP
Find the solution of this system of equations
-5x=-21+6y
-5x+y=-84
how many isosceles triangles appear in this figure?
Hero's Challenge: Cars At A StopLight
There are five cars in line at a stoplight. Each of these cars is a different color and different type of car. Diego is driving the red car. Ingrid is driving the sedan. The green car is immediately behind the white car. The minivan is third in line. Rachel is driving the first car in line. Anton is just behind the driver in the SUV. Yuna is driving the green car. The driver in the yellow car is just in front of the convertible. Rachel is just in front of the blue car. The sedan is white. One of the cars is a pickup truck. Who is driving the pickup truck?
Use synthetic division to find the quotient and the remainder for the problem: (12x^4 + 5^3 + 3x^2 - 5)/(x+1)?,
To use synthetic division to divide a polynomial by a linear expression, follow the steps: arrange the terms, change the sign of the linear expression, bring down the coefficient, multiply and add, write the result, and determine the quotient and remainder.
Explanation:To use synthetic division to divide a polynomial by a linear expression, follow these steps:
Arrange the terms of the polynomial in descending order of their degrees.Change the sign of the linear expression you're dividing by.Write down the coefficient of the term with the highest degree of the polynomial and bring it down.Multiply this coefficient by the changed sign of the linear expression and write the result under the next coefficient.Add these two values together and write the result under the next coefficient. Repeat this process until you've reached the constant term.Write the final result as the quotient and the last value as the remainder.In this case, the quotient is[tex]9x^3 + 4x^2 + 5x + 2[/tex].
1200 calories in 3 liters. Write a unite rate.
Scoring a hole-in-one is the greatest shot a golfer can make. once 7 professional golfers each made holes-in-one on the 8th hole at the same golf course at the same tournament. it has been found that the estimated probability of making a hole-in-one is 12287for male professionals. suppose that a sample of 7 professional male golfers is randomly selected. what is the probability that they all score a hole in one
The sum of 555 consecutive integers is 505505505. What is the third number in this sequence?
Answer: The answer is 101!
Step-by-step explanation:
Call the first number in the sequence x
The next integer in the sequence is x + 1
The sum of the 5 consecutive integers is:
x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4) = 505
5x + 10= 505
5x = 495
x = 99
Since x is the first number, x + 2 is the third integer.
Thus, the third number in the sequence is 101
FULL ANSWERS WITH EVERY STEP PLEASE (10 pts)
for the functions f(x)=3x-6\sqrt(x)+6, and g(x)=7x-12-(4)/(x) find
1- where (f*g)(x) is differentiable
2- where ((f)/(g))(x) differentiable
Two large numbers of the Fibonacci sequence are f(50)=12,586,269,025 and f(51)= 20,365,011,074 if these two numbers are added what number results
Answer:
f(52) = 32,951,280,099
Step-by-step explanation:
In Fibonacci sequence, the sum of the two preceding sequence of the sequence is always equivalent to the next sequence.
For example, this is a Fibonacci sequence 1,2,3,5,8... As you can see that the sum of the two preceding sequence gave the next sequence i.e 1+2 = 3, 2+3 = 5, 3+5 = 8 etc and the chain continues like that.
If we are now given two large numbers of. Fibonacci sequence to bef(50)=12,586,269,025 and f(51)= 20,365,011,074
The next sequence f(52) will be the sum of the preceding sequences f(50) and f(51) that is;
f(52) = f(50) + f(51)
f(52) = 12,586,269,025 + 20,365,011,074
f(52) = 32,951,280,099
The resulting numbers if they are added is 32,951,280,099.
What is the approximate volume of a cone with a height of 9 ft and radius of 3 ft?
Use 3.14 to approximate pi, and express your final answer to the nearest tenth.
@phi,
At LaMar’s birthday party, his parents served slices of plain, sausage, or pepperoni pizza. They also served cups of milk, orange juice, apple juice, or lemonade. If each guest at the party chose one slice of pizza and one type of drink, how many different combinations were possible?
Answer: 12 different combinations were possible.
Step-by-step explanation:
Given: At LaMar’s birthday party, his parents served slices of plain, sausage, or pepperoni pizza.
i.e. The number of types of pizza = 3
They also served cups of milk, orange juice, apple juice, or lemonade.
i.e. The number of types of drinks = 4
Now, if each guest at the party chose one slice of pizza and one type of drink, then the number of different possible combinations are :
[tex]3\times4=12[/tex]
Hence, there were 12 different combinations .
Help Plz!
1. The population of Linton is 12 times as great as the population of Ellmore. The combined population of both towns is 9,646 people. What us the population of Linton?
2. Jessie bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jessie bought?
1)
What is the area of a sector with a central angle of 5π/7 radians and a diameter of 5.6 in.?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
2)
What is the area of a sector with a central angle of 4π/5 radians and a radius of 11 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
The area of the given sectors of circles is required.
The area of the sector is [tex]8.79\ \text{in}^2[/tex]
The area of the sector is [tex]151.98\ \text{cm}^2[/tex]
Area of sector[tex]\theta[/tex] = Central angle = [tex]\dfrac{5\pi}{7}\ \text{rad}[/tex]
d = Diameter = 5.6 in
r = Radius = 2.8 in
Area of a sector is given by
[tex]A=\dfrac{\theta}{2}r^2\\\Rightarrow A=\dfrac{\dfrac{5\times 3.14}{7}}{2}\times 2.8^2\\\Rightarrow A=8.79\ \text{in}^2[/tex]
[tex]\theta=\dfrac{4\pi}{5}\ \text{rad}[/tex]
r = 11 cm
[tex]A=\dfrac{\dfrac{4\times 3.14}{5}}{2}\times 11^2\\\Rightarrow A=151.98\ \text{cm}^2[/tex]
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Next school year 4 out of every 9 students plan to take an elective computer course if there are 2664 students at the high school how many computer students should the school plan for
How many lines of symmetry does a regular hexagon have? 8 6 4 2
Answer:
it is 6 so have a merry christmas
Step-by-step explanation:
NEED HELP ASAP PLEASE
A 72° sector in a circle has an area of 16.4π yd².
What is the area of the circle?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
Solution :
Give that, a 72° sector in a circle ,
Area of Sector in a circle =
[tex] \pi \times r^{2} \times( \frac{\theta}{360} )\\ \:\: where, r = radius\, of\, the\, circle\ \\ \theta = angle \,in \, degrees [/tex]
Suppose radius of circle is r .
then Volume of sector of circle
[tex] \pi \imes r^{2} \times (\frac{72}{360} )= 16.4\pi\\\\r^{2} = \frac{16.4 \pi}{\pi \times \frac{72}{360} } = \frac{16.4 \times 360}{72} [/tex]
Area of a Circle of radius, r, [tex] A = \pi\times r^{2} [/tex]
Put [tex] r^{2} = \frac{16.4 \times 360}{\times 72} [/tex]
Area of Circle, A = [tex] \pi \times \ \frac{16.4 \times 360}{72} =82 \pi[/tex]
given, [tex] \pi =3.14 [/tex]
[tex] volume =82 \times 3.14 = 257.48 [/tex]
Hence, Area of circle= 257.48
Answer:257.48 yd sq
Step-by-step explanation: took de quiz
Which of the following represents the graph of f(x) = 2(x + 3)?
A. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_17.gif
B. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_18.gif
C. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_19.gif
D. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_20.gif
Answer:
c
Step-by-step explanation:
How Many Toys Will Remain?
2. A cake in the shape of a circus tent is used as a centerpiece at a celebration. The cake consists of a cylinder and a cone. The cylinder has a diameter of 12 inches and a height of 14 inches. The cone has a height of 6 inches. What is the volume of the cake? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.