Answer:
line RQ
Step-by-step explanation:
The points on a line can be flipped when naming. For example, line AB is the same as line BA.
A group of workers painted a house. They used 1 1/2 gallons of paint per hour and painted
for 3 1/4 hours.
How many gallons of paint did the workers use?
Answer:
4,875 gallons.
Step-by-step explanation:
1.5 gallons/hour
1.5 / 4 = 0.375 gallons/25mins
1.5 * 3 (hours) + 0.375 = 4.875 gallons
O
X
y
X
y
X
y
X
y
0
2
0
0
-1
0
1
0
5
2
113
1
2
2
8
4
WIN
3
3
4
11
2.5 -2.5-7.5 -12.5
6
W/W
5
6
Select all table’s that represent proportional relationship between x and y
All tables that represent proportional relationship between x and y are:
B. table B.
E. table E.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)
Constant of proportionality, k = 1.
Therefore, the required linear equation is given by;
y = kx
y = x
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
PLEASE HELP !!!
Which equation represents the graph?
y=-1/3x-3
y=3x-3
y=-1/3x+1/3
y=-3x-1/3
Answer:
Step-by-step explanation:
Y=-3x-1/3
The answer should be y=-3x-3. The slope is -3, and the y intercept is -3. I don't see this as an option!
A bag contains 8 red pens, 7 blue pens, and 14 black pens. Denato wants to pull a blue pen from the bag.
What is the sample space for this experiment?
[red, black]
[blue]
[red, blue, black]
[blue, red]
Answer:
Step-by-step explanation:
The sample space represents the set or collection of all possible outcomes. It's often written as S = [outcome1, outcome2, outcome3].
For this problem, there are 3 possible outcomes: red pen, blue pen or black pen. (The fact that Denato wants to pull a blue pen is irrelevant when defining the sample space bc we are just listing the possible outcomes.)
So the answer is [red, blue, black].
If f(x)=x+2 and g(x + 1) = x + 1 then find g. f(4).
Answer:
[tex]x + 2[/tex]
see the below process of the equation:
Step-by-Step Explaination:
Given, f(x)=x+1 and g(x)=x+1
∴g(g(x))=g(x+1)
=(x+1)+1
=x+2
-Thank You By MrIshaan
A 3 1/2 inch by 5 inch photo is to be enlarged to a similar rectangle. If the width is 6 inches what should the length be?
Answer:
4.2, or 4 1/4
Step-by-step explanation:
Usually, "3 1/2 inch by 5 inch" is in the format of "length by width."
Therefore, the original length is 3.5 and width is 5.
If the new width is 6, the scale factor is determined by the following:
n/o, where 'n' is new, and 'o' is old: 6/5 = 1.2. Check the work: 5 * 1.2 = 6.
Therefore, the scale factor is 1.2. Now, multiply the old length by the scale factor to determine the new length:
3.5 * 1.2 = 4.2, or 4 1/4 inches, as there are 8 sections in an inch, and 2/8 = 0.25, which is a quarter, or 1/4.
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The triangle above has the following measures.
m
a=7.5 y
Use the 45-45-90 Triangle Theorem to find the length of the hypotenuse. Include correct units.
Show all your work.
The length of the hypotenuse is 10.61 yd.
We have,
The sum of the angles in a triangle = 180
Now,
Two angles are 45.
This means,
The side opposite to angle 45 are equal.
So,
a = c
And,
a = 7.5 yd
Now,
Applying the Pythagorean theorem.
b² = a² + c²
b² = 7.5² + 7.5²
b² = 112.5
b = √112.5
b = 10.61
Thus,
The length of the hypotenuse is 10.61 yd.
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4.1.3 Bathu Sneakers have been looking into different shoebox sizes: a large box for male shoes and small box for female shoes. The cost of the cardboard to make the boxes is 0,502 cents/cm². Calculate the percentage savings Bathu Sneakers will make if the smaller box is used compared to the normal larger box. Larger Box Total Surface Area = 4 093 cm² 19 cm 26 cm 34,5 cm Smaller Box Total Surface Area = 3 034 cm² 25 cm 17 cm 26 cm (6)
Answer:
Step-by-step explanation:To calculate the savings percentage, we first need to find out the cost of the cardboard required for each box.
For the larger box:
Total Surface Area = 2 * (1926 + 1934.5 + 26*34.5) = 2 * (494 + 655.5 + 897) = 4093 cm²
Cost of cardboard for larger box = 0.502 * 4093 = 2055.986 cents = 20.55986 dollars (rounded to 5 decimal places)
For the smaller box:
Total Surface Area = 2 * (2517 + 2526 + 1726) + 6 * (25-21)* (17-2*1) = 3034 cm²
Note that the additional term in the equation is the surface area of the six sides of the lid and base of the box.
Cost of cardboard for smaller box = 0.502 * 3034 = 1522.268 cents = 15.22268 dollars (rounded to 5 decimal places)
The difference in cost between the larger and smaller boxes is:
20.55986 - 15.22268 = 5.33718 dollars (rounded to 5 decimal places)
The percentage savings can be calculated as follows:
Percentage savings = (difference in cost / cost of larger box) * 100%
= (5.33718 / 20.55986) * 100%
= 25.98%
Therefore, using the smaller box will result in a savings of approximately 26% on cardboard costs for Bathu Sneakers compared to using the normal larger box.
The net below shows a square pyramid. What is the lateral surface area? 8in
7in
The lateral surface area of the square pyramid is 176 in².
The first thing we need to do is find the slant height of the pyramid, which is the height of each of the triangular faces. We can use the Pythagorean theorem to do this:
slant height² = height² + (1/2base)²
slant height² = 7² + (1/28)²
slant height² = 49 + 16
slant height² = 65
slant height = √(65)
Now that we have the slant height, we can find the lateral surface area by multiplying the perimeter of the base by half the slant height. The perimeter of the base is simply 4 times the length of one of the sides, which is 8 inches.
lateral surface area = (perimeter of base * slant height) / 2
lateral surface area = (4 * 8 * √(65)) / 2 lateral surface area = 16 * √(65)
To simplify the radical, we can factor out any perfect squares that are factors of 65:
lateral surface area = 16 * √(65)
lateral surface area = 16 * √(513)
lateral surface area = 16 * √(5) * √(13)
lateral surface area = 16 * √(5) * √(43.25)
lateral surface area = 16 * √(5) * (2 * √(3.25))
lateral surface area = 64 * √(5) = 176.42 square inches.
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Can someone help me with this problem please
Suppose M is a matrix of size 9x10, c is a scalar, and the matrix computation cM is defined. What is the size of matrix cM?
When a scalar quantities is multiplied by a matrix of size 9x10, the resulting matrix will also be of size 9x10.
If we perform the matrix computation cM, where c is a scalar and M is a matrix of size 9x10, the resulting matrix cM will also be of size 9x10.
This is because when we multiply a scalar by a matrix, each element in the matrix is multiplied by the scalar.
Therefore, the resulting matrix has the same dimensions as the original matrix.
To see why this is the case, consider a single element in the resulting matrix cM. Let's say the element is located at row i and column j.
Then, it is given by cM[i,j] = c*M[i,j]. Since M[i,j] is just a single element in the original matrix, multiplying it by the scalar c produces a new scalar.
Therefore, cM[i,j] is also a single element in the resulting matrix cM.
Since each element in the original matrix M is multiplied by the scalar c, the resulting matrix cM will have the same dimensions as the original matrix, i.e., 9x10.
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The product of two numbers is 155952. If one number is 342, find the other
number.
Answer:
456
Step-by-step explanation:
Product means an answer derived from multiplication. Therefore, if the product is 155952, and one value is 342, then the following equation is true:
342x = 155952, or 342 * x = 155952
Divide 155952 by 342 to get: 456.
Check the work in the equation:
342(456) = 155952
155952 = 155952, which is true, so the answer is 456.
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Determine the value of (3³)².
A: 711
B: 645
C: 729
D:12
Answer:
729
Step-by-step explanation:
3^3=27
and 27^2=729
So the final answer is 729!
Answer:
the answer is C: 729
Step-by-step explanation:
3×3×3=27
27×27=729
If it is 7:00 o'clock a.m. on March 1 in Portland, Oregon, what day and time will it be 7777 hours later in Washington, D.C.? Please explain.
Answer:
To determine the day and time 7777 hours later in Washington, D.C., we first need to determine the time difference between Portland, Oregon, and Washington, D.C. Portland is in the Pacific Time Zone, while Washington, D.C., is in the Eastern Time Zone. The time difference between the two zones is 3 hours, with Eastern Time being ahead of Pacific Time.
So, if it is 7:00 a.m. in Portland, it would be 10:00 a.m. in Washington, D.C.
Next, we need to calculate the number of days that pass in 7777 hours. Since there are 24 hours in a day, we can divide 7777 by 24 to get the number of days:
7777 ÷ 24 = 324 remainder 1
So, 7777 hours is equal to 324 days and 1 hour.
Finally, we can add 324 days and 1 hour to the current time in Washington, D.C.:
10:00 a.m. on March 1 + 324 days and 1 hour = 11:00 a.m. on January 20 of the following year.
Therefore, 7777 hours later in Washington, D.C., would be 11:00 a.m. on January 20 of the following year.
Answer: 7777 hours late in Washington D.C. would be 11:00 a.m on January 20th of the following year
Step-by-step explanation:
What is the mean absolute deviation of 8,4,8,8,10,2,4,4
Mean absolute deviation is 2.5.
The mean absolute deviation (MAD) measures how spread out a set of data is by calculating the average distance between each data point and the mean of the data set.
To find the MAD of the given data set {8,4,8,8,10,2,4,4}, we first need to find the mean of the data set.
Mean = (8+4+8+8+10+2+4+4)/8 = 6
Next, we need to find the absolute deviation of each data point from the mean:
|8-6| = 2
|4-6| = 2
|8-6| = 2
|8-6| = 2
|10-6| = 4
|2-6| = 4
|4-6| = 2
|4-6| = 2
To find the MAD, we need to take the mean of the absolute deviations:
MAD = (2+2+2+2+4+4+2+2)/8 = 2.5
Therefore, the mean absolute deviation of the data set {8,4,8,8,10,2,4,4} is 2.5. This means that, on average, the data points in the set are about 2.5 units away from the mean of the set.
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12. ABC-A'B'C' is a reflection. Use this to answer the questions below.
(A) Which figure is the preimage?
(B) Which figure is the images
(C) What are the coordinates of the output?
Input. Output
A(0,9). A
B(-4,4) B
C(0,4). C
(A) The figure before the reflection is called the preimage. In this case, the preimage is ABC. (B) The figure after the reflection is called the image. In this case, the image is A'B'C'. (C) The outputs for the given inputs are:
Input: A(0,9) Output: A(0,9)
Input: B(-4,4) Output: B'(-8,0)
Input: C(0,4) Output: C(0,4)
(C) The coordinates of the output for each input point can be found by reflecting the input point across the line of reflection. In this case, the line of reflection is the perpendicular bisector of the line segment connecting A and C. For point A, the reflection is itself, so the output is (0,9).
For point B, we can find its reflection as follows: draw the line perpendicular to the line of reflection that passes through B, and find the point where it intersects the line of reflection. This point is the midpoint of the line segment connecting B and its image. The reflection of B is (-8,0), and the output is B'. For point C, the reflection is itself, so the output is (0,4).
Reflection is a type of transformation in geometry where an object is flipped across a line. In this case, ABC was reflected across the line of reflection to form A'B'C'. The line of reflection is the perpendicular bisector of the line segment connecting A and C.
The reflection of a point is the point on the other side of the line of reflection that is equidistant from the line. By applying the reflection rule, we can find the coordinates of the output for each input point.
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Which statement is true regarding the parallel and perpendicular lines in the diagram? k Parallel to n and w Perpendicular to m k Parallel to n and n Perpendicular to m w Parallel to n and n Perpendicular to m w Parallel to n and wPerpendicular to m
Answer:
Based on the diagram, we can see that there are four lines: k, n, w, and m. The relationship between these lines is important in understanding their geometric properties.
We can see that line k and line n are both straight lines and never intersect, which means they are parallel to each other. This is indicated by the two small arrows on line k and line n that are pointing in the same direction.
On the other hand, line w intersects line m at a right angle (90 degrees). This means that line w is perpendicular to line m. This is indicated by the small square in the corner where line w and line m meet.
Understanding parallel and perpendicular lines is important in many areas of mathematics and science, such as geometry, trigonometry, physics, and engineering.
Step-by-step explanation:
Answer:
The correct statement is: w is parallel to n and w is perpendicular to m.
Step-by-step explanation:
2. The population of a town was 7,250 in 2014
and 7,375 in 2015. What was the percent
increase from 2014 to 2015 to the nearest
tenth of a percent?
A) 1.5%
B) 1.6%
C) 1.7%
D) 1.8%
E) 2.0%
E
The percentage change of the population is P = 1.7 %
Given data ,
To calculate the percent increase from 2014 to 2015, we need to find the difference between the two population values, divide it by the initial value, and then multiply by 100 to get the percentage.
Population increase = 7,375 - 7,250 = 125
Percent increase = (Population increase / Initial population) * 100
Percent increase = (125 / 7,250) * 100 ≈ 1.7241
Rounding to the nearest tenth of a percent, the percent increase is approximately 1.7%.
Hence , the percentage change is P = 1.7 %
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Fill in the table using this function rule.
y=-6x-3
Substitute each x-coordinate into equation y = - 6x - 3 to find the corresponding y-coordinate:
For x = - 1:y = - 6(-1) - 3 = 6 - 3 = 3For x = 0:y = - 6(0) - 3 = 0 - 3 = - 3For x = 1:y = - 6(1) - 3 = - 6 - 3 = - 9For x = 5:y = - 6(5) - 3 = - 30 - 3 = - 33ABCD is a rhombus. What is the value of x?
B
(3x+10)°
A
8
20
10
12
D
C
(2x+20)°
Answer:
3x+10+2x+20=180(oppite <s of parallogram)
30+3x=180
3x=180-30
3x=150
x=50
Step-by-step explanation:
The opposite angle of rhombus are equal
so,
here,
or,3x+10=2x+20
or,3x-2x=20-10
Therefore x=10
Select the correct answer. What are the solutions to this equation? 7x2 − 28 = 0 A. B. C. D.
Which cone has a volume of 24 лcm³? 3,5 cml 1 2 B = 25 cm 6,5 cml L 3 cm 4.5 cm₁ L 8 cm 7/5 cml B = 4
The cone that has the volume of 24л cm³ is the third cone which has a diameter of 8 cm and a height of 4.5 cm.
What is the Volume of a Cone?The formula for determining the volume of a cone is expressed as the following:
Volume of a cone (V) = 1/3 * πr²h
We are given the following information about the third cone in the image given:
Diameter of the cone = 8 cm
Radius of the cone (r) = 8/2 = 4 cm
Height of the cone (h) = 4.5 cm
Plug in the values:
Volume of a cone (V) = 1/3 * π * 4² * 4.5
Volume of the third cone (V) = 24л cm³
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Please help !!!!!! 20 points
The value of x in the polygon will be 13.25 degrees.
The value of x is 10.
We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.
How to calculate the valueThe sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.
Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees
Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:
Measure of one angle = 3960/24 = 165 degrees
165 = 12x + 6
159 = 12x
x = 13.25
Therefore, the value of x is 13.25 degrees.
Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.
Therefore, we have:
731x+86° = 7380°
Solving for x, we get:
731x = 7294°
x = 10
Therefore, the value of x is 10.
The equation that can be used to find the value of x is:
(9x+48)° + (15x-24)° = (n-2)*180°
24x + 24 = (n-2)*180°
Dividing both sides by 24, we get:
x + 1 = (n-2)*15°
Subtracting 1 from both sides, we get:
x = (n-2)*15° - 1
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Find the value of x for which r || s.
A) 44
B) 14
C) 10
D) Can't be determined.
Answer:
A) 44
Step-by-step explanation:
The given angle measurements are same side interior angles. Therefore, the summation of the two angle measurements will equal 180° (Forming a straight line).
Set the two angle measurements equal to 180:
[tex](3x + 3) + (45) = 180[/tex]
Simplify. First, combine like terms. Like terms are terms that share the same amount of the same variables. In this case, combine 3 with 45:
[tex]3x + 3 + 45 = 180\\3x + (3 + 45) = 180\\3x + (48) = 180[/tex]
Next, isolate the variable, x. Note the equal sign, what you do to one side of the equation, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 48 from both sides of the equation:
[tex]3x + 48 = 180\\3x + 48 (-48) = 180 (-48)\\3x = 180 - 48\\3x = 132[/tex]
Next, divide 3 from both sides of the equation:
[tex]\frac{3x}{3} = \frac{132}{3} \\x = \frac{132}{3} \\x = 44[/tex]
A) 44 is the value for x.
~
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f(x)=x2+1 g(x)=5-x (f+g)(x)=
Answer:
x²-x+6
Step-by-step explanation:
Use (f+g)(x) = f(x)+g(x), substitute and simplify
Faith only read 60% of her goal for 1 week. How would the mean, median, and mode have changed if Faith had met her goal? Explain.
If Faith had met her goal, the mean would have increased from 60 to 100, the median would have remained the same at 60, and the mode would have changed from 60 to 100.
If Faith had met her goal, the mean, median, and mode would have changed. Let's assume her goal for the week was to read 100 pages.
Faith read only 60% of her goal, which is equivalent to 60 pages
(100 pages × 0.6).
If she had met her goal, she would have read 100 pages in total.
The mean would have changed from 60 pages to 100 pages.
Since we only have one data point (60), the median would have remained the same at 60.
The mode would be 60 since that is the only value we have.
If Faith had met her goal, the mode would have changed to 100, as 100 pages would appear most frequently.
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The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.
Supply: p=0.003.x
Demand: p = -0.007x+300
(a) Solve the system of equations defined by the supply and demand models.
(b) What is the equilibrium price?
(c) What is the equilibrium quantity?
a) The solution of the system of equations is, x = 30,000
b) the equilibrium price is, p = 90
c) the equilibrium quantity is, p = 90
Given that;
The price (in S) of a cookbook is determined by the number of cookbooks x demanded by consumers and supplied by the publisher.
Supply: p=0.003.x
Demand: p = -0.007x+300
Hence, We can simplify as;
⇒ 0.003x = - 0.007x + 300
Solve for x;
⇒ 0.003x + 0.007x = 300
⇒ 0.01x = 300
⇒ x = 300/0.01
⇒ x = 30,000
Hence, the equilibrium price is,
p=0.003.x
p=0.003 × 30,000
p= 90
And, the equilibrium quantity is,
p = -0.007x+300
p = -0.007 × 30,000+300
p = - 210 + 300
p = 90
Thus, a) The solution of the system of equations is, x = 30,000
b) the equilibrium price is, p = 90
c) the equilibrium quantity is, p = 90
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Use slopes and y-intercepts to determine if the lines y=−x+3 and −3x−3y=1 are parallel.
Answer:
YES PARALLEL
Step-by-step explanation:
The slopes of
y=−x+3 and −3x−3y=1 are both −1.
Parallel
The net of a triangular prism and its approximate dimensions are shown in the diagram.
4in. 12 in. 12in. 12 in. 12 in. 10.4 in. Which measurement is closest to the total surface area of the triangular prism in square inches?
The measurement closest to the total surface area of the triangular prism is J) 393.6 [tex]in^{2}[/tex] .
To find the surface area of a triangular prism, we need to find the area of all its faces and add them up.
Looking at the net of the triangular prism, we can see that it has two congruent triangles and three rectangular faces.
The area of each triangular face can be found using the formula for the area of a triangle:
Area of a triangle = (1/2) x base x height
In this case, the base of each triangle is 12 inches and the height is 4 inches. So, the area of one triangular face is:
(1/2) x 12 x 4 = 24 [tex]in^{2}[/tex]
The area of each rectangular face can be found using the formula:
Area of a rectangle = length x width
In this case, the length and width of the rectangular faces are:
12 in. x 10.4 in.
12 in. x 12 in.
4 in. x 10.4 in.
So, the area of each rectangular face is:
12 x 10.4 = 124.8 [tex]in^{2}[/tex]
12 x 12 = 144 [tex]in^{2}[/tex]
4 x 10.4 = 41.6 [tex]in^{2}[/tex]
Therefore, the total surface area of the triangular prism is:
2 x 24 + 124.8 + 144 + 41.6 = 393.6 [tex]in^{2}[/tex]
So, the measurement closest to the total surface area of the triangular prism in square inches is J) 393.6 [tex]in^{2}[/tex] .
Correct Question :
The net of a triangular prism and its approximate dimensions are shown in the diagram, 4 in, 12 in, 10.4 in, 12 in, 12 in, 12 in. Which measurement is closest to the total surface area of the triangular prism in square inches?
F) 268.8 [tex]in^{2}[/tex]
G) 432 [tex]in^{2}[/tex]
H) 288 [tex]in^{2}[/tex]
J) 393.6 [tex]in^{2}[/tex]
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x<-5
How do you graph this equation?
To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.
We have,
To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.
Since the inequality is strict (X is less than -5), we will draw an open circle at -5 to indicate that -5 is not included in the solution set.
Next, we shade the portion of the number line to the left of -5, since any value of X less than -5 satisfies the inequality.
Note that the open circle at -5 indicates that X cannot be equal to -5, since the inequality is strict.
Any value to the left of -5 on the number line would satisfy the inequality.
Thus,
To graph the inequality X < -5 on a number line, we start by drawing a number line and marking a point at -5.
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What is the volume of this triangular pyramid
Answer:
The right triangular pyramid volume is given by the formula V = 1 3 × B × h , where B is the area of the triangular base and h is the height (the distance from the apex to the base).
Step-by-step explanation:
Answer:
192 cubic feet
Step-by-step explanation:
The volume V of a triangular pyramid is given by the formula:
V = (1/3) * base area * height
where base area is the area of the triangular base.
In this case, the triangular base has a length of 8 ft and a width of 8 ft, so it is a square with area:
base area = length * width = 8 ft * 8 ft = 64 sq ft
Substituting the given values into the formula, we get:
V = (1/3) * 64 sq ft * 9 ft
V = 192 cubic feet.
Therefore, the volume of the triangular pyramid is 192 cubic feet.
