Barbara drew a scale drawing of a game room. The scale she used was 2 inches : 1 foot. If the actual length of the pool table is 6 feet, how long is the pool table in the drawing?
If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches .
In the question,
it is given that ,
Barbara drew an scale drawing of the game room.
the scale that she used is 1 feet in the actual length is represented by 2 inches in the drawing ,
which means ,
1 feet = 2 inches
to find the length of 6 feet in the drawing ,
6 feet = 6 × 2 inches
= 12 inches
Therefore , If the actual length of the pool table is 6 feet , then the length of the pool table in the drawing is 12 inches .
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Which of the following rules describes the function graphed below? On a coordinate plane, points are at (negative 1, 1), (1, 2), (3, 3), (5, 4). a. Output = Input c. Output = (0.5)(Input) + 1.5 b. Output = (2)(Input) – 3 d. Output = (1.5)(Input) + 3
The rule that describes ( -1, 1), (1, 2), (3, 3), (5, 4) is c. Output = (0.5)(Input) + 1.5
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, On a coordinate plane, points are at ( -1, 1), (1, 2), (3, 3), (5, 4).
By observing the given options we conclude that it is Output = (0.5)(Input) + 1.5 to confirm let's put the values.
Given when input is - 1 output is 1.
∴ 1 = 0.5(-1) + 1.5.
1 = - 0.5 + 1.5.
1 = 1 ( satisfied).
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consider following recurrence relation. what will be the number next in series in place of question mark? 0, 3, 8, 15, 24, 35, 48, ?
The number that will be next in the series will be 63 .
In the question ,
a recurrence relation is given that is 0, 3, 8, 15, 24, 35, 48, ? .
we have to find the number that will come in place of question mark .
On carefully examining the series , we can see that
3 - 0 = 3
8 - 3 = 5
15 - 8 = 7
24 - 15 = 9
35 - 24 = 11
48 - 35 = 13
we can se that increments 3,5,7,9,11,13,... form an Arithmetic Progression
with first term as 3 and common difference as 2 ,
So ,the next increment will be 13+2 = 15
let the next term be "x" .
x - 48 = 15
x = 15 + 48 = 63
the number in place of ? is 63 .
Therefore , The number that will be next in the series will be 63 .
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A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7. 50, and tickets for children cost $3. 50. How many of each type of ticket were purchased?.
23 tickets are purchased for children and 9 tickets are purchased for adults.
Given,
In the question:
A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7. 50, and tickets for children cost $3. 50.
To find the how many of each type of ticket were purchased?
Now, According to the question:
It is given in the question that 32 tickets are purchased by group which cost total $148.
Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x
Now cost of one ticket for adult = $7.50
Total amount spent on adult tickets = 7.50 × (32-x)
Similarly, cost of one ticket for child= $3.50
Total amount spent on children tickets = 3.50 × x =3.5x
Total amount spent by group on tickets = $148
⇒ 7.5 × (32-x) + 3.5x = 148
⇒ 240 - 7.5x + 3.5x = 148
⇒ 7.5x - 3.5x = 240 - 148
⇒ 4x = 92
⇒ x = 23
Children = 23
Adults = 32-x = 32-23 = 9
Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.
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The perimeter of an isosceles triangle is 380 cm and it’s unequal side is 150 find the area of triangle (by Heron’s formula)
Answer:
A ≈ 6538.35 cm²
Step-by-step explanation:
Calculating the area (A) using Heron's formula
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where s is the semi perimeter and a, b, c the 3 sides
here
s = 380 ÷ 2 = 190
given perimeter = 380 and unequal side is 150 , then
equal sides = (380 - 150) ÷ 2 = 230 ÷ 2 = 115 cm
then a = 150, b = 115 , c = 115
A = [tex]\sqrt{190(190-150)(190-115)(190-115)}[/tex]
= [tex]\sqrt{190(40)(75)(75)}[/tex]
= [tex]\sqrt{42750000}[/tex]
≈ 6538.35 cm² ( to 2 dec. places )
Determine whether the following sequence is arithmetic, geometric, or neither. 12,17,22,27
Answer:
Arithmetic
Step-by-step explanation:
The difference between consecutive terms is 5. Thus, this is an arithmetic sequence with a common difference of 5.
PLEASE HURRY
I am having trouble
You got to set it up to boys to girls
Answer:
0,1
Step-by-step explanation:
simplest form
Raman purchased books and stationery items and paid the total amount of rupees 963 if he paid 7% tax what was the net value of the item purchased.
The net value of the items purchased is ₹ 900.
Raman purchased books and stationery items and paid the total amount of rupees 963.
Paid tax = 7%
Let the net value of the items purchased be `x.
VAT = 7%
Selling price = ₹x + (7% of x)
= ₹x+ ₹ ( 7/100 * x)
=₹( x +7 x /100)
= ₹ 107 x /100
But Raman purchased books and stationery items for ₹963.
107x/100 = ₹963
x = 963 x 100/107
x = 900
Hence the answer is the net value of the items purchased is ₹ 900.
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How many solutions does 5 + x/3 = x/3 + 6 + x/9
A. Infinitely many solutions
B. Two solutions
C. No solutions
D. One solution
========================================================
Explanation:
A thing that jumps out at me right away is the presence of x/3 on both sides. When subtracting x/3 from both sides, these terms cancel out and we're left with this equation
5 = 6 + (x/9)
Let's say w = x/9. We now have this equation 5 = 6 + w. Subtract 6 from both sides to isolate w and you should get w = -1
Then plug in w = x/9 and solve for x.
w = -1
x/9 = -1
x = 9*(-1)
x = -9
We get exactly one solution and it is x = -9
--------------
Check:
5 + x/3 = x/3 + 6 + x/9
5 + (-9)/3 = (-9)/3 + 6 + (-9)/9
5 - 3 = -3 + 6 - 1
2 = 3 - 1
2 = 2
We get the same thing on both sides, which leads to a true statement. This causes a domino effect to lead the first equation to be true when x = -9. Therefore, the solution is confirmed.
The graph to the right is the uniform probability density function for a friend who is x minutes late
(a) Find the probability that the friend is between 25 and 30 minutes late.
(b) It is 10 A.M. There is a 10% probability the friend will arrive within how many minutes?
(a)The probability that the friend is between 25 and 30 minutes late is 1/2.
(b) It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.Uniform distribution
a = 0
b = 10
a) P(friend is between 25 and 30 minutes late) = (30 - 25)/(b - a)
= 5/(10-0)
= 1/2
b) Let the time for arrival be A minutes
(A - 0)/(b-a) = 0.10
A = 0.10 x (10 - 0)
A = 1 minute
Hence, The probability that the friend is between 25 and 30 minutes late is 1/2 and It is 10 A.M. There is a 10% probability the friend will arrive within 1 minute.
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Use the diagram to find the measure of angle 2
The measure of angle 2 is 75°
From the question, we have
∠1= 105°
∠2= 180°- 105° (Linear pair)
∠2=75°
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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-4(w + 5) + 2w simplify
Answer:
-2w-20
Step-by-step explanation:
help pls what are the number of hours i need this before 11/20/22
a. Creating a system of equations, the length of each plan A's workout is 3/4 hour, while the length of each plan B's workout is 3/4 hour.
b. x = -8, y = 2.
How to Solve a System of Equations?Write equations of a system that represents the information given and solve accordingly.
Let the length of plan A = x
Length of plan B = y
Equation for Monday would be:
9x + 7y = 12 --> eqn. 1
Equation for Tuesday:
3x + 5y = 6 --> eqn. 2
Multiply eqn. 1 by 3 and eqn. 2 by 9
27x + 21y = 36 --> eqn. 3
27x + 45y = 54 --> eqn. 4
Subtract the equations:
-24y = -18
y = -18/-24
y = 3/4
Plan B's length of workout is: 3/4 hour.
Substitute y = 3/4 into equation 2:
3x + 5(3/4) = 6
3x + 15/4 = 6
3x = 6 - 15/4
3x = 9/4
12x = 9
x = 9/12
x = 3/4
Length of plan A's workout is: 3/4 hour.
b. 2x + 4y = -8 --> eqn. 1
-2x + 3y = 22 --> eqn. 2
Add both equations together:
7y = 14
y = 2
Substitute y = 2 into equation 1:
2x + 4(2) = -8
2x + 8 = -8
2x = -8 - 8
2x = -16
x = -16/2
x = -8
The solution is: x = -8, y = 2.
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The average annual rainfall for a town is 43.2 inches. The average monthly rainfall for the previous 9 months was 4 inches. Did the town exceed its average annual rainfall? If so, by how much?
Answer:
Yes, the town exceeded the average annual rainfall by 0.4 inchesStep-by-step explanation:
The average annual rainfall for a town is 43.2 inches.
This is converted to average monthly as:
43.2 in / 12 = 3.6 inThe difference is:
4 in - 3.6 in = 0.4 inAnswer:
Yeah, they exceeded by 0.4 inches.
Step-by-step explanation:
It is given that,
→ the average monthly rainfall for the previous 9 months was 4 inches.
The monthly rainfall in 12 months,
→ 43.2 inches ÷ 12 months
→ 43.2/12
→ 3.6 inches
Then the difference will be,
→ 4 inches - 3.6 inches
→ 4 - 3.6
→ 0.4 inches
Hence, the difference is 0.4 inches.
can someone please help me with this
Answer:
B
Step-by-step explanation:
given 1 pound = 16 ounces , then
5 pounds = 5 × 16 = 80 ounces
Solve 2y + x + 3 = 0 and 3y - x + 1 = 0 graphically using -4 ≤x ≤ 2
help pls
Answer:
Step-by-step explanation:
We have to the graph from x = -4 to x = 2
2y + x + 3 = 0
Rearrange the equation to make y the subject
2y = -x - 3
y = (-1/2)x -3/2
-3/2 is the y intercept
the gradients is -1/2
since the value is negative, the graph will be sloping downwards
Point your pen at y = -3/2 on the y axis (-3/2 is -1.5)
go 1 point down and 2 points to the right, make a point and connect these 2 dots and make a line across the graph.
Do the same with the other equation:
3y - x + 1 = 0
3y = x - 1
y = (1/3)x -1/3
y intercept is -1/3
gradient is 1/3
point your pen at -1/3 on the y axis, go 1 point up and 3 points to the right
and mark this point and connect these 2 points and make a line across the graph.
for the function g(x)=-1/5 x^2 + 4x+1, find the range of g(x)
Plotting the graph of the quadratic function g(x)=-1/5x^2 + 4x + 1 the range is
y ≥ -19How to determine the range of the quadratic functionThe range of the quadratic function is seen at the vertex were the maximum or minimum y value is seen
The graph of the function g(x)=-1/5x^2 + 4x + 1 is plotted and attached
From the graph the vertex coordinates is v(-10, -16). The y coordinates of the vertex is -19 and this is the minimum values for y
Therefore the range is y ≥ -19
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What expressions represents the multiplex version of the expression below ?
(6x^2 +5) (2x^3+3)
Answer:
12x^5+18x^2+10x^3+15
Step-by-step explanation:
first you apply the distribution property (FOIL) and you get
12x^5+18x^2+10x^3+15
A machine in a factory make 3 1/2 pound of nail in 1 1⁄4 hour. At what rate, in pound per hour, doe the machine make nail?
Answer:
2.8 pounds per hour
Step-by-step explanation:
[tex] \frac{3.5}{1.25} = \frac{350}{125} = \frac{14}{5} = 2.8[/tex]
A scale on a map is 1 200 000. Work out the distance on the map, in cm, if the real distance is 10 km 15 km 4 km
The distance on the map, in cm, given the real distances, and the scale of the map are:
10 km = 5 cm15 km = 7.5 cm4 km = 2 cmHow to find the distance on the map?A scale of 1 : 200, 000 means that every 1 cm on the map is 200, 000 cm on the ground.
To find the distance on the map of 10 km, first convert it to cm:
= 10 km x 100, 000 cm per km
= 1, 000, 000 cm
The distance on the map is therefore:
= 1, 000, 000 / 200, 000 cm scale
= 5 cm on map
The distance of 15 km on the map is:
= (15 km x 100, 000) / 200, 000
= 7.5 cm
The distance of 4 km is:
= (4 x 100, 000) / 200, 000
= 2 cm
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Find the length of YZ when Y is the midpoint of XZ
X
20+2a
Y
8 +6a
Z
XZ=
The length of the line YZ is 26 units
The Y is the mid point of the line XZ
The length of the line XY = 20 + 2a
The length of the line YZ = 8 + 6a
When Y is the mid point of the line XZ, then the length of the line XY is equal to the length of the line YZ
The length of the line XY = The length of the line YZ
Substitute the values in the equation and find the value of a
20 + 2a = 8 +6a
Rearrange and group the like term
6a - 2a = 20 - 8
4a = 12
a = 12 / 4
a = 3
The length of the YZ = 8 +6a
= 8 + 6×3
= 8 + 18
= 26 units
Hence, the length of the line YZ is 26 units
The complete question is:
Find the length of YZ when Y is the midpoint of XZ, if XY = 20+2a and YZ = 8+6a.
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which of the following ratios are connected to 5/20?
multiple choice
a 1/5
b1/4
c 20/100
d 25/100
Answer:
which of the following ratios are connected to 5/20?
multiple choice
a 1/5
c 20/100
d 25/100
d is the option 25/100 and
b 1/4
Giving brainliest to the person who give a right answer with a clear explanation
Answer:
33. AB = √45. CD = √40. Not congruent. AB is greater.
34. EF = 5. GH = √41. Not congruent. GH is greater.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Question 33Given endpoints:
A = (0, 2)B = (-3, 8)Substitute the given endpoints into the formula and solve:
[tex]\begin{aligned}\overline{AB}&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(-3-0)^2+(8-2)^2}\\&=\sqrt{(-3)^2+(6)^2}\\&=\sqrt{9+36}\\&=\sqrt{45}\\& \approx 6.7\; \sf (1 \; d.p.)\end{aligned}[/tex]
Given endpoints:
C = (-2, 2)D = (0, -4)Substitute the given endpoints into the formula and solve:
[tex]\begin{aligned}\overline{CD}&=\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\&=\sqrt{(0-(-2))^2+(-4-2)^2}\\&=\sqrt{(2)^2+(-6)^2}\\&=\sqrt{4+36}\\&=\sqrt{40}\\& \approx 6.3\; \sf (1 \; d.p.)\end{aligned}[/tex]
Therefore, the segments at not congruent.
[tex]\textsf{As\; $\sqrt{45} > \sqrt{40}$ \; then \; $\overline{AB} > \overline{CD}$}.[/tex]
Therefore, the length of segment AB is greater.
Question 34Given endpoints:
E = (1, 4)F = (5, 1)Substitute the given endpoints into the formula and solve:
[tex]\begin{aligned}\overline{EF}&=\sqrt{(x_F-x_E)^2+(y_F-y_E)^2}\\&=\sqrt{(5-1)^2+(1-4)^2}\\&=\sqrt{(4)^2+(-3)^2}\\&=\sqrt{16+9}\\&=\sqrt{25}\\&=5\end{aligned}[/tex]
Given endpoints:
G = (-3, 1)H = (1, 6)Substitute the given endpoints into the formula and solve:
[tex]\begin{aligned}\overline{GH}&=\sqrt{(x_H-x_G)^2+(y_H-y_G)^2}\\&=\sqrt{(1-(-3))^2+(6-1)^2}\\&=\sqrt{(4)^2+(5)^2}\\&=\sqrt{16+25}\\&=\sqrt{41}\\& \approx 6.4\; \sf (1 \; d.p.)\end{aligned}[/tex]
Therefore, the segments at not congruent.
[tex]\textsf{As\; $\sqrt{41} > 5$ \; then \; $\overline{GH} > \overline{EF}$}.[/tex]
Therefore, the length of segment GH is greater.
I really need help! Can anyone please answer this!!
The function f has domain : [-4, 5], range : [0, 9], zero : (3, 0), the function is increasing in intervals at [-4, 0] U [3, 5], decreasing in intervals at (0, 3], the relative minimum values of f : (3, 0), and relative maximum values of f : (5, 9).
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The function f is given in the graph.
According to the given function, the required solution would be as:
The domain and range of f will be :
domain : [-4, 5]
range : [0, 9]
The zero of f will be :
(x, y) = (3, 0)
The function is increasing in intervals at [-4, 0] U [3, 5]
The function is decreasing in intervals at (0, 3]
The relative minimum values of f : (3, 0)
The relative maximum values of f : (5, 9)
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5a<−35 or a−14>1
Algebra 1, high school
Answer:156
Step-by-step explanation:
at the lone butte ranch 6 goats and 5 sheep sell for 305 while 2 goats and 9 sheep sell for 285. Find the cost of a single goat and a single sheep.
By solving a system of equations we can see that each goat costs $30 and each sheep costs $25.
How to find the cost of each animal?Let's define the variables:
x = cost of a goat
y = cost of a sheep.
We can write the system of equations with the given info:
6*x + 5*y = 305
2*x + 9*y = 285
If we subtract 3 times the second equation from the first one, we get:
(6*x + 5*y) - 3*(2*x + 9*y) = 305 - 3*285
-22*y = -550
y = -550/-22 = 25
Now that we know the value of y we can try to find the value of x:
2*x +9*25 = 285
2*x = 285 - 9*25 = 60
x = 60/2 = 30
These are the costs of each animal.
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A person who weighs 150 pounds weighs 25 pounds on the Moon. Suppose an object weighs 80 pounds on the Moon. What’s the objects weight on the Earth?
Answer:
480 lbs
Step-by-step explanation:
First, find the ratio of weight on the moon to weight on the earth. I will put the two known values in a fraction like this:
[tex]\frac{25}{150}[/tex]
Now, I can create a proportion, making sure to keep the same types of measurements in the numerator and denominator. I will use w for the unknown weight on earth.
[tex]\frac{25}{150}=\frac{80}{m}[/tex]
Now, I will simplify the fractions as much as I can.
[tex]\frac{1}{6}=\frac{80}{m}[/tex]
Now, I can see a correlation. 1 times 80 is 80, so 6 times 80 is m. Simplified, here is the answer!
[tex]6*80=m\\480=m\\m=480[/tex]
Answer:
480 pounds
Step-by-step explanation:
we times for objects on earth and divide for objects on the moon by the same number
150
[tex]150 \div x = 25[/tex]
150/-25=-x
-6/-1= -x/-1
6=x
[tex]150 \div 6 = 25[/tex]
so when in object is on earth you multiple by x Wich 6
[tex]80 \times 6 = 480[/tex]
you can also cross multiply
Andrew has picked out some party favors. He calculates that they will cost $7 per guest.
Write an equation that shows how the total cost of the party favors, y, depends on the number of guests, x
Do not include dollar signs in the equation. what does y equal?
Answer:
Step-by-step explanation:
y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Andrew has picked out some party favors.
He calculates that they will cost $7 per guest.
We need to find the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
So y=7x where y is the total cost and x is the number of guests and 7 is the cost per guest.
If there are 2 guests then the total cost will be 14.
Hence y=7x is the equation that shows how the total cost of the party favors, y, depends on the number of guests, x
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Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
3. x-int: (-4,0) , (7,0)
P (3,8)
Answer:
y = -2/7(x + 4)(x - 7)=============================
Givenx- intercepts (-4, 0) and (7, 0),Point P (3, 8).SolutionThe given translates as:
p = -4, q = 7, x = 3, y = 8Use given x - intercepts to get the equation:
y = a(x + 4)(x - 7)Use the coordinates of P to find the value of a:
8 = a(3 + 4)(3 - 7)8 = a*7*(-4)8 = - 28aa = 8 / - 28a = - 2/7The equation of this parabola is:
y = - 2/7(x + 4)(x - 7)Answer:
[tex]\textsf{Intercept form}: \quad y=-\dfrac{2}{7}(x+4)(x-7)[/tex]
[tex]\textsf{Standard form}: \quad y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (-4, 0) and (7, 0) then:
p = -4q = 7Substitute the values of p and q into the formula:
[tex]\implies y=a(x-(-4))(x-7)[/tex]
[tex]\implies y=a(x+4)(x-7)[/tex]
To find a, substitute the given point on the curve P (3, 8) into the equation:
[tex]\implies 8=a(3+4)(3-7)[/tex]
[tex]\implies 8=a(7)(-4)[/tex]
[tex]\implies 8=-28x[/tex]
[tex]\implies a=\dfrac{8}{-28}[/tex]
[tex]\implies a=-\dfrac{2}{7}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=-\dfrac{2}{7}(x+4)(x-7)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=-\dfrac{2}{7}(x^2-3x-28)[/tex]
[tex]\implies y=-\dfrac{2}{7}x^2+\dfrac{6}{7}x+8[/tex]
When 6 less than 3 times a number is increased by 2 it's at least 5 times the same number decreased by 8
Answer: 2>=n
Step-by-step explanation:
3n-6 +2 >= 5n-8
3n-4 >= 5n-8
-4>= 2n -8
4>=2
2>=n
Hope this helped!!