Rewriting the expression based on the information will be 72(1 + z/72).
How to explain the expressionIn order to transform 72 + z into a product based on 72, we can apply the distributive property of multiplication over addition. Essentially, this property maintains that:
a x (b + c) = a x b + a x c
By extension, we can create the following equation:
72 + z = 72 + 1 x z
In order to produce an equivalent expression as a multiple of 72 and another factor, we would then need to use the distributive rule once again:
72 + 1 x z = 72 x 1 + 72 x z/72
Simplification leads us to arrive at:
72 + z = 72(1 + z/72)
Our end result is expressed as a synthesis between 72 and the expression (1 + z/72), namely:
72(1 + z/72).
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Graph the line with slope
3/4
passing through the point (-4,-1)
.
Answer: See attached.
Step-by-step explanation:
First, we will create an equation with the slope given.
y = [tex]\frac{3}{4}[/tex]x + b
Then, we will substitute this value in and solve for b (our y-intercept). Then we will graph the equation.
y = [tex]\frac{3}{4}[/tex]x + b
(-1) = [tex]\frac{3}{4}[/tex](-4) + b
-1 = -3 + b
b = 2
Our final equation:
y = [tex]\frac{3}{4}[/tex]x + 2
See attached for the graph. We will plot the point (0, 2) for our y-intercept and then move 3 units up for every four units right, according to the slope.
Sarah is building a 10-foot-long pen for her pet rabbits. She wants to make gravel bases for two circular food containers to go inside the pen along with its width, as shown in the diagram. Let y represent the width of the pen and x represent the radii of the gravel bases and food containers. What system of inequalities can be used to determine the width of the pen, y, and the radii of the gravel bases, x?
1. The width of the pen must be greater than or equal to the sum of the diameters of the two circular food containers, which is equal to 2x + 2x = 4x:
y ≥ 4x2. The width of the pen must also be less than or equal to the length of the pen, which is 10 feet:
y ≤ 103. The radii of the gravel bases must be greater than or equal to the radii of the food containers, which is equal to x:
x ≥ x4. The radii of the gravel bases must also be less than or equal to half the width of the pen, which is equal to y/2:
x ≤ y/2SYSTEM OF INEQUALITIESSystem of inequalities that can be used to determine the width of the pen, y, and the radii of the gravel bases, x, is:
y ≥ 4xy ≤ 10x ≥ 0x ≤ y/2Answer:
Step-by-step explanation:
The sum of the diameters of the gravel bases cannot exceed the width of the pen, so 2x+2x≤y. Rewrite this to get y≥4x as the first inequality in the system.Next, to write the expression for the cost of the fencing, find the perimeter of the rectangle and multiply the perimeter by the cost per foot of fencing. The pen is a rectangle, so the perimeter is 2(10)+2(y), or 20+2y. Multiply the cost ($4.00 per foot) by the perimeter to get 4(20+2y).Now write an expression for the gravel bases for the circular food containers. Because A=πr2 and the cost of the gravel is $2.00 per square foot, multiply the cost of the material by the sum of these areas to get 2(πx2)+2(πx2).The total cost must be less than or equal to $150, so we can say that 4(20+2y)+2(πx2)+2(πx2)≤150. Finally, simplify and solve for y.80+8y+2πx2+2πx2≤15080+8y+4πx2≤1508y≤70−4πx2y≤8.75−0.5πx2So, this is the system.
y≥4x
y≤8.75−0.5πx2
Does anyone know the answer to this question
Verify Euler’s theorem: (, ) =
3
+
3
.
Please help asap!!!!! I'm confused
The area of the parallelogram is 8.5 square miles. This is found by multiplying the length of one of the parallel sides, 2 miles, by the height, which is given as 4 1/4 miles.
To find the area of a parallelogram, we can multiply the length of one of its parallel sides by the length of its perpendicular height. Therefore, to find the area of this parallelogram, we need to determine its height.
We are given that one of the parallel sides has a length of 4 1/4 mi and the other has a length of 2 mi. We are also given that the length of the perpendicular on one of the parallel sides is 4 1/4 mi, which means that this is the height of the parallelogram.
So, the area of the parallelogram is
Area = base x height
Area = 2 mi x 4 1/4 mi
Area = 8 1/2 mi²
Therefore, the area of the parallelogram is 8 1/2 square miles or 8.5 square miles.
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The distance between cities A and B on a map is 12.5 in. The distance from city B to city C, is 8.5 in, and the distance from C to A is 16.25 in. If the bearing
from A to B is N75°E, find the bearing from C to 4. Round to the nearest tenth of a degree.
Answer:
90
Step-by-step explanation:
Answer:
It seems like the chat transitioned to a different topic. However, based on the search results, it appears that the query was related to solving distance problems using linear equations. One common application of linear equations is in distance problems, where you can create and solve linear equations to find the distance between two points or the rate of travel. Here's an example problem:
Joe drove from city A to city B, which are 120 miles apart. He drove part of the distance at 60 miles per hour (mph) and the rest at 40 mph. If the entire trip took three hours, how many miles did he drive at each speed?
To solve this problem, you can use a system of two linear equations. Let x be the number of miles driven at 60 mph, and y be the number of miles driven at 40 mph. Then you have:
x + y = 120 (total distance is 120 miles) x/60 + y/40 = 3 (total time is 3 hours)
To solve for x and y, you can multiply the second equation by 120 to eliminate fractions and then use the first equation to solve for one of the variables. For example:
x/60 + 3y/120 = 3 x/60 + y/40 = 3 2x/120 + 3y/120 = 3 x/60 + y/40 = 3 x/60 = 3 - y/40 x = 180 - 3y/2 (from the first equation)
Substitute the expression for x into the second equation and solve for y:
x/60 + y/40 = 3 (180 - 3y/2)/60 + y/40 = 3 3 - 3y/160 + y/40 = 3 3 - 3y/160 = 2.75 -3y/160 = -0.25 y = 20
Substitute y = 20 into the expression for x to get:
x = 180 - 3y/2 x = 120
Therefore, Joe drove 120 - 20 = 100 miles at 60 mph and 20 miles at 40 mph.
Step-by-step explanation:
A national pizza chain collected data from 189 stores about pizza orders on a busy Saturday. The number of pizzas ordered from 15 random stores is below. 28, 53, 35, 66, 35, 28, 66, 48, 53, 53, 66, 53, 66, 66, 35 If the sample was representative of the entire chain, what was the mode of the number of pizzas ordered for all 189 stores? A. 50.07 B. 48 C. 53 D. 66
please hurry ;(
The mode of the number of pizzas ordered for all 189 stores is [tex]66[/tex]. The Option D is correct.
How do we get the mode for this datas?Mode refer he most frequent number, that is, the number that occurs the highest number of times. To find mode, we must determine the value that appears most frequently in the sample.
From the given data: [tex]28, 53, 35, 66, 35, 28, 66, 48, 53, 53, 66, 53, 66, 66, 35[/tex]. We see that the value 66 appears 5 times, which is more than any other value.
Therefore, the number 66 is the mode.
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One of the byproducts of nuclear power generation is Uranium-233. Uranium is decaying at a constant 32% rate per day. If 12,880 pounds are produced from a power plant, what will the amount be in 20 days?
Answer:
The amount of Uranium-233 produced after 20 days will be approximately 65.1 pounds.
Step-by-step explanation:
Volume of Prism 2 3/4, 5 1/2, 3 2/5
Volume of the prism given is 51 [tex]\frac{17}{40}[/tex].
The volume of the prism is given by the formula,
Volume of the prism = Base area × height
Base area = 2 3/4 × 5 1/2
= 11/4 × 11/2
= 121 / 8
Volume of the prism = 121 / 8 × 3 2/5
= 121/8 × 17/5
= 2057/40
= 51 17/40
Hence the volume of the prism is 51 [tex]\frac{17}{40}[/tex].
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PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
415.67 = (1/3)(13.4)(11.7)h
415.67 = 52.26h
h = about 7.95 feet
mary read 1/7 pages on monday.there are 490 pages. how many pages did she read?
Answer: 70 pages
Step-by-step explanation: If she read 1/7 pages on monday and the book is 490 pages, divide. 490 ÷ 1/7 = 70. 70 × 7 is 490. So use these operations in future problems. Just make sure to read carefully!
What are the coordinates of the focus of the parabola? y=−1/8x2−2x−4
The coordinates of the focus of the parabola y = -(1/8)x² - 2x - 4 is (-8, 2).
What are the coordinates of the focus of the parabola?y = -(1/8)x² - 2x - 4
Given by the equation y = -(1/8)x² - 2x - 4,
To find the focus of the parabola we first need to put the equation in standard form:
y = a(x - h)² + k
Where (h, k) is the vertex of the parabola, and a is a constant that determines the shape and size of the parabola.
Completing the square on the x terms, we get:
y = -(1/8)(x² + 16x + 64) - 4 + 8
= -(1/8)(x + 8)² + 4
Comparing this to the standard form, we see that the vertex is (-8, 4) and a = -1/8.
Since the coefficient of x² is negative, the parabola opens downwards.
The focus of the parabola is located at a distance of 1/(4a) units from the vertex, on the axis of symmetry, which is a vertical line passing through the vertex.
Substituting the value of a, we get:
= 1/(4a)
= 1/(4(-1/8))
= 2
Therefore, the focus of the parabola is located 2 units below the vertex, on the line x = -8.
So the focus has coordinates (-8, 2).
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NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :) (Do the one highlighted)
The option or function that is NOT an exponential function is (4/7)ˣ.
Why is this so?The function (4/7)ˣ is no exponential because the base (4/7) is smaller or lesser than 1. All exponential functions must have a base that is less than -1 or greater than 1.
The other functions
1) (3/5)ˣ
2) 4ˣ
are both exponential function.
3/5ˣ is a decay function and it's base is less than 1. 4ˣ on the other hand is a growth function. Of course, it's base is greater than 1.
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Which of these fractions is largest A: 6 as a fraction of 30 B: 30 centimetres as a fraction of 2 metres C: 16 pence as a fraction of £1 ? You must show your working.
Answer:
A: 6 as a fraction of 30 = 6/30 = 1/5
B: 30 centimetres as a fraction of 2 metres = 30/200 = 3/20
C: 16 pence as a fraction of £1 = 16/100 = 4/25
To compare these fractions, we need to express them with a common denominator. The smallest common multiple of 5, 20, and 25 is 100. So we can convert each fraction to have a denominator of 100:
A: 1/5 = 20/100
B: 3/20 = 15/100
C: 4/25 = 16/100
Now we can see that the largest fraction is C: 16 pence as a fraction of £1, which is 16/100 or 16%.
Step-by-step explanation:
Mark Brainliest!!
The number of runs scored by the Stars for six games is shown below.
4,9, 2, 4, 1,6
If the Stars scored 14 runs in their seventh game, which of the following statements is true?
OA. The mean increases and the median remains the same.
OB. The median increases and the mean remains the same.
OC. The mean and the median both increase.
O D. The median and the mean both remain the same.
please help me choose which one it is
The correct statement regarding the relations in this problem is given as follows:
Only relation A could represent a linear relationship.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.From the first bullet point, we have that what classifies a linear relation is a constant rate of change.
For relation K, we have that it is not linear, as:
From x = -7 to x = -4, the rate of change is of 5/3.From x = -4 to x = -2, the rate of change is of 1/2. -> different to 5/3.For relation R, we have that it is linear, as it has a constant rate of change.
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What is the initial value of Y=2x+3
Answer:3
Step-by-step explanation: Initial value = y-intercept
Area of triangles
Look at the image below.
6
What is the area of the triangle?
units²
3
Answer:
Please help me by marking me the brainliest.
The area of the triangle is 9 units^2
Step-by-step explanation:
Area of triangle = 1/2(6*3)
=1/2(18)
=9
Day 3
June is setting up an experiment involving lima beans. She places a lima
bean inside a damp paper towel, then places it in a baggie. June takes
another lima bean and places it in a dry paper towel and puts it in a
baggie. She puts both baggies on a windowsill next to each other. She
checks each day to observe the changes.
What testable question is June most likely trying to answer?
A. Can lima beans grow in a paper towel?
B. Does the amount of light affect how fast a lima bean grows?
What does a lima bean look like once it is sprouted?
Which sprouts faster, a moist lima bean or a dry lima bean?
On
The testable question can be Which sprouts faster, a moist lima bean or a dry lima bean?
We have,
June laces a lima bean inside a damp paper towel, then places it in a baggie.
June takes another lima bean and places it in a dry paper towel and puts it in a baggie.
The Experiment is related to moisture because one damp and one dry towel is used.
So, the testable question can be
Which sprouts faster, a moist lima bean or a dry lima bean?
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A train moving 50 miles per hour meets and passes a train moving 50 miles per hour in the opposite direction. A passenger in the first train sees the second train pass in 5 seconds. How long is the second train?
Answer:
The length of the second train is 416.67 meters.
Step-by-step explanation:
mark brainliest
You will purchase 700 frozen treat's the cost to you should be at most 400 your goal is to make a profit of at least $800. Explain to Omar how your decision meets each of the criteria. Include the number of each type of treat in your explanation
The decision meets each of the criteria by: Buying 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each enables the purchase of 700 frozen delights within the $400 budget and satisfies the objective of producing at least $800 in profit.
How did your decision meets each of the criteria?I have made the decision to buy 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each in order to fulfil the requirement of buying 700 frozen delights at a price of no more than $400.
Cost of purchasing 500 popsicles = (500 * $0.50)
Cost of purchasing 500 popsicles = $250
Cost of purchasing 200 ice cream sandwiches =(200 * $1.50)
Cost of purchasing 200 ice cream sandwiches = $300
So, Total cost of purchasing all 700 frozen treats is $550 ($250 + $300) which is within the budget of $400.
I intend to sell the popsicles for $1.50 each and the ice cream sandwiches for $3.00 each in order to meet the requirement of turning a profit of at least $800. This would bring in $1350 in income for the ice cream sandwiches and $750 for the popsicles (500 * $1.50 and 200 * $3.00 respectively).
The objective of producing a profit of at least $800 is met after deducting the expense of buying the frozen treats from the overall income.
Net profit =($1350 - $550)
Net profit = $800
Therefore purchasing 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each satisfies the objective of producing at least $800 in profit.
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A bag contains six yellow tickets numbered
one to six. The bag also contains three
green tickets numbered one to three . You
randomly pick a ticket. It is yellow or has
an odd number.
The probability of yellow or has an odd number is 8/9
Calculating the probability of yellow or has an odd number.From the question, we have the following parameters that can be used in our computation:
Green = 1 to 3
Yellow = 1 to 6
This means that
Odd = 2 + 3
Odd = 5
So, we have
P(Yellow) = 6/9
P(Odd) = 5/9
P(Yellow and Odd) = 3/9
The probability of yellow or has an odd number is
P = 6/9 + 5/9 - 3/9
Evaluate
P = 8/9
Hence, the probability is 8/9
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A
Find the measure of each side indicated.
Round to the nearest tenth.
8)
X
5 C
58°
B
The value of the measure of each side indicated are,
⇒ x = 12.48
⇒ BC = 16
We have to given that;
In triangle ABC;
AC = x
AB = 10
Hence, We can formulate;
⇒ tan 58° = BC / AB
⇒ 1.60 = BC / 10
⇒ BC = 16
By using Pythagoras theorem;
⇒ x² + 10² = 16²
⇒ x² = 256 - 100
⇒ x² = 156
⇒ x = 12.48
Thus, The value of the measure of each side indicated are,
⇒ x = 12.48
⇒ BC = 16
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Which of the following has the polar coordinates negative five comma two pi over 3
Options:
Q
R
U
W
2. There is another surface that Molly does not need to paint, because it won’t show when she displays the model house. Describe that surface. (2 points)
Without additional information about the model house, it is impossible to accurately describe the surface that Molly does not need to paint. It could be any surface that will not be visible when the model house is displayed, such as the underside of a roof, the back of a wall, or the bottom of a floor.
What is the measure of EACH interior angle of a
regular 16-sided polygon?
The measure of each interior angle of a regular 16-sided polygon is 157.5 degrees
How to determine the valueTo determine the value of the interior angle, we need to note that;
The formula for calculating the sum of the interior angles of a polygon is expressed with the expression;
(n -2)180
Such that the variable n in the expression represents the number of sides of the polygon
From the information given, we have that;
(16- 2)180
expand the bracket
14(180)
multiply the values
2520 degrees
Then, we have;
16x = 2520
Make 'x' the subject
x= 157. 5 degrees
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PLS HELP LITERALLY HELP HELPL
[tex]-37 < -12v+1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ v=-11\hspace{5em}-37 < -12(-11)+1\implies -37 < 133 ~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-9\hspace{5em}-37 < -12(-9)+1\implies -37 < 109~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-5\hspace{5em}-37 < -12(-5)+1\implies -37 < 61~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=6\hspace{5em}-37 < -12(6)+1\implies -37 < -71 ~~ \bigotimes[/tex]
The length of the arc intercepted by a central angle of 5 radians in a circle of radius
73 is
The length of the arc intercepted by a central angle of 86" in a circle of radius 15 is
Answer:
The length of the arc intercepted by a central angle of 3 radians in a circle of radius 76 is 228 and the length of the arc intercepted by a central angle of 2 radians in a circle of radius 15 is 30.
Explain:
The following formula determines the length of an arc that a circle's central angle intercepts:
Arc length is equal to (central angle / 2) 2r r r
where r denotes the circle's radius. We can determine the length of the two arcs using the following formula:
For the first circle, with a radius of 76 and a center angle of 3 radians:
Arc length = 3 x 76 = 228
Therefore, in a circle with a radius of 76, the length of the arc that is intercepted by a central angle of 3 radians is 228.
For the second circle, whose radius is 15, and whose center angle is 2 radians:
Arc length = 2 x 15 = 30
As a result, the length of the arc in a circle with a radius of 15 is 30 when it is intercepted by a central angle of 2 radians.
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Julia volunteers at a zoo. She records the number of people in each group of visitors in one day.
Based on Julia's data, if a larger zoo has 600 groups of visitors in a day, how many of them would you expect to be groups of 5 or more?
People in Group 1 2 3 4 5 6 7 8
Frequency
9 52 27 38 16 6 5 7
about
groups
We would expect 138 groups in the larger zoo to have 5 or more people based on the relative frequency of group sizes in Julia's data.
To determine how many groups of 5 or more people we would expect to see in a larger zoo with 600 groups of visitors in a day, we need to use the relative frequency of each group size in Julia's data.
To calculate the relative frequency of each group size, we need to divide the frequency of each group size by the total number of groups:
Group Size Frequency Relative Frequency
1 9 9/150 = 0.06
2 52 52/150 = 0.35
3 27 27/150 = 0.18
4 38 38/150 = 0.25
5 16 16/150 = 0.11
6 6 6/150 = 0.04
7 5 5/150 = 0.03
8 7 7/150 = 0.05
We can see that the relative frequency of groups with 5 or more people is 0.11 + 0.04 + 0.03 + 0.05 = 0.23. This means that we would expect 23% of the 600 groups in the larger zoo to have 5 or more people.
To calculate the actual number of groups with 5 or more people, we multiply the total number of groups by the relative frequency:
Number of groups with 5 or more people = 600 x 0.23 = 138
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Jake and Rafael are training for a bike race. Jake is a beginner and starts by riding up a hill with a 7.9° incline. Rafael is more experienced and rides up a hill with an 18.3° incline. If Jake and Rafael ride 100 ft., how much more horizontal distance did Jake cover?
Responses
4.1 ft.
4.1 ft.
9.6 ft.
9.6 ft.
17.7 ft.
17.7 ft.
19.2 ft.
The horizontal distance more that Jake was able to cover, given the incline, would be A.4.1 ft.
How to find the horizontal distance ?We can find the horizontal distance that both Jake and Raphael covered .
Jake's distance was:
cos ( 7.9 ° ) = adjacent / 100
adjacent = 100 x 0.989
adjacent = 98.9 ft
Rafael's distance was :
cos ( 18. 3° ) = adjacent / 100
adjacent = 100 x 0.951
adjacent = 95.1 ft
The difference and the distance covered in addition by Jake would be:
= 98. 9 - 95. 1
= 3. 8 ft
The closest option is 4. 1 ft.
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