A line segment is shown on the coordinate grid.
What is the domain displayed on the line graph above?
Answer: x = -2 through 1
Step-by-step explanation:
The domain are the x values that exist on the line. The line goes between -2 and 1. Therefore, that's the domain!
compute the equilibrating economic activity *y in terms of other variables. this is the dd schedule, if viewed as a function of e through q.
Economic equilibrium is a condition or state in which economic forces are balanced. In effect, economic variables remain unchanged from their equilibrium values in the absence of external influences.
Economic equilibrium is also referred to as market equilibrium. Economic equilibrium is the combination of economic variables (usually price and quantity) toward which normal economic processes, such as supply and demand, drive the economy. The term economic equilibrium can also be applied to any number of variables such as interest rates or aggregate consumption spending. The point of equilibrium represents a theoretical state of rest where all economic transactions that “should” occur, given the initial state of all relevant economic variables, have taken place.
In a competitive market, demand for and supply of a good or service determine the equilibrium price.
Equilibrium:MARKETS:
Equilibrium is achieved at the price at which quantities demanded and supplied are equal. We can represent a market in equilibrium in a graph by showing the combined price and quantity at which the supply and demand curves intersect.
For example, imagine that sellers of squirrel repellant are willing to sell 500 units of squirrel repellant at a price of $5 per can. If buyers are willing to buy 500units of squirrel repellent at that price, this market would be in equilibrium at the price of $5 and at the quantity of 500 cans.
Disequilibrium:Whenever markets experience imbalances—creating disequilibrium prices, surpluses, and shortages—market forces drive prices toward equilibrium.
A surplus exists when the price is above equilibrium, which encourages sellers to lower their prices to eliminate the surplus.
A shortage will exist at any price below equilibrium, which leads to the price of the good increasing.
For example, imagine the price of dragon repellent is currently $6 per can. People only want to buy 400 cans of dragon repellent, but the sellers are willing to sell 600 cans at that price. This creates a surplus because there are unsold units. Sellers will lower their prices to attract buyers for their unsold cans of dragon repellant.
Changes in equilibrium :Changes in the determinants of supply or demand result in a new equilibrium price and quantity. When there is a change in supply or demand, the old price will no longer be an equilibrium. Instead, there will be a shortage or surplus, and price will subsequently adjust until there is a new equilibrium.
For example, suppose there is a sudden invasion of aggressive unicorns. There will be more people who want to buy unicorn repellent at all possible prices, causing demand to increase. At the original price, there will be a shortage of unicorn repellant, signaling sellers to increase the price until the quantity supplied and quantity demanded are once again equal.
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Complete the paragraph
The missing terms for the congruent angles are;
Complementary angles
m∠1 + m∠3 = 90°
Transitive property of equality
Subtraction property of equality;
Congruent angles.
How to identify congruent angles?Congruent angles are defined as the angles that have equal measure. Therefore, all the angles that have equal measure are called congruent angles.
We are given that;
∠1 and ∠2 are complementary
∠1 and ∠3 are complementary
Now, we are told that m∠1 + m∠2 = 90°. Complementary angles are defined as the 2 angles that sum up to 90 degrees. Thus, ∠1 and ∠2 are complementary by definition.
Similarly, m∠1 + m∠3 = 90°
By the transitive property of equality, we can say that;
m∠1 + m∠2 = m∠1 + m∠3
By the subtraction property of equality;
m∠2 = m∠3
Thus;
∠2 = ∠3 by definition of congruent angles.
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Finding a Missing Endpoint
The new x-coordinate must be 2-2 = 0.
What are endpoints?Many objects in geometry such as line segments, angles, polygons, etc., can be named using endpoints:Points A and B are endpoints for the line segment below. The line segment is named by its endpoints, AB or BA.A ray on the other hand, has only one endpoint as shown below. The ray is named using its endpoint as the first letter, AB.An angle can be named using the common endpoint of the two rays, as shown below. Rays AB and BC share endpoint B and form an angle. This angle can be named as ∠ABC or, using just its endpoint, as ∠B.acc to our question-
Finding the distance between the known endpoint and the midpoint, then applying the same transformation to the midpoint, is the quickest technique to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, hence the new x-coordinate is 2-2 = 0.
Hence,The new x-coordinate must be = 0.
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A short-wave radio antenna is supported by two guy wires, 150 ft and 180 ft long. Each wire is attached to the top of the antenna and anchored to the ground at two anchor points on opposite sides of the antenna. The shorter wire makes an angle of 65° with the ground. How far apart are the anchor points? (Round your answer to the nearest foot.)
The distance between the anchor points of the two guy wires holding radio antenna is 181 feet (to the nearest foot)
How to determine the distance between the two anchor points of the guy wireThe problem will be solved using SOH CAH TOA
let the distance between the 150 ft long guy wire and the radio antenna be x
let the distance between the 180 ft long guy wire and the radio antenna be y
cos 65° = x / 150
x = cos 65° * 150
x = 63.39 ft
The height of the antenna
sin 65° = height of antenna / 150
height of antenna = sin 65 * 150
height of antenna = 135.95
using Pythagoras theorem
(length of guy wire)² = (height of the antenna)² + (anchor distance)²
(anchor distance)² = 180² - 135.95²
anchor distance = √(180² - 135.95²)
anchor distance = 117.97
The anchor points distance apart
= 63.39 + 117.97
= 181 (to the nearest foot)
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What is a counterexample for the conjecture?
If the area of a rectangle is 80 square units, the perimeter must be greater than 35.9 units.
A) A rectangle with length 39.5 units and width 0.5 unit has a perimeter of 80 units and an area of 19.75 square units.
B) A rectangle with length 8 units and width 10 units has a perimeter of 36 units and an area of 80 square units.
C) A rectangle with length 8 units and width 9 units has a perimeter of 34 units and an area of 72 square units.
D) A square with a side length of √80 units has a perimeter of approximately 35.8 units and an area of 80 square units.
The argument against the conjecture The area of a rectangle with a perimeter of 40 units must be at least one square unit. A rectangle with dimensions of 19.99 units long and 0.1 units wide has a 40 unit perimeter and an area of 0.1999 square units.
What is counterexample?An instance or example that refutes the proposition is referred to as a counterexample. To determine if a statement is true or not, logic uses this. Counterexamples typically offer strong arguments in opposition to the assertion under discussion.The goal of the inquiry is to demonstrate any possible relationship between the area and perimeter of a rectangle.acc to our question-
The goal of the inquiry is to illustrate any potential connections between a rectangle's perimeter and area.
The counterexample presented dimensions that revealed the perimeter, which is 40, but omitted to provide the area, which is 1 square unit.
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HURRY! I'LL GIVE BRAINLIEST
what is the relative frequency of all students surveyed who go to cook middle school and prefer energy flow?
Answer:
2/5 = 0.4 = 40%
Step-by-step explanation:
You want the relative frequency of students who go to Cook Middle School and prefer Energy Flow.
Table valuesThe table tells us the number of students who go to Cook Middle School is 35, of which 20 prefer Energy Flow. The total number of students is 50.
Relative frequencyThe relative frequency of interest is ...
(Cook & Energy Flow) / (All students)
= 20/50 = 2/5 = 0.4 = 40%
The relative frequency of students who go to Cook and prefer Energy Flow is 2/5, or 40%.
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Solve the inequality. x² + 4x - 21 ≥ 0
and please explain
Step-by-step explanation:
if the solution has "nice" numbers, we can split the expression into 2 factors in the form
(x + a)(x + b) = x² + (a+b)x + ab
as this is equal to x² + 4x - 21.
ab = -21
so, one is positive and one is negative.
and 4 = a + b
we know the typical factors of 21 : 3×7
and then we see easily : 7-3 = 4
so,
we have
(x + 7)(x - 3) >= 0
this has 2 x-intercepts (x-values when y = 0) :
x = -7
x = 3
because the coefficient of x² is positive (1), we know that the parabola (or quadratic equation) is opening upwards.
that means the y-values for x-values between -7 and +3 are negative (< 0), but the y-values for everything else are positive.
so, the solution are the intervals
x <= -7 and x >= 3
in these areas is the expression x² + 4x - 21 >= 0.
11 Sand costs $98.90 per tonne.
This cost includes a tax of 15%.
Calculate the amount of tax paid per tonne of sand.
The amount of tax paid per tonne of sand is $14.835 as the sand costs $98.90 per tonne.
What is meant by percentage?In mathematics, a percentage is a value or ratio expressed as a fraction of 100.
The term percent is derived from the Latin per centum, which means "hundred" or "by the hundred." The sign for "percent" comes from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and finally disappeared entirely. The "cento" was reduced to two circles divided by a horizontal line, from which the present "%" symbol was derived.
Given,
The cost of one Tonne of sand=$98.90
The tax on one Tonne=15%
The amount of tax per Tonne of sand is,
=(15/100)×98.90
=$14.835
Hence, the amount of tax paid per tonne of sand is $14.835.
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Lilly will be randomly given a paintbrush and
a canvas. If there are 3 good paintbrushes out
of 12 in all and 2 good canvases out of 6 in all,
what is the probability that both her paintbrush
and canvas will not be good?
Answer: The paintbrush will be your magic wand for weaving colors across the canvas. Artist paint brushes become beloved tools the more you use them! As you paint, you will become increasingly familiar with the way the brushes handle the paint and what they can accomplish for you. Pretty soon the paintbrush will become a part of you that you intuitively know how to maneuver.
If you're just starting out in acrylics, it can be a bit overwhelming standing in the paintbrush aisle at the art store, with a vast sea of artist paint brushes spread out before you. The wide selection even makes me dizzy sometimes!
Step-by-step explanation:
Which of the following numbers is a composite number? A. 9 B. 2 C. 29 D. 5
Answer: A. 9
Step-by-step explanation:
In a certain chemical, the ratio of zinc to copper is 4 to 13. A jar of chemical contains 325 grams of copper. How many grams of zinc does it contain
Given -
In a certain chemical, the ratio of zinc to copper is 4 to 13.
The chemical contains 546 grams of copper.
Prove -
How many grams of zinc does it chemical contain.
Answer
suppose that scalar multiple of the zinc and copper be y .
As given
In a certain chemical, the ratio of zinc to copper is 4 to 13.
The chemical contains 546 grams of copper.
Than equation is
13y = 546
13y = 546
y = 42
Zinc contain in the certain chemical = 4y
= 4 42
= 168 grams
Therefore 168 grams of zinc contain in a certain chemical .
A runner completed a 26.2-mile
marathon in 210 minutes.
a. Estimate the unit rate, in miles per minute.
b. Estimate the unit rate, in minutes per mile.
c. Another runner says, “I averaged 10-minute miles in the
marathon.” Is this runner talking about the unit rate
described in part (a) or in part (b)? Explain your reasoning.
Step-by-step explanation:
The answer is: A=210÷26.2=8.2
B=now we have to turn minutes in to haurs 210:60=3.5 now 26.2÷3.5=29.7
Answer:
A) 26.2/210= .125 miles per minute
B) 210/26.2= 8.02 minutes per mile
C) the other runner talks about the same rate as b), not a).
Step-by-step explanation:
A)[tex]\frac{26.2}{210\\}[/tex] and B)[tex]\frac{210}{26.2}[/tex] :)
C)the runner was referring to the time they took to run one mile, so the other runner ran 10 minutes to cover one mile, or as they say, "10 minute miles", which is the rate in minutes per mile.
If they were referring to the rates in a), that would imply the other runner ran 10 miles per minute... which is very unlikely.
find the slope through(0,10) and (24, 6)
Answer:
slope = - [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 10 ) and (x₂, y₂ ) = (24, 6 )
m = [tex]\frac{6-10}{24-0}[/tex] = [tex]\frac{-4}{24}[/tex] = - [tex]\frac{1}{6}[/tex]
WORD PROBLEMS INVOLVING SIMULTANEOUS EQUATIONS:
The cost of a bottle of water is Rsx.
The cost of a bottle ofjuice is Rsy.
The total cost of 9 bottles of water and 3 bottles of juice is Rs 153.
The total cost of 6 bottles of water and 5 bottles of juice is Rs 147.
Find the cost of a bottle of water and the cost of a bottle of juice.
Step-by-step explanation:
9x + 3y = 153
6x + 5y = 147
the first equation can be divided by 3 and then multiplied by 2. and from that we can subtract equation 2 :
9x + 3y = 153 | /3
3x + y = 51 | ×2
6x + 2y = 102
- 6x + 5y = 147
-----------------------
0 -3y = -45
3y = 45
y = 15
3x + y = 51
3x + 15 = 51
3x = 36
x = 12
1 bottle of water costs Rs 12.
1 bottle of juice costs Rs 15.
Factor the expression (72a9b3 − 18a7b5) completely.
The factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
Given expression:
= 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex]
divide by 18 .
= 4[tex]a^{9} b^{3}[/tex] - [tex]a^{7} b^{5}[/tex]
divide by [tex]a^{7}[/tex]
= 4[tex]a^{2}b^{3}[/tex] - [tex]b^{5}[/tex]
divide by [tex]b^{3}[/tex]
= 4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]
= 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
Therefore the factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).
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wade is skiing on a circular ski trail that has a radius of 0.8 km. wade starts at the 3-o'clock position and travels 2.3 km in the counter-clockwise direction. how many radians does wade sweep out? 2.875 correct radians when wade stops skiing, how many km is wade to the right of the center of the ski trail? .7717 incorrect km when wade stops skiing, how many km is wade above of the center of the ski trail?
The solutions are,
The radians wade sweep out is 2.875 radians.
When wade stops skiing, he is 0.799km to the right of the center of the ski trail.
When wade stops skiing, he is 0.003km above the center of the ski trail.
Given that;
Wade is traveling along a 0.8 km-radius circular ski trail. Wade moves 2.3 kilometers counterclockwise starting at the three o'clock position.
Radius (r) = 0.8km
Distance (s) = 2.3km
Here, we need to find three cases, they are;
Case(I): how many radians does wade sweep out;
The relation between radians and radius is given by,
s = rθ
2.3 = 0.8*θ
θ = 2.3/0.8
θ = 2.875
The radians wade sweep out is 2.875 radians.
Case (II): when wade stops skiing, how many km is wade to the right of the center of the ski trail;
Let, Ф = π - 2.875
Ф = 0.266 radians
Then, x = r*cosФ
x = 0.8*cos(0.266)
x = 0.799
When wade stops skiing, he is 0.799km to the right of the center of the ski trail.
Case (III): when wade stops skiing, how many km is wade above the center of the ski trail;
Let, y = r*sinФ
y = 0.8*sin(0.266)
y = 0.003
When wade stops skiing, he is 0.003km above the center of the ski trail.
Therefore, the required solutions are;
The radians wade sweep out is 2.875 radians.
When wade stops skiing, he is 0.799km to the right of the center of the ski trail.
When wade stops skiing, he is 0.003km above the center of the ski trail.
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write the equation for the line through (4,3) with a slope of -1/2 in slope intercept form
Please finish the sentences in the picture below
The completed statement with regards to Chang and Carlotta's methods used for solving the word problem is presented as follows;
Chang's and Carlotta's method use different operations to simplify the expressions in the same order.Chang's method uses variables, but Carlotta's method does not.What is a word problem in mathematics?A word problem in mathematics and science is the verbal presentation of the information in a scenario required to mathematically solve a problem.
The steps to solve the problem is presented as follows;
The amount in the bank account = $50
Amount made per hour by mowing lawns = $8
The number of hours put into mowing lawns in order to have a total of $130 in the account can be found by using the equation;
The amount in the account increases based on the number of hours used for mowing lawns, therefore;
130 = 50 + 8 × h
8·h = 130 - 50 = 80
h = 80/8 = 10
Ten hours of lawn mowing is required to have a total of $130 in the bank.
Chang's method involve the use of expressing the situation mathematically, by use of variables.
Carlotta's method involves the use of verbal expressions to outline the relationship between the variables, simplifying them to arrive at the determining variable that indicates the number of hours require.
Therefore;
The operations used by Chang and Carlotta are differentThe order in which the expressions is simplified is the same in both Chang and Carlotta's assignmentsThere is a variable, h, for the hour in Chang's method, but Carlotta's method does not make use of a variable for the hours that must be used for mowing lawns.Learn more about word problems in mathematics here:
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For a floral arrangement class, Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects.
Alicia wants the arrangement to have twice as many flowers as twigs. Write and solve a system of equations to find the number of twigs and flowers that Alicia will need.
By solving a system of two simultaneous linear equations, it can be calculated that
Alicia will need 3 twigs and 6 flowers
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here, a system of two simultaneous linear equation needs to be solved
Let the number of twigs Alicia needed be x and the number of flowers Alicia needed be y
Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects.
x + y = 9 ..... (1)
Alicia wants the arrangement to have twice as many flowers as twigs
2x = y .... (2)
Putting the value of x in (1)
x + 2x = 9
3x = 9
[tex]x = \frac{9}{3}[/tex]
x = 3
Putiing the value of x in (2),
y = 2 [tex]\times[/tex] 3
y = 6
Alicia will need 3 twigs and 6 flowers
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an airplane ticket has a perimeter of 58 cm and an area of 198 square cm. What are the dimensions of the ticket
The dimensions of the ticket are width is 11 cm and length is 18 cm.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
An airplane ticket has a perimeter of 58 cm and an area of 198 square cm.
Let W is the width of the ticket and L is the length of the ticket
The area of a credentials= L × W
198 = L × W ...(i)
The perimeter of a ticket = 2(L+W)
58 = 2(L+W)
29 = L + W
L = 29 - W ...(ii)
Substitute the value of L = 99 - W in equation (i)
198 = (29 - W) × W
198 = 29W - W²
0 = W² - 29W + 198
[tex]0=\left(W^2-11W\right)+\left(-18W+198\right)[/tex]
[tex]0=W\left(W-11\right)-18\left(W-11\right)[/tex]
[tex]0=\left(W-11\right)\left(W-18\right)[/tex]
W = 18 or 11
Substitute the value of W = 11 in equation (ii)
L = 29 - 11
L = 18
Thus, the dimensions of the ticket are width is 11 cm and length is 18 cm.
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Question 11 of 30
What is the amplitude in the graph of y = 3sin(2x − 1) + 5?
-
Ο A. 1
B. 5
C. 2
D. 3
SUBMIT
3 is the amplitude, -4 is the minimum value, and 2 is the highest value.
What is amplitude?A function's amplitude is the distance that the graph of the function moves above and below its midline. The value of the amplitude when graphing a sine function is comparable to the value of the sine coefficient.the height difference between a periodic function's center line and peak (or trough).As an alternative, we might multiply the height from highest to lowest points by 2.the greatest deviation from equilibrium of a point on a vibrating body or wave in terms of displacement or distance traveled.
acc to our question-
Sin x is changed to sin 2x to modify the function's period from 2 πThe amplitude varies from 1 to 3, with a minimum value of -3 and a maximum value of 3, when sin 2x is substituted with 3 sin 2x.Then we translate 1 unit down by changing 3 sin 2x to 3 sin 2x - 1. Currently, the amplitude is 3, the period is, the minimum value is, the greatest value is, and the value in between is 2.Hence,3 is the amplitude, -4 is the minimum value, and 2 is the highest value
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Which ratio is equivalent to 1:6?
Answer:
2 : 12 and 3 : 24 are the two equivalent ratios
A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels straight down for 68 seconds at a speed of 0.8 feet per second.
She then ascends for 11 seconds at a speed of 3.8 feet per second.
Answer:
-11.8
Step-by-step explanation:
68x0.8
11x3.8
11x3.8=41.8
68x0.8=54.4
54.4-41.8=12.6
Now minus add a minus to it and you get -12.6 FT
Can you help me with this please. It was question on my test but it didn't make any sense since i got a repeating decimal.
3.5g-2.7g=-6
The solution of the linear equation 3.5g - 2.7g = -6 will be negative 7.5.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
If the maximum power of the equation is one. Then the equation will be a linear equation.
The linear equation is given below.
3.5g - 2.7g = -6
Simplify the equation, then we have
3.5g - 2.7g = -6
0.8g = -6
g = - 6 / 0.8
g = - 7.5
The solution of the linear equation 3.5g - 2.7g = -6 will be negative 7.5.
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A solution that is 20% acid and 80% water is mixed with a solution that is 50% acid and water. If twice as much 50% acid solution is used as 20% solution, then what is the ratio of acid to water in the mixture of the solutions?
Answer:
The ratio of acid to water is 2 to 3 in the mixture of the two solutions
This can be thought of as a chemistry problem or a math problem, but both use practically the same process to find the final answer.
So, let's say 2 liters of 50% acid and 1 liter of 20% acid is mixed.
In total, there is 2*(50%) + 1*(20%) of acid, so there is 1 liter of pure acid in 2 liters of 50% acid, and 0.2 liters of pure acid in 1 liter of 20% acid. This in total is 1.2 liters of acid. The total volume is 2 + 1 liters, which is 3 liters. the percentage can be found by dividing the amount of pure acid by the total volume, so 1.2/3, which equals 0.4, or 40%. The ratio would be 40% to 100-40%, or 40% to 60%, or 2 to 3
Toss one dime.
The probability of getting heads
is 1. Predict how many times
you would get heads if you
flipped the dime 200 times.
[?] times
We can get heads for 200 times if we flipped the dime for 200 times.
What do you mean by Probability?
Probability is a mathematical measurement to measure the possibility of happening a particular incident or event mathematically.
Also, from the definition of probability, Probability is the ratio of the Number of Favorable event points to the number of total event points with respect to a particular event or incident.
[tex]Probability=\frac{Number of Favorable event Points}{Number of Total event Points}[/tex]
According to the given problem,
The probability of getting heads is 1.
Total number of flip of dime is 200
so, we can get heads from 200 flips [tex]=200*1=200 Times[/tex]
Hence, we get 200 heads from 200 flips of dime.
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Estimate the answer to 4.8 x 47.1
Answer:
235
Step-by-step explanation:
When estimating the product of two decimals, first round the decimals to their nearest whole numbers.
If the number in the tenth place is less than 5, round down to the nearest whole number.If the number in the tenth place is 5 or more, round up to the nearest whole number.Therefore,
4.8 ≈ 547.1 ≈ 47So an estimate of the product of the two decimals is:
[tex]\implies 4.8 \times 47.1 \approx 5 \times 47[/tex]
Partition 47 into tens and units:
[tex]\implies 5 \times 47 = 5 \times (40 + 7)[/tex]
Apply the distributive property of multiplication over addition:
[tex]\begin{aligned}\implies 5 \times (40 + 7) &= (5 \times 40) + (5 \times 7)\\&=200+35\\&=235\end{aligned}[/tex]
Therefore:
[tex]\boxed{4.8 \times 47.1 \approx 235}[/tex]
Given that ABCD is a rectangle, where EC = 7x -3 and AE=4x + 8. Find DE.
The length of segment DE on the rectangle, considering the midpoint, is given as follows:
DE = 22.67.
What is the midpoint?The midpoint of a segment divides a segment into two segments of equal length, having half the length of the entire segment.
In this problem, the diagonal of the rectangle represented by segment AC has midpoint E, hence the measure of x is calculated as follows:
EC = AE.
The measures are as follows:
EC = 7x - 3.AE = 4x + 8.Hence:
7x - 3 = 4x + 8
7x - 4x = 8 + 3
3x = 11
x = 11/3.
Segment DE is also half of a diagonal, hence it's length is obtained with the numeric value of any segment EC or AE, as follows:
DE = EC = 7x - 3 = 7 x 11/3 - 3 = 77/3 - 9/3 = 68/3 = 22.67.
Missing InformationThe rectangle is given by the image at the end of the answer.
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A set of weights includes a 20 lb barbell and 6 pairs of
weight plates. Each pair of plates weighs 30 lb. lfx
pairs of plates are added to the barbell, the total weight
of the barbell and plates in pounds can be represented
by f(x) = 30x + 20.
This graph represents a continuous function. Also, the domain of this function is 0 ≤ x ≤ 6 and the range of this function is 20 ≤ y ≤ 200.
What is a range?Mathematically, a range can be defined as the set of all real numbers that is associated with the elements of a domain. This ultimately implies that, a range simply refers to the set of all possible output numerical values which are shown on the y-coordinate (y-axis) of the graph of a function.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined and it connects with the range.
This ultimately implies that, a domain is the set of all possible input numerical values to a function. Additionally, the domain of the graph of a function comprises all the input numerical values which are shown on the x-coordinate (x-axis).
From the information provided, the total weight of the barbell and plates in pounds is represented by this function:
f(x) = 30x + 20.
When x = 6, we have:
f(6) = 30(6) + 20.
f(6) = 180 + 20
f(6) = 200 lb.
Therefore, the domain is equal to 0 ≤ x ≤ 6 while the range of this function is 20 ≤ y ≤ 200.
Read more on range here: brainly.com/question/16610662
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