Answer: The domain is all values of x that make the expression defined. The range is the set of all valid y values
Step-by-step explanation:
Therefore , the solution of the given problem of function comes out to be Domain: (-∞, ∞) and Range: (0,∞).
What is function?Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.
Here,
Given : f(x)=[tex]2^{x}[/tex]+1
If a value has not been added, an exponential function's curve normally approaches a horizontal asymptote at y=0 or the x-axis. The curve changes if it has.
The asymptote is unaffected by this function's addition on the exponent because it does not apply to the entire function.
The values of its y-axis remain between 0 and. This is the set of y values, or the range.
However, depending on the leading coefficient, the range of exponentials can vary. If the value is negative, the graph turns inside-out and the range reaches -. It's also lacking in this.
The exponent's addition to 1 moves the function to the left without changing the range.
The x values in exponential functions are often unaffected and all are taken into account in the function. The domain stays the same even while it changes. Its range is (0,∞)
Range: (0,∞)
Therefore , the solution of the given problem of function comes out to be
Domain: (-∞, ∞) and Range: (0,∞).
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You are planning to sell ice cream cones for a school sporting event . You plan to sell 300 ice cream cones. Before selling the ice cream, you give a survey to determine what flavors to sell. The results are below.
• 10% - Mint
• 25% - Strawberry
• 15% - Chocolate chip
• 50% - Vanilla
Based on the survey results, how much of each flavor will you sell at the sporting event
Answer: Based on the survey results, we can calculate the number of ice cream cones to sell for each flavor by multiplying the percentage of the flavor by the total number of ice cream cones to be sold.
Mint: 10% of 300 ice cream cones = 0.1 * 300 = 30 ice cream cones
Strawberry: 25% of 300 ice cream cones = 0.25 * 300 = 75 ice cream cones
Chocolate chip: 15% of 300 ice cream cones = 0.15 * 300 = 45 ice cream cones
Vanilla: 50% of 300 ice cream cones = 0.5 * 300 = 150 ice cream cones
So, based on the survey results, you should sell 30 ice cream cones of Mint flavor, 75 ice cream cones of Strawberry flavor, 45 ice cream cones of Chocolate chip flavor, and 150 ice cream cones of Vanilla flavor.
It's worth mentioning that the sum of the percentages provided, 10+25+15+50 = 100%. Which means that it is a proper survey and the total number of ice cream cones you expect to sell is equal to the survey results.
Step-by-step explanation:
Based on the survey results flavors sold at the sporting event are, 30 mint ice creams, 75 Strawberry icecreams, 45 Chocolate chip icecreams, and 150 Vanilla icecreams.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
The number of different types of ice creams can be obtained as follows,
10% - Mint.
= (10/100)×300.
= 30.
25% - Strawberry.
= (25/100)×300.
= 75.
15% - Chocolate chip.
= (15/100)×300.
= 45.
50% - Vanilla.
= (50/100)×300.
= 150.
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Find the derivative of the function. y = arctan √[(1 − x) /(1 + x)]
y' = ?
and
Find the derivative of the function. y = 3tan−1 [x − √(1 + x^2)]
y' = ?
The derivative function for equations 1 and 2 will be
y' = -1/ [2√(1-x²)] and y' = 3/[2(1 + x²)] respectively
Here we need to find the derivative of
[tex]y = tan^{-1}\sqrt{\frac{1-x}{1+x} }[/tex]
Let x = cos2z
Hence we get
[tex]y = tan^{-1}\sqrt{\frac{1-cos2z}{1+cos2z} }[/tex]
[tex]or, y = tan^{-1}\sqrt{\frac{2sin^{2}z}{2cos^{2}z} }[/tex]
[tex]or, y = tan^{-1}(tanz)[/tex]
or, y = z
Hence dy/dx = dz/dx
We know that
x = cos2z
or, 2z = cos⁻¹x
or, 2 dz/dx = -1/√(1-x²)
Hence dy/dx = -1/ [2√(1-x²)]
The second equation is
[tex]y = 3tan^{-1}[x-\sqrt{1+x^{2}} ][/tex]
Let x = cotz
Hence we get
[tex]y = 3tan^{-1}[cotz-\sqrt{1+cot^{2}z} ][/tex]
[tex]y = 3tan^{-1}[cotz-\sqrt{cosec^{2}z} ][/tex]
or, y = 3tan⁻¹ [cotz - cosecz]
or, y = 3tan⁻¹ [cosz/sinx - 1/sinz]
or, y = 3tan⁻¹ [(cosz - 1)/sinz]
or, y = 3tan⁻¹ [-2sin²(z/2)/{2sin(z/2) cos(z/2)}]
or, y = 3tan⁻¹ [-sin(z/2)/cos(z/2)]
or, y = 3tan⁻¹ [-tan{z/2)]
or, y = 3tan⁻¹ [tan{-z/2)]
or, y = -3z/2
or, dy/dz = -3/2 dz/dx
We have
x = cotz
or, z = cot⁻¹z
or, dz/dx = -1/(1 + x²)
Hence we get
dy/dx = 3/[2(1 + x²)]
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For what value of a the system of equations Ax Y 2 and 6x 2y 3 has a unique solution?
A = 1, y = -2/3, The value of a for which the system of equations has a unique solution is a = -3.
1. Set the first equation equal to 0:
2x + ay = 2
2. Subtract 2x from both sides of the equation to get:
ay = -2
3. Divide both sides of the equation by a to get:
y = -2/a
4. Substitute this value of y into the second equation to get:
6x + 3(-2/a) = 3
5. Multiply both sides of the equation by a and simplify to get:
6ax - 6 = 3a
6. Add 6 to both sides of the equation to get:
6ax = 3a + 6
7. Divide both sides of the equation by 6 to get:
x = (3a + 6)/6
8. The value of a for which the system of equations has a unique solution is a = -3.
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seven pounds of fertilizer can cover 1400 square feet can be covered by 2 pounds of fertilizer
The area for 2 pounds of fertilizer is 400 square feet
How to determine the amount of fertilizer for 2 pounds?
From the question, we have the following parameters that can be used in our computation:
seven pounds of fertilizer can cover 1400 square feet
This means that
7 pounds of fertilizer = 1400 square feet
Divide both sides of the equation by 7
So, we have the following representation
1 pounds of fertilizer = 200 square feet
Multiply both sides of the equation by 2
So, we have the following representation
2 pounds of fertilizer = 400 square feet
Hence, the area is 400 square feet
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Is Y 0 a horizontal line?
As per the following graph, if y = 0,then it makes the horizontal line on graph.
The term graph in math is defined as the visual representation of data or equation.
Here we have given that the value of y = 0.
Here we know that the slope of a horizontal line is zero while the slope of a vertical line is undefined.
Here the following Slopes represent a line's ratio of vertical change to horizontal change.
Whereas horizontal and vertical lines remain constant and never increase or decrease, they're merely straight lines.
Here we have also know that the Horizontal lines have no steepness at all.
Therefore if y=0 is the linear equation to denote the x - axis, then all the points on the x- axis, have their y co-ordinate as 0.
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He starts by running 3 miles during every training session. Each week he plans to increase the distance of his run by 1/4 mile
The arithmetic expression may be used to get the formula T = (11 + w)/4, which is the distance Kane runs in a training session after w weeks.
Every training session, Kane begins out by running 3 miles, and he has a plan to improve that distance by 1/4 mile each week.
The number of weeks is w.
The arithmetic progression may be used to calculate an expression that displays the distance Kane runs during a training session after w weeks.
T = A + (n-1)d is the formula for the nth term in an arithmetic operation, where an is the first term, which is 3, d is the difference between two consecutive terms, which is, is the last term, and n is the total number of terms.
We get, T = (11+w)/4
This is the expression to show the distance Kane runs in a training session after w weeks.
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Complete question - Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the distance Kane runs in a training session after w weeks
Cari says if a triangle has the side lengths of 3, , and 9, then the triangle is a 30-60-90 triangle. Dana says if a triangle has the side lengths of 2, , and 4, then the triangle is a 30-60-90 triangle. Who is correct and why
Similar Figures / Proportion (Level 1)
Triangle OPQ is similar to triangle RST. Find the measure of side ST. Round your
answer to the nearest tenth.
Rounded to the nearest tenth, the measure of side ST is 8.0.
How to find measure of sides?In order to find the measure of side ST, you will need to use the concept of similarity. If two triangles are similar, then their corresponding sides are in proportion. If we let x be the measure of side ST, then we can set up a proportion using the given information:
[tex]OP/PQ = ST/RQ[/tex]
We also know that
[tex]OP/PQ = 2/3[/tex]
and
[tex]RQ = 12[/tex]
So we can substitute these values into the proportion and solve for x:
[tex](2/3) = ST/12[/tex]
[tex]ST = (2/3) * 12[/tex]
[tex]ST = 8[/tex]
Rounded to the nearest tenth, the measure of side ST is 8.0.
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Maria believes that she will get a 1 hit in 10% of her softball games, 2 hits in 30% of her games, 3 hits in 55% of her games, and 4 hits in 5% of her games. About how many hits can Maria expect to have each game
According to the probability or likelihood , Maria can expect 2 hits in the game.
What person founded probability?Blaise Pascal and Pierre de Fermat are recognized as the fathers of probability because they laid the foundation for the field by thinking through a gambling issue posed by Chevalier de Mere in 1654.
[tex]E(X)=x.P(X=x)[/tex]
Given,
[tex]P(X=1)=0.20\\P(X=2)=0.25\\P(X=3)=0.50\\P(X=4)=0.05\\[/tex]
putting in formula,
[tex]E(X) = (1*0.20)+(2*0.25)+(3*0.50)+(4*0.05)=2.4[/tex]
As the number can not be fraction, hence number of hit will be 2.
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what is (-5q-8) - (q+3)
The answer would be −6q−11
Answer:
-6q-11
Step-by-step explanation:
What is the degree of polynomial 5x³ 4x² 7x?
The degree of polynomial in 5x³ 4x² 7x is 3, since the highest power of variable is 3.
What is degree of polynomial?The degree of polynomials, which determines the maximum number of solutions a function could have and how frequently a function will cross the x-axis on a graph, is one of the key ideas in mathematics. Polynomials are also important because they help us understand how functions can be represented mathematically. In the equation involving polynomials, it has the highest exponential power.
In a polynomial equation, a variable's greatest power is its degree. Only the terms with variables are taken into consideration when calculating a polynomial function's degree. The polynomials degree can be determined by looking at the variable term's highest exponential power.
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Find the percent of change. Round to the nearest tenth, if necessary.
During the winter, the grill was marked at $85. In June, the price was changed to $110. 50.
PLEASE THIS IS URGENT
During the winter, the grill was marked at $85. In June, the price was changed to $110. 50. So, 23.08% is the change in percentage.
What is percentage?When the denominator is 100, percentages are really just fractions. We place the percent sign (%) next to the number to indicate that the number is a percentage.
Comparing two amounts while re basing the second amount to 100 is the simplest way to use percentages. The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin term made its way into English. It was later abbreviated to %.
Given that,
the grill was marked at $85
the price was changed to $110. 50.
Now, percentage change:
= [{(110. 50 - 85)/110.50} × 100]
= (0.2308 × 100)
= 23.08%
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A high school has a population of 2035 students and is increasing by 3% each year.
Write an exponential function to model the student population in terms of the number of years from now.
Answer:
Y=7x+67
Step-by-step explanation:
c=⟨–5,8⟩ and d=⟨7,4⟩, find –4c–4d.–4c–4d=
For every 4 children in the class who don’t have glasses 1 student does. If there are 20 students in the class, how many of them have glasses?
Samuel walked in the Labor Day parade. He walked 3 1/8 miles along the parade route and 2 5/6 miles home. For numbers 3a-3c, fill in each blank.
3a. Rounded to the closest benchmark, Samuel walked about. Miles on the parade route.
3b. Rounded to the closest benchmark, Samuel walked about. Miles home.
3c. Samuel walked about. Miles in all
3a) Rounded to the closest benchmark, Samuel walked about 3 Miles on the parade route.
3b) Rounded to the closest benchmark, Samuel walked about 2 Miles home
3c) Samuel walked about 5 Miles in all
We know that when rounding a fraction to the closest benchmark:
1) if the numerator is much smaller than the denominator, round a fraction to 0
2) if the numerator is about half the denominator, round a fraction to 1/2
3) if the numerator is nearly equal to the denominator, round a fraction to 1
Samuel walked 3 1/8 miles along the parade route.
Rounding to the closest benchmark a fraction 3 1/8 woule be
3 1/8
= 3
This means, he walked about 3 Miles on the parade route.
Samuel walked 2 5/6 miles home.
Rounding to the closest benchmark a mixed fraction 2 5/6 woule be
2 5/6
= 2
This means, he walked about 2 Miles homes.
The total distance would be,
d = 3 + 2
d = 5 miles
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Which is a correct expansion of (4x + 1)(2x7 - 2)?
Answer:
So the correct expansion of (4x + 1)(2x7 - 2) is 8x^27 - 8x2 + 2x7 - 2
Step-by-step explanation:
When expanding an algebraic expression like (4x + 1)(2x7 - 2), you can use the distributive property to find the product of each term in the first set of parentheses with each term in the second set of parentheses, and then add them together. The distributive property is the process of multiplying one term in the parentheses by each of the terms outside the parentheses.
Here is the correct expansion of (4x + 1)(2x7 - 2):
(4x + 1)(2x7 - 2) = 4x(2x7) + 4x(-2) + 1(2x7) + 1(-2)
= 8x^27 + -8x2 + 2x71 + -21
= 8x^27 + -8x2 + 2x7 + -2
= 8x^27 - 8x2 + 2x7 - 2
So the correct expansion of (4x + 1)(2x7 - 2) is 8x^27 - 8x2 + 2x7 - 2
It's important to note that you can also use FOIL method which is the acronym for the steps of the distributive property, First, Outside, Inside, Last.
4. Which of these is NOT involved in proving the converse of the Pythagorean theorem?
Ocollecting like terms and applying the distributive property
substitution and construction
congruent triangles
substitution and contradiction
The option that is not involved in proving the converse of the Pythagorean theorem is D. substitution and contradiction
What is a Pythagoras theoremA right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
The converse of Pythagoras' Theorem states that a triangle must have a right angle if the square of one side equals the sum of the squares of the other two sides.
In this case, contradiction isn't involved. The correct option is D.
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7. A stock is worth $21. Its value is increasing at a rate of $0. 25 per week a.
Write an equation for the value y (in dollars) of the stock after x weeks.
b. If this trend would continue, what would be the value of the stock after 20 weeks?
The Equation for the value y is a. y = 21 + 0.25x (where x represents the number of weeks)
b. The value of the stock after 20 weeks would be 21 + (0.25 * 20) = $26.
This equation represents the linear relationship between the value of the stock (y) and the number of weeks (x). The value of the stock is initially $21, and it increases by $0.25 every week. This is represented by the coefficient of x (0.25) in the equation. By plugging in x=20 into the equation, we can find that after 20 weeks, the value of the stock would be $26. This is assuming that the rate of increase remains constant over time.
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Hey guys so I NEEEEEED HELP ON THIS MATH QUESTION, so here it is please help me P.S: LIMITED TIME, P.P.S: LIKE IN 40-74 MINUTES!!! HELP
The approximate diameters of Uranus and Mars are listed below:
Uranus: 5.11×10^4
kilometers
Mars: 6.79×10^3
kilometers
How many times larger is the diameter of Uranus? Write your answer in standard notation, rounding to the nearest tenth.
The number of times the diameter of Uranus is larger than the diameter of Mars is 7.5 times
How to determine the number of times larger is the diameter of UranusFrom the question, we have the following parameters that can be used in our computation:
The diameters of Uranus and Mars
These diameters are given as
Diameter of Uranus: 5.11×10^4 kilometers
Diameter of Mars: 6.79×10^3 kilometers
Express the diameters properly
So, we have the following representation
Diameter of Uranus: 5.11 × 10⁴ kilometers
Diameter of Mars: 6.79 × 10³ kilometers
This means that
Number of times larger = Diameter of Uranus/Diameter of Mars
Substitute the known values in the above equation, so, we have the following representation
Number of times larger = 5.11 × 10⁴ kilometers/6.79 × 10³ kilometers
Evaluate the quotient
So, we have the following representation
Number of times larger = 7.5
Hence, the number of times is 7.5
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identify the vertical and horizontal asymptotes for f(x)=2x^2+4 over x^2-5x+6
The vertical asymptotes are 2 and 3 and horizontal asymptotes is 2
What are horizontal and vertical asymptote?An asymptote is a horizontal/vertical oblique line whose distance from the graph of a function keeps decreasing and approaches zero, but never gets there.
Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function.
Therefore, the denominator is x²-5x+6,
= x²-5x+6 = 0
using factorization method
x²-3x-2x+6 = 0
(x²-3x)(-2x+6) = 0
x(x-3) -2(x-3)
x-2 = 0 or
x-3 = 0
x = 2 or 3
The degree of the power of numerator and denominator are equal, there for the horizontal asymptote y = 2x²/x² = 2
therefore the vertical asymptote is x = 2and 3 and horizontal asymptote is y = 2
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The perimeter of a square is 48. If the perimeter is 4 times than before then find the number of times the area becomes of what it was before.
Answer:
12?
Step-by-step explanation:
Lowkey don't understand the last part of your q but if it's 4 times then if the original was 12 48 is four times bigger
get the standard form and slope-intercept form
1. 5x - 6y - 12 = 0
2. y - 2 = 2/3 (x+3)
3. y -9 = 1/7 (x+4)
4. y-8 = - 7/2 (x - 2)
Answer: To obtain the standard form of a linear equation, we want to rearrange the equation in the form Ax + By = C. Here are the standard forms of the given equations:
5x - 6y = 12
3y - 2x - 6 = 0
7x + y - 63 = 0
14x - y + 16 = 0
To obtain the slope-intercept form of a linear equation, we want to rearrange the equation in the form y = mx + b, where m is the slope and b is the y-intercept. Here are the slope-intercept forms of the given equations:
There is no y-intercept, so this equation does not have a slope-intercept form.
y = (2/3)x + 2
y = (1/7)x + 9
y = (-7/2)x + 8
Step-by-step explanation:
2 Lauren is using 10 pink beads and 5 black a bracelet. Which beads to decorate ratio compares the number of black beads to the total number of beads She is using?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio.
What is ratio?A comparison between two items by means of a number. (arithmetic) comparing two quantities' relative magnitudes (usually expressed as a quotient).
When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 40% are girls, and 14% are boys.
Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). By doing so, you are multiplying information A by information B. Your ratio will be 5/10, for instance, if A is 5 and B is 10.
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Select all the true equations.
Group of answer choices
5+0=0
LaTeX: 15\cdot0=015 ⋅ 0 = 0
1. 4 + 2. 7 = 4. 1
LaTeX: \frac{2}{3}\cdot\frac{5}{9}=\frac{7}{12}2 3 ⋅ 5 9 = 7 12
LaTeX: 4\frac{2}{3}=5-\frac{1}{3}
The true equations are - 15·0 = 015·0, 1.4 + 2.7 = 4.1, and 4(2/3) = 5-(1/3).
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The first equation is -
5 + 0 = 0
This equation is false, as if 0 is added to any number, the result is the same number itself, and not 0.
The second equation is -
15·0 = 015·0
Any number multiplied by 0, gives the result as 0.
In the above equation LHS = RHS = 0.
Hence, this equation is true.
The third equation is -
1.4 + 2.7 = 4.1
Solving LHS -
= 1.4 + 2.7
= 4.1
So, LHS = RHS and hence, this equation is true.
The fourth equation is -
(2/3) · (5/9) = 7/12
Solving LHS -
= (2/3) × (5/9)
= 10/27
Here, LHS ≠ RHS.
Hence, this equation is false.
The fifth equation is -
4(2/3) = 5-(1/3)
Solving LHS -
4(2/3) = 14/3
Solving RHS -
= 5 - 1/3
= (15 - 1)/3
= 14/3
Therefore, LHS = RHS and hence, this equation is true.
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Example You practice paddleboarding for
3 weeks. You paddle the same amount each day
for 5 days each week. You paddle 22.5 miles
altogether. How many miles do you paddle
each day?
Therefore , the solution of the given problem of equation comes out to be 1.45 mph (speed of the current).
Explain equationA mathematical depiction of two equal things, one on either side of a "equals" sign, is called an expression. Equations can be used to solve common problems. To solve challenges in real life, we frequently turn for pre algebra assistance. Lessons in pre-algebra cover the foundational ideas of mathematics.
Here,
The 15 miles that Bob the Boy Scout must paddle upwards against the current takes him 10 hours.
He discovers that paddling 22.5 miles against the current only took him 5 hours when he turns back.
——
Upstream data: rate = d/t = 15/10 = 1.5 mph, distance = 15 miles, time = 10 hours.
————————
Downstream DATA: rate = d/t = 22/5 = 4.4 mph; duration = 5 hours; distance = 22 miles.
———————-
Equations:
upstream: Downstream, b-c = 1.5 mph; b+c = 4.4 mph
2b = 5.9 mph;
2b = 2.95; add and solve for "b" (speed of the boat in still water)
—-
For "c," use the formula
=> b + c = 4.4
=>2.95 + c = 4.4
=> c = 1.45 mph (speed of the current)
Therefore , the solution of the given problem of equation comes out to be 1.45 mph (speed of the current).
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If Jenny earns $375 when she works 5 hours, how much will she earn if she
works 12 hours?
Answer:
She will earn $900.00 in 12 hours.
Step-by-step explanation:
Her unit rate is 75 dollars per hour.
375/5 = $75
75 x 12 = 900
Answer: $900
Step-by-step explanation: 375/5x12.
What are directed segments?
Answer:
A directed segment is a segment that has distance (length) and direction. Hope this helps.
A family drives 4 1/4 miles in 1/10 of an
hour. How many miles will they drive
in 3/4 hour?
Therefore because of this, the answer to the speed problem is that a family can travel 31.875 miles in 3/4 of an hour.
Describe speed.Speed is a tempo that is determined by the distance an entity travels in a predetermined period of time. Numerous methods exist for measuring speed, including miles per hour, laps per minute, and meters per second. The measurements of speed, distance, and time are related. The relationship can be expressed in three different ways:
D = RT, R = DT, & T = DR.
Here,
We are given that
Distance drives by a family=4[tex]\frac{1}{4}[/tex] miles
Time = 1/10
We have to find the rate of speed in miles per hour.
The speed formula will be used to get the velocity in miles per hour.
Distance traveled in a given amount of time equals speed.
=> Speed = 17/4 * 10
=> Speed = 42.5
So, using the calculation, we arrive at 42.5 miles per hour.
The miles traveled in 3/4 miles are therefore:
Distance is calculated as speed times time,
therefore 42.5 * 3/4 would equal 31.875 miles in distance.
Because of this, the answer to the speed problem is that a family can travel 31.875 miles in 3/4 of an hour.
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I need help finding the answer X=6y+24
2x+3y=3