Answer:
See explanation!
Step-by-step explanation:
Let us first give some principle theory to aid our solution.
Considering two functions [tex]A(x)[/tex] and [tex]B(x)[/tex], in order to show that function
which is the inverse of [tex]y=ax[/tex].
Now let as solve our problem. We are given the following:
[tex]f(x)=3x-4\\g(x)=\frac{x+4}{3}[/tex]
Method A: Show that these are inverse functions by finding f^-1 (x) and showing that it is the same as g(x).
Let us take [tex][f(x)=y]=3x-4[/tex] and "exchanging" our variables we have
[tex]x=3y-4\\x+4=3y\\\\y=\frac{x+4}{3}[/tex]
which is exactly the same with our given function of [tex]g(x)=\frac{x+4}{3}[/tex], so proved!
Method B: Show that these are inverse functions by showing that when the output of one function is used for the input of the other function, the final output is equal to the original input value. (you may choose any initial input)
For this case we will use a simple input let us say [tex]x=1[/tex]. Thus taking the [tex]f(x)[/tex] function and plugging in we have:
[tex]f(x=1) = 3(1)-4\\f(1)=3-4\\f(1)=-1[/tex]
Now let us take the output of [tex]f(1)[/tex] which is [tex]-1[/tex] and use it the input to our second function of [tex]g(x)[/tex], so we have:
[tex]g(x=-1) = \frac{(-1)+4}{3}\\ \\g(-1)=\frac{3}{3}\\ \\g(-1)=1[/tex]
so the output of the second function is equal to the original input value of the first function, hence proved!
Method C: Verify that these are the inverse function by showing that f(g(x)) = x AND g(f(x)) = x.
Basically we are asked to prove that both [tex]f(g(x))=g(f(x))=x[/tex]
To do so, we just replace one function into the [tex]x[/tex] value of the other function as follow:
[tex]f(g(x))=3(\frac{x+4}{3} )-4\\\\f(g(x))=x+4-4\\\\f(g(x))=x[/tex]
Lets repeat now for the opposite as follow:
[tex]g(f(x))=\frac{(3x-4)+4}{3}\\ \\g(f(x))=\frac{3x}{3}\\ \\g(f(x))=x[/tex]
Hence proved!
Which expression is equivalent to the one in the picture?
Answer:
d.
Step-by-step explanation:
To convert a root to a fraction in the exponent, remember this rule:
[tex]\sqrt[n]{a^{m}}=a^{\frac{m}{n}}[/tex]
The index becomes the denominator in the fraction. (The index is the little number in front of the root, "n".) The original exponent remains in the numerator.
In this question, the index is 4.
The index is applied to every base in the equation under the root. The bases are 16, 'x' and 'y'.
[tex]\sqrt[4]{16x^{15}y^{17}} = (\sqrt[4]{16})(\sqrt[4]{x^{15}})(\sqrt[4]{y^{17}}) = (2)(x^{\frac{15}{4}}})(y^{\frac{17}{4}}) = 2x^{\frac{15}{4}}}y^{\frac{17}{4}}[/tex]
To find the quad root of 16, input this into your calculator. Since 2⁴ = 16, [tex]\sqrt[4]{16}[/tex] = 2.
For the "x" and "y" bases, use the rule for converting roots to exponent fractions. The index, 4, becomes the denominator in each fraction.
[tex]2x^{\frac{15}{4}}y^{\frac{17}{4}}[/tex]
For his coffee shop, Abdul wants to make a mocha-java blend that will sell for $18/kg. The mocha coffee beans sell for $20/kg, and the java coffee beans sell for $15/kg. How many kilograms of each kind of coffee bean should he use to make 50 kg of the mocha-java blend?
Answer:
Step-by-step explanation:
let
x = kg of mocha beans
y = kg of java beans
so
(1) x + y = 50
(2) 20x + 15y = 18(50)
solve by substitution (or whatever method you prefer):
(x, y) = (30, 20)
Translate the followingame phrase into an algebraic expression using the variable w. Do not simplify.
The perimeter of a rectangle if the width is w centimeters and the length is 7 cm less than twice the width
Width = w cm
Length = 2w-7
Which quantity is proportional to 21⁄3?
Answer:
7/1
Step-by-step explanation:
simplify top and bottom by 3
Does a parralelogram have equal sides
Answer:
A parallelogram has opposite sides parallel and equal in length.
Step-by-step explanation:
Hope this helps. :)
What is the answer to this equation. -g+2(3+g)=-4(g+1)
Answer:
The answer to the given equation -g+2(3+g)=-4(g+1) is g=-2
Step-by-step explanation:
Given -g+2(3+g)=-4(g+1)
To solve the given equation :
-g+2(3+g)=-4(g+1)
Applying the distributive property we get
-g+2(3)+2(g)=-4(g)+(-4)(1)
-g+6+2g=-4g-4
g+6=-4g-4 ( adding the like terms )
g+6-(-4g-4)=-4g-4-(-4g-4)
Applying the distributive property we get
g+6-(-4g)-(-4)=-4g-4-(-4g)-(-4)
g+6+4g+4=-4g-4+4g+4
5g+10=0 ( adding the like terms )
5g+10-10=0-10
5g=-10 ( adding the like terms )
[tex]g=-\frac{10}{5}[/tex]
[tex]g=-2[/tex]
Therefore g=-2
The answer to the given equation -g+2(3+g)=-4(g+1) is g=-2
Ethan needs to save at least $500 to purchase a new dirt bike. So far, he has saved $175. If he hopes to use two-fifths of his next paycheck to cover the remaining amount, how much money must he make in his paycheck
Answer:
$812.5
Step-by-step explanation:
Given: Ethan need to save at least $500.
He has saved so far $175
Ethan hope to use two-fifths of his next paycheck to cover the remaining amount.
Lets assume Ethan´s paycheck amount be "x"
First finding the remaining amount to be covered.
Remaining amount= [tex]\$ 500 - \$ 175= \$ 325[/tex]
∴ The remaining amount to be covered is $325.
As given, Ethan hope to use two-fifths of his next paycheck to cover the remaining amount.
Now, using the inequality to find the amount of paycheck.
⇒ [tex]x\times \frac{2}{5} \geq \$ 325[/tex]
multiplying both side by 5
⇒ [tex]x\times 2\geq 325\times 5[/tex]
divinding both side 2
⇒ [tex]x\geq \frac{1625}{2}[/tex]
∴ [tex]x\geq \$ 812.5[/tex]
Hence, Ethan must make at least $812.5 in his paycheck to cover his remaining anount to buy dirt bike.
How do the 5s in 50.8 and 18.35 compare?
The value of the 5 in 50.8 is 1,000 times the value of the 5 in 18.35.
The value of the 5 in 50.8 is 100 times the value of the 5 in 18.35.
The value of the 5 in 50.8 is 1100 the value of the 5 in 18.35.
The value of the 5 in 50.8 is 11,000 the value of the 5 in 18.35.
The value of the 5 in 50.8 is 1,000 times the value of the 5 in 18.35 ⇒ 1st answer
Step-by-step explanation:
Let us revise some important notes in a number:
Every digit in a number has a place valuePlace value is the value represented by a digit in a numberEx: the place value of 2 in the number 2,345 is 1,000 because 2 is in the thousands place, the place value of 9 in 12.29 is 0.01 because 9 is in the hundredths place∵ The number is 50.8
∵ 5 is in the tens place
∴ The place value of 5 is 10
∵ The number is 18.35
∵ 5 is in the hundredths place
∴ The place value of 5 is 0.01
Let us compare between the places value of 5 in the two numbers
Let x the number which multiplying by the hundredth digit to give the ten digit
∵ 10 = x × 0.01
∴ 10 = 0.01 x
- Divide both sides by 0.01
∴ 1,000 = x
∵ 5 × 10 = 0.05 × 1000
∴ 50 = 50
∴ The value of 5 in 50.8 = 1,000 × the value of 5 in 18.35
The value of the 5 in 50.8 is 1,000 times the value of the 5 in 18.35
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what is the domain of the relation (-2,4) (1,3) (0,-4) (3,2)
The domain of the given relation (-2,4), (1,3), (0,-4), (3,2) is the set of the first elements from each ordered pair, which results in the set {-2, 1, 0, 3}.
The question asks about the domain of a relation consisting of ordered pairs. A relation is a set of ordered pairs, and the domain of a relation is the set of all the first elements from each pair. In the given relation (-2,4), (1,3), (0,-4), (3,2), the domain comprises the first elements of each pair, which are -2, 1, 0, and 3. Therefore, the domain of this relation is the set {-2, 1, 0, 3}.
true or false:the points (6,13),(21,33),(99,137)all lie on the-same line. the equation of the line is y=4/3x +5
The answer is true.
Step-by-step explanation:
To find the points all lie on the same line, we need to substitute the points in the equation of the line, to determine if the values on both sides of the equation are equal.
Substituting the point [tex](6,13)[/tex] in the equation of the line, we get,
[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\13 &=\frac{4}{3}(6)+5 \\&=4(2)+5 \\&=8+5 \\13 &=13\end{aligned}[/tex]
Thus, the values on both sides are equal. The point [tex](6,13)[/tex] lie on the same line.
Substituting the point [tex](21,33)[/tex] in the equation of the line, we get,
[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\33 &=\frac{4}{3}(21)+5 \\&=4(7)+5 \\&=28+5 \\33 &=33\end{aligned}[/tex]
Thus, the values on both sides are equal. The point [tex](21,33)[/tex] lie on the same line.
Substituting the point [tex](99,137)[/tex] in the equation of the line, we get,
[tex]\begin{aligned}y &=\frac{4}{3} x+5 \\137 &=\frac{4}{3}(99)+5 \\&=4(33)+5 \\&=132+5 \\137 &=137\end{aligned}[/tex]
Thus, the values on both sides are equal. The point [tex](99,137)[/tex] lie on the same line.
Thus, all the three points lie on the same plane.
Hence, the answer is true.
All three points (6 , 13), (21 , 33), and (99 , 137) lie on the line y = [tex]\frac{4}{3}[/tex]x + 5. Thus, the statement is True, all three points make the equation true. Option 3 is the correct answer.
To determine whether the points (6,13), (21,33), and (99,137) all lie on the line y = [tex]\frac{4}{3}[/tex]x + 5, we need to substitute the x-values of each point into the equation and see if the corresponding y-values match.
1. For the point (6,13):
Substitute x = 6 into the equation.
⇒ y = ([tex]\frac{4}{3}[/tex]) × 6 + 5
⇒ y = 8 + 5
⇒ y = 13
Since the y-value matches, the point (6,13) is on the line.
2. For the point (21,33):
Substitute x = 21 into the equation.
⇒ y = ([tex]\frac{4}{3}[/tex]) × 21 + 5
⇒ y = 28 + 5
⇒ y = 33
Since the y-value matches, the point (21,33) is on the line.
3. For the point (99,137):
Substitute x = 99 into the equation.
⇒ y = ([tex]\frac{4}{3}[/tex]) × 99 + 5
⇒ y = 132 + 5
⇒ y = 137
Since the y-value matches, the point (99,137) is on the line.
All three points satisfy the equation y = [tex]\frac{4}{3}[/tex]x + 5. Therefore, the statement is True: all three points make the equation true option (3).
Complete question:
True or False:
The points (6,13), (21,33) and (99,137) all lie on the same line. The equation of the line is y = [tex]\frac{4}{3}[/tex]x + 5.
Select the correct explanation.
False, all three points do not make the equation true.True, all three points are positive.True, all three points make the equation true.False, all three points are positive.What times 24 equals -12?
Answer:
-1/2 or/also known as. -0.5
Help?? I seriously don’t understand?
Answer:
A. 30
Step-by-step explanation:
The answer is 30 because x= 12 so that means that x-2 is 10 because x is 12, so since its in parenthesizes that means you do that part of the problem first. So, after we have 10 we will do times 3 since the 3 is also there and it says what is the value. So, therefore the answer is A. 30.
type the correct answer in the box
Answer:
216 cm^2.
Step-by-step explanation:
There are 6 faces on the prism . 3 pairs with the same area.
The surface area = 2*6*10 + 2 * 6*3 + 2*3*10
= 120 + 36 + 60
= 216 cm^2.
Simplify 4(2x^3y^4)^4/2(2x^2y^6)^3. Show your work. Please help ASAP!!
Answer:
The simplified expression to the given expression is [tex]\frac{4x^6}{y^2}[/tex]
Therefore [tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}[/tex]
Step-by-step explanation:
Given fractional expression is [tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}[/tex]
To simplify the given expression as below :
[tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}[/tex]
[tex]=\frac{2(2x^3y^4)^4}{(2x^2y^6)^3}[/tex]
[tex]=\frac{2[(2)^4(x^3)^4(y^4)^4]}{(2)^3(x^2)^3(y^6)^3}[/tex] ( using the property [tex](a^m)^n=a^{mn}[/tex])
[tex]=\frac{2[(2)^4(x^{12})(y^{16})]}{(2)^3(x^6)(y^{18})}[/tex]
[tex]=2[(2)^4(x^{12})(y^{16})](2)^{-3}(x^{-6})(y^{-18})[/tex] ( ( using the property [tex]a^m=\frac{1}{a^{-m}}[/tex] )
[tex]=2[2^{4-3}x^{12-6}y^{16-18}][/tex]( using the property [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=2[2^1x^6y^{-2}][/tex]
[tex]=\frac{4x^6}{y^2}[/tex] ( using the property [tex]a^m=\frac{1}{a^{-m}}[/tex] )
Therefore the simplified expression is [tex]\frac{4x^6}{y^2}[/tex]
Therefore [tex]\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}[/tex]
math question thanks!
Answer:
B C and E
Step-by-step explanation:
The easiest way to know if the graph was a function is the vertical line test
If you can draw a verticle line that interests the graph two or more times it is not a function and if you can't it is a function
what is the domain of the function in this table
Answer:
B. {1, 2, 3, 4}.
Step-by-step explanation:
The domain is the set of x values.
The domain of the function represented by the given table, with the corresponding values of x and y being (1, 2), (2, 4), (3, 3), and (4, 2), is Option B) {1, 2, 3, 4}.
The domain of a function consists of all possible input values (x-values) for which there are corresponding output values (y-values). In the given table, we see the following pairs of values: (1, 2), (2, 4), (3, 3), and (4, 2).
These x-values are explicitly provided in the table, and they are 1, 2, 3, and 4. Therefore, the domain of the function, based on the data in the table, is {1, 2, 3, 4}.
This means that for this specific function, you can input any of these four values into the function, and there are corresponding y-values for each of them. Any other values not listed in the table, such as decimals or negative numbers, are not part of the domain for this function because they do not have corresponding y-values in the given data.
In summary, the domain of the function represented by the table is the Option B). set {1, 2, 3, 4}, which includes the x-values provided in the table.
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Consider the function f(x)=−2/3x+5 .
What is f(5/2) ?
solving algebra 8(2f-3)=4(4f-8)
Answer:
no solution
Step-by-step explanation:
8(2f-3)=4(4f-8)
16f-24=16f-32
16f=16f-8
0=-8
Answer:
No solution
Step-by-step explanation:
8(2f-3)=4(4f-8)
16f-24=16f-32
8=0f
The sum of two consecutive integers is 105 find the integers
The integers are 52 and 53
Solution:
Consecutive numbers are numbers that follow each other in order. They have a difference of 1 between every two numbers
Let the two consecutive integers be x and x + 1
Given that, sum of two consecutive integers is 105
Therefore,
x + x + 1 = 105
Combine the like terms
2x + 1 = 105
2x = 105 - 1
2x = 104
Divide both sides of equation by 2
x = 52
Thus, another integer = x + 1 = 52 + 1 = 53
Thus the integers are 52 and 53
Answer:
52,53
Step-by-step explanation:
a. 12
b. 16
c. 8
d. 4
- casts a shadow 30 feet long. A MHS student standing near the tree casts a shadow 9 feet long. The
udent is 6 feet tall. What is the height of the tree? Show all work. (1 pt) Unit2 LT6
a.
45 feet tall
c.
15 feet tall
b.
24 feet tall
d.
20 feet tall
Tree casts a shadow 30 feet long. A MHS student standing near the tree casts a shadow 9 feet long. The student is 6 feet tall. What is the height of the tree? Show all work
Answer:
Option D
The height of tree is 20 feet tall
Solution:
From given question,
Shadow of tree = 30 feet
Height of tree = ?
Height of student = 6 feet
Shadow of student = 9 feet
We have to find the height of tree
We can solve the sum by proportion
[tex]\frac{\text{height of tree}}{\text{shadow of tree}} = \frac{\text{height of student}}{\text{shadow of tree}}[/tex]
This forms a proportion and we can solve the sum by cross multiplying
[tex]\frac{\text{height of tree}}{30} = \frac{6}{9}\\\\\text{height of tree} = 30 \times \frac{6}{9} = 30 \times \frac{2}{3}\\\\\text{ height of tree } = 10 \times 2 = 20[/tex]
Thus height of tree is 20 feet tall
Giving brainliest again
Answer:
3. times 2 divided by 36
Answer:
L=6
Step-by-step explanation:
3 x 2= 6
36 divided by 6= 6
so L= 6
How do the 3s in 7.315 and 893.5 compare?
The value of the 3 in 7.315 is 100 times the value of the 3 in 893.5.
The value of the 3 in 7.315 is 10 times the value of the 3 in 893.5.
The value of the 3 in 7.315 is 110 the value of the 3 in 893.5.
The value of the 3 in 7.315 is 1100 the value of the 3 in 893.5.
Answer:
1/10 the value is 100% right!
Step-by-step explanation:
On a factory floor, 30 out of every 140 toy robots is defective. What percent is defective?
A. 60%
B. 2.67%
C. 0.6
D. 26.67%
Can you help me? Thanks!
Answer:
[tex]21.43\%[/tex]
Step-by-step explanation:
we know that
To find out the percent of robots which are defective, divided the number of defective robots by the total number of robots and multiply the result by 100
Let
x ----> the number of defective robots
y ----> the total number of robots
p ---> percentage of robots which are defective
so
[tex]p=\frac{x}{y} (100)[/tex]
we have
[tex]x=30\\y=140[/tex]
substitute
[tex]p=\frac{30}{140}(100)[/tex]
[tex]p=21.43\%[/tex]
Completely factor this quadratic expression:
4x to the 2nd power + 12x − 72.
72 rr rvmfklm;vrmfkvfdmlmv;m,fd;vmfd;lvmfl;v fek;
Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case. 1.5% syrup?
Answer:
Ella should add [tex]32\dfrac{5}{6}[/tex] lbs of water.
Total weight of syrup [tex]33\dfrac{1}{3}[/tex] lbs
Step-by-step explanation:
Weight:
Weight of sugar = 0.5 lbs.
Weight of water added = x lbs
Total weight = 0.5 + x lbs
Percentage:
0.5 + x -- 100%
0.5 -- 1.5%
Write a proportion:
[tex]\dfrac{0.5+x}{0.5}=\dfrac{100}{1.5}[/tex]
Cross multiply:
[tex]1.5(0.5+x)=0.5\cdot 100\\ \\0.75+1.5x=50\\ \\1.5x=50-0.75\\ \\1.5x=49.25\\ \\x=\dfrac{49.25}{1.5}=\dfrac{4,925}{150}=\dfrac{197}{6}=32 \dfrac{5}{6}\ lbs[/tex]
Ella should add [tex]32\dfrac{5}{6}[/tex] lbs of water.
Total weight of syrup
[tex]32\dfrac{5}{6}+\dfrac{1}{2}=32\dfrac{5}{6}+\dfrac{3}{6}=33\dfrac{1}{3}\ lbs[/tex]
Answer:
Ella should add 32 5/6 lb of water, and she will have 33 1/3 lb of syrup.
Step-by-step explanation:
Question 45 An art teacher is cleaning up her room at the end of the week. She combines three jars containing 212 ounces, 825 ounces, and 11110 ounces of blue paint in an empty bucket. This bucket is then used to fill one can with 414 ounces of the paint and another can with 358 ounces of the paint. How many ounces of blue paint are still in the bucket? A 778 ounces B 1418 ounces C 22 ounces D 2978 ounces
There are 11,375 ounces are still in the bucket ⇒ (not in the choices)
Step-by-step explanation:
An art teacher is cleaning up her room at the end of the week
She combines three jars containing 212 ounces, 825 ounces, and 11110 ounces of blue paint in an empty bucketThis bucket is then used to fill one can with 414 ounces of the paint and another can with 358 ounces of the paintWe need to find how many ounces of blue paint are still in the bucket
∵ The jars have 212 ounces, 825 ounces, and 11110 ounces of blue paint
∵ She combines all of them in an empty bucket
- Add them to find the quantity of the blue paint in the bucket
∴ The bucket contains = 212 + 825 + 11110
∴ The bucket contains = 12,147 ounces
∵ This bucket is then used to fill one can with 414 ounces of
the paint and another can with 358 ounces
- Add them to find the quantity that used from the bucket
∵ She used = 414 + 358 = 772
∴ 772 ounces is used to fill the two cans
To find how many ounces of the blue paint are still in the bucket subtract from the total amount of paint in the bucked the amount used to fill the two cans
∵ The remainder paint in the bucket = 12,147 - 772
∴ The remainder paint in the bucket = 11,375 ounces
There are 11,375 ounces are still in the bucket
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How do you eliminate the fractions on this to solve by elimination ????????
Answer:
Step-by-step explanation:
Good evening
Answer:
x = 6
y = 2
Step-by-step explanation:
Look at the photo below for the details.
:)
Sharon serves the volleyball with an upward velocity of 23 ft/s. The ball is 3.5 ft above the ground when struck. How long does Barbara have before the ball hits the ground?
We can use the kinematic equation:
h = vi*t + 0.5*a*t^2
where h is the initial height, vi is the initial velocity, a is the acceleration due to gravity (9.8 m/s^2 or 32 ft/s^2), and t is the time.
Since we want to find the time it takes for the ball to hit the ground, we can set h = 0 and solve for t:
0 = 23*t - 0.5*32*t^2 + 3.5
0 = -16t^2 + 23t + 3.5
Using the quadratic formula, we get:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -16, b = 23, and c = 3.5.
t = (-23 ± sqrt(23^2 - 4*(-16)*3.5)) / 2*(-16)
t = (-23 ± sqrt(529)) / (-32)
t = (-23 ± 23) / (-32)
t = 0.125 s or 1.438 s
Since we are looking for the time it takes for the ball to hit the ground, we only want the positive solution:
t = 1.438 s
Therefore, Barbara has about 1.438 seconds before the ball hits the ground.
Final answer:
Barbara has approximately 1.43 seconds before the volleyball served by Sharon with an upward velocity of 23 ft/s and from a height of 3.5 ft hits the ground.
Explanation:
To determine how long Barbara has before the volleyball hits the ground, we need to use the kinematic equations for projectile motion, assuming the ball is moving under the influence of gravity alone. Since Sharon serves the volleyball with an upward velocity of 23 ft/s and the initial height is 3.5 ft, we can use the following kinematic equation:
[tex]s = ut + (1/2)at^2[/tex]
Where:
s is the displacement (which is -3.5 ft because the ball is falling to the ground, hence the negative sign)
u is the initial velocity (23 ft/s upwards, hence positive)
a is the acceleration due to gravity ( [tex]-32 ft/s^2[/tex], negative because it is directed downward)
t is the time
Plugging in the values we get:
[tex]-3.5 = 23t - (1/2)(32)t^2[/tex]
This is a quadratic equation in the form of [tex]at^2 + bt + c = 0[/tex] , where a = -16, b = 23, and c = -3.5. We can solve for t using the quadratic formula [tex]t = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}[/tex]. After calculating, we find that t is approximately 1.43 seconds. However, since time cannot be negative, we take the positive value which is the time it takes for the ball to hit the ground.
Therefore, Barbara has approximately 1.46 seconds before the volleyball hits the ground.
Hakeem shot the basketball 28 times and made 17 baskets. What percent of his shots were baskets?
Answer:
60%
Step-by-step explanation:
To find the percentage of successful basketball shots, divide the number of made shots by the total number shots taken, then multiply by 100. In Hakeem's case, his shooting percentage is approximately 61%.
Explanation:This is a question about calculating a percentage, which is a basic concept in Mathematics. Percentages are a way of expressing a number or proportion as a fraction of 100. In this case, Hakeem made 17 out of 28 basketball shots. This can be expressed as a fraction – 17/28. To convert this fraction into a percentage, you simply multiply it by 100.
Here is the calculation: (17 / 28) * 100 = 60.71. Therefore, Hakeem made approximately 61% of his basketball shots.
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What is the solution to the equation? 13 and three-fourths + x = 7 and one-fourth
The solution of the expression of 13 and three-fourths + x = 7 and one-fourth equation is x = [tex]6\frac{1}{2}[/tex]
To solve this equation, we need to find the value of x (unknown variable) in the given equation:
13 and three-fourths + x = 7 and one-fourth
First, we need to convert the mixed numbers to improper fractions.
13 and three-fourths = [tex]13 + \frac{3}{4} = 13\frac{3}{4}[/tex]
7 and one-fourth = [tex]7 + \frac{1}{4} = 7 \frac{1}{4}[/tex]
Now, the equation becomes:
[tex]13\frac{3}{4} + x =7\frac{1}{4}\\ x = 13\frac{3}{4} - 7\frac{1}{4}\\\\x = 6\frac{1}{2}[/tex]