Eric spend 60 minutes for basketball and 35 minutes for volleyball.
What is Linear Equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.
Here, let Eric plays basketball for x minutes.
and volleyball for y minutes.
Total time spend on playing basketball and volleyball everyday = 95 minutes.
Duration of Basketball 25 minutes more than volleyball
Now, according to question,
x + y = 95 ..........(i)
x - 25 = y ...........(ii)
On solving equation (i) and (ii), we get
x + x - 25 = 95
2x = 95 + 25
2x = 120
x = 120 / 2
x = 60
put value of x in equation (ii), we get
60 - 25 = y
y = 35
Yes, it is possible and clearly described in above calculation.
Thus, Eric spend 60 minutes for basketball and 35 minutes for volleyball.
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Find the value of x which satisfies the following equation.
log2(x−1)+log2(x+5)=4
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 3[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: log_{2}(x - 1) log_{2}(x + 5) = 4[/tex]
[tex]\qquad \tt \rightarrow \: log_{2} \{(x - 1)(x + 5) \} = 4[/tex]
[ log (x) + log (y) = log (xy) ]
[tex]\qquad \tt \rightarrow \: ( x - 1)(x + 5) = {2}^{4} [/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 5x - x - 5 = 16[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x - 5 - 16 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 4x -21 = 0[/tex]
[tex]\qquad \tt \rightarrow \: {x}^{2} + 7x - 3x - 21 = 0[/tex]
[tex]\qquad \tt \rightarrow \: x(x + 7) - 3(x + 7) = 0[/tex]
[tex]\qquad \tt \rightarrow \: (x + 7)(x - 3) = 0[/tex]
[tex]\qquad \tt \rightarrow \: x = - 7 \: \: or \: \: x = 3[/tex]
The only possible value of x is 3, since we can't operate logarithm with a negative integer in it.
[tex]\qquad \tt \rightarrow \: x = 3[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
If f(x)= 3x +2 and g(x)=x^2+1, which expression is expression is equivalent to (fog) (x)
Composite functions occur when we take two functions and input one into the other as x.
Example:
[tex]f(x) = 2x[/tex]
[tex]g(x) = 3x^2[/tex]
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(x) = 2(3x^2)[/tex]
Solving the QuestionWe're given:
[tex]f(x)= 3x +2[/tex][tex]g(x)=x^2+1[/tex]To find [tex](f\circ g)(x)[/tex], input g into f as x:
[tex]f(x)= 3x +2[/tex]
[tex](f\circ g)(x)=3(x^2+1) +2\\(f\circ g)(x)=3x^2+3 +2\\(f\circ g)(x)=3x^2+5[/tex]
Answer[tex](f\circ g)(x)=3x^2+5[/tex]
Which of the following statements is true?
Answer:
Last choice, [tex]\sqrt{15}[/tex] is irrational and [tex]\sqrt{0.001}[/tex] is rational
Step-by-step explanation:
Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers, ex. 0.4
Irrational Numbers: A type of real number which cannot be represented as a simple fraction (non ending decimal), ex. 0.4161446
[tex]\sqrt{15} = 3.8729[/tex] making it irrational
First and third choice are INCORRECT as they state its rational[tex]\sqrt{0.001} = 1/1000[/tex] making it rational
Second choice is INCORRECT as they state its irrationalHence, the last choice is correct
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What is the perimeter in units ?
Answer:
12 + [tex]4\sqrt{5}[/tex] approximates to 20.944
Step-by-step explanation:
VU - 8 units
UW - 4 units
VW - [tex]\sqrt{64+16} = \sqrt{80} =4\sqrt{5}[/tex]
12 + 4sqrt(5)
Answer:
6 (2 + √5) units
Step-by-step explanation:
Finding the length of the 3rd side :
*Applying Pythagorean Theorem*
VW² = 4² + 8²VW² = 16 + 64VW = √80VW = 6√5The perimeter :
4 + 8 + 6√512 + 6√56 (2 + √5) unitsAn arithmetic sequence is shown in the graph.
What is the equation for the nth term of the arithmetic sequence?
an = –3 + 5(n – 1)
an = –3 + 5(n + 1)
an = –3 – 5n
an = –3 + 5n
Answer:
an= -3+5(n-1)
Step-by-step explanation:
Try writing out the terms and finding a pattern. In this case, inserting any plotted x-value into the sequence -3+5(n-1) produces the correct y-value.
Answer:
A.) an = -3 + 5(n - 1)
Explanation:
Given: (1, -3), (2, 2), (3, 7), (4, 12), (5, 17)
Arithmetic Series: a + (n - 1)d
['a' is first term, 'n' determines term position, 'd' is common difference]
Determine the following:
a = -3d = second term - first term = 2 - (-3) = 5Putting into equation:
-3 + (n - 1)5-3 + 5(n - 1)9 out of 10 students prefer maths class over lunch how many students do not prefer math if 200 students were asked?
Answer: 180
Step-by-step explanation: 200 % 2 = 100
9/10 = 90/100
90 * 2 = 180
Answer:
20 students
If 9 out of 10 student prefer math over lunch, then 1 out of ten DO NOT. With this information you can set up a simple proportion: [tex]\frac{1}{10} =\frac{x}{200}[/tex].
To solve for x, you cross multiply as follows:
1*200=10x
200=10x
20=x
Hence, x equals 20, and 20 students do not prefer math over lunch.
Hope I helped!!!!!!!!!!!!!:)
radical 5* radical 2
Answer:
[tex] \sqrt{10} [/tex]
Step-by-step explanation:
Rule: [tex] \sqrt{a} \times \sqrt{b} = \sqrt{ab} [/tex]
[tex] \sqrt{5} \times \sqrt{2} = \sqrt{5 \times 2} = \sqrt{10} [/tex]
How do you round 56.053 to the nearest whole number
Answer:
56
Step-by-step explanation:
all your doing is removing the .053 to get your whole number
Which of the numbers below are whole numbers? Check all that apply.
A. 734.895
B. 0.7538
C. 7
D. 5429.97
E. 616
F. 401119.8
Answer:
7, 616 because there is no floating point
why f is not differentiable at x = 0 , where f(x) is x ^1/3
Therefore the f is continuous on R , i.e. real numbers and f is not differentiable at 0 ,Option A and D is the correct answer.
What is a Function ?A function is a mathematical statement which find relation between independent variable and dependent variable.
It always comes with a defined range and domain.
It is given that :
[tex]\rm f(x) = x^{1/3}\\\\LHD (at\; x = 0) = RHD (at \; x = 0)\\\\\= \lim_{x\rightarrow 0}\dfrac{f(x)-f(0)}{x-0}\\\\=\lim_{h\rightarrow 0}\dfrac{f(0-h)-f(0)}{0-h-0}[/tex]
[tex]=\lim_{h\rightarrow 0}\dfrac{f(0-h)-f(0)}{0-h-0} \\\\= \lim_{h\rightarrow 0}\dfrac{(-h)^{1/3}}{-h}\\\\\lim_{h\rightarrow 0}\dfrac{(-1)^{1/3}(h)^{1/3}}{-1*h}\\\\\lim_{h\rightarrow 0} (-1)^{-2/3}h^{-2/3}[/tex]
if we substitute h = 0 ,
Here, LHD and RHD does not exist at x = 0 So, f(x) is not differentiable at x = 0 .
Therefore the f is continuous on R , i.e. real numbers
and f is not differentiable at 0
Option A and D is the correct answer.
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According to the graph, what is the factorization of x² - 5x+6?
OA. (x-3)(x+2)
OB. (x+3)(x-2)
OC. (x+3)(x+2)
OD. (x-3)(x-2)
y xẻ 5Xtộ
Answer:
OD.(x-3)(x-2)
Step-by-step explanation:
we need two numbers (negative ir positive) that multiply to get 6 abd add to get -5.
so its OD
as -3×-2=6
and -3+-2=-5
The changes in account balances for Elder Company for 2021 are as follows:
Assets $ 480,000 debit
Common stock 250,000 credit
Liabilities 160,000 credit
Paid-in capital—excess of par 30,000 credit
Assuming the only changes in retained earnings in 2021 were for net income and a $50,000 dividend, what was net income for 2021?
The changes in account balances for Elder Company for 2021 are net income will be $160000
We have given debt common stock = $680000
Credit liabilities = 350000
Credit paid in capital = 190000
And an excess of par 30,000 credit Assuming the only changes in retained earnings
So 680000 = 350000+190000+30000+ retained earning
What is the net income?Net income is an entity's income minus the cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.
So retained earning = $110000
Dividend paid = $50000
So Net income = dividend paid + retained earning
Net income = $110000+$50000
Net income = $160000
So option (c) will be the correct answer.
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Which number should replace the ç to make the subtraction problem correct?
9.866
- 7.97ç
1.889
Answer:
7
Step-by-step explanation:
for you to get the missing number just take the complete numbers and minus them then you'll get the incomplete digit needed good day.
graph g(x) = -8|x| +1
Answer:
look the attachment in the above
Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. If it takes the hot water faucet minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?
Do not do any rounding.
Answer:
Or if you don't want any rounding it will be 115.38461538461
Select the correct answer. Which set of vertices forms a parallelogram? OA A2,4), B(3, 3), C6, 4), D(5, 6) OB. A(-1, 1), B(2, 2), C(5, 1), D(4, 1) OC. A(-5, -2), B(-3, 3), C3, 5), D(1, 0) OD. A(-1, 2), B(1, 3), C5, 3), D(1, 1).
Answer:
(6,4)
Step-by-step explanation:
^^^
Cells B1, C1, and D1 contain the values Seat1Row1, Seat2Row1, and Seat3Row1. If cells B1, C1, and D1 were selected, and autofill
used to fill E1, F1, and G1, what would be the auto-filled values?
Seat1Row2, Seat2Row2, Seat3Row2
Seat 2Row2, Seat3Row3, Seat4Row4
Seat 1Row1, Seat2Row2, Seat3Row2
Seat 2Row2, Seat3Row2, Seat4Row2
In the event that cells B1, C1, and D1 were highlighted and then used to fill E1, F1, and G1, the values we would see are A. Seat1Row2, Seat2Row2, Seat3Row2.
What values would be in E1, F1, and G1?When using a spreadsheet, you can autofill succeeding cells if you highlight the preceding ones and then drag the cursor.
If Seat1Row1, Seat2Row1, and Seat3Row1 are in the cells B1, C1, and D1, then the spreadsheet would take note of the "1s" at the end of the values.
When it is then used to autofill the next cells, it would make this a 2 such that we see Seat1Row2, Seat2Row2, Seat3Row2.
If cells H1, I1, and J1 are filled, we would then see Seat1Row3, Seat2Row3, Seat3Row3.
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A clothing manufacturer produces one type of sweater that earns $4 profit for each one sold. The business manager requires that a profit of at least $100 be earned every hour. The product manager estimates that the expenses for running the machine are $45 per hour. What is the least number of sweaters that must be produced each hour to earn a profit of at least $100?
The least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
A clothing manufacturer produces one type of sweater that earns $4 profit for each one sold.
Let x be the number of sweaters that must be produced each hour to earn a profit of at least $100
Total selling price if earns $4 profit for each one sold = 4x
The expenses for running the machine are $45 per hour.
4x - 45 ≤ 100
4x ≤ 145
x ≤ 145/4
x ≤ 36.25
Number of sweater(estimate value) = 37
Thus, the least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.
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Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.
The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]
Horizontal stretch by a factor k: [tex]y = f\left(\dfrac{x}{k}\right)[/tex]
Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.
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Liz earns a salary of $2,200 per month, plus a commission of 5% of her sales. She wants to earn at least
$2,500 this month. Enter an inequality to find amounts of sales that will meet her goal.your
variable represents. Enter the commission rate as a decimal.
Answer:
2200 + 0.5x >= 2500
Step-by-step explanation:
x is the amount of sales
A merchant has 120 liters of oil of one kind, 180 liters of another kind, and 240
liters of the third kind. He wants to sell the oil by filling the three kinds of equal
capacity. What should be the greatest capacity of such a tin?
The merchant needs to fill 60 litres of all types of oils .
What is HCF ?
HCF is the highest common factor, it is the factor in common in more than two numbers.
It is given in the question that
A merchant has 120 litres of oil of one kind, 180 litres of another kind, and 240 litres of the third kind.
He wants to sell the oil by filling the three kinds of equal capacity.
To find the greatest capacity of such a tin , we have to find the highest common factor of the individual capacity.
120=2×2×2×3×5
180=2×2×3×3×5
240=2×2×2×2×3×5
HCF=2×2×3×5=60
The greatest capacity = 60 litres
So the merchant needs to fill 60 litres of all types of oils .
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11. Calculate the weight on earth of an object with a mass of 48 kg. Gravitational acceleration (a) = 9.81 m/s ² Show all steps and formulae used. (3) ✓
Answer:
470.88 N
Step-by-step explanation:
F = ma
48 ( 9.81) = 470.88 N ( 105.958 lbs)
[PLEASE HELP!!!!!!!!!]
Identify which equations have one solution, Infinitely many solutions, or no solution.
y+3.2y=20 +2z-1=42+2-2z|
4.5r=3.2+4.5r 21+4=3x+2
No Solution
One Solution
Infinitely Many Solutions
3z +2.5=3.2+3z
1.1+0+2=3.1+
The list of equations is shown in the picture which equation has No Solution, One Solution, and Infinitely Many Solutions.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have given a linear equation in one variable.
[tex]\rm \dfrac{1}{2}y + 3.2y = 20[/tex]
After solving:
y = 5.40 (one solution)
[tex]\rm \dfrac{15}{2}+ 2z -\dfrac{1}{4}=4z+\dfrac{29}{4} -2z[/tex]
After solving:
[tex]\rm \dfrac{15}{2} -\dfrac{1}{4}=\dfrac{29}{4}[/tex]
[tex]\rm \dfrac{29}{4}=\dfrac{29}{4}[/tex] (Infinitely Many Solutions)
3z + 2.5 = 3.2 + 3z
2.5 = 3.2 (no solution)
Similarly, we can identify which equation has No Solution, One Solution, and Infinitely Many Solutions.
Thus, the list of equations is shown in the picture which equation has No Solution, One Solution, and Infinitely Many Solutions.
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which expression is equivalent to....
Answer:
A^32
Step-by-step explanation:
Done
Answer:
Option D: a³²
Step-by-step explanation:
Powers in this case multiply, 8*4=32
therefore answer D a³² is correct
Question 1 of 10
What is the midpoint of the segment shown below?
O A. (6,3)
O B. (6,5)
O C. (3,5)
OD. (3, 3)
Answer:
[tex]\textsf{C.} \quad \left(3,\dfrac{5}{2}\right)[/tex]
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints of the line segment:
[tex]\textsf{Let }(x_1,y_1)=(-1,2)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(7,3)[/tex]
Substitute the defined endpoints into the midpoint formula and solve:
[tex]\implies \textsf{Midpoint}=\left(\dfrac{7+(-1)}{2},\dfrac{3+2}{2}\right)[/tex]
[tex]\implies \textsf{Midpoint}=\left(3,\dfrac{5}{2}\right)[/tex]
Midpoint
(-1+7/2,2+3/2(6/2,5/2)3,5/2)Pam asks you to help with the catering for the funeral. You decide to use juice concentrate to serve as a refreshing drink. To create this delicious drink, you must dilute the concentrate in the ratio 1:4. You have 2 litres of concentrate. What is the volume of water needed?
In the figure shown below, AC is parallel to DE with transversal BF
Determine the values of x and y
PLEASE SHOW WORK FOR THIS!
x=_______
y=_______
Answer:
X = 142°Y = 38°Given - AC is parallel to DE
angle 3y + 28 = angle X ( Vertically opposite angles are equal).
3y + 28 = X
X + Y = 180° ( supplementary angles).
3y - X = (-28)
Solving both the equation we get
multiply eq 1 with 3
3x + 3y = 540
-X + 3y = (-28)
subtracting
4x = 568
x = 142°
3y + 28 = 142
3y = 142 - 28
3y = 114
y = 38°
Y=3x-7 complete the missing value in the solution to the equation (1,
Answer: (1, -4) or y = -4
Step-by-step explanation:
Given:
y = 3x - 7
Plug in the value of 1 for x - given to us by "(1, ?)
y = 3x - 7
y = 3(1) - 7
Multiply:
y = 3 - 7
Subtract:
y = -4
y = -4
Using the Addition Method, solve for y in the following system of linear equations: 4x – 2y = 6 2x + y = 7
Answer:
y = 2
Step-by-step explanation:
Addition Method:
4x - 2y = 6
2x + y = 7
-2(2x + y) = -2(7)
4x - 2y = 6
-4x - 2y = -14
-4y = -8
y = 2
Substitution Method:
4x - 2y = 6
2x + y = 7
-2y = 6 - 4x
2y = 4x - 6
y = 2x - 3
2x + (2x - 3) = 7
4x - 3 = 7
4x = 10
x = 2.5
2(2.5) + y = 7
5 + y = 7
y = 2
Brainliest, please :)
Hassan used the iterative process to locate StartRoot 0.15 EndRoot on the number line.
A number line going from 0 to 0.9 in increments of 0.1. A point is between 0.4 and 0.5.
Which best describes Hassan’s estimation?
Hassan is correct because StartRoot 0.15 EndRoot almost-equals 0.4
Hassan is correct because the point is on the middle of the number line.
Hassan is incorrect because StartRoot 0.15 EndRoot is less than 0.4.
Hassan is incorrect because the point should be located between 0.1 and 0.2
Hassan is incorrect because √0.15 is less than 0.4, and the value of √0.15 is 0.3872 option third is correct.
What is the iteration method?Iteration is the process of repeating a procedure in order to produce a series of results.
We have:
= √0.15
[tex]= \rm \sqrt{{\dfrac{15}{100}}}[/tex]
[tex]= \rm \sqrt{{\dfrac{3}{20}}}[/tex]
= (1.732)/(4.472)
= 0.3872
√0.15 is less than 0.4.
Thus, Hassan is incorrect because √0.15 is less than 0.4, and the value of √0.15 is 0.3872 option third is correct.
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Answer:
C
Step-by-step explanation:
