The runner completes a 10 miles race in 16 minutes.
According to the question we have been given that,
Runner takes 8 minutes to complete = 5 miles race
We need to find that if the runner is in the same pace then how many miles the runner completes in 16 minutes
This multi-step problem can be solved using the unitary method. That is,
8 minutes = 5 miles
1 minute = 5/8 miles
16 minutes = 5/8*16 miles
= 5*2 miles
= 10 miles
Hence runner completes a 10miles race in 16 minutes
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1/16 x cubed root of 2
Answer:
0.07874506561 or 0.07875
Step-by-step explanation:
cubed root of 2 = 1.25992104989
or 1.260
what is 345x65 how do you should it
Answer: 22425
Step-by-step explanation: hope this helps!!
Answer:
22425
Step-by-step explanation:
a certain book has 396 pages the student has already read 3/8 of the pages and now picks up the book again at time x=0 minutes write the equation that describes the total number of pages of the book read as a function of the number of minutes of further reading. Approximately how much time,in mintues,Will it take to finish reading the book?
The equation that describes the total number of pages of the book read as a function of the number of minutes of further reading is; 2.67x minutes.
The time it will take to finish the whole 396 pages is; 113.3 minutes
How to solve Algebra Word Problems?We are told that the book has 396 pages. Now, the student has read 3/8 of this book.
Thus, number of pages the student has read so far = 3/8 * 396 = 148.5 pages
Now, let the time spent reading these 148.5 pages be x minutes. Thus;
Number of pages read per minute = 148.5/x pages per minute
Number of pages left to finish book = 396 - 148.5 = 247.5 pages
Thus, time to finish remaining pages = 247.5/(149.8/x ) = 1.67x
Thus, time it will take to finish the whole 396 pages = 1.67x + x = 2.67x minutes
The table showing the amount of pages that can be read for specific minutes is attached.
We see that 7 pages are read in two minutes. Thus;
x = (148.5 * 2)/7 = 42.42857 minutes
Thus, time to finish whole book = 2.67 * 42.42857 ≈ 113.3 minutes
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2x-6(x- 3)≥5 solve for x
Answer:
[tex]x \leq \dfrac{13}{4}[/tex]
Step-by-step explanation:
Given inequality:
[tex]2x-6(x-3)\geq 5[/tex]
Expand -6(x - 3):
[tex]\implies 2x-6(x)-6(-3)\geq 5[/tex]
[tex]\implies 2x-6x+18\geq 5[/tex]
Combine like terms 2x - 6x = -4x:
[tex]\implies -4x+18\geq 5[/tex]
Subtract 18 from both sides:
[tex]\implies -4x+18-18\geq 5-18[/tex]
[tex]\implies -4x\geq -13[/tex]
Divide both sides by -1, remembering to reverse the inequality:
[tex]\implies\dfrac{ -4x}{-1}\geq \dfrac{-13}{-1}[/tex]
[tex]\implies 4x\leq 13[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4x}{4}\leq \dfrac{13}{4}[/tex]
[tex]\implies x \leq \dfrac{13}{4}[/tex]
100%
Tia left at 4:30 p.m. to drive to school. It took her 25 minutes to drive there.
What time did Tia get to school? Move numbers to the clock to show the time.
Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 25,50,75,100, ........
The sequence is an arithmetic sequence with d = 25 and the next two terms are 125, 150.
Suppose we are given a sequence: a1, a2, a3, a4, ...
To determine whether the sequence is an arithmetic, geometric, or uncategorized one, we need to check the relation between its consecutive terms.
Arithmetic sequence.
If:
a2 - a1 = a3 - a2 = a4 - a3 = constant
then the given sequence is an arithmetic sequence. Furthermore, the constant d = a2 - a1 is usually called the common difference.
Geometric sequence.
If:
a2/a1 = a3/a2 = a4/a3 = constant
then the given sequence is a geometric sequence. Furthermore, the constant r = a2/a1 is usually called the common ratio.
The given sequence is:
25,50,75,100, ........
Let us check the difference:
50 - 25 = 75 - 50 = 100 - 75 = 25.
We can, then, conclude that the sequence is an arithmetic sequence with d = 25.
To find the next two terms, add 25 to every last terms.
100 + 25 = 125
125 + 25 = 150
Hence the next two terms are: 125, 150.
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Determine whether y varies directly with x . If so, find the constant of variation.
y=12 x
The constant of variation in y = (12) x is (12)
y = kx (Where k is the constant)
Here,
⇒ y = (12) x
So, k = (12)
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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A dump truck brought 1⁄3 of a ton of rock on the first trip, 1⁄2 of a ton on the second trip, but on the third trip, had to take back 4⁄5 of a ton. What was the total weight of the rock left at the construction site?
Answer:
1/30 of a ton of the rock was left at the construction site
Hope this helps :)
Explanation below.
Step-by-step explanation:
1. Make the same denominators to add them which is 6 (LCM).
1/3 + 1/2
2/3 + 3/6 = 5/6
2. Make the same denominator to subtract them since had to take back 4/5 of a ton. 30 would be the Least Common Multiple of 6 and 5.
5/6 - 4/5
25/30 - 24/30 = 1/30
(25 points) Please help me I'm stuck on these 3 questions.
[tex] \bf\bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}[/tex]
Step-by-step explanation:[tex] \bf \longrightarrow \bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( - \frac{4 \times 3 + 1}{4} d + \frac{3}{5} \bigg ) - \bigg(\frac{8 \times 2 + 7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow\bigg( \frac{ - 13}{4}d + \frac{3}{5} \bigg) - \bigg( \frac{23}{8}d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \frac{ - 13}{4}d + \frac{3}{5} + \frac{ - 23}{8} d + \frac{ - 7}{10} [/tex]
[tex] \bf \longrightarrow \bigg( \frac{ - 13}{4}d + \frac{ - 23}{8}d \bigg) + \bigg( \frac{3}{5} + \frac{ - 7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( \frac{(2 \times - 13) + (1 \times - 23) }{8}d \bigg) + \bigg( \frac{(2 \times 3) + (1 \times - 7)}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( \frac{ (- 26) + ( - 23)}{8}d \bigg) + \bigg( \frac{(6) + ( - 7)}{10} \bigg) [/tex]
[tex] \bf \longrightarrow\bigg( \frac{ - 26 - 23}{8} d\bigg) + \bigg( \frac{6 - 7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow\frac{ - 49}{8}d + \frac{ - 1}{10} [/tex]
[tex] \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}[/tex]
4) Which expression is equal to[tex] \bf\bigg( - 2 \frac{1}{2} n + \frac{1}{4} \bigg) + \bigg(3 \frac{3}{4} n - \frac{5}{8} \bigg)[/tex]
[tex] \bf \longrightarrow \boxed{\frac{5}{4}n - \frac{3}{8} } \: {\underline{\underline{ans}}}[/tex]
5) Which expression is equal to[tex] \bf\frac{1}{5}(3x + 10) - \frac{11}{15}x[/tex]
[tex] \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}[/tex]
Step-by-step explanation:[tex] \bf\longrightarrow\frac{1}{5}(3x + 10) - \frac{11}{15}x[/tex]
[tex] \bf\longrightarrow\frac{1}{5}(3x) + \frac{1}{5}(10) + \frac{-11}{15}x[/tex]
[tex] \bf\longrightarrow\frac{3}{5}x + 2 + \frac{-11}{15}x[/tex]
[tex] \bf\longrightarrow\bigg(\frac{3}{5}x + \frac{-11}{15}x\bigg) + 2[/tex]
[tex] \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}[/tex]
The equations of four lines are given. Identify which lines are parallel.
Line 1: y=1/2x−6
Line 2: x−2y=−1
Line 3: y=4x+6
Line 4: y+3=1/4(x−6)
Answer:
Line 1 and Line 2 are parallel.
Type the missing number in this sequence:
-1, -3, -9, ___,
-81
Answer:
-27
there is a pattern of x3 every time :)
3. If the ratio of yellow pigment to blue pigment in a shade of green paint is 2:3, how many
drops of yellow pigment will be needed if 12 drops of blue are used?
Drops of yellow pigment is 8.
A ratio is a comparison of two identical values that makes it simple to compare them. This is how a fraction with a numerator and denominator comparison is expressed. Depending on the ratio formula employed in various parts of mathematical computation, the definitions of the numerator and denominator may change.
For a certain shade of green, y = yellow and b = blue, where y/b = 2/3.
How many yellow drips are needed if there are 12 drops of blue,
y/b = 2/3 = x/12
= 2 × 12 = 3 × x
= 24 = 3x
= 24/3 = x
= x = 8
If you have 12 droplets of blue, you will need 8 drops of yellow.
y/b = 2/3
y = 2/3 × b
Substituting the value b = 12
y = 2/3 × 12
y = 24/3 = 8
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Which of the following is equal to 7^1/4?
A. 4√7
B.√7.4
C. 7^4
D. √7
Answer:
[tex] {7}^{ \frac{1}{4} } = \sqrt[4]{7} [/tex]
The correct answer is A.
What is the average rate of change, please simplify your answer (PICTURE BELOW)
Answer:
[tex]{ \tt{average \: \triangle = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ [/tex]
x1 is -1; y1 is -3 [from graph (-1, -3)]x2 is 3; y2 is 5 [from graph (3, 5)][tex]{ \tt{ = \frac{5 - ( - 3)}{3 - ( - 1)} }} \\ \\ = { \tt{ \frac{8}{4} }} \\ \\ = 2[/tex]
What is the vertex of the following function?
y=4|x|+1
(4,-1)
(0,1)
(4,1)
(-4,1)
Answer:
(0,1)
Step-by-step explanation:
|x| is minimized when x=0, meaning the vertex is at (0,1).
Write a unit for:25 pounds in 10 weeks
The unit is 2.5 Pounds per week.
What is a unit?A unit of measurement is a definite magnitude of a quantity that is defined and adopted by convention or law and is used as a standard for measuring the same type of quantity. Any other such quantity can be expressed as a multiple of the unit of measurement. A length, for example, is a physical quantity.So, this is a fraction of 25 Pounds in 10 Weeks.
We want a unit rate with a denominator of one, so we divide the top and bottom by ten.
= 25 Pounds ÷ 10 Weeks= 2.5 Pounds ÷ 1 Week = 2.5 Pounds per weekTherefore, the unit is 2.5 Pounds per week.
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What are the solutions of the following systems? Explain.
b. 4x+y = 6 12x + 3y = 18
The red snake is 12 inches long. It is 3 times as long as the green snake. Let n represent the green snake. Which number sentence below will solve for n?
A 3x6 inches = 18 inches
B 12 inches x 3 = 36 inches
C 12 inches divided 3= 4 inches
D 12 inches divided 4 = 3 inches
Answer: Your answer would be C.
Step-by-step explanation:
4 x 3 is 12 so, if you divide the 12 by 3 you will get 4 making C your answer.
Currently, you have $80 and your sister has $145. You decide to save six dollars per week of your allowance. Your sister decides to spend her whole allowance plus seven dollars each week. How many weeks will it take for you to have as much money as your sister? Please include an equation.
Answer:
It will take you nearly 11 weeks
Step-by-step explanation:
80+6x = 145
6x = 145-80
6x = 65
x = 65/6 (weeks)
A car gets miles per gallon of gas. It travels for 45 minutes at miles per hour. How many gallons of gas does the car use during that time? Show your work using units and Giant Ones.
Answer:
A car gets 25 miles per gallon of gas. It travels for.45 minutes at 65 miles per hour. How many gallons of gas does the car use during that time?
Answer:
25 miles per gallon of gas
travels 45 minutes and 65 miles per hour
Step-by-step explanation:
Find each measure.
m∠ JLK
The measure of the major arc JLK will be 206°. Then the correct option is B.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
The measure of the minor arc JK will be 154°.
Then the sum of the major arc and minor arc in a circle is 360°.
Then the major arc JLK will be given as,
JLK + JK = 360°
JLK + 154° = 360°
JLK = 206°
The measure of the major arc JLK will be 206°. Then the correct option is B.
Your question was incomplete, but the complete question was attached below.
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Find the length of a segment with endpoint coordinates (2,3) and (8,11)
Answer:
The length is 10.
Step-by-step explanation:
[tex] \sqrt{ {(8 - 2)}^{2} + {(11 - 3)}^{2} } [/tex]
[tex] \sqrt{ {6}^{2} + {8}^{2} } = \sqrt{100} = 10[/tex]
Write each equation in slope-intercept form. x-2 y+3=1
The slope - intercept form of the equation x-2 y+3=1 is y = x/2 + 1 .
What is slope - intercept form?Simply said, the slope-intercept form is the technique to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.
The slope - intercept form is y = mx + c
The given equation is
x-2 y+3=1
Subtract 3 from both sides,
x - 2y = -2
Divide the whole equation by 2
x/2 - y = -1
Rearrange the equation -
y = x/2 + 1
So the equation in slope-intercept form is y = x/2 + 1 , where slope is 1/2 and c = 1.
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Down
Round...
1. 24.263 to the nearest tenth.
3. 341.276 to the nearest hundredth.
5. 299.61 to the nearest whole number.
6. 4,123.499 to the nearest whole number.
7. 5.246 to the nearest hundredth.
Name the property of real numbers illustrated by the equation. -(a-b) = (-1)(a-b)
The equation -(a-b) = (-1)(a-b) has used the property of real numbers is Distributive Property.
Property of Real numbers:
A real number is a value that represents a quantity along a continuous number line. Real numbers can be ordered.
The properties of real numbers are,
Commutative propertyAssociative propertyDistributive propertyIdentity propertyGiven,
The equation is
-(a-b) = (-1)(a-b)
Now we have to find the property used here.
Based on the properties of real number,
The one that exactly matches the equation is Distributive property.
Because the definition of Distributive property is explained through the following,
For three numbers m, n, and r, which are real in nature, the distributive property is represented as:
m (n + r) = mn + mr
The same will be applied in the given equation also.
Therefore, the Distributive property is used in the equation.
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ABCD is a rectangle. The length of AC is 4x-8, and the length of BD is 2x+10. What is the length of one of its diagonals?
Answer:
28 units
Step-by-step explanation:
• the diagonals of a rectangle are congruent , then
AC = BD , that is
4x - 8 = 2x + 10 ( subtract 2x from both sides )
2x - 8 = 10 ( add 8 to both sides )
2x = 18 ( divide both sides by 2 )
x = 9
Then
BD = 2x + 10 = 2(9) + 10 = 18 + 10 = 28
the diagonals are 28 units long
What is the equation of the line that passes through the point (4,-3) and has slope 1/2 ?
F. y= (1/2)x+3
G. y= (1/2)x-1
H. y= (1/2)x-5
I. y=x-(1/2)
The equation of the line passing through the point (4 , -3) and has a slope of 1/2 is H. y = (1/2)x - 5.
The equation of a line can be expressed in different forms: standard form, slope-intercept form, and point-slope form
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Given the slope of 1/2 and a point (4 , -3), use the point-slope form to generate the equation of the line by plugging in the values in the equation.
(y - y1) = m(x - x1)
y - -3 = 1/2(x - 4)
y + 3 = (1/2)x - 2
Isolating the variable y in the left side,
y + 3 = (1/2)x - 2
y = (1/2)x - 2 - 3
y = (1/2)x - 5
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Write the first four terms of an arithmetic sequence with a common difference of 3 and a third term of 10 . Then write both a recursive definition and an explicit formula for this sequence.
The first fur terms of an arithmetic sequence are 4, 7, 10, 13
What is a arithmetic sequence?
It is a series of numbers where the gap between succeeding phrases is always the same. for instance, 5, 7, 9, 11, 13, and 15. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
Given, common difference = 3
third term = 10
formula of arithmetic sequence is an = a + (n-1)d
a3 = a + (3-1)3
10 = a + 6
a = 4
a1 = 4
a2 = a + (n-1)d
a2 = 4 + (1)3
a2 = 7
a4 = a + 3d
a4 = 4 + 3.3
a4 = 13
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1, Find the difference
63-93
2, Find the difference
-4-5
3, Find the difference
-156-(-45)
Answer:
63-93=-30
-4-5=-9
-156-(-45)=-111
Step-by-step explanation:
63-93=-30
-4-5=-9
-156-(-45)=-156+45=-111
Hope this helps!
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Have a great day!
How much more would $10,000 earn in 3 years compounded daily at 1.33%, than compounded semi-annually at 4.33%? Show formulas used
Answer:
Step-by
You have to determine how much more would $10,000 earn in 3 years compounded daily at 1.33% than compounded semiannually at 4.33%.
The first step is to calculate the final amount for both options. To do so, you have to use the following formula:
Where
A is the accrued amount
P is the principal amount
r is the interest rate expressed as a decimal value
t is the time in years
n is the number of compounding periods per year.
→ First, find the accrued amount for P=$10,000, R=1.33%, and t=3 years.
The account compounds daily,
