The unit rate for 4543.08 km in 52.4 hours is 86.7 km.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
4543.08 km = 52.4 hours
Divide 52.4 into both sides.
86.7 km = 1 hour
Thus,
The unit rate is 86.7 km.
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Which expression is equivalent to (ab6)4?
a4b24
ab24
a5b10
ab28
Answer:
a^4b^24
Step-by-step explanation:
We know, (xy)^n = x^ny^n. So,
(ab^6)^4 = a^4b^(6×4)
= a^4b^24
What is 10/83 simplified
Answer:
5/19
Step-by-step explanation:
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answer: To solve a quadratic equation of the form ax^2 + bx + c = 0, there are several steps that Inga could use. Here are three options:
She could complete the square to rewrite the equation in the form (x + p)^2 = q.
She could use the quadratic formula: x = (-b +/- √(b^2 - 4ac)) / (2a).
She could factor the equation to rewrite it in the form (x + r)(x + s) = 0.
Option 1: Completing the square
To complete the square, Inga could add and subtract (b/2)^2 to the equation to get:
a(x^2 + bx + (b/2)^2) - (b/2)^2 = 0
Then, she could rewrite the equation in the form:
a(x + (b/2))^2 = (b/2)^2
Option 2: Using the quadratic formula
To use the quadratic formula, Inga could substitute the values of a, b, and c into the formula to get:
x = (-12 +/- √(12^2 - 4 * 2 * -3)) / (2 * 2)
= (-12 +/- √(144 + 24)) / 4
= (-
Step-by-step explanation:
There are t counters in a box.
Write an expression for the total number of counters.
Answer: 4t
Step-by-step explanation:
You just do t times the amount of boxes you have, which is 4. So you have 4 times t, but in algebra, we don't write the multiplication sign. So the expression would be written as 4t. Yw!
Also please tell me if I was unhelpful/incorrect, thanks!
what is 1+2+3+4+...+1000?
Answer:
[tex]S_{1000}=500500[/tex]
Step-by-step explanation:
[tex]\displaystyle S_n=\frac{n(a_1+a_n)}{2}=\frac{1000(1+1000)}{2}=500*1001=500500[/tex]
3b. There is a line of bushes that grows along one side of Babajide's
backyard. He decides he doesn't need to buy fence for that side since there
are already bushes there. Based on that information, could you decide how
much total fencing Babajide needs? Explain why or why not.
On solving the provided question, we can say that we can assume that it is a rectangular backyard. Since no dimensions are provided therefore, neither volume nor area can be calculated.
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
here,
we can assume that it is a rectangular backyard.
since no dimensions are provided therefore, neither volume nor area can be calculated.
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A line passes through the point (4,-7) and has a slope of -1/2.
Click “show your work” below and show work to write the equation of the line in point-slope form.
Answer:
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
Slope "m"
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~
( 4 , - 7 )
m = [tex]-\frac{1}{2}[/tex]
y - ( - 7 ) = [tex]-\frac{1}{2}[/tex] ( x - 4 )
y + 7 = [tex]-\frac{1}{2}[/tex] ( x - 4 )
T:
Change each denominator to the given denominator. Check if the domain changed.
If yes, state the changes.
12
y = x
x-y
to a denominator of x - y
The domain of the expression
The new expression is -12/(x - y) and the domain is x ≠ y
How to change the denominator?From the question, we have the following parameters that can be used in our computation:
12/(y - x)
Multiply the fraction by 1
So, we have the following representation
12/(y - x) * 1
Express 1 as -1/-1
This gives
12/(y - x) * -1/-1
So, we have
-12/(x - y)
It should be noted that the domain remains the same
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Two cards are drawn at random from a well shuffled pack of cards. What is the probability that
i)both are spades or both are diamonds?
ii)both are queens or both are red coloured?
iii)both are diamonds or neither is a king?
Answer:
Step-by-step explanation:
1 in a tenth of a million. I did the math with all the cards and how many are kinds diamonds or red or queens yk.
The following equations define a system. −2x + y = 10 x + 2y = 5 Which graph represents the system? The graph shows a line that passes through negative 5 comma 0 and 0 comma 2.5. There is a second line that passes through 0 comma 10 and 5 comma 0. The lines intersect at 3 comma 4. The graph shows a line that passes through negative 5 comma 0 and 0 comma 10. There is a second line that passes through 0 comma 2.5 and 5 comma 0. The lines intersect at negative 3 comma 4. The graph shows a line that passes through negative 5 comma 0 and 0 comma negative 2.5. There is a second line that passes through 0 comma negative 10 and 5 comma 0. The lines intersect at 3 comma negative 4. The graph shows a line that passes through negative 5 comma 0 and 0 comma negative 10. There is a second line that passes through 0 comma negative 2.5 and 5 comma 0. The lines intersect at negative 3 comma negative 4.
The graph of the system of linear equations is attached with the answer.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the system of linear equations as given -
- 2x + y = 10
x + 2y = 5
The given system of linear equations is -
- 2x + y = 10
x + 2y = 5
Refer to the graph of the system of linear functions attached. The point (-3, 4) is the solution set of this system of equation.
Therefore, the graph of the system of linear equations is attached with the answer.
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Select the correct answer. What is this equation rewritten in exponential form? log7 343 = 3 A. 37 = 343 B. 73 = 343 C. 343x = 7 D. 343x = 3
The solution to the equation log₇343 = 3 is 7³ = 343
What is an equation?An equation is used to show the relationship between numbers and variables.
The logarithm can be defined as the exponent that raises a base to get a particular number. The law of logarithm states:
logₓm = n is the same as xⁿ = m
Given the equation:
log₇343 = 3
Applying the law of logarithm gives:
7³ = 343
The solution to the equation is 7³ = 343
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PLSS GUYS HELP MEEEEEEEE PLS
The value of x is 10°.
What is a measure of an angle?
Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.
Here, we have
The measure of ∠AOC is 90°.
3x° + 46° +14° = 90°
3*10° + 46 + 14° = 90°
Hence, the value of x is 10.
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The value of x is 10°.
What is a measure of an angle?Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.
What is angle?An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex.
Here, we have
The measure of ∠AOC is 90°.
3x° + 46° +14° = 90°
3*10° + 46 + 14° = 90°
Hence, the value of x is 10.
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A bike shop purchased 12 mountain bikes wholesale for $ 189 . They want to make a 25 % on each bike. What is the sale price of the mountain bike after markup?
The cost of the Bike wholesale after the markup is $236.25
How to determine the cost after the markupFrom the question, we have the following parameters that can be used in our computation:
Bike wholesale = $189
Markup = 25%
The cost of the bike wholesale after the markup is then calculated as
Cost = Bike wholesale * (1 + markup)
Substitute the known values in the above equation, so, we have the following representation
Cost = 189 * (1 + 25%)
Evaluate the products
Cost = 236.25
Hence, the cost is $236.25
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Determine the perimeter of the right triangle shown.
24 units
10 units
8 units
6 units
Answer:
A) 24 units----------------------------------
Find the legs first:
5 - (-3) = 8 units,4 - (-2) = 6 units.Find the hypotenuse using Pythagorean:
[tex]\sqrt{8^2+6^2} =\sqrt{64+36} =\sqrt{100} =10\ units[/tex]Find the perimeter:
P = 8 + 6 + 10 = 24 unitsCorrect choice is A.
Answer:
A) 24 units
Step-by-step explanation:
The perimeter of a triangle is the sum of its side lengths.
From inspection of the given right triangle:
Base = 8 unitsHeight = 6 unitsAs the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the length of the hypotenuse:
[tex]\implies c^2=a^2+b^2[/tex]
[tex]\implies c^2=8^2+6^2[/tex]
[tex]\implies c^2=64+36[/tex]
[tex]\implies c^2=100[/tex]
[tex]\implies c=\sqrt{100}[/tex]
[tex]\implies c=10[/tex]
Therefore, the perimeter of the given triangle is:
[tex]\implies 8+6+10=24 \; \rm units[/tex]
Simplify each expression (I don't know this) please help me out
Answer: solve the same variables
Step-by-step explanation:
1. 3y + 4.1
2. 4x +
3. 5x + 22½
4. 4y²
5. + 25
6. 0
A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses 1 2/3 pounds of gravel. For each pound of gravel, he uses 2/5 pound of cement. He is making enough concrete that he needs to use 3 pounds of sand. How many pounds of cement does he use? PLEASE HELP DUE NOW !! TYYY
A. 1 pound
B. 1 4/15 pounds
C. 2 pounds
D. 2 1/15 pounds
Answer:
C
Step-by-step explanation:
1 pound sand for 1 2/3 pounds gravel.
1 pound gravel for 2/5 pound cement.
3 pounds sand = 3× 1 2/3 = 3 6/3 = 3+2 =
= 5 pounds gravel.
5 pounds gravel = 5 × 2/5 = 2 pounds of cement
a book cost $36 is on 25% discount sale how much does the customer needs to pay for the discounted book
Given,
The cost of the book is $36 There is a 25% discount on all itemTo Find : Amount the customer needs to pay for the discounted book
In order to convert Discount % to Discount we use the formula
[tex]D = \frac{25}{100} X36\\D = 9[/tex]
SP = 36 - 9
SP = $27
PLEASE FAST
Solve the equation for t.
4(t – 2.9) ≥ 3.6
t ≥ 17.3
t ≥ 11.5
t ≥ 3.8
t ≥ 1.6
Answer:3.8
Step-by-step explanation:
Is 1 1/3 an irrational number?
Pls help! Step by step
Answer:
x = 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 6[tex]\sqrt{2}[/tex]
This is the exact value for x. It may be rounded if you wish
Answer:
[tex]x=6\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the given right triangle:
θ = 45°A = 6H = xSubstitute the given values into the cosine trigonometric ratio and solve for x:
[tex]\implies \cos(45^{\circ})=\dfrac{6}{x}[/tex]
[tex]\implies \dfrac{\sqrt{2}}{2}=\dfrac{6}{x}[/tex]
[tex]\implies x\sqrt{2}=6 \cdot 2[/tex]
[tex]\implies x\sqrt{2}=12[/tex]
[tex]\implies x=\dfrac{12}{\sqrt{2}}[/tex]
[tex]\implies x=\dfrac{12}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\implies x=\dfrac{12\sqrt{2}}{2}[/tex]
[tex]\implies x=6\sqrt{2}[/tex]
AMERICA EATS 350 PIZZA SLICES EVERY SECOND HOW MANY DO THEY EAT IN HALF IN HOUR
630,000
Step-by-step explanation:
350x60=21,000
21,000x30=630,000
Before hibernation, a bear weighs 990 pounds. Its weight decreases
by 32% during hibernation. How much does the bear weigh when
it comes out of hibernation? Show your work.
Answer:316.8
Step-by-step explanation:
Answer:316.8
Step-by-step explanation:
In a week, an airline operates a flight from San Francisco to New York once a day. The total travel times for this week are:
Sunday: 343 min.
Monday: 314 min.
Tuesday: 401 min.
Wednesday: 341 min.
Thursday: 359 min.
Friday: 407 min.
Saturday: 378 min.
What was the range of flight times for the route that week?
a. 66 min
b. 93 min
c. 29 min
d. 87 min
Answer:
To find the range of flight times, you need to find the difference between the shortest and longest flight times. The shortest flight time was on Monday at 314 minutes, and the longest flight time was on Friday at 407 minutes. The range is 407 - 314 = 93 minutes. The correct answer is therefore (b) 93 min.
Step-by-step explanation:
A factory that makes nails uses 675 inches of metal to make 450 nails. At this rate, how many inches of metal is needed to make 1 nail?
Answer:1.5 inches
Step-by-step explanation:
find the volume of the cylinder. use 3.14 for π. 5ft 10ft (10 is the radius) PLS HELP :(
Answer:
157[tex]ft^{3}[/tex]
Step-by-step explanation:
Volume = the area of the base times the height.
Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]
a = [tex]\pi[/tex][tex](5^{2})[/tex] I am going to use 3.14 for [tex]\pi[/tex]
a = 3.14(25)
a = 15.7
Volume = 15.7 x 10 = 157
Answer:
785 ft२
Step-by-step explanation:
volume =3.13*5२*10
=3.14*25*10
=785 ft२
3 increased by a
number times 2
factorisé x2 + 14x +49
The expression is factorized to give (x + 7) and (x + 7)
What is factorization?Factorization described a mathematical methods that consists of writing a number or mathematical object as a product of several other factors that are mostly simpler or smaller objects of the same kind.
Given the quadratic equation;
x² + 14x +49
Find the pair factors of 49 that sum up to 14, the numbers are 7 and 7
Now, substitute the numbers in the expression
x² + 7x + 7x + 49
Make into two expressions, we have;
(x² + 7x) + (7x + 49)
factor out the common terms, we get;
x(x + 7)+ 7(x + 7)
Then, we have;
(x + 7)
(x + 7)
Hence, the factorized form is (x + 7) and (x + 7)
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How do I solve this system of equations using the elimination method.(I don't just want the answer, I want an explanation on how to get the answer.)
y=3x+13
2x=y-9
Answer:
y=3x+13
2x=y-9
Step-by-step explanation:
i need to know :(
Answer:
Step-by-step explanation:
Substitute 1 in 2 and solve for x.
2x=y-9
2x=3x+13-9
2x = 3x+4
-x = 4
x = -4
Then use equation 1 to solve for x.
y = 3x+13
y = -12+13
y= 1
Benjamin and Felix are 35 miles apart. At 3:00pm they start jogging towards each other. Benjamin jogs at a pace of 16 minutes per mile. Felix jogs at a pace of 10 minutes per mile. how many miles will Benjamin jog in 45 minutes
Using division operation, since Benjamin jogs at a pace of 16 minutes per mile, in 45 minutes he will jog 2.8 miles.
What is the division operation?The division operation is one of the basic mathematical operations, including addition, subtraction, and multiplication.
The division operation involves dividing the dividend (the numerator) by the divisor (the denominator) to obtain the quotient (the result).
The distance between Benjamin and Felix = 35 miles
Benjamin's jogging pace or speed = 16 minutes per mile
Felix's jogging pace or speed = 10 minutes per mile
The number of miles that Benjamin can jog in 45 minutes = Time/Speed
= 2.8125 miles (45/16)
Thus, Benjamin will jog 2.8 miles in 45 minutes.
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hey could anyone solve this for me and make sure its correct
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, let's use those provided
[tex]R(\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad S(\stackrel{x_2}{15}~,~\stackrel{y_2}{31}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{31}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{5}}} \implies \cfrac{ 24 }{ 10 } \implies \cfrac{12 }{ 5 }[/tex]
keeping in mind that perpendicular lines have negative reciprocal slopes
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{12}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{12}} ~\hfill \stackrel{negative~reciprocal}{ {\Large \begin{array}{llll} -\cfrac{5}{12} \end{array}} }}[/tex]
Step-by-step explanation:
the slope of a line is the ratio
y coordinate change / x coordinate change
when going from one point on the line to another.
the perpendicular slope is simply turning that ratio fraction upside down and flips the sign.
(5, 7) to (15, 31)
x changes by +10 (from 5 to 15).
y changes by +24 (from 7 to 31).
the slope (or gradient) is therefore
+24/+10 = 12/5
the perpendicular slope or gradient is then
-5/12