Evaluate the Expression - show your work :)
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A snail crawls at a pace of 3 cm a minute. What is the snail Pace in feet per hours?
On a coordinate grid, point M is at (−8, 2) and point S is at (10, 2). The distance (in units) between points M and S is ______. (Input only whole numbers, such as 2.)
An open area at a local high school is in the shape of a quadrilateral. two sidewalks crisscross this open area as diagonal of the quadrilateral. If the walkways cross at their midpoints and the walkways are equal in length, what is the shape of the open area?
a rectangle
a rhombus
a parallelogram
a trapezoid
On Monday, the office staff at your school paid $8.77 for 4 cups of coffee and 7 bagels. On Wednesday, they paid $15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel? Explain.
what is 87/96 feet in inches
One root of f(x)=x^3-9x^2+26x-24 is x = 2. What are all the roots of the function?
Answer:
Solutions are[tex]x_{1}=4\\x_{2}=2\\ x_{3}=3[/tex]
Step-by-step explanation:
The given expression is
[tex]f(x)=x^{3}-9x^{2} +26x-24[/tex]
First, we need the divisors of the independent term, which is 24.
24 divisors: 1, 2, 3, 4, 6, 8, 12, 24.
Now, we replace each divisor in the function, and those which gives zero as result, those are gonna be the roots of the equation.
For [tex]x=1[/tex]
[tex]f(1)=(1)^{3}-9(1)^{2} +26(1)-24=1-9+26-24=-6[/tex]
This means [tex]x=1[/tex] is not a solution.
For [tex]x=2[/tex]
[tex]f(2)=(2)^{3}-9(2)^{2} +26(2)-24=8-36+52-24=0[/tex]
So, [tex]x=2[/tex] is the first solution.
For [tex]x=3[/tex]
[tex]f(3)=(3)^{3}-9(3)^{2} +26(3)-24=27-81+78-24=0[/tex]
It's solution.
For [tex]x=4[/tex]
[tex]f(4)=(4)^{3}-9(4)^{2} +26(4)-24=64-144+104-24=0[/tex]
Therefore, all roots are
[tex]x_{1}=4\\x_{2}=2\\ x_{3}=3[/tex]
what function is vertically stretched by a factor of 3 and translated 4 units right from the parent function
A. log_(5) (3x+4)
B. 3log_(5) (x-4)
C. 3(5^x+4)
D. 5^3x-4
Final answer:
The correct function is B, 3log_5(x-4), which represents a logarithmic function that is vertically stretched by a factor of 3 and translated 4 units to the right.
Explanation:
The student is asking about transformations of a parent function, specifically a vertical stretch and a horizontal translation. When a function is vertically stretched by a factor of 3, this involves multiplying the function by 3. A translation of 4 units to the right would mean adjusting the input variable x by subtracting 4. Considering the options given, option B, 3log5(x-4), is the correct answer because it represents a function that has been vertically stretched by a factor of 3 and horizontally translated 4 units to the right from its parent function log5x.
Trigonometric Identities and Applications? help
What is 51.875 rounded to the nearest tenth
Suppose your club is selling candles to raise money. It cost $100 to rent a booth from which to sell the candles. If the candles cost your club $1 and are sold for $5 each, how many candles must be sold to equal your expenses?
25 candles
What is profit and loss ?
Profit or Gain = Selling price – Cost Price
Loss = Cost Price – Selling Price
According to the given question,
Candles sold must cover the expenses = 100
Let x be the no. of candles that needs to be sold to cover the expenses
rent = 100
Cost price of 1 candle = CP = 1
Cost price of x candles = CP = 1x
Selling price of 1 candle = SP = 5
Selling price of x candles = SP = 5x
Therefore, from the above statements we can infer that the profit generated must be equal to the expenses,
So, SP - CP = Profit = 100
5x - x = 100
4x = 100
x = 25
Therefore, we need 25 candles that needs to be sold to cover the expenses
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A runner ran 2/3 of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.
a. How long did it take to run the entire race?
b. How many minutes did it take to run 1 kilometer?
Answer:
it take 31.53 minutes to run the entire race
it take 6.3 minutes to run the 1 km
Step-by-step explanation:
A runner ran 2/3 of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.
[tex]\frac{2}{3} \cdot 5= \frac{10}{3}[/tex]
3.33 km is covered in 21 minutes
So 5 km is covered in [tex]\frac{5 \cdot 21}{3.33}=31.53[/tex]minutes
it take 31.53 minutes to run the entire race
[tex] \frac{10}{3}[/tex] km is covered in 21 minutes
1 km is covered in [tex]\frac{21}{\frac{10}{3} } =6.3[/tex]
It takes to run the entire race is 31 minutes and 30 seconds and it takes to run 1 kilometer is 6 minutes and 18 seconds.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
[tex]\rm speed = \dfrac{distance}{time}[/tex]
A runner ran 2/3 of a 5 kilometers race in 21 minutes. They ran the entire race at a constant speed.
2/3 of 5 km is given as x
[tex]x = \dfrac{2}{3}* 5 = \dfrac{10}{3}[/tex]
Then the speed will be
[tex]\rm speed = \dfrac{\frac{10}{3}}{21} = \dfrac{10}{3*21} = \dfrac{10}{63}[/tex]
a. It takes to run the entire race will be
[tex]\rm Time = \dfrac{5}{ \frac{10}{63}} = \dfrac{63* 5 }{10} =31.5[/tex]
It takes to run the entire race is 31 minutes and 30 seconds.
B. It takes to run 1 kilometer will be
[tex]\rm Time = \dfrac{1}{ \frac{10}{63}} = \dfrac{63* 1}{10} = 6.3[/tex]
It takes to run 1 kilometer is 6 minutes and 18 seconds.
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Class records at rockwood college indicate that a student selected at random has probability 0.75 of passing french 101. for the student who passes french 101, the probability is 0.91 that he or she will pass french 102. what is the probability that a student selected at random will pass both french 101 and french 102? (round your answer to three decimal places.)
To get the probability of two individual events both occurring, you have to multiply the probabilities of their individual events occurring. Therefore in this problem, the probability that a student selected at random will pass both French 101 and French 102 is 0.683 (.75 x .91). The answer is already rounded to three decimal places.
The world's smallest gecko is 3/4 inch long. An adult male Western Banded Gecko is 7 1/3 times as long. How long is an adult male Western Banded Gecko
Older Orchards need more hives per acre Caleb has decided to place 6 hives for every 2 acres on an older peach orchard Zeke one of Caleb workers delivery 10 hives to a 30 acre peach orchard did Zeke follow Calebs decision.how does the table prove your answer.
Don't do a table
Cpm/pert graphically displays the scheduling of tasks required to complete a project.
a. True
b. False
Average speed of Car 1 = 55 mph.
Average speed of Car 2 = 70 mph.
Time elapsed between start of Car 1 and start of Car 2 = 4 minutes.
How long before Car 2 overtakes Car 1? __hour(s).
Let p: x = 4 Let q: y = −2 Which represents "If x = 4, then y = −2”? p ∨ q p ∧ q p → q p ↔ q
Answer:
C. p → q
Step-by-step explanation:
We are given that,
'p' is represented by 'x = 4' and 'q' is represented by 'y = -2'.
That is, we have,
p: x = 4
q: y = -2
The given statement is, 'If x = 4, then y = -2'.
This means that whenever x = 4, then y = -2.
That is, 'x = 4 implies y = -2'.
Thus, it will be represented by p → q.
Mae's cat weighs 5 3/8 pounds. What is the weight written as a decimal
?
A wall map has a scale of 128 miles = 6 inches. The distance between Springfield and Lakeview is 2 feet on the map. What is the actual distance between Springfield and Lakeview? Question 4 options: 42.7 miles 1.13 miles 512 miles 384 miles
You are making lemonade for your lemonade stand. Each liter of lemonade you make uses 3.5 tablespoons of lemonade powder, and you have 14 tablespoons of lemonade powder. Can you make 5 liters of lemonade?
Mariah collects 3 spiders each spider has eight legs.Brian gives her 1more spider. how many legs do Mariah's spiders have altogether?
what is the LCM of 6 and 8
Solve this equation: 3x-1/5-2/9x=124/5
Step 1: Simplify by combining like terms. Which terms can be combined?
A) 3x and -1/5
B) -1/5 and -2/9x
C) 3x and -2/9x
Answer:
The correct option is C.
Step-by-step explanation:
The given equation is
[tex]3x-\frac{1}{5}-\frac{2}{9}x=\frac{124}{5}[/tex]
If two terms have the same variables having same powers, then they are known as like terms.
In the given equation [tex]3x[/tex] and [tex]-\frac{2}{9}x[/tex] are like terms.
So, when we simplify the given equation by combining like terms. we need to combined [tex]3x[/tex] and [tex]-\frac{2}{9}x[/tex] .
Therefore the correct option is C.
The solution to the equation is approximately x = 45.48.
To solve the equation 3x - 1/5 - 2/9x = 124/5, to combine like terms. Like terms are terms that have the same variable and exponent.
The terms in the equation are:
3x (coefficient is 3, and the variable is x)
-1/5 (coefficient is -1/5)
-2/9x (coefficient is -2/9, and the variable is x)
Now, let's identify the like terms that combined:
C) 3x and -2/9x
The terms 3x and -2/9x both have the variable x, so they are like terms and can be combined.
Step 1: Combine the like terms:
3x - 2/9x = (3 - 2/9)x = (27/9 - 2/9)x = (25/9)x
Now, after combining the like terms, the equation becomes:
(25/9)x - 1/5 = 124/5
Step 2: Isolate x on one side of the equation. To do this, we can first get rid of the fraction by multiplying the entire equation by the least common multiple (LCM) of the denominators, which is 45 (LCM of 9 and 5):
45 × [(25/9)x - 1/5] = 45 × (124/5)
This simplifies to:
25x - 9 = 1128
Step 3: Now, isolate x by moving the constant term (-9) to the other side of the equation:
25x = 1128 + 9
25x = 1137
Step 4: Finally, divide by 25 to solve for x:
x = 1137 / 25
x ≈ 45.48
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Identify the quadratic term in the function, f(x)=2x^2-3x+5
A high fountain of water is in the center of a circular pool of water. you walk the circumference of the pool and measure it to be 190 meters. you then stand at the edge of the pool and use a protractor to gauge the angle of elevation of the top of the fountain. it is 55°. how high is the fountain?
The height of the fountain is 43.20m
Data;
circumference = 190mangle = 55 degrees.Circumference of a CircleThe circumference of a circle is given as
[tex]c = 2\pi r[/tex]
Let's calculate the radius of the circle
[tex]c=2\pi r\\r=c/2\pi \\r=190/(2*3.14)\\r=30.25m[/tex]
Assuming the radius of the pool makes a right angle triangle with the top of the fountain;
[tex]tan\theta=\frac{opposite}{adjacent}\\tan55=\frac{x}{30.25}\\ x= 30.25tan55\\x=43.20m[/tex]
From the calculations above, the height of the fountain is 43.20m
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You can use a calculator for this question.
Greg builds a new pond which has a volume of 7.35 m3.
It is 4.2 m long and 50 cm deep.
What is the width of the pond? m
There will be a circular patio with a diameter of 7 metres.
Greg is going to put a tiled edge around the patio.
What is the circumference of the patio? m
Circumference of a circle = 2πr
Use π = 3.14
The number of diagonals in any polygon is whole number. But on the other side the formula of the number of diagonals in any convex polygon is in a fraction form \frac{n(n-3)}{2[tex] . How can you explain this?
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)?
y + 5 = x + 2
y − 2 = x − 5
y − 5 = −(x − 2)
y + 2 = −(x + 5)
We are given point (2,5).
We need to find the equation of line perpendicular to the given line and passes through the point (2, 5).
We know point-slope form :
y-y1 = m(x-x1).
Plugging values of (x1,y1) = (2,5) in above slope-intercept form, we get
y - 5 = m(x-2).
Which matches 3rd option y − 5 = −(x − 2).
So, the correct option is y − 5 = −(x − 2).Answer:
The answer is C.
Step-by-step explanation:
A bedroom is 15 ft long and 12 ft wide. How much will it cost to carpet the room if carpeting coats $22 per square foot. (1 yd=3 ft)