Question 8 of 10The diagonal of a TV is 30 inches long. Assuming that this diagonal forms apair of 30-60-90 right triangles, what are the exact length and width of the TV?A. 60 inches by 60/3 inchesB. 15 inches by 15/5 inchesC. 60/2 inches by 600/2 inchesO D. 15.2 inches by 15.2 inches
Answers
The diagram of the triangle formed is shown below
The length is BC and the width is AB
To find BC, we would apply the cosine trigonometric ratio which is expressed as
Cos# = adjacent side /hypotenuse
hypotenuse = AC = 30
adjacent side = BC
# = 30
Thus, we have
[tex]\begin{gathered} \text{Cos}30\text{ = }\frac{BC}{30} \\ \text{Note, Cos30 = }\frac{\sqrt[]{3}}{2} \\ We\text{ have} \\ \frac{\sqrt[]{3}}{2}=\text{ }\frac{BC}{30} \\ 2BC\text{ = 30}\sqrt[]{3} \\ BC\text{ = }\frac{30\sqrt[]{3}}{2} \\ BC\text{ = 15}\sqrt[]{3} \end{gathered}[/tex]To find AB, we would apply the sine trigonometric ratio which is expressed as
Sin# = opposite side /hypotenuse
hypotenuse = AC = 30
opposite side = AB
# = 30
Thus, we have
Sin30 = AB/30
Recall, sin30 = 0.5
Thus,
0.5 = AB/30
AB = 30 * 0,5
AB = 15
Thus, the correct option is B
Related Questions
which e q u a t i o n s the correct
Answers
The given statement is Four less than a number is nine.
Remember that "less than" refers to subtraction. "A number" refers to a variable x. "is" refers to equality. So, the expression would be
[tex]x-4=9[/tex]C is the answer.Choose the greatest multiple of 10 you can multiply by 30 to get close to,
but not go over, 750. Then, write the product.
Answers
Answer:
20, 600
Step-by-step explanation:
[tex]20 \times 30=600 \\ \\ 30 \times 30=900[/tex]
Answer 250 cause 250 is a multiple of 10 times that by 30 is 750
Hi, I am having trouble with this. Could you help? This month a band plays 3 private parties, each of which pays them the same amount. However, the band also has $200 in travel expenses. Taking those expenses into account, they make a total of $2500. The following month, the band has 5 bar gigs and 2 private parties, plus they make an additional $800 (total) by selling merch, and have a total of $350 in travel expenses. With all expenses factored in, they make a total of $4125. How much, on average, is the band payed per bar gig? (assume they are paid the same amount per party this month as they were last month). Write 2 algebra equations then solve.
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We have two cases. The first month, they played in 3 private parties that payed the same. They had a cost of $200 in travel and, in the end, they made $2500. Let "p" be the paid amount of each party. Since there were 3, they were payed 3*p. If we then substract their expenses of $200, we get the final amount, that should be equal to $2500.
In an equation, this is:
[tex]\begin{gathered} 3p-200=2500 \\ 3p=2500+200 \\ 3p=2700 \\ p=\frac{2700}{3} \\ p=900 \end{gathered}[/tex]So, each party payed $900.
In the second month, they worked on 5 bar gigs and 2 private parties. We already know that each private party pays $900, so, if "b" is the average amount they made in each bar gig, then "5b" will be the total they made in bar gigs and, adding the party amount, we have, in the second month:
[tex]5b+2p=5b+2\cdot900=5b+1800[/tex]The had $350 travel expenses, so we need to substract this and we should end up with the total they made, that was $4125:
[tex]\begin{gathered} 5b+1800-350=4125 \\ 5b+1450=4125 \\ 5b=4125-1450 \\ 5b=2675 \\ b=\frac{2675}{5} \\ b=535 \end{gathered}[/tex]Thus, on average, they were payed $535 per bar gig.
Evaluate the piecewise defined function for the given values of x.F(x)= -x -1 for x<-1, -3 for -1≤x<2, √x-2 for x≥2A. f(-3)B. f(-1)C. f(2)D. f(6)
Answers
Answer:
[tex]\begin{gathered} f(-3)=2 \\ f(-1)=-3 \\ f(2)=0 \\ f(6)=2 \end{gathered}[/tex]Explanation:
Given the piecewise defined function;
[tex]f(x)=\mleft\{\begin{aligned}-x-1for\rightarrow x<-1_{} \\ -3\text{for} \\ \sqrt[]{x-2}\text{ for}\rightarrow x\ge2\end{aligned}\mright.\rightarrow-1\leq x<2[/tex]a) f(-3)
we want to find the value of f(x) at x=-3.
-3 is less than -1, so it falls within the interval x<-1.
[tex]\begin{gathered} f(x)=-x-1 \\ f(-3)=-(-3)-1 \\ f(-3)=3-1 \\ f(-3)=2 \end{gathered}[/tex]b) f(-1)
-1 falls with the second interval
[tex]-1\leq x\leq2[/tex]For this interval, f(x) is always equal to -3.
[tex]\begin{gathered} f(x)=-3 \\ f(-1)=-3 \end{gathered}[/tex]c) f(2)
2 falls within the last interval.
[tex]\begin{gathered} f(x)=\sqrt[]{x-2} \\ f(2)=\sqrt[]{2-2} \\ f(2)=0 \end{gathered}[/tex]d) f(6)
6 falls within the last interval.
[tex]\begin{gathered} f(x)=\sqrt[]{x-2} \\ f(6)=\sqrt[]{6-2} \\ f(6)=\sqrt[]{4} \\ f(6)=2 \end{gathered}[/tex]25÷2 3/8 please help
Answers
25÷2 3/8
Let's remember how to convert
[tex]a\frac{b}{c}=\frac{(a\cdot c)+b}{c}[/tex]Step 1
convert
[tex]\begin{gathered} 2\frac{3}{8}=\frac{(2\cdot8)+3}{8} \\ 2\frac{3}{8}=\frac{19}{8} \\ \end{gathered}[/tex]Step 2
now , we have 25 divided by 19/8
[tex]\begin{gathered} 25\text{ divide by 19/8=}\frac{\frac{25}{1}}{\frac{19}{8}} \\ 25\text{ divide by 2 3/8=}\frac{25\cdot8}{19\cdot1}=\frac{200}{19} \\ 25\text{divide by 2 3/8=}\frac{200}{19} \\ \end{gathered}[/tex]so, the answer is 200/19
For the function, determine whether y varies directly with x. If so, find the constant of variation and write the function rule.Select the correct choice below and, if necessary, fill in the answer box within your choice.O A. Yes, y varies directly with x. The constant of variation is k = and the function rule is(Simplify your answers. Use integers or fractions for any numbers in the expression)No, y does not vary directly with x.
Answers
Answer: No, y does not vary directly with x
Explanation:
y varies directly with x when y divided by x is always the same constant. In this case, we get:
x y y/x
2 6 6/2 = 3
4 14 14/4 = 3.5
5 17 17/5 = 3.4
Since 3, 3.5, and 3.4 are distinct, the answer is No, y does not vary directly with x.
4. Ash is three years older than ShawnCrystal is four times as old as Shawn. Oscaris twice as old as Ash. Altogether their agestotal 49. Find each person's age.
Answers
Shawn's age = 5 years
Ash's age = 8 years
Crystal's age = 20 years
Oscar's age = 16 years
Explanations:Let Ash's age be represented by A
Let the Shawn's age be represented as S
Let the Crystal's age be represented as C
Let Oscar's age be represented as O
Ash is three years older than Shawn
A = S + 3.....................(1)
Crystal is 4 times as old as Shawn
C = 4S................................(2)
Oscar is twice as old as Ash
O = 2A.................................(3)
Altogether, their ages total 49
A + S + C + O = 49 ...............(4)
First, to get Oscar's age in terms of Shawn's age, substitute equation (1) into equation (3)
O = 2 ( S + 3)
O = 2S + 6..................(5)
Substitute equations (1), (2), and (5) into equation (4)
(S + 3) + S + (4S) + (2S + 6) = 49
S + S + 4S + 2S + 3 + 6 = 49
8S + 9 = 49
8S = 49 - 9
8S = 40
S = 40 / 8
S = 5
Shawn's age = 5 years
To get Ash's age, substitute the value of S into equation (1)
A = S + 3
A = 5 + 3
A = 8
Ash's age = 8 years
To get Crystal's age, substitute the value of S into equation (2)
C = 4S
C = 4(5)
C = 20
Crystal's age = 20 years
To get Oscar's age, substitute the value of A into equation (3)
O = 2A
O = 2(8)
O = 16
Oscar's age = 16 years
An aquarium is 0.5 feet wide, 1.5 feet tall, and 2 feet long.The bottom is covered with gravel to a height of 3 inches.The tank will be filled with water to 3 inches below the top.How many gallons of water are needed to fill the aquarium?(Use 1 gallon = 0.134 ft.) Ignore any water that might seepinto the layer of gravel. Round to the nearest tenth.
Answers
Step 1: Find the base area of the tank.
The base of the tank is a rectangle of length 2 ft and width 0.5 ft.
Hence,
[tex]\text{ the base area of the tank }=2ft\times0.5ft=1ft^2[/tex]Step 2: Find the height of the water in the tank.
The height of the tank = 1.5ft
the height of the gravel = 3in = 3/12 ft = 1/4 ft
The water is 3 inches (= 1/4 ft) below the top of the tank.
Hence, we must have that
[tex]\begin{gathered} x+\frac{1}{4}+\frac{1}{4}=1.5 \\ x+0.25+0.25=1.5 \\ x+0.5=1.5 \\ x=1.5-0.5=1\text{ ft} \end{gathered}[/tex]Therefore, the height of the water in the tank is 1 ft.
Step 3: Find the volume of the water in the tank
[tex]\begin{gathered} \text{ the volume of the water is given by} \\ V=\text{ base area of the tank }\times\text{ height of the water} \\ \text{ Where V is the volume of the water} \end{gathered}[/tex]Therefore,
[tex]V=1ft^2\times1ft=1ft^3[/tex]Since 1 gallon is equivalengt to 0.134 ft³ then
[tex]V=\frac{1}{0.134}\text{gallons }=7.5\text{ gallons}[/tex]Hence, the number of gallons of water are needed to fill the aquarium is 7.5 gallons.
What type of sequence and how to write the explicit rule.
Answers
The Solution:
Given the sequence below:
[tex]26,18,10,2,\ldots[/tex]We are required to identify the type of sequence and to find the explicit rule for the given sequence.
Step 1:
To determine the type of sequence, we shall run the following check:
[tex]\begin{gathered} a_2-a_1=a_3-a_2\text{ then it is an Arithmetic sequence} \\ \text{ but if} \\ \frac{a_2}{a_1}=\frac{a_3}{a_2}\text{ then it is a Geometric sequence.} \end{gathered}[/tex]So,
[tex]\begin{gathered} 18-26=10-18 \\ -8=-8 \\ \text{ Then it follows that the sequence is an Arithmetic sequence.} \end{gathered}[/tex]Thus, the sequence is an arithmetic sequence.
Step 2:
To find the explicit rule, we shall use the formula below:
[tex]a_n=a_1+(n-1)d[/tex]In this case,
[tex]\begin{gathered} a_1=\text{ first term=26} \\ n=\text{ number of terms=?} \\ d=\text{ co}mmon\text{ difference=18-26=-8} \end{gathered}[/tex]Substituting these values in the formula, we get
[tex]\begin{gathered} a_n=26+(n-1)(-8) \\ a_n=26-8(n-1) \end{gathered}[/tex]Therefore, the explicit rule of the sequence is :
[tex]a_n=26-8(n-1)[/tex]what do you do in the following problem... "Michael is leaning a 12 foot ladder is leaning against the side of a building. The top of the ladder reaches 10 feet up the side of the building. Approximately how far, to the nearest hundredth, is the bottom of the ladder from the base of the building?"
Answers
The distance between the bottom of the ladder to the base of the building = 6.63 feet
Explanations:The height of the ladder, l = 12 feet
Height of the wall covered by the ladder, h = 10 feet
Distance between the base of the building and the bottom of the ladder = x
Using the pythagoras theorem:
[tex]\begin{gathered} (\text{Hypotenuse)}^2=(opposite)^2+(Adjacent)^2 \\ l^2=h^2+x^2 \\ 12^2=10^2+x^2 \\ 144=100+x^2 \\ 144-100=x^2 \\ 44=x^2 \\ \sqrt[]{44}=\text{ x} \\ x\text{ = }6.63 \end{gathered}[/tex]The distance between the bottom of the ladder to the base of the building = 6.63 feet
the graph of the functiony=f(x)+34can be obtained from the graph ofy=f(x)by which following action?shifting the graph f(x) to the left 34 unitsshifting the graph f(x) to the right 34 unitsshifting the graph f(x) downwards 34 units shifting the graph of f(x) upwards 34 units
Answers
Given data:
The given expression is f(x)+34.
The given graph can be obtained by shifting f(x) in the positive direction of y by 34 units.
F(x)=f(x)+34
Thus, the last option is correct.
(2 pts)9. Arielle took a cash advance of $1500. Her new credit card charges a periodic (daily)interest rate of 0.07%.a) How much interest will Arielle pay for the statement for the month of May whichhas 31 days(2 pts)b) What is the balance that she owes?
Answers
Exercise data
$ 1500
Interest rate = 0.07%= 0.07/ 100 = 0.0007
a) How much interest will Arielle pay for the statement for the month of May which
has 31 days?
Simple Interest=P×I×N
where:
P=principle
I=daily interest rate
N=number of days between payments
Interest= 1500 x (0.07/100) x 31 = $ 32.55
another way to write
Interest= 1500 x (0.0007) x 31 = $ 32.55
b)What is the balance that she owes?
Balance = P x ( 1 + I*t) where t= time.
Balance = 1500 x (1 + 0.0007*31)
Balance = 1500 x (1 + 0.217)
Balance = 1500 x (1 .217)
Balance = 1532.55
another way to solve
Balance = P + Interest
Balance = 1500 + 32.55
Balance = 1532.55
A circle has a radius of 20 inches. Find the length of the arc intercepted by a central angle of 45°. Leave answers in terms of π.A. 5π/2 inchesB. 5π inchesC. 5 inchesD. 4π inches
Answers
radius = 20 inches
angle = θ= 45°
We would apply length of an arc:
[tex]length\text{ of an arc = }\frac{\theta}{360\text{ }}\text{ }\times2\pi r[/tex][tex]\begin{gathered} \text{length of the arc = }\frac{45}{360}\times2\times\pi\times20 \\ =\text{ }\frac{1}{8}\times\text{ 40}\pi \end{gathered}[/tex]Since the options is in terms of π, the answer will be in that form
[tex]\text{length of }arc\text{ = 5}\pi\text{ inches (option B)}[/tex]8. Find the volume of a cone with a diameter of 10 meters and a height of 5.1 metersUse - (π = 3.14)
Answers
Answer:
133.45 m^3
Explanation:
Given:
Diameter of the cone (d) = 10 meters
Then the radius(r) of the cone will be d/2 = 10/2 = 5 meters
Height of the cone (h) = 5.1 meters
Pi = 3.14
We'll go ahead and use the below formula to determine the volume of the cone(V);
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ =\frac{1}{3}*3.14*5^2*5.1 \\ =\frac{1}{3}*3.14*25*5.1 \\ =133.45\text{ m}^3 \end{gathered}[/tex]So the volume of the cone is 133.45 m^3
-99G =2 7-759 -6-5 3-4 -9C4 -1-10 013 -7-8 104[G] + 2[C]
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.Explanation:
we are given the following matrices
To compute
[tex]4|G|+2|C|[/tex]We will simply multiply the entries of G by 4 and C by 2
Thus, we will have
The final step will be to add the terms together
Thus, we will have
What is an equation of the line that passes through the point (3,1) and is parallelto the line 4x + 3y=15
Answers
Explanation
two lines are parallel when their slopes are equal,
Step 1
convert the equation to the form
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}[/tex]to easily find m
[tex]\begin{gathered} 4x+3y=15 \\ \text{subtract 4x in both sides} \\ 4x+3y-4x=15-4x \\ 3y=15-4x \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{15}{3}-4x \\ y=-4x+5 \end{gathered}[/tex]Hence
[tex]\begin{gathered} y=-4x+5\Rightarrow y=mx+b \\ m=\text{slope}=-4 \end{gathered}[/tex]Step 2
Now we have this info to find the equation of the line
[tex]\begin{gathered} P1(3,1) \\ m_1=m_2=-4 \end{gathered}[/tex]apply the formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{replacing} \\ y-1=-4(x-3) \\ y-1=-4x+12 \\ \text{add 1 in both sides} \\ y-1+1=-4x+12+1 \\ y=-4x+13 \end{gathered}[/tex]I hope this helps you
What fraction is represented in the picture below?
Answers
1 5/16
Your answer should be above.
Answer:
A
Step-by-step explanation:
3. Identify the zeros of the equation below: 2x^2 + 23 = 14x
Answers
Simplify the equation.
[tex]\begin{gathered} 2x^2+23=14x \\ 2x^2-14x+23=0 \end{gathered}[/tex]Determine the zeros of the equation by using quadratic formula.
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{14\pm\sqrt[\square]{(-14)^2-4\cdot2\cdot23}}{2\cdot2} \\ =\frac{14\pm\sqrt[]{12}}{4} \\ =\frac{2(7\pm\sqrt[]{3})}{4} \\ =\frac{7}{2}\pm\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]THus zeros of the equation is,
[tex]\frac{7}{2}+\frac{\sqrt[]{3}}{2}[/tex]and
[tex]\frac{7}{2}-\frac{\sqrt[]{3}}{2}[/tex]two trains leave the same city at the same time, one going east and the other going west. If one train is traveling at 65 miles per hour and the other at 72 miles per hour, how many hours will it take for them to be 822 miles apart
Answers
The effect of both trains moving in opposite directions is the same that if one of them was stationary and the other one was moving at 65 + 72 = 137 mph.
Now, we know that distance = speed x time. Let's call the distance d and the time y
We would have:
[tex]d=137t[/tex]Using the distance we're given,
[tex]822=137t[/tex]Solving for t :
[tex]\begin{gathered} 822=137t \\ \rightarrow\frac{822}{137}=t \\ \Rightarrow t=6 \end{gathered}[/tex]It would take 6 hours for them to be 822 miles apart .
For triangle XYZ, m∠X = 38°, m∠Y = (5x − 11)°, and m∠Z = (4x − 45)°. Find m∠Y.
m∠Y = 22°
m∠Y = 43°
m∠Y = 99°
m∠Y = 158°
Answers
The measure of angle Y from triangle XYZ is 99°. Therefore, option C is the correct answer.
Given that, in ΔXYZ, m∠X = 38°, m∠Y = (5x - 11)°, and m∠Z = (4x - 45)°.
What is angle sum property of a triangle?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Using angle sum property of triangle, we get
m∠X+m∠Y+m∠Z=180°
⇒ 38°+(5x - 11)°+(4x - 45)°=180°
⇒ 9x+38-11-45=180
⇒ 9x-18=180
⇒ 9x=180+18
⇒ 9x=198
⇒ x=22°
So, m∠Y = (5×22 - 11)°
=110-11
= 99°
The measure of angle Y from triangle XYZ is 99°. Therefore, option C is the correct answer.
To learn more about the angle sum property of a triangle visit:
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The points (2,11) and (6,33) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
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The slope (m) of the line using the given coordinates is 11/2 and the equation of the slope is plotted on the graph.
What do we mean by slope?The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on a straight line, a slope can be determined using a variety of approaches.A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).So, the slope formula is:
m = y₂ - y₁/x₂ - x₁Now, put the values and calculate as follows:
m = 33 - 11/6 - 2m = 22/4m = 11/2So, the slope equation will be:
y = mx + by = 11/2x + bNow, plot the graph of the equation, taking b = 1.
(Refer to the graph attached below)Therefore, the slope (m) of the line using the given coordinates is 11/2 and the equation of the slope is plotted on the graph.
Know more about slopes here:
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A baseball league has ten teams. How many different end-of-the-season ranking first, second, and third place are there.
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Find out the permutation 10P3
[tex]10P3=\frac{10!}{(10-3)!}=720[/tex]The answer is 720Find the equation for the line that passes through the point (-4,1), and that is perpendicular to the line with the equation
Answers
EXPLANATION
Given:
Point ( - 4, 1)
⇒x = -4 and y = 1
Perpendicular equation
3/4 x + y = -5/4
We need to re-write the above equation in the form y = mx + b
y = -3/4 x -5/4
Compare the above with y=mx + b where m is the slope and b is the intercept.
slope(m) = -3/4
Slope of vertical lines are inverse of one another.
This implies that the slpe of our new equation is:
[tex]m=\frac{-1}{m}=\frac{-1}{-\frac{3}{4}}=\frac{4}{3}[/tex]Next, is to find the intercept of the new equation.
We can find this by substituting m = 4/3 , x = -4 and y = 1 into y=mx + b and then solve for b.
That is;
[tex]\begin{gathered} 1=\frac{4}{3}(-4)+b \\ \\ 1=-\frac{16}{3}+b \\ \\ 1+\frac{16}{3}=b \\ \\ b=\frac{3+16}{3} \\ \\ b=\frac{19}{3} \end{gathered}[/tex]We can proceed to form the new equation by simply substituting the values of m and b into y=mx + b
Hence, the equation is:
[tex]y=\frac{4}{3}x+\frac{19}{3}[/tex]11. 9 Reason Abstractly Explain why astudent who runs 3/4 mile in 6 minutes isfaster than a student who runs 1/2 mile in5 minutes.
Answers
hello
to solve this question, need to calculate their speeds and compare
student A ran 3/4 miles in 6 mins
[tex]\text{speed}=\frac{dis\tan ce}{time}[/tex]now we can substitute the values into the equatio
2y = 14xDirect variationk =Not direct variation
Answers
2y = 14x
divide both sides by 2
so,
y = 7x
direct variation and k = 7
Excluding hydropower, U.S. power plants used renewable energy sources to generate 105 million megawatthours of electricity in 2007. By 2012, the amount of electricity generated had increased to 219 million megawatthours. Let x represent the time (in years) since 2007 and let y represent the number of megawatt hours (inmillions).Because time x is defined in years since 2007, 2007 corresponds to x = 0 and 2012 corresponds to x = 5. Fnd therate of change (slope) of the use of renewable energy sources between 2007 and 2012.
Answers
In order to calculate the rate of change, we just need to divide the difference in megawatt hours generated between 2007 and 2012 by the period of 5 years.
So we have that:
[tex]\text{rate}=\frac{219-105}{5}=\frac{114}{5}=22.8[/tex]So the rate of change is 22.8 millions of megawatt hours generated per year.
1. What is the unit price for each detergent? Brand Size (oz) Price ($) Brand A: $ per ounce A 32 4.80 Brand B: $ per ounce B 48 5.76 Brand C: $ per ounce C с 128 17.92 2. Which detergent is the best buy?
Answers
To determine the unit price for each detergent, i.e. the price per ounce, you have to divide the cost of the detergent by the number of ounces the container has.
Detergent A
Has 32 ounces
Costs $4.80
The unit price can be calculated as:
[tex]\frac{4.80}{32}=0.15[/tex]Detergent A costs $0.15/ounce
Detergent B
Has 48 ounces
Costs $5.76
The unit price can be calculated as the quotient between the price and the amount of detergent:
[tex]\frac{5.76}{48}=0.12[/tex]Detergent B costs $0.12/ounce
Detergent C
Has 128ounces
Costs $17.90
Calculate the unit price by dividing the price by the number of ounces of the container:
[tex]\frac{17.90}{128}=0.139\approx0.14[/tex]Detergent C costs $0.14/ounce.
The best detergent to buy is the one that has the lower unit price, so to determine which one is it you have to compare their price per ounce.
In this case, detergent B has the lower price per ounce and thus it is the best detergent to buy.
Jose Is cooking a roast. The table below gives the temperature (1) of the roast (In degrees Celsius), at a few timest (In minutes) after he removed it from theoven.Timet Temperature R (1)(minutes)(c)010305070226.6205.6157.6119.661.6(a) Find the average rate of change for the temperaturefrom 0 minutes to 10 minutes.0 °C per minute(b) Find the average rate of change for the temperaturefrom 30 minutes to 50 minutes.[ °C per minute
Answers
(a). From the given table,
R(0)=226.6
R(10)=205.6
The average rate of change for the temperature from 0 minutes to 10 minutes is
[tex]\begin{gathered} A=\frac{R(10)-R(0)}{10-0} \\ =\frac{205.6-226.6}{10} \\ =-2.1 \end{gathered}[/tex](a) The average rate of change for the temperature from 0 minutes to 10 minutes is -2.1 (in degree centrigrade)
Minus sign implies that the temperature is deacreasing with increasing time
(b). Again,
R(30)=157.6
R(50)=119.6
The average rate of change for the temperature from 30 minutes to 50 minutes is
[tex]\begin{gathered} A=\frac{R(50)-R(30)}{50-30} \\ =\frac{119.6-157.6}{20} \\ =-1.9 \end{gathered}[/tex](b) The average rate of change for the temperature from 30 minutes to 50 minutes is -1.9 (in degree centrigrade)
Minus sign implies that the temperature is deacreasing with increasing time
If the ratio of m to nis 7 to 6which of the following could be true?
Answers
m = 7/3, n = 2 could be true if the m/n ratio is 7:6. Option-E is correct.
Given that,
Which of the following could be true if the m/n ratio is 7:6.
Option are
A. m = 8, n = 7
B. m = 12,n= 14
C. m=14, n=0
D. m = 42, n = 42
E. m = 7/3, n = 2
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.
Consider each of the m and n values that are provided.
Option-A
m:n = 8:7 ≠ 7 : 6
Option-B
m:n = 12:14 = 6:7 ≠ 7 : 6
Option-C
m:n = 14:0 ≠ 7 : 6
Option-D
m:n = 42:42 = 1:1 ≠ 7 : 6
Option-E
m:n = 7/3 : 2 = 7 : 6
Thus E is the only true ratio
Therefore, m = 7/3, n = 2 could be true if the m/n ratio is 7:6.
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A desk is on sale for $380, which is 20% off the original price. Which equation can be used to determine theamount of money saved, s, in dollars, when purchasing this desk on sale?A s= 0.2(380)BS = (380 = 0.8) - 380Cs= (380 = 0.5) – 380D8 = (380 = 0.8)
Answers
Since the desk was 20% off, the price of $380 represents 80% of the original price.
Step 1. Define an expression to find the original price.
To find this original price, we divide the discounted price of 380 by the percentage it represents: 0.8 (we represent 80% in decimal form as 0.8)
[tex]380\div0.8[/tex]That expression represents the original price.
Step 2. To find the amount saved, we subtract the sale price to the original price:
[tex]s=(380\div0.8)-380[/tex]This expression will give as a result the amount saved s.
Answer:
[tex]s=(380\div0.8)-380[/tex]