you need to subtract 7 in each section of the inequality is
-7< x<2
-7< x and x<2
8.1 km to miles and feet
Given
[tex]8.1\operatorname{km}[/tex]It should be noted that
[tex]\begin{gathered} 1\operatorname{km}=0.621371miles \\ 1\text{mile}=5280\text{feet} \end{gathered}[/tex][tex]\begin{gathered} \text{convert 8.1km to miles} \\ 1\operatorname{km}=0.621371\text{miles} \\ 8.1\operatorname{km}=8.1\times0.621371 \\ 8.1\operatorname{km}=5.0331051\text{miles} \end{gathered}[/tex][tex]\begin{gathered} 8.1\operatorname{km}=5\text{miles}+0.0331051\text{miles} \\ \text{convert 0.0331051miles to fe}et \\ 1\text{miles}=5280ft \\ 0.0331051\text{miles}=0.0331051\times5280feet \\ 0.0331051\text{miles}=174.79feet \end{gathered}[/tex]Hence, 8.1km is 5 miles and 174.79 feet
Find y if the line through (5, 1) and (6, y) has a slope of 3.
Answer:
Y = 32
Step-by-step explanation:
Y = mx + c, with a slope of 3
Y = 3x + c
Substitute values:
1 = 3 (5) + c
1 = 15 + c
c = -14
Rewrite formula:
Y = 3x - 14
Y = 3 (6) + 14
Y = 18 + 14
Y = 32
Hope this helps :)
Answer:
y = 4
Step-by-step explanation:
y = mx + b is the slope intercept form of a line.
We need an m (slope and a b(y-intercept)
They give us the slope, so we have to find the b
slope = 3
y = 1
x = 5
We need and x and y on the line and the point (5,1) gives us that.
y = mx + b
1 = 3(5) + b
1 = 15 + b Subtract 15 from both sides of the equation
-14 = b
Now we have the m (slope of 3) and the b (the y-intercept of -14)
y = mx + b
y = 3x -14 Now plug is the x (6) from the point given and solve for its y
y = 3(6) -14
y = 18 - 14
y = 4
The number of bacteria in a culture increased from 27,000 to 105,000 in five hours. When is the number of bacteria one million if:a) Does the number increase linearly with time?b) The number increases exponentially with time?
We have the following situation regarding the growth of bacteria in a culture:
• The given initial population of bacteria is 27,000
,• After 5 hours, the population increases to 105,000.
Now, we need to find the moment when that population is one million if:
• The population increases linearly with time
,• The population increases exponentially with time
To find the time in both situations, we can proceed as follows:
Finding the moment when the population is one million if it increases linearly with time1. We need to find the equation of the line that passes the following two points:
• t = 0, population = 27,000
,• t = 5, population = 105,000
2. Then the points are:
[tex]\begin{gathered} (0,27000)\rightarrow x_1=0,y_1=27000 \\ (5,105000)\rightarrow x_2=5,y_2=105000 \\ \end{gathered}[/tex]3. Now, we can use the two-point form of the line equation:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \\ y-27000=\frac{105000-27000}{5-0}(x-0) \\ \\ y-27000=\frac{78000}{5}x=15600x \\ \\ y=15600x+27000\rightarrow\text{ This is the line equation we were finding.} \end{gathered}[/tex]4. We can see that the population is given by y. Then if y = 1,000,000, then we need to solve the equation for x as follows:
[tex]\begin{gathered} 1000000=15600x+27000 \\ \\ 1000000-27000=15600x \\ \\ \frac{(1000000-27000)}{15600}=x \\ \\ x=62.3717948718\text{ hours} \\ \\ x\approx62.3718\text{ hours} \end{gathered}[/tex]Therefore, if the population increases linearly with time, the number of bacteria will be one million around 62.3718 hours.
Finding the moment when the population is one million if it increases exponentially with time1. In this case, we also need to find the equation that will give us the time when the number of bacteria is one million. However, since the equation will be exponential, we have:
[tex]\begin{gathered} y=a(1+r)^x \\ \\ a\rightarrow\text{ initial value} \\ \\ x\rightarrow\text{ number of time intervals that have passed.} \\ \\ (1+r)=b\text{ }\rightarrow\text{the growth ratio, and }r\rightarrow\text{ the growth rate.} \end{gathered}[/tex]2. Now, we can write it as follows:
[tex]\begin{gathered} a=27000 \\ \\ x=5\rightarrow y=105000 \\ \\ \text{ Then we have:} \\ \\ 105000=27000(b)^5 \\ \end{gathered}[/tex]3. We can find b as follows (the growth factor):
[tex]\begin{gathered} \frac{105000}{27000}=b^5 \\ \\ \text{ We can use the 5th root to obtain the growth factor. Then we have:} \\ \\ \sqrt[5]{\frac{105000}{27000}}=\sqrt[5]{b^5} \\ \\ b=1.31209447568 \end{gathered}[/tex]4. Then the exponential equation will be of the form:
[tex]\begin{gathered} y=27000(1.31209447568)^x \\ \\ \text{ To check the equation, we have that when x = 5, then we have:} \\ \\ y=27000(1.31209447568)^5=105000 \end{gathered}[/tex]5. Now, to find the time when the number of bacteria is one million, we can proceed as follows:
[tex]\begin{gathered} 1000000=27000(1.31209447568)^x \\ \\ \frac{1000000}{27000}=1.31209447568^x \end{gathered}[/tex]6. Finally, we need to apply the logarithm to both sides of the equation as follows:
[tex]\begin{gathered} ln(\frac{1000000}{27000})=ln(1.31209447568)^x=xln(1.31209447568) \\ \\ \frac{ln(\frac{1000000}{27000})}{ln(1.31209447568)}=x \\ \\ x=13.2974595282\text{ hours} \end{gathered}[/tex]Therefore, if the population increases exponentially with time, the number of bacteria will be one million around 13.2975 hours.
Therefore, in summary, we have:
When is the number of bacteria one million if:
a) Does the number increase linearly with time?
It will be 62.3718 hours
b) The number increases exponentially with time?
It will be around 13.2975 hours
Joan uses the function C(x) = 0.11x + 12 to calculate her monthly cost for electricity.• C(x) is the total cost (in dollars).• x is the amount of electricity used (in kilowatt-hours).Which of these statements are true? Select the three that apply.A. Joan's fixed monthly cost for electricity use is $0.11.B. The cost of electricity use increases $0.11 each month.C. If Joan uses no electricity, her total cost for the month is $12.D. Joan pays $12 for every kilowatt-hour of electricity that she uses.E. The initial value represents the maximum cost per month for electricity.F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
Answer:
The correct statements are:
C. If Joan uses no electricity, her total cost for the month is $12.
F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.
G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
Step-by-step explanation:
Notice that the given function is the equation of a line in the slope-intercept form:
[tex]C(x)=0.11x+12[/tex]From this interpretation, we'll have that the correct statements are:
C. If Joan uses no electricity, her total cost for the month is $12.
F. A graph of the total cost for x ≥ 0 kilowatt-hours of energy used is a straight line.
G. The slope of the function C(x) represents the increase in cost for each kilowatt hour used.
The deposits Ginny makes at her bank each month form an arithmetic sequence. The deposit for month 3 is $150, and the deposit for month 5 is %180. Answer the questions below and show all work.1. What is the common difference for the deposits made each month?2. Write an explicit formula for this arithmetic sequence. 3. What is the amount of Ginny's deposit in the 12th month?4. At what month will Ginny first make a deposit that is at least $500?
SOLUTION
The deposits Ginny makes at her bank each month form an arithmetic sequence. The deposit for month 3 is $150, and the deposit for month 5 is $ 180.
Since it follows an arithmetic sequence, T n = a + ( n- 1 ) d
Month 3 , T 3 = a+ ( 3 - 1 ) d = 150
a + 2 d = 150 --------------------- equ 1
Month 5 , T 5 = a + ( 5 - 1 ) d = 180
a + 4 d = 180 ...........................equ 2
Solving the two equations, we have :
a - a + 4 d - 2 d = 180 - 150
2 d = 30
Divide both sides by 2 , we have:
d = 15
Let us put d = 15 in equ 1 , we have a + 2 d = 150
a + 2 ( 15 ) = 150
a + 30 = 150
a = 150 - 30
a = 120
From the solution,
Month 1 = 120
Month 2 = 120 + 15 = 135
Month 3 = 135 + 15 = 150
Month 4 = 150 + 15 = 165
Month 5 = 165 + 15 = 180
1. What is the common difference for the deposits made each month? d = 15
2. Write an explicit formula for this arithmetic sequence.
Recall that Tn = a + ( n - 1 ) d
Tn = 120 + ( n - 1 ) 15
Tn = 120 + 15 n - 15
Tn = 120 - 15 + 5n
Tn = 105 + 15n
3. What is the amount of Ginny's deposit in the 12th month?
Tn = 105 + 15n
T 12 = 105 + 15 ( 12 )
T 12 = 105 + 180 = 285
4. At what month will Ginny first make a deposit that is at least $500?
Using Tn = 105 + 15 n = 500
105 + 15 n = 500
15 n = 500 - 105
15 n = 395
Divide both sides by 15 , we have :
n = 26 . 33
n = 27
Identify the key features of the graph, including the x - intercepts. Y-intercept, axis of symmetry, and vertex. (3)
The graph of the given finction is:
Here, the x-intercept is at -1 and -6
The y-intercept is at 6
The axis of symmetry is x=-3.5
The vertex is (-3.5,-6.2)
Determine the frequency of each class and the table shown
Given:
The dataset and table with class.
Required:
Determine the frequency of each class.
Explanation:
Answer:
Answered the question.
A rectangular prism has a legth of 5 1/4 m, a width of 4m, and a height of 12 m.How many unit cubes with edge lengths of 1/4 m will it take to fill the prism? what is the volume of the prism?
Volume of a cube with edge lengths of 1/4m:
[tex]\begin{gathered} V_{cube}=l^3 \\ \\ V_{cube}=(\frac{1}{4}m)^3=\frac{1^3}{4^3}m^3=\frac{1}{64}m^3 \end{gathered}[/tex]Volume of the rectangular prism:
[tex]\begin{gathered} V=l\cdot w\cdot h \\ \\ V=5\frac{1}{4}m\cdot4m\cdot12m \\ \\ V=\frac{21}{4}m\cdot4m\cdot12m \\ \\ V=252m^3 \end{gathered}[/tex]Divide the volume of the prism into the volume of the cubes:
[tex]\frac{252m^3}{\frac{1}{64}m^3}=252\cdot64=16128[/tex]Then, to fill the prism it will take 16,128 cubes with edge length of 1/4 mYou are selling drinks at the carnival to raise money for your club. You sell lemonadefor $6 for 2 cups and orange drinks for $9 for 3 cups. Your sales totaled $240. Let xbe the number of cups of lemonade and y be the number of orange drinks. Write anyequation in standard form for the relationship above.
Let x be the number of cups of lemonade sold, and y the number of cups of orange drinks sold, then we can set the following equation:
[tex]6(\frac{x}{2})+9(\frac{y}{3})=240.[/tex]Now, recall that the standard form of a linear equation is:
[tex]Ax+By=C,[/tex]Where, A≥0, B and C are integers.
Simplifying the first equation, we get:
[tex]3x+3y=240.[/tex]Answer:
[tex]3x+3y=240.[/tex]45% of 240 is what number?
We are asked to determine the 45% of 240. To do that we need to multiply 240 by 45/100, that is:
[tex]240\times\frac{45}{100}=108[/tex]therefore, 45 percent of 240 is 108
to find the height of a tree, a group of students devised the following method. A girl walks toward the tree along it's shadow until the shadow of the top of her head coincide with the shadow of the top of the tree. if the girl is 150 cm tall, her distance to the foot of the tree is 13 meters, and the length of her shadow is 3 m, how tall is the tree?
Answer: 8m
Explanation:
Given:
To find the height(h) of the tree, we can use ratio since they are similar triangles.
Triangle 1
Triangle 2
So,
[tex]\begin{gathered} \frac{1.5}{3}\text{ = }\frac{h}{16} \\ \text{Simplify and rearrange} \\ h=\text{ }\frac{1.5}{3}(16) \\ \text{Calculate} \\ h=\text{ 8 m} \end{gathered}[/tex]Therefore, the height of the tree is 8m.
$85000 is invested at 7.5% per annum simple interest for 5 years. Calculate the simple interest.
From the statement of the problem we know that:
• the principal amount of money invested is P = $85000,
,• the rate per year is 7.5%, in decimals r = 0.075,
,• the time is t = 5 years.
The interest earnt I is equal to the difference between the total accrued amount A and the principal amount P:
[tex]I=A-P=P(1+r\cdot t)-P=P\cdot r\cdot t.[/tex]Replacing by the data of the problem we find that the simple interest is:
[tex]I=85000\cdot0.075\cdot5=31875.[/tex]Answer
The simple interest is $31875.
For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chumpkin hide
Let x and y be the number of holes dug by the chipmunk and the squirrel, respectively.
Therefore, the number of hidden acorns by each animal is given by the equations below
[tex]\begin{gathered} a_{chipmunk}=3x \\ a_{squirrel}=4y \end{gathered}[/tex]On the other hand, since the squirrel needed 4 fewer holes, and the number of hidden acorns is the same
[tex]\begin{gathered} y=x-4 \\ and \\ a_{chipmunk}=a_{squirrel} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow3x=4y \\ \Rightarrow3x=4(x-4) \\ \Rightarrow3x=4x-16 \\ \Rightarrow x=16 \end{gathered}[/tex]Hence,
[tex]\Rightarrow16*3=48[/tex]The chipmunk hid 48 acorns.A trail mix brand guarantees a peanut to raisin ratio of 5:2. If a bag of that trail mix contains 30 peanuts, how many raisins are in the bag?
Answer:
12
Explanation:
In the bag, the guaranteed ratio of peanut to raisin = 5:2
Number of peanuts = 30
Let the number of raisins =x
We therefore have that:
[tex]\begin{gathered} 5\colon2=30\colon x \\ \frac{5}{2}=\frac{30}{x} \\ 5x=30\times2 \\ x=\frac{30\times2}{5} \\ x=12 \end{gathered}[/tex]The number of raisins in the bag is 12.
LM is the midsegment of Trapeziod RSXY. may you please help me find what LM is?
Step 1: Problem
Mid-point of a Trapezoid
Step 2: Concept
[tex]LM\text{ = }\frac{RS+\text{ YX}}{2}[/tex]Step 3: Method
RS = 4.1
YX = 8.2
[tex]\begin{gathered} LM\text{ = }\frac{4.1\text{ + 8.2}}{2} \\ LM\text{ = }\frac{12.3}{2} \\ LM\text{ = 6.15} \end{gathered}[/tex]Step 4: Final answer
LM = 6.15
· A) A highway noise barrier is 120 m long is constructed in 2pieces. One piece is 45 m longer than the other one. Findthe length of each piece. B) If you are to construct arectangle with each of the sizes of the pieces being thelength and width then what is the perimeter? c) What would bethe area of that rectangle? (Note: Use an Equation to solve)
A) Let the length of one piece be x. if one piece is 45 m longer than the other one, it means that the length of the other one would be (x + 45) m
Given that the total length of both pieces is 120m, then the equation would be
x + x + 45 = 120
2x + 45 = 120
2x = 120 - 45 = 75
x = 75/2
x = 37.5
Thus, the length of each piece are
37.5 m
37.5 + 45 = 82.5 m
B) The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
Given that
length = 82.5
width = 37.5
then
perimeter = 2(82.5 + 37.5) = 2 * 120
perimeter of rectangle= 240 m
C) the formula for determining area of a rectangle is expressed as
Area = length * width
Area of rectangle = 82.5 * 37.5 = 3093.75 cm^2
Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a = 3.0, b = 4.0, C = 58°
Answer
A = 46.3°
B = 75.7°
c = 3.5
Explanation
We will be using both Cosine and Sine rule to solve this.
For Cosine rule,
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the Cosine rule is given as
c² = a² + b² - 2ab Cos C
a = 3.0
b = 4.0
C = 58°
c² = 3² + 4² - 2(3)(4)(Cos 58°)
c² = 9 + 16 - (24)(0.5299)
c² = 25 - 12.72 = 12.28
c = √12.28 = 3.50
To find the other angles, we will now use Sine Rule
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
[tex]\frac{\text{ Sin A}}{a}=\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]So, we can use the latter parts to solve this
[tex]\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]B = ?
b = 4.0
C = 58°
c = 3.5
[tex]\begin{gathered} \frac{\text{ Sin B}}{4}=\frac{\text{ Sin 58}\degree}{3.5} \\ \text{ Sin B = }\frac{4\times\text{ Sin 58}\degree}{3.5}=0.9692 \\ B=Sin^{-1}(0.9692)=75.7\degree \end{gathered}[/tex]We can then solve for Angle A
The sum of angles in a triangle is 180°
A + B + C = 180°
A + 75.7° + 58° = 180°
A = 180° - 133.7° = 46.3°
Hope this Helps!!!
Find the future value using the future value formula and a calculator in order to achieve $420,000 in 30 years at 6% interest compounded monthly
The present value of in order to achieve $420000 in 30 years at 6% interest compounded monthly is $69737.60
The future value = $420000
The time period = 30 years
The interest percentage = 6%
The interest is compounded monthly
A = [tex]P(1+\frac{i}{f})^{fn}[/tex]
Where A is the final value
P is principal amount
i is the interest rate
f frequency where compound interest is added
n is the time period
Substitute the values in the equation
420000 = P × [tex](1+\frac{0.06}{12} )^{(12)(30)[/tex]
420000 = P × 6.02
P = 420000 / 6.02
P = $69737.60
Hence, the present value of in order to achieve $420000 in 30 years at 6% interest compounded monthly is $69737.60
The complete question is:
Find the present value using the future value formula in order to achieve $420,000 in 30 years at 6% interest compounded monthly
Learn more about compound interest here
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graph the inequality 3x+y<4
Subsituting (0,0) in the inequality,
[tex]\begin{gathered} 3\times0+0<4 \\ 0<4 \end{gathered}[/tex]Hence the line 3x+y=4, demarcating the plane contains the origin.
Thus, the above graph gives the required region of inequality.
4. McKenzie wants to determine which ice cream option is the best choice. The chart below gives the description and prices for her options. Use the space below each item to record your findings. Place work below the chart. A scoop of ice cream is considered a perfect sphere and has a 2-inch diameter. A cone has a 2-inch diameter and a height of 4.5 inches. A cup, considered a right circular cylinder, has a 3-inch diameter and a height of 2 inches. a. Determine the volume of each choice. Use 3.14 to approximate pi. b. Determine which choice is the best value for her money. Explain your reasoning. (That means some division, you decide which.) $2.00 $3.00 $4.00 One scoop in a сир Two scoops in a cup Three scoops in a cup Half a scoop on a cone filled with ice cream A cup filled with ice cream (level to the top of the cup)
McKenzie wants to determine which ice cream option is the best choice.
Part (a)
Volume of Scoop:
A scoop of ice cream is considered a perfect sphere and has a 2-inch diameter.
The volume of the sphere is given by
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]Where r is the radius.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{2}{2}=1[/tex]So, the volume of a scoop of ice cream is
[tex]V_{\text{scoop}}=\frac{4}{3}\cdot3.14\cdot(1)^3=\frac{4}{3}\cdot3.14\cdot1=4.19\: in^3[/tex]Therefore, the volume of a scoop of ice cream is 4.19 in³
Volume of Cone:
A cone has a 2-inch diameter and a height of 4.5 inches.
The volume of a cone is given by
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]Where r is the radius and h is the height of the cone.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{2}{2}=1[/tex]So, the volume of a cone of ice cream is
[tex]V_{\text{cone}}=\frac{1}{3}\cdot3.14\cdot(1)^2\cdot4.5=\frac{1}{3}\cdot3.14\cdot1^{}\cdot4.5=4.71\: in^3[/tex]Therefore, the volume of a cone of ice cream is 4.71 in³
Volume of Cup:
A cup, considered a right circular cylinder, has a 3-inch diameter and a height of 2 inches.
The volume of a right circular cylinder is given by
[tex]V=\pi\cdot r^2\cdot h[/tex]Where r is the radius and h is the height of the right circular cylinder.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{3}{2}=1.5[/tex]So, the volume of a cup of ice cream is
[tex]V_{\text{cup}}=3.14\cdot(1.5)^2\cdot2=3.14\cdot2.25\cdot2=14.13\: in^3[/tex]Therefore, the volume of a cup of ice cream is 14.13 in³
Part (b)
Now let us compare the various given options and decide which option is the best value for money
Option 1:
The price of one scoop in a cup is $2
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{4.19}{\$2}=2.095\: [/tex]Option 2:
The price of two scoops in a cup is $3
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{2\cdot4.19}{\$3}=2.793\: [/tex]Option 3:
The price of three scoops in a cup is $4
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{3\cdot4.19}{\$4}=3.1425[/tex]Option 4:
The price of half a scoop in a cone is $2
The volume of one scoop of ice cream is 4.19 in³
The volume of one cone of ice cream is 4.71 in³
[tex]rate=\frac{\frac{4.19}{2}+4.71}{\$2}=\frac{2.095+4.71}{\$2}=\frac{6.805}{\$2}=3.4025[/tex]Option 5:
The price of a cup filled with ice cream is $4
The volume of a cup is 14.13 in³
[tex]rate=\frac{14.13}{\$4}=3.5325[/tex]As you can see, the option 5 (a cup filled with ice cream) has the highest rate (volume/$)
This means that option 5 provides the best value for money.
Therefore, McKenzie should choose "a cup filled with ice cream level to the top of cup" for the best value for money.
Solve for x in the equation below:3(x - 5) = 5x - (3 - x)
Step 1: We have the following equation:
3(x - 5) = 5x - (3 - x)
Step 2: Solve the parentheses
3x - 15 = 5x - 3 + x
Step 3: Like terms
3x - 5x -x = - 3 + 15
-3x = 12
Step 4: Dividing by -3 at both sides
-3x/-3 = 12/-3
x = -4
Step 5: Let's prove the answer is correct
3 (-4 - 5) = 5 * -4 - (3 - -4)
3 (-9) = -20 -3 - 4
-27 = - 27
The solution is correct
The functions f(m) = 18 + 0.4m and g(m) = 11.2 + 0.54m give the lengths of two differentsprings in centimeters, as mass is added in grams, m, to each separately.
STEP - BY - STEP EXPLANATION
What to do?
Graph each equation on the same set of axis.
Determine the mass that makes the spring the same length.
Determine the length of that mass.
Write a sentence comparing the two springs.
Given:
f(m) = 18 + 0.4m and g(m) = 11.2 + 0.54m
Step 1
Find the x and y-intercept of both function.
f(m) = 18 + 0.4m
f(0) = 18+0.4(0) = 18
0 = 18 + 0.4m
0.4m = -18
m=-45
The x and y -intercept of the function f(m) are (0, 18) and (-45, 0) respectively.
g(m) = 11.2 + 0.54m
g(0) = 11.2 + 0.54(0)
g(0) = 11.2
0 = 11.2+ 0.54m
0.54m = -11.2
m=20.7
The x and y - intercepts are (0, 11.2) and (20.7, 0).
Step 2
Graph the function.
Below is the graph of the function.
Observe from the graph that that the mass that makes the spring the same length is approximately 48.5 grams.
The length at that point is 37.4 centimeters.
Comparison between the two strings.
The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).
ANSWER
b) 48.6 grams
c) 37.4 centimeters
d) The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).
what is the approximation of 3√200
Given the expression:
[tex]\text{ }\sqrt[3]{200}[/tex]Let's simplify the expression and convert its decimal form to get its approximation.
We get,
[tex]\text{ }\sqrt[3]{200}\text{ = }\sqrt[3]{8\text{ x 25}}[/tex][tex]\text{ =2 }\sqrt[3]{25}[/tex]In decimal form:
[tex]\text{ 2 }\sqrt[3]{25}\text{ = 2 x 2.92401773821 = 5.84803547643 }\approx\text{ 5.8}[/tex]Therefore, the approximate equivalent of 3√200 is 5.8.
A train travels at 100 mph any equation can be written that compares the time with the distance to find the domain and range
ok
speed = distance / time
time = distance/speed
[tex]\text{ time = }\frac{dis\tan ce\text{ }}{speed}[/tex][tex]\text{ time = }\frac{dis\tan ce\text{ }}{100}[/tex]or
[tex]\text{ distance = 100 x time}[/tex]Brandon's car used 10 gallons to travel 310 miles. At what rate does the car use gas, in miles per gallon?On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Given:
At 10 gallons, the car is able to cover 310 miles.
Find: At 1 gallon, the car can travel ____ miles.
Solution:
First, let's fill in the number line with the given values.
To solve for the question mark at 1 gallon, simply divide 310 by 10.
[tex]310\div10=31[/tex]Hence, the car uses gas at 31 miles per gallon.
At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner radius is 7 yd and its outer radius is 9 yd.We are going to give a new layer of coating to the path. If one gallon of coating can cover 5v * d ^ 2 how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for pi.)
Subtract the following polynomials 1) (2x + 43) - (-3x-9)2) (f+9) - (12f 79)3) (75 X²)+ 23 + 13) - (15 X² - X + 40)
for 1.
2x+43+3x+9=5x+52
2.
f+9-12f+9=f-12f+9-9=-11f
3.
75x^2 +23x+13-15x^2+x-40=
=60x^2+24x-27
for 2)
23d^3+(7g^9)^13
remember that power to the power means that you need to multipy the exponents
=23d^3+7^13g^117
34x(2x-11)=68x^2-374x
2m(m+3n)=2 m^2+6mn
we have lenght
l=2x+5
w=x+7
area, A= lxw
A= (2x+5)(x+7)
this is the polynomial for the area
if we have x=12
l= (2*12)+5=24+5=29
w=12+7=19
A=29*19=551 ft^2
Give the sample space describing all the outcomes. Then give all of the out comes for the event that the number 3 chosen. Use the format H1 to mean that the coin toss is heads and the number chosen is 1. If there is more than one element in the set separate them with commas
The sample space is composed of all the possible outcomes i.e. of all the possible combinations between the result of tossing the coin and picking the card. There are two possible outcomes for the coin and four for the cards so there will be 8 different combinations in the saple space. These are:
[tex]H1,H2,H3,H4,T1,T2,T3,T4[/tex]Then we must show all the outcomes where the card with the 3 is picked. This set is composed of all the elements with a 3 in the list above. There are two:
[tex]H3,T3[/tex]AnswersThen the answers are:
Sample space: {H1,H2,H3,H4,T1,T2,T3,T4}
Event that the number chosen is 3: {H3,T3}
Point B is on line segment AC. Given BC = 10 and AB = 5, determine the lengthAC.Answer: AC= Anyone know how to solve these???
3
1) Let's sketch that, to better understand this:
2) Considering the Segment Addition Postulate, we can write that:
DF = DE + EF Plug into that the given values
9 = 6 + EF
9-6 = 6-6 + EF
3 = EF
EF =3
3) Hence, the line segment EF is 3 units long
Which of the following statements must be true based on the diagram below!(Diagram is not to scale)O JL is a segment bisector.JL is a perpendicular bisector.OJT is an angle bisectora Lis the vertex of a right angle,Jis the midpoint of a segment in the diagramNone of the above.
From the diagram, we notice that the line JL bisects the angle J into two equal angles. Hence, we can conclude that the correct statement is this:
JL is an angle bisector
An angle bisector are
