Answers
The term that should go in the space to complete the statement is 5.
The complete statement is 5c + 15 = 5(c + 3).
What exactly does it mean to simplify an expression?Simplifying an expression is the same as solving a math problem. When you simplify an expression, you are attempting to write it in the simplest feasible manner.Combining similar terms is a frequent strategy for reducing algebraic expressions. Like Terms have identical variable components (same variable(s) and same exponent(s)).The given statement is 5c + 15 = __(c + 3).
Now, we will combine the like term from the left side of the expression which is 5, and place it on the right side space to make the expression equivalent.
Hence, the complete statement is 5c + 15 = 5(c + 3).
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Related Questions
7- At the school car wash, Kelly washes a car in 13 minutes, and Libby washes a car in 17 minutes, How many more minutes does it take Kelly to wash a car alone than it takes Kelly and Libby to wash a car when working together? Express your answer as a decimal to the nearest tenth.
Answers
Kelly will take 5.64 minutes more to wash the car as compared to Kelly and Libby when they are working together
Time taken by Kelly to wash the car = 13 minutes
Time taken by Libby to wash the car = 17 minutes
Time taken by Kelly and Libby to wash the car together:
LCM of 13 and 17 is 221. So, the total work required to be done is 221 units
Hence, Kelly does 17 units of work each minute and Libby does 13 units of work each minute
If both work together, they will finish the work in = Total work required to be done/ Work done in a minute by Kelly + Work done in a minute by Libby
= 221/(17+13)
= 221/30 = 7.36 minutes
The extra time taken by Kelly working alone = 13-7.36 = 5.64 minutes
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Lucy bought a plant and planted it in a pot near a window in her house. The initial height of the plant was 12 inches and it grew at a rate of 2 inches per month. Make a table of values and then write an equation for H, in terms of t, representing the height, in inches, of the plant tt months after Lucy bought the plant.
I need the equations
Answers
The equation for H, in terns of t, representing the height , in inches, of the plant tt months after Lucy bought the plant is :
H=12+2t
Given, A plant that Lucy had purchased was placed in a pot next to a window in her home. The plant initially stood 12 inches tall and grew at a rate of 2 inches per month.
from the given information, the equation can be framed as:
H = 12 +2t
where the initial height of the plant is increased at a rate of two inches every month.
from the table substitute the value of months in t, to find the height of the plant in that particular month.
t = 0
H=12+2(0)
H=12
hence when t=0 then H=12
t=1
H=12+2(1)
H=12+2
H=14
after a month the height of the plant changes to 14 inches.
t=2
H=12+2(2)
H=12+4
H=16
after two months the height changes to 16 inches.
t=3
H=12+2(3)
H=12+6
H=18
after three months the height changes to 18 months.
t=4
H=12+2(4)
H=12+8
H=20
finally after four months the height of the plant changes to 20 months.
hence we get the required equation as H=12+2t
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Hello can someone help I dont really think I'm correct.
Answers
According to the given number line A is on -7, X is on -2 and E is on 8.
As you can observe in the image below, X is 5 units away from A. At the same time, X is 10 units away from E.
Therefore, point X is double distant from E as far as it is from A.The ratio of this relation would be 2:1 from E to A.
Add 5/6+ 3/4 + 2/3 Simplify the answer and write it as a mixed number, if possible.2122O12
Answers
In order to add those fractions, we need to write them using a commom denominator. We can do so by finding a common multiple for the original denominators:
6, 4 and 3
Since 12 is a multiple of those three numbers, we can use 12 as a new denominator for each of the fractions:
5/6 = (5 * 2)/(6 * 2) = 10/12
3/4 = (3 * 3)/(4 * 3) = 9/12
2/3 = (2 * 4)/(3 * 4) = 8/12
Notice that 10/12 is equivalent to the the original fraction 5/6, because we obtained 10/12 by multiplying both the numerator and the denominator by the same factor. The same applies to the other pairs of fractions.
Now, we can add:
5/6 + 3/4 + 2/3 = 10/12 + 9/12 + 8/12
= (10 + 9 + 8)/12
= 27/12
Now, we can simplify the result by dividing both the numerator and the denominator by the same factor. Since both 27 and 12 are multiples of 3, we can write:
27/12 = (27 : 3)/(12 : 3)
= 9/4
Now, since 9 is greater than 4, we can write the fraction 9/4 as a mixed number:
9 = 8 + 1
= 2*4 + 1
9/4 = (2*4 + 1)/4
= 2*4/4 + 1/4
= 2 + 1/4
= 2 1/4 (using the notation of mixed number)
Several students use stopwatches to measure how quickly a sensitive plantreacts to stimuli. They record the times in milliseconds. Which kind of dataare the students recording?OA. Qualitative dataOB. Audio dataC. Quantitative dataOD. Categorical data
Answers
Given: Several students use stopwatches to measure how quickly a sensitive plant reacts to stimuli. They record the times in milliseconds.
Required: To determine which kind of data the students are recording.
Explanation: The given kinds of data can be summarized as follows-
→Qualitative data determines the quality of a single data. Example: The colour of cars in a parking lot.
→Audio data have the data in the form of audio. Example: The sound of different dogs barking.
→Quantitative data represents the quantity of some data. Example: Recording the number of the height of students in a class.
→Categorical Data represents the data of various categories. Example- Recording some person's age, sex, hair colour, etc.
Hence, measuring how quickly a sensitive plant reacts to stimuli is an example of Qualitative Data.
Final Answer: Option A (Qualitative Data) is correct.
Help me please this is due tn
Answers
To find how many miles can be drove with one gallon, divide 348.3 by 9. This should get you 38.7 mpg.
Since it already provides how many miles can be driven my 40, I’m just going to multiply 38.7 by 7 and add it to the 40.
38.7 x 7 = 270.9
270.9 + 1548 = 1818.9
radius = 3 ¼ydlearning something about area of circle
Answers
Given that the radius of a circle is;
[tex]r=3\frac{1}{4}yd[/tex]Recall that the area of a circle can be calculated using the formula;
[tex]A=\pi r^2[/tex]substituting the value of r;
[tex]\begin{gathered} A=\pi(3\frac{1}{4})^2 \\ A=\pi(\frac{13}{4})^2 \\ A=\pi(\frac{169}{16}) \\ A=33.18yd^2 \end{gathered}[/tex]Therefore
f(x) = x² + 9x from x1 = 4 to x2 = 8.
is the rate of change 21?
Answers
The average rate of change of f(x) on the interval [4, 8] is 21.
How to find the rate of change?
For a function f(x), the rate of change on an interval [a, b] is given by:
R = ( f(b) - f(a))/(b - a)
In this case the function is:
f(x) = x² + 9x
And the interval is [4, 8]
Then the rate of change is
R = ( f(8) - f(4))/(8 - 4)
we will get:
f(8) = 8² + 9*8 = 136
f(4) = 4² + 9*4 + 16 + 36 = 52
Replacing that we get:
R = (136 - 52)/4 = 21
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The half-life of radium is 1690 years. If 50 grams are present now, how much will be present in 800 years?
Answers
In order to determine the amount of radium after 800 years, use the following formula:
[tex]N=N_oe^{-\lambda t}[/tex]where,
N: amount of radium after t years = ?
No: initial amount of radium = 50g
λ: decay constant
t = 800
The decay constant is calculated by using the following expression:
[tex]\lambda=\frac{ln2}{t\frac{_1}{2}}=\frac{ln2}{1960}\approx3.5*10^{-4}[/tex]where t1/2 = 1960 is the half-life.
Now, by replacing λ, No and t = 800 you obtain:
[tex]N=50e^{-(3.5*10-4)(800)}\approx37.68g[/tex]Hence, after 800 years there are approximately 37.68g of uranium
please i need help. can someone please help me
Answers
5 x 5 x 7 = 175 in^3
Bigger Rectangular Prism:
7 x 14 x 11 = 1078 in ^3
Answer:
1078 + 175 = 1,253 in^3
4 strings 5 strings 6 strings 25% off 4 4 8 50% off 6 8 3 Vhat is the probability that a randomly selected Simplify any fractions.
Answers
number of banjos that have 5 or 6 strings: 4 + 8 + 8 + 3 = 23
total number of banjos: 6 + 4 + 4 + 8 + 8 + 3
Blue and yellow dye are mixed in an 8: 3 ratio to make 44 litres of a green-coloured dye. A further 8 litres of yellow dye are added to the mixture. What is the new ratio of blue to yellow dye in its simplest form?
Answers
Answer: The new ratio of blue to yellow dye in its simplest form is 8/5.
Step-by-step explanation:
Blue and yellow dyes are mixed in an 8: 3 ratio to make 44 liters of a green-colored dye. A further 8 liters of yellow dye are added to the mixture. What is the new ratio of blue to yellow dye in its simplest form?
What is the Ratio?
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Calculating the fraction of blue and yellow in the green dye,
Blue dye = 8/(3+8) * 44
Blue dye = 8/11 * 44
Blue dye = 32 liters
Similarly,
yellow dye = 3/11*44
yellow dye = 12
Now
Blue dye + yellow dye = 32+12 = 44
Now yellow dye is increased by 8 liters
the new volume fraction of yellow dye = 12+8
= 20
a fraction of blue dye remains the same,
the ratio of blue dye to new yellow dye in teal color.
= 32/20
=8/5
Thus, the new ratio of blue to yellow dye in its simplest form is 8/5.
Answer:
8/5
Step-by-step explanation:
Is it true that Weight is a function of Height?
Answers
Answer:
Yes
Step-by-step explanation:
The number of height is also the number of wegt
Cylinder a r=4 h = 7 7 b. h= 14.3, r = 8.5
Answers
To calculate the volume of a cylinder you have to multiply the area of the circle by the height of the cylinder.
[tex]\begin{gathered} V=A\cdot h \\ V=\pi r^2\cdot h \end{gathered}[/tex]We know that the radius of the circle is r=4 and the height of the cylinder is h=7, replace both values on the formula to determine the volume:
[tex]\begin{gathered} V=\pi(4^2)\cdot7 \\ V=\pi\cdot16\cdot7 \\ V=112\pi \\ V\approx351.86 \end{gathered}[/tex]The volume of the cylinder is approximately 351.86 cubic units.
The length of a rectangle is (5x+1) inches. The width is (x). Express the area of the
checkerboard in terms of the variable x. Use the formula: A = L-W
14.
Answers
Answer: A = 7x
Step-by-step explanation:
Area = Length x Width
A = L * W
L = 5x + 1 W = x
Plug the length and width into the equation for area.
A = (5x + 1) * x
A = 6x + x
A = 7x
The velocity of a body as a function of time is given as Vt=5e-2t+4 where t is in seconds, and V is in ms. The acceleration in ms2 at t=0.6s is .....
Answers
The velocity of a body as a function of time is given as Vt=5e-2t+4 where t is in seconds, and V is in ms acceleration at t = 0.6s is -10x 0.30119m/[tex]s^{2}[/tex].
The velocity of a body is given by
Vt=5e-2t+4
acceleration a(t)= [tex]v'(t)[/tex]
= d/dt [tex]v'(t)[/tex]
= d/dt 5e-2t+4
= -10[tex]e^{-2t}[/tex]
put t = 0.6
acceleration at t= 0.6= a(0.6)
= [tex]-10e^{-2\times0.6}[/tex]
= -10x [tex]e^{-12}[/tex]
= -10x 0.30119m/[tex]s^{2}[/tex]
What is acceleration?acceleration is the rate of change of the speed of an object with respect to time. Accelerations are vector quantities. The direction of the target's acceleration is obtained from the direction of the net force on the target.
Three types of accelerated motion
Uniform acceleration non-uniform acceleration intermediate acceleration.The term uniform acceleration refers to motion in which an object moves in a straight line with increasing speed at equal intervals of time.
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The standard trampoline has a diameter of 14 feet. What is its circumference?
Answers
The circumference, C, of a circle is computed as follows:
[tex]C=\pi D[/tex]where D is the diameter of the circle. Substituting with D = 14 ft, we get:
[tex]\begin{gathered} C=\pi\cdot14 \\ C\approx44\text{ ft} \end{gathered}[/tex]The circumference of the trampoline is approximately 44 feet
K 370 45° Which equation can be used to find the value of k? 37° - K +45º = 180° 37° + k +45º = 180° 37" + k = 45° 180° 37° -45° - 180°
Answers
The sum of angle on a straight line is always 180 degree.
Determine the equation for the angle.
[tex]k+37+45=180[/tex]Solve this system of equations byusing the elimination method.x - 5y = 164x – 2y = -8([?],
Answers
Given:
There are given two equations:
[tex]\begin{gathered} x-5y=16...(1) \\ 4x-2y=-8...(2) \end{gathered}[/tex]Explanation:
To find the value by using the elimination method, we need to multiply by 4 into the equation (1) and 1 into the multiply by (2):
Then,
From the equation (1):
[tex]\begin{gathered} 4(x-5y=16) \\ 4x-20y=64...(3) \end{gathered}[/tex]And,
From the equation (2):
[tex]\begin{gathered} 1(4x-2y=-8) \\ 4x-2y=-8...(4) \end{gathered}[/tex]Now,
From the equation (3) and equation (4):
[tex]4x-20y-64=4x-2y+8[/tex]Then,
[tex]\begin{gathered} 4x-20y-64-4x+2y-8=0 \\ -20y-64+2y-8=0 \\ -18y-72=0 \\ -18y=72 \\ y=-4 \end{gathered}[/tex]Now,
Put the value of y into the equation (3):
[tex]\begin{gathered} \begin{equation*} 4x-20y=64 \end{equation*} \\ 4x-20(-4)=64 \\ 4x+80=64 \\ 4x=64-80 \\ 4x=-16 \\ x=-4 \end{gathered}[/tex]Final answer:
Hence, the value of x and y is shown below:
[tex](-4,-4)[/tex]You pick a card at random, put it back, and then pick another card at random. 3 4 5 6 7 What is the probability of picking a divisor of 6 and then picking a number less than 5? Simplify your answer and write it as a fraction or whole number.
Answers
Probability = required outcome /all possible outcome
You have 5 cards on the deck. The exercise has reposition, i.e. you put the card back into the deck before picking the next one, so the total number of cards is always 5.
all possible outcome = 5
Divisor of 6 = 3, 6
Probability of picking a divisor of 6 = 2/5
Number less than 5 are : 3 and 4 = 2/5
The intersection between both events is equal to the product of both probabilities since the events are independent.
The probability of picking a divisor of 6 and then picking a number less than 5 is:
P(divisor of 6) and P(no.less than 5) = 2/5 * 2/5 = 4/25
The diameter of a circle is 18 cm. Find its circumference in terms of T. Answer: C = om Submit Answer
Answers
The circumference of a circle is given by the formula:
[tex]C\text{ = 2 }\pi\text{ r}[/tex]The diameter of the circle, d = 18cm
Radius = diameter / 2
r = d/2
r = 18/2
r = 9 cm
[tex]\begin{gathered} C\text{ = 2}\pi(9) \\ C\text{ = 18}\pi \end{gathered}[/tex]Solve the following using substitutionY = -2X + 10.5x - y = 4
Answers
We are to solve the equations
[tex]\begin{gathered} y=-2x+1 \\ 0.5x-y=4 \end{gathered}[/tex]The equation can be rewritten as
[tex]\begin{gathered} y+2x=1------------\text{equation 1} \\ -y+0.5x=4-----------\text{equation 2} \end{gathered}[/tex]Using substitution method
From equation 1
[tex]y=1-2x--------\text{equation 3}[/tex]Substitute 1 - 2x for y into equation 2
This gives
[tex]\begin{gathered} -(1-2x)+0.5x=4 \\ -1+2x+0.5x=4 \\ -1+2.5x=4 \\ 2.5x=4+1 \\ 2.5x=5 \\ x=\frac{5}{2.5} \\ x=2 \end{gathered}[/tex]Therefore, x = 2
Substitute 2 for x into equation 3
This gives
[tex]\begin{gathered} y=1-2(2) \\ y=1-4 \\ y=-3 \end{gathered}[/tex]Therefore the solution to the equations is
x = 2, y = -3
Find the equation of the parabola that has a vertex at (2,0) and a y-intercept of (0,12).Question 19 options:A) y = 3(x + 2)2B) y = (x – 2)2C) y = (x + 2)2D) y = 3(x – 2)2
Answers
SOLUTION
Equation of a parabola is given by the equation
[tex]y=a(x-h)^2+k[/tex]Where (h, h) are the coordinates of the vertex.
From the question given, the vertex is (2, 0)
So, h = 2, k = 0.
The y-intercept is given as (0, 12).
So, this means that x = 0 and y = 12
Substituting the values for h, k, x and y into the equation we have
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ 12=a(0-2)^2+0 \\ \\ 12=a\times-2^2+0 \\ \\ 12=4a \\ \\ a=\frac{12}{4} \\ \\ a=3 \end{gathered}[/tex]Now, let's substitute the value of a into the equation to get equation for the parabola.
This becomes
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ y=3(x-2)^2+0 \\ \\ y=3(x-2)^2 \\ \\ \end{gathered}[/tex]Could someone please help me with this?
Answers
Answer:
1. f(4) = 4
2. g(2) = -4
3. f(-5) = -14
4. g(-3) = 21
5. f(0) = -4
6. g(0) = 0
7. f(3) - 1 = 1
8. f(1/4) = -3.5 or -7/2
9. g(1/4) = -0.9375 or -15/16
10. f(a^2) = 2a^2 - 4
11. f(k+1) = 2k - 2
12. g(2n) = 2n^2 - 8n
13. f(3x) = 6x - 4
14. f(2) + 3 = 3
15. g(-4) = 32
Step-by-step explanation:
here’s a pic of my work:
Lydia is at a coffee shop and knows
she can spend no more than $65
before tax. She sees this price list in
the coffee shop.
Item
Dark Roast Coffee
Pumpkin Spice Coffee
Breakfast Tea
Price per pound
$7.50
$10.50
$23.50
Part A
Write a number in each blank to complete an inequality Lydia can use to find how
many pounds of Pumpkin Spice coffee, p, she can buy along with 2 pounds of
Dark Roast coffee.
Answers
Answer:
10.50p+15≤65
p≤ 100/21
Step-by-step explanation:
Let p represent pounds of Pumpkin Spice coffee.
We have been given that Lydia is at a coffee shop and knows she can spend no more than $65 before tax. She sees this price list in the coffee shop.
Item Price per pound
Dark Roast Coffee
$7.50
Pumpkin Spice Coffee
$10.50
Breakfast Tea
$23.50
Lydia wants to buy 2 pounds of Dark Roast coffee, so the cost of 2 pounds of Dark Roast coffee would be $7.50×2=$15 .
We are told that cost of each pound of Pumpkin Spice coffee is 10.50,socostof′ p'
pounds of Pumpkin Spice coffee would be 10.50
Since Lydia can spend no more than $65 before tax, so the cost of 2 pounds of Dark Roast coffee and 'p' pounds of Pumpkin Spice coffee must be less than or equal to 65.
We can represent this information in an inequality as:
10.50p+15≤65
Therefore, our required inequality would be 10.50p+15≤65
10.50+15-15≤65-75
10.50≤50
Divide both sides by 10.50:
10.50p/10.50 ≤ 50/10.50
P ≤ 50*2/10.50*2
P ≤ 100/21
P ≤ 4.76190
Therefore, Lydia can buy less than or equal to 100/21 pounds of Pumpkin Spice coffee.
If I was asked to think of a number and multiply it by 2, I could write this algebraically as 2x. Write the following algebraically, using x as your unknown. "I think of a number, multiply it by 3, add 4 and square the result."
Answers
Answer: (3x + 4)^2
Step-by-step explanation:
I think of a number => x
Multiply it by 3 => 3x
Add 4 => 3x + 4
Square the result => (3x + 4)^2
Finding the Slope of a LineVy10What is the slope of a line that contains the points (1,9) and (4, 3)?The slope of the line is<88642N2x624.8
Answers
Given the points: (1, 9) and (4, 3)
To find the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{3-9}{4-1}[/tex]m = -2
If you use 15 fl oz of milk how much flour shold be used
Answers
If a costume designer takes 20 hours to make 16 costumes, at what rate per hour are costumes being made?
Answers
Answer:it takes 1 hor 25 minutes to make a costume
Step-by-step explanation:
20 divided by 16 =1.25
Write the correct equation for the following statement.
You decide to rent a limo for prom. The rate is $250 plus $6 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
250+6m
If you travel 45 miles what will be your total bill at the end
of the evening?
Answers
Answer:
Easy;
Substitute m (miles) for 45.
250+6(45)
(6 dollars per mile, times 45 miles, plus the 250 flat rate)
250+270
520
So you would be charged 520 dollars total at the end of the evening.
Hope this helped!