The width of the rectangle below is 6 cm, and its perimeter is 42 cm. What is its area? Its area is cm² Enter the answer Check it Improve this question
Answers
ANSWER
A = 90 cm²
EXPLANATION
This is the rectangle
The perimeter of a rectangle is:
[tex]P=2W+2L[/tex]We know the perimeter is 42cm and the width is 6cm, we can find the length:
[tex]\begin{gathered} 42=2\cdot6+2L \\ 42=12+2L \\ 42-12=2L \\ L=\frac{42-12}{2} \\ L=\frac{30}{2} \\ L=15\operatorname{cm} \end{gathered}[/tex]The area of a rectangle is:
[tex]A=W\times L[/tex]Now that we've found the length we can find the area:
[tex]A=6\operatorname{cm}\times15\operatorname{cm}=90\operatorname{cm}^2[/tex]
Related Questions
Consider the data in the table below. Determine the logarithmic regression model for the data. Round the coefficients in the regression equation to 3 decimal places.
Year 1 2 3 4 5 6 7 8
Average Height 7.4 6 4.9 4.4 4 3.6 3.1 2.7
The regression equation is y
=
Answers
The regression equation, y = -0.6155x + 7.282
Given,
Year, x ; 1 2 3 4 5 6 7 8
Average height, y ; 7.4 6 4.9 4.4 4 3.6 3.1 2.7
Logarithms of y values;
log 7.4 = 0.869log 6 = 0.778log 4.9 = 0.690log 4.4 = 0.643log 4 = 0.602log 3.6 = 0.556log 3.1 = 0.491log 2.7 = 0.431The order of xy pairs;
(1, 0.869), (2, 0.778), (3, 0.690), (4, 0.643), (5, 0.602), (6, 0.556), (7, 0.491), (8, 0.431)
There are 8 xy pairs
Using online calculator, the regression equation get as;
y = -0.6155x + 7.282
Learn more about regression equation here;
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How do you do the slope of two triangles on the same line as the hypotenuse?
Answers
We can say that the triangles is similar if the slope of the hypotenuse is the same.
The slope is Vertical sides divided by the horizontal side.
The upper triangle has vertical side of 3 and a horizontal side of 2 (By counting)
The slope will be m = 3/2
The lower triangle has a vertical side of 6 and a horizontal side of 4.
The slope will be m = 6/4 = 3/2
Since the slope is the same, the triangles are similar. and the slope is m = 3/2
Solve Einstein's formula E = mc? for c where E. m, and c are greater than zero.
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Solve the following equation for c:
[tex]E=mc[/tex]We can divide in both sides by m. Since m is greater than zero, we can do it without problem (because we can not divide by 0).
[tex]\frac{E}{m}=c[/tex]Find the equation of the line that passes through the given points. (Use x as your variable.)(2, 0), (0, −1)
Answers
Find the equation of the line that passes through the given points. (Use x as your variable.)
(2, 0), (0, −1)
step 1
Find out the slope
m=(-1-0)/(0-2)
m=-1/-2
m=1/2
step 2
Find out the equation of the line in slope-intercept form
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
we have
m=1/2
the y-intercept is given -----> (0,-1)
so
b=-1
substitute
y=(1/2)x-1Chase and Heather are traveling towards each other from points that are 469 miles apart. If heather is traveling 7 mph faster than they meet after 7 hours, how fast was each traveling?Chase is traveling ___ mphHeather is traveling ___ mph
Answers
The distance between Chase and Heather is 469 miles
They each travel for 7 hours (when they meet)
The graph of a function f is shown below.Find one value of x for which f(x)=-3 and find f(0).Hey
Answers
One value of x for which f (x ) = -3 is -2 .Therefore,
f(-2) = - 3
f (0) = 1
By the Zero Product Property, if (2x - 1)(x - 5) = 0, then
Answers
Split into two equations:
[tex]\begin{gathered} 2x-1=0_{\text{ }}(1) \\ x-5=0_{\text{ }}(2) \end{gathered}[/tex]From (1) solve for x:
[tex]\begin{gathered} 2x=1 \\ x=\frac{1}{2} \end{gathered}[/tex]From (2) solve for x:
[tex]x=5[/tex]Answer:
x = 1/2 or x = 5
2. Write an expression that can be used to calculate how many hours are needed for a party. Then use yourexpression to tell the number of hours needed for a party with 16 participants and 4 escape puzzles.• (Replace this text with your expression)I• (Replace this text with your answer and work)
Answers
We know that each escape room is scheduled for 20 minutes. So, if there are 8 participants, then they need 160 minutes, which is equivalent to 2.67 hours.
So, the expression would be
[tex]\frac{20\times8}{60}[/tex]On the other hand, if there are 16 participants, then the hours needed are
[tex]2\cdot\frac{20\times8}{60}\approx5.33[/tex]Suppose the population of a town is 5,900 and is growing 2% each year. Write an equation to model the growth in population.
Answers
The equation/formula to model population growth can be given below;
[tex]\begin{gathered} P=P_0\times e^{rt} \\ \text{where P = total population after time t} \\ P_0=orig\text{inal or starting population} \\ r=\text{ rate of growth in percentage} \\ t=\text{time in years} \\ e=\text{Euler's constant = }2.71828 \end{gathered}[/tex]Therefore, for the question using the same formula, we have the model equation as;
[tex]\begin{gathered} P_0=5000 \\ r=2\text{ \% = 2/100=0.02} \\ \text{Then the equation will be;} \\ P=5000\times2.71828^{0.02t} \end{gathered}[/tex]Hence, P = 5000 x 2.71828^0.02t
Find the slope of the line that passes through (10, 10) and (3,1).Simplify your answer and write it as a proper fraction or improper fraction
Answers
The formula for the slpe of line passes through point (x_1,y_1) and (x_2,y_2) is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Determine the slope of line passes through the points.
[tex]\begin{gathered} m=\frac{1-10}{3-10} \\ =\frac{-9}{-7} \\ =\frac{9}{7} \end{gathered}[/tex]So answer is 9/7.
Which of these best describes the profit Frank makes from selling these cards?
Answers
The correct answer is option C.
That is, He makes $1.00 for each 6 boxes he sold.
The sum of two numbers is 32 and the quotient in 3.find the two numbers.
Answers
8 and 24
Explanation:let the two numbers be x and y
Sum of the two numbers = 32
[tex]x\text{ + y = }32\text{ . . . equation 1}[/tex]Quotient = 3
[tex]\begin{gathered} \frac{x}{y}\text{ = 3 . . . equation 2} \\ x\text{ = 3y . . . equation 2} \end{gathered}[/tex]substitute for x in equation 1:
[tex]\begin{gathered} 3y\text{ + y = 32} \\ 4y\text{ = 32} \\ y\text{ = }\frac{32}{4} \\ y\text{ = 8} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = 3(8)} \\ x\text{ = 24} \end{gathered}[/tex]Hence, the two numbers are 8 and 24
For each value of u, determine whether it is a solution to 5u + 6 > 51.
Answers
ANSWER
[tex]u=10[/tex]EXPLANATION
Given
[tex]5u+6>51[/tex]To check if each of the given values is a solution;
We substitute each of the given values into the equation.
Hence, when;
[tex]\begin{gathered} u=-1 \\ \end{gathered}[/tex][tex]5u+6>51[/tex]substitute
[tex]u=-1[/tex]We have;
[tex]\begin{gathered} 5u+6\gt51 \\ 5\left(-1\right?+6>51 \\ -5+6>51 \\ 1>51 \end{gathered}[/tex]Since ;
[tex]1<51[/tex]Hence;
[tex]u=-1[/tex]u = -1 is not a solution.
When
[tex]u=10[/tex][tex]\begin{gathered} 5u+6\gt51 \\ 5\left(10\right?+6>51 \\ 50+6>51 \\ 56>51 \end{gathered}[/tex]Hence;
[tex]u=10[/tex]Is a solution.
When
[tex]u=9[/tex]Substitute u = 9
[tex]\begin{gathered} 5u+6\gt51 \\ 5\left(9\right?+6>51 \\ 45+6>51 \\ 51>51 \end{gathered}[/tex]Hence
[tex]u=9[/tex]is not a solution
Hence, since -6 is less than 9, -6 is not also a solution to the given equation.
Therefore the only solution is;
[tex]undefined[/tex]I want to see if I solved a problem correctly
Answers
The problem gives us two expressions:
[tex]\begin{gathered} y=9x-18 \\ y=18x \end{gathered}[/tex]And we need to solve for x. For that, the first step is to replace "y" on the first expression by the right side of the second expression:
[tex]18x=9x-18[/tex]Now we need to isolate the "x" variable on the left side:
[tex]\begin{gathered} 18x-9x=-18 \\ 9x=-18 \\ \frac{9x}{9}=\frac{-18}{9} \\ x=-2 \end{gathered}[/tex]We can now find "y" by replacing the value of "x" on the second expression:
[tex]y=18\cdot(-2)=-36[/tex]The value of x is equal to -2, and the value of y is equal to -36.
How do I write transformations? More specifically how would I show how a line is being shifted up and down and how can I show said line is being reflected?
Answers
Given an arbitrary line with gradient m, that passes through a point (x1, y1)
The equation of the line is
y - y1 = m( x - x1)
To shift the line up by g units
Then, the new equation becomes
y - y1 + g = m(x - x1)
To shift the line down by g units
Then, the new equation becomes
y - y1 - g = m(x - x1)
Taking the axis of reflection as x = 0
The reflection of the line is
-y - y1 = m( x - x1)
Taking the axis of reflection as y = 0
The reflection of the line is
y - y1 = m( -x - x1)
1- A given line as a slope of – and y-intercept of 8. Which equation represents a line4that is parallel to the given line and passes through the point (-8,-2)?
Answers
Answer:
y=(1/4)x.
Explanation:
Two lines are parallel if their slopes are equal.
The slope of the given line is 1/4, therefore:
• The slope of the new line = 1/4
Thus, the goal is to find the equation of a line with a slope of 1/4 that passes through (-8,-2).
Using the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=\frac{1}{4}(x-(-8)) \\ y+2=\frac{1}{4}(x+8) \\ y+2=\frac{1}{4}x+2 \\ y=\frac{1}{4}x+2-2 \\ y=\frac{1}{4}x \end{gathered}[/tex]The equation of the line is y=(1/4)x.
The 3rd choice is correct.
Find the probabilityA box of chocolates contains three milk chocolates, four dark chocolates, and threewhite chocolates. You randomly select a chocolate. It is a milk chocolate or a darkchocolate.O 0.556O None of the other answers are correct0 0.7000363O 0.818
Answers
In total the box has 10 chocolates. 7 of them are milk or dark chocolate, hence the probability is:
[tex]P=\frac{7}{10}=0.7[/tex]Therefore the probability is 0.7
Find f(8) if f(x) = 5x-1
Answers
Answer
f(8) = 39
Explanation
The question asks us to find f(8), that is, f(x) when x = 8 if
f(x) = 5x - 1
Inserting x = 8
f(8) = (5 × 8) - 1
f(8) = 40 - 1
f(8) = 39
Hope this Helps!!!
Find the volume of the cone on the left. Use 3.14 for i. The volume is m (Type a whole number or a decimal. Round to the nearest hundredth as needed.) 148 m 19 m
Answers
Given data:
The given figure of the cone.
The expression for the volume of the cone is,
[tex]\begin{gathered} V=\frac{1}{3}\pi(r)^2h \\ =\frac{1}{3}\pi(19m)^2(148\text{ m)} \\ \approx55,921.31m^3\text{ } \end{gathered}[/tex]Thus, the volume of the cone is 55,921.31 cubic-m.
Use the diagram to the night to answer questions 1-4 1. Name two points collinear to point K2. Give another name for line b. 3. Name the intersection of line c and plane R. 4. Name a point non-coplanar to plane R
Answers
ANSWER
1. L and J
2.
3.
4.
EXPLANATION
1) We want to name two points that are collinear to K. That is two points that lie on the same line as K.
They are points L and J
2) To name line b,
√ is simplified to x4y5y√. What were the values of H and K in the original question?
Answers
To solve this problem, we will use the following properties of exponents:
[tex]\begin{gathered} \sqrt{a}=a^{\frac{1}{2}}, \\ \sqrt{a}^n=a^{\frac{n}{2}}, \\ a^na^m=a^{nm}. \end{gathered}[/tex]Using the first and second properties we notice that:
[tex]x^4y^5\sqrt{y}=\sqrt{x^{2*4}y^{2*5}y}.[/tex]Simplifying we get:
[tex]\sqrt{x^8y^{10}y}.[/tex]Finally, applying the last property, we get:
[tex]\sqrt{x^8y^{11}}.[/tex]Answer:
[tex]\begin{gathered} H=8, \\ K=11. \end{gathered}[/tex]write the equation of a line in slope intercept form m=-1/8; (8,-5)
Answers
Solution
For this case we have the slope given by:
m = -1/8
And a point given (8,-5) and we can find the equation in the following way:
[tex]-5=-\frac{1}{8}(8)+b[/tex]And we can solve for the intercept b like this:
[tex]b=-5+1=-4[/tex]And the line would be given by:
[tex]y=-\frac{1}{8}x-4[/tex]The percent of change from 30 to 39
Answers
The percent change formula is :
[tex]\%=\frac{N-O}{O}\times100[/tex]where N is the new value and O is the original value.
From the problem, we have O = 30 and N = 39
Using the formula above :
[tex]\%=\frac{39-30}{30}\times100=30\%[/tex]The answer is 30%
Justify each step in the equation solution below with either a property of real numbers (associative, commutative, distributive) or a property of equality (addition or multiplication). 5(x+2)=30 Step 1: 5x+10=30 Justification: Justification Step 2: 5x+10+-10 = 30+-10 5x= 20 Step 3: Justification: 5 x 20 5 5 x=4
Answers
You have the following equation:
[tex]5(x+2)=30[/tex]with the following steps to find the value of x:
5x + 10 = 30 distributive property
5x = 20 addition property of equality (it has added -10 both sides)
x = 4 division property of equality (it has divided by 5 both sides)
please help me I'm not really good with words problem
Answers
we know that
The perimeter of rectangle is equal to
a spinner with 10 equally sized slices has3 Blue slices2 Yellow slices5 Red slicesthe dial is spun & stop at random what is the Probability that the dial Stops on a slice that is NOT blue? write the fraction in the simplest form
Answers
Solution
The number of possible outcomes is 10
We need to find the probability that it is blue
Probability is given as = number of required outcomes/ number of the possible outcome
The probability that the dial Stops on a slice that is blue = 3/10
The probability that the dial Stops on a slice that is NOT blue = 1 - Probability that the dial Stops on a slice that is blue = 1 - 3/10
You hit 9) Consider the set of related x and y values. Which value of g would make it impossible for the set to represent a function? {(8. 67), (5, 28), (g. 19), (9,84)}
Answers
Remember that for any value on the domain of a function, there can only be one value on the range that assigns to it.
We have the set:
[tex]\mleft\lbrace(8,67\mright),(5,28),(g,19),(9,84)\}[/tex]therefore, a value of g that make it impossible for the set to represent a function can be 8, 5 or 9, since those values already have another value assigned from the range.
$1,340 is deposited into a savings account that earns 6% simple interest for three years. What is the balance in the account after 3 years?
Answers
Given:
Pricipal P = %1340.
The rate of interest r = 6% = 0.06.
The numver of years t =3.
The formula to find the amount by simple interest is
[tex]A=P(1+_{}\text{rt)}[/tex]Substitute P=1340, r=0.06, and t=3 in the formula, we get
[tex]A=1340(1+0.06\times3)[/tex][tex]A=1581.2[/tex]The balance in the account after 3 years is $ 1581.20.
1. **Write the equation of the line that is perpendicular to y = -x + 4 and goes through the point (-8,2)
Answers
Write the equation of the line that is perpendicular to y = -x + 4 and goes through the point (-8,2
step 1
Find the slope of the perpendicular line
If two lines are perpendicular, then their slopes are inverse reciprocal
so
the slope of the given line is m=-1/2
therefore
the slope of the perpendicular line is m=2
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=2
point(-8,2)
substitute
2=(2)(-8)+b
solve for b
2=-16+b
b=18
therefore
the equation of the line is
y=2x+18A 5 1/2 ounce strawberry smoothie has 28 1/2 protein of protein in it. Approximately how many grams of protein per ounce are in the smoothie? A. 0.2B. 5.2 C. 4.5
Answers
Method
Divide amount of protein by weight of ounce.
[tex]\begin{gathered} \\ Grams\text{ of protein per ounce = }\frac{28.5}{5.5} \\ =\text{ 5.2} \end{gathered}[/tex]