perimeter of a rectangle is 36 cm . If the length of the rectangle is 12 cm . Find its area.
Answer: 72 cm
Step-by-step explanation:
So since we know its length is 12 cm, that leaves us with finding the width. You could do that by adding the two length's together to get 24, then subtract that from the perimeter to get 12. The widths being added together must equal 12 and be the same, so we can divide by 2 to get 6 cm as the width. Then multiply 6 times 12 to get 72
Answer: A=72 cm²
Step-by-step explanation:
Let the width of the rectangle be x
Hence, P=36 cm l=12 cm
P=2(l+x)
P=2l+2x
P-2l=2x
Divide both parts of the equation by 2
Thus,
[tex]\displaystyle\\x=\frac{P-2l}{2} \\\\x=\frac{36-2(12)}{2}\\\\x=\frac{36-24}{2} \\\\x=\frac{12}{2} \\\\x=6 cm\\\\[/tex]
Area A=l*x
A=12*6
A=72 cm²
As of 2011, the following are the ages at which a country's presidents were inaugurated.
52, 62, 64, 51, 46, 64, 69, 60, 59, 51, 49, 50, 59, 61, 61, 48, 51, 42,
57, 46, 44, 47, 53, 63, 48, 53, 67, 52, 67, 63, 69, 53, 47, 45, 59, 48,
59, 56, 50, 60, 68, 45, 63, 62
Construct a grouped frequency distribution for the data. Use 41-45 for the first class and use the same width for each
subsequent class.
The grouped frequency distribution for the data is given as follows:
41 - 45: 0.0909.46 - 50: 0.25.51 - 55: 0.1818.56 - 60: 0.1818.61 - 65: 0.2045.66 - 70: 0.125.How to obtain the grouped frequency distribution?The relative frequency of an outcome in the context of an experiment is given by the number of outcomes assuming this value divided by the number of total outcomes.
Hence the grouped frequency distribution for the data in this problem is obtained considering the relative frequency of each outcome.
For example, we have that:
There are 44 presidents.4 of them were between 41 and 45.Hence the frequency for the age 41-45 is given as follows:
4/44 = 0.0909.
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24)Jessica wants of make a garland out of 8 roses. 12 daisies and 48 marigolds. How many
arrangements can she make with those flowers so that, there is no flower left & what does they look
like.
Answer:
4
Step-by-step explanation:
Given: Number of roses = 8, Number of daisies =12 and number of marigolds 48.
Since we have given,
Number of roses = 8 , Number of daisies = 12 and number of marigolds = 48.
The factors of 8 = 2 * 2 * 2
The factors of 12 = 2 * 2 * 3
The factors of 48 = 2 * 2 * 2 * 2 * 3
Therefore, greatest common factor of 8, 12 and 48 is 4.
Therefore, the total number of arrangements = 4
Answer: 4
Which pair of sides is perpendicular
Answer:
Step-by-step explanation:
d is the answer
Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
In a town where 1/4 of the days are sunny and 3/4 are cloudy, the next six days are all sunny.
The probability of the combined event that the next six days are all sunny is 1/4096
How to determine the probability all days being sunny?From the question, we have the following parameters that can be used in our computation:
Probability that it is sunny = 1/4
Probability that it is cloudy = 3/4
Number of days = 6
The probability for all six days, it is sunny is represented as
Probability = Probability that it is sunny^Number of days
Substitute the known values in the above equation, so, we have the following representation
Probability = (1/4)⁶
Express as decimal
Probability = (0.25)⁶
Evaluate the exponent
Probability = 1/4096
Hence, the probability is 1/4096
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what is -57.17 as a mixed number
The value of 57.17 as a mixed number is - 57 17/100.
In simple terms, what is a mixed number?A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1. When mixed numbers are simplified, the fraction value remains constant. We can say that the simplified mixed number and the actual mixed number are fractions that are equivalent.
A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the proper fraction that results in the mixed number.
In this case, -57.17 will be:
= -57 + (17/100)
= -57 17/100.
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Question 2 (1 poing
This table shows the total shipping costs for objects of
different weights.
Shipping Costs
$6.00
$3.00
$1.50
O $1.25
Weight of Object
(in pounds)
4
8
12
16
Total Shipping Cost
(in dollars)
5
11
17
23
Based on the information in the table, by how many dollars
does the total shipping cost increase if the weight of an
object increases by 1 pound?
Based on the information in the table, the dollars that the total shipping cost will increase if the weight of an object increases by 1 pound is C. $1.50
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It should be noted that from the information, the table shows the total shipping costs for objects of different weights.
In this case, let the dollar amount be x.
Based on the information, this will be:
4x = 6
Divide
x = 6/4
x = 1.5
In conclusion, the correct option is C.
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Con Beads for Everyone Mrs. Harris wants her nineteen students to each have twenty-four beads to make a bracelet. Mrs. Harris finds beads in bags at the store. There are twelve beads in each bag. How many bags of beads does Mrs. Harris need to buy so she has exactly enough beads for her nineteen students? Each bag of beads costs $0.59. How much will Mrs. Harris spend on the beads? Show all your mathematical thinking.
Answer:
i.She needs 96 bags of beads
ii.She will spend $56.64 on the beads
Step-by-step explanation:
i.19×24=456
12÷456=96
96 bags
ii.96×0.59
=56.64
$56.64
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
The statements that are always true regarding the diagram of interior and exterior angles of a triangle include the following:
C. m∠5 + m∠6 =180°.
D. m∠2 + m∠3 = m∠6.
E. m∠2 + m∠3 + m∠5 = 180°.
What is the Linear Pair Postulate?The Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two (2) adjacent angles would be equal to 180º when two (2) parallel lines are cut through by a transversal:
m∠5 + m∠6 =180°.
What is the exterior angle property?The exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle:
m∠2 + m∠3 = m∠6.
In conclusion, the sum of all the angles formed by a triangle is equal to 180º:
m∠2 + m∠3 + m∠5 = 180°,
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Juan runs out of gas in a city. He walks 12 yards west and then 5 yards south looking for a gas station. How far is he from his starting point?
Answer:17
Step-by-step explanation:when we add the 12+5 together and will be the answer
Which of the following transforms y=x squared to the graph of y=(x+5) squared
The transformation which transforms y = x² to the graph of y = (x + 5)² as required in the task content is; a translation of 5 units leftwards.
Which transformation renders y = x² to the graph of y = (x + 5)²?It follows from the task content that the transformation responsible for the mapping y = x² to the graph of y = (x + 5)² is to be determined.
Since the pre-image graph given in the task content is; y = x².
Recall that a translation of a graph f(x) by k units leftward is represented as; f (x + k).
On this note, the given transformation of y = x² to the graph of y = (x + 5)² as required in the task content can be attributed to;
A horizontal shift of 5 units leftward.
Put simply, the required transformation is; a translation of the graph of y = x² 5 units leftwards.
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What is the equation of a line that is parallel to 2x + 3y = 3 and passes through the point (3, -4)?
Enter your answer as a slope intercept equation (y=mx+b) in the box.
Answer:
y = - [tex]\frac{2}{3}[/tex] x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
given
2x + 3y = 3 ( subtract 2x from both sides )
3y = - 2x + 3 ( divide through by 3 )
y = - [tex]\frac{2}{3}[/tex] x + 1 ← in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{2}{3}[/tex] x + b ← is the partial equation
to find b substitute (3, - 4 ) into the partial equation
- 4 = - 2 + b ⇒ b = - 4 + 2 = - 2
y = - [tex]\frac{2}{3}[/tex] x - 2 ← equation of parallel line
Its in the attachment
Domain: (−∞,∞),{x|x∈R} and Range: (−∞,∞),{y|y∈R} for f(x)=0.5x
What is a function?A relation is a function if it has only One y-value for each x-value.
Given,
Helene is selling cupcakes for $0.50 each.
The function f(x)=0.5x gives the total amount of money Helene makes after selling x cup cakes.
We need to find the domain and range of the function
solve the equation f(x)=0.5x to determine the values of the independent variable x and obtain the domain.
To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).
Domain: (−∞,∞),{x|x∈R}
Range: (−∞,∞),{y|y∈R}
Hence, Domain: (−∞,∞),{x|x∈R} and Range: (−∞,∞),{y|y∈R} for f(x)=0.5x
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What is 12% sugar syrup using 5 grams of sugar
Type the integer that makes the following subtraction sentence true:
- -188 = -559
Submit
Answer: -787
188 is positive, negative and negative equals positive
559 is negative
the answer needs to be negative as 559 is negative so you add 559 and 188 and get 787 and add a negative sign so it's more "negative" than 188. (hard to explain in writing)
-787--188=-559
-787+188=-559
-559=-559
5^55x55^22x55^-95=
Anyone?
Answer:
2.4938705426067307E - 8
Step-by-step explanation:
Can someone help me solve these problems?
Answer:
2. A is false
B is false
C is false
D is true
Mary takes out a loan for $6,000 at a simple interest rate of 12% to be paid back in 36 monthly installments. What is the amount of her monthly payments?
The monthly payment would be an amount of $226.67.
What exactly is a monthly payment?A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.
Mary takes out a loan for $6,000 at a simple interest rate of 12% to be paid back in 36 monthly installments.
The total payback = P× r/100 × T + P
Here P = $6,000 , r = 12, and T = 3 years
The total payback = 6,000 × 12/100 × 3 + 6,000
The total payback = 6,000 × 0.12 × 3 + 6,000
The total payback = $8,160
The total payback of the borrowings will be $8,160 over a three-year period. The monthly payment for this will be,
The monthly payment = Total payback / No. of payment
The monthly payment = 8,160/36
The monthly payment = $226.67
Therefore, the monthly payment would be an amount of $226.67.
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When subtracting two numbers, you add the (_______) of the number being subtracted
Answer:
When subtracting two numbers you add the (additive inverse) of the number being subtracted.
Step-by-step explanation:
That's one of the rules of subtracting integers.
Sample Response: The points on the number line do represent additive inverses. 3 and −3 are a zero pair, and when added they equal zero. The two numbers are the same distance from zero but in opposite directions. The following are reasons why 3 and −3 are additive inverses. Check all of the conditions you included in your response.
When two numbers added together result in 0, this is known as additive inverse. Using this notion, points on a number line are used to depict additive inverse.
Explain the term additive inverse?To get a result equal to 0, add the original number and the additive inverse by simply switching the sign of the integer. On the basis of negation of a original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.The dotted points with the numbers 3 and -3 are the places on the number line.
To determine whether the points show an additive inverse:
Points 1 and 2 add up to 0.
3 + (-3) = (3 - 3) = 0
When two numbers added together result in 0, this is known as additive inverse.
Using this notion, points on a number line are used to depict additive inverse.
Thus, the points therefore display additive inverse.
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*1/2
*4 to 4
*2:1
*8/4
Answer:
1/2
Step-by-step explanation:
shaded sections = 4
total sections = 8
4/8
(4:4)/(8:4)
1/2
Answer:
The answer is 4:4.
Step-by-step explanation:
Solve
13=d÷6 plsssssssssssssssssssssssssssssssssssssss
Find the values of X and Y. State which theorem(s) you used.
Using alternating and corresponding angle theorem, the value of x and y are (8, 146), (86, 94) and (21, 29.5) respectively
Alternate and Corresponding Angle TheoremAlternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent. Corresponding and Alternate angles are the most fundamental angles formed when two parallel lines are intersected by a transversal line.
5)
3x = 5x - 64
Reason: Alternate angles are equal
5x + 3x = 64
8x = 64
x = 8
y + 5x - 6 = 180
Reason: Angles on a straight line are equal to 180
y + 5(8) - 6 = 180
y + 40 - 6 = 180
y + 34 = 180
y = 146
6) x = 86
Reason: Alternating angles are equal to one another
y + 86 = 180
Reason = 94
7) 2y = 59
Reason: Vertical angles are equal
y = 59 / 2
y = 29.5
2y = 3x - 4
Reason: Alternate angles are equal
2(29.5) = 3x - 4
59 = 3x - 4
3x = 59 + 4
3x = 63
x = 21
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Write a variable expression for a number w decreased by 7
Answer:
Let the number be x. "Seven less than a number" means that we need to subtract 7 from unknown number and result would be 34. . Then, x−7=34Add 7 on both sides of the equationx−7+7=34+7x=41.
Step-by-step explanation:
In circle M with m ∠ L M N = 106 and LM=4 units, find the length of arc LN. Round to the nearest hundredth.
The length of arc LN of the circle is 7.40 units rounded to the nearest hundredth.
How to calculate for the length of arc of a circleTo calculate for the length of an arc of a circle, we use 2πr × (θ/360), where r is the radius and θ is the angle formed from the arc.
Thus we evaluate for the length of the arc as follows;
for π = 3.14, r = 4 and θ = 106°
2 × 3.14 × 4 × (106/360)°
25.12 × 0.2944
7.3953
Therefore, the length of the arc 7.3953 and rounded up to 7.40 to the nearest hundredth.
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SAS
HL
State how the triangles can be proven
congruent, if possible.
AAS
ASA
Answer:
SAS or HL
Step-by-step explanation:
SAS, you have two sides and two angles congruent on each triangle
HL, you have two hypotenuses and two right angles congruent
I need to find x and y
Using the same-side interior angles theorem,
[tex]8x+30+6x+24=180 \\ \\ 14x+54=180 \\ \\ 14x=126 \\ \\ \boxed{x=9}[/tex]
Using vertical angles,
[tex]6(9)+24=10y+2 \\ \\ 78=10y+2 \\ \\ 10y=76 \\ \\ \boxed{y=7.6}[/tex]
Francesca is way behind on email. Over winter break, she resolves to deal with 5 emails per
day.
Write an equation that shows the relationship between the number of days Francesca has
been on winter break, x, and the total number of emails she has dealt with, y.
y =
Submit
The equation for the total number of emails Francesca has dealt with is; y = 5x.
Explain the term linear equation?A linear equation is just an algebraic expression of the form y=mx+b, where m represents the slope while b is the y-intercept, while only a constant and the first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equations of two variables."For the stated question-
Five emails are handled by Francesca each day.Assume that Francesca has been away on winter break for 'x' days.Let y represent the overall amount of emails she has handled.Then, the linear equation forms is-
y = 5x
Thus, the equation for the total number of emails Francesca has dealt with is; y = 5x.
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If I get $147.00 every two weeks for child support? In a year how much would that equal up to?
Answer:
Step-by-step explanation:
52 weeks in a year
Divide 52 by 2 = 26 weeks
26 weeks x 147 dollars = 3822 dollars
Thus the answer is 3822 dollars yearly
Answer:$3,528
Step-by-step explanation:
since there are 4 weeks in a month that would mean you would have to multiply 147 by two and that would = to $294.00/month so then you would have to multiply that by 12 so then that would = to $3,528.00 a year.
Find the length of LK.Explain work
Since the three triangles are similar the length of LK will be 8 units.
What is the similarity law for triangles?It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
It is given that,
XW=LK=BC
∠WXY = ∠MLK=∠ABC
WY=10
XY=6
AB=6
ΔWXY ≅ MLK
XW=LK
XW=8
LK= 8 units
Thus, if the three triangles are similar the length of LK will be 8 units.
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