The dimensions of playing card is L = 10 centimeter and W=5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.
Step-by-step explanation:
The given is,
Playing card has an area of 50 square centimeters
A perimeter of 30 centimeters
Step:1
A playing card is in the shape of rectangle,
Formula for perimeter of rectangle is,
[tex]Perimeter, P = 2(l+w)[/tex] .........................(1)
Formula for area of rectangle is,
[tex]Area, A= lw[/tex]......................................(2)
Where, l - Length of rectangle
w - Width of rectangle
Step:2
From the given values equation (1) becomes,
[tex]30 = 2(l+w)[/tex]
[tex]\frac{30}{2}=(l+w)[/tex]
[tex]15 =(l+w)[/tex]
[tex]w=15-l[/tex] .............................(3)
Width value in terms of length is calculated.
Step:2
Equation (2) becomes,
[tex]50 = (15-l)(l)[/tex]
[tex]50= 15l -l^{2}[/tex]
[tex]l^{2}-15l+50=0[/tex]
Solving the above equation,
[tex]=10[/tex]
[tex]l=10 cm[/tex]
Step:3
Equation (3) becomes,
[tex]w=15-l[/tex]
[tex]=15-10[/tex]
[tex]=5[/tex]
w = 5 cm
Result:
The dimensions of playing card is L = 10 centimeter and W = 5 centimeter, If the playing card has an area of 50 square centimeter and a perimeter of 30 centimeters.
Final answer:
By creating an equation system using the area and perimeter formulas for a rectangle, the dimensions of the playing card are found to be either 5 cm by 10 cm or 10 cm by 5 cm.
Explanation:
To determine the dimensions of a playing card given its area and perimeter, we need to set up an equation system based on the properties of a rectangle. Let's call the length L and the width W. The area (A) of a rectangle is A = L × W, which in this case is 50 sq cm. The perimeter (P) is P = 2(L + W) and is given as 30 cm.
From the perimeter, we can rearrange this to find L in terms of W:
30 cm = 2(L + W)
15 cm = L + W
L = 15 cm - W
Now, substituting L in the area equation gives us:
50 cm² = (15 cm - W) × W
This can be rearranged to form a quadratic equation:
0 = W² - 15W + 50
Factoring, we find:
0 = (W - 5)(W - 10)
So we have two solutions, W = 5 cm or W = 10 cm.
If we take W as the width, then L (the length) would be the other dimension, which would be 15 cm - W. So, we have two possible dimension pairs based on the standard card size: (5 cm by 10 cm) or (10 cm by 5 cm).
Examples of irrational numbers
Answer:
1.375, 2/5, 0.06, etc.
Step-by-step explanation:
Basically anything that is not a whole number.
Graph the line x = -3
Answer:
Draw a vertical line passing through (-3,0)
Asphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm3.
What is the volume of the sphere?
Answer:
6
Step-by-step explanation: Hi the answer is 6 because a cylinder is 3 times a cone so the cylinder divided by 3 would be your answer
What is the quotation of 3/8 divided 4
Answer: 3/32
Do Keep Change Flip (KCF)
Keep: 3/8
Change: ÷ into ×
Flip: 4/1 into 1/4
Your New Problem: 3/8×1/4
Multiply
3/8×1/4=3/32
Final Answer: 3/32
Answer:
[tex] \frac{3}{32} [/tex]
Step-by-step explanation:
[tex] \frac{3}{8} \div \frac{4}{1} \\ \frac{3}{8} \times \frac{1}{4} \\ = \frac{3}{32} [/tex]
Rozwiąż poniższe równanie.
Egzamin składał się z 20 pytań za każdą dobrą odpowiedź można otrzymać 7 punktów, a za złą traciło sie 2 punkty. Filip odpowiedział na wszystkie pytania zdobywając 104 punkty. Na ile pytań udzielił błędnej odpowiedzi?
Answer:
18
Step-by-step explanation:
Answer:18 bo 20*7=140 140-104=36 36:2=18
Step-by-step explanation:
lol2
Where's the Lie?
Here are three statements that Tiana wrote about this
exponential
One of the statements is a lie. Which is it?
A. For very large values of x, the exponential has very large
values of y.
OB. The y-intercept of the exponential is (0,1).
C. The point (-2,4) is on the exponential.
Explain how you know it's a lie.
Answer:
A.
Step-by-step explanation:
As the x value is increasing the y is decreasing because the graph shows exponential decay.
The graph of a simple exponential function always pass through (0,1)
The statement that is a lie is (a) For very large values of x, the exponential has very large values of y.
From the graph, we have the following highlights
The graph passes through point (0,1); this means that the y-intercept is (0,1).The graph passes through (-2,4)The above highlights mean that options (b) and (c) are true, while option (a) is a lie
Option (a) is a lie because, as the value of x increases, the value of y increases.
Read more about exponential functions at:
https://brainly.com/question/11487261
How do you solve for mass if KE=0.5mv2
Answer:
[tex]m=\frac{2KE}{y^{2} }[/tex]
Triangle ABC was translated according to the rule (x, y) = (x + 1.5, y-3.5) to create the image AA'B'C' shown on the
coordinate plane
Which graph shows the pre-image, ABC?
Answer:
Option D
Step-by-step explanation:
Hope this helps! :)
The coordinates of the preimage will be at A(-2.5, 5.5), B(-2.5, 2.5) and C (-6.5, 2.5)
What is translation?Translation is a transformation technique for changing the size and position of an object on the x-y plane.
From the given diagram, the coordinate A'B'C' is given as:
A' = (-1, 2)
B' = (-1, -1)
C' = (-5, -1)
If the triangle ABC was translated according to the rule (x, y) = (x + 1.5, y-3.5) to create the image A'B'C'
A (x + 1.5, y-3.5) = (-1, 2)
x + 1.5 = -1
x = -2.5
y - 3.5 = 2
y = 5.5
Hence A = (-2.5, 5.5)
B = (x + 1.5, y-3.5) = (-1, -1)
x + 1.5 = -1
x = -2.5
y - 3.5 = -1
y = 2.5
Hence B = (-2.5, 2.5)
C (x + 1.5, y-3.5) = (-5, -1)
x + 1.5 = -5
x = -6.5
y - 3.5 = -1
y = 2.5
Hence C = (-6.5, 2.5)
Hence the graph that shows the pre image ABC is attached below
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#SPJ5
Helppppppppppp please am struggling :(
Answer:
x = 30°
Step-by-step explanation:
The complete circle is 360°, thus
arc AB = 360° - 300° = 60°
The tangent- secant angle ABT is half the measure of the intercepted arc AB, that is
x = 0.5 × 60° = 30°
Answer:
Its x = 30°
Step-by-step explanation:
Round your answer to the nearest hundredth.
Answer:
8.06
Step-by-step explanation:
A² + B²= C²
4² + B² = 9²
16 + B² = 81
B² = 81 - 16
B² = 65
B = [tex]\sqrt65[/tex]
B = 8.06225775
Rounded = 8.06
Answer: 26⁰
Step-by-step explanation:
I hope this help
What is the area of the figure? 6-sided concave polygon with side with 40 inches, 10 inches, 22 inches, 40 inches, 18 inches, and 50 inches. 180 square inches 190 square inches 1200 square inches 1120 square inches
Answer:
1120 square inches or OPTION D
Step-by-step explanation:
40 × 50 = 2000
(50 - 10) × (40 - 18) =
40 × 22 = 880
2000 - 880 = 1120
Please Help With This Problem
A.) SAS Postulate
B.) SSS Postulate
C.) AAS Theorem
D.) You cannot prove that the triangles are congruent.
Answer:
SAS POSTULATE
Step-by-step explanation:
ON SIDE IS COMMON
TWO SIDES ARE CONGRUENT TO EACHOTHER
WHILE SAME WITH THE TWO ANGLES
1) The local fire company is having a raffle to raise money for Fourth of July fireworks. They
will sell one thousand tickets at $10 each. They will award one first prize of $300, one second
prize of $150, and one third prize of $50. The other tickets will win nothing. What is the
expected value of a ticket?
O
- $0.50
O $300.00
O $9.50
O - $9.50
Answer:
negative - $9.50
Step-by-step explanation:
The expected value of a ticket of the local fire company given the price and the expected values is $-9.50.
What is the expected value?
The expected value is the sum of the prizes added to the cost.
Expected value = value of the prizes - cost
(300 + 150 + 50 + 0) - (10 x 1000)
500 - 10,000
- 9500
Expected value of a ticket = - 9500 / 1000 = -9.50
To learn more about addition, please check: https://brainly.com/question/349488
A grocery store finds that the number of boxes of a new cereal sold increases each week. In the 1st week, only 20 boxes of the cereal were sold. In the 2nd week, 53 boxes of the cereal were sold and in the 3rd week 86 boxes of the cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence.
what is the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n?
Use this rule to calculate how many boxes of cereal will be sold during the 7th week.
Answer:
218 boxes of cereal
Step-by-step explanation:
To get the explicit rule, find the difference between each week:
53-20 = 33
86-53 = 33
The explicit rule is:
aₓ = 33x - 13
or
f(x) = 33x - 13
If you use this rule, you can plug in 7 for x and you get:
218 boxes of cereal
At the time of her grandson’s birth, a grandmother deposits $13,000 in account that pays 2.5% compounded monthly. What will be the value of the account at the child’s twenty-first birthday, assuming that no other deposits or withdrawals are made during this period
Answer:
19, 300 i think thats correct im sorry if not
Step-by-step explanation:
15) Solve. −x2 = 2x − 15 A) x = 3, x = 5 B) x = −3, x = 5 C) x = 3, x = −5 D) x = −3, x = −5
Answer:
x=-5 x=3
Step-by-step explanation:
−x2 = 2x − 15
Add x^2 to each side
x^2−x2 =x^2+ 2x − 15
0 = x^2+ 2x − 15
Factor
What two numbers multiply to -15 and add to 2
5*-3 = -15
5-3 =2
(x+5) (x-3) =0
Using the zero product property
x+5 =0 x-3=0
x+5-5=0-5 x-3+3=0+3
x=-5 x=3
I need help
please
:^
Answer:
48 batches of muffins
Step-by-step explanation:
There are 4 cups in 1 quart
4 quarts in 1 gallon
there are 3 gallons
3 gallons = 3(4 quarts)
3 gallons = 12 quarts
12 quarts = 12(4 cups)
12 quarts = 48 cups
48 cups per batch = 48 batches of muffins
A circle has a central angle that measures 23º and the arc length is 12pi. Find the measure of the radius in radians. Round answers to nearest hundredth.
Answer:
The radius of the circle is 93.91
Step-by-step explanation:
In order to calculate the radius of this circle we can apply the formula to find the arc length. This formula is shown below:
length = [(angle)*pi*radius]/180
Since we want to find the radius we can isolate that variable, as shown:
(angle)*pi*radius = length*180
radius = (length*180)/(angle*pi)
radius = (12*pi*180)/(23*pi) = (12*180)/23
radius = 93.91
How would you dilate the point (-3,2) by a scale factor of 1/2
you would multiply each value by the scale factor
Sarah has 10 apples and 2 go missing. How many does she have now?
Answer:
8
Step-by-step explanation:
10 take away 2 is 8.
Find the equation of the line.
Answer:
y= -2x +5
Step-by-step explanation:
Answer:
y=-2x+5
Step-by-step explanation:
ok an easy way to tell is on the y axis when x=0 the lnumber that y is,is the regualar number. Then if you go down and over till you get another point is you x. down is like 2x but if you went over 3 it would be 2/3x but since you only going over once it is just 2x. and the minus is because your going down
Round to the nearest ten thousand and then subtract
Kayla randomly surveyed the eight-grade classes at her school and found that 12 out of 50 own a pet. Based on these data, how many of the 150 eight-grade students in kayla’s school would be expected to own a pet?
Answer: The answer should be 36
Answer:
36 students
Step-by-step explanation:
Set up a proportion
12/50=x/150
Cross multiply
50x=1800
Divide by 50 on both sides
x=36
So 36 out of 150 8th grades students would be expected to own a pet
Hope this helps! :)
5. Cameron is 48.6 inches tall and
Kellen is 50 inches tall. How
much taller is kellen?
Answer:
the answer is 1.4 inches taller
Step-by-step explanation:
What are the primary ways to finance your business?
Answer:
Step-by-step explanation:
finding financing in any economic climate can be challenging, whether you're looking for start-up funds, capital to expand or money to hold on through the tough times. ...
Step-by-step explanation: the primary ways to finance your business are through savings, credit cards, friends and family, loans from lending networks or programs, angel investors, business loans and lines of credit, factoring, and purchase order funding.
In the circle below, diameter CD is perpendicular to chord AB as shown. Radii OB and OA are drawn.
(a) How could we prove that OEB is congruent to OEA? Explain.
(b) What does your answer tell you must be true about segments AE and BE ? Why?
(c) If the diameter of circle O is 20 and CE 4, then determine the length of AB . Show how you arrived at your answer.
Answer:
The length of AB is 16 units.Step-by-step explanation:
(a)We know that [tex]\angle OEB = 90\°[/tex], by given, so it's a right angle, by definition.
[tex]\angle OEA[/tex] and [tex]\angle OEB[/tex] are adjacent angles on a straight angles. That means they are sumplementary angles by definition.
[tex]\angle OEA + \angle OEB = 180\°\\ \angle OEA = 180\° -90\°\\\angle OEA = 90\°[/tex]
Therefore, [tex]\angle OEA = \angle OEB[/tex].
(b)Sides AE and BE are congruent, because the congruence between those right angles, and the congruence between the other corresponding sides justify the congruence between sides AE and BE.
Notice that the hypothenuses of each right triangle are congruent, because they are also radius of the circle, which means they are congruent by definition.
Additionally, side OE is a common leg for both right triangles.
Therefore, sides AE and BE are congruent.
(c)We know that [tex]d=20[/tex] and [tex]CE=4[/tex], that means the radius is
[tex]r=\frac{d}{2}=\frac{20}{2}=10[/tex]
Notice that the chord AB is formed by AE and BE by sum of segments.
We know the hypothenuses are equal to 10 units of length, because they are radius.
Additionally,
[tex]OC=OE+EC[/tex], by sum of segments.
[tex]10=OE+4\\OE=10-4\\OE=6[/tex]
Which means the common leg is 6 units long.
Now, we use the Pythagorean's theorem to find the missing leg
[tex]OB^{2}=EB^{2}+OE^{2}\\ 10^{2}=EB^{2}+6^{2}\\100-36=EB^{2}\\EB=\sqrt{64}\\ EB=8[/tex]
But, [tex]AB=AE+EB[/tex], by sum of segments.
[tex]AB=8+8=16[/tex], because [tex]AE=EB[/tex] we said before.
Therefore, the length of AB is 16 units.
t/(5/12)=(-3/10)
what is t ???
Answer:
t = - [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Given
[tex]\frac{t}{\frac{5}{12} }[/tex] = - [tex]\frac{3}{10}[/tex]
Multiply both sides by [tex]\frac{5}{12}[/tex]
t = [tex]\frac{5}{12}[/tex] × - [tex]\frac{3}{10}[/tex] ← cancel 5 and 10 by 5 and 3 and 12 by 3, leaving
t = [tex]\frac{1}{4}[/tex] × - [tex]\frac{1}{2}[/tex] = - [tex]\frac{1}{8}[/tex]
What is the volume (in cubic feet) of the composite shape rounded to the nearest whole number.
https://lh4.googleusercontent.com/vUIfZHaKxbdifO93idzlasRKfEgvrv14A-EqM3jgStNqNpMzpBqIf2mI5R_S4juEGlQnyVlZfDxjJFMkbmYu5Gt7LyBl241M1XtOtKLHXRidvyOygtO4tvdkcTuU=w147
Answer:
109.956
Step-by-step explanation:
Formula for Volume of Cylinder: V = (pi)r^2H
84.823 + 25.133 = 109.956 (in cubic feet)
What is the correlation coefficient for the data shown in the table?
Answer:
they all equal 15
Step-by-step explanation:
Answer: The answer is 1.
Step-by-step explanation:
The correlation coefficient is “r” on the regression calculator. When you put the data into the calculator r=1.
Please help fast!!!!
Answer:
C
Step-by-step explanation:
The exponent is negative so you put the number under 1 with the exponent positive
Answer:
I think the correct answer should be C
Step-by-step explanation:
2-4= -2