Answer:
The length of the shorter part of the wire is 24 centimeters.
Step-by-step explanation:
Let [tex]L[/tex] the total length of the piece of wire, where [tex]L-x[/tex] and [tex]x[/tex] are the perimeters of the greater and lesser squares. All lengths are measured in centimeters. Since squares have four sides of equal length, the side lengths for the greater and lesser squares are [tex]\frac{L-x}{4}[/tex] and [tex]\frac{x}{4}[/tex]. From statement we find that the sum of the areas of the two squares ([tex]A[/tex]), measured in square centimeters, is represented by the following expression:
[tex]A = \left(\frac{L-x}{4} \right)^{2}+\left(\frac{x}{4} \right)^{2}[/tex] (1)
And we expand this polynomial below:
[tex]A = \frac{L^{2}-2\cdot L\cdot x +x^{2}}{16} + \frac{x^{2}}{16}[/tex]
[tex]A = \frac{L^{2}-2\cdot L\cdot x +2\cdot x^{2}}{16}[/tex]
[tex]2\cdot x^{2}-2\cdot L\cdot x +L^{2}-16\cdot A = 0[/tex] (2)
If we know that [tex]L = 76\,cm[/tex] and [tex]A = 205\,cm^{2 }[/tex], then the length of the shorter part of the wire is:
[tex]2\cdot x^{2}-152\cdot x +2496 = 0[/tex]
By the Quadratic Formula, we determine the roots associated with the polynomial:
[tex]x_{1} = 52\,cm[/tex], [tex]x_{2} = 24\,cm[/tex]
The length of the shorter part of the wire corresponds to the second root. Hence, the length of the shorter part of the wire is 24 centimeters.
find angle X on the given figure. m
Answer:
x = 61°
Step-by-step explanation:
In a rhombus, the diagonals bisect the angles, thus
∠ BAE = ∠ DAE = 29° , then ∠ A = 58°
∠ ADE = ∠ CDE = x , then ∠ D = 2x
In a rhombus, consecutive angles are supplementary
∠ A and ∠ D are consecutive angles , then
58 + 2x = 180 ( subtract 58 from both sides )
2x = 122 ( divide both sides by 2 )
x = 61°
solve for x round your answer to the nearest tenth
Answer:
13.7
Step-by-step explanation:
Pythagorean theorem converse
Answer:
The value of x is 13.7.
Step-by-step explanation:
☆We are going to use the Pythagorean theorem to solve this.
☆Pythagorean Theorem:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
☆Remmeber: a = leg, b = leg, c = hypotenuse or the diagonal.
☆Let's plug in according to the pythagorean theorem and solve!
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {x}^{2} + {9.2}^{2} = {16.5}^{2} \\ {x}^{2} + 84.64 = 272.25 \\ \frac{ \: \: \: \: \: \: \: \: - 84.64 = - 84.64}{ {x}^{2} = \sqrt{187.61} } \\ x = 13.7[/tex]
Kate used 2/5 of a pound of sugar to bake cookies. She used another 3/4 of a pound of flour for the cookies. How many pounds of sugar and flour did she use in all? ASAP ANSWER PLS
Answer:
c. 1 3/20
Step-by-step explanation:
a guess hopefully you are right
y=x+3
y=x-3
Solve these equations
Answer:
what is x?
Step-by-step explanation:
Answer:
No solutions
Step-by-step explanation:
The variable Q varies inversely as the cube of V. FK is the constant of variation, which equation represents this situation?
A. qv^3=k
B. q^3v=k
C. q/v^3=k
D. q^3/v=k
Step-by-step explanation:
When 2 variables are inversely proportional to each other, their product is a constant.
Since Q and V³ are inversely proportional to one another, QV³ = k. (B)
Please help please please ASAP
Answer:
choose the first one.
0.87
Answer:
Use your calculator
Step-by-step explanation:
Press the cos button COS( - should look like that... Then fill it out COS(30) make sure to add the closed parenthesis so you dont get an error. And then BAM you got your answer and dont have to look anymore up. XD
What is the simplified form of
of (-7xº+5x²-x+6)-(-8x2 + x +3)?
ОА.
-x + 4x2 - x+3
OBX + 4x² - x+3
ocx - 4x² – 2-3
D. -15x + 6x? - X+9
Please I need help immediately
Note: Your answer choices remain a little unclear. But, I have solved the concept and solution, so you can easily figure it out.
Answer:
[tex]\left(-7x^0+5x^2-x+6\right)-\left(-8x^2+x+3\right)=13x^2-2x-4[/tex]
Step-by-step explanation:
Given the expression
[tex]\left(-7x^0+5x^2-x+6\right)-\left(-8x^2+x+3\right)[/tex]
solving the expression
[tex]=-7x^0+5x^2-x+6-\left(-8x^2+x+3\right)[/tex]
apply the rule: [tex]a^0=1,\:a\ne \:0[/tex]
[tex]=-7+5x^2-x+6-\left(-8x^2+x+3\right)[/tex]
[tex]=-7+5x^2-x+6+8x^2-x-3[/tex]
simplify
[tex]=13x^2-2x-4[/tex]
Therefore, the simplified form is:
[tex]\left(-7x^0+5x^2-x+6\right)-\left(-8x^2+x+3\right)=13x^2-2x-4[/tex]
Note: Your answer choices remain a little unclear. But, I have solved the concept and solution, so you can easily figure it out.
The five marathon runners weigh an average weight of 92 pounds, Nicole weighs 89 pounds, Jon weighs 95 pounds, Jenny and Kim weigh 90 pounds each, How much does Jordin weigh?
Answer:
Jordin weighs 96 pounds
Step-by-step explanation:
The Mean Value of a Data Set
The mean or average of a data set is found by adding all numbers and then dividing by the number of values in the set. Written as a formula:
[tex]\displaystyle \bar x=\frac{\sum x_i}{n}[/tex]
Where xi is the value of each data and n is the total number of values.
We are given the average weight of n=5 marathon runners:
[tex]\bar x=92[/tex]
Multiplying the formula by n and expanding the sum:
[tex]n\bar x=\sum x_i=x_1+x_2+x_3+x_4+x_5[/tex]
We are given the weighs of four of the runners:
[tex]5*92=89+95+90+90+x_5[/tex]
[tex]460=364+x_5[/tex]
Solving for x5:
[tex]x_5 = 460-364=96[/tex]
Jordin weighs 96 pounds
Find the circumference of a circle with radius of 18 in
Answer: 113.1 in.
Step-by-step explanation:
C=2πr=2·π·18≈113.09734in
Hope this helped! :)
Select the correct answer.
Determine which equation has the same solutions as the given equation.
x2 − 10x − 11 = 0
A.
(x − 5)2 = 21
B.
(x − 10)2 = 21
C.
(x − 10)2 = 36
D.
(x − 5)2 = 36
Answer:
D. [tex]\displaystyle (x - 5)^2 = 36[/tex]
Step-by-step explanation:
All you are doing is converting this Quadratic Equation to a Vertex Equation in Vertex Form by completing the square:
[tex]\displaystyle [\frac{b}{2}]^2 \\ \\ x^2 - 10x - 11 = 0 → x^2 - 10x + 25 - 36 = 0→ (x - 5)^2 - 36 = 0 \\ \\ (x - 5)^2 = 36[/tex]
It is that simple, is it not?
I am joyous to assist you at any time.
can someone pls help me !!!
Answer:
I dont know the answer, but I am going to give you a lot of luck, so good luck!
Step-by-step explanation:
Solve for x. I need help :,) thank you if you help!
Answer: if its a multiple of a 345 triangle then its congruent x is 36 if othersides ate multiples of 20 ie
Sides are
60 80 100 is a 345 right triangle
Step-by-step explanation:
plzz helpp guys
At the beginning of an environmental study, a forest covered an area of 1500 km . Since then, this area has decreased by 2.4% each year. Lett be the number of years since the start of the study. Let y be the area that the forest covers in km². Write an exponential function showing the relationship between y and t.
Answer:
[tex]y = 1500(0.024)^t[/tex]
Step-by-step explanation:
Given
[tex]a = 1500km[/tex] -- initial area
[tex]b = 2.4\%[/tex] -- rate
[tex]t = time[/tex] --- (years)
Required
Represent as an exponential function
An exponential function has the form:
[tex]y = ab^t[/tex]
Where
[tex]a = initial\ value[/tex]
[tex]b = rate[/tex] and [tex]b \ne 1[/tex]
[tex]t= time[/tex]
Substitute values for a and b, we have:
[tex]y = 1500 * (2.4\%)^t[/tex]
Convert percentage to decimal
[tex]y = 1500 * (0.024)^t[/tex]
[tex]y = 1500(0.024)^t[/tex]
Hence, the exponential function that represents the scenario is: [tex]y = 1500(0.024)^t[/tex]
Divide. Write the quotient in lowest terms.
5 divide 3 1/3
Answer:
3/2 or 1 1/2
Step-by-step explanation:
5÷3 1/3
5/1 ÷ 10/3 because you have to get it into an improper fraction form in order to divide
5/1 × 3/10 because you have to multiply the first number by the reciprocal
5 and 10 cancel out so you would have 2 at the bottom
3/2 or 1 1/2
Draw an ordered stem and leaf diagram to show this information.
245, 250, 251, 253, 258, 264, 267, 269, 273, 276
Key:
2415 means
Answer:
24|5
25|0;1;3;8
26|4;7;9
27|3;6
Step-by-step explanation:
key in the bottom right:
24|5means 245
What is the area, in square feet, of the trapezoid below?
Answer:
68.75
Step-by-step explanation:
Measure the length of the parallel sides and add them together. Then multiply this number by the height of the area. Then multiply by ½ or divide by two to find the square footage of the trapezoid.
13.6 + 5.9= 19.5
19.5 + 8 = 27.5
27.5 x 5 = 137.5
137.5 x 1/2 = 68.75
c2-1/4=0 equation maths
Answer:
c=1/8
Step-by-step explanation:
2c-1/4=0
2c=1/4
2c/2=1/4/2
c=1/4x1/2
c=1/8
This recipe makes 18 cupcakes.
Deepak only wants to make 12 cupcakes.
How much of each ingredient does he need?
Recipe: Makes 18 cupcakes
12 ounces butter
6 ounces sugar
9 ounces flour
3 eggs
Answer:
Deepak only wants to make 12 cupcakes. Recipe: 8 ounces butter 4 ounces sugar 6 ounces flour 2 eggs
Step-by-step explanation:
Answer:
8 ounces of butter, 4 ounces of suger, 6 ounces of flour, 2 eggs
Step-by-step explanation:
The difference of two numbers is 18. Their sum is 66. What are the numbers? List the numbers from least to greatest.
How do you write 1/12 as a decimal?
Answer:
I think it's 0.083
Step-by-step explanation:
Answer:
0.0833333 (3 is repeating)
Step-by-step explanation:
One spring day, Zoey noted the time of day and the temperature, in degrees
Fahrenheit. During that time, the temperature rose, stayed steady, and fell, at
different rates! On the set of axes below, Zoey created a graph of temperature over
time.
How long did the temperature hold steady for?
Answer:
2 hours
Step-by-step explanation:
Each square=1 hour
2 squares= 2 hours
Lupe is the manager of the football team, and she has to plan a team dinner for Saturday night. She knows that one large pizza can feed 3 players and one sandwich tray can feed 4 players. Lupe needs to order enough food for the 72 players on the team. (a) Write a linear equation to represent the number of pizzas (x) and the number of sandwich trays (y) she could purchase to feed the football players.
Answer:
3x + 4y = 72
Step-by-step exlanation:
Number of pizzas = x
Number of sandwich trays = y
one large pizza can feed 3 players
one sandwich tray can feed 4 players
Total players = 72
The linear equation is
3x + 4y = 72
To rent a certain meeting room, a college charges a reservation fee of $38 and an additional fee of $7.40 per hour. The history club wants to spend less then $75.00 on renting the meeting room.
What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t.
Answer:
the anwser is 55 easy hope this helps;)
Step-by-step explanation:
What is the range of the following numbers:
12,20,18,25,6
Answer:
19
Step-by-step explanation:
You need to find the biggest and smallest number; 25,6
Then you subtract 6 from 25
25-6=19
I hope this helps!!!!!!!
Answer:
19
Step-by-step explanation:
The range is the difference between the highest and the lowest number
So 6, 12, 18, 20, 25 and 25-6 = 19
Please help please please ASAP please please
Step-by-step explanation:
ac is the answer
.............
A baker needs 8 1/2 cups of flour for a sheet cake recipe. He has 4 2/3 cups of flour in a canister and buys 5 1/4 cups more.
How much flour does he have left after he makes the sheet cake?
Enter your answer as a mixed number in simplest form.
I dont know if i asked this question already but, I cant find it, but i need help now!
Answer: 1 5/12 cups of flour leftover
Step-by-step explanation: First, add 4 2/3 + 5 1/4. This gives you 9 11/12. 9 11/12 - 8 1/2 = 1 5/12.
The baker has [tex]1\frac{5}{12}[/tex] cups of flour left after making the sheet cake.
What is Fraction?A fraction represents a part of a whole.
Given that baker needs [tex]8\frac{1}{2}[/tex] cups of flour for a sheet cake recipe.
Baker has [tex]4\frac{2}{3}[/tex] cups of flour in a canister and buys [tex]5\frac{1}{4}[/tex] cups more.
The flour he has in total = [tex]4\frac{2}{3}[/tex] + [tex]5\frac{1}{4}[/tex]
=14/3 +21/4
=56+63/12
=119/12
To find how much flour the baker has left after making the sheet cake, we can subtract the amount needed from the total amount:
119/12 - 17/2 = (119 - 102) / 12 = 17/12
Therefore, the baker has [tex]1\frac{5}{12}[/tex] cups of flour left after making the sheet cake.
To learn more on Fractions click:
https://brainly.com/question/10354322
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CAN SOMEONE HELP ME ??? This is areas and volumes of similar solids!!!!!! It’s urgent!!
Answer:
Step-by-step explanation:
let x be the unknown volume
5/7=50/x
x=70
Answer:
137.2 m³
Step-by-step explanation:
Given the ratio of sides a : b , then
ratio of volumes = a³ : b³
Here ratio of sides = 5 : 7 , then
ratio of volumes = 5³ : 7³ = 125 : 343
let x be the volume of the larger prism then by proportion
[tex]\frac{50}{125}[/tex] = [tex]\frac{x}{343}[/tex] ( cross- multiply )
125x = 17150 ( divide both sides by 125 )
x = 137.2
That is volume of larger prism is 137.2 m³
Help me please thank you
6th Grade Math! Can you please help?
Answer:it is c and d
Step-by-step explanation:
What is it???????? Nada
Answer:
g(3)= -1
Step-by-step explanation:
from the graph f(3)= -1
so, g(3) = -4 * (-1) + 7 = 12