quilt squares are cut on the diagonal to form triangular quilt pieces. the hypotenuse of the resulting triangles is 16 inches long.what is the side of each piece. A.8in B.8and 3 in C.16and 2in D. 8and2in.
Answers
The right triangle formed is shown below
From the diagram,
x represents the side of the square. Recall that a square has equal sides
To find x, we would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = 16
one leg = other leg = x
By substituting these values into the formula,
16^2 = x^2 + x^2
16^2 = 2x^2
256 = 2x^2
Dividing both sides by 2,
2x^2/2 = 256/2
x^2 = 128
Taking square root of both sides, we have
[tex]\begin{gathered} x\text{ = }\sqrt[]{128}\text{ = }\sqrt[]{2\times64}\text{ = }\sqrt[]{2}\text{ }\times\text{ }\sqrt[]{64} \\ x\text{ = 8}\sqrt[]{2} \end{gathered}[/tex]The correct option is 8√2 in
Related Questions
I need help with this practice problem Having a tough time solving properly
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
r = 7 sin (2θ)
Step 02:
polar equation:
r = 7 sin (2θ):
r = a sin nθ
n odd ==> n petals
n even ===> 2n petals
n = 2 ===> 2*2 petals = 4 petals
graph:
length of the petals:
r = 7 sin (2θ)
θ = 45°
r = 7 sin (2*45°) = 4.95
The answer is:
4.95
Tents-R-Us makes and sells tents. Tents-R-Us' motto is“Keep It Simple.” The company decides to makes justthree sizes of tents: the Mini, the Twin, and theFamily-Size. All the tents they make have equilateraltriangular ends as shown at right.1. For the Twin, each edge of the triangle will be 8 ft. Find the heightof the tent at the center, correct to the nearest inch. One way to findthis height is to make an accurate scale drawing and measure.
Answers
The company decides to make just three sizes of tents: the Mini, the Twin, and the Family-Size.
The shape of these tents is an equilateral triangle.
Part 1:
For the Twin, each edge of the triangle will be 8 ft.
The height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Where a is the length of the edge of the triangle.
Since we are given that a = 8 ft
[tex]\begin{gathered} h=a\cdot\frac{\sqrt[]{3}}{2} \\ h=8\cdot\frac{\sqrt[]{3}}{2} \\ h=4\sqrt[]{3} \\ h=6.9\: ft \end{gathered}[/tex]Therefore, the height of the Twin tent at the center is 6.9 ft
Part 2:
The Mini tent will have edges 5 ft long.
The height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Where a is the length of the edge of the triangle.
Since we are given that a = 5 ft
[tex]\begin{gathered} h=a\cdot\frac{\sqrt[]{3}}{2} \\ h=5\cdot\frac{\sqrt[]{3}}{2} \\ h=4.3\: ft \end{gathered}[/tex]Therefore, the height of the Mini tent at the center is 4.3 ft
Part 3:
The Family-Size tent will have a height of 10 ft at the center.
Recall that the height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Re-writing the formula for edge (a)
[tex]a=h\cdot\frac{2}{\sqrt[]{3}}[/tex]Since we are given that h = 10 ft
[tex]\begin{gathered} a=h\cdot\frac{2}{\sqrt[]{3}} \\ a=10\cdot\frac{2}{\sqrt[]{3}} \\ a=\frac{20}{\sqrt[]{3}} \\ a=11.6\: ft \end{gathered}[/tex]Therefore, the length of edges of the Family-Size tent is 11.6 ft
If A={a,c} and B={d,g,w} then complete the Following:a. Find AxBb. Find n(AxB)c. write a multiplication equation involving numerals related to the parts in (a) and (b)...a. AxB = {____} Type an ordered pair. Use commas to separate answers as needed
Answers
Given the two sets:
[tex]\begin{gathered} A=\mleft\lbrace a,c\mright\rbrace \\ B=\mleft\lbrace d,g,w\mright\rbrace \end{gathered}[/tex]we can write the product set of A and B in the following form:
[tex]AxB=\mleft\lbrace(a,d\mright),(a,g),(a,w),(c,d),(c,g),(c,w)\}[/tex]next, we have that the number of elements in A is 2 and the number of elements in B is 3, then, we have:
[tex]n(AxB)=2\cdot3=6[/tex]finally, the equation that involves the numerals of the previous parts is:
[tex]n(AxB)=n(A)\cdot n(B)[/tex]where n(A) and n(B) represents the number of elements in A and B respectively.
Write an expression for the sequence of operations described below.1)) multiply 7 by 8, then divide f by the resultDo not simplify any part of the expression.Submit
Answers
We need to write an expression for the operations:
[tex]\begin{gathered} \text{ multiply 7 by 8} \\ \\ \text{dived f by the result} \end{gathered}[/tex]The first operation (multiplication) can be represented as:
[tex]7\cdot8[/tex]The second operation (the division of f by the previous result) can be represented as:
[tex]f\div(7\cdot8)[/tex]Notice that we need the parenthesis to indicate that the product is the first operation to be done.
Answer:
[tex]f\div(7\cdot8)[/tex]Solve the following system of linear equations using elimination.
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Answers
By applying the elimination method, the solutions to this system of three linear equations include the following:
x = 2.y = -2.z = 0.How to solve these system of linear equations?In order to determine the solutions to a system of three linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.
Given the following system of linear equations:
x – y - 3z = 4 .........equation 1.
2x + 3y – 3z = -2 .........equation 2.
x + 3y – 2z = -4 .........equation 3.
From equation 1 and equation 3, we would eliminate x as follows:
x – y - 3z = 4
x + 3y – 2z = -4
-4y - z = 8 .........equation 4.
Next, we would pick a different pair of linear equations to eliminate x:
(x – y - 3z = 4) × 2 ⇒ 2x - 2y - 6z = 8
2x - 2y - 6z = 8
2x + 3y - 3z = -2
-5y - 3z = 10 ........equation 5.
From equation 4 and equation 5, we would eliminate z to get the value of y:
(-4y - z = 8) × 3 ⇒ -12y - 3z = 24
-12y - 3z = 24
-5y - 3z = 10
-7y = 14
y = 14/7
y = -2.
For the value of z, we have:
-4y - z = 8
z = -4y - 8
z = -4(-2) - 8
z = 8 - 8
z = 0
For the value of x, we have:
x – y - 3z = 4
x = 4 + y + 3z
x = 4 - 2 + 3(0)
x = 2
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CS 18 and 105 calories in each juice box The rules for two horseback riding packages are shown below. Go Galloping Horseback Rides $6 equipment fee plus S10 per hous hours horseback riding and let yepresent the total cost of the package. Write a system of equations to represent this situation let x represent the number of Lucky Horseshoe Stables $12 equipment fee plus hour 259 Calories What is the solution to the system of equations? What does the solution represent?
Answers
8A) Let x represent the number of hours of horseback riding.
Let y represent the total cost of the package
If Lucky horseshoe stables is used for x hours, the equation for the total cost would be
y = 7x + 12
If Go galloping horseshoe rides is used for x hours, the equation for the total cost would be
y = 10x + 6
Thus, the equations are
y = 7x + 12
y = 10x + 6
B) To solve the system of equations, we would substitute the first equation into the second equation. It becomes
7x + 12 = 10x + 6
10x - 7x = 12 - 6
3x = 6
x = 6/3
x = 2
y = 7x + 12 = 7 * 2 + 12
y = 14 + 12
y = 26
The solution of the system of equations is (2, 26)
Use U-Subscription to solve the following polynomial. Compare the imaginary roots to the code breaker guide. Hi this is a project and this is one of the questions, I have the guide so ignore the code piece part.
Answers
We will substitute the variable x with the variable u using the following relation:
[tex]u=x^2[/tex]Then, we can convert the polynomial as:
[tex]4x^4+2x^2-12=4u^2+2u-12[/tex]We can use the quadratic equation to calculate the roots of u:
[tex]\begin{gathered} u=\frac{-2\pm\sqrt[]{2^2-4\cdot4\cdot(-12)}}{2\cdot4} \\ u=\frac{-2\pm\sqrt[]{4+192}}{8} \\ u=\frac{-2\pm\sqrt[]{196}}{8} \\ u=\frac{-2\pm14}{8} \\ u_1=\frac{-2-14}{8}=-\frac{16}{8}=-2 \\ u_2=\frac{-2+14}{8}=\frac{12}{8}=1.5 \end{gathered}[/tex]We have the root for u: u = -2 and u = 1.5.
As u = x², we have two roots of x for each root of u.
For u = -2, we will have two imaginary roots for x:
[tex]\begin{gathered} u=-2 \\ x^2=-2 \\ x=\pm\sqrt[]{-2} \\ x=\pm\sqrt[]{2}\cdot\sqrt[]{-1} \\ x=\pm\sqrt[]{2}i \end{gathered}[/tex]For u = 1.5, we will have two real roots:
[tex]\begin{gathered} u=1.5 \\ x^2=1.5 \\ x=\pm\sqrt[]{1.5} \end{gathered}[/tex]Then, for x, we have two imaginary roots: x = -√2i and x = √2i, and two real roots: x = -√1.5 and x = √1.5.
Answer:
Let u = x²
Equation using u: 4u² + 2u - 12
Solve for u: u = -2 and u = 1.5
Solve for x: x = -√2i, x = √2i, x = -√1.5 and x = √1.5
Imaginary roots: x = -√2i and x = √2i
Real roots: x = -√1.5 and x = √1.5
From least to greatest. -1.4-1.02 -1.20
Answers
We could put these values in the number line:
Therefore, the order of the numbers from least to greatest is:
-1.4 , -1.20 , -1.02
The least number between all the options given is -1.4 because if you see, all numbers are negative, so, when a negative number is greater, as the amount after the negative sign becomes greater, the number is going to be least. That's the reason of the order.
Sydney is making bracelets, 3 bracelets require 21 beads. The number of braclets varies directly with the number of beads.
Write an equation in the form of y = ax then find the amount o
beads needed for 32 bracelets.
Answers
Step-by-step explanation:
"varies DIRECTLY with" means there is an y = ax relationship.
y = number of bracelets
x = number of beads
3 = a×21
a = 3/21 = 1/7
now, when we have 32 bracelets
32 = 1/7 × x
32×7 = x = 224
224 beads are needed for 32 bracelets.
Pattern Exercise Mins Components Fitnes 0 5 1 9 2 25 3 89 4 ? What do you notice about the pattern of components from minute to minute? 2. State the value for the question mark. I E O BI
Answers
We can calculate how much each component increases, this is shown in the following image:
So we can see that the pattern in which the components increase from minute to mites is that starts by adding 4, then they add 4x4=16, then they add 16x4=64, and so on:
So the rule is that the next increase is the previous increase multiplied by 4.
Thus, the next increase in components (the question mark) should be:
The previous one +256, which gives:
[tex]?=89+256=345[/tex]Answer: 345
For which values of A, B, and C will Ax + By = C be a horizontal line through the point (−4, 2)?
Answers
The set of values {A = 0, B = 1, and C = 2} to have a completely horizontal line.
What is a horizontal line?A horizontal line is defined as a line with slope m = 0 that is parallel to the x-axis.
A horizontal line across (-4,2) informs us of two things.
A horizontal line with slope m = 0 is parallel to the x-axis.
The line crosses the point (-4,2).
Ax + By = C has m = B/A = 0 slope and intersects point (-4,2).
Then, B = A×0 indicates that any constant A will work, and the Ax term disappears.
Ax + By = C then becomes y = C. To find C, use the point (-4,2).
⇒ C = 2
This line's equation is y = 2, and any point (x,2) matches the equation.
Therefore, the set of values {A = 0, B = 1, and C = 2} to have a completely horizontal line.
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Answer:
Step-by-step explanation:
17
A rectangle is 2 4/5 meters wide and 3 1/2 meters
long. What is its area?
Answers
Answer: Area = l × w
= 3.5 × 2.8
= 9.8 meters2
Step-by-step explanation:
Describe and justify the methods you used to solve the quadratic equations in parts A and B.
Answers
We know that give any pair of real numbers A and B, the following statement will be true:
[tex]A\cdot B=0[/tex]if, and only if
[tex]\begin{gathered} A=0 \\ or \\ B=0 \end{gathered}[/tex]Now, if we factor a quadratic equation into two factors A and B, and use the fact we've just mentioned, we can then equal each factor to zero, solve for x and get the solutions to said quadratic equation.
I need to order the numbers least to greatest for the numbers: sq root of 144 234/3 and 68.12
Answers
So, the order would be 8.25, 8.832 and 12
A music club charges an initial joining fee of $24.00. The cost per CD is $8.50. The graph shows the cost of belonging to the club as a function of CDs purchased. How will the graph change if the cost per CD goes up by $1.00.? (The new function is shown by the dotted line.)
Answers
Given the function with a graph that shows the cost of belonging to the club as a function of CDs purchased
linear function with the form
[tex]y=x[/tex]since the new graph has a new cd cost up by $1.00
then the new line is
Correct answer
Option C
factor completely5r^3-10r^2+3r-6
Answers
You have the following polynomial:
5r³ - 10r² + 3r - 6
In order to factorize the given polynomial, use synthetic division:
5 -10 3 -6 | 2
10 0 6
5 0 3 0
The remainder is zero in the previous division, then, r - 2 is a factor of the given polynomial, the other factor is formed with the coefficients of the division, just as follow:
5r³ - 10r² + 3r - 6 = (r - 2)(5r² + 3)
Hence, the factor are (r - 2)(5r² + 3)
Answer:(r-2) x (5r^2+3)
Step-by-step explanation:
express the fuction graphed on the axes below as a piecewise function
Answers
Concept
Find the equation of line for the second line.
x1 = -2 y1 = 1
x2 = -4 y2 = 2
Next, apply equation of a line formula
[tex]\begin{gathered} \frac{y-y_1}{x-x_1\text{ }}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \frac{y\text{ - 1}}{x\text{ + 2}}\text{ = }\frac{2\text{ - 1}}{-4\text{ + 2}} \\ \frac{y\text{ - 1}}{x\text{ + 2}}\text{ = }\frac{1}{-2} \\ -2(y\text{ - 1) = 1(x + 2)} \\ -2y\text{ + 2 = x + 2} \\ -2y\text{ = x} \\ y\text{ = }\frac{-1}{2}x \end{gathered}[/tex]Final answer
The graphed as a piecewise function is given below
Irlene has just returned from a business trip in Britain with £200 of uncashed traveller's cheques. How much would she receive from the bank when she converts the currency back to Canadian dollars, assuming that the bank offers an exchange rate of C$1.00 = £0.5544 and charges a 0.65% fee to convert the traveller's cheques to Canadian funds? For full marks your answer(s) should be rounded to the nearest cent.
Answers
The converted money in Canadian dollars is $111.6.
Given that, Irlene has just returned from a business trip in Britain with £200 of uncashed traveler's cheques.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the converted Canadian dollars be x.
x = 200 × 0.5544 + 0.65% of 200 × 0.5544
= 110.88 + 0.0065 × 110.88
= 111.60072
≈ 111.6
Therefore, the converted money in Canadian dollars is $111.6.
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The height of a tree is x feet. If it grows ½ times the original height, choose the correct expression that denotes the situation.
Answers
ANSWER
1.5(x)
EXPLANATION
The tree is originally x feet tall. If it grows 1/2 this height it means that now it is 1/2x taller, or we can express this as a decimal, 0.5x. If we add these two heights we'll have the new height of the tree:
[tex]x+0.5x=(1+0.5)x=1.5x[/tex]For what values of b will F(x) = logb x be a decreasing function?A.0 < b < 1B.0 > b > -1C.b > 0D.b < 0
Answers
Given:
There is a function given as below
[tex]F(x)=\log_bx[/tex]Required:
For what value of b the given function in decreasing
Explanation:
The given function is logarithm function
also written as
[tex]F(x)=\frac{log\text{ x}}{log\text{ b}}[/tex]The base b is determines that if the function is increasing or decreasing
here
for
[tex]0the given function is decreasingfor
[tex]b>1[/tex]the given function is increasing
Final answer:
[tex]0
What was the initial population at time t=0?Find the size of the bacterial population after 4 hours.
Answers
Answer;
[tex]\begin{gathered} a)\text{ 195 bacteria} \\ b)\text{ 3,291,055,916 bacteria} \end{gathered}[/tex]Explanation;
a) We want to get the initial population of the bacteria
We start by writing a formula that links the initial bacteria population to a later bacteria population after time t
[tex]A(t)=I(1+r)^t[/tex]where A(t) is the bacteria population at time t
I is the initial bacteria population
r is the rate of increase in population
t is time
Now, let us find r
At t = 10; we know that A(t) = 2I
Thus, we have it that;
[tex]\begin{gathered} 2I=I(1+r)^{10} \\ (1+r)^{10}\text{ = 2} \\ 1+r\text{ = 1.0718} \\ r\text{ = 1.0718-1} \\ r\text{ = 0.0718} \end{gathered}[/tex]Now, let us find I, since we have r. But we have to make use of t= 80 and A(t) = 50,000
Thus, we have;
[tex]\begin{gathered} 50,000=I(1+0.0718)^{80} \\ I\text{ = }\frac{50,000}{(1+0.0718)^{80}} \\ I\text{ = 195} \end{gathered}[/tex]The initial population is 195 bacteria
b) For after 4 hours, we have to convert to minutes
We know that there are 60 minutes in an hour
So, in 4 hours, we have 4 * 60 = 240 minutes
Now, we proceed to use the formula above with I = 195 and t = 240
We have that as;
[tex]\begin{gathered} A(240)=195(1+0.0718)^{240} \\ A(240)\text{ = 3,291,055,916 bacteria} \end{gathered}[/tex]Assume that Jim Bruce and Valerie are 3 of the 17 members of the class, and that of the class members will be chosen randomly to deliver their reports during the next class meeting. What is the probability that Jim Bruce and Valerie are selected in that order?
Answers
The probability that Jim, Bruce and Valerie are selected in that order is P = 1/680
Given,
Number of students in a class = 17
Jim, Bruce and Valerie are 3 of the 17.
Three of students from the class are randomly chosen to deliver their reports during the next class meet.
We have to find the probability that Jim, Bruce and Valerie are selected in that order;
Here,
The total number of possible selection;
S = ⁿCr
Where, n = 17 and r = 3
Then,
S = ¹⁷C₃
S = 17! / 14! x 3!
S = 680
Therefore,
The probability that Jim, Bruce and Valerie are selected in that order is P = 1/680
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HELP ASAP!!!
Find the square of 1-4i.
Answers
ANSAWER:
−15+8i
Explanation:
First, you can expand the square of the bynomial:
Simplify the expression by combing like terms.21v + 8 - 12v - 7 + 3t - t
Answers
We need to simplify the like terms.
"The like terms are whose with the same variable and exponent"
Therefore, the like terms are:
21v - 12v = 9v
8 - 7 = 1
3t - t = 2t
Now, the result is :
9v + 2t + 1
Hence, the correct answer is option D.
. Identify the difference. -2-(-6)
Answers
In this case,
This difference is made this way:
-2 - (-6) =
-2 +6 = 4
So there we have this identity. The minus before the parentheses turns the minus into plus sign.
Can someone explain how I would know the difference between a 2:7 ratio and 7:2 ratio when a point partitions the line? Thank you!
Answers
Solution
For this case we can do the following:
We can understand 7/2 as the reciprocal of 2/7 and we can create the following diagram
A baker need 2/3 cup of sugar,but he can only find a 1/2 cup measure,so he decides to estimate, Which of the following would result in the correct amount of sugar?A)One Full scoop plus 1/3 of a scoopB)One Full scoop plus 1/2 of a scoop C) Two ScoopsD)3/4 of a scoop
Answers
He needs 2/3 cup of sugar . But he can only find 1/2 cup measures.
what is the length of the dominant line in the time graph below? l leave your answer in simplest radical form.
Answers
Let's first calculate the lenght of the side of the rectangle.
[tex]l=\sqrt[]{8^2+5^2}=\sqrt[]{64+25}=\sqrt[]{89}[/tex]so we get that the dotted line is:
[tex]d=\sqrt[]{2^2+89}=\sqrt[]{93}[/tex]so the answer is square root of 93
Here is a right triangle with a missing side length what is the missing side length
Answers
Right Triangles
A right triangle is recognized because it has an interior angle of 90°.
In right triangles, the Pythagora's Theorem is satisfied.
Being a and b the shorter sides (also called legs) of the triangle, and c the longer side (called hypotenuse), then:
[tex]c^2=a^2+b^2[/tex]The triangle shown in the image has the two legs of values a=15 and b=8. The hypotenuse is c=x, thus:
[tex]x^2=15^2+8^2[/tex]Operating:
[tex]x^2=225+64=289[/tex]Solving for x:
[tex]x=\sqrt[]{289}=17[/tex]x = 17
3x - 4y = 65x + 8y = -1
