Three sides measuring 5 in., 12 in., and 14 in.
Explanation:First of all, you need to know some facts about every triangle:
FIRST FACT:
If two sides of a triangle are [tex]a \ and \ b[/tex], then the third side must be less than [tex]a+b[/tex]. Why? because if its length is exactly [tex]a+b[/tex], then you can't build up a triangle, but you'll have a line segment. In other words:
[tex]a<b+c \\ \\ b<a+c \\ \\ c<a+b[/tex]
SECOND FACT:
The internal angles of any triangle add up to 180°. So if ∠A, ∠B and ∠C are the internal angles of a triangle, then:
[tex]\angle A +\angle B+ \angle C=180^{\circ}[/tex]
__________________________
So let's analyze each case:
Case 1. Three angles measuring 25 degrees, 65 degrees, and 90 degrees :
[tex]\angle A=25^{\circ} \\ \\ \angle B=65^{\circ} \\ \\ \angle C=90^{\circ} \\ \\ \\ \angle A +\angle B+ \angle C=25^{\circ}+65^{\circ}+90^{\circ}=185^{\circ} \neq 180^{\circ}[/tex]
The sum is greater than 180 degrees, so these angles can't form a triangle
Case 2. Three angles measuring 50 degrees, 50 degrees, and 50 degrees [tex]\angle A=50^{\circ} \\ \\ \angle B=50^{\circ} \\ \\ \angle C=50^{\circ} \\ \\ \\ \angle A +\angle B+ \angle C=50^{\circ}+50^{\circ}+50^{\circ}=150^{\circ} \neq 180^{\circ}[/tex]The sum is less than 180 degrees, so these angles can't form a triangle
Case 3. Three sides measuring 5 in., 12 in., and 14 in. [tex]a=5 \\ \\ b=12 \\ \\ c=14 \\ \\ \\ 5<12+14\rightarrow 5<26 \\ \\ 12<5+14 \rightarrow 12<19 \\ \\ 14<5+12 \rightarrow 14<17[/tex]The inequalities are true, so these sides form a triangle.
Case 4: Three sides measuring 4 ft, 8 ft, and 14 ft
[tex]a=4 \\ \\ b=8 \\ \\ c=14 \\ \\ \\ 4<8+14\rightarrow 4<22 \\ \\ 8<4+14 \rightarrow 8<18 \\ \\ 14<4+8 \rightarrow 14<12 \ NOT \ TRUE![/tex]
Since the third inequality is not true, then we can't form a triangle with these sides.
mike made a fruit basket of the total fruit 5 were apples 5/8 were bananas and 1/4 were oranges,how many pieces of fruit did mike use?
Answer: 5 7/8
Step-by-step explanation: 5 + 5/8 + 1/4= 5 7/8
The total number of pieces of fruit Mike used is [tex]40.[/tex]
Based on the information given.
1. Let [tex]\( T \)[/tex] be the total number of pieces of fruit.
2. Mike has [tex]5[/tex] apples.
3. [tex]\(\frac{5}{8}T\)[/tex] are bananas.
4. [tex]\(\frac{1}{4}T\)[/tex] are oranges.
Since these fractions represent parts of the total fruit, the sum of the apples, bananas, and oranges should equal the total number of pieces of fruit:
[tex]\[5 + \frac{5}{8}T + \frac{1}{4}T = T\][/tex]
Rewrite the equation with all terms having the same denominator:
[tex]\[5 + \frac{5}{8}T + \frac{2}{8}T = T\][/tex]
Combine the fractions on the left side:
[tex]\[5 + \frac{7}{8}T = T\][/tex]
Subtract [tex]\(\frac{7}{8}T\)[/tex] from both sides to isolate the constant term:
[tex]\[5 = T - \frac{7}{8}T\][/tex]
[tex]\[5 = \frac{1}{8}T\][/tex]
Multiply both sides by [tex]8[/tex] to solve for [tex]\( T \)[/tex]
[tex]\[5 \times 8 = T\][/tex]
[tex]\[T = 40\][/tex]
The measure of arc XZ is 32°.
What is the measure of XYZ?
A. 32°
B. 64°
C. 148°
D. 16°
Given:
Measure of arc XZ = 32°
To find:
The measure of XYZ
Solution:
The measure of inscribed angle is half of the measure of the intercepted arc.
[tex]$\Rightarrow m\angle XYZ = \frac{1}{2}m(ar XZ)[/tex]
[tex]$\Rightarrow 32^\circ = \frac{1}{2}m(ar XZ)[/tex]
Multiply by 2 on both sides.
[tex]$\Rightarrow 2\times 32^\circ =2\times \frac{1}{2}m(ar XZ)[/tex]
[tex]$\Rightarrow 64^\circ =m(ar XZ)[/tex]
The measure of angle XYZ is 64°.
ATTACHEMENTS ADDED 10 PTS 5TH GRADE MATH
Answer:
18.6
Step-by-step explanation:
18 squares and six lines in one square
Its 0.08 because 18 shaded squares and a grand total of 100 tiny square so you get 18/100 which is also = to 0.08 so you get your answer!!
A rectangular parking area measuring 5000 ft squared is to be enclosed on three sides using chain-link fencing that costs $5.50 per foot. The fourth side will be a wooden fence that costs $7 per foot. What dimensions will minimize the total cost to enclose this area, and what is the minimum cost?
Answer:
Dimensions: 75.3778 ft and 66.3325 ft
Minimum price: $1658.31
Step-by-step explanation:
Let's call the length of the parking area 'x', and the width 'y'.
Then, we can write the following equations:
-> Area of the park:
x * y = 5000
-> Price of the fences:
P = 2*x*5.5 + y*5.5 + y*7
P = 11*x + 12.5*y
From the first equation, we have that y = 5000/x
Using this value in the equation for P, we have:
P = 11*x + 12.5*5000/x = 11*x + 62500/x
To find the minimum of this function, we need to take its derivative and then make it equal to zero:
dP/dx = 11 - 62500/x^2 = 0
x^2 = 65000/11
x = 250/sqrt(11) = 75.3778 ft
This is the x value that gives the minimum cost.
Now, finding y and P, we have:
x*y = 5000
y = 5000/75.3778 = 66.3325
P = 11*x + 62500/x = $1658.31
The dimensions that would minimize the total cost are [tex]66.3 \text{ by } 75.4[/tex]
The minimum cost is [tex]\$1658.3[/tex]
Let the sides of the rectangle be [tex]a[/tex] and [tex]b[/tex],
Let the total cost be given by [tex]T=7a+5.5(2b+a)[/tex]
The area, [tex]5000=a\times b \implies a=\frac{5000}{b}[/tex]
Substitute the formula for [tex]a[/tex] into the formula for [tex]T[/tex] to solve for [tex]b[/tex]
[tex]T=\frac{62500}{b}+11b[/tex]
To find the dimensions that would minimize the total cost,
Differentiate to get where the gradients equal zero[tex]\frac{dT}{db}=11-\frac{62500}{b^2}=0[/tex]
when
[tex]b=\pm \frac{250}{\sqrt{11}}[/tex]
Find the second derivative to find the minima[tex]\frac{d^2T}{db^2}=\frac{125000}{b^3}[/tex]
For minima, [tex]\frac{125000}{b^3}>0[/tex]
This means, [tex]b=+\frac{250}{\sqrt{11}}\approx 75.4 ft[/tex] is a minima
The corresponding value of [tex]a=\frac{5000}{b}=\frac{5000}{250}\times\sqrt{11}=20\sqrt{11}\approx 66.3 ft[/tex]
To find the minimum cost, substitute the above minimum value for [tex]b[/tex] into the formula for the total cost
[tex]T=500\sqrt{11}=\$1658.3[/tex]
Learn more about minima and maxima: https://brainly.com/question/2541083
can someone help me answer this question
Answer:
Top Surface Area = π×82
= 201.06192982975 meters2
Bottom Surface Area = π×82
= 201.06192982975 meters2
Lateral Surface Area = 2π×8×4
= 201.06192982975 meters2
Total Surface Area = 603.18578948924 meters2
Step-by-step explanation:
Cindy is shopping for a television. The original price is $612. Store A has the television on clearance for 30% off. Store B has it on clearance for 25% off, and Cindy has a 10% off coupon to use at Store B. At which store will she pay less? How much less?
Answer:
She will pay less at store B
Step-by-step explanation:
30% off of $612 is $428.4
25% off of $612 is $459
Remember she has a coupon for 10% off
10% off of 459 is $413.1
She would save $198.9
Answer:
Step-by-step explanation: store b
What is the total surface area of the square pyramid? 48square meters 64 square meters 76 square meters 88 square meters
Answer: 64m is the answer
Answer:
64 Square Meters is the Right answer...
Step-by-step explanation:
I took the test and got it right:D
f(x) = 3x + 2, f(5) = _
Answer:
17
Step-by-step explanation:
f(x) = 3x + 2
f(5) = 3(5) + 2 = 17
1. Almost No Fat Banana Bread Makes 12 servings
You need to serve 48 people for a school event. Adjust the
recipe. Everyone will have 1 piece each.
Final answer:
To serve 48 people with the 'Almost No Fat Banana Bread' when the original recipe serves 12, multiply the quantities of each ingredient in the recipe by 4.
Explanation:
To adjust the recipe for 'Almost No Fat Banana Bread' to serve 48 people, where the original recipe makes 12 servings, you need to multiply the quantities of each ingredient in the recipe by 4. Since you are aiming to serve 1 piece each to 48 people and the original recipe serves 12, the calculation is:
Number of servings needed ÷ Original number of servings per recipe = Multiplier
48 servings needed ÷ 12 servings per recipe = 4
Therefore, you will multiply each ingredient by 4 to make enough banana bread for 48 servings.
Write the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1). Include your work in your final answer. Type your answer in the box provided to submit your solution.
The slope of the lines passing through given points is [tex]\frac{5}{12}[/tex].
Step-by-step explanation:
Given,
The given two points are (6,6) and (-6,1).
To find the slope of the line passing through the points.
Formula
The slope of the line passing through ([tex]x_{1} ,y_{1}[/tex]) and ([tex]x_{2} ,y_{2}[/tex]) is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Now,
Putting, [tex]x_{1}=6, y_{1}=6, x_{2}=-6, y_{2}= 1[/tex] we get,
Slope = [tex]\frac{1-6}{-6-6}[/tex] = [tex]\frac{-5}{-12}[/tex] = [tex]\frac{5}{12}[/tex]
Hence,
The slope of the lines passing through given points is [tex]\frac{5}{12}[/tex].
Answer:
y=5/12 x+21/6
Step-by-step explanation:
A bag contains pennies nickels dimes and quarters. There are 50 coins in all. Of the coins 14 percent are pennies and 42 percent are dimes. There are 4 more nickels than pennies. How much money does the bag contain?
Final answer:
The bag contains 7 pennies, 11 quarters, 21 dimes, and 11 nickels. The value of the bag is $5.47.
Explanation:
Let's denote the number of pennies as P, nickels as N, dimes as D, and quarters as Q.
From the given information, we can form the following equations:
P + N + D + Q = 50 (since there are 50 coins in total).P = 0.14 * 50 = 7 (since 14% of the coins are pennies).D = 0.42 * 50 = 21 (since 42% of the coins are dimes).N = P + 4 (since there are 4 more nickels than pennies).Substituting the values of P and D into the first equation, we can solve for Q:
7 (pennies) + (P + 4) (nickels) + 21 (dimes) + Q (quarters) = 50
11 + 7 + 21 + Q = 50
39 + Q = 50
Q = 50 - 39 = 11
Now, we can calculate the value of the coins:
Value of pennies: 7 * 0.01 = $0.07
Value of nickels: (7 + 4) * 0.05 = $0.55
Value of dimes: 21 * 0.10 = $2.10
Value of quarters: 11 * 0.25 = $2.75
The total value of the coins in the bag is $0.07 + $0.55 + $2.10 + $2.75 = $5.47.
Q4. The dimensions of a rectangular sheet of metal are 9.96m by 5.08 m. Find
a. the perimeter of the metal, correct to 1 significant figure
b. the area of the metal, correct to the nearest 0.1 m2
Answer:
a) 30m
b) 50.6m²
Step-by-step explanation:
Perimeter = 2(length + width)
= 2(9.96 + 5.08)
= 30.08 m
Area = length × width
9.96 × 5.08
50.5968 m²
Polly sold 34 Snow Cones at
her stand. The amount of each
flavor sold is shown in the bar
graph.
Based on the information in
the graph, which flavors of
snow cones were chosen by
50% of the customers?
Answer:
Melon and Swirl is 50% and Cherry and Grape is 50%
1. 5x + 2 = 27
how to work backwards on this type of problem
Robby is considering taking out a cash advance on his credit card to purchase a new television. His credit card offers cash
advances up to $500.00 at an interest rate of 28%. If the television costs $350.00 and Robby plans to pay the balance of in 6
months, how much extra will he pay in interest to purchase the television?
a $29.14
b. $63.18
C. $174.48
d. $379.08
Answer:
the answer is A.
Step-by-step explanation:
Answer:
A. $29.14
Step-by-step explanation:
if 5^x = 1/125, find the value of x
The answer is the following:
X = -3
Answer:
Step-by-step explanation:
hello :
5^x = 1/125
5^x = (1/5)^5 but : 1/5 = 5^-1
so : x= -1
please answer quickly! Carolyn makes and sells necklaces. The material to make each neckalce costs $3.20. She has 12 necklaces to sell and wants to make a total profit of $54. The following equation describes the situation.
Carolyn found that x = 7.7 and determined that she will make a profit of $7.70 on each necklace . Which error did Carolyn make?
The solution means that she should charge $7.70 for each necklace.
The solution means that each necklace costs $7.70 to make.
The solution to the equation is not x = 7.7.
Carolyn did not distribute the parentheses when solving.
Answer:
A
Step-by-step explanation:
i took the test
Stephanie works at a store that sells clothing accessories. The supply
function for scarves is P = Q-12, where Pis the price and Q is the quantity of
scarves. If Stephanie sells the scarves for $11 apiece, how many scarves can
the store make?
O
A. 34 scarves
O B. 12 scarves
O c. 23 scarves
O D. 11 marves
Answer:
23 scarves
Step-by-step explanation:
To solve this you need to plug the price Stephanie sells the scarves for, $11, in for P in the equation and solve for Q.
11 = Q - 12Add 12 to both sides: 23 = QThe quantity she can make is 23 scarves.
James's dad drove a total of 140 miles last week,
He drove the same number of miles each day and he drove every day.
How many miles did he drive each day?
Answer:
140/24= 5 i think this is the answer
Step-by-step explanation:
Lucy made fewer baskets than Herbert but more basket than fredda.Kwan did not make fewer basket than Herbert.who made the fewest basket?
Answer:
Fredda
Step-by-step explanation:
what is the slope of the line y= 1/2x + 1?
Answer:
The slope is 1/2
Hope that helps:)
what is the answer to this question jhit .
Answer:
the answer is 54
Step-by-step explanation:
hope it helps. can I get brainly please
ΔA'B'C' was constructed using ΔABC and line segment EH.
2 triangles are shown. Line E H is the line of reflection. Line segment B B prime has a midpoint at point D. Line segment A A prime has a midpoint at point F. Line segment C C prime has a midpoint at point G.
For to be the line of reflection between and , which statements must be true? Select three options.
BD = DB'
DF = FG
m∠EFA = 90°
The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
ΔABC is not congruent to ΔA'B'C'.
Answer:1,3,4
Step-by-step explanation:
There are two questions there. Feel free to just answer one. I’m stuck on these last two.
Answer:
7. option D
8. option D
Step-by-step explanation:
7. we can assume the height of the radio tower to be x. We're given with its shadow,the height of the person and also their shadow. Since we have 3 known values and an unknown, we can make a proportion comparing the tower's height to the height of the person.
∴ 6/10 = x/ 400
⇒ x= (6 * 400)/10 = 240 feet.
8. The question is similar to the above question where again we have 3 knowns and one unknown. Let us assume the length to be x. We'll again compare the length of the two photographs and make it as a proportion.
∴ 4/6 = x/10
⇒ x = (4 * 10)/6 = 6.7 in
Hope that answers your questions!
Answer:
Someone already answered so you mine will be useless, anyway have a nice day :D
Step-by-step explanation:
Find the area of the shape shown below
Answer:
240 units²
Step-by-step explanation:
Since it's a composite figure, find the area of the rectangle then the triangle
rectangle
A = wl
A = 20*10
A = 200 units²
Triangle
A = 1/2 wh
A = 1/2 (20)(4)
A = 1/2 (80)
A = 40 units²
Add them together and get 240 units²
The box-and-whisker plot below shows the age distribution of people at a family reunion.
16
24
32
40
48
56
64
Ages
The stem-and-leaf plot below shows the same data.
089
10 1 4 5
3 3 5 6 6
1 6 6 8 9 9 9
0 1 2 4 6
To 236
01
Answer: CCCCCC
Step-by-step explanation:
Refer to the following photo please
10 points easy question
Answer:
I would like to say both reflections and rotational
Step-by-step explanation:
ALGEBRA 2 PROBLEM! PLEASE HELP ME!
Answer:
A
Step-by-step explanation:
cos(60) = adjacent/hypotenuse
½ = B/5
B = 5/2
B = 2.5
How many solutions does this equation have?
4x − 10
2
= 2x − 5
A) no solution
B) exactly one solution
C) exactly two solutions
D) infinitely many solutions
Answer:
d
Step-by-step explanation:
x=3 then the equation has one soultion like 3=3
The equation is a linear equation with one variable then the solution will be exactly one. Then the correct option is B.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The linear equation is given.
4x − 10² = 2x − 5
In the equation above equation, the number of variables is one.
And the equation is a linear equation which means the degree of the x is one then the solution will be unique.
More about the linear system link is given below.
https://brainly.com/question/20379472
In a arithmetic sequence with a^1=12, d=3 which term is equal to 159?
Answer:
50th term is 159
Step-by-step explanation:
nth term=159
a + (n -1)*d = 159
12 + (n-1)*3= 159
(n - 1)*3 = 159 - 12
(n - 1)*3 = 147
n -1 = 147/3
n - 1 = 49
n = 49 + 1
n= 50
Answer: n=50th term
Step-by-step explanation:
An= a1+(n-1)d
An= nth term
A1= first term
N= nth position
D= common difference
An =159
A1= 12
D= 3
N= ?
Substitute the values
An=a1+(n-1)d
159=12+(n-1)3
Collect like terms
159-12=(n-1)3
147=3n-3
147+3=3n
150=3n
N=150/3
N= 50
Therefore 50th term will give 156