Answer:
60 square inches
Step-by-step explanation:
In triangle KLM, KL = LM = 13in, KM = 10in. Use the Heron's formula to find the area:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]
where p is half of the perimeter and a, b, c are sides lengths.
Then
[tex]\dfrac{a+b+c}{2}=\dfrac{13+13+10}{2}=18\ in[/tex]
and
[tex]A=\sqrt{18\cdot (18-13)\cdot (18-13)\cdot (18-10)}=\sqrt{18\cdot 5\cdot 5\cdot 8}=5\sqrt{9\cdot 2\cdot 4\cdot 2}=5\cdot 3\cdot 2\cdot 2=60\ in^2.[/tex]
100 - [tex]2^{3}[/tex] x 3 + [tex]8^{2}[/tex] ÷ 4 = _____
Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
------------------------------------------------------------------------------
[tex]100-2^3\times3+8^2\div4\\\\=100-8\times3+64\div4\\\\=100-24+16\\\\=76+16\\\\=\boxed{92}[/tex]
One label on a package of bolts says that each bolt has a diameter of 0.55 inch. To be in the package, the percent error of the diameter must be less than 6%. A test on the production line shows a bolt with a diameter of 0.52 inch. Should this bolt go into the package?
The bolt with a diameter of 0.52 inch has a percent error of approximately 5.45% from the advertised 0.55 inch, which is within the acceptable margin of less than 6%. Therefore, it should be included in the package.
Explanation:The question revolves around determining if a bolt with a diameter of 0.52 inch should be packaged given that the labeled diameter is 0.55 inch and the allowable percent error is less than 6%. To calculate the percent error, we use the formula: Percent Error = (|Actual Value - Theoretical Value| / Theoretical Value) × 100%. Applying the numbers: Percent Error = (|0.52 - 0.55| / 0.55) × 100% = (0.03 / 0.55) × 100% ≈ 5.45%.
Since the percent error of 5.45% is less than 6%, the bolt with a diameter of 0.52 inch should be included in the package. This decision is based on the calculated percent error being within the accepted tolerance level.
Please someone help
Answer:
a. opens: upward
b. a.o.s.: x = 1
c. vertex: (1, -4)
d. x-intercepts: (-1, 0), (3, 0); y-intercept: (0, -3)
Step-by-step explanation:
A:By looking at the graph, we can see that the parabola opens upward. This means that its a-value is positive.
B:The axis of symmetry is the line that passes exactly through the center of the parabola. It always starts with x = __, because it is a vertical line.
The center of this parabola is at the x-value of 1, so we can say that the equation of the axis of symmetry is x = 1.
C:The vertex is at the highest or lowest point of the parabola, also known as the maximum or minimum point. Since this graph opens up, the vertex is at the minimum point.
Look at the graph and find the point where the parabola opens upwards. This point is at the x-value of 1 and the y-value of -4, so the vertex of the parabola is at (1, -4).
D:Again, look at the graph provided to find the x and y-intercepts. On the x-axis, the parabola crosses through at the x-values of -1 and 3, so the x-intercepts are (-1, 0) and (3, 0).
The parabola crosses the y-axis at the y-value of -3, so the y-intercept of the parabola is (0, -3).
Double Delicious Bakery sells a dozen double chocolate dounts for $7.80
A) What is the price per donut? B) What is the cost of 1 and 1/2 dozen donuts?
Answer:
A) each donut costs $0.65
B) the price for 1 and 1/2 dozen of donuts (18 donuts) is $11.70
Step-by-step explanation:
For a you have to divide $7.80 by 12 (since its a dozen) and thats how you get $0.65
For b you have to multiply the price of each donut ($0.65) by the 1 and 1/2 dozen (18 donuts) and thats how you get $11.70
A) The price per donut is approximately $0.65, and B) the cost of 1 and 1/2 dozen donuts is $11.70.
Certainly, let's break it down:
A) To find the price per donut, divide the total cost by the number of donuts in a dozen:
Price per donut = $7.80 / 12 ≈ $0.65
B) Calculate the cost of 1 dozen:
Cost of 1 dozen = $7.80
Now, for [tex]\( \frac{1}{2} \)[/tex] dozen, multiply the price per donut by 6 (half of 12):
Cost of [tex]\( \frac{1}{2} \)[/tex] dozen = $0.65 × 6 = $3.90
Add the cost of [tex]\( \frac{1}{2} \)[/tex] dozen to the cost of 1 dozen:
Total cost for 1 and [tex]\( \frac{1}{2} \)[/tex] dozen = $7.80 + $3.90 = $11.70
In summary, A) the price per donut is approximately $0.65, and B) the cost of 1 and [tex]\( \frac{1}{2} \)[/tex] dozen donuts is $11.70.
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Hüseyin draws a fox with a scale of 3 units on his graph paper represents 15cm. The fox has an actual height of 80cm. What is the height, in units, of the fox in Hüseyin's drawing?
Answer:
The height of the fox in Huseyin's drawing is, 16 units
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
As per the statement: Huseyin draws a fox with a scale of 3 units on his graph paper represents 15 cm. The fox has an actual height of 80 cm.
⇒ We are given Scale of 3 units.
On graph paper the length of fox is 15 cm.
The fox has an actual height = 80 cm
let x be the height in units of the fox in Huseyin's drawing.
By definition of proportion;
[tex]\frac{3}{15} = \frac{x}{80}[/tex]
by cross multiply we get;
[tex]3 \times 80 = 15x[/tex]
Simplify:
240 = 15x
Divide both sides by 15 we get;
x = 16 units.
Therefore, the height of the fox in Huseyin's drawing is, 16 units
Answer:
16 units
Step-by-step explanation:
khan academy
Stock yield is found by the annual dividend divided by?
Answer:
Stock Yield = [tex]\frac{Annual Dividend}{Current Stock Price}[/tex]
Step-by-step explanation:
Stock yield is found by the annual dividend divided by the current stock price.
There is an inverse relationship between the stock yield and the current stock price.
For example, let's assume we have some shares of Company ABC, which pays $1.20 per share in annual dividends and the current stock price is $12.00, then by using the formula above we can calculate the stock yield of the Company ABC as,
Stock Yield of company ABC = [tex]\frac{Annual Dividend}{Current Stock Price}[/tex]
= [tex]\frac{\$1.20}{\$12.00}[/tex]
= 0.1
= 10%
The graph of the line passes through the points (0,-2) and (6,0). What is the equation of the line?
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-(-2)}{6-0}\implies \cfrac{0+2}{6}\implies \cfrac{2}{6}\implies \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-2)=\cfrac{1}{3}(x-0) \\\\\\ y+2=\cfrac{1}{3}x\implies y=\cfrac{1}{3}x-2[/tex]
Given:
DE bisects AC
<1 congruent <2
Prove:
ABCD is a parallelogram
By using the properties of angle bisectors and congruent triangles, we can demonstrate that ABCD has both pairs of opposite sides parallel, proving it is a parallelogram.
Proof that ABCD is a Parallelogram
To prove that quadrilateral ABCD is a parallelogram:
DE bisects AC, meaning D is the midpoint of AC, and E is the midpoint of BD.
Since <1 is congruent to <2, triangles ADE and CDE are congruent by the Angle-Side-Angle (ASA) criterion.
If these triangles are congruent, then AD = DC and AE = EC by corresponding parts of congruent triangles (CPCTC).
Since DE bisects AC and BD, triangles ADE and CDE are mirror images.
Consequently, AD is parallel to BC, and AB is parallel to CD.
Because opposite sides are congruent and parallel, we conclude that ABCD is a parallelogram.
what's the difference between 0.2 and 0.02
Which of the following has a translation rule of Move 3 Right and Down 4?
(x+3, y+4)
(x+3, y-4)
(x-3, y-4)
(x-3, y+4)
Answer:
(x-3, y+4) hope this helps.
Answer:
The correct answer option is (x + 3, y - 4).
Step-by-step explanation:
If we are talking about the translation rule with respect to the origin (0, 0), then the correct option will be (x + 3, y - 4).
Since moving to the right on the x axis means a positive addition so moving three units right will mean 'plus 3'.
While moving down means that the value of y is going in negative so it will be (y - 4)
The value of square root -9 is not -3 because ___.
Answer:
IT HAS THE NEGATIVE SIGN BY THE 9
Step-by-step explanation:
Answer:
The value of square root -9 is not -3 because -9 is a negative number which will then have to be turned into a postive. So, the square root of -9 is 3.
Step-by-step explanation:
the average u.s. citizen throws away about 1,606 lb of trash each year. find this rate in pounds per month, to the nearest tenth
Answer:
The average U.S. citizen throws away about 133.8 pounds of garbage a month.
Step-by-step explanation:
First take the total amount of trash thrown away in a year (1,606), and divide it by the number of months in a year (12).
1,606 / 12 = 133.833333
You would get 133.833333 and would round it to the nearest tenth and get 133.8.
Answer:
133.83 lb/month, or 133.8 lb/month to the nearest tenth.
Step-by-step explanation:
Here we need to find the unit rate of throwing stuff away.
To do this, divide 1,606 lb by 12 months, since we want the answer in pounds per month:
1,606 lb
------------- = 133.83 lb/month, or 133 5/6 lb/month
12 mos
Lucio is buying candy he buys 1.7 pounds of gummy bears which cost $1.88 per pound and 0.8 pounds of caramels which cost $2.72 per pound what was the total cost of candy
Lucio spent a total of $5.37 on candy by purchasing 1.7 pounds of gummy bears at $1.88 per pound and 0.8 pounds of caramels at $2.72 per pound, and then summing both costs.
Explanation:To calculate the total cost of candy that Lucio is buying, we compute the cost of each candy type separately and then add those costs together. He buys 1.7 pounds of gummy bears at $1.88 per pound and 0.8 pounds of caramels at $2.72 per pound.
For the gummy bears: 1.7 pounds × $1.88 per pound = $3.196
For the caramels: 0.8 pounds × $2.72 per pound = $2.176
To find the total cost, we add the cost of gummy bears and caramels. Therefore, the total cost is $3.196 + $2.176 = $5.372. After rounding to two decimal places, we conclude that Lucio spent a total of $5.37 on candy.
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An elevator building code requires at least 2.2 square feet per person. The depth of an elevator box is 7 feet. How wide must the elevator be to legally accommodate 15 people? Round to the nearest tenth if necessary.
Answer:
4.7
Step-by-step explanation:
Multiply 15 by 2.2. And get 33
Divide 33 by 7 and get 4.7
Hope it helps!
Final answer:
To accommodate 15 people, the elevator must be approximately 4.7 feet wide.
Explanation:
The question is asking us to calculate the width of the elevator box that can legally accommodate 15 people, given that the elevator building code requires at least 2.2 square feet per person and the depth of the elevator is 7 feet.
First, we need to find out the total area required for 15 people:
Total area = Number of people × Area per person = 15 × 2.2 square feet
Total area = 33 square feet
As we have the depth of the elevator, we can now calculate the width:
Total area = Width × Depth
Width = Total area / Depth
Width = 33 sq ft / 7 ft
Width ≈ 4.7 feet
Therefore, the elevator must be approximately 4.7 feet wide to accommodate 15 people as per the building code's requirements.
Please explain in full sentence for full credit
Answer:
The median of the histogram is scores ranging from 70-80
Step-by-step explanation:
Median of a histogram is always the "class interval" in which the MIDDLE NUMBER falls in.
If we add up all the bars (y-axis), we see HOW MANY NUMBERS in total there are. So we have:
[tex]1+2+1+2+6+9+13+5=39[/tex] numbers in total
What is the middle number out of 39 numbers?
It is: [tex]\frac{n+1}{2}[/tex] th number where [tex]n=39[/tex] for this problem
So, the middle number is : [tex]\frac{39+1}{2}=\frac{40}{2}=20[/tex]th number
Which class interval does the 20th number fall into?
First class interval has 1, so total is 1Second class interval has 2, so total is 1+2=3Third class interval has 1, so total is 3+1=4Fourth class interval has 2, so total is 4+2=6Fifth class interval has 6, so total is 6+6=12Sixth class interval has 9, so total is 12+9=21So, definitely, 20th number falls into the sixth class interval which is "70-80".
Hence, the median of the histogram is scores ranging from 70-80.
please help me with this geo problem
Answer:
x = 1.25y = 1.75Step-by-step explanation:
Find x
8/10 = 5/(5 + x) Cross multiply8*(5 + x) = 10*5 Combine on the right8(5 + x) = 50 Remove the brackets on the left.40 + 8x = 50 Subtract 40 from both sides.40-40 +8x = 50-40 Combine8x = 10 Divide by 88x/8 = 10/8 Dividex = 1.25Find y
7/(7 + y) = 8/10 Cross multiply8*(7 + y) = 10 * 7 Combine the right8(7 + y) = 70 Remove the brackets.56 + 8y = 70 Subtract 56 from both sides56 - 56 + 8y = 70 - 56 Combine8y = 14 Divide by 8y = 1.75Which fraction is equivalent to [tex]\frac{25}{35}[/tex]
A) [tex]\frac{2}{3}[/tex]
B) [tex]\frac{20}{30}[/tex]
C) [tex]\frac{3}{5}[/tex]
D) [tex]\frac{5}{7}[/tex]
[tex]\dfrac{25}{35}=\dfrac{25:5}{35:5}=\dfrac{5}{7}\to\boxed{D)}[/tex]
I don’t understand this I don’t need an explanation can someone just please help me please
Answer:
1
Step-by-step explanation:
You can only make one because once an angle is given, the only possibility is to connect the two sides. You can't change it to an obtuse triangle with that.
Everyone else will be a congruent to the first one triangle.
SAS stands for "side, angle, side" and means that we have two congruent triangles where we know two sides and the included angle are equal.
can someone help me and show the work pls.
(1 & 2/3) ft = (1 ft) + (2/3 ft)
(1 & 2/3) ft = 12 inches + 12*(2/3) inches
(1 & 2/3) ft = 12 inches + 8 inches
(1 & 2/3) ft = 20 inches
If the tree grows 5 inches per year, then it will take 4 years to get to 20 inches since 5*4 = 20. You can also divide to get 20/5 = 4.
So it takes 4 years for the tree to grow 1&2/3 feet tall.
Answer:
4 years
Step-by-step explanation:
Okay, so basically write a proportion
5 inches/per year
Then, find out how many inches are in 1 2/3 feet
1 2/3 = 1 8/12
Meaning there 1 2/3 feet is 1 foot and 8 inches. We know a foot is 12 inches. so then you just add 12 + 8 which is 20
Now going back to your proportion
5 inches/ per year =20 inches/x years
We know 5 goes into 20 4 times. Meaning to get to 20, your'e going to have to multiply the numerator by 4. But whatever you do to the numerator, you must do to the denominator. So multiply 1 x 4 which is 4 meaning it is going to take 4 years for the tree to grow 1 2/3 feet.
Help please ASAP I got this wrong I wanna know why and what is the right answer give explanation please
Answer:
B. The total price depends on the number of crates
Step-by-step explanation:
We can immediately rule out C & A because the two factors in the graph are crates and total price. So both the number of crates and total price will be part of our answer, but pumpkins aren't shown on the graph at all.
This leaves us with B & D. Using common sense we know that the number of crates isn't going to change if the total cost changes but rather the total cost will change depending on how many crates you buy.
I hope that helps u understand & answers ur question! (If u have a question about anything I just said lmk and I'll be glad to tell u what I mean)
Good luck! :)
Solve the system of linear equations by graphing. x−y=7 0.5x+y=5
To solve the system of equations x - y = 7 and 0.5x + y = 5, convert both to y = mx + b form, graph them, and identify the intersection point as the solution.
Explanation:Solving the System of Linear Equations by GraphingTo solve the system of linear equations:
we aim to express each equation in the
y = mx + b
form, where
m
is the slope and
b
is the y-intercept, to make them easy to graph.
Step 1: Rearrange the EquationsRearrange the first equation to isolate y:
y = x - 7
The second equation rearranges to:
Both equations are now in a form where they can be graphed easily.
When these equations are graphed, the point where they intersect is the solution to the system. For simplicity, this explanation does not involve the actual graphing, but you can use graph paper or a graphing calculator:
Draw the line y = x - 7, which has a slope of 1 and crosses the y-axis at -7.Draw the line y = -0.5x + 5, which slopes downward and crosses the y-axis at 5.The intersection point gives the solution to the system.
The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is . What is the standard form of the equation for this line?
Answer:
Point-Slope form: [tex]y+1=-\frac{6}{15}(x+5)\\[/tex]
standard form: [tex]2x+5y=-15[/tex]
Step-by-step explanation:
The standard form is given by: [tex]Ax+By=C[/tex]
The point-slope form is given by: [tex]y-y_1=m(x-x_1)[/tex]
point [tex](10,-7)[/tex] as point [tex](x_2,y_2)[/tex]
We also know that the slope [tex]m[/tex] is given by [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's find the slope:
[tex]m=\frac{-7-(-1)}{10-(-5)}=-\frac{6}{15}[/tex]
1. So, point slope form can be written as:
[tex]y-(-1)=-\frac{6}{15}(x-(-5))\\y+1=-\frac{6}{15}(x+5)\\[/tex]
2. Rearranging this equation and bringing all x's and y's to one side and the number to another side will give us the standard form. So:
[tex]y+1=-\frac{6}{15}x-2\\y+\frac{6}{15}x=-2-1\\y+\frac{6}{15}x=-3[/tex]
But A, B, and C (standard form) needs to be integers, so to get rid of the denominator , we multiply the whole equation by 15. So we have:
[tex]y+\frac{6}{15}x=-3\\15y+6x=-45[/tex]
We can factor out a 3, so it becomes:
[tex]15y+6x=-45\\5y+2x=-15[/tex]
So standard form is [tex]2x+5y=-15[/tex]
how do you factor 24a + 12b - 30?
Answer:
6(4a+3b-5)
Step-by-step explanation:
They all share a common factor of 6 so we can factor out the six, 6(4a+3b-5)
Answer:
2a+b=5/2
Step-by-step explanation:
given the expression
24a + 12b - 30
Step one :
To solve this we need to look for a common factor
Here 6 is a common factor
So divide all through by 6
24a/6+12b/6-30/6
4a+2b-5
4a+2b=5
Step two :
We can still factor 2 out for the terms with variables
2(2a+b)=5
2a+b=5/2
Library officials in a library find that too many people aren't returning their books on time. Thus, they made a new rule in which their patrons pay 1 cent for the first day the book is overdue, 2 cents for the second day, 4 cents for the third day and so on. After 15 days there are no more charges. What is the total late fee for one book after 15 days?
Answer:
None
Step-by-step explanation:
it says that there are no late fees after the 15th day
Answer:
32767
Step-by-step explanation:
the geometric sequence 2^{n-1}
and you have to find the sum of the first 15 term of the sequence
Based on the two graphs, which school would you expect to have a higher standard deviation from the mean and why?
Check out the attached image below. It shows the bar graphs of each school. As you can see in figure 2 (Cleveland highschool), the data is more spread out compared figure 1. So this has a higher standard deviation. The standard deviation measures spread. The larger the standard deviation is, the more spread out the values will be. It can be thought of as a measure of how distant each value is from the mean.
Every number has two qualities: a sign and a distance from zero true or false
Answer:
Yes. The statement is absolutely True
Step-by-step explanation:
Answer:
Yes the statement is true for real numbers.
Step-by-step explanation:
Yes. Every real number has two qualities: a sign and a distance from zero
Real numbers are points along a continuous infinite number line with its midpoint at 0.
These have a sigh either positive or negative. Like the numbers less than zero, or on the left side of zero on a number line are negative and the numbers on the right are positive.
Joshua is trying to decide if there is a relationship between a driver's age and the number of traffic tickets they get he surveys 150 people in three towns and recorded their age how many tickets they got in the last year in the town they live in he creates a graph of his data what is the independent variable
Hello!
The number of tickets is dependent on age, so age is the independent variable.
Think of it as a y = mx equation. In this equation, x is the input, and y changes depending on the value of x inputted.
In this situation, y is the number of tickets, as y changes depending on the age x inputted. x is age, the independent variable.
Answer:
Its C) the number of tickets
Step-by-step explanation:
I WILL MARK BRAINEST! (if right)
1. What is 8/34% expressed as a fraction?
A. 8/100
B. 7/80
C. 7/40
D. 8/25
Thank you so much for Helping..(if you did)
Answer:
5/8
Step-by-step explanation:
62.5% = 62.5/100
=0.625
=0.625/1 x 1000/1000
=625/1000
=5/8
A health club charges non-members $5 per day to swim and $9 per day for an exercise class. Members pay a yearly fee of $300 plus $4 per day to attend an exercise class and no swim fee. If Robert swims and takes an exercise class every time he goes to the gym, which equation shows the number of days he must use the gym to make the membership worthwhile?
Answer:
22 days PLEASE GIVE BRAINLIEST
Step-by-step explanation:
Nonmember:
swim: $5
exercise: $9
Per day: 9 + 5 = $14
Member:
$300 per year plus $4 per day for an exercise class. $0 for swimming
300 ÷ 14 = 21.428 21 days x $14 = $294 22 days x $14 = $308
So.... if he goes to the gym at least 22 days he will save money with the membership.
Answer:
The answer is D.) 5d+9d = 300 + 4d
Step-by-step explanation:
The equation states that for each day he attends to the gym to swim and exercise without a membership he has to pay for both, which is $5 and $9 respectively. This is each day that he attends.
However, if he HAS a membership, he only has to pay the $300 yearly fee once, and then $4 everyday he attends afterwards to do both swimming and exercising.
Now, in order to find out when the membership is worth it you need to find out when the membership cost and the non-membership cost is equal. so on one side of the equation you'll need the non-membership costs, and on the other side we'll put the membership cost.
So, for the non-membership cost, every day he goes it'll cost him $5 to swim and $9 to exercise, meaning that one side of the equation is 5d (d represents days) + 9d
And for the membership side we have the $300 initial, one-time fee, and then the $4 a day he has to pay to attend. This is equivalent to 300+4d
Finally, we put both equations together in a way to show that we want both sides to be equal, i.e
5d+9d = 300+4d
Thus our answer is D
830000 in scientific notation
Answer:
8.3 * 10 ^5
Step-by-step explanation:
830000
To change this to scientific notation, we move the decimal 5 places to the left. The exponent will be positive 5 because we moved it to the left
8.3 * 10^ +5
8.3 * 10 ^5