If you are examining a triangle with given measurements for one leg and the hypotenuse, how will you determine the measure of the unknown leg? Explain.
By using Pythagoras theorem, length of one leg of triangle can be determined.
Given:
A triangle with length of one leg and the hypotenuse
According to question,
Let the length of one leg of triangle which can be base [tex](b)[/tex] or perpendicular [tex](p)[/tex] and hypotenuse represented by [tex](h)[/tex].
Now, using Pythagoras theorem which states that if a triangle is right-angled ([tex]90[/tex] degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
From the figure,
In [tex]\Delta AOB, \;\angle O=90^\circ[/tex]
[tex]\rm{H^2=P^2+B^2}\\\rm{AB^2=AO^2+OB^2[/tex]
[tex]h^2=p^2+b^2[/tex]
[tex]b=\sqrt{h^2-p^2}\\[/tex]
or
[tex]p=\sqrt{h^2-b^2}\\[/tex]
Therefore, length of one leg of the triangle is determined by using Pythagoras theorem.
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A rectangular floor space in a community center is 40 ft long and 32 ft wide. A volunteer is setting up chairs on the floor space. Each chair needs an area of approximately 4 ft by 5 ft.
Which estimate best approximates the number of chairs that can be set up on the floor space?
A. 20
B. 60
C. 260
D. 320
Answer:
60
Step-by-step explanation:
Just confirming for the K12 students ;)
A family took a trip. They spent $90.71 for gasoline, $153.00 on meals, $197.00 on amusements, and $73.38 on miscellaneous expenses. How much did the trip cost?
Based on the information marked in the diagram, ABC and XYZ must be congruent.
Can somebody help ??
A. True
B. False
Answer: The answer i false
Step-by-step explanation:
The Big Dipper ice cream store charges 25 cents for a cone and 75 cents for each scoop of ice cream added to the cone. What will a customer pay for a double dip ice cream cone?
Roll a 5 win 6 dollars roll a 6 win 12 dollars if you play one time what is your expected reward
how do you subtract 42 minutes from 1 hour ,25 minutes.explain what to do and why you do it?
Make t the subject of the formula
15 POINTS
What is the equation of the following graph in vertex form?
(parabolic function going down from the left through the point negative four comma zero and turning at the point negative three comma negative one and going up through the point negative two comma zero and then through the point zero comma eight and continuing up towards infinity)
y = (x − 3)2 − 1
y = (x + 3)2 − 1
y = (x − 4)2 − 2
y = (x − 4)2 + 8
Answer with explanation:
→The given curve is Quadratic,having two real roots,as it cuts X axis at two distinct points that is at ,-2 and -4.
→Graph is symmetrical about line , x=-3.
→This curve is a Parabola,opening in upward direction ,that is having Y axis as Axis of Symmetry.
→Parabola is defined as locus of all the points such that distance from fixed point called focus, to distance from fixed line called Directrix ,is always Constant.
→Point which divides PARABOLA in two symmetrical parts is called Vertex having coordinates (-3,-1).
Equation of parabola having vertex ,(-3,-1) and opening in Upward Direction,that is in vertical direction, is given by:
General Equation: Equation of parabola passing through point (a,b) and opening in upward direction and having focus (k,h) is
y-b=4 k× (x-a)²
So, the equation of parabola will be
→y-(-1)=4 k[x-(-3)]²
→y+1==4 k(x+3)²-----(1)
This parabola also passes through (-4,0) and (-2,0).
→0+1=4 k×(-4+3)²
→1=4 k×(-1)²
[tex]1=4 k\\\\k=\frac{1}{4}[/tex]
If you will substitute , x=-2 and y=0 in equation 1,you will get same value of k.
Equation of Parabola ,that is equation 1,can be written as
[tex]y+1=4\times\frac{1}{4}(x+3)^2\\\\y+1=(x+3)^2\\\\ y=(x+3)^2-1[/tex]
Option B: y=(x+3)²-1
Heidi has $4.55. She needs to buy bolts at the hardware store . Bolts cost$0.13 each. How many bolts can Heidi buy.
Which linear equation has a slope of 3 and a y-intercept of –2?
Y=3x-2, or B.
Answer:
I believe the answer is A.
Step-by-step explanation:
What are the solutions of the inequality? 12x – 3x + 11 > 4x – (17 – 9x) a. x > –7 b.x > −1411 c. x < −1411 d.x < 7
The daily intakes of milk (in ounces) for ten randomly selected people were: 26.0 13.0 13.5 14.8 19.1 13.6 21.6 30.8 15.8 14.1 find a 99% confidence interval for the population standard deviation σ.
To establish a 99% confidence interval for the population standard deviation, we first need to calculate the sample standard deviation of the data. We then use the Chi-Square distribution with the appropriate degrees of freedom to get the interval. The formula [√((n-1)*s²/χ²0.995,n-1), √((n-1)*s²/χ²0.005,n-1)] can be applied.
Explanation:This question refers to constructing a 99% confidence interval for the population standard deviation using the information from a sample. The mentioned sample comprises measures of daily intakes of milk in ounces for ten randomly selected people. To address this, first, we need to calculate the sample standard deviation. After that, we use Chi-Square distribution (χ² distribution) to create the confidence interval for the standard deviation since population standard deviation (σ) is unknown.
Let's denote:
n as number of observations: n=10s as sample standard deviationχ²(α/2,n-1) as the χ² value for α/2 (± z-score for standard normal distribution) with n-1 degrees of freedom99% confidence interval for the population standard deviation σ can be found using the formula:
[√((n-1)*s²/χ²0.995,n-1), √((n-1)*s²/χ²0.005,n-1)]
Here, χ²0.995,n-1 and χ²0.005,n-1 represent the values from χ² distribution table corresponding to 0.005 and 0.995 (For 99% confidence interval, α=1-0.99=0.01. α/2=0.01/2=0.005) with n-1 degrees of freedom.
Please note that all numbers should be rounded according to the context, and the final values are but estimates that should not be treated as 100% accurate.
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A computer salesperson's monthly income depends on the amount of his sales. his monthly income is a salary of $1575 plus 9% of his monthly sales. write a linear equation for his monthly income for sales of x dollars. ( i=mx+b ).
The solution is, 1575 + 0.9x, is a linear equation for his monthly income for sales of x dollars.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Here, we have,
given that,
A computer salesperson's monthly income depends on the amount of his sales.
his monthly income is a salary of $1575 plus 9% of his monthly sales.
Fixed salary = $1575
Commission = 9% = 0.09
Monthly Sales = x
Monthly income = 1575 + 0.9x
Answer: Monthly income = 1575 + 0.9x
Hence, The solution is, 1575 + 0.9x, is a linear equation for his monthly income for sales of x dollars.
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GEOMETRY HELP 70 POINTS FAST!!!!!!!
FIND SURFACE AREA. IT’S OKAY IF YOU DID ONE BUT I WOULD PREFER IF YOU DID BOTH THANKS
how do i answer this question
[tex]7 - 3x = 2x + 7 - 5x[/tex]
Susan and betsy bought sport supplies for summer camp. susan bought six basketballs and one soccer ball for $27. betsy bought four basketballs and two soccer balls for $22. how much do basketballs cost? how much do soccer balls cost?
N a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are: 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68. what is the mean?
what is the inch equivalent of 32.5 mm to the nearest 0.0001
At the start of an experiment , there are 30 bacteria dish. The bacteria population is expected to grow at a rate of 180% each day. Which is the best prediction for the bacteria population after 7 years?
A.51,750
B.40,479
C.2682
D.1837
Which equation can be used to find the volume of this solid?(Please see attached picture)
V=3*5*4
V-3+5+4
V=5*4
V=3*5
Marie is buying an ice-cream sundae. There are 3 sizes of sundaes, 15 different ice-cream flavors, and 5 different toppings. How many ways can Marie choose a sundae?
Jamal baked muffins for the school bake sale. He made 12 corn muffins and 15 blueberry muffins. What is the ratio of blueberry muffins to all muffins?
Answer:
5:9
Step-by-step explanation:
How many turning points are in the graph of the polynomial function?
2 turning points
3 turning points
4 turning points
5 turning points
If you flip 3 coins, what is the probability of landing on heads only 2 times? list your answer as a fraction in simplest form.
How many dimes in 1898.59
A principal of $3900 is invested at 6.5% interest, compounded annually. How much will the investment be worth after 5 years? Use the calculator provided and round your answer to the nearest dollar.
Answer:
The answer would to be able to multiply the answers together. For example, the answer for this question would be 5,343 dollars rounded to the nearest tenth.
Step-by-step explanation:
The circle graph shows the portions of the time that Ralph spent playing different games.
Which two types of games did Ralph spend a total of 9/10 of his time playing?
Choose exactly two answers that are correct. exactly two plz!!
A.
Truck Rider
B.
Space Cadet
C.
Trivia Tasks
D.
Wizard Maze
Which choice is similar to the figure shown?
The Comegna family wants to build a human pyramid when they go to the beach this summer. They will put one person on top and add 2 more people for each descending row.
a. How many people will be in the seventh row?
PLEASE HELP!! the rest are in the attachment