The problem can be solved using the Pythagorean theorem. The lengths of the legs of the triangle are calculated as 15 inches for the shorter leg and 21 inches for the longer leg.
Explanation:In solving this mathematical problem, we can employ the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides- This theorem is normally written as a² + b² = c². We can let one leg of the right triangle be 'a', the other leg be 'a+6' (since one leg is 6 inches longer than the other), and the hypotenuse is 25 inches. From the equation, we substitute a and b with the values and get:
a² + (a + 6)² = 25²
This equation is solved to get the lengths of the legs. Solving results in 'a' being 15 inches (the shorter leg) and 'a+6' equals to 21 inches (the longer leg).
Learn more about Pythagorean theorem here:https://brainly.com/question/28361847
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Help please geometry
carlotta is constructing an equilateral triangle. she has already constructed the line segment and arc shown.
Answer:
Place the point of the compass on point Q and draw an arc that intersects the first arc, using the same width for the opening of the compass as the first arc.
Step-by-step explanation:
She is constructing an equilateral triangle. This means that all 3 sides must be congruent. She has drawn an arc by placing her compass on point P and setting it to the width of segment PQ. This arc passes through point Q.
In order to ensure that the sides are congruent, she must keep her compass the same width. She will now go to the opposite end of the segment, point Q, and construct an arc that runs through point P. The goal is to intersect her first arc at a point that will serve as the third vertex of the triangle.
The next step in constructing an equilateral triangle after drawing the line segment and the first arc is;
Option B; Place the point of the compass on point Q and draw an arc that intersects the first arc using the same width for the opening of the compass as the first arc.
To answer this question, we will enumerate all the steps required to construct an equilateral triangle.
Step 1; Construct a line segment PQ to serve as the length of the side of the equilateral triangle and label the 2 endpoints P and Q.
Step 2; Place one leg of the compass at point P and with the other leg at point Q, swing an arc above line PQ
Step 3; Without Changing the width of the compass, place the first leg at point Q and with the second leg now at point P, swing another arc to intersect the first arc.
Step 4; Label the point of intersection R and draw a straight line from P to R and from Q to R to complete the equilateral triangle.
Looking at the given options, the one that tallies with step 3 which is the next step for the question is Option B.
Read more at; https://brainly.com/question/13159957
Will a polynomial times a polynomial always equal a polynomial?
Answer:
yes, it will always be a polynomial but depending on how many terms it has, the answer may change
Step-by-step explanat
Point R is located at (3,2) and point S is located at (8,15)
What are to coordinates of the point that partitions The directed line segment RS in a 1:4 ratio?
Answer:
was this right
Step-by-step explanation:
PLEASE PLEASE HELP ME QUICK!!!!
Will give brainiest to first answer!
Which of the following inequalities is graphed on the coordinate plane?
A. y > x
B. y is less than or equal to x
C. y is greater than or equal to x
D. y < x
Answer:
u have a solid line...means there is an equal sign in the problem...so that eliminates 2 of them right away...so A and D are incorrectit is shaded below the line....this means it is less then...that eliminates option C leaving u with only one answer choiceso ur answer is : B. y is less then or equal to x
Step-by-step explanation:
Write a two proof column
Given: 4y=2x-10 ; y=6
Prove: x=17
What is the slope of the line passing through the points (2, −5) and (4, 1)?
a.−45
b.54
c.3
d.2
P(x) = x2 – 1 and q(x)=5(x-1), which expression is equivalent to (p – q)(x)?
Answer: The required expression is [tex]x^2-5x+4.[/tex]
Step-by-step explanation: We are given that
[tex]p(x)=x^2-1,\\\\q(x)=5(x-1).[/tex]
We are to find the expression that is equivalent to (p-q)(x).
We know that for any two functions f(x) and g(x), we have
[tex](f-g)(x)=f(x)-g(x).[/tex]
Therefore we get
[tex](p-q)(x)\\\\=p(x)-q(x)\\\\=(x^2-1)-(5(x-1))\\\\=x^2-1-5x+5\\\\=x^2-5x+4.[/tex]
Thus, the required expression is [tex]x^2-5x+4.[/tex]
Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She wants to make at least $65 dollars. She is only allowed to work 13 hours per week. Write and graph a system of inequalities to represent this situation.
Answer:
inequalities are x + y ≤ 13 and 4x + 7y ≥ 65
Step-by-step explanation:
Given: Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She wants to make at least $65 dollars. She is only allowed to work 13 hours per week.
We have to write and graph the system of inequalities to represent this situation.
Let she babysits for x hours per week
and she works as a tutor for y hours per week
Then given she is allowed to work for 13 hours per week.
this inequality is stated as x + y ≤ 13
Mary babysits for $4 per hour if she babysits for x hours then she get 4x
She also works as a tutor for $7 per hour if she teach for y hours then she get 7y
also, she wants to make at least $65 dollars.
Then, this inequality is represented as 4x + 7y ≥ 65
Plotting of this two inequality is represented as graph shown below.
In a sale there is 10% of all prices.a chair costs £63 in the sale.hoow mutch was it before the sale?
A palm reader gets paid $80 for each palm she reads, and her goal is to earn $2240 reading palms this month. If she has already read 4 palms this month, how many more palms must she read in order to reach her goal?
A.24
B.28
C.20
D.32
what is 875/1000 simplified
Please help with this question thank you!
Can someone please help me?
John Made a rectangle pen for his dog using 28 feet of fencing. If the width of the pen is 2 feet more than one-half the length, what is the length and width of the pen?
The length of the pen is
A) 6 feet
B) 7 feet
C) 8 feet
A statement and portions of the flowchart proof of the statement are shown.
Which reason should appear in the box labeled 1?
Linear Pair Postulate
Substitution Property of Equality
Angle Congruence Postulate
Ruler Postulate Angle
Answer:
Substitution Property of Equality
Step-by-step explanation:
I just took this test, that was the answer
A proof is a mathematical statement that shows that a postulate is true. The statement that should appear in the box is:
Substitution Property of Equality
Given that:
[tex]\angle PQR = 17^o[/tex]
[tex]\angle RQS = 13^o[/tex]
Then, we have:
[tex]\angle PQS = \angle PQR + \angle RQS[/tex]
Substitute the values of PQR and RQS
[tex]\angle PQS = 17^o + 13^o[/tex]
Because the values of PQR and RQS are substituted to get: [tex]\angle PQS = 17^o + 13^o[/tex]
This means that the reason that should appear in the box is: Substitution Property of Equality
Read more about proofs at:
https://brainly.com/question/1949419
Suppose that the distance a car travels varies directly with the amount of gasoline it uses. a certain car uses 11 gallons of gasoline to travel 198 miles. how many miles can the car travel if it has 10 gallons of gasoline?
Tony is putting 42 oranges into 4 boxes. Each box holds 12 oranges.
How many more oranges are needed to fill all the boxes?
Given 7x + 11y = N, what is the highest number N can be to produce an answer of No solution. (X,y) must be positive.
Given △ABC≅△JKL , m∠B=55° , and m∠L=25° , what is the measure of ∠J ? Enter your answer in the box.
Answer:
m∠J = 100° is the answer.
Step-by-step explanation:
Given : ΔABC ≅ ΔJKL,
m∠B = 55°
m∠L = 25°
To find : ∠J
Since in both the triangles ABC and JKL
m∠A ≅ m∠J
m∠B ≅ m∠K = 55°
m∠C ≅ m∠L = 25°
Since measure of ∠K and ∠L are known then we can calculate the third angle j
m∠J + m∠K + m∠L = 180°
55° + 25° + m∠J = 180°
80° + m∠J = 180°
m∠J = 180 - 80
= 100°
Therefore, m∠J = 100° is the answer.
How old is Kristaps Porzingis
Kristaps Porzingis was born on August 2, 1995. As of the knowledge cutoff in 2023, he is 27 years old. For the latest information, current sources should be consulted as his age changes annually.
Explanation:The age of Kristaps Porzingis, a professional basketball player, can be determined by knowing his date of birth. Kristaps Porzingis was born on August 2, 1995. As of the knowledge cutoff in 2023, he would be 27 years old. It is always advised to check current sources for the most up-to-date information as the age of a living person changes every year.
As of my last knowledge update in January 2022, Kristaps Porzingis was born on August 2, 1995. To determine his current age, you can subtract his birth year from the current year. However, please note that I do not have real-time information, and his age might have changed since my last update. I recommend checking the latest sources, such as news articles, the official NBA website, or Porzingis' official social media accounts, for the most up-to-date information on his age.
If you pop 3 bags of popcorn in 15 minutes how many bags did you pop per minute
Samantha bought a shirt for $14.98. She gave the cashier a $20 bill. Which operation(s) finds the amount of change Samantha received?
subtract the cost of the shirt from the amount she gave the cashier
20.00 - 14.98 = 5.02
using subtraction she would get $5.02 back in change
A guy is standing 112 m from a building. the angle of elevation from where hes standing on the ground to the top of the building is 62 degrees
how tall is the building
Is y=4x-1 and 12x=3y+7 parallel, perpendicular, or neither
Answer:
Neither is the answer.
Step-by-step explanation:
If a line y = m₁x + c₁ and y = m₂x + c₂ are perpendicular to each other then m₁ × m₂ = -1
If both the lines are parallel to each other then m₁ = m₂
Now two lines have been given as
y = 4x - 1 ----------(1)
12x = 3y + 7
3y = -12x + 7
y = -4x + [tex]\frac{7}{3}[/tex]------(2)
Now from equation (1) and equation (2),
m₁ = 4 and m₂ = -4
Since m₁ ≠ m₂
Therefore, these lines are not parallel
m₁ × m₂ = 4 × (-4) = -16
Therefore, both the lines are neither parallel nor perpendicular.
Stan and hilda can mow the lawn in 45 min if they work together. if hilda works twice as fast as stan, how long would it take stan to mow the lawn alone?
Write an equation for a rational function with: vertical asymptotes at x = -4 and x = 4 x-intercepts at x = -6 and x = 5 horizontal asymptote at y = 8
A rational function with the required characteristics is f(x) = 8(x + 6)(x - 5) / (x + 4)(x - 4), considering vertical asymptotes, x-intercepts, and a horizontal asymptote.
Explanation:To write an equation for a rational function with given characteristics, we need to incorporate the vertical asymptotes, x-intercepts, and horizontal asymptote into our function.
Firstly, vertical asymptotes at x = -4 and x = 4 suggest that the denominator of our function will be in the form (x + 4)(x - 4), as setting x to -4 or 4 will make the denominator zero, which creates the asymptotes.
Secondly, x-intercepts at x = -6 and x = 5 indicate that the numerator will have factors that become zero at these x-values. Hence, the numerator should be(x + 6)(x - 5).
Finally, for the function to have a horizontal asymptote at y = 8, the degree of the numerator and denominator must be the same, and the leading coefficients of the numerator and denominator must have a ratio that equals 8. To achieve the horizontal asymptote, we multiply the numerator by 8, thus the leading coefficients of the numerator and denominator are in the ratio 8:1.
Combining all these elements gives us our rational function: f(x) = 8(x + 6)(x - 5) / (x + 4)(x - 4)
A computer is normally $899 but it is discounted to $799. What percent of the original price does Shawn pay?
You purchase a pair of jeans for $24.99 and a t-shirt for $12.49. Assume sales tax is 7.5%
What is your subtotal? $
What is the tax? $
What is your total? $
A car is traveling at a constant velocity. After two hours the car has traveled 90 miles. After five hours the car has traveled 225 miles. Assuming a linear equation fits this situation, what are the ordered pairs that you would use to find the linear equation
Two airplanes leave chicago's midway airport at the same time, traveling in opposite directions. one travels at 25 miles per hour faster than the other. after 2 hours they are 490 miles apart. find the speed of each airplane.
Final answer:
The first airplane travels at 110 miles per hour, and the second airplane travels at 135 miles per hour.
Explanation:
The question deals with two airplanes leaving Chicago's Midway Airport at the same time and heading in opposite directions.
One travels at a speed that is 25 miles per hour faster than the other.
After 2 hours, they are 490 miles apart, and we need to find the speed of each airplane.
Let's define the speed of the slower airplane as x miles per hour.
Then, the faster airplane's speed would be x + 25 miles per hour.
Since they are traveling in opposite directions for 2 hours, we can set up the equation:
2x + 2(x + 25) = 490
Solving for x will give us the speed of the slower airplane, and x + 25 will give us the speed of the faster airplane.
2x + 2x + 50 = 490
4x + 50 = 490
4x = 440
x = 110
Thus, the speed of the slower airplane is 110 mph, and the faster airplane is 135 mph (110 mph + 25 mph).