Answer:
Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple
Step-by-step explanation:
The given side lengths are;
21, 28, and 35
From the given side lengths, the greatest common factor = 7
Therefore, we have;
3 × 7, 4 × 7, and 5 × 7
A Pythagorean triple is formed by three numbers, 'a', 'b', and, 'c', which are both positive and integers, that are related as follows;
c² = a² + b²
Therefore, for the three numbers, we get;
3, 4, and 5 is a Pythagorean triple
5² = 3² + 4²
Multiplying both sides by 7² gives;
(5)² × (7)² = (3)² × (7)² + (4)² × (7)²
By the laws of indices, (a·b)ⁿ = aⁿ × bⁿ
Therefore;
(5 × 7)² = (3 × 7)² + (4 × 7)²
Therefore, multiplying every length of the Pythagorean triple by the same whole number results in a Pythagorean triple.
(The relationship can also be shown using similar triangles, as multiplying the side lengths of a triangle by the same whole number, gives a similar triangle, having the same relationship between its sides)
Ifx = 2 and y=6, evaluate the following expression:
3(3y - 4x)
An equilateral triangle with side length 20 cm is shown in the diagram, work out the area of the triangle.Give your answer rounded to 1 DP.
Answer:
173.2 cm²
Step-by-step explanation:
Use the equilateral triangle area formula, A = [tex]\frac{\sqrt{3}}{4}[/tex]a²
Plug in the side length and solve:
A = [tex]\frac{\sqrt{3}}{4}[/tex]a²
A = [tex]\frac{\sqrt{3}}{4}[/tex](20)²
A = [tex]\frac{\sqrt{3}}{4}[/tex](400)
A = 173.2
So, the area of the triangle is approximately 173.2 cm²
What is the measure of <JHM
25
45
50
90
Kelly is going two work two part-time jobs during the school year. When she works for her dad, she will make $8.00 per hour. When she works at a day care center, she will make $14.00 per hour. To pay her car payment, Kelly needs to make at least $84.00 a week and can work no more than 10 hours total per week. Write an inequality to represent the difference combinations of hours working for her dad,X, and hours working for the daycare center,Y, Kelly can work if she wants to earn at least $84 per week
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of hours Kelly works for her dad per week and y represent the number of hours Kelly works in the daycare center per week.
Since she wants to make $84 per week, hence:
8x + 14y ≥ 84 (1)
Also, she can work a maximum of 10 hours per week, hence:
x + y ≤ 10 (2)
Using equation 1 and 2 and plotting the constraints on geogebra online graphing tool, the solution to the problem is at points:
A(0, 6), B(0, 10) and C(9.3, 0.7)
The plot below shows the lengths of 555 neck warmers that Mary knit for a family of giraffes. A line plot labeled volume of juice in fluid ounces shows, moving left to right, labeled tick marks at four, four and one-half, five, five and one-half, six, six and one half, and seven. Dots are plotted as follows: 1 dot above four and one-half; 2 dots above five; 1 dot above six and 1 dot above six and one-half. A line plot labeled volume of juice in fluid ounces shows, moving left to right, labeled tick marks at four, four and one-half, five, five and one-half, six, six and one half, and seven. Dots are plotted as follows: 1 dot above four and one-half; 2 dots above five; 1 dot above six and 1 dot above six and one-half. The shortest warmer was blue. The two longest warmers were pink. How much longer was the combined length of the pink warmers than the length of the blue warmer?
Answer: The answer is 8
Step-by-step explanation:
It’s Kinda obvious if your teachers asks u to explain its 12 1/2 - 4 1/2 which equals 8 1
2
+
4 1
2
=
17
Calculation steps:
12 1
2
+
4 1
2
= (12 + 4) + (
1
2
+
1
2
)
= 16 +
1 + 1
2
= 16 +
2
2
= 16 +
2 ÷ 2
2 ÷ 2
= 16 +
1
1
= 8 hope this helps
Answer:
Answer is 8
Step-by-step explanation:
I know because I got the answer right!
7th grade math help me pleaseeee
Answer:
Step-by-step explanation:
the first one is a negative correlation
may anyone help me please and thank you so much !
Answer:
16 m
Step-by-step explanation:
The situation can be solved by proportion of corresponding sides in 2 right triangles.
let x be the length of shadow cast by oak tree, then
[tex]\frac{9}{12}[/tex] = [tex]\frac{12}{x}[/tex] ( cross- multiply )
9x = 144 ( divide both sides by 9 )
x = 16
Length of shadow is 16 m
I really need the answer now pls help me asap!!
Answer:
1 A
2 B
3 D
4 B
5 A
6 D
7 C
8 B
9 C
Step-by-step explanation:
1 A
2 B
3 D
4 B
5 A
6 D
7 C
8 B
9 C
Solve the equation for x.
Answer:
x = 7
Step-by-step explanation:
2x + 34 = 4x + 20
2x = 14
x = 7
Can anyone solve this question for me urgent! With work please. Thank you!
Answer:
P = 75*
Step-by-step explanation:
In a (Gallup poll, 26.6% of 5000 people reported a Body Mass Index (BMl) greater than 30, which is classified as obese. The 5000 people polled are a random sample of adults, aged 18 and older, from the United States population. Choose the correct interpretation for the 98% confidence interval for the proportion of the population who arc obese? A. The proportion of adults in the United States, aged 18 or older, who are obese is between 0.2515 and 0.2805. B. We are 98% confident the proportion of adults polled who are obese is between 0.2515 and 0.2805. C. In 98% of all samples, the proportion of adults polled who are obese will be between 0.2515 and 0.2805. D. We are 98% confident that the proportion of adults in the United States, aged 18 or older, who are obese is between 0.2515 and 0.2805.
Answer:
D. We are 98% confident that the proportion of adults in the United States, aged 18 or older, who are obese is between 0.2515 and 0.2805.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
26.6% of 5000 people reported a Body Mass Index (BMl) greater than 30
This means that [tex]\pi = 0.266, n = 5000[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.266 - 2.327\sqrt{\frac{0.266*0.734}{5000}} = 0.2515[/tex]
The upper limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.266 + 2.327\sqrt{\frac{0.266*0.734}{5000}} = 0.2805[/tex]
The correct interpreation is that we are 98% confident that the proportion of adults in the United States, aged 18 or older, who are obese is between 0.2515 and 0.2805, which means that the correct answer is given by option D.
Which point would not be a solution to the system of linear inequalities shown below? y\ge x+5\hspace{50px}y\ge\frac{2}{3} x+6 y≥x+5y≥ 3 2 x+6 (12, 7) (-12, 1) (-12, 9) (-12, 6)
Answer:
(12,7) is not a solution
Step-by-step explanation:
Given
[tex]y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6[/tex]
Required
Point that is not a solution
We have:
[tex]y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6[/tex]
Substitute [tex]\frac{2}{3}x + 6[/tex] for y in the first inequality
[tex]\frac{2}{3}x + 6 \ge x + 5[/tex]
Collect like terms
[tex]\frac{2}{3}x - x \ge 5-6[/tex]
[tex]-\frac{1}{3}x \ge -1[/tex]
Solve for x (the inequality will change because we are to divide by a negative number_
[tex]x \le -1/-\frac{1}{3}[/tex]
[tex]x \le 3[/tex]
Without solving further, we can conclude that the first option is not a solution.
Because (12,7) implies that [tex]x =12[/tex]
Compare [tex]x =12[/tex] to [tex]x \le 3[/tex], then [tex]x \le 3[/tex] is false
figure B is a scaled copy of figure A. What is the scale factor from figure A to B
If f(x) = 2x-5, then 114) is
O 17
05
04
3
What is the obesity threshold weight for a young adult American male?
Answer:
If your BMI is 18.5 to 24.9, it falls within the normal or Healthy Weight range. If your BMI is 25.0 to 29.9, it falls within the overweight range. If your BMI is 30.0 or higher, it falls within the obese range.
Step-by-ste
Answer:
218.7 lbs is your answer
There is a 30% chance of snow on each of the next three days. What is the probability of getting snow on one of these days?
Answer:
30%
Step-by-step explanation:
Rhonda deposited $3000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. a) Write an equation that can be used to find B, her account balance after t years. b) Find the amount in her bank account after 6 years to the nearest cent
Answer:
below
Step-by-step explanation:
that is the procedure above
Is (x - 2) a factor of y = x3 + 2x2 - 9x - 18 ?
A: Yes
B: No
C: Cannot be determined
help pls. cant figure it out
Answer:
m=3
Step-by-step explanation:
add the m on the right side, 4m+3=15
subract the 3 on the left side, 4m=12
divide by four to isolate m, m=3
Answer:
[tex]3m+3=15-m[/tex]
[tex]3m+3=-m+15[/tex]
[tex]3m+m=15-3[/tex]
[tex]4m=12[/tex]
[tex]Divide\ both\ sides \ by\ 4[/tex]
[tex]\frac{4m}{4} =\frac{12}{4}[/tex]
[tex]\boxed{\boxed{\underline{\textsf{\textbf{m=3}}}}}[/tex]
-------------------------hope it helps...have a great day!!A ball was kicked off a picnic table at the park and its height, h, in metres, above the ground after time, t, in seconds, is represented by h = 0.5 + 16t- 2t^2.
a) What is the height of the picnic table?
b) Complete the square to determine the maximum height of the ball?
Step-by-step explanation:
the picnic table height is 0.5 because it's the constant
and the maximum height is 28
my answer is in the image above
Describe how you would factor x^2 + 10x - 24. Be specific.
Answer:
if u have more doubts feel free to ask :)
Step-by-step explanation:
x² + 10x -24
x² + 12x - 2x - 24
x(x + 12) -2(x + 12)
(x + 12) (x - 2)
Factors of 24 : ±1 , ±2 , ±3 , ±4 , ±6 , ±8 , ±12, ±24. Combination of +12 and -2 gives "10" the middle term also " 24"
A box of cereal has the following measurements: length = 16.5 cm; width = 4 cm; height = 30.25 cm. What is the volume of the cereal box?
Pls help me I’m failing math with a 55
Answer:
[tex]1996.5[/tex]
Step-by-step explanation:
[tex]16.5 X 4 X 30.25[/tex]
Hope this helped, please give brainliest
Thank you!
Answer:
To calculate the volume of a object, all you need to do is multiply the length, width and height. In this equation, that would be 1996.5cm or 786.02362204 inches
Step-by-step explanation:
Hope this helped, please give brainlist
Thank you
x- (-3) is the same as x + (-3).
O True
O False
Answer:
false
Step-by-step explanation:
because x - (-3)
= x+3
and x + - 3
= x - 3
so they are not the same
hope this helps
Answer:
False
Step-by-step explanation:
If u minus you go the opposite direction
And you have negative 3
So you do the opposite direction of -3 which is +3
So x+3
which of the following are solutions to the quadratic equation? x^2+3x-10=0
Answer:
-5 and 2
Step-by-step explanation:
That is where it intersects on the x-axis, so therefore it is the solution.
Please help asap!! I will mark you as brainliest :)
Answer:
3, 0, -5, -6
Step-by-step explanation:
7)
when x= -8, f(x) = 8-5 or 3
when x= -5 f(x) = 5-5 or 0
when x= 0, f(x) = 0-5 or -5
when x=1, f(x) = -1-5 or -6
can someone pls help for brainlest
Answer:
The answer to the question is B,2:55
Answer:
2:55 B
Step-by-step explanation:
Each number 1 2 3 etc are counting by 5's. 11, five times is 55. It cannot be D because the shorter needle determines the hour and the longer one is on 11. It can't be A because counting by 5 starts with 1 not 12 it rotates clockwise not anti-clockwise. It can't be C because for it to be 50, it would need to be on the 10 not on 11.
can someone please help me i need to calculate the are of a trapezium which is 6cm 15cm 9cm, please help
Answer:
Step-by-step explanation: The parallel sides of a trapezium are called the bases and the distance between them is the height. Therefore if 6cm and 15cm are the bases and 9cm is the height, then the area is A= ½(b1+b2)×h, where b1 is 6cm and b2 is 15cm and h is 9cm. Therefore the Area= ½(6+15)×9=94,5cm.
Answer:
shush its hard like my
Step-by-step explanation:
Suppose when solving a system of linear equations in two variables, both variables happen to cancel, leaving you with a false statement. How should this be interpreted?
A. The system of equations has infinitely many solutions.
B. The system of equations has no solution.
C. The system of equations is unsolvable.
D. The system of equations has been solved incorrectly.
Step-by-step explanation:
C. The system of equations is unsolvabl
((PLEASE HELPP)
Arrange the systems of equations in order from least to greatest based on the number of solutions for each system.
1.)-5x+y=10
-25x+5y=50
2.)3x-7y=9
-4x+5y=1
3.)y=6x-2
y=6x-4
Answer:
1 has 1 solution
2 has one solution
3 has no solutions The lines are parallel
pls help its my last day of school and a have only a few mins to submit
Answer:
slope = 1/2
y intercept = 2
slope intercept form = y = 1/2x + 2
Step-by-step explanation:
Answer:
Slope: 2
y-intercept: 2
Slope intercept form: y=2x+2
Step-by-step explanation:
Hope this helps!
