Using Pythagoras' Theorem please solve it.
[tex] \huge\underline\mathcal{Answer \: - }[/tex]
Pythagoras theorem states that the square of hypotenuse equals the sum of square of other two sides.
therefore ,
[tex](25) {}^{2} = (x + 3) {}^{2} + 4 { }^{2} (x + 2) {}^{2} \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16(x {}^{2} + 4 + 4x) \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16x {}^{2} + 64x + 64 \\ \\ \longrightarrow \: 625 = 17x {}^{2} + 70x + 73 \\ \\ \longrightarrow \: 17x {}^{2} + 70x + 73 - 625 = 0 \\ \\ \longrightarrow \: 17x {}^{2} + 70x - 552 = 0[/tex]
now using quadratic formula ,
[tex]x = \frac{ - b \: \pm \: \sqrt{b {}^{2} - 4ac} }{2a} \\ [/tex]
here , a = 17 , b = 70 , c = -552
substituting the values in the equation above ,
[tex]x = \frac{70 \: \pm \: \sqrt{70 {}^{2} - 4(17)( - 552)} }{2 \times 17} \\ [/tex]
after simplifying we get ,
[tex]\boxed{x = 4} \: \: or \:\boxed{ x = \frac{ - 138}{7} } \\ [/tex]
since length can't be negative , therefore the other value will be neglected and hence ,
[tex]\boxed{value \: of \: x \: = \: 4 \: cm}[/tex]
hope helpful ;-;
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Work Shown:
As you mentioned, we'll use Pythagoras' Theorem aka Pythagorean Theorem.
[tex]a^2+b^2 = c^2\\\\(x+3)^2+(4(x+2))^2 = 25^2\\\\(x+3)^2+16(x+2)^2 = 625\\\\(x^2+6x+9)+16(x^2+4x+4) = 625\\\\x^2+6x+9+16x^2+64x+64 = 625\\\\17x^2+70x+73 = 625\\\\17x^2+70x+73-625 = 0\\\\17x^2+70x-552 = 0\\\\[/tex]
Next, we'll use the quadratic formula with a = 17, b = 70, c = -552.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-70\pm\sqrt{(70)^2-4(17)(-552)}}{2(17)}\\\\x = \frac{-70\pm\sqrt{42436}}{34}\\\\x = \frac{-70\pm206}{34}\\\\x = \frac{-70+206}{34} \ \text{ or } \ x = \frac{-70-206}{34}\\\\x = \frac{136}{34} \ \text{ or } \ x = \frac{-276}{34}\\\\x = 4 \ \text{ or } \ x \approx -8.1176\\\\[/tex]
Ignore the negative x value solution. The sides (x+3) and 4(x+2) will be negative values if we plugged in x = -8.1176, but negative side lengths do not make sense.
This makes x = 4 the only possible solution.
----------------
If x = 4, then,
vertical leg = x+3 = 4+3 = 7horizontal leg = 4(x+2) = 4*(4+2) = 4*6 = 24This is a 7-24-25 right triangle.
We can confirm this using the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\7^2+24^2 = 25^2\\\\49+576 = 625\\\\625 = 625 \ \ \ \checkmark[/tex]
Of 85 entries in the parade, 19 were
marching bands. How many entries were
not marching bands?
AGAIN PLS HELP ME I NEED IT
Answer: Yes, No, No, Yes
Step-by-step explanation:
Goal: Substitute all the ordered pairs into the equation.
1) (1,-3)
5(1) + 2(-3) = -1
5 + -6 = -1
-1 = -1
Yes
2) (2,8)
5(2) + 2(8) = -1
10 + 16 = -1
25 = -1
No
3) (-4, -6)
5(-4) + 2(-6) = -1
-20 + -12 = -1
-32 = -1
No
4) (-3, 7)
5(-3) + 2(7) = -1
-15 + 14 = -1
-1 = -1
Yes
PLS PLS HELP ASAP!!!
translate the image using the rule below
Answer:
t=(1,-3) c=(-2,-2) r=(-3,-5)
Step-by-step explanation:
add 2 to each x value and subtract 4 from each y value
A veterinarian recorded a cat's resting heart rate to be 120 beats over a 45-second time period. Complete the table to find the constant of proportionally in beats per minute.
Btw I'm in 7th grade
Number of Minutes: 0.25 0.5 0.75 1
Number ofHeartbeats: ? ? ?
The table will be:
Number of Minutes: 0.25. 0.5. 0.75 1
Number of heartbeats: 0.6675 1.335 2 2.67
How to calculate the value?The veterinarian recorded a cat's resting heart rate to be 120 beats over a 45-second time period. The constant will be:
= 120 / 45
= 2.67
Therefore, to find the heartbeat, we have to multiply the numbers of minutes by 2.67. This is illustrated as:
= 2.67 × 0.25 = 0.6675
This illustrates the concept of multiplication.
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Select the correct answer.
-
The function f(x) has been transformed to give g(x). Which of the following functions represents g(x)?
A. 9(z) = 2z²
B. 9(2) = () z²
C. g(z)=()=²
D. g(z) = 42²
c.
Step-by-step explanation:
you can check the the correct answer by giving tables value for eg f(x)= 2 g(f(x))= 1/2(2)²=2
as you can see in the graph g(x) (2,2)
If x is a positive integer, this expression is equivalent to what?
Given:
[tex]\text{ Th expression is }4x^{\frac{1}{2}},\text{ x is a positive integer.}[/tex]Required:
Which option is equivalent?
Explanation:
The equivalent for is
[tex]\begin{gathered} =4x^{\frac{1}{2}} \\ =4\sqrt{x} \end{gathered}[/tex]Answer:
Option B is correct answer.
What is the value of V?
V-22+v+32+v=180
V-22+v+32+v=180
V+v+v=170
3v=170
v=56.67
If the assumptions for the large sample confidence interval for the population proportion are not met, what adjustments can be made?.
A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.
A 95% confidence interval gives you a 5% chance of being wrong. A 90% confidence interval gives you a 10% chance of being wrong. In comparison to a 99% confidence interval, a 95% confidence interval is smaller (for example, plus or minus 4.5 percent instead of 3.5 percent).
When constructing a confidence interval for a propotion, if the condition of proportion requires 10 individuals in each category is not met, then confidence interval should be adjusted.
The number of individuals in each category is increased by 2 and sample size increases by 4.
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market researchers often report disposable income. this is your income after tax deductions. your gross income is $4,000 per month. your federal tax is 10%, state tax is 7%, city tax is 3%, and you pay 7% to social security. what is your monthly disposable income?
Answer:
The monthly disposable income will be $2,920.
Step-by-step explanation:
In the figure ZX = 2x + 1 YW = 3x - 1 and YX = 1, find perimeter of VYZ
The perimeter of triangle VYZ is 12 units.
How to find the perimeter of a triangle?The perimeter of a triangle is the sum of the whole sides of the triangle.
In other words, the perimeter of a triangle is the total distance covered by its boundaries or the sides.
Therefore,
perimeter of ΔVYZ = VY + ZY + ZV
Therefore,
VY = ZY = ZV = XW
Hence,
YW = YX + XW
Therefore,
XW = YW - YX
YW = 3x - 1
YX = 1
Hence,
XW = 3x - 1 - 1
XW = 3x - 2
Therefore,
perimeter of ΔVYZ = 3x - 2 + 3x - 2 + 3x - 2
perimeter of ΔVYZ = 9x - 6
ZX = YW
2x + 1 = 3x - 1
2x - 3x = - 1 - 1
-x = -2
x = 2
Therefore,
perimeter of ΔVYZ = 9(2) - 6
perimeter of ΔVYZ = 18 - 6
perimeter of ΔVYZ = 12 units
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Determine if the relation is a
function. Use set builder and
interval notation for the
domain and range.
Function: Yes No
Domain:
Range:
Answer:
It would be helpful if you add more info on the question
Step-by-step explanation:
A diner serves a stack of potato slices that is 2.8 centimeters tall. The thickness of a potato is .35 centimeters. How many potato slices are in the stacks?
Given that a diner serves a stack of potato slices that is 2.8 centimeters tall. The thickness of a potato is 0.35 centimeters.
We have to determine the number of potato slices in the stacks.
The number of potato slices in the stack is given by:
[tex]\frac{2.8}{0.35}=8[/tex]Thus, the number of potato slices in the stack is 8.
Question 5Which of the following is equivalent to (2 – 2) (x - 1)
what is an example of data organization and analysis
The answer choices which represents an example of data organisation and analysis are;
Choice A; Drawing a pie chart to show the percentage of sunny days, rainy days, and cloudy days without precipitation.
Choice C. Running a weather station.
Choice E; Summing the number of days with precipitation, summing the number of sunny days, and summing the number of cloudy days without precipitation.
Data organisation and Analysis.The concept above as the name implies involves the process of gathering data in a bid to further carry out analysis and consequently, draw inferences from such analysis.
Therefore, the answer choices A, C and E represent such activities which involve data organisation and analysis.
Complete question:
What is an example of data organisation and analysis?
Check all that apply.
A. Drawing a pie chart to show the percentage of sunny days, rainy days, and cloudy days without precipitation
B. Rejecting extreme data
C. Running a weather station
D. Transferring the weather data to a computer application
E. Summing the number of days with precipitation, summing the number of sunny days, and summing the number of cloudy days without precipitation.
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An example of data organization and analysis include:
A. drawing a pie chart to show the percentage of sunny days rainy days and cloudy days without precipitation.
E. summing the number of days with precipitation summing the number of sunny days and summing the number of cloudy days without precipitation
What is data organization?Data organization and analysis are accomplished by a process of categorizing and organizing data based on its category and how it is studied. A is an example of data organizing and analysis.
Drawing a pie chart to display the percentage of sunny days, rainy days, and cloudy days without precipitation - in this example, data organization is done through charts and graphs, with data classification visible. e is another example.
Summing the number of days with precipitation, sunny days, and cloudy days without precipitation - in this example, data organizing is done solely through summation of numbers, with no graphs or charts to graphically portray the data.
In conclusion, the correct options are A and E.
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Which of the following activities are examples of data organization and analysis?
Check all the apply.
A. Drawing a pie chart to show the percentage of sunny days, rainy days, and cloudy days without precipitation
B. Rejecting extreme data
C. Running a weather station
D. Transferring the weather data to a computer application
E. Summing the number of days with precipitation, summing the number of sunny days, and summing the number of cloudy days without precipitation.
3 movie tickets cost $36. At this rate, what is the cost per ticket?
Answer:
12
Step-by-step explanation:
36 divided by 3 is 12
Please do number one please thank you
1. Which part of Emily's statement is the hypothesis?
'Then you might live in Oregon' is the hypothesis.
How is the hypothesis part found in the statement?
Emily says 'if you live in a state that borders California , then you might live in Oregon.'
Emily is not sure about the exact state that is bordering California.Emily so uses the word might because of uncertainty and gives a possibility of the state to be Oregon.There may be more than one state bordering California and Emily hypothetically mentions it might to OregonWhat is hypothesis?
Hypothesis is a speculative assumption made to uncover and evaluate the ramifications of its logical or empirical implications. It's an idea for a possible explanation of a phenomenon.A working hypothesis is a hypothesis that has been tentatively accepted and is proposed for further study in a process that starts with an informed guess or thinking.To learn more about hypothesis, refer:
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4-2(5x-1)>5x+3 how do I solve this
For the data in the table, write an equation for the direct variation.
The equation of direct variation is,
[tex]\begin{gathered} y=kx \\ k=\frac{y}{x} \end{gathered}[/tex]Substitute the values of y and x.
[tex]\begin{gathered} k=\frac{5.4}{4} \\ k=1.35 \end{gathered}[/tex]So, the obtained equation will be y=1.35(x).
Let's check with the values of x.
1) If x=4
[tex]\begin{gathered} y=1.35x \\ y=1.35(4) \\ y=5.4 \end{gathered}[/tex]2) If x=2
[tex]\begin{gathered} y=1.35x \\ y=1.35(2) \\ y=2.7 \end{gathered}[/tex]3) If x=-2
On a map of a campground, the Sleepy Bear cabin is located at (-14,-10) and the Deer Run cabin is located at (-14,-6). How far apart are the two cabins? (Just type in the number)
Answer: -4 over 0 (I think) I hope this helps a little bit
Step-by-step explanation: Finding the slope
(-14,-10) and (-14,-6)
Use your Y values and subtract them -10-(-6) or -10 + 6= -4 that will be your numerator
Use your 2 X values and subtract them -14-(-14) or -14+14=0 that will be your denominator
Slope will be -4 over 0
Which system is responsible for carrying this oxygen to the muscles?
Answer:
The circulatory system
Step-by-step explanation:
Is this math? lol
:]
i need help show the work
Answer:
9
Step-by-step explanation:
Use Exponent rule:
[tex]\sf \boxed{(a*b)^m = a^m*b^n}[/tex]
[tex]\sf \dfrac{4(3x)^2}{(2x)^2} = \dfrac{4 * 3^2*x^2}{2^2*x^2}\\[/tex]
[tex]\sf = \dfrac{4 * 9 *x^2}{4*x^2}\\\\= 9[/tex]
Choose the statements that are true about a cube with side length 1 unit.
It has a volume of 6 cubic units.
It has a volume of 1 cubic unit.
It has a volume of 3 cubic units.
It is called a "one block."
It can be used to measure volume.
It is called a "unit cube."
The answer to the mentioned statement are :
first statement is WRONG
the second statement is RIGHT
The third statement is also WRONG
the fourth statement is RIGHT
fifth statement is RIGHT
sixth statement is WRONG
The side of the given cube is 1 unit.
This means that the Length= Breadth = Height = 1 unit because it is cube
This means that the volume can be described as
( side ) ³
that is 1 × 1 × 1 = 1 cubic unit
thus the first statement is WRONG
However the second statement is RIGHT
The third statement is also WRONG
since it is a cube whose volume is 1 cubic unit
thus we can say that it is one block
Thus the fourth statement is RIGHT
fifth statement is RIGHT
sixth statement is WRONG
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A painter
mixes 2%, pints
of yellow paint with
4 pints of red paint to make a certain shade of
orange paint. How many pints of yellow paint
should be mixed with 10 pints of red paint
to
make
this shade of orange?
In linear equation, 0.005 pints are pints of yellow paint should be mixed with 10 pints of red paint to make this shade of orange.
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations. As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.Given,
A painter mixes 2%, pints of yellow paint with 4 pints of red paint
So to make this shade of orange ⇒
10 red pints × (2 % yellow pints/ 4 red pints) ≈ 0.005 pints
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May I please get help with this. I have tried multiple times but still could not get the correct answers for them
ANSWER
[tex]\frac{2}{5}[/tex]EXPLANATION
To find the scale factor of the model to the sculpture, we have to divide one set of measurements of the model and sculpture.
Let us divide the length of the model by that of the sculpture:
[tex]\begin{gathered} \frac{10}{25} \\ \Rightarrow\frac{2}{5} \end{gathered}[/tex]That is the scale factor of the model to the real sculpture.
what is 25 + 20x factor
Answer:
5(4x+5)
Step-by-step explanation:
25+20x
=5(5+4x)
:]
Question
Solve 2y−18x=−26 for y.
Answer:
-26
Step-by-step explanation:
If Sarah needs 3 cups of flour for 2 batches of cookies, How many cups of flour would she need for 18 batches of cookies?
Answer:
24 = 18
Step-by-step explanation:
3 cups = 2 cookies
Meaning she needs 24 cups of flower for 18 cookies
What type of reasoning is used to find the next amount of train cars? Explain your answer.
Using an arithmetic sequence, it is found that the next amount of train cars is of 6.
What is an arithmetic sequence?For an arithmetic sequence, the difference between consecutive terms is constant, called common difference d.
The nth term of an arithmetic sequence is given by the following rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
In the context of this problem, from the image, the number of train cars can be modeled by the following sequence:
(0, 2, 4, ...)
Which is an arithmetic sequence with:
A first term of 0.A common ratio of 2.Hence the next term of the sequence is given by:
4 + 2 = 6.
As 4 is the last term and 2 is the common ratio.
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(5y-23) (2x+13) 47 (3x) find the values of c and y
The value of variable x and y are 24 and 19 respectively.
How to find angles?We have to find the variables x and y of the angles.
Therefore,
using angles in a triangle,
2x + 13 + 47 + 5y - 23 = 180
2x + 5y = 180 - 13 - 47 + 23
2x + 5y = 143
Using corresponding angles,
180 - (2x + 13) = 47 + 3x
180 - 2x - 13 = 47 + 3x
180 - 47 - 13 = 3x + 2x
120 = 5x
x = 120 / 5
x = 24
Hence,
2(24) + 5y = 143
5y = 143 - 48
5y = 95
y = 95 / 5
y = 19
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