Answer:
x = 4 , x = 2.4
Step-by-step explanation:
[tex]\frac{4}{x-2}[/tex] + [tex]\frac{3}{x-3}[/tex] = 5
multiply through by (x - 2)(x - 3)
4(x - 3) + 3(x - 2) = 5(x - 2)(x - 3)
4x - 12 + 3x - 6 = 5(x² - 5x + 6)
7x - 18 = 5x² - 25x + 30 ( subtract 7x - 18 from both sides )
0 = 5x² - 32x + 48
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 5 × 48 = 240 and sum = - 32
the factors are - 20 and - 12
use these factors to split the x- term
0 = 5x² - 20x - 12x + 48 ( factor the first/second and third/fourth terms )
0 = 5x(x - 4) - 12(x - 4) ← factor out (x - 4) from each term
0 = (x - 4)(5x - 12)
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
5x - 12 = 0 ⇒ 5x = 12 ⇒ x = 2.4
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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(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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4-2(5x-1)>5x+3 how do I solve this
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]
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
Need help with this
Answer:
<XMN = 122°
Step-by-step explanation:
An angle around a point is 360°
If LMN = 145° then the rest would be 360 - 145
360 - 145 = 215
4x + 5 + 6x - 10 = 215
Simplify = 10x - 5 = 215
work out = 215 + 5 = 220 ÷ 10 = 22
x = 22
XMN = 6x - 10
6 × 22 = 132
132 - 10 = 122
XMN = 122
Question 5Which of the following is equivalent to (2 – 2) (x - 1)
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 ;-;
======================================================
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]
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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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
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)
:]
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)
How do you write 2.467 x 10^10 in standard form?????? helpppp
Answer: 24670000000
Step-by-step explanation:
1) First, the scientific form can help you learn that each 10 in a power will increase the number its multiplying by 10.
Since we know that when multiplying a decimal number by 10, it would move the decimal once to the right. We can apply this to the equation by moving the decimal to the right 10 times.
2) Answer
12345678910 <= This indicates the decimal moving one place
24670000000.00
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:
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
Which system is responsible for carrying this oxygen to the muscles?
Answer:
The circulatory system
Step-by-step explanation:
Is this math? lol
:]
Question
Solve 2y−18x=−26 for y.
Answer:
-26
Step-by-step explanation:
place the numbers in order from least to greatest…PLS HELP!
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number. If the numbers are arranged from the greatest to the least, then it is called descending order.
Absolute Value Calculator: Heron's Calculator
Coterminal Angle Calculator: Graphing Functi...
Step-by-step explanation:
Answer:
1. -[tex]\sqrt{13}[/tex] = -3.605...
2. -18/5 = -3.6
3. -[tex]\sqrt{12.25}[/tex] = -3.5
4. -|3.4| = -3.4
5. |-3.6| = 3.6
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.
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.
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 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.
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
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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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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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
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:
Tracy is cutting out a rectangular board to construct a bookshelf.
The board is to have a perimeter of 38 inches, and its length is to be 5 inches shorter than double the width.
Let x be the width of the board.
State the expression for the length of the board in terms of x.
Answer:
28 inch
Step-by-step explanation:
half of 38 would be 19, and take away 5 from both 19. Equally each width ( top and bottom ) 14 inch and each lenght ( Left and right ) 5 inch. so x representing width would be 14 + 14= 28 inch.
14
5 5
14
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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