Answer:
[tex]\Longrightarrow: \boxed{\sf{25x^2-30x+9}}[/tex]
Step-by-step explanation:
Isolate the term of x from one side of the equation.
Use the perfect square formula.
[tex]\underline{\text{PERFECT SQUARE FORMULA:}}[/tex]
[tex]\Longrightarrow: \sf{(A-B)^2=A^2-2AB+B^2}[/tex]
(5x-3)²
(5x-3)²= (5x)²-2*5x*3+3²
Solve.
[tex]\sf{(5x)^2-2*5x*3+3^2=\boxed{\sf{25x^2-30x+9}}}[/tex]
Therefore, the final answer is 25x²-30x+9.Answer:
25x² - 30x + 9Step-by-step explanation:
The identity
(a - b)² = a² - 2ab + b²In this case, a = 5x and b = 3, so substituting the values :
(5x - 3)²(5x)² - 2(5x)(3) + (3)²25x² - 30x + 9show division using an array 1. 24÷4 Quotient= Remainder=
Answer:
Quotient: 6
Remainder: None
Step-by-step explanation:
24 divided by 4 is 6.
Find AC for the quadrilateral
The quadrilateral ABCD is an isosceles trapezoid, and the length of AC for the quadrilateral is 19 feet
How to determine the length of AC?The quadrilateral ABCD is an isosceles trapezoid
This means that:
Opposite sides are equalThe diagonals are also equalFrom the above highlights, we have:
AC = 7ft + 12ft
Evaluate the sum
AC = 19 ft
Hence, the length of AC for the quadrilateral is 19 feet
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Read more about quadrilaterals at:
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Difference of squares. Pls help algebra factoring polynomials 10 points
Answer:
4x(squared)-36
Step-by-step explanation:
=(2x+−6)(2x+6)
=(2x)(2x)+(2x)(6)+(−6)(2x)+(−6)(6)
=4x^2+12x−12x−36
=4x^2 −36
Identify the slope and y-intercept of each of the following lines. Then graph each line.
5x - 3y = 18
Do I put the answer on the attached graph?
Answer:
Yes, but you have to write what the slope and y-intercept of the equation is as well.
Step-by-step explanation:
(Not sure if you wanted the full answer or just if you should graph it but I'm putting it here anyways :^P)
First convert the equation from standard form to slope-intercept form.
5x-3y=18 -> 5x-18-3y -> 5/3x-6=y
5/3x is the slope and 6 is the y-intercept!
Then graph the equation.
First rewrite the equation in slope intercept form
slope intercept form: y = mx + b [ where m is slope and b is y-intercept ]
[tex]\sf \rightarrow 5x - 3y = 18[/tex]
[tex]\sf \rightarrow - 3y = 18-5x[/tex]
[tex]\sf \rightarrow y = \dfrac{-5x+18}{-3}[/tex]
[tex]\sf \rightarrow y = \dfrac{-5x}{-3} + \dfrac{18}{-3}[/tex]
[tex]\sf \rightarrow y = \dfrac{5}{3}x -6[/tex]
comparing with y = mx + b, Here we can identify that the
slope: [tex]\sf \frac{5}{3}[/tex] and y-intercept: [tex]\sf -6[/tex]x-intercept: ( then y will be 0 )
[tex]\sf \hookrightarrow \dfrac{5}{3}x -6=0[/tex]
[tex]\sf \hookrightarrow \dfrac{5}{3}x=6[/tex]
[tex]\sf \hookrightarrow x=\dfrac{18}{5}[/tex]
[tex]\sf \hookrightarrow x = 3.6[/tex]
In order to graph the line
First put the x = 3.6 in the x axisSecondly put y = -6 in the y axisThen using a scale/ruler draw a straight line through this points.Graph:
Overtime Hours Worked A random sample of 15 registered nurses in a large hospital showed that they
worked on average 44. 2 hours per week. The standard
deviation of the sample was 2. 6. Estimate the mean of
the population with 90% confidence.
Overtime Hours Worked A random sample of 15 registered nurses in a large hospital showed that they worked on average 44. 2 hours per week. we can estimate with 90% confidence that the population mean of overtime hours worked by registered nurses in the hospital is between 42.5 and 45.9 hours per week.
What is t-distribution?The t-distribution is a probability distribution that is used to estimate the population mean of a normally distributed variable when the sample size is small or the population standard deviation is unknown.
To estimate the population mean with a 90% confidence interval, we can use a t-distribution with n-1 degrees of freedom, where n is the sample size.
First, we need to calculate the standard error of the mean, which measures the variability of sample means around the population mean. The formula for the standard error of the mean is:
SE = s / sqrt(n)
where s is the sample standard deviation and n is the sample size.
In this case, s = 2.6 and n = 15, so:
SE = 2.6 / sqrt(15) = 0.671
Next, we need to find the critical value of the t-distribution with 14 degrees of freedom and a 90% confidence level.
We can look this up in a t-table or use a calculator to find that the critical value is approximately 1.761.
Finally, we can calculate the confidence interval using the formula:
CI = X ± tα/2 * SE
where X is the sample mean, tα/2 is the critical value of the t-distribution, and SE is the standard error of the mean.
In this case, X = 44.2 and tα/2 = 1.761, so:
CI = 44.2 ± 1.761 * 0.671
CI = (42.5, 45.9)
Therefore, we can estimate with 90% confidence that the population mean of overtime hours worked by registered nurses in the hospital is between 42.5 and 45.9 hours per week.
For more details regarding t-distribution, visit:
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Rewrite the rational expression with the given denominator.
Answer:
49t²r³
Step-by-step explanation:
Hello!
6r is multiplied by 7r³ to get to 42r^4. To keep a fraction proprtional, both numerator and denominator must be multiplied by the same amount.
We have to multiply 7t² by 7r³ to find the missing value.
Multiply:
7t² * 7r³49t²r³The missing value is 49t²r³
Answer number 10 please thank you
Answer:
35%
Step-by-step explanation:
My sister need the anwser for this question: What is the area of a triangle with a base (b) of 12cm and a height (h) of 4cm?
Answer:
24 cm²
Step-by-step explanation:
You can show your sister how to use the formula for the area of a triangle.
The base dimension is substituted for the letter b, the height is substituted for the letter h, and then the arithmetic is carried out.
A = 1/2bh
A = (1/2)(12)(4) = (6)(4) = 24 . . . . square centimeters
Which fraction is equivalent to 4/9
A 14/19
B 2/3
C 6/11
D 8/18
Two sides of a rectangle are (2x+5)cm and (4-x)cm. Find it's area.
Answer:
The area of the rectangle = x + 20
Step-by-step explanation:
The explanation is in the attachment
SORRY FOR MY BAD HANDWRITING
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Diameter = 50 cm
In terms of , what is the area of the circle?
Answer:
1,962.5
Step-by-step explanation:
r=d/2
50 / 2 = 25
25 = r
A= πr²
3.14 x 25²=1,962.5
[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex]
Below is a list of the steps used to construct a square inscribed in a circle.
Step M - Place the compass point at the endpoint of the diameter and the pencil at
the center of the circle to construct an arc.
Step N - Draw in two diameters using the points where the small arc intersects the
line segments and the center.
Step O - Construct a small arc by placing the compass point where the diameter
intersects the line segment and the pencil on the center of the circle.
Step P - Construct a line segment between the two points where the arc intersects the
circle.
Step Q - Draw line segments between the four points where the two constructed
diameters intersect the circle.
Which list shows these steps in the correct order?
M, N, O, P, Q
M, P, O, N, Q
O, P, M, Q, N
P, O, M, Q, N
Answer:
B: M,P,O,N,Q
Step-by-step explanation:
Sowy if i am wrong pls don't go hard on me.
Answer:
b
Step-by-step explanation:
took the test
Help asap! take your time not pushing its for my sis
Answer:
A. Whatever that is in the parenthesis should be solve first.
Answer:
A is the correct option you should always solve the bracket first if you know about BIDMAS
B- BRACKET
I- INDICES
D- DIVISION
M- MULTIPLICATION
A- ADDITION
S- SUBTRACTION
you are taking a trip at the same time as another family. your family traveled 1.900 miles in 2 days, their family traveled 2.700 miles in 3 days. who is traveling faste
Answer:
your family
Step-by-step explanation:
1,900/2 = 950
2,700/3 = 900
your family travels 950 miles every day whereas their family travels 900 miles every day :)
enter the value of x such that blah blah blah look at the picture
Answer:
x=6
Step-by-step explanation:
Create equivalent expressions in the equation that all have equal bases, then solve for x.
use properties of logarithms to expand the logarithmic expression as much as possible.
help please!
Step-by-step explanation:
Begin by separating the division. Division in the argument of a logarithm function is equivalent to subtracting the log of the numerator and denominator:
[tex]ln( \frac{ {x}^{9} \sqrt{ {x}^{2} + 7} }{ {(x + 7)}^{7} } ) = ln( {x}^{9} \sqrt{ {x}^{2} + 7 } ) - ln(( {x + 7})^{7} )[/tex]
Multiplication under a logarithm means addition:
[tex] ln( {x}^{9}) + ln( \sqrt{ {x}^{2} + 7 }) - ln(( {x + 7})^{7} )[/tex]
Log rules say that exponents can be dragged to the front as coefficients:
[tex]9ln(x) + \frac{1}{2} ln( {x}^{2} + 7) - 7ln(x + 7)[/tex]
Solve each equation.
a.8x=2/3
b.1 1/2=2x
c.5x=2/7
d.1/4x=5
e.1/5=2/3x
Answer:
a) x = 1/12
b) x = 3/4
c) x = 2/35
d) x = 20
e) x = 3/10
Step-by-step explanation:
a) 8x = 2/3
8x/8 = (2/3) / 8
x = 2/3 * 1/8
x = 2/24
x = 1/12
b) 1 1/2 = 2x
3/2 = 2x
(3/2) / 2 = 2x/2
3/2 * 1/2 = x
3/4 = x
x = 3/4
c) 5x = 2/7
5x/5 = (2/7) / 5
x = 2/7 * 1/5
x = 2/35
d) 1/4x = 5
1/4x * 4 = 5 * 4
x = 20
e) 1/5 = 2/3x
1/5 * 3/2 = 2/3x * 3/2
3/10 = x
x = 3/10
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can anyone help pls?
[tex]7 \frac{5}{8} + 4 \frac{2}{3} [/tex]
to find:the simplest form.
solution:[tex] \frac{61}{8} + \frac{14}{3} [/tex]
[tex] = \frac{(61 \times 3) + (14 \times 8)}{8 \times 3} [/tex]
[tex] = \frac{183 + 112}{24} [/tex]
[tex] = \frac{295}{24} [/tex]
[tex] = 12 \frac{7}{24} [/tex]
hence, the correct answer is option D.
For each decimal, find two integers closest to it. 11.6. | < 11.6< <
The decimal number 11.6 is to one decimal place, and the closest integers to 11.6 are 11 and 12
How to determine the closest integer?The decimal number is given as:
11.6
The above decimal number is between the digits 11 and 12
This means that the closest integers to 11.6 are 11 and 12
Read more about decimal at:
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the slope of the line below is -3. use the coordinates of the labeled point to find a point-slope equation of the line.
Answer:
B
Step-by-step explanation:
point (5,-7) slope ( -3) form of the line would be
(Y- -7) = - 3(x-5)
y+7 = -3 (x-5)
You buy 4 health bars and 3 health drinks for $10. Your friend buys 6 health bars and 2 health drinks for $10. Each health bar costs how much and each health drink costs how much
Using a system of equations, it is found that:
The cost of a health bar is of $1.The cost o a health drink is of $2.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Cost of a health bar.Variable y: Cost of a health drink.You buy 4 health bars and 3 health drinks for $10, hence:
4x + 3y = 10.
Your friend buys 6 health bars and 2 health drinks for $10, hence:
6x + 2y = 10
2y = 10 - 6x
y = 5 - 3x.
Replacing on the first equation:
4x + 3y = 10
4x + 3(5 - 3x) = 10
-5x = -5
5x = 5
x = 1
Then:
y = 5 - 3x = 5 - 3 = 2.
The cost of a health bar is of $1.The cost o a health drink is of $2.More can be learned about a system of equations at https://brainly.com/question/24342899
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Jose is wrapping a stack of 100 coins in a paper holder. Each coin is 1/8 inch thick and has a diameter of 1 inch. How many square inches of paper will Jose need to cover the stack of coins? Use 3.14 for ππ.
Answer:
10.205 inches²
Step-by-step explanation:
What is being described is essentially a cylinder (like a tin can)!Note: for this question let's assume the paper's thickness doesn't matterIf there's 100 coins, each being 1/8 inch thickThe height of the cylinder must be 100 * 1/8 = 12.5 inchesTo find the area of the bottom and top of our cylinder let's first calculate 1 side:The area of a circle = π × r²area = π × (1/8)² = π/16 inches²two circles is just double the area: 2 * π/16 = π/8Now that we know the height and the area of the top + bottomWe can now use the cylinder formula for surface areaA = 2πrh + 2πr² (notice how we've already done 2πr² with our circles!)A = 2 × π × 1/8 × 12.5 + π/8A = (13π) / 4 = (13 × 3.14) / 4 = 10.205 inches²Which expression represents the phrase below?
8 less than the product of 6 and a number, x
A. 8 - 6x
B.6x-8
C.(6+x)-8
D.8-(6+x)
A coin is tossed 20 times with the following results:
HHHTTTTHTTHHTTHTHHHH
What is the experimental probability of the coin landing on tails?
Using it's concept, it is found that there is a 0.45 = 45% experimental probability of the coin landing on tails.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For an experimental probability, these number of outcomes are taken from previous trials.
In this problem, 9 out of 20 trials resulted in tails, hence the experimental probability is given by:
p = 9/20 = 0.45 = 45%.
More can be learned about probabilities at https://brainly.com/question/14398287
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How do you do this? I am really confused
Answer:
Step-by-step explanation:
ok, so this is an infinitly repeating function, so you can write it as:
sqrt(12-x)
Although, x is also equal to sqrt(12-x), so
x = sqrt(12-x), and
x^2 = 12-x
x^2-12+x = 0
now just apply the quadratic formula and you're good
hope i helped :D
Calculate the perimeter of the shape below. Show ur work!
Answer:
22 is the perimeter.
Step-by-step explanation:
You find the perimeter by adding up all of the sides of a shape. 9 + 9 = 18. 18 + 4 = 22.
You and 3 friends go bowling. You bowl for 2.5 hours. You play 3 games and the total cost is $42.
Find the average rate of games per hour
Answer:
if you play 3 games and the total cost equals to 42
then just do 42 divided by 3 which is 14 so that should be your answer!
Step-by-step explanation:
im very sorry if i get it wrong im only trying to help
so i hope its correct
Just need the answer
Answer:
Step-by-step explanation: if 5/2:2/5 then 4/5 of a pint= 10/2 and you now only need 1/5 of a pint so you have to divid 5/2 by 2. that will give you 1.25 and 1.25 as a fraction is 5/4. now you need to change the fraction 10/2 so that you can add them. Equation for that is 10/2 times 2/2 that gives you 20/4 and 20/4+ 5/4=25/4 or 6 1/4(six and one fourth) of a cup
Solve using the square root method
Answer:
x=3 and x= -3
Step-by-step explanation:
Sorry for my handwriting I know it's not the best but I hope it helps
Answer:
x=-1.13389341903
Step-by-step explanation:
square root of 63=7.93725393319
÷-7=-1.13389341903
this should be the answer
A submarine traveled to St. Vincent and
back. It took four hours less time to get
there than it did to get back. The average
speed on the trip there was 15 km/h. The
average speed on the way back was 10
km/h. How many hours did the trip there
take?
Answer:
8 hrs to get there ( 12 hrs to get back)
Step-by-step explanation:
rate * time = distance distance is the same for both trips
15 km/hr * (t-4) = 10 ( t)
15t - 60 = 10 t
5t = 60
t = 12
t-4 = 8 hrs