Answers
The algebraic expression for √(4+x)(10-x), which is 121.
To find the value of √(4+x)(10-x) algebraically, we start by simplifying the given equation:
√(4+x) + √(10-x) = 6
To eliminate the square roots, we can square both sides of the equation:
(√(4+x) + √(10-x)\()^2 = 6^2\)
Expanding the left side using the binomial formula, we get:
(4+x) + 2√[(4+x)(10-x)] + (10-x) = 36
Simplifying further:
14 + 2√[(4+x)(10-x)] = 36
Subtracting 14 from both sides:
2√[(4+x)(10-x)] = 22
Dividing both sides by 2:
√[(4+x)(10-x)] = 11
Now we can square both sides again to get rid of the square root:
[(4+x)(10-x)] = \(11^2\)
Simplifying further:
(4+x)(10-x) = 121
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Related Questions
Which of these shapes will tessellate without leaving gaps? A. Hexagon B. Octagon C. Pentagon D. Circle
Answers
The shape that can tessellate without leaving gaps is the hexagon (option A).
The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).
A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.
On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.
A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.
In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).
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Blane Company has the following data: Total sales $800,000 Total variable costs $300,000 Fixed costs $200,000 Units sold 50,000 units What will income from operations be if units sold double to 100,000 units?
Answers
The operating income is $800,000.
What is operating income?Operating income is the amount of revenue left after deducting the operational direct and indirect costs from sales revenue.
Given that, Blane Company has the following data: Total sales $800,000 Total variable costs $300,000 Fixed costs $200,000 Units sold 50,000 units
Operating income = sales - variable costs - fixed costs
Selling price per unit = total sales/unit sold
= 800,000/50,000 = $16
Variable cost per unit = total variable costs/unit sold
= 300,000/50,000 = $6
Operating income = (16x100,000) - (6x100,000) - (200,000)
Operating income = $800,000
Hence, the income from operations is $800,000
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Four students spun a spinner with 16 equal sections, numbered 1 through 16.
Andrea spun 50 times.
Dominique spun 5 times.
Raul spun 25 times.
Seth spun 20 times.
Use the results to answer the questions.
Which student’s data would be most representative of the spinner?
Option for answer:
A. Andrea
B. Dominique
C. Raul
D. Seth
Which two students would have the largest changes between their data displays?
Option for answer:
A. Andrea and Dominique
B. Andrea and Raul
C. Dominique and Seth
D. Raul and Seth
Answers
Answer:
the answers are A and B
Step-by-step explanation:
Answer:
A and A
Step-by-step explanation:
Right on edge 2023
1. A survey of 36 students was conducted to find out how many students enjoy playing volleyball, and 17 said they did. If 648 students were surveyed, how many would say they enjoy playing volleyball?
Answers
The total number of students calculated with the method called simplification and who are playing volleyball is 206.
How simplification method work?
In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.
According to the question, the given survey data for the playing volleyball is written below and it is solved by the simplification method:
survey of students: 36
play volleyball: 17
As per question, the simplification expression for the given statement which state that, if the survey of 648 students how many students play volleyball?
Therefore, the required simplified expression can be written as:
Required expression: 648÷36= 18
Now, playing volleyball =18×17=206 students play volleyball
Hence, the total number of students calculated with the method called simplification who are playing volleyball is 206.
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The Revenue and Cost equations for a company are known to be polynomials of order 1 and 2 respectively. It is also known that the graphs of the two equations meet at points A(1,1) and B(5,9) while the third point of the cost function is C(2,0), obtain the following: a) The Revenue equation and the cost equation (8 marks) b) What do the common solutions to the two equations signify?
Answers
Answer: a) Let the revenue equation be R(x) = mx + b, where m and b are constants. Since the revenue equation is a polynomial of order 1, it can be written in this form.
Let the cost equation be C(x) = ax² + bx + c, where a, b, and c are constants. Since the cost equation is a polynomial of order 2, it can be written in this form.
We know that the graphs of the two equations meet at points A(1,1) and B(5,9). Therefore, we have the following two equations:
R(1) = m(1) + b = 1 (1)
R(5) = m(5) + b = 9 (2)
We can solve for m and b by solving the system of equations (1) and (2):
m = 2
b = -1
Therefore, the revenue equation is R(x) = 2x - 1.
We also know that the third point of the cost function is C(2,0), which gives us:
a(2)² + b(2) + c = 0
4a + 2b + c = 0
Using points A(1,1) and B(5,9), we can set up two more equations:
a(1)² + b(1) + c = 1 (3)
a(5)² + b(5) + c = 9 (4)
Simplifying (3) and (4), we get:
a + b + c = 1 (5)
25a + 5b + c = 9 (6)
Subtracting (5) from (6), we get:
24a + 4b = 8
6a + b = 2
Multiplying (5) by 6 and subtracting it from (6), we get:
19a + 3b = 3
Solving these two equations simultaneously, we get:
a = -1/5
b = 13/5
Substituting these values of a and b into equation (5), we get:
c = 3/5
Therefore, the cost equation is C(x) = (-1/5)x² + (13/5)x + (3/5).
b) The common solutions to the revenue and cost equations are the points where the company breaks even, i.e. where the revenue earned is equal to the cost incurred. These points are important because they represent the minimum amount of sales the company needs to make in order to avoid making a loss. In this case, the common solutions represent the points where the company earns just enough revenue to cover its costs.
Step-by-step explanation:
Solve for x! It's for circles, and I don't understand how to figure it out. So if someone could help, that would be great!
Answers
Answer:
x = 5
Step-by-step explanation:
The only thing the circle does for you is tell you that the angle between the lines marked 3 and 4 is a right angle. A tangent line is always at right angles to the radius at that point.
So, you have a 3-4-x right triangle. The Pythagorean theorem applies:
3² +4² = x²
9 + 16 = x² = 25
x = √25
x = 5
_____
Comment on the answer
This is a 3-4-5 right triangle. You will meet them a lot, so it is useful to remember these side ratios form a right triangle.
Write a numerical expression to represent the phrase "the sum of 25 and the cube of 9." Do not evaluate the expression.
Answers
Answer:
25 + 9^3
Step-by-step explanation:
what percent of 36 is 24?
Answers
Answer:
66.67
Step-by-step explanation:
Answer:
66.67
Step-by-step explanation:
24 / 36 x 100 is 66.67%
What are the solutions of 3x^2- x +7=0?
O A. x =
о
B. x =
O C. x =
2-9i
2+9i or x = 2-⁹⁰
6
6
1+iv83 or x =
6
-i√/83
6
1+9i
1-9i
¹+9 or x = 1-⁹
O D. x = 2+√83 or x = 2-i√/83
6
6
Answers
Answer:
x = (1 +i√83)/6 or x = (1 -i√83)/6
Step-by-step explanation:
You want the solutions to the quadratic equation 3x² -x +7 = 0.
Quadratic formulaThe solutions to the equation ax² +bx +c = 0 are given by the formula ...
\(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)
The given equation has a=3, b=-1, c=7, so the solutions are ...
\(x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(3)(7)}}{2(3)}=\dfrac{1\pm\sqrt{-83}}{6}\\\\\\\boxed{x=\dfrac{1+i\sqrt{83}}{6}\quad\text{or}\quad x=\dfrac{1-i\sqrt{83}}{6}}\)
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five and sixty seven thousandths in decimal form
Answers
Answer:
5.067 is the correct answer
Answer:
5.067
Step-by-step explanation:
"five and.." , the and=decimal point. (5.)
the 7 is right before the thousandths, so it is in the third row (aka the thousandth spot, or the third 0 away from the decimal point. .000).
The six is in the place before the seven, so it gets placed in the hundreds spot (.007).
There is no number before the sixty, so it is placed as a zero (.067)
So, all together its 5.067
A bird house company earns a weekly profit according to the function f(x)=−0.40x2+80x−200 where x is the number of bird feeders built and sold.
a) Find the number of bird feeders that the company must sell in a week to obtain the maximum profit.
b) Find the maximum profit.
Answers
a) The number of bird feeders that the company must sell in a week to obtain the maximum profit = 100
b) Maximum profit = 3800
Maximum profit
Maximum profit is the level of output where MC equals MR. As long as the revenue of producing another unit of output (MR) is greater than the cost of producing that unit of output (MC), the firm will increase its profit by using more variable input to produce more output.Given that ,
f(x)=−0.40\(x^{2}\)+80x−200
f'(x) = -0.40 x \(2x\) + 80
= - 0.80\(x + 80\)
f''(x) = - 0.80
a) For Maximum and minimum profit
f'(x) = 0
- 0.80\(x\) + 80 = 0
0.80 \(x\) = 80
\(x\) = 80 / 0.80
= 80 /80 x 100
\(x\) = 100
for x = 100 , f''(x) = -0.80
f''(x) < 0
Therefore, for x = 100 profit is maximum
Number of bird feeders = 100
b)Maximum profit
f(x) = -0.40 \(x^{2}\) + 80 \(x\) - 200
= -0.40 x 100 x 100 + 8000 - 200
= - 4000 + 8000 - 200
= 4000 - 200
= 3800
Therefore maximum profit = 3800
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if u answer correct you get brainliest!!
Find the value of x such that the date set has a mean of 118
101, 123, 104, 112, 106, x
x = ___
Answers
Answer:
x=162
Step-by-step explanation:
101 + 123 + 104 + 112 + 106 + 162 / 6 = 118
how would someone use the cross product property on an equation with 3 different values instead of two? I provided an example image
Answers
Using the cross product for the proff of Pythagoras theorem, the correct step is
By the cross product property, AB² = BC multiplied by BD
What is cross product propertyThe cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).
For the similar triangles, the ratio is as follows
BD / BA = BA / BC
BA² = BD * BC
and AB = BA, hence
BA² = BD * BC
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Given two independent random samples with the following results: n1=8x‾1=186s1=33 n2=7x‾2=171s2=23 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.
Answers
Answer:
The point of estimate for the true difference would be:
\( 186-171= 15\)
And the confidence interval is given by:
\( (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753\)
\( (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753\)
Step-by-step explanation:
For this case we have the following info given:
\( \bar X_1 = 186\) the sample mean for the first sample
\( \bar X_2 = 171\) the sample mean for the second sample
\(s_1 =33\) the sample deviation for the first sample
\(s_2 =23\) the sample deviation for the second sample
\(n_1 = 8\) the sample size for the first group
\(n_2 = 7\) the sample size for the second group
The confidence interval for the true difference is given by:
\( (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}\)
We can find the degrees of freedom are given:
\( df = n_1 +n_2 -2 =8+7-2= 13\)
The confidence level is given by 90% so then the significance would be \(\alpha=1-0.9=0.1\) and \(\alpha/2=0.05\) we can find the critical value with the degrees of freedom given and we got:
\( t_{\alpha/2}= \pm 1.77\)
The point of estimate for the true difference would be:
\( 186-171= 15\)
And replacing into the formula for the confidence interval we got:
\( (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753\)
\( (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753\)
Find the amount to administer
Ordered: Vistaril 0.4 g PO BID
On Hand: Vistaril 25 mg/5 mL
Answers
Answer:
3mg per BID vistrail
Step-by-step explanation:
if 12 grams of coffee costs x dollars and each gram makes y cups of coffee wha is the cost of one cup of coffee in terms of x and y
Answers
By dividing the total cost of the 12 grams of coffee (x) by the quantity of cups the 12 grams produce, one can get the price of a cup of coffee (12y).
The price of the coffee required to create one cup of coffee must be taken into account before attempting to calculate the cost of one cup of coffee. The price for 12 grams of coffee is specified in this instance (x). We also know that x cups of coffee may be made from every gram of coffee. We must divide the total cost of the 12 grams of coffee (x) by the number of cups the 12 grams produce in order to determine the price of one cup of coffee (12y). As a result, we will know how much one cup of coffee will cost in terms of x and y. Knowing this equation can help you estimate your coffee expenses and determine the price per cup.
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If triangle DEF is classified as equilateral, which statement must be true? aAt least two sides are congruent. bTwo sides are perpendicular. cAll three sides are congruent. dTwo sides are parallel.
Answers
All three sides are congruent. Option C is correct
Explanations:
According to the given question, the triangle DEF is classified as equilateral. An equilateral triangle is a triangle that has all its sides and angles to be equal as shown:
Hence the statement true about the equilateral triangle is that all three sides are congruent.
Answer: All three sides are congruent......
Step-by-step explanation: pic vvvvvvvvvvvvvvvv
how do you find the interquartile range in a histogram?
Answers
Answer:
heres your answer :)
Step-by-step explanation:
Step 1: Put the numbers in order. ...
Step 2: Find the median. ...
Step 3: Place parentheses around the numbers above and below the median. Not necessary statistically, but it makes Q1 and Q3 easier to spot. ...
Step 4: Find Q1 and Q3. ...
Step 5: Subtract Q1 from Q3 to find the interquartile range.
Which ordered pair is a solution of the equation?
7x– 5 = 4y – 6
Answers
Answer:
7x-4y=-11
Step-by-step explanation:
Answer:
Neither in K.A
Step-by-step explanation:
Make sure put some choices before you ask we wouldn't know .
Thank me later !
What is |–6.5|?........................................................
Answers
Answer: 6.5
Step-by-step explanation:
\(|-6.5| = 6.5\)
_________
how does a plane relate to a circle
Answers
Answer:
Planes and circle both have flat surface that extends infinitely in all directions.
Convert each measure to the equivalent metric unit.
8 cm = mm
7 km = m
18 g = kg
43 kg = g
234 L = mL
1 346 mL = L
0.81 km = cm
0.05 dm = dam
1.32 cg = kg
3.7 mcg = mg
Answers
Answer..
Q 1, 80 mm
2, 7000
3,
Determine whether the following sequence converges or diverges and describe whether it does do so monotonically or by oscillation. Give the limit when the sequence converges.
{(-1.00000005)^n}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. The sequence diverges by oscillation.
b. The sequence converges monotonically. It converges to:________
c. The sequence converges by oscillation. It converges to:________
d. The sequence diverges monotonic ally.
Answers
Answer:
a
Step-by-step explanation:
(-1.00000005)^n
as n becomes very large, the function increases in both positive and negative direction.
If n=1, -1.00000005
if n=2, 1.0000001
if n= 3, -1.00000015
if n=20, 1.000001
if n=21, -1.00000105
I have another riddle.
If you buy one rabbit and a rabbit can produce 5 per year, then how many rabbits will you have in 9 years?
Answers
Total number of rabbits produced in 9 years will be 45.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a rabbit can produce 5 new rabbits per year
Total number of rabbits produced in 9 years will be -
n = 5y = 5 x 9 = 45 new rabbits
Therefore, total number of rabbits produced in 9 years will be 45.
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Jordan is running a 10 kilometer race. He runs 2 5/8 kilometers and stops for a drink of water. He runs 3 1/4 more miles before stopping to stretch. How many more miles Jordan need to run in order to finish the race.
Answers
Answer:
4 1/8km
Step-by-step explanation:
if you have done 3 1/4km you can multiply the fraction by 2 so you get 3 2/8.
so now we have 2 5/8km and 3 2/8.
(its always easier to have the fractions the same denominator)
now we add the whole numbers first.
2 km + 3km = 5km.
now the fractions.
5/8 km + 2/8 km = 7/8km.
now add them both together and we get.
5 7/8 km.
take that answer away from 10.
we get 4 1/8km.
Using Symmetry and the Empirical Rule A standardized test is approximately normally distributed with a mean score of 78 and a standard deviation of 3. Use the symmetry of the normal curve and apply the Empirical rule to answer the questions. Make a sketch of the curve to help you determine the areas. Note: You must use the Empirical Rule values 68 % , 95 % , and 99.7% in your computations. The computer calculator will not give you the correct answer. What percent of students scored less than 78? 75 % de What percent of students scored between 75 and 78? What percent of students scored between 72 and 81? Se % What percent of students scored between 69 and 75?
Answers
a. About 50% of the students scored less than 78.
b. Approximately 68% of the students scored between 75 and 78.
c. Approximately 95% of the students scored between 72 and 81.
d. Approximately 99.7% of the students scored between 69 and 75.
a) The normal curve is symmetrical, meaning that the area to the left of the mean is equal to the area to the right of the mean. Since the mean score is 78, 50% of the students scored above 78 and 50% scored below 78.
b) To apply the Empirical Rule, we will assume that 68% of the data falls within one standard deviation of the mean, which in this case is 3 points. So, 68% of the students scored between 75 and 81.
c) The percentage of students who scored between 72 and 81 can be found by subtracting the area to the left of 72 from the area to the left of 81. Using the Empirical Rule, we know that 95% of the observations are within two standard deviations of the mean, so the area between 72 and 81 is equal to 95%.
d) The percentage of students who scored between 69 and 75 can be found by subtracting the area to the left of 69 from the area to the left of 75. Using the Empirical Rule, we know that 99.7% of the observations are within three standard deviations of the mean, so the area between 69 and 75 is equal to approximately 99.7%.
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Raj weighs five books and rounds the weights to the nearest tenth. Which of the weights round to 1.5 pounds?
1.48 pounds
1.42 pounds
1.45 pounds
1.58 pounds
1.52 pounds
Ignore the other questions on there
Answers
A square has a perimeter of 12x+52 units. Which expression represents the side leagth of the square in units
Answers
Answer:
12x/2 or 52/2
Step-by-step explanation:
Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.
Consider the following function.
p(x)=1−12x
Plot two points on the line to graph the function.
Answers
We can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.
What is functiοn?A functiοn frοm a set X tο a set Y is an assignment οf an element οf Y tο each element οf X. The set X is called the dοmain οf the functiοn and the set Y is called the cοdοmain οf the functiοn.
A functiοn, its dοmain, and its cοdοmain, are declared by the nοtatiοn f: X→Y, and the value οf a functiοn f at an element x οf X, denοted by f(x), is called the image οf x under f, οr the value οf f applied tο the argument x.
Functiοns are alsο called maps οr mappings, thοugh sοme authοrs make sοme distinctiοn between "maps" and "functiοns" (see § Other terms).
Tο plοt twο pοints οn the line fοr the functiοn p(x) = 1 - 12x, we can chοοse any twο values οf x and find the cοrrespοnding values οf p(x).
Fοr example, if we chοοse x = 0, then p(0) = 1 - 12(0) = 1, sο the pοint (0,1) is οn the line.
If we chοοse x = 1, then p(1) = 1 - 12(1) = -11, sο the pοint (1,-11) is οn the line.
Therefοre, we can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.
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What is the MAXIMUM of the data set: 24, 25, 29, 30, 31, 31, 32, 34, 34?