Answer:
[tex]x+\cfrac{1}{x} =7[/tex]================
Given:[tex]x^2+\cfrac{1}{x^2} =47[/tex]Add 2 to both sides of equation:
[tex]x^2+\cfrac{1}{x^2}+2 =47+2[/tex]Then follow the steps:
[tex]x^2+\cfrac{1}{x^2}+2*x*\cfrac{1}{x} =49[/tex][tex](x+\cfrac{1}{x})^2=7^2[/tex]Take square root of both sides to get:
[tex]x+\cfrac{1}{x} =\pm\ 7[/tex]We are taking the positive value as we are told x > 0, hence the answer is 7.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
x + 1/x = 7[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \qquad❖ \: \sf \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 47[/tex]
[tex] \qquad❖ \: \sf \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 - 2 = 47[/tex]
( adding and subtracting 2, doesn't change the value )
[tex] \qquad❖ \: \sf \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 = 47 + 2[/tex]
[tex] \qquad❖ \: \sf \: {x}^{2} + \cfrac{1}{ {x}^{2} } + \bigg(2 \sdot x \sdot \cfrac{1}{x} \bigg) = 49[/tex]
( x cancel out, so no change in value )
[tex] \qquad❖ \: \sf \: \bigg(x + \cfrac{1}{x} \bigg) {}^{2} = 49[/tex]
( use identity a² + 2ab + b² = (a + b)² )
[tex] \qquad❖ \: \sf \: \bigg(x + \cfrac{1}{x} \bigg) {}^{} = \sqrt{49} [/tex]
[tex] \qquad❖ \: \sf \: x + \cfrac{1}{x} {}^{} = \pm7[/tex]
since we have to take positive value, i.e greater than 0
[tex] \qquad❖ \: \sf \: x + \cfrac{1}{x} {}^{} = 7[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Therefore, the required value is 7
Describe the steps you used to solve the equation and
find the amount of Carrie's allowance.
Linear equation:a+a+8=22
Answer:
Carrie's allowance is 7.
Step-by-step explanation:
Use the equation to find a.
a+a+8=22
First, combine like terms.
2a+8=22
Subtract 8 from both sides.
2a+8-8=22-8
2a=14
Divide 2 from both sides.
2a/2=14/2
a=7
Hope this helps!
If not, I am sorry.
Identify the center and the radius of a
circle that has a diameter with endpoints at (2, 7)
and (8, 9).
Using the mid-point concept, we have that:
The center is (5,8).The radius is of 3.16 units.What is the mid-point concept?The mid-point between two points is the halfway point between them, and is found using the mean of the coordinates.
The center of the circle is the mid-point of the coordinates of the diameter, hence:
x = (2 + 8)/2 = 5.y = (7 + 9)/2 = 8.The radius is the distance between the center and the end-points of the diameter, hence, applying the formula for the distance between two points:
[tex]r = \sqrt{(5 - 2)^2 + (8 - 7)^2} = \sqrt{10} = 3.16[/tex]
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please help me I don't understand this
Answer:
A. perimeter 200
area 2356
B. Perimeter
C. Area
Step-by-step explanation:
A. Perimeter = 2(base+ height) = 2(62+38)= 200
BASE *HEIGHT (62*38)= 2356
Answer:
(a) Perimeter = 200 inches
Area 2356 inches squared
(b) Area
(c) Perimeter
Step-by-step explanation:
(a) Perimeter = [tex]2(62+38)=200[/tex] inches
Area = [tex]38\times62=2356[/tex] inches squared
(b) Area (rectangle)
(c) Perimeter (line)
Jackie buys 5 books at $27 each and pays for them with 20 dollar bills. How many $20 bills does she need to pay for all the books?
Answer:
7
Step-by-step explanation:
5 x 27 = 135
135 ÷ 20 = 6.75
round up to 7
What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 7.2 cm? Enter your answer as a decimal in the box
The measure in radians for the central angle of the circle is; 0.9 radians.
What is the angle measure in radians of the central angle?Since, the length of the arc is given as 7.2cm and it's radius is 8cm.
It follows that the angle measure of the central angle can be evaluated as follows;
7.2 = (A/6.28) × 2× 3.14 × 8
7.2 = 8A
A = 7.2/8
A = 0.9 radians.
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Select the correct answer. The graph of function f is shown. An exponential function with vertex at (1, 3) and passes through (minus 2, 10), (8, 2) also intercepts the y-axis at 4 units. Function g is represented by the equation. Which statement correctly compares the two functions?
The statement which correctly compares the two functions is that: A. they have the same y-intercept and the same end behavior as x approaches ∞.
What is a function?A function is a mathematical expression which can be used to define and show the relationship that exist between two or more variables in a data set.
By critically observing the graph which models the function f (see attachment), we can logically deduce that the y-intercept is at four (4).
Also, from the table of function g (see attachment), we have:
At x = 0, g(x) = g(0) = 4.
In conclusion, the statement which correctly compares the two functions is that they have the same y-intercept and the same end behavior as x approaches infinity (∞).
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Complete Question:
The graph of function f is shown.
Which statement correctly compares the two functions?
A. They have the same y-intercept and the same end behavior as x approaches ∞.
B. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
C. They have the same x- and y-intercepts.
D. They have the same x-intercept and the same end behavior as x approaches ∞.
A una excursion van 40 niños acopmañados por 30 adultos.Pasaran la noche en cabañas iguale,pero lod niños y los adultos deben dormir separados.Cuantas menos cabañas ocupen,menos pagaran ¿cuantas cabañas deben ocupar para pagar lo menos posible?¿cuantos dormiran en cada cabaña?
El número máximo de ocupantes es el máximo común divisor de los dos números, es decir, 10 personas por cabaña. Se debe pagar siete cabañas para minimizar costes.
¿Cuántas cabañas deben ser pagadas por los excursionistas?
En esta pregunta desconocemos la capacidad de cada cabaña, solo conocemos que todas las cabañas tienen el mismo aforo. En consecuencia, puede haber más de una respuesta, aunque con la restricción de que cada cabaña tiene el mismo número de hospedados.
Inicialmente, descomponemos factorialmente los números de adultos y niños:
Niños
40 = 2³ × 5
Adultos
30 = 2 × 3 × 5
El número máximo de ocupantes por cabaña es el máximo común divisor de los dos números, es decir, 2 × 5 = 10. Por tanto, los excursionistas deben pagar siete cabañas para minimizar costes.
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24. Write the equation of the line that has a slope of -1/5 and a y-intercept of 8 in standard
form. Ax+By=C "Hint: Write the equation in slope-intercept or point slope form first, then
re-write in standard form.
Answer:
x + 5y = 40
Step-by-step explanation:
the equation of the line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{1}{5}[/tex] and c = 8 , then
y = - [tex]\frac{1}{5}[/tex] x + 8 ( multiply through by 5 to clear the fraction )
5y = - x + 40 ( add x to both sides )
x + 5y = 40 ← in standard form
⊰________________________________________________________⊱
Answer:
See Below.
Step-by-step explanation:
[tex]\large\begin{gathered}\sf{First, \ let's \ write \ the \ equation \ in \ slope-intercept \ form.}\\\sf{ Slope-Intercept \ form \ is \curvearrowright} \\\boxed{y=mx+b}}\\\sf{Substitute \ the \ pieces \ of \ information \ we \ have \curvearrowright\\\sf{ y=-\dfrac{1}{5}x+8}\\\sf{Now, if \ we \ multiply \ the \ entire \ equation \ by \ 5, \ we'll \ have:} \\\sf{5y=-x+40}\\\sf{And \ finally, move \ \bf{x} \ \sf{to \ the \ left \ with \ the \ opposite \ sign: x+5y=40.}\end{gathered} \bigstar \\\bigstar[/tex]
Done!!
⊱______________________________________________________⊰
[tex]\overbrace{C}\underbrace{A}\overbrace{L}\underbrace{L}\overbrace{I}\underbrace{G}\overbrace{R}\underbrace{A}\overbrace{P}\underbrace{H}\overbrace{Y}[/tex]
Answer two questions about Equations AAA and BBB:
\begin{aligned} A.&&5x&=3x \\\\ B.&&5&=3 \end{aligned}
A.
B.
5x
5
=3x
=3
1) How can we get Equation BBB from Equation AAA?
The answers to the question about the equations are as follows:
1) A. Only add to or remove from one side.
2) B. No
1) As can be seen, the equations' left sides vary, while their right sides remain the same.
We must eliminate the difference in order to make them equal.
Formula A: 5x -2 + x = x -4
Formula B. 5x + x = x- 4
Equation B is created by multiplying the left side of equation A by 2.
The available response in this instance is:
A. Only increase or decrease an amount from one side.
2) The answers to the equations will differ since they are not identical.
Answer option:
B. No
The question was incomplete. The complete question was as follows:
Give two answers about Equations A and B:
A. 5x-2+x = x-4
B. 5x+x = x-4
1) From Equation A, how do we derive Equation B?
A. Only increase or decrease an amount from one side.
B. Increase/decrease the same amount on both sides.
C. Use the distributive principle to rewrite one (or both) sides.
D. Rewrite one (or both) sides using similar wording.
2) Are the equations equal in the light of the initial response? Do they share the same solution, in other words?
(1) Yes (2) No
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Answer:
Step-by-step explanation:
What is the slope-intercept form of the equation of the line containing the points (−2, 4) and (6, 0)?
The slope-intercept form of the equation of the line containing the points (−2, 4) and (6, 0) will be y =0.5 x+ 5.
What is the slope?A numerical assessment of a line's angle relative to the ground is known as the slope.
The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.
The slope of the line is found as;
[tex]\rm m = \frac{y_2-y_1}{x_2-x_1} \\\\ m = \frac{0-4}{6-(-2)} \\\\ m = \frac{-4}{8} \\\\ m = \frac{-1}{2}[/tex]
The standard line equation is;
y-y₁=m(x-x₁)
[tex]\rm y-4= \frac{-1}{2}(x-(-2)) \\\\ 2y-8 = x+2 \\\\ 2y =x+10 \\\\ y = 0.5 x + 5[/tex]
Hence, the slope-intercept form of the equation of the line containing the points (−2, 4) and (6, 0) will be y =0.5 x+ 5.
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Marcus was going up 10 stairs in his office. Write an absolute value expression for the given statement.
1. -10
2. |10|
3. |-10|
4. ±10
I need the answers for number 9 and 10
Rebecca bought 15 cupcakes for her birthday party, each cupcake was 3$ plus tax, the total bill was $47.25 how much tax did she pay on each cupcake
The tax paid by Rebecca on each cupcake was $0.15 or 15 cents, in the buying of 15 cupcakes for $47.25, where the cost of each was $3 plus taxes.
The tax is the amount paid to the government for buying and selling of goods are services.
In the question, we are informed that Rebecca bought 15 cupcakes, where each cupcake cost $3 plus taxes and the total bill to Rebecca was $47.25.
It implies that the cost of 15 cupcakes along with their taxes = $47.25.
Therefore, the cost of 1 cupcake along with its taxes = $47.25/15 = $3.15.
The cost of 1 cupcake is given as $3 plus taxes.
The total cost of 1 cupcake was $3.15.
Thus, the tax on 1 cupcake = $3.15 - $3 = $0.15 = 15 cents.
Thus, The tax paid by Rebecca on each cupcake was $0.15 or 15 cents, in the buying of 15 cupcakes for $47.25, where the cost of each was $3 plus taxes.
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A box is to be constructed with a rectangular base and a height of h cm. the length, l, of the box is 10 cm, and the width, w, is twice the height. which quadratic equation best models the volume of the box? v = lwh
Answer:Answer: We know it has a length of 10 cm, and the width is h times 2.
Step-by-step explanation: So the equation we should write is volume = 10 x (h x 2) x h.
Step-by-step explanation:
will give brainliest if done properly
Answer:
[tex]\sf \boxed{ \sf y - 3 = \dfrac{3}{2} (x - 6)}[/tex]
Explanation:
[tex]\sf Given \ equation: y = \dfrac{3}{2} x - 5[/tex]
Comparing it with slope intercept form "y = mx + b" where 'm' is slope and 'b' is y-intercept.
Here slope: 3/2 and y-intercept: -5
Parallel slope has the same tangent slope.
Pass through point (x, y) = (6, 3)
Equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\rightarrow \sf y - 3 = \dfrac{3}{2} (x - 6)[/tex]
Directions: Indicate product of FOIL for the problem:
(x-2)(x+2)Last
ty <33
Answer:
x^2 -4
Step-by-step explanation:
(x-2)(x+2)
We want to FOIL
First x*x = x^2
Outer x*2 =2x
Inner -2 *x = -2x
Last -2*2 = -4
Add them together
x^2+2x-2x-4
Combine like terms
x^2 -4
One year, there were about 3,000 institutions of higher learning in the U.S. (including junior colleges and community colleges). As part of a continuing study of higher education, the Carnegie Commission took a simple random sample of 400 of these institutions. The average enrollment in the 400 sample schools was 3,700, and the SD was 6,500. The Commission estimates the average enrollment at all 3,000 institutions to be around 3,700; they put a give-or-take number of 325 on this estimate. There were about 600,000 faculty members at institutions of higher learning in the U.S. As part of its study, the Carnegie Commission took a simple random sample of 2,500 of these faculty persons. On the average, these 2,500 sample persons had published 1.7 research papers in the two years prior to the survey, and the SD was 2.3 papers. If possible, find an approximate 95%-confidence interval for the average number of research papers published by all 600,000 faculty members in the two years prior to the survey. If this isn't possible, explain why not.
Thus an approximate 95% confidence interval for the average enrollment of all 60,000 faculty members in the two years prior to the survey. which implies that the given statement is true.
According to the statement
Average sample =3700
SD sample =6500
Sample size =400
EV average =3700
SE average =325
Population size =3000
The boundaries of the 68% confidence interval are then 1 standard error from the estimated average:
EV average+1⋅SE average =3700+1⋅325=3700+325=4025
EV average−1⋅SE average =3700−1⋅325=3700−325=3375
Thus an approximate 95% confidence interval for the average enrollment of all 60,000 faculty members in the two years prior to the survey. which implies that the given statement is true.
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FIND THE AREA - GEOMETRY
The area of regular hexagon is 166.27688 inch².
What is area?The area is the amount of space within the perimeter of a 2D shape.
Given:
side = 8 inch
Using
Area of regular hexagon = 3 √3/2 * a²
= 3 √3/2 * 8*8
=96√3
= 166.27688 inch²
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Which ordered pair is not a solution of the linear equation shown?
OA) (2, 1)
OB) 1,
OC) (4,8)
OD) (-2,-1)
Answer:
C
Step-by-step explanation:
to calculate these kinds of questions we can simply plug in the points given in the equation (x,y ) places where 4 is substituted in x place and 8 in y . so in choice "C" if we put 4 in x's place in the equation we would have to divide it by 2 and multiply by 1 which gives us 2 not 8.
Please help ill give whoever answers the best the brainliest answer :)))
Answer:
Step-by-step explanation:
A rational number can be in the form of a whole/natural number, integers, fractions and recurring decimals
In this case, 5 is a whole number, integer (can be a fraction too) , and of course, is a rational number.
As of which options to choose, read the above sentence carefully :)
Answer:
Natural, Integer, Rational, Whole
Step-by-step explanation:
First, we should know the definition of the word choices.
1) Natural Numbers: We can also count it as 'counting numbers'. Natural numbers are numbers that are a whole excluding the number 0. Some examples are 1, 2, 3, 4, 5 ... and so on.
2) Irrationals: They are numbers that cannot be written in a fraction form. Some examples are [tex]\sqrt{2} , \sqrt{3} , \sqrt{4} , \pi ...[/tex] etc.
3) Integers: They are a whole number that can be a negative, positive, or even a zero. Natural numbers are included in integers. Examples are -2, -1, 0, 1, 2, and so on.
4) Rationals: They are numbers that can be expressed in a fraction form, so it is the opposite of 'irrationals'. Examples are -1/2, 1/2, 2/4, 2/1 ... etc.
5) Whole Numbers: They are numbers that aren't a fraction. It can only be a positive number and a zero, so some examples would be 0, 1, 2, 3, 4, 5 ... and so on.
With these in mind, we can now solve the question. The number 5 is a natural, integer, rational, and a whole number.
Writing Exercises
296. Which method do you prefer to use when multiplying two binomials: the Distributive Property, the FOIL method, or the Vertical Method? Why?
Answer:
kskwnneokjwonannwknwonw
Answer:
Hence we prefer FOIL method when multiplying two binomials.
Step-by-step explanation:
Explanation
We have to explain when multiplying two binomials which method we prefer from Distributive Property, the FOIL method, or the Vertical Method.We prefer the FOIL method because the method is the quickest than the other two methods for multiplying two binomials and requires fewer calculations when finding the product of binomials. it works only for binomial.Which of the following statements are true? Select all that apply.
To solve a simultaneous equation on a graph, it is important to:
Draw the graph of the two equationsFind the two lines that intersect at a common pointThis common point would then be used to find the solution of the pair of simultaneous equations.What is a Graph?This refers to the diagram that is used to show the relationship between variables that are measured along a pair of axes.
Hence, we can see that your question is incomplete so I gave you a general overview to help you get a better understanding of the given concept.
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Charlotte is 195 years younger than Rachel. 2 years later, Rachel will be thrice as old as Charlotte. Find their ages after 2 years. (Estimate the age to the nearest whole number).
Charlotte is 96 years old and Rachel is 292 years old
How to determine their ages?Let c represent Charlotte's age and r represents Rachels's age
From the question, we have:
c = r - 195
2 years later, we have:
r + 2 = 3(c + 2)
Expand the equation
r + 2 = 3c + 6
Subtract 2 from both sides
r = 3c + 4
Substitute r = 3c + 4 in c = r - 195
c = 3c + 4 - 195
Evaluate the like terms
-2c = -191
Divide by -2
c = 95.5
Approximate
c = 96
Substitute c = 96 in r = 3c + 4
r = 3*96 + 4
Evaluate
r = 292
Hence, Charlotte is 96 years old and Rachel is 292 years old
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Use AABC to find the value of cos A
(Please use photo provided)
Answer:
40/41
Step-by-step explanation:
cos = adjacent/hypotenuse
adj = 40, hyp = 41
The function f(x) = StartRoot negative x EndRoot is shown on the graph. On a coordinate plane, an absolute value graph starts at (0, 0) and goes up and to the left through (negative 4, 2). Which statement is correct?
Explanation:
From the given graph of f(x) = √-x
After analyzing,
The domain is x ≤ 0Domain interval notation: (-∞, 0)The range is f(x) ≥ 0Range interval notation: (0, ∞)Above from all options, D.) The domain of the function is all real numbers less than or equal to 0.
Geometry help ??!!??!&&
Answer:
AB = 14
Step-by-step explanation:
We can add the segments together to find the total
AB + BC = AC
This will allow us to find x
4x+2 + 3x-1 = 22
Combine like terms
7x +1 = 22
Subtract 1 from each side
7x+1-1 = 22-1
7x = 21
Divide by 7
7x/7 = 21/7
x = 3
Now we can find the length of AB
AB = 4x+2 = 4(3)+2 = 12+2 = 14
How do you solve this?
It looks like your equations are
7M - 2t = -30
5t - 12M = 115
Solving by substitution
Solve either equation for one variable. For example,
7M - 2t = -30 ⇒ t = (7M + 30)/2
Substitute this into the other equation and solve for M.
5 × (7M + 30)/2 - 12M = 115
5 (7M + 30) - 24M = 230
35M + 150 - 24M = 230
11M = 80
M = 80/11
Now solve for t.
t = (7 × (80/11) + 30)/2
t = (560/11 + 30)/2
t = (890/11)/2
t = 445/11
Solving by elimination
Multiply both equations by an appropriate factor to make the coefficients of one of the variables sum to zero. For example,
7M - 2t = -30 ⇒ -10t + 35M = -150 … (multiply by 5)
5t - 12M = 115 ⇒ 10t - 24M = 230 … (multiply by 2)
Now combining the equations eliminates the t terms, and
(-10t + 35M) + (10t - 24M) = -150 + 230
11M = 80
M = 80/11
It follows that
7 × (80/11) - 2t = -30
560/11 - 2t = -30
2t = 890/11
t = 445/11
Divide x ^ 4 + x - 1 by x - 1
Answer:
Graph for (x^4+x-1)/(x-1)
Step-by-step explanation:
Graph for (x^4+x-1)/(x-1)
The required, divide is given by [tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex]
Fraction of polynomial is, in the numerator and in the denominator of a fraction there is polynomial function
[tex]=x^3+\frac{x^3+x-1}{x-1}\\[/tex]
[tex]=x^3+x^2+\frac{x^2+x-1}{x-1}\\[/tex]
[tex]=x^3+x^2+x+\frac{2x-1}{x-1}\\[/tex]
[tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex]
Thus the required, divide is [tex]=x^3+x^2+x+2+\frac{1}{x-1}[/tex].
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If a savings account has an interest rate of 1.60%, and compounds monthly, what is the apy?
Step-by-step explanation:
monthly interest rate calculation example convert the annual rate from a percent of a decimal by dividing by 100 / 100 is equal to 0.10.9 divide that number 12 to get monthly interest rate in the decimal forms 0.10 upon 12 is equal to zero zero eight three
if 1€=1.50 Australian $ how many Australian $ can be made from €40?
solution:
1€=1.50
$x=€40
By using chain rule
1 × x =1.50×40
so,x=60
Hence,60 Australian $ can be exchanged from €1.5