The system of equations of two unknowns is formulated and solved.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ x\times y = 4 \\ x^2+y^2 = 17 \end{matrix}\right. \ \Longrightarrow \ y=\dfrac{4}{x}} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+\left (\dfrac{4}{x} \right )^2=17\ \Longrightarrow\ x^4+16=17x^2 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{align*} 0&=(x^2)^2-17(x^2)+16\\ =(x^2-16)(x^2-1) \\ \ \ \ \ \ \ \ \ \ \ =(x+4)(x-4)(x+1)(x-1) \end{gathered}$}[/tex]
Possible number pairs are 4, 1 and -4, -1 .
The segment AC is?
A- the adjacent
B- the hypotenuse
C- The opposite
D- The tangent
Answer:
B
Step-by-step explanation:
the hypotenuse........
Answer:
B
Step-by-step explanation:
The hypotenus is always opposite to the right and angle and always the longest side
In 9th grade Jade started a college fund with
$15,000 at a rate of 6.3% compounded bi-
annually. How much money will she have in 4
years?
Answer:
this is the answer I got hope it helps
Evaluate l-x-2yl for x = -2 and y = 3.
Step-by-step explanation:
|...| means absolute value of "...". that means always the "+" value of "...", even if it is negative.
in other words
|-x| = x
|x| = x
|-x - 2y| for x = -2 and y = 3
|- -2 - 2×3| = |2 - 6| = |-4| = 4
Is 0.2775 a rational number
Answer:
yes it is
Step-by-step explanation:
It is a rational number, as it can be written as a fraction.
What is the area of the parallelogram?
A parallelogram has a base of 3 feet and height of 2 and one-half feet.
7 and one-half feet squared
9 feet squared
10 and one-half feet squared
12 feet squared
Answer:
7 and one-half feet squared
Step-by-step explanation:
3 x 2.5 = 7.5
Find the function to which the given series converges within its interval of convergence. Use exact values. 1 3 x 9 x 2 2 ! 27 x 3 3 ! 81 x 4 4 ! 243 x 5 5 !
It looks like the series could be
[tex]\displaystyle 1 + 3x + \frac{9x^2}{2!} + \frac{27x^3}{3!} + \cdots = \sum_{n=0}^\infty \frac{3^nx^n}{n!} = \sum_{n=0}^\infty \frac{(3x)^n}{n!}[/tex]
Recall that
[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]
It follows that the given series is the power series expansion for [tex]\boxed{e^{3x}}[/tex].
justify whether the solution makes sense.
a. Are the two triangles similar?
b. How do you know? Justify.
Answer:
They are identical triangles.
Step-by-step explanation:
Angles in a triangle add up to 180 degrees.
The triangle with 39 and 90 has a missing angle of 51 degrees, and the triangle with 51 and 90 vice versa.
✎ let's answer it
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
it's ↓
( identical triangle)
by #galadohannadivine29For a two-tailed test with a sample size of 20 and a. 20 level of significance, the t value is _____.
Using a t-distribution calculator, it is found that the critical value for the hypothesis test is of t = 1.3277.
How to find the critical value of the t-distribution?The critical value is found considering three inputs:
The tail.The significance level.The amount of degrees of freedom, which is one less than the sample size.Hence, for a two-tailed test, with a 0.2 significance level and 19 df, the critical value is of t = 1.3277.
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What is the surface area in square inches of a basketball that has a diameter of 9 inches
if its diameter is 9, that means its radius is half that, or 4.5.
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4.5 \end{cases}\implies \begin{array}{llll} SA=4\pi (4.5)^2\implies SA=81\pi \\\\\\ SA\approx 254.47~in^2 \end{array}[/tex]
The surface area of the basketball with diameter of 9 in will be 254.34 in².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given that, a basketball has a diameter of 9 inches we need to find its surface area,
Since, the basketball is in the shape of the sphere and the surface area of the sphere = 4π×radius²
Therefore, the surface area of the basketball =
= 4×3.14×(9/2)²
= 4×3.14×4.5×4.5
= 254.34 in²
Hence the surface area of the basketball with diameter of 9 in will be 254.34 in².
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help please I will give you the brianliest
Answer:
66
Step-by-step explanation:
A=12×11/2=66
Hope this helps:)
What is the equation of the line that passes through the point (5,3) and has a slope of -1/5 ?
Answer: y=-1/5x+4
Step-by-step explanation: use the equation y=mx+b (x,y)->(5,3) 5 is an x value and 3 is a y value so you want to plug in these values into the equation. 3=-1/5(5)+b. We already know our slope so just plug it into m. Now multiply -1/5 and 5 which is -1. 3=-1+b you want to isolate b so you can find the intercept. Add one to both sides so it cancels out. 4=b we found our y-intercept so we can write the equation now. y=-1/5x+4
Find the volume of the rectangular prism below
V = L * W * H
Answer:
40[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
V = L × W × H
V = 1.5 × 6 × 4.5
V = 40.5 or 40[tex]\frac{1}{2}[/tex]
Answer:
40 1/2ft
Step-by-step explanation:
H(4 1/2 )x W(1 1/2) = 6.75
HW(6.75)x L(6) = 40.5
Urgent Question, 50 points and will mark brainliest.
Part A
Describe a relationship that can be modeled by the function represented by the graph, and explain how the function models the relationship.
Part B
Identify and interpret the key features of the function in the context of the situation you described in part A.
A key feature is there is a constant y-value level between x values from 0 to 15 and there is a parabolic curve from x-values of 15 to 65. The vertex is at (3, 45)
How to get the relationship between graphs?A) This is a parabolic graph and from the graph, we see that, the y-values remain the same from x-values of 0 to 15. Thereafter the x-values increases with a corresponding decrease in y-values until the vertex point before increase in x-values with corresponding increase in y-values.
A relationship could be: Battery percentage remains at the mark of 40 for the first 15 minutes of use. Thereafter, it begins to decrease parabolically until 45 minutes when it it is almost at 0 level and is charged before it starts to increase in a parabolic manner again for another 20 minutes when it increases linearly.
B) A key feature is there is a constant y-value level between x values from 0 to 15 and there is a parabolic curve from x-values of 15 to 65. The vertex is at (3, 45)
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evaluate f(x) = 3/6x+6 when x = -1
a) undefined
b) 0
c) 3
d) 3/36
Answer:
a) Undefined.
Step-by-step explanation:
[tex]f(x) = \dfrac 3{6x+6} = \dfrac{3}{6(x+1)} = \dfrac{1}{2(x+1)}\\\\\\f(-1) =\dfrac{1}{2(-1+1)}= \dfrac{1}{0}[/tex]
True or false: f(x) represents a function.
A. True
B. False
Answer:
A.) True
Step-by-step explanation:
A set of outputs and inputs becomes a function when there is only one output per input. In this case, each "x" value only has one "y" value, making it a function.
Write each of the following products in standard form. Show the work that
leads to your final answers.
(a) (x+8)(2x-3)
(b) (x-5)²
[tex]\textbf{a)}\\\\~~~(x+8)(2x-3)\\\\=2x^2 -3x + 16x - 24\\\\=2x^2 +13x -24\\\\\textbf{b)}\\\\~~~(x-5)^2\\\\=(x-5)(x-5)\\\\=x^2 -5x -5x+25\\\\=x^2 -10x +25[/tex]
A website offers a free trial membership for an online streaming service from a list of 25 channels. Another website is also offering a free trial, but you chose from a list of 30 different channels. If you can only pick one from each service, how many outcome pairs can you have
There are 750 many outcome pairs you can have
How to determine the number of outcome pairs?The given parameters are:
Website 1 = 25
Website 2 = 30
The number of outcome pairs is calculated as:
Outcome = Website 1 * Website 2
So, we have:
Outcome = 25 * 30
Evaluate the product
Outcome = 750
Hence, there are 750 many outcome pairs you can have
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To convert a distance between miles and feet, you can use the equation f=5280m. In this equation, what is the role of f
David's phone battery level drops 6 percentage points each hour when he is not playing a game on it. When David does play a game on his phone, the phone battery level drops 18 percentage points each hour. On a particular day, the phone battery level was at 100 percentage points at 12:00 noon and at 22 percentage points at 6:00 P.M. If David did not charge his phone during this time, how many hours did he spend playing the game between 12:00 noon and 6:00 P.M. on that day
The number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be 3.5 hours.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
David's phone battery level drops 6 percentage points each hour when he is not playing a game on it.
When David does play a game on his phone, the phone battery level drops 18 percentage points each hour.
On a particular day, the phone battery level was at 100 percentage points at 12:00 noon and at 22 percentage points at 6:00 P.M.
If David did not charge his phone during this time.
Then the number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be
Let x be the number of no gaming hours and y be the number of gaming hours.
Then the equation will be
6x + 18y = 100 - 22
6x + 18y = 78
x + 3y = 13 ...1
x + y = 6 ...2
By solving the equations 1 and 2, we have
x = 2.5 hours and y = 3.5 hours
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If f(x) = 3x² - 4 and g(x) = x+2, find (f - g)(x).
Answer:
for the x values: -2,-1,0,1,2
y-values: 13, 6, 5, 4, -3
Step-by-step explanation:
What are the missing sides in the triangle written as integers or as decimals rounded to the
nearest tenth? The figure is not drawn to scale.
x= 18; y = 15.6
x= 12.7; y = 15.6
x= 12.7;y=9
x=9; y = 12.7
The value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9
TrigonometryFrom the question, we are to determine the values of the missing sides
From the diagram,
Opposite = 9
Adjacent = y
Hypotenuse = x
Included angle = 45°
Using SOH CAH TOA, we can write that
[tex]tan 45^\circ= \frac{9}{y}[/tex]
[tex]1 = \frac{9}{y}[/tex]
∴ y = 9
Since the triangle is a right triangle, we can write that
x² = y² + 9² (Pythagorean theorem)
x² = 9² + 9²
x² = 81 + 81
x² = 162
x = √162
x = 12.7
Hence, the value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9
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8 9/10 x 1 4/5 = ? please answer soon and thanks
Answer:
16 1/50
Step-by-step explanation:
First, turn the fractions into improper fractions.
8 9/10 can be 89/10 and 1 4/5 can be 9/5.
Then you multiply them together:
89/10 * 9/5= 801/50
Now, since 801/50 is 16.02 turn that into a mixed fraction. It becomes 16 1/50.
That's your answer.
solve the proportion
Answer:
The answer would be 5.
Step-by-step explanation:
To solve proportions, you multiply the denominator (6) by the numerator (15). 15 times 6 is equal to 90. You then divide 90 by the denominator (18) to get an answer of 5. I hope this helps you! Have a great day! :)
A store sells almonds for $7 per pound, cashews for $10 per pound, and walnuts for $12 per pound. A customer buys 12 pounds of mixed nuts consisting of almonds, cashews, and walnuts for $118. The customer buys 2 more pounds of walnuts than cashews. The matrix below represents this situation.
If the reduced row echelon form of this matrix represents the amount of each type of nut the customer buys, which statement is a possible interpretation of the results?
One possible interpretation of the results is that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 2 pounds of walnuts to achieve a total cost of $118.
To determine the amount of each type of nut the customer buys, we can set up a system of equations based on the given information.
Let's use the variables:
A = pounds of almonds
C = pounds of cashews
W = pounds of walnuts
From the given information, we can create the following equations:
A + C + W = 12 (since the customer buys a total of 12 pounds of mixed nuts)
7A + 10C + 12W = 118 (since the total cost of the nuts is $118)
W = C + 2 (since the customer buys 2 more pounds of walnuts than cashews)
We can now represent this system of equations as a matrix:
[1 1 1 12]
[7 10 12 118]
[0 -1 1 2]
To find the reduced row echelon form of this matrix, we can use Gaussian elimination or a similar method. Solving the system of equations represented by the matrix, we obtain the following reduced row echelon form:
[1 0 2 6]
[0 1 -3 4]
[0 0 0 0]
Now, let's interpret the results:
From the reduced row echelon form, we can deduce that there are infinitely many solutions to this system of equations. This means that there are multiple possible combinations of almond, cashew, and walnut quantities that satisfy the given conditions.
One possible interpretation of the results could be that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 0 pounds of walnuts. This satisfies the equation A + C + W = 12, and the total cost of nuts is $7 * 6 + $10 * 4 + $12 * 0 = $42 + $40 + $0 = $82. However, since the given total cost is $118, this interpretation is not valid.
Another possible interpretation could be that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 2 pounds of walnuts. This satisfies all the given conditions. The equation A + C + W = 12 holds true, and the total cost is $7 * 6 + $10 * 4 + $12 * 2 = $42 + $40 + $24 = $106, which matches the given total cost of $118.
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The archway of the main entrance of a university is modeled by the quadratic equation y = -x2 6x. the university is hanging a banner at the main entrance at an angle defined by the equation 4y = 21 − x. at what points should the banner be attached to the archway?
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The archway of the main entrance of a university is modeled by the quadratic equation
y = -x² + 6x ....1
The university is hanging a banner at the main entrance at an angle defined by the equation
4y = 21 − x ....2
Then the banner attached to the archway will be
From equations 1 and 2, we have
4(-x² + 6x) = 21 - x
-4x² + 24x = 21 - x
4x² - 25x + 21 = 0
4x² - 21x - 4x + 21 = 0
x(4x - 21) - 1(4x - 21) = 0
(4x - 21)(x - 1) = 0
x = 5.25, 1
Then the value of y will be
When x = 5.25, then we have
y = -(5.25)² + 6(5.25)
y = 3.938
When x = 1, then we have
y = -(1)² + 6(1)
y = 5
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
The graph is given below.
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When a number is halfway between two multiples of one hundred, round to _____.
A. zero
B. the smaller multiple
C. the nearest fifty
D. the larger multiple
Answer:
D. The larger multiple
Step-by-step explanation:
n7nj7j
which of the following is a statement of the triangle inequality theorem
Answer:
A
Step-by-step explanation:
Pick any two sides....their sum must be greater than the third side....
a+b > c
a+c > b
c + b > a
Can you help me solve this equation I been trying to search a video explaining this but nothing and I gaved up studying for six days and now I am trying to get back to track anyways ... The equation is a linear equation : f(x)=-x-11 with the following
1.4f(-2)+5f(1)
2.-5f(12)-2f(-9)
3. 3f(5)x f(2)
4.f(9)/f(-6)
Answer:
4 I promise
jhjhhhhjjj bug check txt TC gym c rectify txt
Solve for g.
-15 + 3g = 2g
g =?
Answer:
g = 15
Step-by-step explanation:
Rearrange unknown terms to the left side of the equation: 3g - 2g = 15
Combine like terms: g = 15
Answer: g = 15
What is the theoretical probability of drawing a blue marble from a bag containing 6 Green marbles, 9 yellow marbles and 5 blue marbles?
Answer:
1/20
Step-by-step explanation:
number of favourable outcomes/number of outcomes