[tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
Like terms are terms whose variables (and their exponents such as the 2 in [tex]x^{2}[/tex]) are the same. Like terms can easily be added and substracted. Such questions just need like terms to be bought together and simplified
Infinite number of equations or expressions can be written for the given question. So writing one possibility for the given question,
= [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex]
which sums up to
= [tex]-2x^{2} +3x+3[/tex]
Thus [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
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Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→0 e3x − 1 − 3x x2
It looks like the limit is
[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2}[/tex]
L'Hôpital's rule works in this case; applying it twice gives
[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2} = \lim_{x\to0} \frac{3e^{3x} - 3}{2x} = \lim_{x\to0} \frac{9e^{3x}}{2} = \boxed{\frac92}[/tex]
Find the area of a circle with a diameter of 16.
Either enter an exact answer in terms T or use 3.14 for TT and enter your answer as a decimal
Answer:
Step-by-step explanation:
Area of circle:
area = π · r · r
Radius= [tex]\frac{16}{2}[/tex]= 8
[tex]3.14\times { 8 }^{ 2 }[/tex] = 200.96 [tex]cm^2\\[/tex]
A bird (B) is spotted flying 6,000 feet from a tower (). An observer (0) spots the top of tower (T) at a distance of 9,000 feet. What is the angle of depression from the bird (B) to the
observer (0)?
Using relations in a right triangle, it is found that the angle of depression is of θ = 56.31º.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that:
The opposite side to the angle of depression is the top of tower, at a height of 9000 feet.The adjacent side to the angle is the distance to the bird, of 6000 feet.Hence, considering θ as the depression angle, we have that:
tan(θ) = 9000/6000
tan(θ) = 1.5
θ = arctan(1.5)
θ = 56.31º.
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What is the sum of this infinite geometric series?
[tex]\qquad \qquad \textit{sum of an infinite geometric sequence} \\\\ \displaystyle S=\sum\limits_{i=0}^{\infty}\ a_1\cdot r^i\implies S=\cfrac{a_1}{1-r}\quad \begin{cases} a_1=\stackrel{\textit{first term}}{\frac{1}{8}}\\ r=\stackrel{\textit{common ratio}}{\frac{2}{3}}\\ \qquad -1 < r < 1 \end{cases}[/tex]
[tex]\displaystyle\sum_{k=0}^{\infty} ~~ \underset{a_1}{\frac{1}{8}}\underset{r}{\left( \frac{2}{3} \right)}^k\implies S=\cfrac{ ~~ \frac{1}{8} ~~ }{1-\frac{2}{3}}\implies S=\cfrac{ ~~ \frac{1}{8} ~~ }{\frac{1}{3}}\implies S=\cfrac{3}{8}[/tex]
Complete the equation.
2 x 4 =
X 2
Answer:
4 is correct answer.
Step-by-step explanation:
That because it contains property of communicative. That is a×b=b×a.
A 2-quart carton of non-dairy creamer costs $1.04. What is the price per cup?
In the diagram below, if < ACD = 48 °, find the measure of < ABD.
Answer:
d
Step-by-step explanation:
the opposite angles of a cyclic quadrilateral sum to 180° , that is
∠ ABD + ∠ ACD = 180°
∠ ABD + 48° = 180° ( subtract 48° from both sides )
∠ ABD = 132°
Select the correct answer. emily wants to find the number that appears in the middle of a set of 25 numbers arranged in ascending order, in a spreadsheet. which statistical function will help her do so? a. mode b. rank c. median d. average
The correct answer is option (C) median.
The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.
What is the mean, median and mode?The mean, median, and mode are the three most commonly used measures of central tendency for populations that do not have much data, that is, they do not need to be grouped.
The mean, also known as average, is the value obtained by dividing the sum of a cluster of numbers by the number of them.
When arranging the numbers from least to largest, the median sits exactly in the middle of the values that are above. The median is a set that is a value that is in the middle of the other values.
The number that appears most frequently in a set of numbers is called the mode.
So, The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.
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A dairy farmer decides to sell three fifth of her 500 cows. How many cows will she be left with after the deal is complete?
Find the dicontinuities of the function. f(x) = x2 12x 27 x2 4x 3 . there is a removable discontinuity at ( , ).
The removable discontinuity of the given function is (-3, -3).
What are the discontinuities of the function?
Discontinuous functions are functions that are not a continuous curve - there is a hole or jump in the graph. It is an area where the graph cannot continue without being transported somewhere else.The given function is [tex]f(x) = \frac{x^{2}+ 12x + 27 }{x^{2} + 4x +3}[/tex]
f(x)=(x²+12x+27)/(x²+4x+3)=(x²+9x+3x+27)/(x²+3x+x+3+
=(x+9)(x+3)/(x+3)(x+1)=(x+9)/(x+1)
The holes in the graph by factoring and cancelling are (-3, -3).
Therefore, the removable discontinuity of the given function is (-3, -3).
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Answer: first answer is -3 for both and second is x=-1
Step-by-step explanation:
Test the claim that the proportion of people who own cats is larger than 60 t the 0. 10 significance level?
The null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.
Given that the significance level is 0.10.
We are required to form the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% the significance level.
Hypothesis is a statement which is tested for its validity. Null hypothesis is the statement which is accepted or not by z test,t test,f test ,chi-square test or any other test.
We have to take opposite of the statement to form a null hypothesis. Since we have to check whether the proportion of people who owns cats is larger than 60% of the significance level, we have to assume that it is smaller than 60% of the significance level.
60% of the significance level=0.60*0.10=0.06.
Null hypothesis is [tex]H_{0}[/tex]:μ<0.06
Hence the null hypothesis to test the claim that the proportion of people who owns cats is larger than 60% of the significance level is [tex]H_{0}[/tex]:μ<0.06.
Question is incomplete.The question should include the following:
Find the null hypothesis for the testing.
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10. Ali's crystal ball grants two-fifths of one-fifth of
all wishes. This is ?% of all wishes.
(A)
2
(B)
25
(C) 8
(D) 60
Answer:
C
Step-by-step explanation:
2/5 x1/5 = 2/25 If you divide 2 by 25, you get.08. To change a decimal into a percent, you move the decimal two places to the right to get 8%
How do you determine the
solution to a system of equations
when graphing? Is it possible to
have more than 1 solution when
graphing? Is it possible to have no
solutions? How?
When graphing, the intersections of the graphs represent the solutions of the system.
How to determine the solutions of a system by graphing?
When graphing a system of equations, you just need to graph both equations in the same coordinate axis.
The solutions of the system are all the points where the graphs of the two equations intersect.
This means that if there is only one intersection, there is one solution.
But we can have more than one intersection, like in the case where at least one of the equations is a polynomial of degree 2 or more.
And there is also the case that the graphs never intersect, like in parallel lines, in these cases we have no solutions.
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At the movie theatre, child admission is $6.80 and adult admission is $9.90. On Thursday, twice as many adult tickets as child tickets were sold, for a total sales
of $984.20. How many child tickets were sold that day?
Number of child tickets:0
Answer:
37 child tickets / 74 adult tickets
Step-by-step explanation:
I randomly picked a number and increased or decreased whether the solution was too high or low (guess and check)
The number of child tickets sold that day is 37.
We have,
Let's assume the number of child tickets sold is "C" and the number of adult tickets sold is "A."
The cost of a child ticket: $6.80
The cost of an adult ticket: $9.90
The total sales for the day: $984.20
The number of adult tickets sold is twice the number of child tickets sold:
A = 2C
To find the number of child tickets sold, set up an equation based on the total sales:
6.80C + 9.90A = 984.20
Substituting the value of A from equation 4:
6.80C + 9.90(2C) = 984.20
Simplifying the equation:
6.80C + 19.80C = 984.20
26.60C = 984.20
C = 984.20 / 26.60
C ≈ 37
Therefore,
37 child tickets were sold that day.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
○ [tex]h = \frac{2A}{b}[/tex]
Step-by-step explanation:
We are given:
[tex]A = \frac{1}{2} b h[/tex]
To solve for [tex]h[/tex], we have to rearrange the equation to make [tex]h[/tex] the subject:
[tex]A = \frac{1}{2} b h[/tex]
⇒ [tex]2A = bh[/tex] [multiplying both sides by 2]
⇒ [tex]\frac{2A}{b} = h[/tex] [dividing both sides by b]
⇒ [tex]h = \frac{2A}{b}[/tex] [swapping sides]
G.CO.5 △ABC undergoes a series of transformations to create △A'B'C'. Which of the following series of transformations will carry △ABC onto △A'B'C'?
Triangle ABC was reflected over the y axis and translated 3 units down to form triangle A'B'C'.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle ABC was reflected over the y axis and translated 3 units down to form triangle A'B'C'.
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What two nonnegative real numbers with a sum of have the largest possible product?.
The two non negative real numbers with a sum of 60 that have the largest possible product are 30 and 30.
What are non negative numbers?
Non-negative numbers are those that are either zero or positive (remember that 0 and 0 are the same). An integer that is either positive or zero is considered a non-negative integer. It is the result of adding all the natural numbers together with zero. It can be defined as the set "0, 1, 2, 3,...," and is also known as Z.
An integer that is either positive or zero is considered a non-negative integer.
Let us assume the two non negative numbers are [tex]x[/tex] and [tex]y[/tex].
According to the question,
Sum of two non negative numbers = 60
⇒ [tex]x+y=60[/tex]
⇒ [tex]y=60-x[/tex]
Their product will be given as,
⇒ [tex]P=xy[/tex]
⇒ [tex]P=x(60-x)[/tex]
⇒ [tex]P=60x-x^2[/tex]
For the product to be largest [tex]P'(x)=0[/tex]
⇒ [tex]P'(x) = 60-2x[/tex]
⇒ [tex]60-2x=0[/tex]
⇒ [tex]2x=60[/tex]
⇒ [tex]x=30[/tex]
Now, for the value of [tex]y[/tex]
⇒ [tex]y=60-x[/tex]
⇒ [tex]y=60-30[/tex]
⇒ [tex]y=30[/tex]
Therefore, the two non negative numbers are 30, 30.
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write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (-6,6) and is perpendicular to the line that has an x-intercept of 5 and a y-intercept of -15
Answer:
[tex]y=-\dfrac{1}{3}x+4[/tex]
Step-by-step explanation:
Slope of line with given x and y intercepts
The x-intercept is when y = 0.
Therefore, if the x-intercept is 5 ⇒ (5, 0).
The y-intercept is when x = 0.
Therefore, the y-intercept is -15 ⇒ (0, -15).
Inputting these two points into the slope formula to find the slope of this line:
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-15-0}{0-5}=3[/tex]
Slope of function f(x)
If the function f(x) is perpendicular to the above line, then the slope of function f(x) is the negative reciprocal of the slope of the line.
[tex]\implies \sf slope\:of\:f(x)=-\dfrac{1}{3}[/tex]
Equation of f(x) in point-slope form
Use the found slope and the point (-6, 6) with the point-slope form of a linear equation to find the equation of function f(x):
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x-(-6))[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x+6)[/tex]
Expand and rearrange so that the equation is in the slope-intercept form of y=mx+b:
[tex]\implies y-6=-\dfrac{1}{3}x-2[/tex]
[tex]\implies y=-\dfrac{1}{3}x+4[/tex]
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Please help!
The graph shows a system of inequalities.
Which point is a solution to the system?
(0,-1)
(2,3)
(4,0)
(6,-6)
Check the picture below.
find the value of n:
[tex]\frac{10}{n} =\frac{15}{6}[/tex]
The difference between the record high and low temperaturs in Charlotte, North Carolina, is 109°F. The record low temperature was -5°F. Write and solve an equation to find the record high temperature.
Answer: 104 degrees farenheit
Step-by-step explanation: H = record high temperature. -5 + 109 = H. -5+109 = 109 + (-5) = 109-5 = 104. H = 104.
Answer:
104
Step-by-step explanation:
Let x = record high and y = record low temperature in Charlotte. The difference between the records high and low, x and y, is 109 degrees Fahrenheit, so x - y = 109. Record low is -5, so x - (-5) = 109.
x + 5 = 109
x = 104
ANSWER ASAP!
what is the value of a₁₇ if a₁₃=26 and the recursive form of a geometric sequence is aₙ=1/2aₙ₋₁
please answer with atleast some detail
The 17th term of the geometric sequence given in the problem is:
[tex]a_{17} = \frac{13}{8}[/tex]
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
As a function of the mth term, the nth term can also be given as follows:
[tex]a_n = a_mq^{n - m}[/tex]
In this problem, we have that:
[tex]a_{13} = 26, q = \frac{1}{2}[/tex]
Hence the 17th term is:
[tex]a_{17} = a_{13}q^{4}[/tex]
[tex]a_{17} = 26 \times \frac{1}{16}[/tex]
[tex]a_{17} = \frac{13}{8}[/tex]
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Need this quick ! Correct answers appreciated
(Selected answer is not known to be correct it just won’t let me un select an answer)
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \:g(f( - 5)) = 5[/tex]
[tex]\textsf{\underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:f(x) = |2x + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = | - 1| [/tex]
[tex]\qquad❖ \: \sf \:f( - 5) = 1[/tex]
next,
g(f(-5)) represents value of y at x = f(-5) = 1
hence,
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\sf \:g(f( - 5)) = 5[/tex]Find the absolute maximum and minimum values of f on the set d. f(x, y) = xy2 7, d = {(x, y) | x ≥ 0, y ≥ 0, x2 y2 ≤ 3}
Assuming you mean [tex]f(x,y) = xy^2[/tex] over the domain
[tex]D = \left\{(x,y) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } x^2 + y^2 \le 3\right\}[/tex]
we first observe that [tex]f(x,y) = 0[/tex] for all [tex](x,y)[/tex] on the coordinate axes.
There are no critical points elsewhere in the interior of [tex]D[/tex], since
[tex]\dfrac{\partial f}{\partial x} = y^2 = 0 \implies y=0[/tex]
[tex]\dfrac{\partial f}{\partial y} = 2xy = 0 \implies x = 0 \text{ or } y = 0[/tex]
Parameterize the circular arc boundary by [tex]x=\sqrt3\cos(t)[/tex] and [tex]y=\sqrt3\sin(t)[/tex], where [tex]0\le t\le\frac\pi2[/tex]. Then
[tex]f(x(t), y(t)) = g(t) = 3\sqrt3 \cos(t) \sin^2(t) = 3\sqrt 3 (\cos(t) - \cos^3(t))[/tex]
Find the critical points of [tex]g[/tex].
[tex]g'(t) = -3\sqrt3 \sin(t) + 9\sqrt3 \cos^2(t) \sin(t) = 0[/tex]
[tex]-3 \sin(t) (1 - 3 \cos^2(t)) = 0[/tex]
[tex]\sin(t) = 0 \text{ or } 1 - 3 \cos^2(t) = 0[/tex]
[tex]\sin(t) = 0 \text{ or } \cos^2(t) = \dfrac13[/tex]
[tex]\sin(t) = 0 \text{ or } \cos(t) = \pm\dfrac1{\sqrt3}[/tex]
In the first case, we get
[tex]t = \sin^{-1}(0) + 2n\pi \text{ or } t = \pi - \sin^{-1}(0) + 2n\pi[/tex]
where [tex]n[/tex] is an integer; the only solution on the boundary of [tex]D[/tex] is [tex]t=0[/tex] corresponding to the point [tex](\sqrt3,0)[/tex].
In the second case, we get
[tex]t = \cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]
with only one relevant solution at [tex]t=\cos^{-1}\left(\frac1{\sqrt3}\right)[/tex] corresponding to [tex](1,\sqrt2)[/tex].
In the third case, we get
[tex]t = \cos^{-1}\left(-\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]
but there is no [tex]t[/tex] in this family of solutions such that [tex]0\le t\le\frac\pi2[/tex].
So, we find
[tex]\min\left\{xy^2 \mid (x,y) \in D\right\} = 0 \text{ at } (0,0)[/tex]
(but really any point on either axis works)
[tex]\max \left\{xy^2 \mid (x,y) \in D\right\} = 2 \text{ at } (1,\sqrt2)[/tex]
Select the correct answer from each drop-down menu.
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point and its radius is
units.
The required answers are:
1) The center of the circle = (4, 8)
2) The radius of the circle = 2.5 units
3) The equation of the circle = (x - 4)² + (y - 8)² = 6.25
What is the equation of a circle?The equation of the circle which has a center at (h, k) and a radius of 'r' units is (x - h)² + (y - k)² = r²
To calculate radius 'r', we have r = sqrt( (x1 - h)² + (y1 - k)²)
Where (x1, y1) is the point that lies on the circle.
Calculation:Given that,
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5)
We know that the longest chord on a circle is nothing but the diameter of the circle.
So, the center is the midpoint of the diameter. I.e.,
(h, k) = ([tex]\frac{4+4}{2}[/tex], [tex]\frac{5.5+10.5}{2}[/tex])
⇒ (h, k) = (4, 8)
Therefore, the center of the circle is (4, 8)
Then, the radius is calculated by
r = sqrt( (x1 - h)² + (y1 - k)²)
⇒ r = [tex]\sqrt{(4-4)^2+(5.5-8)^2}[/tex]
⇒ r = 2.5 units
Thus, the radius of the circle is 2.5 units.
So, the equation of the circle with center (4, 8) and radius of 2.5 units is,
(x - h)² + (y - k)² = r²
⇒ (x - 4)² + (y - 8)² = 2.5²
⇒ (x - 4)² + (y - 8)² = 6.25
Thus, the equation of the circle is x - 4)² + (y - 8)² = 6.25.
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Which of the equations below represents
this ellipse?
a. x^2/4+y^2/20=1
b. x^2/2+y^2/10=1
c. x^2/100+y^2/4=1
d. x^2/4+y^2/100=1
The equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
What is the equation of the ellipse represented in the graph?
Herein we have a representation of an ellipse in the image attached aside, ellipses are characterized by the following standard formula:
(x - h)² / a² + (y - k)² / b² = 1 (1)
Where:
(h, k) - Coordinates of the centera, b - Lengths of the semiaxesPlease notice that ellipse will be vertical if b > a, otherwise it will be horizontal. The graph exhibits a vertical ellipse centered at the origin and therefore we conclude that (h, k) = (0, 0) and b > a (b = 10, a = 2). Finally, the equation that represents the graph of the ellipse is x² / 4 + y² / 100 = 1. (Correct choice: D)
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(b) Expand and simplify (x - 3) (2x + 3)(4x + 5)
Answer:
8x³ - 2x² - 51x - 45
Step-by-step explanation:
(x - 3)(2x + 3)(4x + 5) ← expand the 2nd/3rd factors using FOIL
= (x - 3)(8x² + 10x + 12x + 15)
= (x - 3)(8x² + 22x + 15)
multiply each term in the second factor by each term in the first factor.
x(8x² + 22x + 15) - 3(8x² + 22x + 15) ← distribute parenthesis
= 8x³ + 22x² + 15x - 24x² - 66x - 45 ← collect like terms
= 8x³ - 2x²- 51x - 45
Expand first 2 bracket first to get:
2x^2 + 3x - 6x - 9 & simplify, then expand with last bracket.
2x^2 - 3x - 9 (4x + 5)
2x^2 x 4x = 8x^4
2x^2 x 5 = 10x^2
Repeat for the next two numbers next to the bracket.
You get => 8x^3 + 10x^2 - 12x^2 - 15x - 36x - 45
Final simplified answer of:
8x^3 - 2x^2 - 51x - 45
Hope this helps!
Which function is positive for the entire interval [-3, -2]?
Answer:
A function that is positive in the entire interval [-3, -2] is -x2 - 5x - 5.
Answer:
The second function (second graph and choice)
Step-by-step explanation:
If you look at the second function you will see that within the closed interval [-3,-2] the graph y values are positive
First choice is incorrect since at x = -2 the y value is negative
Third choice incorrect since at x = -2, y value is negative
Fourth choice incorrect since y value is negative for x = -2
What is the domain of the function y = X+ 6 -7?
x>-7
x>-6
x>6
x>7
The domain of the function y = √(x + 6) - 7 is x > -6
How to determine the domain of the function?The equation of the function is given as
y = √(x + 6) - 7
Set the radical greater than 0
x + 6 > 0
Subtract 6 from both sides of the equation
x > -6
Hence, the domain of the function y = √(x + 6) - 7 is x > -6
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The domain of the function in discuss described as; y = √x+6 -7 is; x >= -6.
What is the domain of the function described as in the task content above?According to the task content, it follows that the domain of.the function can be evaluated by means of the characteristics associated with the square root.
The function given is; y = √x+6 -7
Since, the square root of a negative number renders a complex number as it's results, it follows that; x+6 >= 0.
Hence, x >= -6.
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a homeowner has budgeted $10,000 for some home remodeling. a contractor has told him the labor and the cost of materials will be about the same amount. the homeowner wants to have about $3,000 left over for furnishings. how much will the homeowner be able to spend on labor and on materials?
Answer:
$3,500 labor and $3,500 materials
Step-by-step explanation:
furnishings + labor + materials = 10,000
furnishings = 3000
3000 + labor + materials = 10,000
labor = materials
3000 + labor + labor = 10,000
2(labor) = 7,000
labor = 7,000/2
labor = 3,500
labor = materials = 3,500