hello
the first equation given was
[tex]-11(x-2)=8x-2=8+11[/tex]let's resolve each side of the equations
for the first one,
[tex]\begin{gathered} -11(x-2)=8x-2 \\ -11x+22=8x-2 \\ \text{collect like terms} \\ 8x+11x=22+2 \\ 19x=24 \\ \text{divide both sides by coefficient of x} \\ \frac{19x}{19}=\frac{24}{19} \\ x=\frac{24}{19} \end{gathered}[/tex]now let's test for the other side of the equation
[tex]\begin{gathered} 8x-2=8+11 \\ 8x-2=19 \\ 8x=19+2 \\ 8x=21 \\ \text{divide both sides by the coeffiecient of x} \\ \frac{8x}{8}=\frac{21}{8} \\ x=\frac{21}{8} \end{gathered}[/tex]from the calculations above, the two equations are not equal
[tex]\frac{24}{19}\ne\frac{21}{8}[/tex]Solve the following equation. -13 + 8 = ?-5210 -21
1. In order to solve the equation we need to apply the correct order of operations. In this case we have a sum of two numbers with different signs. In this cases we subtract the values of the numbers and preserve the signal of the greatest value. With this in mind:
[tex]-13\text{ + 8 = -5}[/tex]The correct answer is -5.
2. Solve the following equation, 6 -11 =?
We need to apply the same property on this question. We have a sum of numbers with different signs, therefore we need to subtract their values and mantain the signal of the greatest one.
[tex]6\text{ - 11 = -5}[/tex]Find the area of each sector. round to the hundredths place
Given data:
The given radius is PQ=r=2.8 in.
The expression for the area of the shaded region is,
[tex]\begin{gathered} A=\frac{(360^{\circ}-311^{\circ})}{360^{\circ}}\pi(r)^2 \\ =\frac{(360^{\circ}-311^{\circ})}{360^{\circ}}\pi(2.8)^2 \\ =3.35in^2 \end{gathered}[/tex]Thus, the area of the shaded region is 3.35 sq-inches.
Given that A and B are two mutually exclusive events, find P (A or B) for the following:P(A) = 0.45 and P(B) = .39
In general,
[tex]P(A\text{ or B)=P(A)+P(B)-P(A and B)}[/tex]However, since we have two mutually exclusive events, they can't both occur at the same time, so
[tex]P(A\text{ and B)=0}[/tex]So in this case,
[tex]P(A\text{ or B)=0.45+0.39-0=}0.84[/tex]and so, P(A or B)=0.84
Given that 4-2i is a zero, factor the following polynomial
We must factor the following polynomial:
[tex]f(x)=x^4-23x^3+196x^2-784x+1120.[/tex]We must use the fact that 4 - 2i is a zero and the Complex Conjugate Root Theorem.
(1) The Complex Conjugate Root Theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.
Knowing that a = 4 - 2i is a root, and using this theorem, we conclude that b = 4 + 2i is also a root of f(x).
(2) The factorize form of f(x) is:
[tex]\begin{gathered} f(x)=1\cdot(x-a)(x-b)(x-c)(x-d), \\ =(x-4+2i)(x-4-2i)(x-c)(x-d). \end{gathered}[/tex]Where a = 4 - 2i, b = 4 + 2i, c and d are roots.
(3) Making the product of the last equation, we get:
[tex]f(x)=1\cdot x^4+(-8-c-d)\cdot x^3+(20+8c+8d+cd)\cdot x^2+(-20c-20d-8cd)\cdot x+20cd.[/tex]Comparing the coefficients of x³ and the constant term with the polynomial of the statement, we see that we must have:
[tex]\begin{gathered} -8-c-d=-23\Rightarrow c=-d-8+23=15-d, \\ 20cd=1120\Rightarrow d=\frac{1120}{20c}=\frac{56}{c}. \end{gathered}[/tex]Replacing the second equation in the first equation, and solving for c, we get:
[tex]c=7.[/tex]Using the equation for d, we get:
[tex]d=8.[/tex](4) Using the results above, we write the factorized form of the polynomial:
[tex]f(x)=(x-4+2i)(x-4-2i)(x-7)(x-8).[/tex]Answer[tex]f(x)=(x-4+2i)(x-4-2i)(x-7)(x-8)[/tex]Solve for x. The triangles in each pair are similar please question number 14
Given that the triangle CDE is similar to triangle CML, it means that the ratio of their corresponding sides are equal. It means that
CD/CM = DE/ML = CE/CL
CD = 20 + 12x + 2 = 12x + 22
CE = 30 + 12 = 42
20/12x + 22 = 12/42
By cross multipying, it becomes
12(12x + 22) = 20 * 42
144x + 264 = 840
144x = 840 - 264 = 576
x = 576/144
x = 4
Using the equation from Part E (V=1/2πr↑2↓h), what is the approximate volume of one refraction cup? What is the relationship between this value and the value from Part D (V=50.24cm↑3)? Use 3.14 for pi.
Given:
The figure with diameter 8 cm and height 2 cm.
Required:
Find the volume.
Explanation:
We know the volume
[tex]\begin{gathered} \text{ Volume = Area of semi-circular base}\times\text{ height} \\ \text{ Volume = }\frac{\pi r^2}{2}\times h \end{gathered}[/tex]We have diameter 8 cm. So radius will be half that is 4 cm and height is 2 cm.
So,
[tex]\begin{gathered} V=\frac{3.14\times4^2}{2}\times2 \\ V=50.24\text{ }cm^3 \end{gathered}[/tex]Answer:
Hence, volume is 50.24 cm cube.
Graph the image of the given triangle under a dilation with a scale factor of 1/4 and center of dilation (0,0)
Answer
Explanation
When figures drawn on the coordinates system are dilated (enlarged or reduced), wg
mike bought four new baseball cards to add to his collection the next day his dog ate half of the collection. there are twenty -nine cards left. How many did he start with?
Since the dog ate half of the collection, and 29 remained, we deduce that twice the value of remaining cards must be the value of the total collection with the 4 new cards. Simply multiply 29 by 2 and subtract four from the previous result and this is the answer.
29*2= 58
58 - 4 = 54
Answer: He started with 54 cards.
how many mold spores would there be after 10 days? How many spores were there two days prior to you finding the bread?
Answer:
[tex]\begin{gathered} P=208.926\cdot10^6\text{ spores after 10 days.} \\ P=3094.85\text{ spores after 2 days} \end{gathered}[/tex]Step-by-step explanation:
We can models this situation by using exponential growth, which is represented by the following formula:
[tex]\begin{gathered} P=P_0\cdot e^{rt} \\ \text{where,} \\ P=\text{Total population after time t} \\ P_0=\text{ starting population} \\ r=\text{rate of growth} \\ t=\text{time} \\ \text{Euler's number} \end{gathered}[/tex]Therefore, for a starting population of 192 mold spores, and since it quadrupled every day.
After 10 days:
If they quadruple every day, then P/P0=4 when t=1.
[tex]\begin{gathered} 4=e^{r(1)} \\ \text{Taking Ln on both sides:} \\ r=\ln (4)\approx1.39 \\ \text{After 10 days, substituting t=10} \\ P=192\cdot e^{1.39(10)} \\ P=208.926\cdot10^6\text{ spores after 10 days.} \end{gathered}[/tex]Now, after 2 days:
[tex]\begin{gathered} P=192\cdot e^{1.39(2)} \\ P=3094.85\text{ spores after 2 days} \end{gathered}[/tex]Find a exact value of the function
Given the functions:
[tex]\begin{gathered} f(\theta)=\sin \theta \\ g(\theta)=\cos \theta \end{gathered}[/tex]we will find the value of [g(θ)]² when θ = 60
So,
[tex]\lbrack g(\theta)\rbrack^2=(\cos \theta)^2[/tex]Substitute with θ = 60
So,
[tex]\lbrack g(\theta)\rbrack^2=(\cos 60)^2=(\frac{1}{2})^2=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}[/tex]So, the answer will be option → A. [g(θ)]² = 1/4
A rectangular page is to contain square inches of print. The margins on each side are to be inches. Find the dimensions of the page such that the least amount of paper is used.
Let l represent the length of the printed rectangular region of the page.
Given that the area of the printed rectangular region is 36, then
width of the printed portion or region = 36/l
The margin left on both sides is 1.5 inches. Thus,
length of page = l + 1.5(2) = l + 3
width of page = 36/l + 1.5(2) = 36/l + 3
Area = length x width
Area = (l + 3)(36/l + 3)
Area = 36 + 3l + 108/l + 9
Area = 36 + 9 + 3l + 108/l
A(l) = 45 + 3(l + 36/l)
We would minimise A(l)
For Amin, A'(l) = 0
3(1 - 36/l^2) = 0
3 = 0 or 1 - 36/l^2 = 0
1 = 36/l^2
l^2 = 36
l = ±√36
l = ±6
Also,
A''(l) > 0
A''(l) = 3(0 - 36(-2)l^-3) = 72/l^3
Substituting l = 6,
72/6^3 > 0
Thus,
l = 6 gives Amin
The dimensions would be
length = l = 6 + 3 = 9
width = 36/6 + 3 = 6 + 3 = 9
Length = 9 inches
width = 9 inches
a chef is going to use a mixture of two brands of italian dressing. the first brand contains 5% vinegar and the second brand contains 15% vinegar. the chef wants to make 300 milliliters of a dressing that is 9% vinegar. how much of each brand should she use?
The chef will end up with 300 mL of a dressing that is 9% vinegar. Let's calculate how much vinegar will the dressing have:
Therefore,
[tex]v=\frac{300\times9}{100}\rightarrow27[/tex]He'll have 27mL of vinegar.
Now, we know that x mL of the 5% dressing plus y mL of the 15% one will give the chef a total of 27mL of vinegar. Therefore,
[tex]\begin{gathered} x(\frac{5}{100})+y(\frac{15}{100})27 \\ \\ \rightarrow0.05x+0.15y=27 \end{gathered}[/tex]And that x mL of the 5% dressing plus y mL of the 15% one will give the chef a total of 300mL of dressing. Therefore,
[tex]x+y=300[/tex]We have a system of equations:
[tex]\mleft\{\begin{aligned}0.05x+0.15y=27 \\ x+y=300\end{aligned}\mright.[/tex]Let's clear y from equation 2 and replace in equation 1:
[tex]\begin{gathered} x+y=300\rightarrow y=300-x \\ \\ 0.05x+0.15y=27\rightarrow0.05x+0.15(300-x)=27 \\ \rightarrow0.05x+45-0.15x=27\rightarrow-0.10x=-18\rightarrow x=\frac{-18}{-0.10} \\ \\ \rightarrow x=180 \end{gathered}[/tex]Thereby,
[tex]\begin{gathered} y=300-x\rightarrow y=300-180 \\ \\ \rightarrow y=120 \end{gathered}[/tex]The chef would have to use 180mL of the dressing that's 5% vinegar, and 120mL of the one that's 15% vinegar.
Point G is the point (3, -1). Which point is 5 units from point G
We have
Point G( 3,-1)
Then
Point A is 4 units to left from Point G
Point D is 4 units up, from Point G
and
Point B is 5 units left,from Point G
Then answer is
OPTION B) Point B
Question 10 of 10 A cereal company estimates that its monthly cost is C(x) = 400x² + 300x and its monthly revenue is R(x) = 0.6x3 + 900.rº 400x + 700, where x is in thousands of boxes sold. The profit is the difference between the revenue and the cost. What is the profit function, P(x)? O A. P(x) = 0.6r% 1300x2 + 100x700 B. P(x) = 0.6x3 + 500.700x + 700 N O c. P(x) = 0.623 500 | 7003 700 O D. P(x) = 0.623 1300 100% -700
Here, we want to write the profit function P(x)
Mathematically, the profit function is the difference between the revenue function and the cost function
This will be;
[tex]P(x)\text{ = R(x) - C(x)}[/tex]Using the values of the individual function, we have;
[tex]undefined[/tex]Analyze the data sets below. Data Set A Data Set B 25 26 27 28 29 30 31 32 33 34 35 25 26 27 28 29 30 31 32 33 34 35 Which of the following statements are true? Select all that apply. Data Set A is relatively symmetric and Data Set B is skewed left. The means of the data sets are within 3 units from each other. The data sets have the same standard deviation. The mean of Data Set A is 27.95 and the mean of Data Set B is 30. O Type here to search
We need to find the mean of the 2 data set. For data set A, we get
[tex]\operatorname{mean}=\frac{3\cdot25+3\cdot26+27+2\cdot28+29+30+2\cdot31+32+2\cdot33+34+3\cdot35}{20}[/tex]which gives
[tex]\operatorname{mean}=\frac{594}{20}=29.7[/tex]The mean fot data set B is
[tex]\operatorname{mean}=\frac{3\cdot25+4\cdot26+4\cdot27+2\cdot28+2\cdot29+30+2\cdot31+32+34}{20}[/tex]which gives
[tex]\operatorname{mean}=\frac{559}{20}=27.95[/tex]By means of these results, we can cancel out options 2 and 4.
Lets find the median for data set A. The median is the middle number in the sorted. For set A the median is between the 10th number and 11th number, that is, its between 29 and 30. Then the median is
[tex]\operatorname{median}=\frac{29+30}{2}=29.5[/tex]Similarly, the median for data set B is between 10th number and 11th number, that is,
[tex]\operatorname{median}=\frac{27+27}{2}=27[/tex]So, we can conclude for data set A that the mean and median are close in value because mean=29.7 and median=29.5. Which corresponds to option 6.
Now,
- option 1 is incorrect because data set B is skewed right.
- option 2 is incorrect because mean for A is 29.7 and for B is 27.95
- option 3 is incorrect because the values of set A are more spread than set B
- option 4 is incorrect for the same reason than option 2
- option 5 is correct for the same reason that option 3 and because the values for set B are more focalized around the mean.
- option 6 is correct because for data set A the mean and median are close in value: mean=29.7 and median=29.5
How many solutions does the following equation have?[tex] - 6(x + 7) = - 4x - 2[/tex]A. No solutionB. Exactly one solutionC.Endless solutions
1/5your9 av uurinnTask Card #118 + 26
18 + 26
Adding 18 and 26 will give 44
The graph of the relation G is shown belowGive the domain and range of G.Write your answers using set notation. Domain=Range=
Answer:
• Domain = {-3, -1}
,• Range = {-3, -1, 2}
Explanation:
The points on the given graph of G are:
[tex](-3,-1),(-3,2)\text{ and }(-1,-3)[/tex]Domain
The domain of a relation is the set of the values of x for which the relation is defined.
• The domain of G = {-3, -1}
Range
The range of a relation is the set of the values of y for which the relation is defined.
• The range of G = {-3,-1,2}
10. If the cost per person to rent a van varies inversely with the number of people sharing thecost, which table could represent this situation?
SOLUTION
Since the cost per peson varies inversely with number of people, this means that as the number of persons increases progressively, the cost per person should decrease progressively and vice versa.
Looking at the options, it is only in option D where, as the number of persons increases, the cost per person decreases progressively.
Therefore, the correct answer is option D.
How many solutions are there to the equation 3cosx=sinx on the interval [0, 2π]1236
3 cos x = sin x
Divide each side by cos x
3 cos x / cos x = sin x / cos x
3 = tan x
Take the inverse tan of each side
tan ^-1(3) = tan^-1( tan (x))
Since tan has a period of pi, there are 2 solutions in the interval of [0, 2pi]
On a piece of paper, graph y< -*x+2. Then determine which answer choice matches the graph you drew.
D. graph D
Explanation
Step 1
graph the function as a line
convert
[tex]\begin{gathered} y<-\frac{3}{4}x+2\rightarrow y=-\frac{3}{4}x+2 \\ \end{gathered}[/tex]
to graph, find 2 coordianates
a) when x=0
[tex]\begin{gathered} y=-\frac{3}{4}x+2 \\ y=-\frac{3}{4}\cdot0+2 \\ y=0+2,\text{ y=2} \\ so,\text{ we have P1(0,2)} \end{gathered}[/tex]b) when
x=-4
[tex]\begin{gathered} y=-\frac{3}{4}x+2 \\ y=-\frac{3}{4}\cdot-4+2 \\ y=3+2 \\ y=5 \\ P2(-4,5) \end{gathered}[/tex]now, using two points draw a line
Step 2
we are looking fro values under this line, so the answer is
D. graph D
Donations were collected for the sports fund. Mr. Wilson was able to collect 7donations in the amounts of: $106, $100, $10, $20, $54, $165, $184, and $200.Which measure of central tendency would be best?
Given the following question:
Centeral tendecy also refers to the mean of a data set:
106, 100, 10, 20, 54, 165, 184, 200
In order to find the mean we have to add all the numbers together, and then divide that answer by the total amount of numbers in the set.
[tex]\begin{gathered} 106+100=206 \\ 206+10=216 \\ 216+20=236 \\ 236+54=290 \\ 290+165=455 \\ 455+184=639 \\ 639+200=839 \\ =839 \end{gathered}[/tex]Now we divide by the total amount of numbers in the set, which in this case they're eight numbers in this set:
[tex]\begin{gathered} 839\div8=104.875 \\ m=104.875 \end{gathered}[/tex]The mean of this data set is "104.875."
B-10 8.410-2864-2N-4-68-1046B) f(x) = -1x - 3| +2OC) f(x) = -x + 21 +3x-axis108.Which absolute value equation represents the graph?OA) f(x) = -3|x + 3
Looking at the graph we can see that the "vertex" of the modular function is at (-2, 3), then, we can affirm that the expression is something with
[tex]f(x)=a|x+2|+3[/tex]We can also see it goes down for large values of x, then the value of "a" must be negative, looking at the possible answers we can verify that the expression is
[tex]f(x)=-|x+2|+3[/tex]The letter C is the correct answer
A plane intersects a prism to form a cross section that is a poygon with five sides. The minimum number of sides that the polygon at the base of the prism must have is?
According to the given data we have the following:
A plane intersects a prism to form a cross section that is a poygon with five side, therefore the original shape needs to have less than 5 sides.
According to the figure of the prism, it should have between 3 or 4 sides.
But 3 sides could no be, because that would be a triangle, which can't be cut into a 5 sided prism.
Therefore, The minimum number of sides that the polygon at the base of the prism must have is 4.
Convert as indicated.100 ounces to pounds100 oz = lb(Simplify your answer.)
ANSWER :
6.25 pounds
EXPLANATION :
Note that 1 pound = 16 ounces
Converting 100 ounces into pounds :
[tex]100\text{ }\cancel{ounces}\times\frac{1\text{ }pound}{16\text{ }\cancel{ounces}}=6.25\text{ }pounds[/tex]What is the equation in slope-intercept form for the line that passes through the point (8,-3) and has a nice of -2?
To find the slope of the line you can replace the information given in the general equation of the line in its slope-intercept form and solve for m, that is,
[tex]\begin{gathered} y=mx+b \\ \text{ Where m is the slope of the line and} \\ b\text{ is the y-intercept} \end{gathered}[/tex]So, you have
[tex]\begin{gathered} (x,y)=(8,-3) \\ b=-2 \\ y=mx+b \\ \text{ Replacing} \\ -3=m\cdot8-2 \\ \text{ Solving for m} \\ -3=8m-2 \\ \text{ Add 2 from both sides of the equation} \\ -3+2=8m-2+2 \\ -1=8m \\ \text{ Divide by 8 into both sides of the equation} \\ \frac{-1}{8}=\frac{8m}{8} \\ \frac{-1}{8}=m \end{gathered}[/tex]Then the slope of the line is
[tex]m=-\frac{1}{8}[/tex]Now, since you already have the slope and the y-intercept, you can know what the equation of the line is in its slope-intercept form
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{8}x-2 \end{gathered}[/tex]Therefore, the equation in slope-intercept form for the line that passes through the point (8,-3) and has a y-intercept of -2 is
[tex]y=-\frac{1}{8}x-2[/tex]And the correct answer is A.
the radius of a circle is 1 what is the length of an arc that subtends an angle of pi/4 radians.
In order to calculate the length of this arc, we can use a rule of three, knowing that the complete circle has an angle of 2π and a length of 2πr:
[tex]\begin{gathered} \text{angle }\to length \\ 2\pi\to2\pi r \\ \frac{\pi}{4}\to x \\ \\ x\cdot2\pi=\frac{\pi}{4}\cdot2\pi r \\ x=\frac{\pi}{4}\cdot r \\ x=\frac{\pi}{4} \end{gathered}[/tex]So the length of the arc is π/4.
ANSWER ASAP!! HELP!! Logan drew AABC on the coordinate plane, andthen reflected the triangle over the y-axis to formAA'B'C'. Which statement is not true about thesetwo triangles?A. AABC = AA'B'C'B. The two triangles have the same anglemeasures.C. The vertices of AABC and AA'B'C' have thesame coordinates.D. The triangles have the same side lengths.
The right option is C because the measure of the angle dont change just change the coordinates of the vertices
what is
[tex]5\times10^{-4}[/tex]there is an invisible dot in front of 5
[tex]5.0000[/tex]if the exponent of ten is negative we will move the point to the left, if it is positive to the right
on this case is negative and the number is for it means than move the dot 4 places to the left
[tex]0.0005[/tex]so, the right option is B
Write an equation in slope intercept form for a line passing through the pair of points. Graph the line. (4, -2) and (8, -9)
The slope-intercept form of a line is:
y = mx + b
where m is the slope and b the y-intercept.
The slope is computed as follows:
[tex]m\text{ =}\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2, y2) are two known points. Replacing with (4, -2) and (8, -9):
[tex]m=\frac{-9-(-2)}{8-4}=-\frac{7}{4}[/tex]Replacing with the point (4, -2) and m = -7/4 into the general equation, we get:
-2 = (-7/4)4 + b
-2 = -7 + b
-2 + 7 = b
5 = b
Then, the equation is:
y = -7/4x + 5
The graph is
The midpoint of AB is M(-1, 7). If the coordinates of A are (4, 8) what are the coordinates of B?
The coordinates of B are (-6,6), using the midpoint concept.
MidpointThe midpoint of two points is given by the mean of the coordinates of these two points.
This is applicable for both the x-coordinate and for the y-coordinate, that is, we have to find the mean of each of the coordinates.
In the context of this problem, we have that:
The mean of the x-coordinates is of -1.One of them is of 4, and the other is of x.Hence the x-coordinate of B is calculated as follows:
-1 = (4 + x)/2
4 + x = -2
x = -6.
For the y-coordinate, we have that:
The mean is of 7.One of them is of 8, and the other is of y.Thus the y-coordinate of B is calculated as follows:
7 = (8 + y)/2
8 + y = 14
y = 6.
Thus the coordinates are:
B(-6,6).
More can be learned about the midpoint concept at https://brainly.com/question/25886396
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