Answer:
[tex]\sqrt{85}[/tex]
Step-by-step explanation:
Let's use the distance formula to solve for the distance between the two given points!
d = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 }[/tex]
Now, we input the points:
(5-(-2) + (-2-4)
(which will equal...)
(7) + (-6)
Now we input the solutions we got here to the distance formula:
[tex]d =\sqrt{(7)^2 + (-6)^2[/tex]
(we simplify....)
[tex]7^2 = 49\\(-6)^2 = 36[/tex]
input these solutions into the distance formula again...
[tex]\sqrt{49 + 36} = \sqrt{85}[/tex]
85 is not a number that can be square rooted properly, nor does it have any perfect squares available to divide equally.
Therefore, we conclude that the distance between A(5, -2) and B(-2,4) is [tex]\sqrt{85}[/tex].
The data can be modeled by the following system of linear equations.
-3x+10y = 160
x+2y=164
Equation 1
Equation 2
Equation 1 is modeled for the percentage of never-married American adults, y, x years after 1970 and Equation 2 is modeled for the percentage of married
American adults, y, x years after 1970. Use these models to complete parts a and b.
a. Determine the year, rounded to the nearest year, when the percentage of never-married adults will be the same as the percentage of married adults. For
that year, approximately what percentage of Americans, rounded to the nearest percent, will belong to each group?
In year
the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately % percentage of
Americans will belong to each group.
After 4 years the percentage of never-married adults will be the same as the percentage of married adults.
The data can be modeled by the following system of linear equations.
-3x+10y = 160
x+2y=164
Multiply the second equation with 3
-3x + 10y = 160 .....equation 1
3x + 6y = 492........equation 2
adding equation 1 and 2
16y = 652
y = 40.75
x + 2y = 164
x = 164 - 2 (40.75)
x = 82.5
Let the number of years be t
-3x+10y x t = x+2y
t = 4x - 8y
t = 330 - 326
t = 4 years
Therefore, after 4 years the percentage of never-married adults will be the same as the percentage of married adults.
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the perimeter of a geometric figure is the sum of the lengths of the sides the perimeter of the pentagon five-sided figure on the right is 54 centimeters A.write an equation for perimeter B.solve the equation in part a C.find the length of each side i need help solve this word problem
A.
The perimeter of the pentagon is the sum of the 5 sides of the figure
the sum of the five sides = x + x + x+ 3x +3x (centimeter)
=> 9x
we are also told that the perimeter is 54 centimeter
=> 9x = 54
B.
to solve the equation 9x = 54
divide both sides by the coefficient of x
[tex]\begin{gathered} \frac{9x}{9}=\frac{54}{9}\text{ } \\ x\text{ = 6} \end{gathered}[/tex]C. to get the length of each sides, substitue the value for x=6 into the sides so that we will have
6, 6, 6, 3(6), 3(6)
=> 6, 6, 6, 18,18 centimeters
Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.10-(-3,6)(-6,3(0,3)-10(-3,0)1010
Question:
Solution:
An equation of the circle with center (h,k) and radius r is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]This is called the center-radius form of the circle equation.
Now, in this case, notice that the center of the circle is (h,k) = (-3,3) and its radius is r = 3 so that the center-radius form of the circle would be:
[tex](x+3)^2+(y-3)^2=3^2[/tex]To obtain the general form, we must solve the squares of the previous equation:
[tex](x+3)^2+(y-3)^2-3^2\text{ = 0}[/tex]this is equivalent to:
[tex](x^2+6x+3^2)+(y^2-6y+3^2)\text{ - 9 = 0}[/tex]this is equivalent to
[tex]x^2+6x+9+y^2-6y\text{ = 0}[/tex]this is equivalent to:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]so that, the general form equation of the circle would be:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]thus, the correct answer is:
CENTER - RADIUS FORM:
[tex](x+3)^2+(y-3)^2=3^2[/tex]GENERAL FORM:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]A committee of five members is to be randomly selectedfrom a group of nine freshman and seven sophomores.Which expression represents the number of different committeesof three freshman and two sophomores that can be chosen?
The answer would be the product of the number of 3 freshman groups by 2 sophomores groups.
The number of 3 freshman groups is given by
[tex]C^9_3=\frac{9\times8\times7}{3\times2\times1}=84[/tex]The number of 2 sophomore groups is given by
[tex]C^7_2=\frac{7\times6}{2\times1}=21[/tex]Now, doing their product
[tex]21\times84=1764[/tex]We have 1764 different committees of three freshman and two sophomores.
If the two triangles shown below are similar based on the giveninformation, complete the similarity statement, otherwise choose the"Not Similar" button.А18 in9 inHB7 in14 inACAB-ANot Similar
1) Two triangles are similar if they have congruent angles and proportional sides (for each corresponding leg).
2) So let's check whether there are similar triangles by setting a proportion:
[tex]\begin{gathered} \frac{HC}{CA}=\frac{JH}{CB} \\ \frac{9}{18}=\frac{7}{14} \\ Simplify\text{ both:} \\ \frac{1}{2}=\frac{1}{2} \end{gathered}[/tex]3) So yes they are similar, i.e. ΔCAB ~ΔHGJ
A local real estate company has 5 real estate agents. The number of houses that each agent sold last year is shown in the bar graph below. Use this bar graph to answer the questions.
Given:
Rachel sold 4 houses.
Heather sold 4 houses.
Kaitlin sold 12 houses.
Lena sold 11 houses.
Deshaun sold 3 houses.
Required:
a) We need to find which agent sold the most houses.
b) We need to find the number of houses Lna soldemore than Heather.
c) We need to find the number of agents who sold fewer than 4 houses.
Explanation:
a)
The greatest number of houses sold =12 houses.
Kaitlin sold 12 houses.
Answer:
The agent Kaitlin sold the most houses.
The agent sold 12 houses.
b)
Lena sold 11 houses.
Heather sold 4 houses.
The difference between 11 and 4 is 11-4 =7.
Answer:
Lena sold 7 housmore than Heather
Can you please help me solve this and the test statistics and p value
The claim is that the population mean for the smartphone carrier's data speed at airports is less than 4.00 Mbps
The parameter of the study is the population mean, symbolized by the Greek letter mu "μ"
The researchers believe is that his value is less than 4, you can symbolize this as:
[tex]\mu<4[/tex]This expression does not include the "=" symbol, which indicates that it represents the alternative hypothesis. The null and alternative hypotheses are complementary, so if the alternative hypothesis represents the values of μ less than 4, then the null hypothesis, as its complement, should represent all other possible values, which are those greater than and equal to 4. You can represent this as:
[tex]\mu\ge4\text{ or simply }\mu=4[/tex]The statistical hypotheses for this test are:
[tex]\begin{gathered} H_0\colon\mu=4 \\ H_1\colon\mu<4 \end{gathered}[/tex]Option A.
In the display of technology, you can see the data calculated for the test.
The second value shown in the display corresponds to the value of the test statistic under the null hypothesis, you have to round it to two decimal places:
[tex]t_{H0}=-2.432925\approx-2.43[/tex]The value of the test statistic is -2.43
The p-value corresponds to the third value shown in the display.
The p-value is 0.009337
To make a decision over the hypothesis test using the p-value you have to follow the decision rule:
- If p-value ≥ α, do not reject the null hypotheses.
- If p-value < α, reject the null hypotheses.
The significance level is α= 0.05
Since the p-value (0.009337) is less than the significance level of 0.05, the decision is to reject the null hypothesis.
Conclusion
So, at a 5% significance level, you can conclude that there is significant evidence to reject the null hypothesis (H₀: μ=4), which means that the population mean of the smartphone carrier's data speed at the airport is less than 4.00 Mbps.
The ratio of the volume of two spheres is 8:27. What is the ratio of their radii?
We have that the volume of the spheres have a ratio of 8:27.
[tex]undefined[/tex]This means that the relation between linear measures, like the radii, will be the cubic root of that ratio
A rectangular prism has a legth of 5 1/4 m, a width of 4m, and a height of 12 m.How many unit cubes with edge lengths of 1/4 m will it take to fill the prism? what is the volume of the prism?
Volume of a cube with edge lengths of 1/4m:
[tex]\begin{gathered} V_{cube}=l^3 \\ \\ V_{cube}=(\frac{1}{4}m)^3=\frac{1^3}{4^3}m^3=\frac{1}{64}m^3 \end{gathered}[/tex]Volume of the rectangular prism:
[tex]\begin{gathered} V=l\cdot w\cdot h \\ \\ V=5\frac{1}{4}m\cdot4m\cdot12m \\ \\ V=\frac{21}{4}m\cdot4m\cdot12m \\ \\ V=252m^3 \end{gathered}[/tex]Divide the volume of the prism into the volume of the cubes:
[tex]\frac{252m^3}{\frac{1}{64}m^3}=252\cdot64=16128[/tex]Then, to fill the prism it will take 16,128 cubes with edge length of 1/4 mUse the appropriate differenatal formula to find© the derivative of the given function6)3(16) 96) = (x²-1) ²(2x+115
1) We need to differentiate the following functions:
[tex]\begin{gathered} a)\:f(x)=x\sqrt[3]{1+x^2}\:\:\:\:Use\:the\:product\:rule \\ \\ \\ \frac{d}{dx}\left(x\right)\sqrt[3]{1+x^2}+\frac{d}{dx}\left(\sqrt[3]{1+x^2}\right)x \\ \\ \\ 1\cdot \sqrt[3]{1+x^2}+\frac{2x}{3\left(1+x^2\right)^{\frac{2}{3}}}x \\ \\ \sqrt[3]{1+x^2}+\frac{2x^2}{3\left(x^2+1\right)^{\frac{2}{3}}} \\ \\ f^{\prime}(x)=\sqrt[3]{1+x^2}+\frac{2x^2}{3\left(1+x^2\right)^{\frac{2}{3}}} \end{gathered}[/tex]Note that we had to use some properties like the Product Rule, and the Chain Rule.
b) We can start out by applying the Quotient Rule:
[tex]\begin{gathered} g(x)=\frac{(x^2-1)^3}{(2x+1)} \\ \\ f^{\prime}(x)=\frac{\frac{d}{dx}\left(\left(x^2-1\right)^3\right)\left(2x+1\right)-\frac{d}{dx}\left(2x+1\right)\left(x^2-1\right)^3}{\left(2x+1\right)^2} \\ \\ Differentiating\:each\:part\:of\:that\:quotient: \\ \\ ------- \\ \frac{d}{dx}\left(\left(x^2-1\right)^3\right)=3\left(x^2-1\right)^2\frac{d}{dx}\left(x^2-1\right)=6x\left(x^2-1\right)^2 \\ \\ \frac{d}{dx}\left(x^2-1\right)=\frac{d}{dx}\left(x^2\right)-\frac{d}{dx}\left(1\right)=2x \\ \\ \frac{d}{dx}\left(x^2\right)=2x \\ \\ \frac{d}{dx}\left(1\right)=0 \\ \\ \frac{d}{dx}\left(2x+1\right)=2 \\ \\ Writing\:all\:that\:together: \\ \\ f^{\prime}(x)=\frac{6x\left(x^2-1\right)^2\left(2x+1\right)-2\left(x^2-1\right)^3}{\left(2x+1\right)^2} \\ \end{gathered}[/tex]Thus, these are the answers.
Find the expression for the possible width of the rectangle.
Given the area of the rectangle is given by the following expression:
[tex]A=x^2+5x+6[/tex]The area of the rectangle is the product of the length by the width
So, we will factor the given expression
To factor the expression, we need two numbers the product of them = 6
and the sum of them = 5
So, we will factor the number 6 to find the suitable numbers
6 = 1 x 6 ⇒ 1 + 6 = 7
6 = 2 x 3 ⇒ 2 + 3 = 5
So, the numbers are 2 and 3
The factorization will be as follows:
[tex]A=(x+3)(x+2)[/tex]So, the answer will be the possible dimensions are:
[tex]\begin{gathered} \text{Length}=x+3 \\ \text{Width}=x+2 \end{gathered}[/tex]8.[–/1 Points]DETAILSALEXGEOM7 9.2.012.MY NOTESASK YOUR TEACHERSuppose that the base of the hexagonal pyramid below has an area of 40.6 cm2 and that the altitude of the pyramid measures 3.7 cm. A hexagonal pyramid has base vertices labeled M, N, P, Q, R, and S. Vertex V is centered above the base.Find the volume (in cubic centimeters) of the hexagonal pyramid. (Round your answer to two decimal places.) cm3
Solution
- The base is a regular hexagon. This implies that it can be divided into equal triangles.
- These equal triangles can be depicted below:
- If each triangle subtends an angle α at the center of the hexagon, it means that we can find the value of α since all the α angles are subtended at the center of the hexagon using the sum of angles at a point which is 360 degrees.
- That is,
[tex]\begin{gathered} α=\frac{360}{6} \\ \\ α=60\degree \end{gathered}[/tex]- We also know that regular hexagon is made up of 6 equilateral triangles.
- Thus, the formula for finding the area of an equilateral triangle is:
[tex]\begin{gathered} A=\frac{\sqrt{3}}{4}x^2 \\ where, \\ x=\text{ the length of 1 side.} \end{gathered}[/tex]- Thus, the area of the hexagon is:
[tex]A=6\times\frac{\sqrt{3}}{4}x^2[/tex]- With the above formula we can find the length of the regular hexagon as follows:
[tex]\begin{gathered} 40.6=6\times\frac{\sqrt{3}}{4}x^2 \\ \\ \therefore x=15.626947286066 \end{gathered}[/tex]- The formula for the volume of a hexagonal pyramid is:
[tex]\begin{gathered} V=\frac{\sqrt{3}}{2}b^2\times h \\ where, \\ b=\text{ the base} \\ h=\text{ the height.} \end{gathered}[/tex]- Thus, the volume of the pyramid is
[tex]\begin{gathered} V=\frac{\sqrt{3}}{2}\times15.626947286066^2\times3.7 \\ \\ V=782.49cm^3 \end{gathered}[/tex]80.39 rounded to nearest whole number
Answer:
80
Step-by-step explanation:
It is 80 because .39 is not quite 4.
so in a instance like this you would round .39 to .4 and .4 cant be rounded up to .5 so it would go down because it is to the nearest whole number to instead of it being 81 ( if it could be rounded to 80.5 ), it goes to just 80.
One way to help with rounding is:
" 4 and below let it go
if its 5 and above give it a shove. " rugrat k aka rgr k
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3. The data in the table gives the number of barbeque sauce bottles (y) that are sold with orders of chicken wings (x) for each hour on a given day at Vonn's Grill. Use technology to write an equation for the line of best fit from the data in the table below. Round all values to two decimal places.
1) Let's visualize the points
2) To find the equation for the line of best fit we'll need to follow some steps.
2.1 Let's find the mean of the x values and the mean of the Y values
2.2 Now It's time to find the slope, with the summation of the difference between each value and the mean of x times each value minus the mean over the square of the difference of the mean of x and x.
To make it simpler, let's use this table:
The slope then is the summation of the 5th column over the 6th column, we're using the least square method
[tex]m=\frac{939.625}{1270.875}=0.7393\cong0.74[/tex]The Linear coefficient
[tex]\begin{gathered} b=Y\text{ -m}X \\ b=14.625-0.73(19.875) \\ b=0.11625\cong0.12 \end{gathered}[/tex]3) Finally the equation of the line that best fit is
[tex]y=0.73x+0.12[/tex]El contratista encargado de construir el
cerco perimetral desea saber la expresión
algebraica correspondiente al perímetro de
todo el lote
Medidas:
25p-8
40p+2
El perímetro del lote tiene una medida de 130 · p - 12 unidades.
¿Cuál es la longitud del cerco perimetral para un lote?
El perímetro es la suma de las longitudes de los lados de una figura, un rectángulo tiene cuatro lados, dos pares de lados iguales. En consecuencia, el perímetro del lote es el siguiente:
s = 2 · w + 2 · l
Donde:
w - Ancho del lote.l - Largo del lote.s - Perímetro del lote.Si sabemos que w = 25 · p - 8 y l = 40 · p + 2, entonces el perímetro del lote es:
s = 2 · (25 · p - 8) + 2 · (40 · p + 2)
s = 50 · p - 16 + 80 · p + 4
s = 130 · p - 12
El perímetro tiene una medida de 130 · p - 12 unidades.
ObservaciónNo se ha podido encontrar una figura o imagen asociada al enunciado del problema. Sin embargo, se puede inferir que el lote tiene una forma rectangular debido a las medidas utilizadas. En consecuencia, asumimos que la medida del ancho es igual a 25 · p - 8 unidades y del largo es igual a 40 · p + 2 unidades.
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The statement listed below is false. Let p represent the statement.
We will have that the negation of the statement would be:
*That product did not emerge as a toy in 1949. [Option B]
Explain when you can cancel a number that is in both the numerator and denominator and when you cannot cancel out numbers that appear in both the numerator and the denominator.
Let me write here an example of a common number/term in both numerator and denominator that we can cancel.
[tex]\frac{4xy}{4}=xy[/tex]In the above example, we are able to cancel out the common number 4 because they are stand alone numbers. We can divide 4 by 4 and that is 1. Hence, the answer is just xy.
Another example:
[tex]\frac{(x+2)(x-1)}{(x+2)(2x-1)}=\frac{(x-1)}{(2x-1)}[/tex]In the above example, we are able to cancel out (x + 2) because this term is a common factor to both numerator and denominator.
In the example, we can also see that -1 is a common number however, we cannot cancel it out because the number -1 is not a standalone factor. It is paired with other number/variable. (x - 1) and (2x - 1) are both factors but are not the same, that is why, we are not able to cancel that.
Another example:
[tex]\frac{(x+2)+(x-1)}{(x+2)+(2x-1)}=\frac{(x+2)+(x-1)}{(x+2)+(2x-1)}[/tex]As we can see above, (x + 2) is a common term however, we cannot cancel it. We can only cancel common terms if they are common factors of both numerator and denominator. (Notice the plus sign in the middle. )
The term (x + 2) above is not a factor of the numerator and denominator, hence, we cannot cancel it.
Write an equation of variation to represent the situation and solve for the indicated information Wei received $55.35 in interest on the $1230 in her credit union account. If the interestvaries directly with the amount deposited, how much would Wei receive for the sameamount of time if she had $2000 in the account?
he two-way frequency table given shows the results from a survey of students who attend the afterschool program.
Takes Art Class Doesn't Take Art Class Total
Plays a Sport 45 120
Doesn't Play a Sport 45
Total 225
Does the data show an association between taking an art class and playing a sport?
There is a strong, positive association.
There is a strong, negative association.
There is a weak, positive association.
There is a weak, negative association.
The association between the variables art class and playing a sport is classified as follows:
There is a strong, negative association.
What is the association between the two variables?The association between variables can be classified either as positive or as negative, as follows:
Positive: both variables behave similarly, either both increases or both decreasing.Negative: the variables behave in an inversely manner, with one increasing and the other decreasing, or vice-versa.In the context of this problem, it is found that of the students that take art class, the majority do not play a sport, while among those who do not take art class, the majority play a sport, hence there is a strong and negative association between the two variables.
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I’m confused on this question. I just have to choose which one
SOLUTION:
Case: Circle theorems
Method:
From the given circle
Theorem: The angle at the center of the circle is twice the angle at the circumference formed by the same segment.
The implication to the circle in the question is:
[tex]\begin{gathered} \hat{mST}=2m\angle2 \\ OR \\ m\angle2=\frac{1}{2}(\hat{mST}) \end{gathered}[/tex]Final answer
[tex]m\operatorname{\angle}2=\frac{1}{2}(\hat{mST})[/tex]The table below shows possible outcomes when two spinners that are divided into equal sections are spun. The first spinner is labeled with five colors, and the second spinner is labeled with numbers 1 through 5. Green Blue Pink Yellow Red 1 Gi B1 P1 Y1 R1 1 2 . G2 B2 P2 Y2 R2 3 G3 B3 P3 Y3 R3 4 G4 B4 P4 Y4 R4 5 G5 B5 P5 Y5 R5 According to the table, what is the probability of the first spinner landing on the color pink and the second spinner landing on the number 5?
Answer:
P = 0.04
Explanation:
The probability is equal to the number of options where the first spinner is landing on the color pink and the second spinner is landing on the number 5 divided by the total number of options.
Since there is only one option that satisfies the condition P5 and there are 25 possible outcomes, the probability is:
[tex]P=\frac{1}{25}=0.04[/tex]So, the answer is P = 0.04
call Scott's is collecting canned food for food drive is class collects 3 and 2/3 pounds on the first day in 4 and 1/4 lb on second day how many pounds of food has they collected so far
The food collected on first day,
[tex]\begin{gathered} 3\frac{2}{3} \\ =\frac{3\times3+2}{3} \\ =\frac{9+2}{3} \\ =\frac{11}{3} \end{gathered}[/tex]The food collected on second day,
[tex]\begin{gathered} 4\frac{1}{4} \\ =\frac{4\times4+1}{4} \\ =\frac{16+1}{4} \\ =\frac{17}{4} \end{gathered}[/tex]The total amount of food collected can be calculated as,
[tex]\begin{gathered} T=\frac{11}{3}+\frac{17}{4} \\ =\frac{11\times4+17\times3}{3\times4} \\ =\frac{44+51}{12} \\ =\frac{95}{12} \\ =7\frac{11}{12} \end{gathered}[/tex]Therefore, the total amount of food collected so far is 7 11/12 pounds.
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, thenthe unit cost is given by the function C(x) = 0.5x? - 260x +53,298. How many cars must be made to minimize the unit cost?Do not round your answer.
Okey, here we have the following function:
[tex]C(x)=0.5x^2-260x+53298[/tex]Considering that "a" is a positive coefficient, then it achieves the minimum at:
[tex]x=-\frac{b}{2a}[/tex][tex]\begin{gathered} x=-\frac{(-260)}{2(0.5)} \\ =\frac{260}{1} \\ =260 \end{gathered}[/tex]Now, let's find the minimal value of the quadratic function, so we are going to replace x=260, in the function C(x):
[tex]\begin{gathered} C(260)=0.5(260)^2-260(260)+53298 \\ C(260)=0.5(67600)-67600+53298 \\ =33800-67600+53298 \\ =19498 \end{gathered}[/tex]Finally we obtain that the number of cars is 19498.
help meeeeeeeeee pleaseee !!!!!
The composition of the two functions evaluated in x = 2 is:
(f o g)(2) = 33
How to find the composition?Here we have the next two functions:
f(x) = x² - 3x + 5
g(x) = -2x
And we want to find the composition:
(f o g)(2) = f( g(2))
So we need to evaluate f(x) in g(2).
First, we need to evaluate g(x) in x = 2.
g(2) = -2*2 = -4
Then we have:
(f o g)(2) = f( g(2)) = f(-4)
f(-4) = (-4)² - 3*(-4) + 5 = 16 + 12 + 5 = 28 + 5 = 33
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help pleaseeeeeeeeeeeeeeeee
Answer:
b) 28
c) 52
Step-by-step explanation:
f(2) = -2³ + 7(2)² - 2(2) + 12
= -8 + 28 - 4 + 12
= 28
f(-2) = -(-2)³ + 7(-2)² - 2(-2) + 12
= 8 + 28 + 4 + 12
= 52
help meeeeeeeeee pleaseee !!!!!
The simplified answer of the composite function is as follows:
(f + g)(x) = 2x + 3x²(f - g)(x) = 2x - 3x²(f. g)(x) = 6x³(f / g)(x) = 2 / 3xHow to solve composite function?Composite functions is a function that depends on another function. A composite function is created when one function is substituted into another function.
In other words, a composite function is generally a function that is written inside another function.
Therefore,
f(x) = 2x
g(x) = 3x²
Hence, the composite function can be simplified as follows:
(f + g)(x) = f(x) + g(x) = 2x + 3x²
(f - g)(x) = f(x) - g(x) = 2x - 3x²
(f. g)(x) = f(x) . g(x) = (2x)(3x²) = 6x³
(f / g)(x) = f(x) / g(x) = 2x / 3x² = 2 / 3x
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I need help with this question can you please help me
Given the following question:
[tex]\begin{gathered} x^2+3x-5=0 \\ \text{ Convert using the quadratic formula:} \\ x^2+3x-5=0=x_{1,\:2}=\frac{-3\pm\sqrt{3^2-4\cdot\:1\cdot\left(-5\right)}}{2\cdot\:1} \\ x_{1,\:2}=\frac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \left(-5\right)}}{2\cdot \:1} \\ \text{ Solve} \\ 3^{2}-4\times1(-5) \\ 1\times-5=-5 \\ 3^2-4\times-5 \\ 3^2=3\times3=9 \\ =29 \\ =\sqrt{29} \\ x_{1,\:2}=\frac{-3\pm \sqrt{29}}{2\cdot \:1} \\ \text{ Seperate the solutions:} \\ x_1=\frac{-3+\sqrt{29}}{2\cdot \:1} \\ x_2=\frac{-3-\sqrt{29}}{2\cdot\:1} \\ \text{ Simplify} \\ 2\times1=2 \\ x=\frac{-3+\sqrt{29}}{2} \\ x=\frac{-3-\sqrt{29}}{2} \end{gathered}[/tex]Your answers are the first and second options.
Consider the following functions round your answer to two decimal places if necessary
Solution
Step 1:
[tex]\begin{gathered} f(x)\text{ = }\sqrt{x\text{ + 2}} \\ \\ g(x)\text{ = }\frac{x-2}{2} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} (\text{ f . g\rparen\lparen x\rparen = }\sqrt{\frac{x-2}{2}+2} \\ \\ (\text{ f . g\rparen\lparen x\rparen }=\text{ }\sqrt{\frac{x\text{ +2}}{2}} \end{gathered}[/tex]Step 3
Domain definition
[tex]\begin{gathered} The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values \\ \:for\:which\:the\:function\:is\:real\:and\:defined. \\ \mathrm{The\:function\:domain} \\ x\ge \:-2 \\ \\ \:\mathrm{Interval\:Notation:}\text{ \lbrack-2, }\infty) \end{gathered}[/tex]Final answer
Julia found the equation of the line perpendicular toy = -2x + 2 that passes through (5.-1).Analyze Julia's work. Is she correct? If not, what washer mistake?1 y25= 1/2 (-2) + 6Yes, she is correct,No, she did not use the opposite reciprocal for theslope of the perpendicular line.No, she did not substitute the correct x and yvaluesNo she did not apply inverse operations to solve forthe y-intercept.3+5b=555y=x5.5
The given line is
[tex]y=-2x+2[/tex]The line passes through (5, -1),
Perpendicular lines have opposite slopes, so we use the following equation to find the new slope knowing that the slope of the given line is -2.
[tex]\begin{gathered} m\cdot m_1=-1 \\ m\cdot(-2)=-1 \\ m=\frac{-1}{-2} \\ m=\frac{1}{2} \end{gathered}[/tex]Now, we use the slope, the point, and the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=\frac{1}{2}(x-5) \\ y+1=\frac{1}{2}x-\frac{5}{2} \\ y=\frac{1}{2}x-\frac{5}{2}-1 \\ y=\frac{1}{2}x+\frac{-5-2}{2} \\ y=\frac{1}{2}x-\frac{7}{2} \end{gathered}[/tex]Therefore, the equation of the new perpendicular line is[tex]y=\frac{1}{2}x-\frac{7}{2}[/tex]So, she's not correct, she didn't substitute the correct x and y values.
The right answer is C.The previous tutor helped me with solution but we got cut off before we could graph I need help with graphing please
We want to graph the following inequality system
[tex]\begin{gathered} x+8\ge9 \\ \text{and} \\ \frac{x}{7}\le1 \end{gathered}[/tex]First, we need to solve both inequalities. To solve the first one, we subtract 8 from both sides
[tex]\begin{gathered} x+8-8\ge9-8 \\ x\ge1 \end{gathered}[/tex]To solve the second one, we multiply both sides by 7.
[tex]\begin{gathered} 7\cdot\frac{x}{7}\le1\cdot7 \\ x\le7 \end{gathered}[/tex]Now, our system is
[tex]\begin{gathered} x\ge1 \\ \text{and} \\ x\le7 \end{gathered}[/tex]We can combine those inequalities into one.
[tex]1\le x\le7[/tex]The number x is inside the interval between 1 and 7. Graphically, this is the region between those numbers(including them).