The sine functions are given as:
[tex]\begin{gathered} y=13\sin (\frac{8\pi}{7}) \\ \\ y=7\sin (\frac{\pi}{7}) \end{gathered}[/tex]the figure below is reflected over x axis and then translated up 4 units what are the coordinates of the image of point V after the transformation
(1,10)
1) Considering that there was a reflection over the x-axis then we can write it down:
Reflection Rule about the x-axis
Pre-image Image
(x, y) (x, -y)
V(1,-6) (1, 6)
2) Then let's translate it up to 4 units adding 4 units to the
Pre-image Image
(x, y) (x, y+4)
V(1,6) (1, 10)
3) Hence, point V is going to be located at (1,10)
What is the solve for m:mg = W
ANSWER
[tex]m=\frac{W}{g}[/tex]EXPLANATION
We want to solve the given equation for m:
[tex]mg=W[/tex]This implies that we want to make m the subject of the formula.
To do this, we have to divide both sides of the equation by g and simplify:
[tex]\begin{gathered} \frac{mg}{g}=\frac{W}{g} \\ m=\frac{W}{g} \end{gathered}[/tex]That is the solution for m.
Quadrilateral ABCD will be translated 1 unit to the left and 4 units down. Then it will be dilated by ascale factor of 2 about the origin.1211109876BА643D7.891012511Z-8-53-8-4- 12 - 11 - 104-3-212-1 0- 1-2-3-4-5-6-7-8-9-10-11-12What is the location of point D after these transformations?O (-8, 12)(-8,-4)O (-2,-1)O (-2,3)
We have a figure to which we apply two transformations: a translation, 1 unit to the left and 4 units down, and a dilation by a factor of 2 about the origin.
We then can write the rules for a generic point (x,y) when this transformations are applied.
For a translation 1 unit to the left and 4 units down, it means that the x-coordinate is 1 unit less, as the left indicates smaller values, and the y-coordinate is 4 units less, as down indicates smaller values too. Then, the rule is:
[tex](x,y)\longrightarrow(x-1,y-4)[/tex]Now, a dilation of factor k around the origin can be written for a generic point (x,y) as:
[tex](x,y)\longrightarrow(kx,ky)[/tex]Then, if k=2 and we apply it to our transformed point we get:
[tex](x,y)\longrightarrow(x-1,y-4)\longrightarrow(2(x-1),2(y-4))=(2x-2,2y-8)[/tex]Then, the effect of the two transformations is:
[tex](x,y)\longrightarrow(2x-2,2y-8)[/tex]Applying this to the point D(-3,2) we get:
[tex]D=(-3,2)\longrightarrow D^{\prime}^{\prime}=(2(-3)-2,2(2)-8)=(-6-2,4-8)=(-8,-4)[/tex]Answer: the transformed point D'' is (-8,-4) [Second option]
Find the scale factor from Figure A to Figure B and the center of dilation for each figure.1.2.BSt-SF=2.5Scak focorBА/А
Since the horizontal side of the triangle goes from 6 units to 2 units that means that the scale factor is 1/3.
Since the figures have the same center we conclude that the center of dilation is the origin, that is the point (0,0).
find a polynomial equation that has double zeros at x = -3, and x = 4
A double zero occurs in a polynomial when a factor is repeated, or in other words, squared. Since the polynomial has double zeros, then, we get
[tex]f(x)=(x+3)^2(x-4)^2[/tex]By expanding this result, we have
[tex]f(x)=(x^2+6x+9)(x^2-8x+16)[/tex]which gives
[tex]f(x)=x^4-8x^3+16x^2+6x^3-48x^2+96+9x^2-72x+144[/tex]By combining similar terms, we have
[tex]undefined[/tex]If Tobias has 2 times as many quarters as nickels and they have a combined value of 275 cents, how many of each coin does he have?
Given:
Tobias has 2 times as many quarters as nickels.
They have a combined value of 275 cents.
To find:
The number of each coin.
Explanation:
Let q be the number of quarters.
Let n be the number of nickels.
Since he has 2 times as many quarters as nickels.
[tex]q=2n.........(1)[/tex]We know that,
[tex]\begin{gathered} 1\text{ }quarter=25\text{ }cents \\ 1\text{ }nickel=5\text{ }cents \end{gathered}[/tex]According to the problem,
[tex]25q+5n=275........(2)[/tex]Substituting equation (1) in (2), we get
[tex]\begin{gathered} 25(2n)+5n=275 \\ 50n+5n=275 \\ 55n=275 \\ n=\frac{275}{55} \\ n=5 \end{gathered}[/tex]From (1), we get
[tex]q=2n=2(5)=10[/tex]Therefore, the number of quarters is 10 and the number of nickels is 5.
Final answer:
• The number of quarters is 10.
,• The number of nickels is 5.
Can you please answer a and fill in the blanks please I need help
A) Given the sequence:
11, 14, 19, 26, 35.....
We can see the common differnce increases by 2.
Thus, the explicit function is:
[tex]undefined[/tex]A taco truck sells drinks as shown in the table.What is the total number of ounces in 9 largeand 17 small size drinks?Question 5 of 826 Oz424 ozSizeOunces Price32$3LargeSmall616 oz1,040 oz8$2SUBMITShe
1 Large size drink = 32 ounces
1 Small size drink = 8 ounces
9 large size drinks = 32 x 9
9 large size drinks =
Bob pays 7% interest on his $40,000 college loan and 9% interest on his $19,000 car loan. What average interest rate doeshe pay on the total $59,000 he owes? Round your answer to the nearest tenth of a percent.
SOLUTION:
Step 1:
In this question, we are told that:
Bob pays 7% interest on his $40,000 college loan and 9% interest on his $19,000 car loan.
We are told to calculate the average interest rate does he pay on the total $59,000 he owes.
Step 2:
For us to calculate the average interest rate does he pay on the total $59,000 he owes:
We need to do the following:
[tex]\frac{(\frac{7}{100}\text{ x 40,000 ) + ( }\frac{9}{100}\text{ x 19,000)}}{59,000}\text{ x }\frac{100}{1}[/tex]=
[tex]\frac{2800\text{ + 1710}}{59000}\text{ x }\frac{100}{1}[/tex]=
[tex]\frac{4510}{59000}\text{ x }\frac{100}{1}[/tex]=
[tex]\begin{gathered} 0.0764\text{ x 100} \\ =\text{ 7.64 \%} \\ \approx\text{ 7. 6 \% ( to the nearest tenth )} \end{gathered}[/tex]CONCLUSION:
The final answer is 7. 6% ( to the nearest tenth)
I need help with this practice problem solving In addition, after you review what branch of mathematics do you think this problem is? Just curious
Given
The equation,
[tex]x^3=-4+4i[/tex]To find all the solutions of the given equation in polar form.
Explanation:
It is given that,
[tex]x^3=-4+4i[/tex]That implies,
[tex]\begin{gathered} x=(-4+4i)^{\frac{1}{3}} \\ x=(4)^{\frac{1}{3}}(-1+i)^{\frac{1}{3}} \end{gathered}[/tex]Now, consider
[tex]\begin{gathered} z=-1+i \\ \Rightarrow r=\sqrt{x^2+y^2} \\ =\sqrt{(-1)^2+1^2} \\ =\sqrt{1+1} \\ =\sqrt{2} \end{gathered}[/tex]Also,
[tex]\begin{gathered} \theta=\tan^{-1}|\frac{y}{x}| \\ =\tan^{-1}|\frac{1}{-1}| \\ =\tan^{-1}|-1| \\ =\tan^{-1}(1) \\ =\frac{\pi}{4} \end{gathered}[/tex]Since (x,y) lies in 2nd quadrant.
Then,
[tex]\begin{gathered} \varphi=\pi-\theta \\ =\pi-\frac{\pi}{4} \\ =\frac{3\pi}{4} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} z=r(\cos\varphi+i\sin\varphi) \\ =\sqrt{2}e^{i(\frac{3\pi}{4})} \end{gathered}[/tex]That implies,
[tex]\begin{gathered} x=(4)^{\frac{1}{3}}\lbrace(\sqrt{2}e^^{i(\frac{3\pi}{4})})\rbrace^{\frac{1}{3}} \\ =(2^2)^{\frac{1}{3}}(2^{\frac{1}{2}})^{\frac{1}{3}}(e^{i(\frac{3\pi}{4})})^{\frac{1}{3}} \\ =\sqrt[6]{32}(e^{i(\frac{3\pi}{4})})^{\frac{1}{3}} \\ =\sqrt[6]{32}\lbrace cis(\frac{3\pi}{4})\rbrace^{\frac{1}{3}} \end{gathered}[/tex]Now,
[tex]Add\text{ }2k\pi\text{ to }\varphi=\frac{3\pi}{4}[/tex]That implies,
[tex]x=\sqrt[6]{32}\lbrace cis(\frac{3\pi}{4}+2k\pi)\rbrace^{\frac{1}{3}}[/tex]By applying De-movers theorem,
[tex]x=\sqrt[6]{32}\lbrace cis\frac{1}{3}(\frac{3\pi}{4}+2k\pi)\rbrace[/tex]Put k=0,1,2 in the above equation.
That implies,
[tex]\begin{gathered} When\text{ }k=0, \\ x=\sqrt[6]{32}\lbrace cis\frac{1}{3}(\frac{3\pi}{4})\rbrace \\ =\sqrt[6]{32}\lbrace cis(\frac{\pi}{4})\rbrace \\ When\text{ }k=1, \\ x=\sqrt[6]{32}\lbrace cis\frac{1}{3}(\frac{3\pi}{4}+2\pi)\rbrace \\ =\sqrt[6]{32}\lbrace cis\frac{1}{3}(\frac{3\pi+8\pi}{4})\rbrace \\ =\sqrt[6]{32}\lbrace cis(\frac{11\pi}{12})\rbrace \\ When\text{ }k=2, \\ x=\sqrt[6]{32}\lbrace cis\frac{1}{3}(\frac{3\pi}{4}+4\pi)\rbrace \\ =\sqrt[6]{32}\lbrace cis\frac{1}{3}(\frac{3\pi+16\pi}{4})\rbrace \\ =\sqrt[6]{32}\lbrace cis(\frac{19\pi}{12})\rbrace \end{gathered}[/tex]Hence, the solutions are,
[tex]x=\sqrt[6]{32}\lbrace cis(\frac{\pi}{4})\rbrace,\sqrt[6]{32}\lbrace cis(\frac{11\pi}{12})\rbrace,\sqrt[6]{32}\lbrace cis(\frac{19\pi}{12})\rbrace[/tex]B. The sum of the measuresof two complimentaryangles is 90°. Find themeasure of the anglelabeled x.
B)
Given that angles (3x -10) and x are complementary, then we can write the following equation:
(3x -10) + x = 90º Definition of Complementary angles
3x-10 +x = 90º Combine like terms
4x -10 = 90 Add 10 to both sides
4x=100 Divide both sides by 4
x=25º
2) So , Angle x = 25º and m angle 3x- 10 is 65º
Which expression is equivalent to -20 + (-50) + (-90)? A. -20 - (-50) - (-90) B. -20 - (-50) + (-90)C. -(20 + 50) + (-90) D. -20 + (-50) - (-90)
ANSWER
Option C is the correct option
EXPLANATION
To find which of the expressions is equivalent. We have to expand the brackets in each of he expressions and find the answer.
We must remember that:
+ * + = +
+ * - = -
- * + = -
- * - = +
For the expression given:
-20 +(-50) + (-90)
= -20 - 50 - 90
= -160
OPTION A
-20 -(-50) - (-90)
= -20 + 50 + 90
= 120
OPTION B
-20 - (-50) + (-90)
= -20 + 50 - 90
= -60
OPTION C
-(20 + 50) + (-90)
= -20 - 50 - 90
= -160
As we can already see, Option C is the correct option.
3) if a swimmer swims 85.4 yards in five minutes, how many meters will he/she swim in 70 seconds?
Remember that
1 yard=0.9144 meters
so
85.4 yd=85.4*0.9144=78.09 m
5 minute=5*60=300 seconds
Applying proportion
78.09/300=x/70
solve for x
x=(78.09/300)*70
x=18.2 metersMonty documented the amount of rain his farm recelved on a monthly basis, as shown in the table. Month, x Rainfall (in.), y NN 3 4.5 5 5 3 Part 1 out of 2 Is the relationship linear? Why or why not? Complete the explanation. The change between months (select) constant, but the change in the amount of rain (select) constant. So, the relationship (select) M linear. Check Next
We have the following:
It is not a linear relationship, because the behavior is not linear, nor is it proportional. When the months increase it does not necessarily increase rainfall, therefore it is not linear
The answer is:
The change between months is constant, but the chanfe in the amount of rain is not constant. So, the relationship is not linear
y(s)= int 0 ^ e^ 4 cos z^ 0 z^ 2 dx then; y^ prime (s)=
Given the following integral:
[tex]y(s)=\int\frac{cos\text{ }z^9}{z^2}dz[/tex]We will find y'(s)
As we know the integral is the inverse of the differentiation
So, the first derivative of the integral can be obtained by removing the integral sign
So, the answer will be:
[tex]y^{\prime}(s)=\frac{cos\text{ }z^9}{z^2}[/tex]Find the number of points of intersection in the given graph.
Answer:
2
Step-by-step explanation:
The graphs meet at two points - (1,2) and (-2,-1).
The nth term of a sequence is represented byWhat is the limit of the the nth term as x becomes increasingly large?O
When we had a fraction with 2 polynomials, the limit of nth term when n became large depends of the degree of the polynomials.
In this case, the numerator has a degree of 5 and the denominator has a degree of 4. Since the degree of the numerator is greater than the degree of the denominator, the limit doesn't exist
MULTIPLE CHOICE. Vanessa is making a banner for the game. She has 20 square feet of fabric. What shape will use most or all of the fabric?a. a square with a side length of 4 feetb. a rectangle with a length of 4 feet and a width of 3.5 feetc. a circle with a radius of about 2.5 feet
we know that
The area of fabric is 20 square feet
so
Verify each option
a) a square with a side length of 4 feet
the area of a square is
A=b^2
we have b=4 ft
substitute
A=4^2=16 ft^2
16 ft^2 < 20 ft^2 ------> is ok
b) a rectangle with a length of 4 feet and a width of 3.5 feet
the area of rectangle is
A=LW
substitute
A=4(3.5)=14 ft^2
14 ft^2 < 20 ft^2 --------> is ok
c) a circle with a radius of about 2.5 feet
The area of a circle is
A=pir^2
A=(3.14)(2.5)^2=19.63 ft^2
19.63 ft^2 < 20 ft^2 ------> is ok
therefore
the answer is option C
Suppose aa represents some number of radians where 0
Answer:
cos(−a)= 0.7
sin(−a)= -0.7
Explanation:
Given the follwoing
cos(a)=0.7 and sin(a)=0.7 where a is within the interval 0
cos(-a) = cos a
sin(-a) = -sina
Substitute the given value in the expression;
Since cos a = 0.7
cos(-a) = 0.7
Also since sin a = 0.7
sin(-a) = -0.7
What is the solution to the equation 1.6m − 4.8 = −1.6m? (5 points)m = 0.5m = 0.7m = 1.5m = 3
Given:
[tex]1.6m-4.8=-1.6m[/tex]Find-:
The value of "m"
Explanation-:
[tex]\begin{gathered} 1.6m-4.8=-1.6m \\ \\ 1.6m+1.6m=4.8 \end{gathered}[/tex][tex]\begin{gathered} 1.6m+1.6m=4.8 \\ \\ 3.2m=4.8 \\ \\ m=\frac{4.8}{3.2} \\ \\ m=1.5 \end{gathered}[/tex]The value of m is 1.5
Write each expression in expanded form. Then rewrite the product in exponential form.Only do A, B, and C
Write each expression in expanded form.
(a)
[tex]\begin{gathered} 4^{3\text{ }}.4^4=4^3\times4^4 \\ =4\times4\times4\times4\times4\times4\times4 \end{gathered}[/tex](b)
[tex]\begin{gathered} (-3)^5.(-3)^{2\text{ }}=(-3)^5\text{ }\times(-3)^2 \\ =(-3)^{}\times(-3)^{}\times(-3)^{}\times(-3)^{}\times(-3)\times(-3)\times(-3) \end{gathered}[/tex](c)
[tex]\begin{gathered} (-2)^8.(-2)^7=(-2)^8\text{ }\times(-2)^7 \\ =(-2)^{}\times(-2)\text{ }\times(-2)^{}\times(-2)\times(-2)\times(-2)\times(-2)\times(-2)\times(-2)\times(-2)\times(-2)\times(-2)\times(-2)\times(-2)\times(-2) \end{gathered}[/tex]Rewriting in exponential form
(a)
[tex]\begin{gathered} 4^3.4^4=4^{3+4} \\ \text{ = 4}^7 \end{gathered}[/tex](b)
[tex]\begin{gathered} (-3)^5.(-3)^2=(-3)^{5+2} \\ \text{ = (-3)}^7 \end{gathered}[/tex](c)
[tex]\begin{gathered} (-2)^8.(-2)^7=(-2)^{8+7}\text{ } \\ =(-2)^{15} \end{gathered}[/tex]A . write an equation B . how much money would the babysitter make if she babysat for 20 hours total ?
Answer:
y = 3/2 x +1
For 20 hours is 31
Explanation:
The equation of a line with slope m and y-intercept b is
[tex]y=mx+b[/tex]The two points that lie on the line of best fit are (6, 10) and (4, 7); therefore, the slope is
[tex]m=\frac{\Delta y}{\Delta x}=\frac{10-7}{6-4}=\frac{3}{2}[/tex]Therefore, our equation becomes
[tex]y=\frac{3}{2}x+b[/tex]The y-intercept is found by putting in x = 4 and y = 7 in the equation
[tex]7=\frac{3}{2}(4)+b[/tex]Solving for b gives
[tex]\begin{gathered} 7=6+b \\ \boxed{b=1} \end{gathered}[/tex]Hence the equation of the line is
[tex]y=\frac{3}{2}x+1[/tex]With the equation of the line in hand, we now find the amount of money earned with 20 hours of babysitting.
[tex]y=\frac{3}{2}(20)+1[/tex][tex]\boxed{y=31.}[/tex]Hence, the answers are
y = 3/2 x +1
For 20 hours is 31
factor by grouping[tex](4y^3 + 28y^2) + (y + 7)[/tex]
We have the following expression given:
[tex](4y^3+28y^2)+(y+7)[/tex]We can start selecting as common factor 4y^2 and we got:
[tex]4y^2(y+7)+(y+7)[/tex]Now we can select y+7 as common factor and we got:
[tex](y+7)\left\lbrack 4y^2+1\right\rbrack [/tex]So then our final answer would be:
[tex](y+7)(4y^2+1)[/tex]If -xy-x=y+3 then find the equations of all tangent lines to the curve when y=1
1) Let's firstly plug into the equation, the quantity of y=1
[tex]\begin{gathered} -xy-x=y+3 \\ -x-x=1+3 \\ -2x=4 \\ \frac{-2x}{-2}=\frac{4}{-2} \\ x=-2 \\ (-2,1) \end{gathered}[/tex]Note that after we plugged into that we have a point (-2,1).
2) Now, let's take the first derivative from the original equation. In this case, we need to take an implicit differentiation as you can see it below:
[tex]\begin{gathered} \frac{d}{dx}\lbrack-xy-x\rbrack=\frac{d}{dx}\lbrack y+3\rbrack \\ -\frac{d}{dx}\lbrack xy\rbrack-\frac{d}{dx}\lbrack x\rbrack=\frac{d}{dx}\lbrack y\rbrack+\frac{d}{dx}\lbrack3\rbrack \\ -xy^{\prime}-y-1=y^{\prime} \\ y^{\prime}=-\frac{y+1}{x+1} \end{gathered}[/tex]3) Let's now find the slope:
Tom is training for a 6 mile race. The following scatter plot shows the distance he has run and the time it took for each run. What is a good prediction of how long it will take Tom to run the 6 mile race?A) 55 minutes B) 50 minutesC) 60 minutes D) 70 minutes
We are given the scatter plot which shows the distance he has run and the time it took for each run.
We are asked to determine a good prediction of how long it will take Tom to run the 6 mile race?
One way to predict the time is by drawing a line that best fits the given data.
As you can see, from the line of best fit, the time corresponding to the 6 miles is around 60 minutes.
Therefore, 60 minutes is a good prediction of how long it will take Tom to run the 6 mile race.
Sue has 12 baseball cards. She buys four packs of cards, and then she has a total of 36 cards. Which of the following represents the given situation?
SOLUTION:
She has 12 baseball cards initially.
She later bought four packs of cards, meaning each pack contains 'x' number of cards, making the total number of cards in the four packs to be 4x.
Then the total of all the cards sumed up to be 36.
The statement that captures this information is;
4x + 12 = 36
Question Help please!To find simple interest, you multiply the principal (in dollars), the interest rate (as a decimal), andthe time in years. The equation 24 = 400.0.015•4 shows how to find the simple interest for acertain account after 4 years. What is the interest rate (as a percent)? How much is the simpleinterest? What is the principal?What is the interest rate (as a percent)?OA. 24%OB. 1.5%OC. 400%OD. 0.015%Click to select your answer and then click Check Answer.Clear AllCheck And2 pansremainingQuestion 2Review progressBackof 9Next →
The interest rate is 1.5%
Here, we want to select which of the option represent the interest rate
From the question, we can see that 400 represents the principal, with 4 representing the number of years. Thus, we have 0.015 as the interest rate
What we have to do here however is to convert this to percentage
Mathematically, that would be;
[tex]0.015\text{ = }\frac{15}{1000}\text{ = }\frac{1.5}{100}=\text{ 1.5\%}[/tex]A patteren is shown below what is the patteren rule? How many cubes are in the tenth image if the patteren contiues ? How about the 100th image show your thinking below
Answer
a) Pattern rule = 2n - 1
b) Tenth image = 19 cubes
c) 100th image = 199 cubes
Explanation
We need to first see that the number of cubes increase in a steady pattern
1 cube
3 cubes
5 cubes
7 cubes
We can see that the number of cubes increases like an arithmetic progression with
First term = a = 1
Common difference = d = 2
The nth term of an arithmetic progression is given as
nth term = a + (n - 1)d
a = first term = 1
d =common difference = 2
n = number of terms
nth term = 1 + (n - 1)2
nth term = 1 + 2n - 2
nth term = -1 + 2n = 2n - 1
b) The 10th term
n = 10
10th term = 2n - 1 = 2(10) - 1 = 20 - 1 = 19 cubes
c) 100th image
n = 100
100th image = 2n - 1 = 2(100) - 1 = 200 - 1 = 199 cubes
Hope this Helps!!!
Which answer choice shows 4 + 0.3 + 0.09 written in standard form?A.43.9B.4.39C.0.439D.0.0439
Place values:
As each is in a different place value, when we add them neither will affect the other, meaning:
[tex]4+0.3+0.09=4.39[/tex]Answer: B 4.39
I have a math question on homework i need hell with.
ΔEFG is translated to ΔE'F'G' using the rule:
[tex](x,y)\to(x+8,y-3)[/tex]To determine the coordinates of each vertex of the triangle after translation you have to add 8 to each x-coordinate of the vertices of ΔEFG and subtract 3 to each y-coordinate.
The addition of 8 units to the x-coordinate will give as a result a horizontal translation of 8 units to the right.
The subtraction of 3 units to each y-coordinate will give as a result a vertical translation of 3 units down.
ΔEFG to ΔE'F'G'
E(-4,8) → E'(-4+8,8-3)= E'(4,5)
F(-2,10) → F'(-2+8,10-3)= F'(6,7)
G(-3,9) → G'(-3+8,9-3)= G'(5,6)
After the translation, the vertices of ΔE'F'G' will have the coordinates:
E'(4,5)
F'(6,7)
G'(5,6)