Answers
Solution
67)
[tex]\begin{gathered} sec\theta\text{ = }\frac{1}{cos\theta} \\ Cross\text{ multiply} \\ sec\theta\text{ }\times\text{ cos}\theta \\ \frac{1}{cos\theta}\text{ }\times cos\theta \\ =\text{ 1} \end{gathered}[/tex]68)
Draw a right angle triangle:
[tex]\begin{gathered} sin\theta\text{ = }\frac{opposite}{hypotenuse}\text{ = }\frac{a}{c} \\ cos\theta\text{ = }\frac{adjacent\text{ }}{Hypotenuse}\text{ = }\frac{b}{c} \\ tan\theta\text{ = }\frac{opposite}{adjacent\text{ }}\text{ = }\frac{a}{b} \end{gathered}[/tex][tex]\begin{gathered} \\ \frac{sin\theta\begin{equation*}\end{equation*}}{cos\theta}\text{ = }\frac{a}{c}\text{ }\div\text{ }\frac{b}{c} \\ =\text{ }\frac{a}{c}\text{ }\times\text{ }\frac{c}{b} \\ =\text{ }\frac{a}{b} \\ Hence,tan\theta\text{= }\frac{sin\theta}{cos\theta} \end{gathered}[/tex]
Related Questions
Find the relationship between zeros and x-intercepts of the polynomial x2 + 15x + 54.They are equal to zeroThey are oppositesThey are sameThey are different
Answers
Given:
x2 + 15x + 54.
Required:
Find the relationship between zeros and x-intercepts of the polynomia
Explanation:
Although the zeroes of
[tex]\begin{gathered} x^2+15x-9 \\ \\ are\text{ -6,-9} \\ \\ And\text{ the x-intercepts of it are -6 and -9 } \\ \\ \\ they\text{ mean different things.} \end{gathered}[/tex]Required answer:
They are different
The image of the point (-9,0) under a translation is (-12, -4). Find thecoordinates of the image of the point (-1, -2) under the same translation.
Answers
The image of the point (-9,0) under a translation is (-12, -4). Find the
coordinates of the image of the point (-1, -2) under the same translation.
we have
(-9,0) ------- >(-12,-4)
so
the rule of tye translation is
(x,y) -------> (x-3, y-4)
the translation is 3 units at left and 4 units down
Apply the rule point (-1, -2)
(-1, -2) --------> (-1-3, -2-4)
(-1, -2) --------> (-4, -6)
answer
(-4, -6)
Please help I need an answer ASAP!!!!!!!!!!!!!!!!!!
Answers
Answer:
{-5,-3,0}
Step-by-step explanation:
Since you need it ASAP, the domain is listed above. No explanation.
Can you help me solve? Sarah deposited $1,400 for one year at 10% compounded semi-annually. a. How many times was interest added to Sarah's account? (The lesson is on Compound Interest)
Answers
Given the following question:
Sarah deposited $1400 for one year
10% compounded semi-annually
Semi-annually means twice a year or it occurs twice in a year.
Since semi-annually means twice a year we know that the amount of times interest was added to Sarah's account was twice a year.
How many times was interest added to Sarah's account?
A: Two times
the question is hard to write i will take a picture of it when I met you!
Answers
Answer
The score on her next test that would keep her mean and median the same would be 95. Because her mean and median are already 95, another score of this value would not alter the mean or the median.
Explanation
To answer this, we need to first obtain the current mean and median
96, 95, 98, 92, 94, 93, 97
The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
Σx = 96 + 95 + 98 + 92 + 94 + 93 + 97 = 665
N = 7
Mean = (Σx)/N
Mean = (665/7) = 95
Median
The median is the variable that falls in the middle of the distribution when all the variables are arranged either in ascending or descending order.
So, to obtain the median for this, we have to arrange all the scores in data.
96, 95, 98, 92, 94, 93, 97
92, 93, 94, 95, 96, 97, 98
We can easily see that the number in the middle is the fourth number and that number is 95
So, currently the mean and the median are already the same score, 95, so, the score that she needs to get in her next test to keep the mean and median equal is still 95.
Hope this Helps!!!
What is the base for each curve and where should I shift for each? I’ve been getting this wrong because I don’t know which way to shift and what the base should be for both
Answers
Answer:
Here is the graph of the equation and its inverse.
The inverse is the purple graph.
Explanation:
• The base of the equation is 8.
,• There is no vertical shift to the graph because there's no constant added to the function f(x) = 8^x.
,• In addition, there is no horizontal shift to the graph because there's no constant added to the exponent x.
Which of the following is equivalent to 0=2x^2+8x-24 when completing the square ?
Answers
We will have that the following will be the equivalent;
[tex](x+2)^2=16[/tex]geometry_I dont know how to calculate 80/360 pie r^2
Answers
Hello there. To solve this question, we'll have to remember some properties about circular sectors.
Given a circular sector of a circle with radius R:
Suppose the length of the arc AB is alpha (in radians).
From a well-known theorem about angles in a circle, we know that the angle generating this arc from the center has the same measure, that is:
So we want to determine the area of the sector knowing the radius and the length of the arc.
First, we know that the area of the full circle is given by:
[tex]A=\pi\cdot R^2[/tex]The sector is a fraction of this circle, that means that:
[tex]A=kA_{sector}[/tex]A is a multiple of Asector.
In fact, this proportionality constant is the ratio between the central angle and the angle alpha forming the sector, that is
[tex]k=\dfrac{2\pi}{\alpha}[/tex]It is also possible to have alpha in degrees, but we have to convert the center angle to degrees as well, so we get
[tex]k=\dfrac{2\pi\cdot\dfrac{180^{\circ}}{\pi}}{\alpha\cdot\dfrac{180^{\circ}}{\pi}}=\dfrac{360^{\circ}}{\alpha^{\circ}}[/tex]As we want to solve for the area of the sector, we have that:
[tex]A_{sector}=A\cdot\dfrac{\alpha^{\circ}}{{360^{\circ}}}=\dfrac{\alpha^{\circ}}{360^{\circ}}\cdot\pi R^2[/tex]Okay. With this, we can solve the question.
We have the following circle:
In this case, notice R = 18 yd and the length of the arc is 80º. This gives us the angle alpha:
Now, we take the ratio between the angle and the total angle applying the formula:
[tex]A_{sector}=\dfrac{80^{\circ}}{360^{\circ}}\cdot\pi\cdot18^2[/tex]Square the number
[tex]A_{sector}=\dfrac{80^{\circ}}{360^{\circ}}\cdot\pi\cdot324[/tex]Simplify the fraction by a factor of 40º
[tex]A_{sector}=\dfrac{2}{9}\cdot\pi\cdot324[/tex]Multiply the numbers and simplify the fraction
[tex]A_{sector}=\dfrac{648\pi}{9}=72\pi[/tex]This is the area of this sector.
here are several recipes for sparkling lemonade. for each recipe describe how many table spoons of lemonade mix it takes per cup of sparkling water. REST ON THE PICTURE
Answers
Given:
Recipe 1: 4 tablespoons lemonade mix and 12 cups of sparkling water
Recipe 2: 4 tablespoons lemonade mix and 6 cups of sparkling water
Recipe 3: 3 tablespoons lemonade mix and 5 cups of sparkling water
Recipe 4: 1/2 tablespoons lemonade mix and 3/4 cups of sparkling water
Asked:
1) For Recipe 1, how many tablespoons lemonade mix per cup of sparkling water?
2) For Recipe 2, how many tablespoons lemonade mix per cup of sparkling water?
3) For Recipe 3, how many tablespoons lemonade mix per cup of sparkling water?
4) For Recipe 4, how many tablespoons lemonade mix per cup of sparkling water?
Solution:
1) Recipe 1
We will divide the cups by 12 to make 1 cup. Then divide 4 by 12 as well.
12 cups = 4 tablespoons
12 cups/12 cups = 4 tablespoons/12 cups
1 cup = 1/3 tablespoon per cup
2) Recipe 2
We will divide the cups by 6 to make 1 cup. Then divide 4 by 6 as well.
6 cups = 4 tablespoons
6 cups/6 cups = 4 tablespoons/6 cups
1 cup = 2/3 tablespoon per cup
3) Recipe 3
We will divide the cups by 5 to make 1 cup. Then divide 3 by 5 as well.
5 cups = 3 tablespoons
5 cups/5 cups = 3 tablespoons/5 cups
1 cup = 3/5 tablespoon per cup
4) Recipe 4
We will divide the cups by 3/4 to make 1 cup. Then divide 1/2 by 3/4 as well.
3/4 cups = 1/2 tablespoons
3/4 cups/3/4 cups = 1/2 tablespoons/3/4 cups
[tex]\begin{gathered} \frac{\frac{3}{4}}{\frac{3}{4}}=\frac{\frac{1}{2}}{\frac{3}{4}} \\ 1=\frac{1}{2}\cdot\frac{4}{3} \\ 1=\frac{4}{6} \\ 1=\frac{2}{3} \end{gathered}[/tex]1 cup = 2/3 tablespoon per cup
ANSWERS:
Recipe 1: 1/3 tablespoon per cup
Recipe 2: 2/3 tablespoon per cup
Recipe 3: 3/5 tablespoon per cup
Recipe 4: 2/3 tablespoon per cup
Select the statement that accurately describes the following pair of triangles 1. ABC~YZX~by SAS2. ABC~YXZ~by SAS3. ABC~ZYX~by SAS4. ABC~ZXY~by SAS5.ABC~XZY~by SAS6. ABC~XYZ~by SAS7. Triangles are not similar
Answers
Step 1: Let's recall what is SAS:
"SAS" means "Side, Angle, Side"
Step 2: Let's use The Law of Cosines to calculate the unknown side of the triangles given:
Formula of The Law of Cosines is:
[tex]a^2=b^2+c^2\text{ - }2\text{ bc }\cdot\text{ }\cos \text{ (}\angle A\text{)}[/tex]
In the triangle ABC, we have:
b = 15, c = 21 and angle A is 75 degrees
Step 3: Substitute the values given in the formula
[tex]a^2=15^2+21^2\text{ - 2 }\cdot\text{ 15 }\cdot\text{ 21 }\cdot\mathring{Cos(75}\circ)[/tex][tex]a^2\text{ = 225 + 441 - }630\ast\text{ 0.2588}[/tex][tex]a^2\text{ = 666 - 163.044 = 502.956 }\Rightarrow\text{ a = 22.43}[/tex]Step 4: Let's use The Law of Sines to find the smaller of the other two angles
[tex]\sin \text{ }\angle B\text{ }\frac{\square}{\square}21\text{ }=\text{ }\sin \text{ (75) }\frac{\square}{\square}\text{ 22.43}[/tex][tex]\sin \text{ }\angle B=\text{ (}0.966\text{ }\ast\text{ 21) / 22.43}[/tex][tex]\sin \angle\text{ B = 0.9044 }\Rightarrow\text{ B = }\sin ^{-1}\text{ (0.9044)}[/tex][tex]\angle B\text{ = 64.74}\circ\text{ }\Rightarrow\text{ }\angle C\text{ = 180 - 64.74 - 75 = 40.26}\circ[/tex]Step 5: Find the last angle, recalling that the interior angles of a triangle add up to 180 degrees
[tex]\angle\text{ C = 180 - 64.74 - 75 = 40.26}\circ[/tex]Now, we have the sides and the angles of triangle ABC:
Sides = 15,21, 22.43
Angles = 75, 64.74, 40.26
Given f(x)=9x and g(x)=3x2+2, find the following expressions.
(a) (f◦g)(4) (b) (g◦f)(2) (c) (f◦f)(1) (d) (g◦g)(0)
Answers
Value of the expressions for the given functions f(x) =9x , g(x) =3x² +2 is given by:
a. (fog)(4) = 450
b. (gof)(2) =974
c. (fof)(1) = 81
d. (gog)(0) = 14
As given in the question,
Given functions are:
f(x) =9x
g(x) =3x² +2
Value of the expressions for the given functions f(x) =9x , g(x) =3x² +2 are as follow:
a. (fog)(4)
= f(g(4))
= f( 3(4²)+2)
= f(50)
= 9×50
=450
b. (gof)(2)
=g(f(2))
=g(9(2))
=g(18)
=3(18)² +2
=974
c. (fof)(1)
= f(f(1))
= f(9(1))
=f(9)
=9×9
=81
d. (gog)(0)
=g(g(0))
=g(3(0²) +2)
=g(2)
=3(2)² +2
=14
Therefore, Value of the expressions for the given functions f(x) =9x , g(x) =3x² +2 is given by:
a. (fog)(4) = 450
b. (gof)(2) =974
c. (fof)(1) = 81
d. (gog)(0) = 14
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Which choice is equivalent to the quotient below? √64/√16a) √4/4b) √8/2c) 2d) √2
Answers
Answer: option c
Question 3 of 32Which conic section is defined by the set of all points in a plane for which thesum of the distances to two fixed points equals a certain constant?уFocusFocusO A. EllipseOB. ParabolaC. Hyperbola
Answers
We can see from the graph that we have a conic section in which we have the sum of the distances to two fixed points equals a certain constant.
As we can see from the question, we have:
1. Then we have that for this figure if we have that:
[tex]F_1P+F_2P=constant[/tex]2. In words, we have the sum of the distance from one of the focus, F1, to the point P, and the distance from the focus, F2, to the point P is always constant.
An example of the ellipse is the movement of the planets around the Sun. The planets move around the Sun forming an ellipse, in which the Sun is one of the focus.
We can also say that this figure is a stretched circle, and it is known as Ellipse.
Therefore, in summary, the conic section defined by the set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant is the Ellipse (option A).
What is 72 hours to 3 days in ratio form
Answers
Answer:
3:3 / 1:1
Step-by-step explanation:
72 hours is 3 days
8 CHILDREN PARTICIPATE IN A IN A CONTEST. FOUR DIFFERENT PRIZES ARE AWARDED T0 THE WINNER AND THE FIRST,SECOND AND THIRD RUNNER UPS. IN HOW MANY DIFFERENT WAYS CAN THE FOUR PRIZES BE AWARDED?
Answers
We have that there are 8 participants and 4 prizes, in this problem, it's important the order of the prizes too.
Now, for the first time, there are 8 possibilities for awarding the winner prize.
For the second moment, there are just 7 possibilities for awarding the first runner-up.
Then, we have that there are 6 possibilities for awarding the second runner-up.
And, finally, we have 5 possibilities for awarding the third runner-up.
So, we have that all the ways are represented as:
[tex]8\ast7\ast6\ast5=1680[/tex]And since the order of the 4 prizes is important to get a specific prize, we have:
[tex]\frac{1680}{4!}=70[/tex]Then the correct answer would be 70.
I need help finding the answer to this problem. My math teacher mentioned that it isn't exactly an arithmetic sequence so thats why I am having difficulties.
Answers
A table is given to complete the arithmetic sequence.
To complete the table, we need to determine the common difference first:
Based on the table,
In the following exercise a formula is given along with the values of all but one of the variables in the formula. Find the value of the variable that is not given S=2LW+2WH+2LH; S=108,L=3 W = 4
Answers
Question:
In the following exercise, a formula is given along with the values of all but one of the variables in the formula. Find the value of the variable that is not given
S=2LW+2WH+2LH;
S=108,
L=3
W = 4
Solution:
Consider the following equation:
[tex]S=2LW+2WH+2LH[/tex]now, if we replace the given data, in the previous equation, we obtain:
[tex]108=2(3)(4)+2(4)H+2(3)H[/tex]this is equivalent to:
[tex]108=24+8H+6H[/tex]this is equivalent to:
[tex]108-24=14H[/tex]this is equivalent to:
[tex]14H=84[/tex]thus, solving for H, we get:
[tex]H\text{ = }\frac{84}{14}=\text{ 6}[/tex]Then, we can conclude that the value of the variable that is not given is:
[tex]H\text{ = 6}[/tex]Which of the following expressions are equivalent? Justify your reasoning.4A.1B.-1х10C.√x5 4 2X X X1 1 13 3 3D. X X X
Answers
B and D.
B .
[tex]\frac{1}{x^{-1}\text{ }}=\text{ 1 }\times x^1=x[/tex]D. Since all terms have the same base, we can add exponents.
[tex]x^{\frac{1}{3}}\times x^{\frac{1}{3}}\times x^{\frac{1}{3}}^{}=x^{(\frac{1}{3}+\frac{1}{3}+\frac{1}{3})}=x^1=x^{}[/tex]A sofa is on sale for $363 which is 34% less than a regular price what is the regular price
Answers
Given that a sofa is on sale for $363, which is 34% less than the regular price.
To determine: The regular price.
Let the regular price be Y. If the regular price is Y, then the 34%regular price would be
[tex]\begin{gathered} P_{\text{less}}=(100-34)\text{ \% of \$Y} \\ P_{\text{less}}=66\text{ \% of Y} \end{gathered}[/tex]It should be noted that the 34 % less the regular price is the price on sale. Then,
[tex]\begin{gathered} P_{\text{less}}=\text{ \$363} \\ \text{Therefore,} \\ 66\text{ \% of Y = \$363} \\ \frac{66}{100}\times Y=363 \\ \frac{66Y}{100}=363 \\ 66Y=363\times100 \\ 66Y=36300 \\ Y=\frac{36300}{66} \\ Y=550 \end{gathered}[/tex]Hence, the regular price of the sofa is $550
if a trend line had the equation [tex]y = - 3.7x + 0.68[/tex]what y-value would you expect to obtain when x has the following values? a. 13; b. 0; c. 5.8; d. 7.7
Answers
Step 1: Write out the equation given in the question
[tex]y=-3.7x+0.68[/tex]Step 2: Solve for y by substituting each of the values of x given in the question
[tex]\begin{gathered} (a)\text{when x=13} \\ y=-3.7(13)+0.68 \\ y=-48.1+0.68 \\ y=-47.42 \end{gathered}[/tex][tex]\begin{gathered} (b)\text{when x=0} \\ y=-3.7(0)+0.68 \\ y=0+6.8 \\ y=0.68 \end{gathered}[/tex][tex]\begin{gathered} (c)\text{when x=5.8} \\ y=-3.7(5.8)+0.68 \\ y=-21.46+0.68 \\ y=-20.78 \end{gathered}[/tex][tex]\begin{gathered} (d)\text{ when x=7.7} \\ y=-3.7(7.7)+0.68 \\ y=-28.49+0.68 \\ y=-27.81 \end{gathered}[/tex]Hence, when x= 13, y= -47.42; x=0, y= 0.68; x=5.8, y=-20.78; x=7.7, y=-27.81
The revenue from the sale of a product is given by the function R=400x−x3. Selling how many units will give positive revenue?
Answers
ANSWER:
Selling more than 0 and less than 20 units will give positive revenue.
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]R=\: 400x-x^3[/tex]Now, we propose the following inequality:
[tex]\begin{gathered} 400x-x^3>0 \\ \text{ solving for x:} \\ x\cdot(400-x^2)>0 \\ x\cdot(x-20)\cdot(x+20)>0 \\ \text{ therefore:} \\ x>0 \\ x-20>0\rightarrow x>20 \\ x+20>0\rightarrow x>-20 \\ \text{ in interval form:} \\ (-\infty,-20)\cup(0,20) \end{gathered}[/tex]Since negative units cannot be sold, we are then interested in the range from 0 to 20, therefore, if more than 0 and less than 20 units come in, the revenue will be positive.
Dave the plumber charges a standard rate of $30 for a project plus $40 per hour. He needs to make at least $1310 per week to cover all of his expenses. Create an inequality that can be used to find the minimum number of hours he will need to work on a single project in one week to meet his goal.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Plumber:
rate:
$30
$40 per hour
total amount = $1310
inequality:
total hours = ?
Step 02:
x = hour
y = 40 x + 30
40x + 30 ≥ 1310
Step 03:
40x + 30 - 30 ≥ 1310 -30
40x / 40 ≥ 1280 / 40
x ≥ 32
The answer is:
40x + 30 ≥ 1310
He needs to work 32 hours to cover all of his expenses.
HELP NOW!!!! use the graph of the function y = 4x to answer the following questions. The domain of the function is to because an exponent can be any real number. On a coordinate plane, an exponential function approaches the x-axis in quadrant 2 and increases exponentially in quadrant 1.
Answers
The domain of the function is negative infinity (-∞) to positive infinity (∞) because an exponent can be any real number.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain simply refers to the set of all possible input numerical values (x-values) to a function. Additionally, the domain of a graph consist of all the input numerical values (x-values) that are located on the x-coordinate.
By critically observing the graph of this function (see attachment), we can reasonably and logically deduce the following about its domain:
Domain = [-∞, ∞].
In conclusion, the range of this function is from zero (0) to positive infinity (∞) because 4^x is always positive.
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Complete Question:
Use the graph of the function y = 4x to answer the following questions. The domain of the function is _____ to _____ because an exponent can be any real number.
On a coordinate plane, an exponential function approaches the x-axis in quadrant 2 and increases exponentially in quadrant 1.
Describe the transformation to get from f(x) to g(x) Pls help this is driving me crazy.
g(x)=f(x)-4
g(x)=f(x+6)
g(x)=(1)/(2)f(-x)
g(x)=-f(5x)
g(x)=3f(x+4)-6
g(x)=-f((3)/(2)x)-5
Answers
Answer:
10. A translation of 4 units down.
11. A translation of 6 units left.
12. A reflection in the y-axis, followed by a vertical compression by a factor of ¹/₂.
13. A horizontal compression by a factor of ¹/₅, followed by a reflection in the x-axis.
14. A translation of 4 units left, followed by a vertical stretch by a factor of 3, followed by a translation of 6 units down.
15. A horizontal compression by a factor of ²/₃, followed by a reflection in the x-axis, followed by a translation of 5 units down.
Step-by-step explanation:
Transformations
[tex]\textsf{For $a > 0$}:[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}.[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}.[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.[/tex]
Question 10[tex]\textsf{Given}: \quad g(x)=f(x)-4[/tex]
Therefore, the transformation to get from f(x) to g(x) is:
Translation of 4 units down.Question 11[tex]\textsf{Given}: \quad g(x)=f(x+6)[/tex]
Therefore, the transformation to get from f(x) to g(x) is:
Translation of 6 units left.Question 12[tex]\textsf{Given}: \quad g(x)=\dfrac{1}{2}f(-x)[/tex]
Therefore, the series of transformations to get from f(x) to g(x) is:
Reflection in the y-axis.Vertical compression by a factor of ¹/₂.Question 13[tex]\textsf{Given}: \quad g(x)=-f(5x)[/tex]
Therefore, the series of transformations to get from f(x) to g(x) is:
Horizontal compression by a factor of ¹/₅.Reflection in the x-axis.Question 14[tex]\textsf{Given}: \quad g(x)=3f(x+4)-6[/tex]
Therefore, the series of transformations to get from f(x) to g(x) is:
Translation of 4 units left.Vertical stretch by a factor of 3.Translation of 6 units down.Question 15[tex]\textsf{Given}: \quad g(x)=-f\left(\dfrac{3}{2}x\right)-5[/tex]
Therefore, the series of transformations to get from f(x) to g(x) is:
Horizontal compression by a factor of ²/₃.Reflection in the x-axis.Translation of 5 units down.Perform the indicated operation and express the result as a simplified complex number. (5−6i)(4+8i)
Answers
we have the expression
[tex](5-6i)(4+8i)[/tex]Apply distributive property
[tex]\begin{gathered} (5)(4)+(5)(8i)-(6i)(4)-(6i)(8i) \\ 20+40i-24i-48i^2 \\ Reemmber\text{ that }i^2=-1 \\ 20+40i-24i-48(-1) \\ 20+40i-24i+48 \\ combine\text{ like terms} \\ (68+16i) \end{gathered}[/tex]It took Eric 11 hours to drive to a family reunion. On the way home, he was able to increase his average speed by 18 mph and makethe return drive in only 8 hours. Find his average speed on the return drive.Step 1 of 3: Complete the following table by entering the missing values, using x to represent the unknown quantity.
Answers
The Solution:
Given the initial values as below:
[tex]\begin{gathered} \text{Let the original speed/ rate be x} \\ \text{Time(t)}=11\text{ hours} \\ So,\text{ we have the distance(d) to be:} \\ d=x\times11=11x\ldots eqn(1) \end{gathered}[/tex]The average speed was increased by 18m/h and a return time of 8 hours only.
[tex]\begin{gathered} \text{ speed(s)=(x+18) m/h} \\ \text{ Time(t)=8 hrs} \\ So, \\ d=(x+18)(8)=8x+144\ldots eqn(2) \end{gathered}[/tex]Equating both eqn(1) and eqn(2), we get
[tex]\begin{gathered} 11x=8x+144 \\ 11x-8x=144 \\ 3x=144 \\ \text{Dividing both sides by 3} \\ \frac{3x}{3}=\frac{144}{3} \\ \\ x=48\text{ m/h} \end{gathered}[/tex]The distance is
[tex]d=11x=11\times48=528m[/tex]Thus, the average speed on his return drive is:
[tex]\text{ Average speed=x}+18=48+18=66\text{ m/h}[/tex]Therefore, the correct answer is 66 m/h
Original values:
x=48m/h
t=11 hrs
d=528m
Return Drive:
x=66m/h
t=8 hrs
d=528m
It takes 2 1/2 poster boards to display half of your project. how many poster boards will you need for your entire project? Please help me thank you
Answers
Since 2 1/2 boards can display half of your project. You will need two 2 1/2 boards to display your full project. Multiply 2 1/2 by 2 and we get
[tex]2\frac{1}{2}\times2=\frac{5}{2}\times2=\frac{10}{2}=5[/tex]Therefore, you need 5 boards to display your entire project.
Create an example of a linear system that would best be solved using the substitution method. Explain your reasoning
Answers
An example of a linear system that would be solved using the substitution method is "A man bought 2 pens and a book that cost $3 for a total cost of $5. Find the cost of the pen.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the man bought 2 pens and a book that cost $3 for a total cost of $5.
This will be:
2p + b = 5
Substitute b = 3
2p + 3 = 5
Collect like terms
2p = 5 - 3
2p = 2
Divide
p = 2/2
p = 1
The cost of the pen is $1.
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He'll am just trying to make sure I did this right
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EXPLANATION
Number of books = 12
Bill = $112
Amount spent = $16
Cost = $12/book
The variable is the number of books--> x
which type of equation is this 4x-3=y
Answers
Answer:linear
Step-by-step explanation:
linear