which of the following is equivalent to the expression below? 3(5-2i)A. 15-2iB. 15-6iC. 8-2iD. 8-5i
Answers
ANSWER:
B. 15 - 6i
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]3\left(5-2i\right)[/tex]We apply the distributive property and we are left with the following:
[tex]\begin{gathered} 3\left(5-2i\right)=3\cdot \:5-3\cdot \:2i \\ \\ 3\left(5-2i\right)=15-6i \end{gathered}[/tex]Therefore, the correct answer is B. 15 - 6i
Related Questions
Answer the questions below.(a)The 10 members of the swim team completed the following numbers of laps at today's practice: 78,79,81,82,84,85,86,87,88,89.Which measure should be used to summarize the data?MeanMedianMode(b)A car dealer has used cars for sale for the following amounts: $3400,$3600,$3700,$3800,$3900,$4000,$4100,$4300,$7600.Which measure should be used to summarize the data?MeanMedianMode(c)A data set shows the age of each resident at Lakeview Retirement Home.Which measure gives the age shared by the most residents?MeanMedianMode
Answers
Answer
Explanation
(a) The first step is to arrange the numbers of laps in ascending order:
78, 79, 81, 82, 84, 85, 86, 87, 88, 89.
Show all work to receive credit. Write verbal questions in at least one complete sentence.For each of the following questions, decide if the data is qualitative or quantitative. If it is quantitative, decide if it’s discrete or continuous. Explain the reason for your answer. a)Janelle is collecting data on the number of ounces of water drank by college students during a typical math class. What type of data is this?
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To answer this question let's remember the definitions of qualitative and quantitative data:
• Qualitative data is data that describes the attributes or properties of what we are studying.
,• Quantitative data that describes certain quantity or amount. It is usually express by numbers with some unit associated it with it and it can be discrete or continuous. Discrete data is described by particular numbers in a range and continuos data is described by any number in any range.
With this in mind we conclude that Janelle is measuring qualitative data, since she is measuring the amount of water the student takes, furthermore this is continuous data since each student can drink any amount of water, that is, we can even divide the ounces in any decimal.
Find the lengths of the diagonals of rectangle WXY Z where WY-2x + 34 and XZ = 3x – 26The length of each diagonal isunits.
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To solve the exercise, you can first draw a picture to better understand the statement. So,
Now, in a rectangle, the lengths of the diagonals measure the same. So,
[tex]\begin{gathered} WY=XZ \\ -2x+34=3x-26 \end{gathered}[/tex]To solve for x first subtract 34 from both sides of the equation
[tex]\begin{gathered} -2x+34-34=3x-26-34 \\ -2x=3x-60 \end{gathered}[/tex]Subtract 3x from both sides of the equation
[tex]\begin{gathered} -2x-3x=3x-60-3x \\ -5x=-60 \end{gathered}[/tex]Divide by -5 into both sides of the equation
[tex]\begin{gathered} \frac{-5x}{-5}=\frac{-60}{-5} \\ x=12 \end{gathered}[/tex]Finally, replace the value of x in the length of any of the diagonals, for example, the diagonal WY
[tex]\begin{gathered} WY=-2x+34 \\ WY=-2(12)+34 \\ WY=-24+34 \\ WY=10 \end{gathered}[/tex]Therefore, the length of each diagonal is 10 units.
Ken is building an outdoor walking path with pavers. Pavers are sold 10 for $8 or $1 per paver. Ken needs 52 pavers to complete the walking path what is the least amount that 52 pavers cost?
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Ken is building an outdoor walking path
Pavers are sold 10 for $8 or $1 per paver
Ken needs 52 pavers to complete the walking path
if 10 pavers is sold for $8
52 / 10 = 5 remainder 2
This means he is going to buy 50 pavers for
5 x $8 = $40
Remaining two pavers
Since, 1 paver is sold for $1
The 2 pavers will be sold for $2
$40 + $2 = $42
The least amount that 52 pavers will cost is $42
Use trig ratios to find the missing side of the triangle below. Show all of your work. Round your answer to the nearest 10th.
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Answer:
[tex]x\approx12.7[/tex]Step-by-step explanation:
To solve this situation, we can use trigonometric ratios or relationships to find x. Trigonometric ratios are represented by the following diagram and formulas:
Therefore, to find x, use the sen relationship:
[tex]\begin{gathered} \sin (65)=\frac{x}{14} \\ x=14\cdot\sin (65) \\ x=12.688 \\ \text{ Rounding to the nearest 10th:} \\ x\approx12.7 \end{gathered}[/tex]equation or special characters
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Inverse table.
- What undoes sine?
writen as:
[tex]\sin ^{-1}[/tex]called: inverse sine
also called: arcsine
- What undoes cosine?
written as
[tex]\cos ^{-1}[/tex]called: inverse cosine
also called: arccosine
- What undoes tangent?
written as
[tex]\tan ^{-1}[/tex]called: inverse tangent
also called: arctangent
Table of sine, cosine, tangent for 30, 45 and 60 degrees.
what is a division expression with a quotient that is greater than 8 divided by 0.001
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SOLUTION
Write out the given expression
[tex]\frac{8}{0.001}[/tex]An expression with a quotient that is greater than the expression above is to increase the numerator and leave the denominator unchanged
Hence, we have
[tex]\frac{9}{0.001}is\text{ greater than }\frac{8}{0.001}[/tex]Therefore
The division expression with a quotient that is greater than 8 divided by 0.001 is
9/0.001
Simplify the square root:square root of negative 72 end rootAnswer choices Include:2 i square root of 186 i square root of 218 i square root of 22 i square root of 6
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We need to simplify the next square root:
[tex]\sqrt[]{-72}[/tex]First, we need to rewrite the expression as:
[tex]\sqrt{-72}=\sqrt[]{-1}\ast\sqrt[]{72}[/tex]Where √-1 = i
Therefore:
[tex]\sqrt{-1}\ast\sqrt{72}=\sqrt[]{72}\text{ i}[/tex]Finally, we can simplify inside of the square root:
[tex]\sqrt[]{72}i=\sqrt{6\ast6\ast2}i=\sqrt{6^2\ast2}i=6i\sqrt[]{2}^[/tex]Therefore, the correct answer is "6 i square root of 2".
Lucy you will use more than one out of two half s cup but less than one whole cup of flour for a recipe what fraction of a cup might lessy use explain
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Given:
Leslie will use more than ½ cup but less than 1 whole cup of flour for a recipe.
Let's find the fraction of a cup Leslie might use.
To find the fraction of a cup Leslie might use, find the fraction that is less than 1 whole and still more than ½.
To find the fraction of a cup Leslie might use, we have the fraction:
[tex]\frac{3}{4}[/tex]This is because the fraction, ¾, is less than 1 whole and it is still more than ½.
¾ is ¼ less than 1 whole and ¼ greater than ½
Therefore, the fraction of a cup Leslie might use is ¾
ANSWER:
[tex]\frac{3}{4}[/tex]Graph the following relation. Use the graph to find the domain and range (in interval form) and indicate whether the graph is the graph of a function.y=1/2x-4Domain:Range:Is it a function? Yes or no pick the correct one
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EXPLANATION :
From the problem, we have a linear function :
[tex]y=\frac{1}{2}x-4[/tex]We need 2 points to graph this function.
when x = 0 :
[tex]\begin{gathered} y=\frac{1}{2}(0)-4 \\ y=-4 \end{gathered}[/tex]when x = 2
[tex]\begin{gathered} y=\frac{1}{2}(2)-4 \\ y=-3 \end{gathered}[/tex]Plot the points (0, -4) and (2, -3)
Since the function is a continuous line, the domain and range are all real numbers.
Domain = (-∞, ∞)
Range = (-∞, ∞)
and since the graph is a line with a defined slope, this is a function
Which points are separated by a distance of 6 units? O A. (2, 4) (2, 2) B. (1,8) (1,2) c. (3, 1) (3,6) D. (5,6) (5,5)
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Recall that the distance formula is given by
[tex]d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}[/tex]We are asked to find out which of the given points have a distance of 6 units?
Let us analyze each option.
A. (2, 4) (2, 2)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({2-2_{}})^2+({2-4})^2} \\ d=\sqrt[]{({0})^2+({-2})^2} \\ d=\sqrt[]{4}^{} \\ d=2 \end{gathered}[/tex]Option A does not have a distance of 6 units, so it is not the correct option.
B. (1,8) (1,2)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({1-1})^2+({2-8})^2} \\ d=\sqrt[]{({0})^2+({-6})^2} \\ d=\sqrt[]{36}^{} \\ d=6 \end{gathered}[/tex]As you can see, the distance between these points is exactly 6 units.
Therefore, Option B is the correct answer.
c. (3, 1) (3,6)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({3-3})^2+({6-1})^2} \\ d=\sqrt[]{(0)^2+({5})^2} \\ d=\sqrt[]{25} \\ d=5 \end{gathered}[/tex]Option C does not have a distance of 6 units, so it is not the correct option.
D. (5,6) (5,5)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({5-5})^2+({5-6})^2} \\ d=\sqrt[]{({0})^2+({-1})^2} \\ d=\sqrt[]{1}^{} \\ d=1 \end{gathered}[/tex]Option D does not have a distance of 6 units, so it is not the correct option.
2. Write the equation of g(x) given the table below. X -2 --1 1 g(x) 3 6 12
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let us first calculate the slope:
[tex]m=\frac{6-3}{-1--2}=\frac{3}{1}=3[/tex]having the slope, we can use the slope-point equation and we get that
[tex]\begin{gathered} y-12=3(x-1)=3x-3 \\ y=3x-3+12=3x+9 \end{gathered}[/tex]so g(x)=3x+9
Which values of x would make a polynomial equal to zero if the factors of thepolynomial were (x+6) and (x+9)?
Answers
Given
(x+6) and (x+9) are the factors of a polynomial.
To find: Which values of x would make a polynomial equal to zero?
Explanation:
It is given that,
(x+6) and (x+9) are the factors of a polynomial.
Then, the polynomial can be written as,
[tex]p(x)=(x+6)(x+9)[/tex]Also, if (x+a) is a factor of a polynomial p(x).
Then, p(-a)=0.
Therefore,
For the factors (x+6) and (x+9),
The polynomial p(x) is zero at x=-6, and x=-9.
Hence, the answer is x = -6, -9.
find the answer fast pleaseee
Answers
Answer: (2 · (-4y)) + (2 · 2x) + (2 · (-3))
Step-by-step explanation: Distribute the 2 by multiplying each term in the parentheses by 2.
in the diagram, AB=9, DB=5, and BC=12. if m< B = 90, what is the perimeter of ADC ?
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To answer this question, we can draw the triangle as follows:
We can start answering this question, finding the value of the side AC (one of the sides of the triangle ADC (not shown)). Then, we can apply the Pythagorean Theorem to find AC (the hypotenuse in this case). Thus, we have:
[tex]AC^2=AB^2+BC^2\Rightarrow AC^2=(9)^2+(12)^2=81+144[/tex]Then, we have:
[tex]AC^2=225\Rightarrow\sqrt[]{AC^2}=\sqrt[]{225}\Rightarrow AC=15[/tex]Then, the measure of the side AC = 15.
Now, we need to find the measure of the side DC. We can also need to apply the Pythagorean Theorem to find it:
We have that DB = 5, and BC = 12. Then:
[tex]DC^2=DB^2+BC^2=5^2+12^2=25+144\Rightarrow DC^2=169[/tex]Now, we need to take the square root to both sides of the expression to solve for DC:
[tex]\sqrt[]{DC^2}=\sqrt[]{169}\Rightarrow DC=13[/tex]To find the perimeter of the triangle ADC, we have:
1. AD = AB - DB ---> AD = 9 - 5 ---> AD = 4 (we deduce this from the given data in the question.)
2. AC = 15 (found in the first step using the Pythagorean Theorem.)
3. DC = 13 ((found in the second step using the Pythagorean Theorem.)
Therefore, the perimeter of the triangle ADC is the sum of all of its sides, then, we have:
[tex]P_{\text{trangleADC}}=AD+AC+DC\Rightarrow P_{triangleADC}=4+15+13=32[/tex]Therefore, the perimeter of the triangle ADC is equal to 32 units.
(We can apply the Pythagorean Theorem twice since we have a right triangle in both cases: triangle ABC and triangle DBC.)
If you select one card at random from a standard deck of 52 cards, what is the probability that the card is black OR a 6?
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Since there are 52 cards in the standard deck
Since half of them are in black
Then the probability of getting a black card is
[tex]\begin{gathered} P(b)=\frac{\frac{52}{2}}{52} \\ P(b)=\frac{26}{52} \end{gathered}[/tex]Since there are 4 cards of 6, then
The probability of getting 6 is
[tex]P(6)=\frac{4}{52}[/tex]OR in probability means adding, then
The probability of getting a black card or a 6 is
[tex]\begin{gathered} P(b\text{ or 6)=}\frac{26}{52}+\frac{4}{52} \\ P(b\text{ or 6) =}\frac{30}{52} \end{gathered}[/tex]We can simplify it by dividing up and down by 2
[tex]\begin{gathered} P(b\text{ or 6)=}\frac{\frac{30}{2}}{\frac{52}{2}} \\ P(b\text{ or 6)=}\frac{15}{26} \end{gathered}[/tex]The answer is P(b or 6) = 30/52 OR 15/26
Rachel is bowling with her friends. Her bowling ball has a radius of 4.1 inches. As she bowls she tracks the location of the finger hole above the ground. She starts tracking the location when the finger hole is at the 12 o'clock position and she notices that she got some backspin on the ball and it rotates counter-clockwise.Write a function f that determines the height of the finger hole above the ground (in inches) in terms of the number of radians a the ball has rotated since she started tracking the finger hole. (Note that aa is a number of radians swept out from the 12-o'clock position.)f(a)=
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Given that radius is r= 4.1 inches.
let track the location of finger hole is at 12 o'clock.
i.e. the angle is 0 degree.
at 12 o'clock
[tex]\theta=0[/tex]Now when the finger hole changed by 45 degree:
[tex]\theta=45[/tex]Now convert 45 degree into radians:
[tex]\begin{gathered} \theta=45\times\frac{\pi}{180} \\ \theta=\frac{\pi}{4} \end{gathered}[/tex]So angle is such that:
[tex]\begin{gathered} \theta\in\lbrack0,\frac{\pi}{4}\rbrack \\ 0\leq\theta\leq\frac{\pi}{4} \end{gathered}[/tex]Now calculate the measure of function in polar coordinates:
[tex]\begin{gathered} \theta=0,\text{ f(}\theta\text{)}=r \\ \theta=\frac{\pi}{2},\text{ f(}\theta)=r\cos \theta \end{gathered}[/tex]Taking measurement of function:
[tex]\begin{gathered} f(\theta)=r+r\cos \theta \\ f(\theta)=r(1+\cos \theta) \end{gathered}[/tex]So the function become and the limit is:
[tex]f(\theta)=r(1+\cos \theta),\text{ 0}\leq\theta\leq\frac{\pi}{4}[/tex]find the smallest non negative value for x in degrees that makes the equation cot (x) = 0 true.
Answers
It is given that,
cot (x) = 0
To find the smallest non-negative value for x in degrees:
So that,
[tex]\begin{gathered} \cot (x)=0 \\ \cot (x)=\cot (90^{\circ}) \\ x=90^{\circ} \end{gathered}[/tex]Hence, the smallest value of x is 90 degrees.
Question 3The length of a rectangle is 5 less than three times the width. Ifthe perimeter is 174, which equation could be used to find thedimensions?A4x - 5 = 1746x - 10 = 174B8x - 10 = 174D8x = 1741 point Can someone also help me with the rest
Answers
ANSWER
B. 8w - 10 = 174
EXPLANATION
The length of the rectangle is 5 less than 3 times the width.
Let the length be L.
Let the width be w.
This means that:
L = 3 * w - 5
L = 3w - 5
The perimeter of a rectangle is given as:
P = 2(L + w)
The perimeter of the rectangle is 174. This means that:
174 = 2L + 2w
Recall:
L = 3w - 5
=> 174 = 2(3w - 5) + 2w
174 = 6w - 10 + 2w
=> 8w - 10 = 174
That is Option B
What are the Characteristics for rhombus
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The characteristics of a rhombus are the following:
• Opposite sides are parallel ang congruent (equal)
,• The diagonal lines are bisectors (they cut in half) the internal angles
,• The two diagonals have different legths (usually represented by d and D)
,• The point where the two diagonals meet is the center of the rhombus
These are some unfinished calculations. Complete them to find each difference
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for 2nd question
[tex]\begin{gathered} 9\frac{4}{8}-5\frac{1}{8}=\frac{76}{8}-\frac{41}{8} \\ =\frac{76-41}{8}=\frac{35}{8}\text{ or 4}\frac{3}{8} \end{gathered}[/tex]for 3rd question,
[tex]\begin{gathered} 9\frac{4}{8}-3\frac{5}{8}=\frac{76}{8}-\frac{29}{8} \\ =\frac{76-29}{8}=\frac{47}{8}\text{ or 5}\frac{7}{8} \end{gathered}[/tex]for 4th question,
[tex]\begin{gathered} 5\frac{1}{8}-3\frac{5}{8}=\frac{41}{8}-\frac{29}{8} \\ =\frac{41-29}{8}=\frac{12}{8}=\frac{3}{2}\text{ or 1}\frac{1}{2} \end{gathered}[/tex]#5There are 357 students at Rydell MiddleSchool. The students were asked to choosetheir favorite class. Of the 21 students inHomeroom A, 8 students chose CSI as theirfavorite. Based on these results, how manyof the students in Rydell Middle Schoolwould you expect to choose CSI as theirfavorite class?
Answers
We could write the following proportion and then solve for x:
Therefore, we could expect that 136 students chose CSI as their favorite class in Rydell Middle School.
10. A system of equations is shown below.3x - y = 10y = 4x-8What is the value of x - y of the solution to the system?C. 14A -98D. 62B-18
Answers
Given:
3x - y = 10
y = 4x-8
Required:
What is the value of x - y of the solution to the system?
Explanation:
3x - y = 10
y = 4x-8
substitute into one of the equations
[tex]\begin{gathered} 3x-(4x-8)=10 \\ \\ combine\text{ like terms} \\ \\ -x+8=10 \\ \\ -x=2 \\ \\ x=-2 \end{gathered}[/tex][tex]\begin{gathered} substitute\text{ value of x} \\ \\ 3\times(-2)-y=10 \\ \\ -6-y=10 \\ \\ -y=10+6 \\ \\ -y=16 \\ \\ y=-16 \end{gathered}[/tex][tex]\begin{gathered} substitute\text{ value into x-y:} \\ \\ -2-(-16) \\ \\ -2+16 \\ \\ 14 \end{gathered}[/tex]Required answer:
C. 14
john wants to purchase a boat that costs $1,500. He signs an installment agreement requiring a 20% down payment. How much will john need for the down payment
Answers
Answer:
$300 down payment
Step-by-step explanation:
John wants to purchase a boat that costs $1,500. He signs an installment agreement requiring a 20% down payment. How much will john need for the down payment
20% = 0.20
0.20 * 1,500 = $300 down payment
In the diagram below of parallelogram ROCK,mZC is 70° and mZROS is 65º.Oс70%650RSK.What is mZKSO?
Answers
Answer:
∠KSO = 135°
Explanation:
On a parallelogram, the opposite angles have the same measure. It means that the measure of ∠R is:
∠R = ∠C
∠R = 70°
On the other hand, the sum of the interior angles of a triangle is equal to 180°, so we can calculate the measure of ∠RSO as:
∠RSO = 180 - ∠ROS - ∠R
∠RSO = 180 - 65 - 70
∠RSO = 45°
Because the angles RSO, ROS, and R form the triangle ROS.
Finally, ∠RSO and ∠KSO form a straight line, so their sum is equal to 180°. Then, we can calculate ∠KSO as:
∠KSO = 180 - ∠RSO
∠KSO = 180 - 45
∠KSO = 135°
Then, the answer is 135°
which statement describes the sequence -9,-3,3,9,15,
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This sequence can be represented by the following formula:
an = 3(2n - 5)
n ∈ N
How does linear inequality work?
Answers
To graph a inequality we first need to grapg the equality, in this case the line y=3-1/3x, and then we check which of the two sets of points fullfil the inequality and paint this set. in this case the inequality is estrict so it doesn't include the boundary line.
f(x) = 2.5x - 10.5if X= 2
Answers
Answer:
-5.5
Explanation:
Gven the below function;
[tex]f(x)=2.5x-10.5[/tex]when x = 2, it means we should substitute x = 2 into the above function or find f(2);
[tex]\begin{gathered} f(2)=2.5(2)-10.5 \\ =5-10.5 \\ =-5.5 \\ \therefore f(2)=-5.5 \end{gathered}[/tex]A company needs to create a concrete foundation 3 feet deep measuring 56‘ x 26‘, outside dimensions, with walls 5 inch thick how many cubic yards of concrete will they need?
Answers
We are asked to determine the volume of the concrete wall with the given dimensions. To do that we will determine the volume of the exterior prism with dimensions 56ft, 26ft, and 3ft. This volume is given by the product of its dimensions:
[tex]V_e=(56ft)(26ft)(3ft)[/tex]Solving the operations we get:
[tex]V_e=4368ft^3[/tex]Now, we need to determine the interior volume. That is the prism that is inside the foundation. To determine the dimensions we need to convert 5 inches to feet. To do that we will use the following conversion factor:
[tex]1ft=12in[/tex]Multiplying by the conversion factor we get:
[tex]5in\times\frac{1ft}{12in}=0.42ft[/tex]Now we determine the length and width of the inside prism. To do that we use the following:
Therefore, we need to subtract 2 times 5 inches to each of the exterior dimensions to get the inner dimensions, therefore, the interior volume is:
[tex]V_i=(56ft-2(5in))(26ft-2(5in))(3ft)[/tex]Substituting the inches we get:
[tex]V_i=(56ft-0.83ft)(26ft-0.83ft)(3ft)[/tex]Solving the operations:
[tex]V_i=4165.89ft^3[/tex]Now, the volume of the wall is the difference between the exterior volume and the interior volume. Therefore:
[tex]V=V_e-V_i[/tex]Substituting the values we get:
[tex]\begin{gathered} V=4368ft^3-4165.89ft^3 \\ V=202.11ft^3 \end{gathered}[/tex]Since we need to express the solution in cubic yards we will use the following conversion factor:
[tex]1yd^3=27ft^3[/tex]Multiplying by the conversion factor we get:
[tex]202.11ft^3\times\frac{1yd^3}{27ft^3}=7.49yd^3[/tex]Therefore, 7.5 cubic yards are needed.
How do I turn 19/40 in to a % thanks
Answers
multiply the expression by 100 to make it into percentage :
[tex]\begin{gathered} \frac{19}{40\text{ into percenatge }}\text{= 0.475}\times100\text{ } \\ \\ \frac{19}{40\text{ into percenatge }}\text{== 0.475}\times100 \\ \frac{19}{40\text{ into percenatge }}\text{= 47.5\%} \end{gathered}[/tex]Answer : 47.5 %