Answer: the complex solutions are:
Step-by-step explanation: x = 5i , -5i , 3/5 ,-2
How many pairs of parallel edges are there this rectangular prism
Answer:
6 i think
Step-by-step explanation:
if you count the top and bottom one, thats 2, the two sides, and the front and back. add 2+2+2 which is 6.
Which of the following equations describes the line shown below? Check allthat apply.(-5,6)(-1,-1)
Options E and F are the correct options
Here, we need to get the equation of the line that passes through the two points given
Mathematically, the equation of a line can be generally expressed as ;
y = mx + c
where m is the slope of the line and c is the y-intercept of the lien ( where it crosses the y-axis)
To get the slope m , we are goint to use the formula below;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_{2\text{ - }}x_1} \\ \\ x_{1\text{ }}=-5,x_2=-1,y_1\text{ = }6,y_2\text{ = -1} \end{gathered}[/tex]Substituting these values into the slope equation , we have
m = (-1-(6))/(-1-(-5)) = -7/4
The equation is now in the form;
y = -7x/4 + c
what is left is to get the y-intercept
We can get the value of the y-intercept by substituting for x and y using any of the points
Let us use the second point
Here, x = -1 and y = -1
Thus;
-1 = -7(-1)/4 + c
-1 = 7/4 + c
c = -1-7/4 = -11/4
So the complete equation of the line is;
y = -7x/4 - 11/4
To properly answer the questions, we need the forms in the options that looks like or can be manipulated arithmetically to look like what we have as our answer
We proceed with each of the options one after the other to see if they can be written in the form of our answer
Option A
y - 5 = -7/4 ( x + 6)
Opening the bracket and evaluating;
y - 5 = -7x/4 - 42/4
y = -7x/4 -42/4 + 5
y = -7x/4 -22/4
we can see this is not a correct option
Option B
y - 6 = -4/7 (x + 5)
Multiply through by 7
7y - 42 = -4x - 20
7y = -4x - 20 + 42
7y = -4x + 22
divide through by 7
y = -4x/7 + 22/7
We can see this is incorrect also
Option C
y - 1 = -4/7(x-1)
Multiply through by 7
7y - 7 = -4x + 4
7y = -4x + 4 + 7
7y = -4x + 11
divide through by 7
y = -4x/7 + 11/7
This is incorrect too
Option D
y + 1 = -4/7 ( x + 1)
Multiply through by 7
7y + 7 = -4x - 4
7y = -4x -4 -7
7y = -4x - 11
y = -4x/7 - 11/7
This is incorrect also
Option E
y - 6 = -7/4 (x + 5)
Multiply through by 4
4y - 24 = -7x - 35
4y = -7x - 35 + 24
4y = -7x -11
y = -7x/4 - 11/4
This is a correct option
Option F
y + 1 = -7/4 ( x + 1)
Multiply through by 4
4y + 4 = -7x - 7
4y = -7x - 7-4
4y = -7x - 11
y = -7x/4 - 11/4
This is a correct option too
Triangle J is shown below. James drew a scale version of Triangle J using a scale factor of 4 and labeled it Triangle K. What is the area of triangle K
James used a scale factor of 4 to draw a scale representation of Triangle J and named it. Triangle K’s surface area is 10.
What are the triangle’s three main components?Every triangle has three corners and three sides (angles). The vertex of a triangle is the intersection of two sides.
Any one of a triangle’s three sides might serve as its foundation, although most frequently it is the bottom side.
Below, Triangle J is depicted. James used a scale factor of 4 to create a scale version of Triangle J that he dubbed Triangle K.
How big is triangle K’s surface area?Area= 1/2 bh
=(1/2)*4*5
=10In such a case, K’s triangle’s area is 10.
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Note: The question is incomplete in the portal. Here is the total question,
Question: Triangle J is shown below. James drew a scaled version of Triangle J using a scale factor of and labeled it Triangle K. What is the area of Triangle
A line passes through the point (4,-7) and has a slope of -6 write an equation in slope intercept form for this line
find 5 consecutive odd integers who's sum is -45(solve algebraically)
let the consecutive odd integers be
x, x+ 1, x+ 2, x + 3, x + 4
Average = sum / total number
Average = -45
Total number = 5
-45 = x + x + 1 + x + 2 + x + 3 + x + 4 / 5
Introduce cross multiplication
-45 x 5 = x + x + 1 + x + 2 + x + 3 + x + 4
-225 = x + x + x + x + x + 1 + 3 + 4 + 5
-225 = 5x + 16
If f(x)=x²-3x+5 and g(x)=-2x, find the following composition.
(f ° g)(2)
(f ° g)(2) = ____ (Simplify your answer.)
The value of the composite function (fog)(2) is equivalent to 0
Composite functionsA mathematical procedure called "function composition" combines two functions, f and g, to produce a third function, h, where g is the sum of f and
Given the functions below;
f(x) = x^2-3x+5
g(x) = -2x
Determine the composite function (gof)(2)
(fog) = f(g(x))
f(g(x)) = g(x^2-3x+5)
f(g(x)) = -2(x^2-3x+5)
f(g(2)) = -2(2^2-3(2)+2)
f(g(2)) = -2(0) = 0
This gives the equivalent composite value
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Adding: If the two values have the same sign, then?
And use the same sign.
and use the same sign
Using the addition rule with different signs, we know that the resultant answer will have the same sign.
What is Addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.Same Sign - When adding absolute values, use the same sign for the result.Different Signs - Denote the result with the same sign as the number with the bigger absolute value after subtracting the smaller absolute value from the larger absolute value.Subtracting signs - The opposite of an integer number is added when subtracting an integer.A general example to help you recognize patterns:
Adding Integers:
(−3)+2=−121+(−28)=−79+(−9)=0Subtracting Integers:
−3−(−9)=−3+9=6−7−8=−7+(−8)=−15Therefore, using the addition rule with different signs, we know that the resultant answer will have the same sign.
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How do I turn the contents of the passage into an equation?Her phone bill, the cost of diapers, and the subscriptions and pizza for her son. I guess I have to give her an amount to start with, so I’ll go with she started with $100.What if the subscriptions and pizza were 65. The diapers were 30. And her phone bill is 150. Can you show how much she paid toward the diapers and phone bill?
Let G be the cost os monthly game subscriptions, P the cost of a wekly phone bill, D = $30 the cost of a package of 42 diapers, F the cost of pizza on fridays and W the amount she receives each workday.
Then, for a initial amount I = $100, the money M she still have after the events in the text is given by:
[tex]\begin{gathered} M=(W+I)-(G+P+D+F) \\ M=(W+100)-(G+P+30+F) \\ M=W+70-G-P-F \end{gathered}[/tex]If F + G = $65 and P = $150, we have:
[tex]\begin{gathered} M=W+70-65-150 \\ M=W-145 \end{gathered}[/tex]If we are considering only how much she payed for the diapers and the phone bill, we have:
[tex]D+P=30+150=\text{ \$}180[/tex]
Please help I will mark branlist
Answer: True
Step-by-step explanation:
I believe it's true since a quadratic equation can either have one real solution, two real solutions, or no real solutions. Hope this helps.
how many 4 letter code words can be made using the letters in the word pencil
Combination is a way of selecting items from a collection where the order of selection does not matter.
The number of 4-letter code words that can be made using the letters in the word pencil is 15.
What is combination?Combination is a way of selecting items from a collection where the order of selection does not matter.
We have,
Total number of letters in the word pencil = 6
i,e P E N C I L
Combination formula:
[tex]^nC_r[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
Here,
n = 6
r = 4
The number of 4-letter code words that can be made using the letters in the word pencil:
[tex]^6C_4[/tex] = 6! / 4! 2! = (6 x 5) / 2= 15
Thus,
The number of 4-letter code words that can be made using the letters in the word pencil is 15.
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Simplify using exponent: B³ x B⁵
HELPPPPPP
Answer:
B⁸
Step-by-step explanation:
When you have the same base, which in this case is B, you add the exponents and you get 8.
Hope this helps!
P.S, could I get Brainliest? Thanks!
what is the displacement of a hiker who first walks 1.5 km north, then walked back 0.45 km south, then walks 3.2km north?
Answer:
5.0 km.
Step-by-step explanation:
Answer: 4.25 Km
Step-by-step explanation:
First you're going to consider the first number given as the main one to start with. (1.5 km)
The question told you that the hiker first went north so you can consider north positive, then he walked back south 0.45 km.
So far your calculation should be 1.5 - 0.45 = 1.05
Then the hiker walks again north with a distance of 3.2 km
so now add that to your value (1.05) as 1.5 and 3.2 are going to the same direction and 0.45 is only opposing them
Final calculation: 1.05 + 3.2 = 4.25 (1.5 - 0.45 + 3.2)
Another way of explaination if you didn't get this one:
The two values 1.5 and 3.2 are mentioned to be in the same direction (north), while 0.45 is mentioned to be opposing them going south, so you can either consider it as
(+)1.5 + 3.2 - 0.45 (But this one would make more sense)
Or
- 1.5 - 3.2 + 0.45
Hope you understood and good luck with your studies :D
I was explained this by another tutor but it didn't make too much sense
Given a right angle triangle
The hypotenuse of the triangle = x
The adjacent side to the angle 50 = 6
We will find x using the cosine function as follows:
[tex]\begin{gathered} \cos 50=\frac{adjacent}{hypotenuse} \\ \\ \cos 50=\frac{6}{x} \\ \\ x=\frac{6}{\cos 50}=9.334 \end{gathered}[/tex]Rounding to the nearest tenth
So, the answer will be x = 9.3
Central Bank pays 8.5% interest, compounded daily, from the date of deposit to the date of withdrawal. The daily interest rate (to the nearest millionths place) forJuly 28 (92 days in the quarter) on this account is:0.000198.0.0002070.000231.0.000216None of these choices are correct.
ofGiven the yearly interest rate as 8.5%
To find the daily interest, we will divide the yearly interest rate by 365 as shown below:
[tex]\text{daily interest rate=}\frac{yearly\text{ interest rate}}{365}[/tex][tex]\text{daily interest rate=}\frac{\frac{8.5}{100}}{365}=\frac{0.085}{365}=0.0002328767[/tex]Hence, the daily interest rate (to the nearest millionths place)= 0.000232, The third option
The diameter of Mars is about 9^4 kilometers. Write 9^4 as a product. Then find the value of the product.
The graphs below have the same shape. f(x) = x2What is the equation of the graph of g(x)?10g(x)f(x)X10510-10O A. g(x) = (x+3)2B. g(x) = (x - 3)2C. g(x) = x2 - 3D. g(x) = x2 + 3
The equation of f(x) is
[tex]f(x)=x^2[/tex]The graph of g(x) is shifted 3 units to the left. This is a horizontal translation.
For horizontal translation, we follow the following rule >>>
Let parent function be f(x), then
• f(x+a) is the parent translated "a" units left
,• f(x-a) is the parent translated "a" units right
Thus, following the rule, we can clearly say that g(x) = f(x+3)
We can write >>
Evaluate f(3) for f(x)=2x+6
Which graph represents this equation?y = 3:2 - 61ОА.+X-4No26-24-6B.24N- 2C.
To determine which one is the graph of the equation:
[tex]y=\frac{3}{2}x^2-6x[/tex]We can finc the x-intercepts of the equations, we know that this happens when y=0, then we have:
[tex]\frac{3}{2}x^2-6x=0[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{3}{2}x^2-6x=0 \\ x(\frac{3}{2}x-6)=0 \\ \text{then} \\ x=0 \\ or \\ \frac{3}{2}x-6=0 \\ \frac{3}{2}x=6 \\ x=\frac{2}{3}\cdot6 \\ x=4 \end{gathered}[/tex]This means that the the graph have to cross the x axis in the values x=0 and x=4.
Looking at the options we notice that the only graph that do this is option B, therefore the gaprh of the equation is shown on B.
Can you help me find the slope, y-intercept, and the equation based off this chart?
y-interceptis As given by the question
There are given that the value of x and y.
Now,
For finding the value of the slope, choose two-point from the given table
So,
Suppose the two points are:
[tex](1,\text{ 5) and (}3,\text{ 3)}[/tex]Now,
From the formula of slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=1,y_1=5,x_2=3,y_2=3[/tex]Put all the above value into the given formula
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3_{}-5_{}}{3_{}-1_{}} \\ m=-\frac{2}{2} \\ m=-1 \end{gathered}[/tex]Hence, the value of the slope is -1.
Now,
For the equation of the line that is based on the given chart, use two supposes point and the given slope.
So,
The two poin and slope is:
[tex](1,\text{ 5) and (3, 3) and m=-1}[/tex]Then,
From the formula of two point form;
[tex](y-y_1)=m(x-x_1)[/tex]Where,
[tex]x_1=1,y_1=5,x_2=3,y_2=3,\text{ m=-1}[/tex]Then,
Put all the given value into the above formula
So,
[tex]\begin{gathered} (y-y_1)=m(x-x_1) \\ (y-5_{})=-1(x-1_{}) \\ (y-5)=-x+1 \\ y-5+x-1=0 \\ y+x-6=0 \end{gathered}[/tex]Hence, the equation of the line is:
[tex]y=-x+6[/tex]Now,
To find the y-intercept, put x=0 and solve for x
So,
The y intercept of the given equation is:
[tex]\begin{gathered} y=-x+6 \\ y=-(0)+6 \\ y=6 \end{gathered}[/tex]Hence, the y-intercept is (0, 6)
x + y = 5 17x + 4y = 46 ) Find the solution to the system of equations. Write it as an ordered pair below.
we have
x + y = 5 -----> equation A
17x + 4y = 46 ------> equation B
Solve the system by substitution
step 1
isolate the variable x in equation A
x=5-y ------> equation C
step 2
substitute equation C in equation B
17(5-y)+4y=46
solve for y
85-17y+4y=46
17y-4y=85-46
13y=39
y=3
Find the value of x
x=5-y
x=5-3=2
thereforethe solution is the ordered pair (2,3)Build Understanding ACTIVITY When two lines are cut by a third line, the third line is called a transversal. The intersections of the lines form eight angles, including five special types of angle pairs. When the two lines cut by a transversal are parallel, as shown, the angles in any of the special pairs will be either congruent or supplementary. 1/2 3/4 5/6 7/8 1 The term alternate means that two angles are on opposite sides of the transversal. A. Alternate interior angles are angles on opposite sides of the transversal inside the parallel lines. Measure a pair of alternate interior angles with a protractor. Name the angles you found. Are they congruent or supplementary?
Answer
First of, let us explain what congruent and supplementary mean.
Congruent angles are equal to each other.
Supplementary angles add up to give 180 degrees.
A) Alternate interior angles are congruent. Examples of alternate interior angles from the image include
- angles 3 and 6.
- angles 4 and 5.
B) Alternate exterior angles are congruent. Examples of alternate exterior angles from this image include
- angles 1 and 8.
- angles 2 and 7.
C) Same-side interior angles are supplemetary. Examples of same-side interior angles from the image include
- angles 3 and 5.
- angles 4 and 6.
D) Same-side corresponding angles are also supplementary. Examples of same-side exterior angles from the image include
- angles 1 and 7.
- angles 2 and 8.
E) Corresponding angles for two parallel lines are congruent. Examples of corresponding angles from the image include
- angles 1 and 5.
- angles 2 and 6.
- angles 3 and 7.
- angles 4 and 8.
Hope this Helps!!!
HELP PLEASE AND THANK YOUMelinda and Paul ran in a marathon. this this graph shows the relationship between the distance and the time they each run. Melinda ran a constant speed of 5 mph. Paul ran at a ____ constant speed than Melinda. an equation that could represent the relationship between Paul's distance and his time is y = _____x, where x is the time in hours and y is the distance in miles Paul ran.THE ANSWER CHOICES ARE 1) FASTER OR SLOWER 2) 1 , 3 , 5 , 7 to complete the sentence !
When a line is steeper than other one it means it has a greater slope. In this case the slope represents the speed of Melinda and Paul. As shown in the picture, the line that represents Paul's movement has a greater slope than the one that represents Melinda's, it means Paul ran at a faster constant speed than Melinda.
If Melinda ran at a constant velocity of 5mph and Paul ran faster than her, an equation that could represent the relationship between Paul's distance an his time has to have a greater slope than 5, which is 7.
tommie works at a local store on the weekends. He earns $11.50 per hourr. tommie will get a 10% raise after working 4 weeks. How much will he make per hour after his raise?
Tommie will earn $12.65 per hour after his 10% raise after 4 weeks.
What is Percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Given is tommie who earns $11.50 per hour and he will get a 10% raise after working 4 weeks.
The amount tommy will earn after 10% raise can be calculated as follows-
10% of 11.50
10/100 x 11.5
1.15
Earnings per hour after raise = 11.5 + 1.15 = $12.65
Therefore, tommie will earn $12.65 per hour after his 10% raise after 4 weeks.
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I want answer. I need t’s solution.And I want explanation too.
we have the equation
[tex]log(\frac{1,000}{253.95})=12tlog(1+\frac{0.08}{12})[/tex]Solve for t
That means
Isolate the variable t
[tex]t=\frac{log(\frac{1,000}{253.95})}{12log(1+\frac{0.08}{12})}[/tex][tex]t=17.2[/tex]PLS HELP ASAP WILL GIVE BRAINLIST
The angles in the parallelogram is as follows:
a = 27°b = 55°c = 55°How to find angles in a parallelogram?A parallelogram is a quadrilateral with opposite sides equal to each other and opposite side parallel to each other.
The diagonal of a parallelogram bisect each other.
Therefore, the angles a, b and c in the parallelogram can be found as follows:
180 - 118 - 35 = a (sum of angles in a triangle)
180 - 153 = a
a = 27 degrees.
Therefore, let's find angle b.
62 + 63 + b = 180 (sum of angles in a triangle)
125 + b = 180
180 - 125 = b
b = 55 degrees
Let's find the angle c
Hence,
b = c (alternate angles)
Therefore,
c = 55 degrees.
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hhhelpppppppppppppppppp meeeeeeeee
Answer: she does an average of -0.07
Step-by-step explanation:
add the all up which equals -0.35 divide that by how many there are which equals -0.07
Question 1 (10 points)
Listen ▶
Twelve major Earthquakes had Richter magnitudes shown here.
6.8 6.0 7.5 6.8 6.2 6.0 7.0 5.2 6.2 6.3 7.0 5.2
Find Mean
5.35
6.35
7.35
6.95
for the first week of January,Patricia Morgan worked 46 hours. Patricia earns $9.70 an hour. her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours. calculate the following for the first week of January ( round your responses to the nearest cent if necessary) regular pay amount, overtime pay, gross pay
Answer
Regular pay = $388
Overtime pay = $87.3
Gross pay = $388 + $87.3
= $475.3
Explanation
During the first week of January, Patricia Morgan worked 46 hours at a rate of $9.70 per hour for regular hours.
For overtime, the pay is 1.5 times the normal rate. That is, 1.5 × $9.70 = $14.55
So, working for 46 hours, that is, 40 hours regular pay rate, and 6 hours overtime pay rate.
Regular pay = 40 × $9.70 = $388
Overtime pay = 6 × $14.55 = $87.3
Gross pay = Regular pay + Overtime pay
= $388 + $87.3
= $475.3
Hope this Helps!!!
Convert 489 degrees into radians.10.54 radians9 radians8.53 radians15.73 radians
To convert the degree to radian use this rule
[tex]x(radian)=\frac{x^{\circ}}{180}\times\pi[/tex]Substitute x by 489 and pi by 22/7
[tex]\begin{gathered} x(radian)=\frac{489}{180}\times\frac{22}{7} \\ \\ x(radian)=8.53 \end{gathered}[/tex]The answer is 8.53 radians the 3rd choice
Suppose that Kevin's checking account shows a balance of $910.25 at the beginning of the month. During this month, he makes deposits of $175.35, $472.25, $235.40, and $450.15, and he writes checks for $307.50, $289.25, $150.30, and $327.00. Find the end-of-the-month balance in his account.
Answer:
The answer is $1,169.35
Step-by-step explanation:
Deposits is when you put money into your account, so, you'll add what he deposits. which will be $2,242.4, Next when he writes a check it means he took money out of his account so you'll subtract. You'll add up the amount of checks he wrote and subtract your answer with the deposits so, $2,243.4, - $1,074.05 = 1,169.35 and thats how you get your answer.