1) Let's multiply the second equation by -2, to eliminate x
2x -3y=-11
x+3y = 8
2) Now let's add both equations
2x -3y=-11
-2x-6y = -16
--------------------
-9y = -27
3) Divide both by -9
y=3
4) Plug y=3 into the simpler original equation, to make calculations easier:
x +3y=8
x+3(3) =8
x +9 =8 Subtract 9 from both sides
x = 8-9
x=-1
So, after multiplying it we add both equations to eliminate one variable either x or y.
find all other zeros of p (x)= x^3-x^2+8x+10, given that 1+3i is a zero. ( if there is more than one zero, separate them with commas.)edit: if possible please double check answers would high appreciate it.
Since we have that 1 + 3i is one zero of p(x), then we have that its conjugate is also a root, then, we have the following complex roots for p(x):
[tex]\begin{gathered} x=1-3i \\ x=1+3i \end{gathered}[/tex]also, notice that if we evaluate -1 on p(x), we get:
[tex]\begin{gathered} p(-1)=(-1)^3-(-1)^2+8(-1)+10=-1-1-8+10 \\ =-10+10=0 \end{gathered}[/tex]therefore, the zeros of p(x) are:
x = 1-3i
x = 1+3i
x = -1
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The objective function ( S for score ) in the given linear programming problem is S = 3x + 5y , the correct option is (a) .
In the question ,
it is given that ,
number of points that a multiple choice question gives = 3 points
number of points that a short answer gives gives = 5 points ,
let the number of multiple choice questions be = x
let the number of short answer questions be = y ,
the final score is denoted by S ,
So , the function , to represent the above situation is ,
S = 3x + 5y
Therefore , The objective function ( S for score ) in the given linear programming problem is S = 3x + 5y , the correct option is (a) .
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Simplify the expression below. Share all work/thinking/calculations to earn full credit. You may want to do the work on paper and then upload an image of your written work rather than try and type your work. \sqrt[4]{ \frac{162x^6}{16x^4} }
Express the following expression in the form of a + bi : (16 + 6i) ((12 - 10i) - (2 - 5i))
Given:
There is an expression given as below
[tex]\left(16+6i\right)(\left(12-10i\right)-(2-5i))[/tex]Required:
We need to simplify the given expression and express in form of a+ib
Explanation:
[tex]\begin{gathered} (16+6i)((12-10i)-(2-5i)) \\ =(16+6i)(12-10i-2+5i) \\ =(16+6i)(10-5i) \\ =160-80i+60i+30 \\ =190-20i \end{gathered}[/tex]Final answer:
a + ib = 190 - 20i
Subtract and simplify: (6 + 10i) – (11 + 7i)
Given:
an expression is given as (6 + 10i) - (11 + 7i)
Find:
we have to subtract and simplify the expression.
Explanation:
(6 + 10i) - (11 + 7i) = 6 + 10i - 11 -7i = (6 - 11) + ( 10i - 7i) = -5 + 3i
Therefore, (6 + 10i) - (11 + 7i) = -5 + 3i
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 18 people took the trip. She was able to purchase coach tickets for $170 and first class tickets for $1010. She used her total budget for airfare for the trip, which was $10620. How many first class tickets did she buy? How many coach tickets did she buy:
Explanation
Let the number of people with coach tickets be x and the number of people with first class tickets be y. Since the trip goers contained a total of 18 people we will have;
[tex]x+y=18[/tex]A coach ticket cost $170 dollars and the first class tickets cost $1010. Also, Sarah spent a total of $10620 to buy the tickets. This would give us;
[tex]170x+1010y=10620[/tex]We will now solve the equation simultaneously.
[tex]\begin{gathered} \begin{bmatrix}x+y=18\\ 170x+1010y=10620\end{bmatrix} \\ isolate\text{ for x in equation 1}\Rightarrow x=18-y \\ \mathrm{Substitute\:}x=18-y\text{ in equation 2} \\ 170\left(18-y\right)+1010y=10620 \\ 3060+840y=10620 \\ 840y=10620-3060 \\ 840y=7560 \\ y=\frac{7560}{840} \\ y=9 \\ \end{gathered}[/tex]We will substiuite y =9 in x=18-y. Therefore;
[tex]\begin{gathered} x=18-9=9 \\ x=9 \end{gathered}[/tex]Answer: From the above, Sarah bought 9 coach tickets and 9 first-class tickets.
For questions 5-6, g(x) is a transformation of f(x) = x2. What is the function g(x) that is represented by the graph? QUESTION 5
The transformation in question 5 shows a shift to the left by 3 units.
A shift to the left by b units has the rule:
[tex]f(x)\to f(x+b)[/tex]Therefore, the shift to the left by 3 units will yield the function:
[tex]x^2\to(x+3)^2[/tex]Hence, the function g(x) will be:
[tex]g(x)=(x+3)^2[/tex]Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Equations that have the roots of x = 2 and x = -2 are:
(A) x² - 4 = 0(D) 4x² = 16What exactly are equations?In mathematical formulas, the equals sign is used to indicate that two expressions are equal. A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation. Like 3x + 5 = 15, for instance. Equations come in a wide variety of forms, including linear, quadratic, cubic, and others. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, equations true for x = 2 and x = -2 are:
Roots of x = -2:
x² = 4x² - 4 = 0Roots of x = 2:
x² = 4Now, multiply 4 on both sides as follows:
4x² = 16Therefore, equations that have the roots of x = 2 and x = -2 are:
(A) x² - 4 = 0(D) 4x² = 16Know more about equations here:
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Correct question:
Which equations are true for x = –2 and x = 2? Select two options
A. x2 – 4 = 0
B. x2 = –4 3
C. x2 + 12 = 0
D. 4x2 = 16
E. 2(x – 2)2 = 0
The English Channel is the waterway between England and France. It is about 21 kilometers across, and many people have successfully swam across it. In the United States, many pools at gyms are 25 yards long, and 1 lap equals the pool length.Assuming a person swims in a straight line, how can you calculate the number of complete laps a person must swim in a 25-yard pool to equal swimming across the English Channel?A) First, convert the distance across the channel to approximately 13 miles. Next, convert the distance in miles to 22,880 feet. Then, convert the pool length to 75 feet. Finally, multiply the distance by 1 lap 75 ft. to get about 305 laps.B) First, convert the distance across the channel to approximately 34 miles. Next, convert the distance in miles to 179,520 feet. Then, convert the distance in feet to 59,840 yards. Finally, multiply the distance by 1 lap 25 yd. to get about 2,394 laps.C) First, convert the distance across the channel to approximately 34 miles. Next, convert the distance in miles to 59,840 feet. Then, convert the pool length to 75 feet. Finally, multiply the distance by 1 lap 75 ft. to get about 798 lapsD) First, convert the distance across the channel to approximately 13 miles. Next, convert the distance in miles to 68,640 feet. Then, convert the distance in feet to 22,880 yards. Finally, multiply the distance by 1 lap 25 yd. to get about 915 laps.
The first step to find the correct answer indeed is to convert the distance across the channel from kilometers to miles.
Because 1 km is equal to approximately 0.62 miles, 21 kilometers will be just 21 times the 0.62 miles. From this, we are able to calculate the following:
[tex]\begin{gathered} 25\operatorname{km}=25\times0.62mi \\ 25\operatorname{km}\text{ }\cong13mi \end{gathered}[/tex]From this, we are able to say that the correct answer is not B or C.
Now, because 1 mi is equal to 5,280 ft, we can say that 13 mi is equal to 13 times 5,280 ft. From this, we calculate:
[tex]\begin{gathered} 13mi=13\times5,280ft \\ 13mi=68,640ft \end{gathered}[/tex]From this, we are able to say that the correct answer is not A also. To convert it to yards, we need to remember that 1 foot is equal to (1/3) yards, which means that 68,640 ft is equal to 68,640 times (1/3) yards. Calculating, we get the following:
[tex]\begin{gathered} 68,640ft=68,640\times\frac{1}{3}yd \\ 68,640ft=22,880yd \end{gathered}[/tex]Because the lap in the pool is 25 yd, we need to DIVIDE, not to multiply, the distance of the channel in yards we found by the distance of the pool, which is 25 yd.
From this, we get the following answer:
[tex]N_{of\text{ laps}}=\frac{22,880yd}{25\frac{yd}{lap}}=915.2\text{ laps}[/tex]From this, we know that the number of laps a person who wants to swim the same distance of the channel mentioned is equal to approximately 915 laps
And the final answer is D.
Help me please just plot the points on the graph
As per given by the question,
There are given that the equation,
[tex]y=4x-2[/tex]Now,
For plot the point on the grpah;
Put the value of x is 0 in the given equation and find the value of y,
So,
[tex]\begin{gathered} y=4x-2 \\ y=4(0)-2 \\ y=-2 \end{gathered}[/tex]And,
Put the value of y is 0 in the given equation to find the value of x,
So;
[tex]\begin{gathered} y=4x-2 \\ 0=4x-2 \\ 4x=2 \\ x=\frac{2}{4} \\ x=0.5 \end{gathered}[/tex]The point on the graph is,
[tex](0,\text{ -2) and (0.5, 0)}[/tex]Hence, the grpah of the given equation is;
You have a $250 gift card to use at a sporting goods store. a) Write an inequality that represents the possible numbers x of pairs of socks you can buy when you buy 2 pairs of sneakers. PRIO *12 SALE PRICE $80 b) Can you buy 8 pairs of socks? Explain.
Sale price 12
number of socks =X
Sneakers sprice 80
Amount disposable 250
Then
Part a)
250 - 2•80 = 12X
250 - 160 = 12X
90 ≥ 12 X
Part b)Can buy 8 pairs?
Answer NO , because 90 < 12•8
find the value of x,y,z
Answer: x =116 degrees
y = 88 degrees
Explanation:
[tex]\begin{gathered} \text{ Find the value of x, y, and z} \\ To\text{ find z} \\ \text{Opposite angles are supplementary in a cyclic quadrilateral} \\ 101\text{ + z = 180} \\ \text{Isolate z} \\ \text{z = 180 - 101} \\ \text{z = 79 degre}es \\ To\text{ find x} \\ 2(101)\text{ = x + 86} \\ 202\text{ = x + 86} \\ \text{Collect the like terms} \\ \text{x = 202 - 86} \\ \text{x = 116 degr}ees \\ \text{ find y} \\ 2z\text{ = y + 70} \\ z=\text{ 79} \\ 2(79)\text{ = y + 70} \\ 158\text{ = y + 70} \\ \text{y = 158 - 70} \\ \text{y = 88 degre}es \end{gathered}[/tex]Therefore, x = 116 degrees, y = 88 degrees, and z = 79 degrees
An online store started its business with 15 sales per week. If their sales increased 18% each week, use an exponential model to find the week in which they exceeded 1000 sales per week. Remember, A= P(1+r)^t26 weeks31 weeks38 weeks15 weeks
Given,
The initial sale is 15.
The rate of increase of sale per week is 18 %.
The final sale is 1000.
The week at which the sales exceeds 1000 is:
[tex]\begin{gathered} 1000=15\times(1+\frac{18}{100})^t \\ \frac{1000}{15}=(\frac{118}{100})^t \\ \frac{200}{3}=(1.18)^t \\ log\text{ \lparen}\frac{200}{3})=t\text{ log\lparen1.18\rparen} \\ t=25.37 \end{gathered}[/tex]The sales of the business reach to 1000 in 25th week.
Hence, the sales of the business exceed to 1000 in 26th week.
Drag each expression to the correct location on the model. Not all expressions will be used.552 + 25r + 2071
Given
[tex]\frac{5x^2+25x+20}{7x}[/tex]To find: The equivalent rational expression.
Explanation:
It is given that,
[tex]\frac{5x^2+25x+20}{7x}[/tex]That implies,
[tex]\frac{5x^2+25x+20}{7x}[/tex]step by step guide I am stuck at the part where you have to divide, I have split them up into 2 and got GCF for p on first term and 6 on second term
We have the next expression:
[tex]pq\text{ - pr + 6q-6r}[/tex]Factorize using factor by grouping.
First, let's find the common terms. The one who is in all terms or majority terms.
In this case, let's use p:
[tex]p(q-r)+6q-6r[/tex]Factorize the common term 6.
[tex]p(q-r)+6(q-r)[/tex]Look at the expressions, both are multiply by (q-r), so we can rewrite the expression like this:
Factorize the common term (q-r)
[tex](q-r)(p+6)[/tex]how do I solve this linear equations by substitution x=5 x + y = 4
Substitute 5 for x in the equation x+y=4 to obtain the value of y.
[tex]\begin{gathered} 5+y=4 \\ y=4-5 \\ =-1 \end{gathered}[/tex]So solution of the equations is (5,-1).
Ramesh leaves 2/3 of his property for his wife and 1/4 for his son and remaining for his daughter what part does his daughter receive Help me fast
complete the Pattern 444 4440 44,400 there are three empty lines I need to finish the pattern
Given:
d. 444 4,440 44,400
e. 9.5 950 9500
The pattern for d as you can see all numbers have 444 but they keep adding extra 0's to each number.
So the next number should have another extra 0 after 44400.
The pattern for all parts a to e seem to be multiplying each number by 10 or dividing by 10 that is why for d. 444 has no 0's but then if you multiply by 10 you get 4440.
If you do 4440*10 you get 44400.
Answer:
The same pattern applies to e.
For the first blank divide 9.5 by 10 so then 9.5 ÷ 10 = 0.95
For the 2nd blank. Multiply by 10 to 95,000 so you get 950,000. Notice how 950,000 has an extra 0.
3rd blank should be 9500000
x[tex] {x}^{3} {y}^{8} term(x + y) ^{11} [/tex]find the coefficient of the given term in the binomial expansion
Using the binomial theorem, we have that the expansion of (x+y)^11 is:
[tex]\begin{gathered} (x+y)^{11}= \\ x^{11}+11x^{10}y+55x^9y^2+165x^8y^3+330x^7y^4+462x^6y^5+462x^5y^6+330x^4y^7+165x^3y^8+55x^2y^9+11xy^{10}+y^{11} \end{gathered}[/tex]notice that the coefficient of the term x^3 y^8 is 165
what is the scale factor from triangle PQR to triangle STU
To find the scale factor from one triangle to another we need to divide the measurements of the second triangle by the corresponding measurements of the first triangle.
Since we need the scale factor from triangle PQR to triengle STU we need to divide the measurements of STU by the corresponding measurements of triangle PQR.
Sides PR and SU are corresponding sides, so we sivide 12 by 8:
[tex]\frac{12}{8}=\frac{3}{2}[/tex]To confirm, we also divide the measurements of sides UT and RQ:
[tex]\frac{9}{6}=\frac{3}{2}[/tex]Thus, the scale factor is: 3/2 = 1.5
In the function rule for simple interest A(t)=P(1+rt), is P a variable? Explain.
P is a variable in the function rule for simple interest A(t)=P(1+rt).
What is a variable?Mathematically, a variable is any number, vector, matrix, function, argument of a function, set, or element of a set.
A variable assumes any possible values in a mathematical expression, problem, or experiment.
A simple interest function showing the amount after some periods is given as A(t)=P(1+rt). In this function, P represents a variable (the principal amount) because it can change depending on the amount invested or borrowed.
Thus, P is a variable in the simple interest function because it can assume any value.
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Answer:
when buying a house
Step-by-step explanation:
fing the probability of .14 .73 .03 is
The probabilities are:
*0.14 -> 14%.
*0.73 -> 73%.
*0.03 -> 3%.
Toy It Examine the worked problem and solve the equation. 4 4 1 (x) 1 = 9 3 3 1 1 + 3 3 4 3 :9+ 3 3 28 The solution is x=
Given:
[tex]\frac{4}{3}(x)-\frac{1}{3}=9[/tex]Let's evaluate and solve for x.
First step:
Add 1/3 to both sides of the equation
[tex]\begin{gathered} \frac{4}{3}(x)-\frac{1}{3}+\frac{1}{3}=9+\frac{1}{3} \\ \\ \frac{4}{3}(x)=\frac{28}{3} \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} 4x(3)\text{ = 28(3)} \\ \\ 12x\text{ = }84 \end{gathered}[/tex]Divide both sides by 12:
[tex]\begin{gathered} \frac{12x}{12}=\frac{84}{12} \\ \\ x=7 \end{gathered}[/tex]ANSWER:
x = 7
Which point on the number line below best represents V30?
We should try different squared numbers that are bigger and smaller than 30 as:
[tex]\begin{gathered} \sqrt{16}=4 \\ \sqrt{25}=5 \\ \sqrt{36}=6 \end{gathered}[/tex]Since 30 is between 25 and 36, the square root of 30 is going to be between 5 and 6. So the point that best represents the square root of 30 is M.
Answer: Point M
-5 > 5 + x/3 I am so confused on these things
Let's solve the inequality:
[tex]\begin{gathered} -5>5+\frac{x}{3} \\ -5-5>\frac{x}{3} \\ -10>\frac{x}{3} \\ -10\cdot3>x \\ -30>x \\ x<-30 \end{gathered}[/tex]Therefore the solution for the inequality is:
[tex]x<-30[/tex]In interval form this solution is written as:
[tex](-\infty,-30)[/tex]This means that x has to be less than -30 for the inequality to be true.
9+7d=16 how do i slove it
9 + 7d = 16
________________
Can you see the updates?
___________________
9 + 7 d = 16
1. we subtract 9 from the two sides
9 - 9 + 7 d = 16 -9
0 + 7 d = 7
2. We divide by 7 both sides
(7 d)/ 7 = 7/ /7
7/7= 1
d= 1
____________________
Answer
9 + 7d = 16
7d= 16 - 9
d= 7/ 7= 1
d= 1
Find the equation of the linear function represented by the table below in slope-intercept form.xy1-52-73-94-11
Answer:
[tex]y=-2x-3[/tex]Explanation:
Given the table:
x | 1 2 3 4
y | -5 -7 -9 -11
Find the slope using the two point formula.
Take the points (1, -5) and (2, -7).
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-7-(-5)}{2-1} \\ =\frac{-7+5}{1} \\ =-2 \end{gathered}[/tex]Substitute the value of the slope into the slope-intercept form y = mx+c.
[tex]y=-2x+c[/tex]Plug the point (1, -5) into y = -2x+c to find c.
[tex]\begin{gathered} -5=-2+c \\ c=-5-(-2) \\ =-3 \end{gathered}[/tex]Thus, y = -2x - 3, which is the required equation of the given linear function.
how to write the indicated expression for[tex] \frac{1}{2} m \: inches \: in \: feet[/tex]
Answer:
Rewriting the given expression in feet gives:
[tex]\frac{1}{24}m\text{ feet}[/tex]Explanation:
We want to write the expression below in feet.
[tex]\frac{1}{2}m\text{ inches in f}eet[/tex]Recall that;
[tex]\begin{gathered} 1\text{ foot = 12 inches} \\ 1\text{ inch = }\frac{1}{12}foot \end{gathered}[/tex]so, converting the expression to feet we have;
[tex]\begin{gathered} \frac{1}{2}m\text{ inches =}\frac{1}{2}m\times\frac{1}{12}feet \\ =\frac{1}{2}\times\frac{1}{12}\times m\text{ f}eet \\ =\frac{1}{24}m\text{ f}eet \end{gathered}[/tex]Therefore, rewriting the given expression in feet we have;
[tex]\frac{1}{24}m\text{ feet}[/tex]a) graph the following transformation b) draw asymptotec) set domain and range
Given the function :
[tex]f(x)=\log _5x+2[/tex]The graph of the function will be as shown in the following picture
The function will have a vertical asymptote which is the line : x = 0
As shown in the figure :
Domain = ( 0 , ∞ )
Range = ( -∞ , ∞ ) or all real numbers
-3х – 10у = -20 -5x — бу = 20
You can solve a system of equations by graphing
The solution of a system of linear equations is the intersection point both graphs
using a graphing tool
the solution is the point (-10,5)
so
x=-10
y=5
the solution is the intersection point both lines
I will solve the system by substitution
we have
-3х – 10у = -20 --------> equation A
-5x — бу = 20 --------> equation B
isolate the variable y in the equation A
10y=-3x+20
y=-0.3x+2 --------> equation C
substitute equation C in equation B
-5x-6(-0.3x+2)=20
solve for x
-5x+1.8x-12=20
-3.2x=20+12
-3.2x=32
x=-10
substitute the value of x in the equation C
y=-0.3x+2
y=-0.3(-10)+2
y=3+2
y=5
the solution is x=-10 and y=5