jv + b
where b = 8, v = 4 and j = -6
Therefore
jv + b = (-6)(4) + 8 = -24 + 8 = -16
The volume of the oceans and their seas is nearly 1.5 . 109 cubic kilometers. Write this number in Standard Form A:0.00000000015km³ B: 1,500,000,000km³ C: 0.0000000015km³ D: 15,000,000,000km³
Given data:
[tex]\text{1}.5\cdot10^9[/tex]the above number in standard form is.
1,500,000,000km³.
The answer is option c. 1,500,000,000km³
Americans said money mistakes cost them $1,230, on average, last year alone, According to U.S. Census Bureau data from 2018, the latest release, the median household income was $61,372. What percent of their income did they lose on mistakes?
EXPLANATION.
The first thing to do is analyze the data that the exercise gives us, it tells us that a year the cost of error for money was 1230, but the income was 61,372, for this exercise we must find the percentage with a rule of three .
The exercise is as follows.
The total income 61,372 represents 100 percent, how much does 1230 represent?
[tex]undefined[/tex]A certain college has been raising tuition every year since the year it opened. The function T = 12,000 (1+.03)* represents the tuition, T, after x years. If the college opened in the year 1990, what was the tuition in 2020?
What value is a discontinuity of x^2+5x+2/x^2+2x-35
Solution:
Given the expression:
[tex]\frac{x^2+5x+2}{2x^2+2x-35}[/tex]A function f(x) has disconituity at x=a if
[tex]\lim_{x\to a}f(x)[/tex]exists and is finite.
The function is thus undefined at x=a or when
[tex]\lim_{x\to a}(f(x))\ne f(a)[/tex]From the given function, we have
[tex]\begin{gathered} \frac{x^2+5x+2}{x^2+2x-35} \\ factorize\text{ the denominator,} \\ \frac{x^2+5x+2}{x^2-5x+7x-35}=\frac{x^2+5x+2}{x(x-5)+7(x-5)} \\ \Rightarrow\frac{x^2+5x+2}{(x-5)(x+7)} \end{gathered}[/tex]The function is undefined at
[tex]\begin{gathered} x-5=0 \\ \Rightarrow x=5 \\ x+7=0 \\ \Rightarrow x=-7 \end{gathered}[/tex]Hence, there is discontinuity at
[tex]x=5,\text{ x=-7}[/tex]Multiply 1.42 x 0.3
the given problem is 1.4*0.3
here the answer is 0.42
[tex]undefined[/tex]find the values for A and B. explain of show your reasoning
Answer:
The value of a is 5, and b is 6.
Explanation:
The points on the line are (6,10), (a,8), (4,b) and (2,2).
• The slope of a straight line is always constant.
First, determine the slope using the points (6,10) and (2,2).
[tex]\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{10-2}{6-2} \\ =\frac{8}{4} \\ =2 \end{gathered}[/tex]Next, using points (6,10) and (a,8):
[tex]\begin{gathered} m=\frac{10-8}{6-a} \\ 2=\frac{2}{6-a} \\ \text{Cross multiply} \\ 2(6-a)=2 \\ 12-2a=2 \\ -2a=2-12 \\ -2a=-10 \\ a=-\frac{10}{-2} \\ a=5 \end{gathered}[/tex]Next. using points (6,10) and (4,b):
[tex]\begin{gathered} m=\frac{10-b}{6-4} \\ 2=\frac{10-b}{2} \\ \text{Cross multiply} \\ 10-b=2\times2 \\ 10-b=4 \\ b=10-4 \\ b=6 \end{gathered}[/tex]The value of a is 5 and b is 6.
I need some help please Find the inverse function of the given function.1. F(x)= x^2-4/2x^2
to solve this problem, we can follow some steps
step 1
replace f(x) with y
[tex]\begin{gathered} f(x)=\frac{x^2-4}{2x^2} \\ y=\frac{x^2-4}{2x^2} \end{gathered}[/tex]step 2
replace every x with a y and every y with an x
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \end{gathered}[/tex]step 3
solve for y
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \text{cross multiply both sides} \\ 2y^2\times x=y^2-4^{} \\ 2y^2x=y^2-4 \\ \text{collect like terms} \\ 2y^2x-y^2=-4 \\ \text{factorize y}^2 \\ y^2(2x-1)=-4 \\ \text{divide both sides by 2x - 1} \\ \frac{y^2(2x-1)}{(2x-1)}=-\frac{4}{(2x-1)} \\ y^2=-\frac{4}{2x-1} \\ \text{take the square root of both sides} \\ y=-\sqrt[]{\frac{4}{2x-1}} \end{gathered}[/tex]therefore the inverse of f(x) is
[tex]f^{-1}(x)=-\sqrt[]{\frac{4}{2x-1}}[/tex]Solve the following equation for x by using the quadratic formula. If there is more than one solution, enter your solutions as a comma-separated list, like "1, 3".2x^2+9x+7=0
Answer:
Explanation:
Given the equation:
[tex]2x^2+9x+7=0[/tex]• The coefficient of x², a=2
,• The coefficient of x, b=9
,• The constant, c=7
Substitute these values into the quadratic formula:
[tex]\begin{gathered} x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\ \implies x=\dfrac{-9\pm\sqrt[]{9^2-4(2)(7)}}{2\times2}=\dfrac{-9\pm\sqrt[]{81-56}}{4}=\dfrac{-9\pm\sqrt[]{25}}{4} \\ \implies x=\dfrac{-9\pm5}{4} \end{gathered}[/tex]Thus, the values of x are:
[tex]undefined[/tex]
Scott borrowed $8000 at a rate of 19%, compounded annually. Assuming he makes no payments, how much will he owe after 8 years? Round your answer to the nearest cent
To answer this question we will use the following formula for compounded interest:
[tex]A=A_0(1+r)^t,[/tex]where A is the final amount, A₀ is the initial amount, r is the interest rate as a decimal number, and t is the number of times that the interest rate is applied.
Substituting A₀=8000, r=0.19, and t=8 we get:
[tex]A=8000(1+0.19)^8\text{.}[/tex]Simplifying the above result we get:
[tex]\begin{gathered} A=8000(1.19)^8, \\ A\approx32171.08 \end{gathered}[/tex]Answer: $32171.08.
[4]How many solutions does the system of equations have?y = 7x-4y = 7x + 2 One Soluton Infinite Solutions No Solution
Given system of equations:
[tex]\begin{gathered} y\text{ = 7x - 4} \\ y\text{ = 7x + 2} \end{gathered}[/tex]Let us attempt to solve the equations
From equation 1:
[tex]y\text{ = 7x -4}[/tex]Substituting the expression for y into equation 2:
[tex]\begin{gathered} y\text{ = 7x + 2} \\ 7x\text{ -4 = 7x + 2} \\ \text{Collect like terms} \\ 7x\text{ - 7x = 2 + 4} \\ 0\text{ = 6} \end{gathered}[/tex]This imples that there is no solution to the system of equations.
We can plot the graph of the equations to better visualize and see that the lines don't intersect
The lines are parallel and do not intersect. Hence, there is no solution to the system of equations
What is the slope of a line that goes through (2,6) and (4,12)?
Answer:
Slope = 3
Explanation:
To determine the slope of the line that goes through the given points: (2,6) and (4,12), we use the slope formula.
[tex]\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Substituting the points, we have:
[tex]\begin{gathered} \text{Slope}=\frac{12-6}{4-2} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]The slope of the line is 3.
Solve for x. 3 0 - 7 21 Answer: Submit Answer
Cross multiply:
[tex]3\cdot21=x\cdot7[/tex]Isolate x:
[tex]63=7x[/tex][tex]\frac{63}{7}=x[/tex][tex]x=9[/tex]7. On Friday, Stock 1 dropped 3/4 point and Stock 2 dropped 5/8 point. Based on this information, which statement is true? Stock 2 dropped more Stock 1 dropped more The stocks dropped the same amount O Both stocks sold at the same price Clear selection
Let's divide each fraction
[tex]\begin{gathered} \frac{3}{4}=0.75 \\ \frac{5}{8}=0.625 \end{gathered}[/tex]As you can observe, 3/4 is greater than 5/8.
Hence, Stock 1 dropped more.Solve for h.A=3h Can anyone help me?
You have the following expression:
[tex]A=3h[/tex]In order to solve for h, use the division property of equality. In this case divide by 3 both sides:
[tex]\begin{gathered} \frac{A}{3}=\frac{3h}{3} \\ \frac{A}{3}=h \end{gathered}[/tex]Hence, the solution for h = A/3
given the function f defined by the formula f(x)=2x+1 find the following: Evaluate f(0)
At a given function:
[tex]\text{ f(x) = 2x + 1}[/tex]At f(0), it means that we substitute x by 0.
We get,
[tex]\text{ f(x) = 2x + 1}[/tex][tex]\text{ f(0) = 2(0) + 1}[/tex][tex]\text{ f(0) = 1}[/tex]Therefore, f(0) = 1.
*i will give you brainliest and 100 pts* Find the value of y. 3 cm 5 cm х 6 cm 2 cm 3cm. y = [?] cm Enter a decimal rounded to the nearest tenth. Enter
We have to use the secant theorem, which states
[tex](y+3)\cdot3=(9+2)\cdot2[/tex]Then, we solve for y
[tex]\begin{gathered} 3y+9=11\cdot2 \\ 3y=22-9 \\ y=\frac{13}{3}=4.3 \end{gathered}[/tex]Hence, y is equal to 4.3 cm.need help with the the association property etc
Line 1:
[tex](2+x)x[/tex]Line 2:
[tex]x(2+x)[/tex]Line 1 to Line 2 is:
Commutative property of Multiplication.
Line 3:
[tex]x(x+2)[/tex]Line 2 to Line 3 is:
Commutative property of Addition
if ace of 21 = 856 find ace 20 and ace of 22 given a common ratio of 1/4.
Answer:
[tex]a_{20}=214,a_{22}=3424[/tex]Explanation:
We are told that the common ratio between the numbers is 1/4, meaning each consquetive number is
To get rid of radicals in the denominator of a fraction, you should rationalize the denominator by multiplying the fraction by a helpful form of _____.A.the denominatorB.xC.1D.the numerator
Given:
To get rid of radicals in the denominator of a fraction
Required:
you should rationalize the denominator by multiplying the fraction by what
Explanation:
In fraction, a number is said to be a quotient, in which the numerator is divided by the denominator.
there are three types of fraction
1. Proper fraction
2. Improper fraction
3. Mixed
Final answer:
But to get rid of radival in the denominator of a fraction, you should rationalize the denimonator by multiplying the fraction with 1
17. Write the equation of the line in slope-intercept form with the given information. 17. Passes through (-2, 6) with a slope of (-1/4)
Given:
Slope of line is m = -1/4 and passes through point (-2,6).
Explanation:
The general equation of line with slope m and passing through point (x_1,y_1) is,
[tex]y-y_1=m(x-x_1)[/tex]Determine the equation of line passing through point (-2,6) and have slope of -1/4.
[tex]\begin{gathered} y-6=-\frac{1}{4}(x-(-2)) \\ y-6=\frac{-1}{4}\cdot x-\frac{1}{4}\cdot2 \\ y=-\frac{x}{4}-\frac{1}{2}+6 \\ y=-\frac{x}{4}+\frac{11}{2} \end{gathered}[/tex]So equation of line is,
y = -x/4 + 11/2
Question is in the picture.The options underneath are $100 per person $15 per person $10 per person and eight dollar per person I chose $100 but I need it to be explained
The graph provided plots the cost of a hall against the number of guests. The blue graph represents "Cosmic Hall".
The cost per person is the slope of the line that represents the hall in consideration.
The slope is calculated using the formula:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]From the graph, two points can be picked as shown below:
[tex]\begin{gathered} (x_1,y_1)=(0,6000) \\ (x_2,y_2)=(500,10000) \end{gathered}[/tex]Hence, the slope is calculated to be:
[tex]\begin{gathered} slope=\frac{10000-6000}{500-0}=\frac{4000}{500} \\ slope=8 \end{gathered}[/tex]Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote atx = 2 and x = 1.
Solution
Step 1
Horizontal Asymptotes of Rational Functions
The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.
If N is the degree of the numerator and D is the degree of the denominator, and…
N < D, then the horizontal asymptote is y = 0.
N = D, then the horizontal asymptote is y = ratio of leading coefficients.
N > D, then there is no horizontal asymptote.
Step 2
Identify Vertical Asymptotes of a Rational Function
Factor the numerator and denominator.
Simplify by canceling common factors in the numerator and the denominator.
Set the simplified denominator equal to zero and solve for x.
Step 3
x = 2 and x = 1
x - 2 and x - 1
The denominator expression will be (x-2)(x-1)
Step 4
[tex]\begin{gathered} The\text{ rational fraction is} \\ \\ y=\frac{1}{(x-2)(x-1)} \end{gathered}[/tex]Final answer
[tex]y\text{ = }\frac{1}{(x-2)(x-1)}[/tex]Use synthetic division to find the result when 4x3 + 13x2 + 6x + 9 is divided byx + 3.
To solve this question, observe the figure and observe the steps below:
1) Organize the coefficient of the dividend according to the figure.
2) Write the zero of the divisor according to the figure.
3) Write down the first coefficient (4).
4) Multiply the coefficient by -3 and write it below 13 (second coefficient). Then, sum the result (-12) with 13. Write the answer (1).
5) Do the same with the other values, according to the figure.
6) The coefficients of the quotient are the values in green and the remainder is the value in red.
Answer: The quotient is:
[tex]4x^2+1x+3[/tex]The value y of a computer after its purchase is given by y(t)=3200-200t
Problem Statement
The question gives us an equation that gives us the value of a computer after its initial value at purchase. The equation given is:
[tex]\begin{gathered} y(t)=3200-200t, \\ \text{where,} \\ t=years\text{ afer year of purchase} \\ y=\text{value of the computer} \end{gathered}[/tex]We are asked to find:
a. The y-intercept and its meaning.
b. The slope and its meaning
Solution
To solve this question, we simply need to compare the equation given to the general slope-intercept equation. The general slope-intercept equation is given by:
[tex]\begin{gathered} y(t)=mt+c \\ \text{where,} \\ c=y-\text{intercept} \\ m=\text{slope of the equation} \end{gathered}[/tex]With this equation, we can compare with the equation given in the question:
[tex]\begin{gathered} y=mt+c \\ y=3200-200t \\ \text{This implies that:} \\ \\ \text{slope(m)}=-200 \\ y-\text{intercept}=3200 \end{gathered}[/tex]Thus, let us answer the questions:
a. The y-intercept and its meaning:
The y-intercept is 3200.
When we vary the time variable in the equation given, we can get a sense of what this y-intercept means. This is done below:
[tex]undefined[/tex]You have $5,000 to invest and want it to grow to $20,000 in two years. What interest rate would you need to find to make this possible?I wan answer and explanation.
ANSWER
The interest rate is 150%
EXPLANATION:
Given that;
The initial amount is $5000
The total amount $20, 000 after 2 years
Total period of the investment is 2 years
To find the interest rate, follow the steps below
1. Find the interest on the investment after two years
In the given data,
The initial amount (principal) is $5000
The total amount after 2 years is $20, 000
Recall that,
Total amount = Interest + principal
20, 000 = interest + 5000
subtract 5000 from both sides of the equation
20, 000 - 5,000 = interest + 5000 - 5000
15,000 = interest
Therefore, the interest on the investment after 2 years is $15, 000
Step 2; Find the interest rate using the simple interest formula
[tex]\text{ I }=\text{ }\frac{P\times R\times T}{100}[/tex]Where
I is the interest
P is the principal
R is the interest rate
T is the time of the investment
[tex]\begin{gathered} \text{ 15, 000 }=\text{ }\frac{5000\times\text{ r}\times\text{ 2}}{100} \\ \text{ } \\ \text{ 15000 }=\text{ }\frac{10,000r}{100} \\ \text{ 15, 000 }=\text{ 100r} \\ \text{ Divide both sides by 100} \\ \frac{15,000}{100}\text{ }=\text{ }\frac{100r}{100} \\ \text{ r }=\text{ 150\%} \end{gathered}[/tex]Therefore, the interest rate is 150%
The gas/oil ratio for a certain chainsaw is 50 to 1.a. How much oil (in gallons) should be mixed with 13 gallons of gasoline? b. If 1 gallon equals 128 fluid ounces, write the answer to part a in fluid ounces.
1) We can write the following ratio for this, considering the ratios and the quantities:
a)
[tex]\begin{gathered} \frac{50}{1}=\frac{13}{x} \\ 50x=13 \\ x=\frac{13}{50}\text{ (or 0.26g)} \end{gathered}[/tex]Notice that on the left side, the ratio gas/oil, and on the right side is the quantity of gas and the unknown quantity of oil.
So, so far we have 13/50 gallons of oil that must be mixed with gasoline.
b) For now, we need to convert that from gallons to fluid ounces so we can write out the following product:
[tex]\begin{gathered} x=\frac{13}{50}\times128 \\ x=33.28fl\text{ oz} \end{gathered}[/tex]So 13/50 or 0.26 gallons of oil. b) 33.28 fl oz.
Using y= sin x OR y= cos x [Sinusoidal function] as the parent function, make your own transformations (5 units right, reflect on x axis, 2 units down, horizontal compression with factor 2). Then graph and state domain and range.
Using
[tex]y=\sin (x)[/tex]5 units right: Let's use the following rule:
[tex]\begin{gathered} y=f(x-5) \\ so\colon \\ y=\sin (x-5) \end{gathered}[/tex]Reflect on x-axis: Let's use the following rule:
[tex]\begin{gathered} y=-f(x) \\ so\colon \\ y=-\sin (x-5) \end{gathered}[/tex]2 units down: Let's use the following rule:
[tex]\begin{gathered} y=f(x)-2 \\ so\colon \\ y=-\sin (x-5)-2 \end{gathered}[/tex]Horizontal compression with factor 2: Let's use the following rule:
[tex]\begin{gathered} y=f(2x) \\ so\colon \\ y=-\sin (2x-5)-2 \end{gathered}[/tex]Let's graph the parent function, and the new function:
The blue graph is the parent function and the red graph is the new function after the transformations applied.
The domain and the range of the new function are:
[tex]\begin{gathered} D\colon\mleft\lbrace x\in\R\mright\rbrace_{\text{ }}or_{\text{ }}D\colon(-\infty,\infty) \\ R\colon\mleft\lbrace y\in\R\colon-3\le y\le-1\mright\rbrace_{\text{ }}or_{\text{ }}R\colon\lbrack-3,-1\rbrack \end{gathered}[/tex]Mrs. Thornton asked her students to draw a figure with a perimeter of 4x + 4. Shown below are 4 drawings madeby her students. (They are not drawn to scale.) Which one is NOT correct?А2x+11B2x2C.X + 4XDX+ 1X+ 1сdba
The perimeter is 4x+4
the formula of the perimeter of a rectangle is
[tex]P=2l+2w[/tex]for the first drawing
[tex]P=2(2x+1)+2(1)=4x+2+2=4x+4[/tex]It is correct
for the second drawing
[tex]P=2(2x)+2(2)=4x+4[/tex]It is correct
for the third drawing
[tex]P=2(x+4)+2x=2x+8+2x=4x+8[/tex]It is not correct
for the fourth drawing
[tex]P=2(x+1)+2(x+1)=2x+2+2x+2=4x+4[/tex]it is correct
As we can see the incorrect draw is C.
Find the equation of the line using the given information and the point slope form. Express the equation in slope intercept form points (5,6) Points(-1,4)
step 1
Find out the slope
m=(4-6)/(-1-5)
m=-2/-6
m=1/3
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=1/3
point(5,6)
substitute
6=(1/3)(5)+b
solve for b
6=(5/3)+b
b=6-5/3
b=13/3
therefore
y=(1/3)x+13/3The distance d (in inches) that a beetle travels over time + (inseconds) is given by the function d (t) = 2t^3 . Find the averagespeed of the beetle from t1 = 0 second to t2 = 2 seconds.inches/second
Given distance,
[tex]d(t)=2t^3[/tex]Let v is the speed of the beetle.
It is given by
[tex]v=\frac{d(t)}{t}[/tex]Now,
[tex]\begin{gathered} v=\frac{2t^3}{t} \\ v=2t^2 \end{gathered}[/tex]At t = 0 sec.
[tex]\begin{gathered} v=2t^2 \\ v=2\times0 \\ v=0 \end{gathered}[/tex]At t = 2 sec.
[tex]\begin{gathered} v=2t^2 \\ v=2\times2^2 \\ v=8\text{ m/sec} \end{gathered}[/tex]So, the average speed of the beetle is 8 m/sec.