In this problem, want to find the equation of a line that will be parallel to a given function through a point.
Recall that parallel lines have the same slope.
We are given the line
[tex]y=-1[/tex]and the point
[tex](-5,4)[/tex]Notice that the equations is technically in slope-intercept form, by the value of the slope will be 0:
[tex]y=0x-1[/tex]Therefore, the slope of the line through (-5,4) will also be zero. We can use that information to find the equation.
Using the form
[tex]y=mx+b[/tex]we can substitute the point and the slope to solve for b:
[tex]\begin{gathered} 4=0(-5)+b \\ \\ 4=b \end{gathered}[/tex]So, the equation of our line is:
[tex]y=0x+4\text{ or }\boxed{y=4}[/tex]Hey I need help on this question so today I want you help me solve it please
Definitions in Algebra
A variable is a letter or symbol that represent numbers in a general way.
A coefficient is a number that multiplies a variable
A term is a combination of numbers and variables, all of them multiplied.
An exponent represents multiple products, like 2*2*2= 2^3
The answer is shown in the image below:
Hello Professor i was confused in this question, will appreciate if u could help me with it!
The hypotenuse is 20 V 3
Explanation:Given that longer leg = 30
Hypotenuse is given as:
[tex]\begin{gathered} 2\times\frac{30}{\sqrt[]{3}} \\ \\ =\frac{60}{3}\sqrt[]{3} \\ \\ =20\sqrt[]{3} \end{gathered}[/tex]Determine the value of x Round results to an appropriate number of significant digits
Given
Find
The value of x.
Explanation
length of AB = 22 - 3 = 19
using the trignometric ratios , we have
[tex]\begin{gathered} \sin13\degree=\frac{BD}{AB} \\ \sin13\degree=\frac{\frac{x}{2}}{19} \\ \sin13\degree\times38=x \\ 8.548=x \end{gathered}[/tex]Final Answer
Therefore , the length of x is 8.548
What is the equation, in slope-intercept form, of a line that passes through the points(-8,5) and (6,5)?
Given the points (-8,5) and (6,5), we can find the equation of the line first by finding the slope with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]in this case, we have the following:
[tex]\begin{gathered} (x_1,y_1)=(-8,5) \\ (x_2,y_2)=(6,5) \\ \Rightarrow m=\frac{5-5}{6-(-8)}=\frac{0}{6+8}=0 \\ m=0 \end{gathered}[/tex]since the slope is m = 0, we have that the line is a horizontal line that goes through the points (-8,5) and (6,6), then, the equation of the line is:
[tex]y=5[/tex]in slope-intercept form the equation would be:
[tex]y=0x+5[/tex]If f (x) = 4x^3 - 25x^2 – 154x+ 40 and (x - 10) is a factor, what are the remaining factors?
Ralph collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25pounds each week. Write an equation in slope-intercept form for the total of pounds, y, ofaluminum cans after x weeks. How long will it take Ralph to collect 400 pounds?
slope intercept form:
y= mx+b
Where:
m= slope
b= y-intercept
total pounds: y
number of weeks: x
the total number of pounds must be equal to the pounds already collected (100) plus the product of the number of weeks (x) and the number of pounds collected per week (25)
y= 100+25x
To collect 400 pounds, replace y by 400 and solve for x ( weeks)
400 = 100+25x
400-100= 25x
300=25x
300/25 = x
12 = x
12 weeks to collect 400 pounds
I need help on this i tried and it was wrong
Given the Division:
[tex]420\div10[/tex]You can identify that have to divide 420 by 10. This means that you need to move the Decimal Point 1 place to the left. Notice that, if you do this, you get:
[tex]=42.0[/tex]Notice that now the digit that was placed in the Ones Place, is in the Tenths Place. Therefore, each original digit was shifted one place to the right.
Hence, the answer is:
Describe the two different methods shown for writing the complex expression in standard form. Which method do you prefer? Explain
The first method simlpy executes the distributive property of multiplication over addition, and the definition of the imaginary number, i.
The second method factored out 4i first then perform the operation on the terms left inside the parenthesis , then executes the distributive property of multiplication over addition and the definition of the imaginary number, i.
I prefer the first method . It's simple and straight forward,
I’ve done all the other parts, I simply need you to graph the proabola!
Given
[tex]y=x^2-4x+3[/tex]Find
Graph the parabola of the given function
Explanation
[tex]y=x^2-4x+3[/tex]solve the equation
[tex]\begin{gathered} x^2-4x+3=0 \\ x^2-3x-x+3=0 \\ x(x-3)-(x-3)=0 \\ (x-1)(x-3)=0 \\ x=1,3 \end{gathered}[/tex]vertex can be found by using the formula,
[tex]-\frac{b}{2a}=-\frac{-4}{2}=2[/tex]x = 2 , substitute this in equation to get y value,
y = -1
if x = 0 then y =3 and if y= 0 then x = 1, 3
Final Answer
I buy 8640 in3 of stuffing for a crafts project, but the instructions are in ft3. How many ft3 of fabric do I have?
We need to convert 8640 in³ into ft³.
1 in³ is equal to 0.0005787037 cubic feet.
Hence, we can convert it using the rule of three:
Then:
1 in³----------- 0.0005787037ft³
8640 in³ ----------- x
where x= (8640in³*0.0005787037 ft³)1 in³
x = 5ft³
Hence, you have 5ft³ of fabric.
Question 13 (3 points)
Intel's microprocessors have a 1.8% chance of malfunctioning. Determine the
probability that a random selected microprocessor from Intel will not malfunction.
Write the answer as a decimal.
EXPLANATION
The probability that Event A happening is the following:
[tex]P(A)[/tex]
The probability of Event A not happening is the following:
[tex]100-P(A)[/tex]Therefore, we have:
[tex]P(Malfunctioning)+P(Non\text{ Malfunctioning\rparen=100\%}[/tex]Plugging in the terms into the expression:
1.8 + P(Not malfunctioning) = 100%
Subtracting -1.8 to both sides:
[tex]P(Not\text{ malfunctioning\rparen=100-1.8}[/tex]Subtracting numbers:
[tex]P(Not\text{ malfunctioning\rparen=98.2}[/tex]In conclusion, the probability of not malfunctioning is 0.982
Determine the height of the lift, in metres, above the gym floor. show all your work algebraically. round to the nearest cm, if necessary.
Height of lift = x + x = 2x
We can find x using triangle ABC by the cosine rule
[tex]\begin{gathered} x^2=5.6^2+5.6^2-2(5.6)(5.6)\cos40^0 \\ x^2=62.72-48.04352 \\ x^2=14.67648 \\ x=\sqrt{14.67648} \\ x=3.831m \end{gathered}[/tex]Height of lift = 2 X 3.831m = 7.662m
This will be converted to cm by multiplying by 100
Height of lift = 7.662 X 100 cm
= 766.2 cm
= 766cm ( nearest cm )
Hence the answer is 766cm
In a charity triathlon, Mark ran half the distance and swam a quarter of the distance when he took a quick break to get a drink of Gatorade he was just starting to bite the remaining 12 miles what was the total distance of the race?
The formula G=H⋅R tells us how much gross pay G a person receives for working H hours at an hourly rate of pay R. Find G.H = 37 hours and R = $6The gross pay is $? .
Given:
a.) H = 37 hours
b.) R = $6
Let's find the gross pay, G:
[tex]\text{ G = H x R}[/tex][tex]=\text{ 37 x 6}[/tex][tex]\text{ G = }222\text{ = \$222}[/tex]Therefore, the gross pay is $222.
Dolphin 1 dove 200 feet underwater. Dolphin 2 dove 30% farther. After dolphin 2 dove down, it ascended 25 1/2 feet, then descended 40 1/2 feet. How far under the water is the dolphin?
Data:
Dolphin 1: 200ft
Dolphin2:
30% farther: 200ft+60ft=260ft
-Find the 30% of 200
[tex]200\cdot\frac{30}{100}=60[/tex]Ascende 25 1/2 feet and then descended 40 1/2 feet:
Substract to the initial 260ft the 25 1/2 ft and add 40 1/2:
[tex]260-25\frac{1}{2}+40\frac{1}{2}[/tex]To sum or substract mixed numbers write it as fractions:
[tex]\begin{gathered} 25\frac{1}{2}=\frac{50}{2}+\frac{1}{2}=\frac{51}{2} \\ \\ 40\frac{1}{2}=\frac{80}{2}+\frac{1}{2}=\frac{81}{2} \end{gathered}[/tex]Then You have:
[tex]260-\frac{51}{2}+\frac{81}{2}[/tex]You can also write the 260 as a fraction with the same denominator (2):
[tex]\begin{gathered} \frac{520}{2}-\frac{51}{2}+\frac{81}{2} \\ \\ =\frac{520-51+81}{2}=\frac{550}{2}=275 \end{gathered}[/tex]Then, the dolphin 2 is 275 feet under the waterSolve for y Simplify your answer as much as possible Find by linear equation.
Given the equation:
[tex]-7=\frac{3y+7}{4}-\frac{9y-5}{2}[/tex]We will solve the equation to find y
Multiply the equation by 4 to eliminate the denominators
[tex]\begin{gathered} 4(-7)=4\cdot\frac{3y+7}{4}-4\cdot\frac{9y-5}{2} \\ \\ -28=(3y+7)-2(9y-5) \\ -28=3y+7-18y+10 \end{gathered}[/tex]Combine the like terms
[tex]\begin{gathered} -28=(3y-18y)+(7+10) \\ -28=-15y+17 \\ \end{gathered}[/tex]Subtract (17) to both sides
[tex]\begin{gathered} -28-17=-15y+17-17 \\ -45=-15y \end{gathered}[/tex]Divide both sides by (-15)
[tex]\begin{gathered} \frac{-45}{-15}=\frac{-15y}{-15} \\ \\ y=3 \end{gathered}[/tex]So, the answer will be y = 3
Shown in the equation are the steps a student took to solve the simple interest formula A=P(1+rt) for r
Given:
We're given the steps a student took to solve the simple interest formula.
To find:
The algebraic error in student's work.
Step-by-step solution:
Let us first solve the equation and then we will spot the error in the solution:
A = P(1 + rt)
A = p + prt
A - p = prt
A - p / pt = r
Upon comparing both solutions, we can clearly see that the student made a mistake in the second step in the multiplication process.
The student should write A = p + prt in the second step in place of
A = p + rt, because p is multiplied with the whole bracket.
Unit 6 lesson3 plsss help
From the triangles ∠ABC ≅ ∠MNP.
Given we have two triangles ABC and PNM
Both triangles have same shape but different angles.
we need to find ∠ABC ≅ ?
we can notice that :
∠A ≅ ∠M
∠B ≅ ∠N
∠C ≅ ∠P
hence these angles are similar to each other.
So, ∠ABC ≅ ∠MNP.
Hence we get the answer as ∠ABC ≅ ∠MNP.
Learn more about Triangles here:
brainly.com/question/2217700
#SPJ1
How long will it take for an investment of 2900 dollars to grow to 6800 dollars, if the nominal rate of interest is 4.2 percent compounded quarterly? FV = PV(1 + r/n)^ntAnswer = ____years. (Be sure to give 4 decimal places of accuracy.)
ANSWER :
The answer is 20.3971 years
EXPLANATION :
The compounding interest formula is :
[tex]FV=PV(1+\frac{r}{n})^{nt}[/tex]where :
FV = future value ($6800)
PV = present value ($2900)
r = rate of interest (4.2% or 0.042)
n = number of compounding in a year (4 : compounded quarterly)
t = time in years
Using the formula above :
[tex]6800=2900(1+\frac{0.042}{4})^{4t}[/tex]Solve for t :
[tex]\begin{gathered} \frac{6800}{2900}=(1.0105)^{4t} \\ \text{ take ln of both sides :} \\ \ln(\frac{6800}{2900})=\ln(1.0105)^{4t} \\ \operatorname{\ln}(\frac{6800}{2900})=4t\operatorname{\ln}(1.0105) \\ 4t=\frac{\ln(\frac{6800}{2900})}{\ln(1.0105)} \\ t=\frac{\ln(\frac{6800}{2900})}{4\ln(1.0105)} \\ t=20.3971 \end{gathered}[/tex]What is the APY for money invested at each rate?(A) 14% compounded semiannually(B) 13% compounded continuously
APY means Annual Percentage Yield
The APY is given by the formula:
[tex]\text{APY}=\lbrack(1+\frac{r}{n}\rbrack^n-1[/tex]where r is the rate (in decimals)
n is the number of times the interest was compounded
A) For the money invested at 14% compounded semiannually
r = 14% = 14/100
r = 0.14
n = 2
Substitute n = 2, r = 0.14
[tex]\begin{gathered} \text{APY = \lbrack{}1+}\frac{0.14}{2}\rbrack^2-1 \\ \text{APY}=\lbrack1+0.07\rbrack^2-1 \\ \text{APY}=\lbrack1.07\rbrack^2-1 \\ \text{APY}=0.1449 \\ \text{APY}=0.1449\times100\text{ \%} \\ \text{APY}=14.49\text{ \%} \end{gathered}[/tex]B) For the money invested at 13% compounded continuously
Which of the following options correctly represents the complete factored form of the polynomial F(x)= x - x2 - 4x-6?
Notice that:
[tex]F(3)=3^3-3^2-4\cdot3-6=27-9-12-6=27-27=0.[/tex]Therefore 3 is a root of the given polynomial.
Now, we can use this root to factor the polynomial:
[tex]F(x)=(x-3)\frac{x^3-x^2-4x-6}{x-3}.[/tex]Using the synthetic division algorithm we get that:
[tex]\frac{x^3-x^2-4x-6}{x-3}=x^2+2x+2.[/tex]The roots of the above polynomial are:
[tex]\begin{gathered} x=-1+i, \\ x=-1-i\text{.} \end{gathered}[/tex]Therefore:
[tex]F(x)=\mleft(x-3\mright)(x+1+i)(x+1-i)\text{.}[/tex]Answer:
[tex]F(x)=(x-3)(x+1+i)(x+1-i)\text{.}[/tex]You draw 7 cards from a standard deck of cards. What is the probability of drawing 3 diamonds and 2 clubs?
Solution
For this case we can do the following:
[tex]p=\frac{\text{possible}}{\text{total}}[/tex]and we can find the answer with this:
[tex]p=\frac{(13C3)(13C2)(26C2)}{52C7}=0.0541[/tex]Find the volume of a cone with a height of 10cm and diameter of 6cm. Round to the nearest tenth. Use 3.14 for .
We can find the volume of a cone using the formula
[tex]V=\frac{\pi r^2h}{3}[/tex]Where
h = height
r = radius
Remember that
[tex]d=2r\Rightarrow r=\frac{d}{2}[/tex]Therefore, let's find out the radius first, the problem says that the diameter is 6cm, then
[tex]r=\frac{6}{2}=3\text{ cm}[/tex]The radius is 3cm and the height is 10cm, let's use it in our formula:
[tex]\begin{gathered} V=\frac{\pi\cdot(3)^2\cdot10}{3} \\ \\ V=30\pi \end{gathered}[/tex]The problem also say to use = 3.14, then the volume is
[tex]\begin{gathered} V=30\cdot3.14 \\ V=94.2 \end{gathered}[/tex]Therefore, the volume is
[tex]V=94.2\text{ cm}^3[/tex]
Choose the best description of its solution. If applicable, give the solution.
Given:
[tex]\begin{gathered} -x-3y=-6\ldots\text{ (1)} \\ x+3y=6\ldots\text{ (2)} \end{gathered}[/tex]Adding equation(1) and equation(2)
[tex]\begin{gathered} -x-3y+x+3y=-6+6 \\ 0=0 \end{gathered}[/tex]The system has infinitely many solution .
They must satisfy the equation:
[tex]y=\frac{6-x}{3}[/tex]Which of the following best describes terms that have the same degree in the same radicand? A. like rational termsB. like fractional termsC. like radical termsD. like polynomial terms
Two radical expressions are called like terms if they have the same degree and the same radicand.
So, like radical terms, best describes terms that have the same degree and the same radicand.
Like radicals are those, that have the same root number and radicand.
So, the correct answer is option C.
how do we do this one there two parts to i t
Given:
[tex]8\sqrt{y}=x-5y[/tex]Find: differentiation
Explanation: on differentitaion with respect to x
[tex]\begin{gathered} 8\sqrt{y}=x-5y \\ \frac{8}{2}y^{\frac{-1}{2}}\frac{dy}{dx}=1-5\frac{dy}{dx} \\ 4y^{\frac{-1}{2}}\frac{dy}{dx}+5\frac{dy}{dx}=1 \\ (4y^{\frac{-1}{2}}+5)\frac{dy}{dx}=1 \\ \frac{dy}{dx}=\frac{1}{4y^{\frac{-1}{2}}+5} \end{gathered}[/tex][tex]\begin{gathered} \frac{-4}{2}y^{\frac{-3}{2}}\frac{dy}{dx}\frac{d^2y}{dx^2}+5\frac{d^2y}{dx^2} \\ 0=(-2y^{\frac{-3}{2}}\frac{dy}{dx}+5)\frac{d^2y}{dx^2} \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]put the value of
[tex]\frac{dy}{dx}[/tex]we get,
[tex]\begin{gathered} (-2\frac{y^{\frac{-3}{2}}}{4y^{\frac{-1}{2}}+5}+5)\frac{d^2y}{dx^2}=0 \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]For the equation E=, h is a proportionality con- stant. When 1-14, E =20. So, if n=7, what is the conesponding value of 6? O 40 O 0.1 O 10 0 0.025 O 0.25
Substitute 14 for n and 20 for E in the equation to determine the value of proportionality constant.
[tex]\begin{gathered} 20=\frac{h}{14} \\ h=20\cdot14 \\ =280 \end{gathered}[/tex]Substitute 280 for h and 7 for n in the equation to obtain the value of E.
[tex]\begin{gathered} E=\frac{280}{7} \\ =40 \end{gathered}[/tex]So value of E is 40.
theres 2 fill in the blank boxes and 3 drop down menus, below i will list the options in the drop down menus.box 1 - apply quotient identities, apply Pythagorean identities, apply double-number identities, apply even-odd identities.box 2 - apply cofunction identities, use the definition of subtraction, apply even-odd identities, Write as one expresssion combine like terms.box 3 - apply cofunction identities, apply double-number identities, apply Pythagorean identities, apply even-odd identities.
Solution
Box 1 : Apply Quotient Identities
[tex]cotx-tanx=\frac{cosx}{sinx}-\frac{sinx}{cosx}[/tex]The answer for the first box is
[tex]\begin{equation*} \frac{cosx}{sinx}-\frac{sinx}{cosx} \end{equation*}[/tex]Box 2: Write as one expression
[tex]\begin{gathered} cotx-tanx=\frac{cosx}{s\imaginaryI nx}-\frac{s\imaginaryI nx}{cosx} \\ cotx-tanx=\frac{cosx(cosx)-sinx(sinx)}{sinxcosx} \\ cotx-tanx=\frac{cos^2x-sin^2x}{sinxcosx} \end{gathered}[/tex]The answer for the second box is
[tex]\frac{cos^{2}x-s\imaginaryI n^{2}x}{s\imaginaryI nxcosx}[/tex]Before the box 3, please note the identity
Note: Trigonometry I dentities
[tex]\begin{gathered} cos^2x-s\mathrm{i}n^2x=cos2x \\ 2sinxcosx=sin2x \end{gathered}[/tex]Box 3: Apply Double - Number Identities
[tex]\begin{gathered} cotx-tanx=\frac{cos^{2}x-s\imaginaryI n^{2}x}{s\imaginaryI nxcosx} \\ Applying\text{ the above trigonometry identities} \\ cotx-tanx=\frac{cos2x}{sinxcosx} \\ cotx-tanx=\frac{cos2x}{sinxcosx}\times\frac{2}{2} \\ cotx-tanx=\frac{2cos2x}{2sinxcosx} \\ cotx-tanx=\frac{2cos2x}{sin2x} \end{gathered}[/tex]Answer below! Thank you :) and try to explain how you got it!
The value of the equation that we have here is given as 16r² + 24
How to solve the expressionThe equation that we are to simplify here is given as -2r(-13r+5r-12).
In order to open the brackets we would have to multiply -2r with all of the values that are in the bracket.
The mathematical signs that are used in the question have to be well thought of as well before the calculation is done
We would have 26r² - 10r² + 24
26r² - 10r² + 24
because they have the same powers they would be able to subtract
16r² + 24
Read more on linear expressions here:
https://brainly.com/question/14323743
#SPJ1
Linear Expressions MC)
Simplify -2r(-13r+5r-12).
O-162-24r
162+24
162+24r
O-162 + 24r
Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2–8x+2
We have to calculate the zeros of the function with the quadratic formula.
[tex]f(x)=x^2-8x+2[/tex][tex]\begin{gathered} x=\frac{-(-8)}{2\cdot1}\pm\frac{\sqrt[]{(-8)^2-4\cdot1\cdot2}}{2\cdot1}=\frac{8}{2}\pm\frac{\sqrt[]{64-8}}{2}=4\pm\frac{\sqrt[]{56}}{2}=4\pm\sqrt[]{\frac{56}{4}}=4\pm\sqrt[]{14} \\ \\ x_1=4+\sqrt[]{14}\approx4+3.742=7.742 \\ x_2=4-\sqrt[]{14}\approx4-3.742=0.258 \end{gathered}[/tex]The roots are x1=7.742 and x2=0.258, both reals., both