The general form of a quadratic equation is expressed as
ax^2 + bx + c = 0
In order to write the equation, we would substitute values for a, b and c. If a = 3, b = 8, c = 25, the equation would be
3x^2
PLEASE HELP: Which of the following are identities? Check all that apply. A. (sin x + cos x)^2 = 1 + sin 2x B. sin 3x - sinx/ cos3x + cosx = tan xC. sin 6x = 2 sin3x cos3x D. sin 3x/sin x cos x = 4 cos x - sec x
All the options are correct
Explanations:A quick and smart way is to substitute a value for x in each of the options and verify if the right hand side equals the left hand side
Let x = 30
A) (sin x + cos x)² = 1 + sin 2x
(sin 30 + cos 30)² = 1.866
1 + sin 2(30) = 1.866
Therefore (sin x + cos x)² = 1 + sin 2x
B)
[tex]\begin{gathered} \frac{\sin3x-\sin x}{\cos3x+\cos x}=\tan x \\ \frac{\sin3(30)-\sin30}{\cos3(30)+\cos30}=0.577 \\ \tan \text{ 30 = 0.577} \end{gathered}[/tex]Therefore:
[tex]\frac{\sin3x-\sin x}{\cos3x+\cos x}=\tan x[/tex]C) sin 6x = 2 sin3x cos3x
sin 6(30) = 0
2 sin3(30) cos3(30) = 0
Therefore sin 6x = 2 sin3x cos3x
This can also be justified by sin2A = 2sinAcosA
D.
[tex]\frac{\sin3x}{\sin x\cos x}=\text{ 4}\cos x-\sec x[/tex][tex]\begin{gathered} \frac{\sin 3(30)}{\sin 30\cos 30}=\text{ 2.31} \\ 4\cos 30-\sec 30=\text{ }2.31 \end{gathered}[/tex]Options A to D are correct
Translate to an algebraic expression.10 more than dThe translation is
10 more than d is the same as d plus 10, so the algebraic expression is:
d + 10
Answer: d + 10
Use the words to complete the sentences :1) Downards,2) 15,3) Ascending,4) does,5) upwards,6) Positive,7) Does not,8) Negative,9) Descending,10) 16,11) 3, 12) 3.51) The Graph a plane -----. 2) The line is slanting ------- and therefore has a ------ slope.3) It takes the plane ------ seconds to touch the ground.4) The plane starts at ------- kilometers in the sky .5) Graph ------ touch the origin (0, 0) .
According to the given graph, we have the following:
1) The graph represents a plane descending.
2) The line is slanting downwards and therefore has a negative slope.
3) It takes the plane 15 seconds to touch the ground.
4) The plane starts at 3 kilometers in the sky.
5) Graph does not touch the origin (0,0).
The given graph shows a decreasing line, starting at y = 3, and reaching y = 0 when x = 15.
Find the perimeter of the square.
Width = 4x
Length = 36 – 5x
Answer:
The perimeter of the square is 64 units===========================
GivenA square with dimensions:
Width = 4x,Length = 36 - 5x.To findThe perimeterSolutionSquare has all sides equal:
width = length4x = 36 - 5x4x + 5x = 369x = 36x = 4Each side is:
4*4 = 16 unitsPerimeter:
P = 4*16 = 64 unitsThe perimeter of the square is found as 64 units.
What is defined as the perimeter of the square?The perimeter of such a square is indeed the total length of all of its sides. As a result, we can calculate the perimeter of the a square besides adding its four sides.A square's sides are all equal. As a result, the perimeter of such a square is determined by multiplying the side of a square by four.For the given question,
The dimension of the square are given as;
Width = 4xLength = 36 – 5xFor square, as all sides are equal.
Then,
Width = Length
Put the values.
4x = 36 – 5x
9x = 36
x = 4
Put in dimensions.
Width = 4×4 = 16 unitsLength = 36 – 5×4 = 16 units.The perimeter of square is;
Perimeter = 4 × side
Perimeter = 4 × 16
Perimeter = 64 units.
Thus, the perimeter of the square is found as 64 units.
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Miguel Valdez sells appliances. He is paid an 8% commission on the first $5,000 worth of sales, 10% on the next $5,500, and 15% on all sales over $10,500. What is his commission on $14,910 worth of sales?
Total Sales = 14910
8% on 5000
10% on 5500
15% on
14910 - 10500 = 4410
So,
15% on 4410 [this is the excess of 10,500]
Converting percentages to decimal:
8% = 8/100 = 0.08
10% = 10/100 = 0.1
15% = 15/100 = 0.15
Total Commission
[tex]0.08(5000)+0.1(5500)+0.15(4410)=1611.5[/tex]$1611.50Let E be the event where the sum of two rolled dice is less than 9. List the outcomes in E^c
The Solution:
Let the outcomes when two dice are tossed be as summarized in the picture attached below:
If the area of the rectangle is 4836 square feet find the length of the rectangle
Solution
- Let the length of the rectangle be x
- Let the width of the rectangle be y.
- Thus, we can interpret the lines of the question as follows:
[tex]\begin{gathered} \text{ The length is 30 less than 6 times the width can be written as} \\ x=6y-30\text{ (Equation 1)} \\ \\ \text{The area of the rectangle is 4836. This is written as:} \\ xy=4836\text{ (Equation 2)} \end{gathered}[/tex]- Now, let us solve these two equations simultaneously.
- We shall proceed by solving the system of equations graphically.
- Wherever the graphs of Equation 1 and Equation 2 intersect represents the solution to the system of equations
- The plot of the equations is given below
- Observe that the graphs cross at two points. The first point is positive and the other, negative.
- Since we cannot have negative lengths (x) or width (y), we can discard the negative coordinates.
- Thus, the length (x) and width (y) are given below:
[tex]\begin{gathered} \text{length(x)}=156 \\ \text{width(y)}=31 \end{gathered}[/tex]Final Answer
The length of the rectangle is 156 feet
Alleen's bi-weekly gross pay is $829.70. She sees that $174.25 was deducted for taxes. What percent of Alleen's bi-weekly gross pay has been withheld for tax? Round to the nearest whole percent. (1 point)
O 21%
20%
2%
O 1%
jeslie ann has a 48 month installment loan of 82.91. the amount she borrowed was 3600
Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome of credit.
Step 1
Loan Amount(p)= 3600
Number of Payments per year(n)= 12
Time in Years (t)=4
Installment Payment (m)=83.81
Total amount paid in 48 installments= 4022.88
Amount Paid - Amount Financed = 4022.88 - 3500 = 522.88 in finance charges.
To determine the annual percentage rate. Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome.
Finance Charge/ Amount financed × 100= 522.88/ 3600× 100= 14.5
To use Table , look for 48 in the far left-hand column under the heading Number of Payments. Then move across to the right until you find the value closest to 14.5. In this case, 14.5 is in the table. The value 7 is at the top of this column. The yearly percentage rate is therefore around 7. Monthly payments are 83.81. After 12 payments have been made, 30 payments remain. Therefore, P = 83.81 and n = 30. Use the APR table to calculate V . In the Number of Payments column, find the number of remaining payments, 30, and then look to the right until you reach the column headed by 7%, the APR. intersect at 9.30. Thus, V = 9.30.
:[tex]u=nPV/100+V\\u=30*83.81*9.30/100+9.30=213[/tex]
Total due amount = Total remaining payment including interest- saving on interest + 12th monthly payment= 2514.3- 213.934+ 83.81= 2384.17
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Which of the following equations could you solve by first adding six and then dividing by negative three?
3x - 6 = -9
6 - 3x = -9
-3x - 6 = -9
x/-3 + 6 = -9
Answer:
-3x-6=-9
Step-by-step explanation:
[tex]-3x-6=-9[/tex]
[tex]+6[/tex] [tex]+6[/tex]
[tex]-3x = -3[/tex]
[tex]-3x/-3 = -3/-3[/tex]
[tex]x=1[/tex]
how far a hawk can fly in 15 days
Answer : 1500 miles
According to the distance time relationship
Distance = Rate x time
From the figure given, the hawk flies 500 miles in 5 days
We can find our rate using the above parameters
Since, distance = rate x time
Rate = distance / time
Rate = 500 / 5
Rate = 100 miles / day
Since, the rate remains constant
How far the hawk can fly in 15 days can be calculated as follows
Time = 15 days
Rate = 100
Distance = ?
Disatnce = rate x time
Distance = 100 x 15
Distance = 1500 miles
The Hawk can fly 1500 miles in 15 days
Sketch the vectors u and w with angle θ between them and sketch the resultant.|u|=45, |w|= 25, θ=30°
Step 1
Find the resultant of the vectors
[tex]undefined[/tex]The composition of functions
Answer: g(f(5)) = 352
Step-by-step explanation:
The question being asked is the same as finding g(f(5)).
What this means is to find f(5), and then plug that value into g(x) as x and solve.
f(5) = 4(5) + 1 = 20 + 1 = 21
g(f(5)) = g(21) = 21^2 - 4(21) - 5 = 441 - 84 - 5 = 357 - 5 = 352
Note: You could also find g(f(x)), and then plug 5 in as x and solve.
Start by plugging f(x) into g(x) such that you get g(x = f(x))
g(f(x)) = (4x + 1)^2 - 4(4x + 1) - 5
Now, replace x with 5 and solve to get g(f(5)).
g(f(5)) = (4(5) + 1)^2 - 4(4(5) + 1) - 5 = 352
Ben, Claire and Devon are training for a triathalon. Today, they are practicing their swimming by swimming one mile. Ben swam 0.77 of the mile before stopping. Claire swam 3/5 of the mile and Devon swam 82% of the mile before stopping. Who swam the farthest distance? Who swam the shortest distance?
Given:
Ben, Claire, and Devon are swimming one mile.
Ben swam 0.77 of the mile before stopping.
So, the distance Ben swam = 0.77 x 1 = 0.77 mile
Claire swam 3/5 of the mile.
So, the distance Claire swam = 3/5 x 1 = 3/5 = 0.6 miles
Devon swam 82% of the mile before stopping.
So, the distance Devon swam = 82% of 1 mile = 0.82 x 1 = 0.82 miles
Arrange the distances in order from the largest to the least:
0.82, 0.77, 0.6
So, the answer will be:
The farthest distance is for Devon = 0.82 miles
The shortest distance is for Claire = 0.6 miles
how do I find the slope
you can find the slope taking two points of a graph or function,
identify the rightmost point and apply this equation
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x2,y2) is the rightmost point and (x1,y1) is the other point
If i have two points (3,4) and (6,2)
the rigthmost point is (6,2) because 6 is greater than 3 and these two numbers are x, the place where I can locate myself horizontally or left or right
so, apply the equation
[tex]\begin{gathered} m=\frac{2-4}{6-3} \\ m=\frac{-2}{3} \\ \end{gathered}[/tex]So, the slope is
[tex]-\frac{2}{3}[/tex]What is the slope and y-intercept of the equation y = -2/3x + 1Group of answer choicesSlope = 2/3; y-intercept = 0Slope = 1; y-intercept = -2/3Slope = -2; y-intercept = 3Slope = -2/3; y-intercept = 1
The form of the linear equation is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
The given equation is
[tex]y=-\frac{2}{3}x+1[/tex]Let us compare the given equation with the form above, then
[tex]m=-\frac{2}{3}[/tex]and the value of b is
[tex]b=1[/tex]The slope of the line is the coefficient of x
The y-intercept is the numerical term
The slope = -2/3
The y-intercept = 1
The right answer is D the last answer
In any question like that, put the equation in the form
y = m x + b
m is the slope
b is the y-intercept
If an account is compounded annually at 9%, how much interest will a principal of $12,300 earn in 16 months? Round your answer tothe nearest cent. Note: Assume 365 days in a year and 30 days in a month.
From the question, we have the given information.
[tex]\begin{gathered} \text{Principal =\$12300} \\ \text{rate}=9\text{\%} \\ \text{number of times compounded =1} \\ \text{Time =16 months =}\frac{4}{3}years \end{gathered}[/tex]We will use the formula below to solve the question
[tex]\text{Amount =P(}1+\frac{r}{n})^{nt}[/tex]Therefore;
[tex]\begin{gathered} \text{Amount}=12300(1+\frac{9}{100})^{\frac{4}{3}} \\ =12300(\frac{109}{100})^{\frac{4}{3}} \\ =13797.71 \end{gathered}[/tex]Since the Amount = 13797.71, we can get the interest by using the formula below.
[tex]\begin{gathered} \text{Interest= Amount- Principal} \\ =13797.71-12300 \\ =1497.71 \end{gathered}[/tex]Answer: Interest =$1497.71
If $19,000.00 is invested in an account for 30 years. Find the value of the investment at the end of 30 years if the interestis:(a) 7% simple interest:(b) 7% compounded monthly:
Hello there. To answer this question, we need to remember some properties in simple and coumpound interests investments.
For simple interest, the balance will be equal to P(1 + rt), in which P is the amount invested, r is the interest rate in years and t is the time (can be either years of months).
For compound interest, the balance will be equal to P(1 + r)^t.
So, using the values P = $19,000.00 and the time is equal to 30 years, we have for:
a) 7% simple interest
It means that r = 7% and then we can use the first formula
19000(1 + 0.07*30)
We converted the rate to decimals above
Multiplying the values, we have:
19000(1 + 2.1)
19000*3.1
$58.900
b) 7% compounded monthly
First, we need to convert the time from years to months, multiplying by 12
30*12 = 360 months
Using the second formula, we have:
19000(1 + 0.07)^(360)
Sum the values into parenthesis
19000*1.07^(360)
Hello! I need some guidance please. Having trouble with which graph is correct
Given:
[tex]y\ge3x+3[/tex]Required:
to show which graph is correct for the inequality.
Explanation:
Given graph is correct for the equation.
Required answer:
The given graph is correct.
For the line that passes through Y(3,0), parallel to DJ with D(-3,1) and J(3,3), complete the following: Find the slope. Write an equation in point-slope form. Graph the line.Slope:Point-slope form:
I am going to graph the situation on an external graphing utility and show you the answer, it will take a
minute, stay with me.
[tex]m\text{ = }\frac{rise\text{ }}{\text{run}}=\frac{change\text{ in y}}{\text{change in x}}=\frac{3}{1}=3[/tex][tex]y\text{ = mx+b}\rightarrow\text{ b =-1}[/tex]So the equation of the line is.
[tex]y\text{ =3x -1}[/tex][tex]y\text{ -1 = m(3-0)}[/tex]Through (1,-2) parallel to y=-2x+5
Answer:
Step-by-step explanation:The line parallel to y = -2x + 5 that passes through the point(1,1)
Has the same slope, m but a different y intercept (0,b)
So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b
y = mx + b
m = -2
1 = -2(1) + b
1 = -2 + b
Add 2 to both sides of the equation to solve for b
1 + 2 = b
3 = b
The line is
y = -2x + 3
If a projectile is fired straight upward from the ground with an initial speed of 224 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2.+224t Find the maximum height of the projectile.
The height reached by the projectile is 784 feet.
What is the maximum height of the projectile?
The projectile experiments an uniformly accelerated motion due to gravity, whose height is represented by the quadratic equation:
h(t) = - 16 · t² + 224 · t
Where t is the time, in seconds.
In this problem we need to find the maximum height reached by the projectile, which can be found by finding the vertex form of the quadratic equation:
h(t) = - 16 · (t² - 14 · t)
h(t) - 16 · 49 = - 16 · (t² - 14 · t + 49)
h(t) - 784 = - 16 · (t - 7)²
The maximum height of the projectile is 784 feet.
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Triangle A is rotated 90° about the origin. Which triangle shows the image?
Rotation 90° about the origin.
First, choose a point from triangle A.
For example: (-2,2)
For any point (x,y) rotated 90° =(-y,x)
So:
(-2,2) becames = (-2,-2)
Triangle D
Is my answer correct help please
Answer:
No, the correct answer is C.
Step-by-step explanation:
Five less than a number m = m - 5. and not 5 - m, so false.
Using trigonometry functions find the value missing in the diagram round to the nearest whole number
Given a right angle triangle
As shown:
Given ∠58
the opposite side to the angle = 22
The adjacent side to the angle = x
So,
[tex]\begin{gathered} \tan 58=\frac{\text{opposite}}{\text{adjacent}} \\ \\ \tan 58=\frac{22}{x} \end{gathered}[/tex]solve for x:
[tex]x=\frac{22}{\tan 58}\approx13.747[/tex]round to the nearest whole number
So, the answer will be x = 14
Use the given rounded values, the properties of logsand your knowledge of logarithmic functions to find thevalue of each log expression. Show your work.
We want to find the value for
[tex]\log _425[/tex]To do that, first let's rewrite this expression as
[tex]\log _425=\log _45^2[/tex]Using the following property
[tex]\log _ab^c=c\log _ab[/tex]We can rewrite our expression as
[tex]\log _45^2=2\log _45[/tex]Using the given value on the text, we get our answer
[tex]\log _425=2\log _45=2\cdot1.2=2.4[/tex]A 39 -ft ladder leans against a building so that the angle between the ground and the ladder is 85∘
How high does the ladder reach the building? __________ ft
The height of the building is 38.85 ft.
Given;
length of the ladder, x = 39 ft
the angle between the ground and the ladder, θ = 85°
let the height of the building be h.
Construct this triangle, the ladder forms the hypotenuse side of the right angle triangle, the height of the triangle is the opposite side of the triangle while the base of the triangle is the adjacent side of the triangle.
Apply the following trig ratio to determine the height of the triangle;
sin(θ) = opposite/hypotenuse
sin(85°) = h/39
h = 39sin(85°)
h = 38.85 ft
Therefore, the height of the building is 38.85 ft (approx.).
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A rectangular room is 1.5 times as long as it is wide, and its perimeter is 26 meters. Find the dimension of the room.The length is :The width is :
The rectangular room is 1.5times as long as it is wide and its perimeter is 26m. Let "x" represent the room's width, then the length of the room can be expressed as "1.5x"
The perimeter of a rectangle is equal to the sum of twice the width and twice the length following the formula:
[tex]P=2w+2l[/tex]We know that:
P=26m
w=x
l=1.5x
Then, replace the measurements on the formula:
[tex]\begin{gathered} 26=2x+2\cdot1.5x \\ 26=2x+3x \end{gathered}[/tex]From this expression, you can calculate x, first, add the like terms:
[tex]26=5x[/tex]Second, divide both sides by 5 to determine the value of x:
[tex]\begin{gathered} \frac{26}{5}=\frac{5x}{5} \\ 5.2=x \end{gathered}[/tex]The width is x= 5.2m
The length is 1.5x= 1.5*5.2= 7.8m
A bag of marbles contains 6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble. What is the
probability of reaching into the bag and selecting a yellow marble?
73.
13
16
26
Answer:
2/13
Step-by-step explanation:
Out of a total 13 marbles , 2 are yellow 2 out of 13 = 2/13
Answer:
2/13
Step-by-step explanation:
6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble = 13 marbles
P( yellow) = number yellow / total
= 2/13
x- sq root 6 is a factor of x^4-36 true or false
We want to know if (x-sqroot(6)) is a factor of (x^4 - 36)
That's mean:
[tex](x^4-36)=(x-\sqrt[]{6})\text{ P(x)}[/tex]Where P(X) is a polinomial.
In this case, if x = sqroot(6) the polinomail (x^4 - 36) must be zero, that's mean sqroot(6) is a root (or a zero) of (x^4-36).
So, if we evaluate (x^4 - 36) in x=sqroot(6):
[tex](\sqrt[]{6})^4-36=6^2-36=0[/tex]So, the answer is true.
