Answer:
B) y = 2x
Explanation:
We were given the following details:
The straight line passes through the origin; it passes through the point (0, 0)
The straight line passes through the point (1, 2)
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,2) \end{gathered}[/tex]The general equation of a straight line is given by:
[tex]\begin{gathered} y=mx+b \\ where: \\ m=slope \\ b=y-intercept \end{gathered}[/tex]We will obtain the equation of the straight line as shown below:
I. Obtain the slope of the straight line
[tex]\begin{gathered} \begin{equation*} slope,m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \end{equation*} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-0}{1-0} \\ m=\frac{2}{1}=2 \\ m=2 \\ \\ \therefore slope,m=2 \end{gathered}[/tex]The slope of the straight line is 2
II. Obtain the y-intercept
Method 1:
The y-intercept refers to the point where the straight line crosses the y-axis.
In this case, the straight line crosses the y-axis at the origin (0, 0). This implies that:
[tex]\begin{gathered} b=0 \\ Remember:y=mx+b \\ \Rightarrow y=2x+0 \\ y=2x \end{gathered}[/tex]Method 2:
Using the point-slope equation:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-0=2(x-0) \\ y-0=2x-0 \\ y=2x \\ \\ \therefore y=2x \end{gathered}[/tex]Therefore, the answer is B (y = 2x)
Calvin is building a staircase pattern as shown in the figure. Each block is one foot high. How many blocks would it take to build steps that would be 10 feet high?
This is an example of an arithmetice series.
Step 1: Write out the formula for finding the nth term of an arithmetric series
[tex]undefined[/tex]suppose you are buying CDs and DVDs from AMAZON for gifts CDs cost $4 each and DvDs cost 8$ each you want to spend less than 40$ on all of the gifts you need at least 4 gifts altogether graph a system of linear inequalities to model the scenario and give two solutions combinations of CDs and DVDs they could sell to meet their goal
x + y ≤ 4
4x +8y ≤ 40
(1,2) and (2,2) are two possible solutions.
Check the graph below, please.
1) Gathering the data
CD = $4
DVD = $8
budget: $40
2) Notice the word at least. We can write two inequalities, one relating the price of each item and the budget. And the other one relating the number of CDs and DVDs to be bought.
x=CD, y= DVD
x + y ≤ 4 4 CDs and DVDs, altogether
4x +8y ≤ 40 The price of each item, as coefficient and the budget of $40
2.2) Let's plot those inequalities
Let's pick two solutions, for the common region shaded by both graphs.
Like (2, 2) and (1, 2)
3) If we plug into those inequalities we can verify them. So the answers are:
x + y ≤ 4
4x +8y ≤ 40
(1,2) and (2,2) are two possible solutions.
which values of a and b make the following equation true
Solution
Given that
[tex](5x^7y^2)(-4x^4y^5)=-20x^{7+4}y^{2+5}=-20x^{11}y^7[/tex]Comparing the indiced,
a = 11, b = 7
Option A
-20k - 5) + 2k = 5k + 5A k = 0B) k = 4k = 1D) k = 2
The equation is:
[tex]\begin{gathered} -2(k-5)+2k=5k+5 \\ \end{gathered}[/tex]We can distribute the -2 into the parenthesis
[tex]\begin{gathered} -2k+10+2k=5k+5 \\ 10=5k+5 \\ \end{gathered}[/tex]now we solve for k
[tex]\begin{gathered} 10-5=5k \\ 5=5k \\ \frac{5}{5}=k \\ 1=k \end{gathered}[/tex]A faraway planet is populated by creatures called Jolos. All Jolos are either green or purple and either one-headed or two-headed. Balan, who lives on this planet, does a survey and finds that her colony of 852 contains 170 green, one-headed Jolos; 284 purple, two-headed Jolos; and 430 one-headed JolosHow many green Jolos are there in Balans colony?A.260B.422C.308D. 138
A. 260
Explanation
Step 1
Let
[tex]\begin{gathered} green\text{ jolos,one-headed jolo=170} \\ \text{Purple ,two-headed jolos=284} \\ one\text{ headed jolos=430} \end{gathered}[/tex]as we can see
the total of green-one headed jolo is 170
and the total for one headed jolo is =430
so, the one-headed in counted twice
[tex]\begin{gathered} total\text{ of gr}en\text{ jolos= }430-170 \\ total\text{ of gr}en\text{ jolos= }260 \end{gathered}[/tex]so, the answer is
A.260
I hope this helps you
The table below gives the grams of fat and calories in certain food items. Use this data to complete the following 3 question parts.Fat (x)31391934432529Calories580680410590660520570b. Describe the correlation seen in the scatter plot.is it positve or negative or no correlation?
b. We can see throught the scatter plot that as the grams of fat increaseas, so does the calories in certain food, therefore there is a directly proportion relationship between them.
It is a positive relationship because while one increases, the other one too.
given two sides of a triangle, find a range of possible lengths for the third side.9yd, 32yd
We have to use the Triangle Inequality Theorem, which states that any of the 2 sides of a triangle must be a greater sum than the third side.
So, to find the correct range of lengths, we have to use the difference of the two sides and their addition to calculate the interval.
[tex]\begin{gathered} 32-9Therefore, the range of possible lengths is 23A circle has a radius of 5.5A. A sector of the circle has a central angle of 1.7 radians. Find the area of the sector. Do not round any intermediate computations. Round your answer to the nearest tenth
Answer:
The circle has the following parameters:
[tex]\begin{gathered} \text{Radius = }5.5ft \\ \text{Angle = 1.7 Radians} \end{gathered}[/tex]We have to figure out the area of the sector of this circle that has the given angle and radius.!
[tex]\begin{gathered} A(\text{sector) = }\frac{1.7r}{2\pi r}\times2\pi(5.5)^2ft^2 \\ =(1.7\times5.5)ft^2 \\ =9.35ft^2 \end{gathered}[/tex]This is the area of the sector that we were interested in.!
1-3. Adaptive Practice Powered by KnewtonDue 1Goal ♡ ♡ ♡A square rug has an area of 121 ft2. Write the side length as a square root. Then decide if the sidelength is a rational number.The rug has side length7 ft.Is the side length a rational number?YesNoView progressSubmit and continue
Area of a square: Side length ^2
121 = s^2
Solve for s ( side length)
√121 ft= s
Rational numbers can be expressed as a fraction of 2 integers.
√121=11 =11/1
The side length is √121 ft and is a rational number.
State if the give binomial is a factor of the given polynomial [tex](9x ^{3} + 57x^{2} + 21x + 24) \div (x + 6)[/tex]
We want to find out if (x+6) is a factor of the polynomial
[tex]9x^3+57x^2+21x+24[/tex]In order to find this, we can use the factor theorem.
If we have a polynomial f(x) and want to find if (x-a) is a factor of this polynomial, we plug in x = a into the function and if we get 0, (x-a) is a factor(!)
Now, let's plug in:
x = -6 into the polynomial and see if we get a 0 or not.
Steps shown below:
[tex]\begin{gathered} 9x^3+57x^2+21x+24 \\ 9(-6)^3+57(-6)^2+21(-6)+24 \\ =-1944+2052-126+24 \\ =6 \end{gathered}[/tex]AnswerSince it doesn't produce a 0, (x + 6 ) is not a factor of the polynomial given.
Solve the following equation3(x+1)=5-2(3x+4)
The given equation is expressed as
3(x+1)=5-2(3x+4)
The first step is to open the brackets on each side of the equation by multiplying the terms inside the bracket by the terms outside the bracket. It becomes
3 * x + 3 * 1 = 5 - 2 * 3x + - 2 * 4
3x + 3 = 5 - 6x - 8
3x + 6x = 5 - 8 - 3
9x = - 6
x = - 6/9
x = - 2/3
y=f(x) is the particular solution to the differential equation dy/dx=(x(y-1))/4, with the initial condition of f(1)=3. write an equation for the line tangent to the graph of f at the point (1,3) and use it to approximate f(1,4)
We are given the following differential equation:
[tex]\frac{dy}{dx}=\frac{x(y-1)}{4}[/tex]Since this equation gives the value of the slope of the tangent line at any point (x,y). To determine the equation of such line we need to use the general form of a line equation:
[tex]y=mx+b[/tex]Since in a tangent line the slope is equivalent to the derivative we may replace that into eh line equation like this:
[tex]y=\frac{dy}{dx}x+b[/tex]Now we determine the value of dy/dx at the point (1,3):
[tex]\frac{dy}{dx}=\frac{(1)(3-1)}{4}=\frac{2}{4}=\frac{1}{2}[/tex]Replacing into the equation of the line:
[tex]y=\frac{1}{2}x+b[/tex]Now we replace the point (1,3) to get the value of "b":
[tex]3=\frac{1}{2}(1)+b[/tex]Solving for "b":
[tex]\begin{gathered} 3=\frac{1}{2}+b \\ 3-\frac{1}{2}=b \\ \frac{5}{2}=b \end{gathered}[/tex]Replacing into the line equation:
[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]And thus we get the equation of the tangent line.
To approximate the value of f(1.4) we replace the value x = 1.4 in the equation of the tangent line:
[tex]y=\frac{1}{2}(1.4)+\frac{5}{2}[/tex]Solving the operation:
[tex]y=3.2[/tex]Therefore, the approximate value of f(1.4) is 3.2
Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the
option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, Interest will accrue at 4.29%.
If Rich decides to make no payments during the 4.5 years, the Interest will be capitalized at the end of that period.
a. What will the new principal be when he begins making loan payments?
b. How much interest will he pay over the life of the loan?
The $7,900 10 year, federal unsubsidized student loan has a new principal and interest paid as follows;
a. The new principal of the loan after 4.5 years is approximately $9,543.75
b. The interest on the loan is approximately $3,016.27
What are unsubsidized student loans?Unsubsidized loans are loans that are not based on financial need of undergraduate and graduate students.
The future value of the loan is found using the formula;
[tex]FV = PV\cdot \left(1+\dfrac{r}{100} \right)^n[/tex]
Where;
FV = The future value of the loan
PV = The present value of the loan = $7,900
r = The interest rate of the loan = 4.29%
n = The number of years = 4.5 years
Which gives;
[tex]FV = 7900\times \left(1+\dfrac{4.29}{100} \right)^{4.5}\approx 9543.75[/tex]
The new principal of the loan when he begins to make loan payments is $9,543.75
b. The payment (amortization) formula is presented as follows;
[tex]A = P\cdot \dfrac{r\cdot (1+r)^n}{(1+r)^n-1}[/tex]
Which gives;
[tex]A = 9543.75\times \dfrac{0.0429\cdot (1+0.0429)^{5.5}}{(1+0.0429)^{5.5}}{-1} \approx 1984.78[/tex]
The amount paid annually ≈ $1,984.78
The amount paid in 5.5 years ≈ 1984.78 × 5.5 = 10,916.27
The interest paid = $10,916.27 - $7,900 = $3,016.27
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which value of your makes the equation 8.6 + y = 15 true?y=23.6y=1.7y=129y=6.4
y=6.4
1) Let's find out then, solving that equation.
8.6 + y = 15 Subtract 8.6 from both sides
y= 15 -8.6
y=6.4
8.6 + 6.4 = 15
15 = 15 True
2) Hence the value of y that makes it true is 6.4
R(-2,3) S(4,4) T(2,-2) state the coordinates of R'S'T' after a dilation of 2
We are given the following coordinates.
R(-2,3)
S(4,4)
T(2,-2)
We are asked to state the coordinates of R'S'T' after dilation of 2
A dilation of 2 means that we have to multiply the original coordinates (RST) by 2 to get the new coordinates (R'S'T')
Since the scale factor is 2 (greater than 1) the new image will result in enlargement.
Please note that with dilation the figure remains the same only the size of the image changes.
The new coordinates (R'S'T') are
R'(-2×2, 3×2) = (-4. 6)
S'(4×2, 4×2) = (8, 8)
T'(2×2, -2×2) = (4, -4)
Therefore, the
Solve equations: 1. 3x-4=232. 9-4x=173.6(x-7)=364. 2(x-5)-8= 34
1.
3x-4=23
First, add 4 to both sides of the equation:
3x-4+4 =23+4
3x =27
Divide both sides of the equation by 3.
3x/3 = 27/3
x= 9
Angel's bank gave her a 4 year add on interest loan for $7,640 to pay for new equipment for her antiques restoration business. The annual interest rate is 5.27% How much interest will she pay on the loan? $_______How much would her monthly payments be? $________(round to nearest cent)
From the information given,
Principal = 7640
Number of years = 4
Recall, 1 year = 12 months
4 years = 4 * 12 = 48 months
rate = 5.27/100 = 0.0527
The amount of the principal to be paid each month = 7640/48 = 159.17
Amount of interest owed each month = (7640 * 0.0527)/12 = 33.55
Amount required to be paid by the borrower each month = 159.17 + 33.55 = 192.72
Total interest to be paid on the loan = 7640 * 0.0527 * 4 = 1610.51
The first answer is $1610.51
The second answer is $33.55
If the side adjacent to the 55° angle is five units, what equation should be used to solve for the hypotenuse
For a given Right angled triangle, equation for hypotenuse is,
AB = 5/ Sin55°
Right angled triangle :
A right triangle or right-angled triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry. Right angled triangle is also known as an orthogonal triangle, or rectangled triangle.
In a right angle triangle ΔABC
m∠A = 55°
BC = 5 units
SinA = BC / AB
sin55° = 5/AB
or,
AB = 5/ Sin55°
as, Sin55° = 0.81915204
AB = 5/0.81915204
AB = 6.1038
Thus,
For a given Right angled triangle, equation for hypotenuse is,
AB = 5/ Sin55°
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Solve each inequality 15 > 2x-7 > 9
Given the inequality expression
15 > 2x-7 > 9
Splitting the inequality expression into 2:
15 > 2x-7 and 2x - 7 > 9
For the inequality 15 > 2x-7
15 > 2x-7
Add 7 to both sides
15 + 7 > 2x - 7 + 7
22 > 2x
Swap
2x < 22 (note the change in signg
2x/2 < 22/2
x < 11
For the inequality 2x - 7 > 9
Add 7 to both sides
2x-7+7 > 9 + 7
2x > 16
Divide both sides by 2
2x/2 > 16/2
x > 8
Combine the solution to both inequalities
x>8 and x < 11
8 < x < 11
Hence the solution to the inequality expression is n)8 < x < 11
2x/2 < 22/2
x < 11
For the inequality 2x - 7 > 9
Add 7 to both sides
5 + 7 > 2x - 7 + 7
22 > 2x
Swap
2x < 22 (note the change in si)5 + 7 > 2x - 7 + 7
22 > 2x
Swap
2x < 22 (note the change in si)1
Solve for x. Enter the solutions from least to greatest.6x^2 – 18x – 240 = 0lesser x =greater x =
Answer:
x = -5
x = 8
Explanation:
If we have an equation with the form:
ax² + bx + c = 0
The solutions of the equation can be calculated using the following equation:
[tex]\begin{gathered} x=\frac{-b+\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-b-\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]So, if we replace a by 6, b by -18, and c by -240, we get that the solutions of the equation 6x² - 18x - 240 = 0 are:
[tex]\begin{gathered} x=\frac{-(-18)+\sqrt[]{(-18)^2-4(6)(-240)}}{2(6)}=\frac{18+\sqrt[]{6084}}{12}=8 \\ x=\frac{-(-18)-\sqrt[]{(-18)^2-4(6)(-240)}}{2(6)}=\frac{18-\sqrt[]{6084}}{12}=-5 \end{gathered}[/tex]Therefore, the solutions from least to greatest are:
x = -5
x = 8
whats the simplest form of— 3х + 7 – 2x +11 — x
The given expression is
[tex]-3x+7-2x+11-x[/tex]We have to reduce like terms. -3x, -2x, and -x are like terms. 7 and 11 are like terms.
[tex]-3x-2x-x+7+11=-6x+18[/tex]Then, we factor out the greatest common factor, observe that 6 is the greatest common factor
[tex]6(-x+3)[/tex]Hence, the simplest form is 6(-x + 3).To factor 9x^2 - 4, you can first rewrite the expression as: A. (3x-2)^2B. (x)^2 - (2)^2C. (3x)^2 - (2)^2D. None of the above
We have the expression 9x^2-4.
We know that both terms are squares, so we can express this as:
[tex]9x^2-4=(3x)^2-2^2[/tex]This is as much as we can transform this expression.
The answer is C.
What is the probability it lands between birds B and C?
B. 1/9
Explanation
The probability of an event is the number of favorable outcomes divided by the total number of outcomes.
[tex]P(A)=\frac{favorable\text{ outcomes}}{\text{total outcomes}}[/tex]Step 1
Let A represents the event that the birds lands between b and c
a)so, in this case the favorable outcome is that the birds lands between b and c, the length bewtween b and c is
[tex]BC=2\text{ in}[/tex]and , the total outcome is the total lengt, so total outcome = AD
[tex]\begin{gathered} AD=10\text{ in+ 2 in +6 in} \\ AD=18\text{ in} \end{gathered}[/tex]b) now,replace in the formula
[tex]\begin{gathered} P(A)=\frac{favorable\text{ outcomes}}{\text{total outcomes}} \\ P(A)=\frac{2i\text{n }}{18\text{ in}}=\frac{1}{9} \\ P(A)=\frac{1}{9} \end{gathered}[/tex]therefore, the answer is
B. 1/9
I hope this helps you
Jim invested $4,000 in a bond at a yearly rate of 4.5%. He earned $540 in interest. Howlong was the money invested? (just type the number don't write years)
Answer:
3 years
Explanation:
The interest simple interest rate formula is
[tex]undefined[/tex]Convert the following complex number into its polar representation:2-2√3i
Given:
[tex]=2-2\sqrt{3}i[/tex]Find-:
Convert complex numbers to a polar representation
Explanation-:
Polar from of the complex number
[tex]z=a+ib=r(\cos\theta+i\sin\theta)[/tex]Where,
[tex]\begin{gathered} r=\sqrt{a^2+b^2} \\ \\ \theta=\tan^{-1}(\frac{b}{a}) \end{gathered}[/tex]Given complex form is:
[tex]\begin{gathered} z=a+ib \\ \\ z=2-i2\sqrt{3} \\ \\ a=2 \\ \\ b=-2\sqrt{3} \end{gathered}[/tex][tex]\begin{gathered} r=|z|=\sqrt{a^2+b^2} \\ \\ r=|z|=\sqrt{2^2+(2\sqrt{3})^2} \\ \\ =\sqrt{4+12} \\ \\ =\sqrt{16} \\ \\ =4 \end{gathered}[/tex]For the angle value is:
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{b}{a}) \\ \\ \theta=\tan^{-1}(\frac{-2\sqrt{3}}{2}) \\ \\ =\tan^{-1}(-\sqrt{3}) \\ \\ =-60 \\ \\ =-\frac{\pi}{3} \end{gathered}[/tex]So, the polar form is:
[tex]\begin{gathered} z=r(\cos\theta+i\sin\theta) \\ \\ z=4(\cos(-\frac{\pi}{3})+i\sin(-\frac{\pi}{3})) \end{gathered}[/tex]Use the formula:
[tex]\begin{gathered} \sin(-\theta)=-\sin\theta \\ \\ \cos(-\theta)=+\cos\theta \end{gathered}[/tex]Then value is:
[tex]\begin{gathered} z=4(\cos(-\frac{\pi}{3})+i\sin(-\frac{\pi}{3})) \\ \\ z=4(\cos\frac{\pi}{3}-i\sin\frac{\pi}{3}) \end{gathered}[/tex]Ellie earned a score of 590 on Exam A that had a mean of 650 and a standarddeviation of 25. She is about to take Exam B that has a mean of 63 and a standarddeviation of 20. How well must Ellie score on Exam B in order to do equivalently wellas she did on Exam A? Assume that scores on each exam are normally distributed.
Answer
15
Ellie needs to score 15 on Exam B in order to do equivalently as well as she did on Exam A.
Explanation
Since both distributions are normally distributed, we will use the standardized scores of Ellie on both exams to answer this question.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ
where
z = standardized score or z-score
x = score in the distribution or in the exam
μ = Mean
σ = Standard deviation
So, we will find the standardized score on Exam A and use that standardized score to find the equivalent score on exam B.
For exam A,
z = ?
x = 590
μ = 650
σ = 25
z = (x - μ)/σ
z = (590 - 650)/25
z = (-60/25) = -2.4
For exam B, to find the equivalent score with a standardized score of -2.4
z = -2.4
x = ?
μ = 63
σ = 20
z = (x - μ)/σ
-2.4 = (x - 63)/20
(x - 63)/20 = -2.4
Cross multiply
x - 63 = (20) (-2.4)
x - 63 = -48
x = 63 - 48
x = 15
Hope this Helps!!!
What is the dot product? U=-5,5,-5 v=6,5,-7
The dot product is given by:
[tex]u\cdot v=u_1v_1+u_2v_2+\cdots+u_nv_n_{}[/tex]therefore:
[tex]\begin{gathered} u\cdot v=(-5\cdot6)+(5\cdot5)+(-5\cdot-7) \\ u\cdot v=-30+25+35 \\ u\cdot v=30 \end{gathered}[/tex]19. If p(x) = 3x^2 - 4 and r(x) = 2x^2 - 5x+1 find -5r*(2a)
We have two polynomials:
[tex]\begin{gathered} p(x)=3x^2-4 \\ r(x)=2x^2-5x+1 \end{gathered}[/tex]We have to find -5*r*(2a). This can be written as:
[tex]-5\cdot r\cdot(2a)=(-5\cdot2a)\cdot r=-10a\cdot r[/tex][tex]\begin{gathered} -10a\cdot r(x)=-10a\cdot(2x^2-5x+1) \\ -10a\cdot2x^2-10a(-5x)-10a\cdot1 \\ -20ax^2+50ax-10a \end{gathered}[/tex]Answer: -5r(2a) = -20ax^2+50ax-10a
I need help with my math prep
Answer:
I can help!
Step-by-step explanation:
raw the hyperbola for each equation in problem l. the partial
B. given the equation of the hyperbola :
[tex]\begin{gathered} 9x^2-y^2=9 \\ \\ \frac{x^2}{1}-\frac{y^2}{9}=1 \end{gathered}[/tex]The graph of the hyperbola will be as following :
As shown in the figure :
vertices are : (-1,0) and (1,0)
Foci are ( -3.2 , 0) and (3.2 , 0)
End points are (0,-3) and (0,3)
Asymptotes are : y = 3x and y = -3x