To write the equation of the line that passes through (10,80) (5,65)
we will use the formula;
[tex]y-y_1\text{ =}\frac{y_{2-}y_1}{x_2-x_1}(x-x_1)[/tex]x₁ = 10 y₁ = 80 x₂ = 5 y₂ = 65
substituting the above into the formula;
[tex]y\text{ - 80 = }\frac{65\text{ - 80}}{5\text{ - 10}}(\text{ x - 10)}[/tex]we will go ahead and simplify
[tex]y\text{ - 80 = }\frac{-15}{-5}(x-10)[/tex]y- 80 = 3(x - 10)
y- 80 = 3x - 30
y -3x -80 + 30 = 0
y - 3x - 50 = 0
The above is the equation of the line.
To write in a slope-intercept form simply means to write it in the form;
y = mx + b
where m is the slope and b is the intercept
Hence;
y = 3x + 50
The above is the equation of the line in a slope-intercept form
In a triangle ABC, a line BP is drawn from B so that P lies on the side AC. For the triangle, AP=27mm, BP=30mm, BC=82mm and the angle APB=76∘ apply. Determine the area of triangle ABC
SOLUTION
The diagram for this is shown below
From the diagram above, considering triangle BPC, let us find angle C
Using sine rule, we have
[tex]\begin{gathered} \frac{sinC\degree}{30}=\frac{sin104\degree}{82} \\ sinC=\frac{30\times sin104\degree}{82} \\ C=sin^{-1}\frac{30sin104}{82} \\ C=20.79\degree \end{gathered}[/tex]From the same triangle BPC to get angle B, we have
[tex]\begin{gathered} B+P+C=180\degree \\ B+104+20.79=180 \\ B+124.79=180 \\ B=55.21\degree \end{gathered}[/tex]From the same triangle BPC, using sine rule to get the side PC, which I called x, we have
[tex]\begin{gathered} \frac{sinB}{x}=\frac{sinP}{82} \\ \frac{sin55.21\degree}{x}=\frac{sin104\degree}{82} \\ x=\frac{sin55.21\times82}{sin104\degree} \\ x=69.404mm \end{gathered}[/tex]This makes the side AC to become
[tex]27+69.404=96.404mm[/tex]So, to get the area of the triangle ABC, we have that
[tex]Area=\frac{1}{2}|AC|\times|BC|\times sinC[/tex]Applying we have
[tex]\begin{gathered} Area=\frac{1}{2}|96.404|\times|82|\times sin20.79\degree \\ =1402.94mm^2 \end{gathered}[/tex]Hence the answer is approximately 1402.94 square-millimeters to the nearest hundredth
Determine the magnitude and direction of vector a = (3,8) Round to the nearest tenths. |a| =theta =
Recall the definitions of the magnitude and direction of a vector:
[tex]\begin{gathered} \parallel a\parallel=\sqrt[]{3^2+8^2}=\sqrt[]{73}=8.5 \\ \theta=\tan ^{-1}(\frac{8}{3})=69.4^{\circ} \end{gathered}[/tex]3. John opens a checking account with $100. He writes a check for $110. The back
charges an overdrawn fee of $25. What is his account balance?
John's account balance after considering the withdrawal and the overdrawn fee is -$35
What does it mean for an account to be overdrawn?
An account is overdrawn if the money withdrawn from it is more than the account balance, in this scenario, the check presented whose value is $110 is more than the account balance, which was the account by which the account was opened initially, hence, John's account can be said to be overdrawn.
Account balance=initial balance-amount withdrawn-overdrawn fee
Note overdrawn fee and amount withdrawn would be shown as negative values because they are obligations against the account balance
initial balance=$100
amount withdrawn=$110
overdrawn fee=$25
Account balance=$100-$110-$25
Account balance=-$35
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For any positive numbers, a, b and d, with b = 1, logb = d•log b a
The exponent multiplies the logarithm of the base
So:
[tex]\log_ba^d=d\log_ba[/tex]The answer is option C
2 is subtracted from the square of a numberWrite as an algebraic expression.
Answer:
x²-2
Explanation:
Let the number be x.
The square of the number = x²
If 2 is subtracted from the square of the number, we have:
[tex]x^2-2[/tex]Therefore, an algebraic expression for the statement "2 is subtracted from the square of a number" is x²-2.
The diameter of the moon is
3,474,000 meters. Which is the
best estimate of the diameter of the
moon?
The best estimate of the diameter of the moon is 3.474×10⁶.
The best estimate of the diameter will be calculated by converting the number into scientific notation. To convert the number into scientific notation it is broken into two parts.
First number is coefficient which has to range between 1 and 10. So, as per the digits, 3.474 will be the coefficient.
The 10 will be written along with exponent. There are three digits after the decimal followed by three zeroes. Therefore, the 10 and exponent will be written as 10⁶.
So, the complete number estimating the diameter of moon is 3.474×10⁶.
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How do you write a point slope form equation from this graph?
Answer: y-1=3(x-3)
this in the correct answer. you take one point on the line and substitues x and y of the point into the equation. M is your slope. y-y1=m(x-x1)
how would I answer and what would be the answer?
there is a zero at x = 1 (option D)
Explanation:
a) The graph shows it is going up (increasing towards both the y axis and x axis).
This graph will give a positive leading coefficient.
As a result, the equation will have a positive leading coefficient not a negative one.
b) zeros of a polynomial are the values of x when the line crossses the x axis.
From our graph, the line doesn't cross the x axis at x = 6.
As a result, there is no zero of -6.
Multiplicity tells us the number of times the number of times a factor occurs.
Since part of the statement is wrong, it makes the whole statement wrong
c) The degree of this graph is odd. Its equation is 3rd degree
d) From the graph, the line crosses the x axis at x = 1 (2nd tick line)
Each tick line represents 0.5
The zero is the value of x when it crosses the x axis
As a result the polynomial has a zero at x = 1
The correct option is there is a zero at x = 1 (option D)
Kendall rode her bike 7 miles in 45 minutes. If she maintains this speed, how far can she ride in 2 hours? Round your answer to the nearest tenth of a mile.
Kendall can ride about ___ miles in 2 hours.
Answer:
18.7 miles
Step-by-step explanation:
You want to know how far Kendall can ride her bike in 2 hours if she rides at the speed of 7 miles in 45 minutes.
ProportionThe question assumes that distance is proportional to time, so the distance (d) of interest can be written in the proportion ...
miles/minutes = 7/45 = d/120 . . . . . . 120 minutes is 2 hours
Multiplying by 120, we have ...
d = 120(7/45) = 7(8/3) = 18 2/3 ≈ 18.7
Kendall can ride about 18.7 miles in 2 hours.
Someone please help I’m stuck. The question is 13. (L4)
Donna is right. 115° angle and ∠3 are supplementary.
From the figure, we are discussing about the 115° angle and ∠3.
Donna says that m∠3 = 65° because the 115° angle and ∠3 are supplementary. That is their sum = 180°.
From the figure, it is clear that the 115° angle and ∠2 are supplementary.
So ∠2 = 180° -115° = 65°.
Now ∠2 and ∠3 are corresponding angles formed between the parallel lines m and q. Since corresponding angles are equal, m∠2 = m∠3.
Thus m∠3 = 65°.
Thus 115° + m∠3 = 115° + 65° = 180°
As the sum of the 115° angle and m∠3 = 180°, they are supplementary.
Hence Donna is correct.
Luis said that 115° and ∠3 are alternate but they are not. Alternate angles are those which are formed in the interior and on the opposite sides of the transversal cutting two parallel lines. They are of same size. But here, m∠3 ≠ 115°.
So Luis is not right.
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Suppose the population of a small town increases from 12,334 to 16,049. What is the percentincrease in the population, rounded to the nearest tenth of a percent?
First, we compute the population increase:
[tex]16049-12334=3715.[/tex]Now we divided the above result by the initial population:
[tex]\frac{3715}{16049}\approx0.23147.[/tex]Finally, we multiply by 100 and round to the nearest tenth of percent:
[tex]100\cdot0.23147=23.147\approx23.1.[/tex]Answer: 23.1%
X centimetersThe perimeter of a geometric figure is the sum of the lengths of its sides. The perimeter ofthe pentagon (five-sided figure) on the right is 54 centimeters.a. Write an equation for perimeter.b. Solve the equation in part (a).c. Find the length of each side.X centimetersx centimeters3x centimeters3x centimetersa. Choose the correct answer below.O A. x + x + x + 3x + 3x = 54OB. 9x5 = 54O C. X + x + x + x + x = 54OD. X + x + x + 3x + 3x = 9
The perimeter of a geometric figure is the sum of it's side lengths.
We have a pentagon with side lengths equal to:
x, x, x, 3x, and 3x
a)
The perimeter of this pentagon is:
P = x + x + x + 3x + 3x
Since the perimeter is given as 54 cm:
x + x + x + 3x + 3x = 54
Answer: Option A
b) Solve the equation in part a)
Collecting all like terms:
9x = 54
Dividing by 9:
x = 54 / 9
x = 6 cm
c) Find the length of each side.
The sides are
x=9 cm
x=9 cm
x=9 cm
3x=27 cm
3x=27 cm
Purchases of streamed music can be modeled by f (t) = 3.7 + 0.84 ln(t +1), where f (t) is measured in billions of dollars and t is measured in years, with t=0 corresponding to 2012.
a. What was the amount spent by consumers on streamed music in 2014? Use the correct units.
b. How fast was the amount spent by consumers on streamed music changing in 2014?
Use the correct units.
If the purchases of streamed music can be modeled by function f(t) = 3.7+0.84 ln(t+1)
Part a
The amount spent by consumers on streamed music in 2014 is 4.62 billion
Part b
The amount spent by consumers on streamed music changing in 2014 at the rate of 0.28 billions per year
The purchases of streamed music model
f(t) = 3.7+0.84 ln(t+1)
Where f(t) is measure in billion of dollar
t is the measured in years
Part a
We have to find the amount spent by consumer on streamed music in 2014.
t = 0 corresponding to the year 2012
Then 2014 corresponding to t = 2
Substitute the value of t in the equation
f(2) = 3.7+0.84 ln(2+1)
f(2) = 3.7+0.922
f(2) = 4.62 billion
Part b
Differentiate the model with respect to x
f'(t) = 0.84×[tex]\frac{1}{t+1}[/tex]
t = 2
Substitute the value in the equation
f'(2) = 0.84×[tex]\frac{1}{2+1}[/tex]
f'(2) = 0.28 billions per year
Hence, if the purchases of streamed music can be modeled by f(t) = 3.7+0.84 ln(t+1)
Part a
The amount spent by consumers on streamed music in 2014 is 4.62 billion
Part b
The amount spent by consumers on streamed music changing in 2014 at the rate of 0.28 billions per year
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Deriving the equation of parabola given its focus and directrix
The equation of the parabola from its focus and vertex is 5x = 4y² .
A parabola is a mirror-symmetrical, roughly U-shaped planar curve. The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.
A line and a point (the focus) are two components of one definition of a parabola (the directrix). There is less emphasis on the directrix. The parabola is the location of the endpoints in that plane that are equally spaced away from the directrix and the focus.
Another approach to define a parabola is as a conic section formed by the union of a right circular conical area with a plane parallel to another axis perpendicular to the conical surface.
from the figure the parabola is opening on the right side.
Hence the general equation of the parabola is is y² = 4ax
Now from the focus we get 4a = 5
or, a = 5/4
Hence the equation of the parabola is 5x = 4y².
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Fig. A is a scaled image of fig. B. Fig. A maps to fig. B with a scaled factor of 1.75. What’s the value of x?
Given:
• Length of top base of figure A = 3
,• Length of top base of figure B = x
,• Scale factor = 1.75
Given that figure A is a scale image of figure B, let's find the value of x.
To find the value of x since figure A is a scale image of figure B, multiply the corre
help l need to finish this
Answer:
Your answer is [tex]y = 2x - 2[/tex]
Step-by-step explanation:
Just test it out on all of them, it fits.
second drop-down options are can not be proven congruent and can be proven congruent
Solution
For this case the answer is:
Side-Angle-Side (SAS)
Since we have two sides congruent and also one angle
I don't understand how to write the equations using this diagram.
Given the segment on the picture, we can write the following 3 equations:
[tex]\begin{gathered} PR=PQ+QR \\ QS=QR+RS \\ PT=PR+RT \end{gathered}[/tex]the economys real gdp was 100 billion in 2019 and 240 billion in 2020. its population was 15 million in 2019 and 15 million in 2020. what is the growth rate of real gdp per capita from 2019 to 2020
The growth rate of real gdp per capita from 2019 to 2020 is 40%
Given,
The real gdp of an economy in 2019 = 100 billion = 100, 000, 000, 000
The real gdp of an economy in 2020 = 240 billion = 240, 000, 000, 000
The population in 2019 = 15 million = 15, 000, 000
The population in 2020 = 15 million = 15, 000, 000
Growth rate of real gdp per capita =( increased gdp × 100) / (initial gdp)
Here,
Initial gdp = 100,000,000,000 / 15,000,000 = 6666.67
Increased gdp = 240,000,000,000 / 15, 000, 000 = 16000
Now,
Growth rate of real gdp per capita =( increased gdp × 100) / (initial gdp)
Growth rate of real gdp per capita = (16000 × 100) / 6666.67 = 240
That is,
The growth rate of real gdp per capita from 2019 to 2020 is 40%
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What is the perimeter of a rectangle with a length of:
3+√3
and a width of:
4+ √5
Answer:
7√8
Step-by-step explanation:
3+√3+4√5
3+4+√3+√5
7+√8
Find the value of x:a) 2+3−6=−5b) 2(2+1)=5−1
In order to find the value of x in the expression, we need to isolate the terms with the variable 'x' in one side of the equation, and the variables without 'x' in the other side.
Then, we divide the whole equation by the number multiplying 'x', so we have just 'x' in one side of the equation.
So we have that:
a)
[tex]\begin{gathered} 2+3x-6x=-5x \\ 3x-6x+5x=-2 \\ 2x=-2 \\ x=\frac{-2}{2}=-1 \end{gathered}[/tex]So the value of x is -1.
b)
[tex]\begin{gathered} 2\left(2+1\right)=5-1 \\ 4x+2=5x-1 \\ 4x-5x=-1-2 \\ -x=-3 \\ x=3 \end{gathered}[/tex]So the value of x is 3
Hi, can you help me to solve this problem, please !!!
the y intercept of the curve of the function is 0.
y intercept is the point at which the curve of the function intersects the y axis.
here,
the curve intersects the Y axis at the origin.
coordinates of the origin are:
(0, 0)
So, the y intercept will be:
y = 0
Therefore, we get that, the y intercept of the curve of the function is 0.
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ROYAL ACADEMY TUTORS Empowering you to conquer your world Question 21 To travel overseas, Mr. Leeto borrows an account of money after 20 months (period), he pays back a once-off amount of R15 000 (FV) How much did he borrow (PV) (to two decimal places) if interest rate is 13% (interest rate) per annum compounded monthly (P/YR)
The amount that he borrow (PV) if interest rate is 13% (interest rate) per annum compounded monthly (P/YR) is: $12,235.90.
How to find the amount borrowed?First step is find to the number of months
n = 20 months / 12
n = 1.66666666
Now let find the amount borrowed
A= P/ ( 1+ r) ^ n
Where:
A = Amount
P = Principal
r = interest rate
n = time
Hence.
A = 15,000 / ( 1+ 0.13) ^ 1.66666666
A = 15,000 / (1.13)^ 1.66666666
A = 15,000 / 1.2259
A = $12,235.90
Therefore $12,235.90 is the amount borrowed.
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A parallelogram has one angle that measures 24°. What are the measures of the other three angles in the parallelogram?°, °, and °
Answer:
[tex]24\degree,156\degree,\text{ and 156}\degree[/tex]Explanation:
Here, we want to get the measure of the other three angles in a parallelogram
The angle rules in a parallelogram are:
i) Opposite angles are equal to each other
ii) The two adjacent angles add up to 180 degrees
From what we have, one of the angles is 24 degrees
The measure of the last two angles would be:
[tex]180-24\text{ =156}\degree[/tex]need help with this choices:x coordinatey coordinatey axisx axis not equal toequal toinput output
First, let's remember that the zeros of a function are the points where the graph intersects the x-axis, that is, those points where an x-coordinate intersects the x-axis since its output is y=0.
Therefore, the following paragraph should be filled in as follows:
You find a zero of a linear function from a graph identifying the x coordinate of any point of intersection with the x-axis, from an equation by setting the output equal to 0, and from a table by identifying the input values when the output is 0.
PLS HELP!! WILL MARK BRANLIEST What are the coordinates of the midpoint of segment whose endpoints are A(-2,7) and B(4,-2)?
Make sure to use decimals, if necessary, and write with no spaces in the format (x,y) with you solving for x and y.
When we want to determine the midpoint of two points on a line segment, we must first determine the coordinates of the two points. Then we divide the sum of the abscissa [tex](x)[/tex] by [tex]2[/tex] to find the abscissa of the midpoint and divide the sum of the ordinates [tex](y)[/tex] by [tex]2[/tex] to find the ordinate of the midpoint.
Let the coordinates of our midpoint be [tex]F(a,b)[/tex].
[tex]F(a)=\frac{4+(-2)}{2}=1[/tex][tex]F(b)=\frac{7+(-2)}{2} =\frac{5}{2}=2.5[/tex]We found our midpoint.
[tex]F(a,b)=(1,2.5)[/tex]Points B and C lie on a circle with center O and a radius of 15 units. If the length of arc BC is 21 units, what is m *BOC in radians?
Given:
[tex]\begin{gathered} r=15\text{ }units \\ \hat{BC}=21\pi\text{ }units \end{gathered}[/tex]To find:
The angle BOC.
Explanation:
Using the length of the arc formula,
[tex]\begin{gathered} l=r\theta \\ 21\pi=15\theta \\ \theta=\frac{21\pi}{15} \\ \theta=\frac{7}{5}\pi \end{gathered}[/tex]The angle is
[tex]\angle BOC=\frac{7}{5}\pi[/tex]Final answer:
The angle is
[tex]\angle BOC=\frac{7}{5}\pi[/tex]all you need is on the photo this is homework please i really needed heeeeelp
the zeros of the graph tell us the time needed for the tank to be drain.
(2t-7)(2t-9)
please help me ASAP!!!
This is the correct answer, this is because it only function that the inverse is correctly represented
[tex]\begin{gathered} y\text{ = }\sqrt[3]{x+3} \\ y^3=\text{ x+3} \\ x=y^3-3 \\ f^{-1}(x)=x^3-3 \end{gathered}[/tex]Lin knows that angle A is congruent to angle D. She claims that triangles ABC and DEF must be similar. Convince Lin that the triangles are not similar.
The triangles are not similar.
Similar triangles are what?Triangles that are comparable to one another are those that have an equal number of corresponding sides and corresponding angles.
If the respective sides of two triangles are proportional and the corresponding angles are congruent, then the triangles are said to be comparable. To put it another way, similar triangles have the same shape but may differ in size. In addition, if the corresponding sides of the triangles are identical in length, the triangles are congruent.
Here, the ratio of the sides are not similar
AB/AC= 4/10 = 2/5
DE/DF= 8/19
Hence, 2/5≠8/19
therefore, the triangles are not similar.
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