Use the figure below for the following problems (not drawn to scale).
Given: m/1 = 70,
What is m/4?
O a 125⁰
.Ob
70°
Oc
40°
Od
55°
5
6
The measure of angle 4 is 125° for the given triangle.
According to the question,
We have the following information:
A figure is given of triangle and its exterior angles.
m∠1 = 70°
Now, the two sides (with line on them) of the triangle are equal. So, it means that it is an isosceles triangle.
We know that sum of three angles of a triangle is 180°.
Let's take the two equal angles to be x°.
x+x+70 = 180
2x+70 = 180
2x = 180-70
2x = 110
x = 110/2
x = 55°
We know that angles made on a straight line is 180°.
∠4 and angle x will make a straight line.
∠4 = 180-55
∠4 = 125°
Hence, the correct option is A.
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In 2012, the population of a city was 5.04 million. The exponential growth rate was 1.65% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 7 million?
d) Find the doubling time.
Answer: It will take 24 years to have 7 million.
Step-by-step explanation:
1.65% of 5.04 million is 83,160.
2018 is 6 years from 2012.
83,160 x 6 = 498,960.
498,960k + 5,040,000mil =5,538,960mil. still not quite 7 million.
498,960k x 4 = 1,995,840mil.
1,995,840mil + 5,040,000mil = 7,035,840mil.
It will take the city 24 years to have 7 million.
-2 = 3x + 8/2 Solve for x.
Simplify your answer as much as possible.
Answer:
x= -2
Step-by-step explanation:
-2 = 3x + 8/2
-2+2=3x+4+2 (add 2 to both sides)
0=3x+6
-6=3x+6-6
3x=-6
x=-6/3
x= -2
A radioactive compound with mass 100 grams decays at a rate of 5.8% per hour. Which equation represents how many grams of the compound will remain after 2 hours?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 5.8\%\to \frac{5.8}{100}\dotfill &0.058\\ t=\textit{hours}\dotfill &2\\ \end{cases} \\\\\\ ~\hfill A=100(1 - 0.058)^{2} ~\hfill[/tex]
The equation represents the grams of the compound will remain after 2 hours will be;
⇒ C = 100 (1 - 0.058)²
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A radioactive compound with mass 100 grams decays at a rate of 5.8% per hour.
And, Time = 4 hours
Now,
Since, We know that;
Amount for Exponential Decay is,
⇒ [tex]C = P (1 - r)^t[/tex]
Where, C is current amount, P is initial amount, r is rate and t is timeeee
Substitute all the values, we get;
The equation represents the grams of the compound will remain after 2 hours will be;
⇒ C = 100 (1 - 0.058)²
Thus, The equation represents the grams of the compound will remain after 2 hours will be;
⇒ C = 100 (1 - 0.058)²
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help please and thankyou 4
The ratios of the right triangle to solve for x is as follows;
sin x = 6 / 10cos x = 5 / 10tan x = 4 / 6How to find the angles of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The sides of a right angle triangle can be named base on the position of the angles.
The sides of a right angle triangles are hypotenuse sides, opposite and adjacent side. The hypotenuse side is the longest side of the right triangle.
Therefore, let's find the ratio that can be used to find the angle x.
Triangle PNM
sin x = opposite / hypotenuse
sin x = 6 / 10
Triangle ABC
cos x = adjacent / hypotenuse
cos x = 5 / 10
Triangle DEF
tan x = opposite / adjacent
tan x = 4 / 6
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P
E
MD
AS
Simplify using
order of operations.
14 + 6 x 2-16+8
Answer: 18
Step-by-step explanation:
There are no parenthesis or exponents, so you use multiplication first.
6 x 2 = 12
That makes your equation 14 + 12 - 16 + 8
Now you only have adding and subtracting left, which you’ll do from left to right.
14 + 12 = 26
26 - 16 + 8
26 - 16 = 10
10 + 8 = 18
Hope this helps!
Determine whether AB and CD are parallel, perpendicular, or neither for A (-1,-1), B (1,5), C (1,2), D (5,4). Graph each line to verify your answer.
Answer:
you can do the favour of marking the answer brainlest pls
Rational zeros of polynomial function
Help!
Zeros of the given polynomial are -2, 2, -3/2, 3/2
What are zeroes of a polynomial?Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.
Given a polynomial 1/4(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36)
1/4(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36) = 0
(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36) = 0
4[tex]x^{4}[/tex] - 16[tex]x^{2}[/tex] - 9[tex]x^{2}[/tex] + 36= 0
4[tex]x^{4}[/tex]([tex]x^{2}[/tex] - 4) - 9([tex]x^{2}[/tex] - 4) = 0
(4[tex]x^{4}[/tex]-9)([tex]x^{2}[/tex] - 4) = 0
(x+2)(x-2)(2x+3)(2x-3) = 0
x = -2, 2, -3/2, 3/2
Hence, Zeros of the given polynomial are -2, 2, -3/2, 3/2
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Given the equation y=78x+15, what is the value of y when x is 4?
Answer:327
Step-by-step explanation:
Because you already have the equation, all you need to do is plug in the value for X. If X is equal to 4, our equation would look like this:
y = 78 * 4 + 15
Because of order or operations (PEMDAS), we do multiplication first.
y = 312 + 15
y = 327
Hope this helped!
determine the sum of the first 8 terms of the geometric sequence if the first term is 5, the common ratio is -2 and the 8th term is -640
Answer:
-425
Step-by-step explanation:
You want the sum of the first 8 terms of the geometric series with first term 5 and common ratio -2.
Series sumThe sum is given by the formula ...
Sn = a1·(r^n -1)/(r -1) . . . . . . a1 = first term, r = common ratio
The sum of 8 terms of the given series is ...
S8 = 5·((-2)^8 -1)/(-2 -1) = 5(255/-3) = -1275/3 = -425
The sum of 8 terms is -425.
Express this equation
Which of these statements are true? Choose all answers that apply: (Choice A) Greater width relates to greater area as long as the width is less than 10 (Choice B) Greater width relates to greater area as long as the width is more than 10 (Choice C) To get the greatest area, the width should be 10 (Choice D) To get the greatest area, the width should be 20
The true statement about the function of area of by rectangle and width of rectangle are:
Greater width relates to greater area as long as the width is less than 10 To get the greatest area, the width should be 10The correct answer option is options A and D
Which width gives the maximum area of rectangle?A rectangle is a quadrilateral having opposing sides parallel and four right angles.
At point (x, y) = (10, 100) the area is maximum.
This means that the area of the rectangle is maximum when width is 10m.
If the width of the rectangle is more than 10m, the area reduces or decreases.
Therefore, the statement Greater width relates to greater area as long as the width is more than 10 m is false.
The statement "To get the greatest area, the width should be 20" is false.
Complete question:
Simon has a certain length of fencing to enclose a rectangular area. The function A, models give the rectangles area (in square meters) as a function of its width (in meters).
Wlhich of these statements are true?
A. Greater width relates to greater area as long as the width is less than 10.
B. Greater width relates to greater area as long as the width is more than 10.
C. To get the greatest area, the width should be 10
D. To get the greatest area, the width should be 20
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Alex invests $300 in a company. He will receive 6% simple interest annually for the next 5 years.
After 5 years, Alex will have earned in interest.
Answer: After 5 Years Alex will receive 90 Dollar.
Step-by-step explanation 5 x 6% of 300 = 30% is 90 Dollar.
Find the original price given each total amount and rate of increase. Round to the nearest cent if necessary. 83.82. 10%
The original amount is $92.202.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.
Given:
Total amount = 83.82
rate of increase = 10%
So, the original amount
= 83.82 + 83.82 x 0.1
= 83.82 + 8.382
= $92.202
Hence, the original amount is $92.202.
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The gold trophy has 27 racers, she will 12 racers on the racetrack that runs.
How many racers did she have runs?
She will have run a total of 2.25 racers in 27 racers
How to determine the number of racers?From the question, we have the following parameters that can be used in our solution:
Total number of racers = 27 racers
Number of racers in a run = 12 racers
From the above parameter, we can calculate the total number of racers using the following equation
The total number of racers is calculated as
Total number of racers in the run = Total number of racers/Number of racers in a run
Substitute the known values in the above equation
So, we have the following equation
Total number of racers in the run = 27/12
Evaluate the quotient
Total number of racers in the run = 2.25
Hence, the total number of racers in the run is 2.25 racers
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Solve the equation for y
2.5y = 5x -5
Answer:
y=2x-2
Step-by-step explanation:
2.5y=5x-5
/2.5. /2.5
y=2x-2
Hopes this helps please mark brainliest
Answer:
y=2x−2
Step-by-step explanation:
The slope-intercept form is
y=mx+b, where m
is the slope and b
is the y-intercept.y =mx+b
Divide each term in 2.5y=5−5 by 2.5
and simplify. y=2x−2
In ΔHIJ, h = 730 cm, i = 390 cm and ∠J=35°. Find the area of ΔHIJ, to the nearest square centimeter.
The area of the triangle ΔHIJ is 42805 square centimeters.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the area of a given ΔABC can be obtained by (1/2)×a×c×sin(∅/2)
where sin(Ф/2) is the included angle.
Given, ΔHIJ, h = 730 cm, i = 390 cm and ∠J=35°.
∴ The area of the ΔHIJ is (1/2)×730×390×sin(35/2) square centimeter.
= 142,350×sin(17.5) square centimeter.
= 42805 square centimeters.
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John walks at a constant rate of 8 miles every 3 hours. What is the rate written as miles per hours
The rate written in miles per hour is 2.67 mph.
What is constant rate?
A rate of change is constant when, at any given point along the function, the ratio of the output to the input remains constant. The slope is another name for the rate of change that is constant. A linear function will change at a constant rate.
Let, John walks at a constant rate of 8 miles every 3 hours.
Therefore, the rate per hour is,
[tex]\frac{8}{3} = 2.6666\\ = 2.67 miles per hour.[/tex]
Therefore, the rate written in miles per hour is 2.67 miles per hour.
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C The graph
represents the
balance in
Jimena's
checking account
based on the
number of days
since her last
paycheck.
9. The graph can be represented by
y = 450x - 25.
True or False? If false rewrite statement correctly
Answer:
False
Step-by-step explanation:
The correct answer is y = -25x + 450
Joseph takes out a loan that gathers compound interest.
The table below shows the value of the loan over time.
a) What is the rate of interest per annum?
Give your answer as a percentage to 1 d.p.
b) Work out the value of the loan 10 years after it starts.
Give your answer in pounds (£) to the nearest 1p.
Start
£7500.00
After 1 year
£7965.00
After 2 years
£8458.83
Answer:
a) 6.2%
b) £13,687
Step-by-step explanation:
a)
To find the rate of interest, we first find the interest itself.
£7965.00 - £7500.00 = £465.00
Using this, we find the rate of interest in percentage as a fraction of the original loan.
(£7500.00 ÷ £465.0) × 100 = 6.2%
Thus, the rate of interest is 6.2%.
b)
Compound interest is found using the formula
[tex]A = P(1 + \frac{r}{100})^{t}[/tex]
Where
A = final amount
P = initial principal balance
r = interest rate
t = number of time periods elapsed
Thus, with an initial balance of £7500, an interest rate of 6.2% and a time period of 10 years, calculated per annum, we can plug the numbers into the formula, giving us
[tex]A = 7500(1 + \frac{6.2}{100})^{10}[/tex]
[tex]=[/tex] £13,686.94
≈ £13,687 (to nearest £1)
Some things to note: number of time periods elapsed mean the amount of times it is compounded; if the question says compounded quarterly for 3 years, t = 12 as it is compounded 4 times a year for 3 years, giving is 12 time periods. This also applies to monthly, bi-weekly etc.
the quotient of Y and 9 is greater than 4
X=11 find X if y is 2
Answer:
it is 3 0 o 90 not up okbg 56
A population of beetles grows by 25% every month. If the beetle population starts
with 1, 600 beetles, which equation represents the population, P, after t months?
OP= 1,600(0.25)*
OP= 1,600(1.25)
OP 1,600 +0.25t
OP= 1,600 +1.25t
Answer:
Step-by-step explanation:
A movie theater sends out a coupon for 45% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant.
The equation where y is the price of the ticket with the coupon, and x is the original price of the ticket.
y= 0.55 x.
Given:
A movie theater sends out a coupon for 45% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket.
If x is the price of the ticket without the coupon, and the theater offers a discount if you have a coupon, then having a coupon means that the price a person ultimately pays (y) is the original price (x) minus a 45% of this price:
y= x -0.45 x
By association: y= (1-0.45) x
and then y= 0.55 x.
The line should be in the first quadrant because the first quadrant allows you to represent a situation in which the dependent variable (y) and the independent variable (x) are both positive. This is the case in this exercise, because both prices, the one without discount (x) and the one with discount (y) are necessary positive (you can not pay a negative price!).
Hence we get the required equation.
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Sarah took a survey asking students if they prefer summer or winter sports. She found that 12 out of 18 students prefer summer sports. Determine what fraction of students prefers winter sports. Write your response in simplest form. Explain how you found your answer.
Answer: 2/3
Step-by-step explanation:
12 out of 18 prefer summer sports so as a fraction it would be 12/18 = 6/9 = 2/3
Answer:
33.3333%
Step-by-step explanation:
EXPLANATION
Based on the given conditions, formulate: (18-12) ÷ 18
Calculate the sum or difference:[tex]\frac{6}{18}[/tex]
Cross out the common factor:[tex]\frac{1}{3}[/tex]
Rewrite a fraction as a decimal: 0.333333
Multiply a number to both the numerator and the denominator: 0.333333x[tex]\frac{100}{100}[/tex]
Write as a single fraction:[tex]\frac{33.33333x100}{100}[/tex]
Calculate the product or quotient:[tex]\frac{33.333}{100}[/tex]
Rewrite a fraction with denominator equals 100 to a percentage: 33.3333%
Answer: 33.3333%
a cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 7.5. what are the dimensions of such a cylinder which has maximum volume? radius
At that particular critical point, the second derivative needs to be negative in order to obtain the dimensions of the cylinder with the maximum volume. The values of the function that contain both variables are then substituted to obtain the dimensions.
A right circular cone with a height of 2.5 and a base radius of 7.5 inscribes the given cylinder.
Assume that h is the height and r is the radius of the cylinder. Using triangles that are similar, express h in terms of r as follows:
2.5/7.5 = 2.5-h/r
2.5r = 18.75 x 7.5 x 2.5 h = 2.5 x 1/3r
V= πr²h is the formula for the cylinder's volume.
As a result, only write the volume in terms of r.
V= r2h V= r2(2.5-1/3r)
V= 2.5πr² - 1/3πr³
As a result, the cylinder must have dimensions of r=5 and h=0.83.
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Solve the following:-
[tex]\sf \cfrac{x}{11} + 16 = 30[/tex]
Answer:
x = 154
Step-by-step explanation:
[tex]\frac{x}{11}[/tex] + 16 = 30 ( subtract 16 from both sides )
[tex]\frac{x}{11}[/tex] = 14 ( multiply both sides by 11 to clear the fraction )
x = 11 × 14 = 154
Answer:
x = 154
Step-by-step explanation:
Given equation,
→ (x/11) + 16 = 30
Now the value of x will be,
→ (x/11) + 16 = 30
→ x/11 = 30 - 16
→ x = 14 × 11
→ [ x = 154 ]
Hence, value of x is 154.
How to solve this mathematical question
Answer:
Part B: (0, -6)
Part C: x = -1
Part D: (-1, -8)
Explanation:
see the attached pdf
Rain fell at a constant rate for 2 hours on Friday. During that time, the total amount of rain that fell was 3/4 inch. what is the rate, in inches per hour, at which rain fell during that time on Friday?
3 1/3
1 7/8
8/15
3/10
The rate, in inches per hour, at which the rain fell during that time on Friday is 3/8 inches per hour.
Time for which the rain fell = 2 hours
The total amount of rain that fell = 3/4 inch
So, in 2 hours, the amount of rain that fell = 3/4
In 1 hour, the amount of rain that fell = 3/8 inches
Hence, The rate, in inches per hour, at which the rain fell during that time on Friday = 3/8 inches per hour.
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2. Create a graph in the workspace provided to model the relationship that that exists if the school store is selling 5 pens (x) for $2.00 (y). Then find the constant rate of change.
Answer: The constant of variation, k , is 54
Step-by-step explanation: Step 1: Check whether the graph is a straight line. If the graph is not a straight line, it does not represent a proportional relationship. Step 2: Check whether the line goes through the origin. If the graph does not go through the origin, it does not represent a proportional relationship.