The equation for the circle whose endpoints are A(1,4) and B(5,4) is written in diameter form [tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0
A circle is what?A circle is a closed two-dimensional object in which every point in the plane is equally spaced from a certain point known as the "center" The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles. In the plane, the circle formula is as follows:
The coordinate coordinates (x,y) are equal to (x-h)2 + (y-k)2 = r2.
The centre of a circle is located at (h,k), and its radius is measured in units of r.
The equation of a circle having end points of the diameter as (x1,y1) and (x2,y2) is (x−x1)(x−x2)+(y−y1)(y−y2)=0.
we have (1,4) and (5,4) as (x1,y1) and (x2,y2)
(x−(1))(x−(5))+(y−(4))(y−(4))=0
⇒ ([tex]x^{2}[/tex] -5x -1x + 5 ) + ( [tex]y^{2}[/tex] -4y -4y + 16 ) = 0
[tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0
The equation for the circle whose endpoints are A(1,4) and B(5,4) is written in diameter form [tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0.
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Not understanding this question
The unknown angle in the triangle is as follows:
∠E = 100 degrees.
How to find angles in a triangle?The sum of angles in a triangle is 180 degrees.
In the diagram, BCD is cut by transversal ACE , AB and perpendicular to BCD and CE ≅ ED.
Therefore,
∠ACB = 180 - 50 - 90 (sum of angles in a triangle)
∠ACB = 180 - 140
∠ACB = 40 degrees
Therefore,
∠ACB ≅ ∠DCE
Hence,
∠DCE = 40 degrees.
Triangle CDE is an isosceles triangle since CE ≅ DE.
Hence,
∠CDE = 40 degrees
∠E = 180 - 40 - 40
∠E = 180 - 80
∠E = 100 degrees.
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The yearly profits of a company is $25,000. The profits have been decreasing by 6% per year.
Part A: Write an exponential function that represents this scenario. Format your answer like: A(t)=a\left(1\pm r\right)^{t}A(t)=a(1±r)
t
An Exponential Function that can depict this situation is [tex]A(t) = 25000(0.94)^{t}[/tex]
What is an Exponential Function?
An exponential function is a mathematical function of the following form: [tex]f(x)=a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.
Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula [tex]y=a(1-r)^{x}[/tex] wherein y is the final amount, a is the original amount, r is the decay factor, and x(or t) is the amount of time that has passed.
Given :
The initial amount is 25,000, and the rate of decay is 6%, or 0.06.
Write the exponential Decreasing function.
[tex]A(t) = a(1-r)^{t}[/tex]
Substitute 25,000 for a and 0.06 for r.
[tex]A(t)=25,000(1-0.06)^{t} = 25,000(0.94)^{t}[/tex]
Hence , the Situation can be represented by [tex]A(t) = 25000(0.94)^{t}[/tex]
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47.5 min to jog 5 mi, min to jog 11 mi
Answer:
104.5 min
Step-by-step explanation:
47.5:5=x:11
1. Simplify
9.5:1=x:11
2.Solve
x=104.5
You're given AIKJ with m/JIK = 53°, m/IKJ = (82-5x), and m/KJI = (7z+24)°. What is mZIKJ? Your final answer might not look to
scale. Do NOT round your answer.
Angle ∠IKJ is 29.5 degrees for triangle IKJ.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The given triangle is IKJ.
The angles are given as follow.
∠JIK = 53°,
∠IKJ = (82-5x), and
∠KJI = (7x+24)°.
We need to find the angle ∠IKJ .
By angle sum property of triangle, the sum of three angles is 180 degrees.
∠JIK+∠IKJ+∠KJI = 180
Fifty three plus eighty two minus five times of x plus seven times of x plus twenty four equal to one hundred and eighty.
53+82-5x+7x+24=180
Add the like terms
159+2x=180
One hundred fifty nine plus two times of x equal to one hundred eighty.
subtract 159 on both sides
2x=21
Divide both sides by 2.
x=10.5
So ∠IKJ is 82-5(10.5)=29.5 degrees.
Hence, the value of angle ∠IKJ is 29.5 degrees.
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The price of the shirt was $38. It was reduced by 20% and then again by 10%.
Answer:$26.6
Step-by-step explanation:
Answer:
= 26.6
Step-by-step explanation:
38 * 20/100 = 38 *1/5 = 7.6
38 - 7.6 = 30.4
38 * 10/100 = 38 *1/10 = 3.8
30.4 - 3.8 = 26.6
The sales tax rate is 4.315% for the city and 4% for the state. Find the total amount paid for 2 boxes of chocolates at $17.07 each.
PLS HELP ME
Answer: $18.49
Step-by-step explanation:
First, add both the tax rate, 4.315 + 4 = 8.315%
Then take 17.07 divided by 100%, then times 8.315% = $1.42
Then add 17.07 + 1.42 = $18.49
50 PTS Determine if you can use the hypotenuse-leg congruency property to prove the triangles are congruent.
A. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if a leg of one triangle is congruent to a leg of the other triangle.
B. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the hypotenuses are congruent.
C. Yes, the hypotenuse-leg congruence property can be applied.
D. No, the hypotenuse-leg congruence property cannot be applied, because we don't know if the triangles are right triangles.
PLEASE HELP GIVING BRAINLIEST!!!!!!!!!!!!!!!!!!!!
Select all that apply. Which equations could you use to solve the following problem? Seventy-eight is 55% of what number? p = (0.85)78 = 78 = (0.55) w =
Answer:
x/78 = 55/100
Step-by-step explanation:
if an analyst is studying the wait times at a clinic and the only list of patients available is on hard copy, which sampling technique is the easiest to use?
Sampling technique is the easiest to use here is systematic sampling.
Given :
if an analyst is studying the wait times at a clinic and the only list of patients available is on hard copy .
The sampling technique in this scenario is used is systematic sampling.
Systematic sampling :
Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval.
k = N/n
where
k = systematic sampling interval
N = population size
n = sample size.
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In 1983, a pair of jeans cost $66.35. If a pair of jeans costs $118.10 today, what is the CPI? a. 152 b. 156 c. 178 d. 184 Please select the best answer from the choices provided A B C D
The value of CPI will be 178.
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;
In 1983, a pair of jeans cost $66.35.
And, A pair of jeans costs $118.10 today.
Now,
Since, In 1983, a pair of jeans cost $66.35.
And, A pair of jeans costs $118.10 today.
Hence, The value of CPI will be;
CPI = 118.10 × 100 / 66.35
= 11810 / 66.35
= 178
Thus, The value of CPI will be 178.
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Solve for x.
Thank you
Answer:
12
Step-by-step explanation:
The measure of each interior angle is [tex]\frac{180(8-2)}{8}=135^{\circ}[/tex].
[tex]\implies 135=9x+27 \\ \\ 15=x+3 \\ \\ x=12[/tex]
Factor the following expression.
5x5 - 3x² - 10x³ +6
(x2 – 2) (5x3 – [?]
Answer:
(x²-2) (5x³-3)
Step-by-step explanation:
rearrange terms
5x⁵-10x³-3x²+6
find one factor
(x²-2) (5x³-3)
Help mehhhhhhh please
Answer:
Jordan
Step-by-step explanation:
The composite number was 21.
21 can be divided by 3 and 7.
Answer: Jordan.
Step-by-step explanation:
Prime numbers are special numbers that have no divisors other than itself and [tex]1[/tex]. Prime numbers are observed in the lists created by the students.
Compound numbers are numbers that can be written as the product of at least two prime numbers. When we look at Jordan's list, we will see that the number [tex]21[/tex] breaks this rule. Because the number [tex]21[/tex] is the product of both prime numbers [tex]3[/tex] and [tex]7[/tex]. It is not a prime number. It is a composite number.
Jessica deposits her summer babysitting earnings, $600, in a savings account. How many years will it take her to earn $150 in interest at a simple annual rate of 5%? Enter the correct number in the formula.
150 = (600) (.05) (?)
this is a middle school question not high school sorry
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 150\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 150 = (600)(0.05)(t) \implies \cfrac{150}{(600)(0.05)}=t\implies 5=t[/tex]
Find what K is in this question
Answer:
[tex]\huge\boxed{\sf k = 3}[/tex]
Step-by-step explanation:
Given that,[tex]5+6i+(-2+ki)=3+9i\\\\5 + 6i-2+ki=3+9i\\\\Combine \ like \ terms\\\\5-2+6i+ki=3+9i\\\\3+(6+k)i=3+9i\\\\Comparing \ both \ sides\\\\6 + k = 9\\\\Subtract \ 6 \ both \ sides\\\\k = 9-6\\\\k = 3\\\\\rule[225]{225}{2}[/tex]
Solve the following equation for x:
3(x+5) = 1/9
8
4
-8
None of these choices are correct.
The solution to the linear equation 3(x + 5) = 1/9 is
x = -4 26/27.
The correct answer is option D; None of these choices are correct.
How to solve linear equation?3(x + 5) = 1/9
open parenthesis
3x + 15 = 1/9
Substract 15 from both sides
3x = 1/9 - 15
3x = (1-135)/ 9
3x = -134/9
divide both sides by 3
x = -134/9 ÷ 3
Multiply by the reciprocal of 3
x = -134/9 × 1/3
= -134/27
x = -4 26/27
Therefore, -4 26/27 is the solution that satisfies the equation 3(x + 5) = 1/9
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The square root of (-5x)^3, for which values of x does this expression make sense?
Answer: Yes it does, it is -125x to the power of 3.
Step-by-step explanation:
Answer:MONKEY
Step-by-step explanation:
CAUSE I SAID DO
Through a given point not contained in a given line, there exists ___ ___ line parallel to the given line. (two words)
There is ONLY ONE __ line parallel to the provided line that passes through a certain point that is not contained in the supplied line.
What do parallel lines mean?Parallel lines are any two or more lines that are in the same plane but never cross one another ( never intersect). Both have the same slope and are equally far from one another.
We have a line and a point outside the line;
from that point, we can generate many lines, but only one of those lines will be parallel to the line as it is. From a point, we can make many lines, but that point can only create one line that will be parallel to a given line.
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What is the area of AFGH?
-10 -8 -6
H
Area =
-4 -2
square units
104
-8
6
4
2
0
2
-4
-6
-8
-10
4
6
8
00
F
X
10
G
Answer:
-2 = x 4-2 square units
Step-by-step explanation:
sum = as per as chart
Henry took 42.7 minutes to complete an exam Laticia took 28.7 minutes to complete the same exam who completed their exam first
Answer:
Unless these took place in different time periods, Laticia did first.
Step-by-step explanation:
28.7 < 42.7
Ivan,Bella, and Ian agreed to hare a pizza which wa cut into 10 lice. Ivan at 40% of the pizza
Using the percentage writing form, we know that Ivan ate 4 pizza slices.
What are percentages?By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage.
The percentage calculation formula is (value/total value)100%.
Add all percentages as numbered values, divide by the total number of sets, and you get the average percentage.
The results by 100.
So, we know that:
Ivan ate 40% of the pizza.
And the pizza was cut into 10 slices.
Rewrite the percentage value as:
4/100 = 0.4
We can calculate how many slices Ivan consumed by multiplying the percentage value by the number of slices:
10 + 0.4 = 4
Hence, Ivan ate 4 slices of pizza.
Therefore, using the percentage writing form, we know that Ivan ate 4 pizza slices.
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How many ways can you answer a 5 multiple choice question test, where there are 4 choices for each question
There are 1024 ways to answer the 5 multiple choice question having 4 options
What is permutation ?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. A permutation is a term that describes the variety of possible arrangements or orders of objects.
We have 5 multiple choice questions.
And we are given four options to solve the question
Repeating is permitted (you can answer "c" on all of the questions if you want to)
So ,
We will use permutation to solve the question
[tex]n^{r}[/tex]
r is number of questions = 5
n is number of choices = 4
[tex]4^{5}[/tex] = 4×4×4×4×4 = 1024
There are 1024 ways to answer the 5 multiple choice question having 4 options
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A belt connects two pulleys. Larger pulley has a radius of 60cm and the smaller pulley has a radius of 20cm. The smaller pulley runs at 48 revolutions per min
a) how many revolutions per minute does the larger pulley run at? [hint: find the circumference of each pulley]
(i got 16 rev per min i don't know if that's correct)
b) find angular speed of the smaller pulley in radians per min
c) find the angular speed of the larger pulley in radians per min
d) find the speed of the smaller pulley in cm per min
Therefore the solution to this question of 2 pulleys is )16 rpm
b)360 rad/min c)39.6 rad/min d) 7200cm/min
What is Angular speed?A pseudovector used in physics to express how quickly an object's angular position or orientation changes over time is called an angular velocity, rotational velocity, or angular frequency vector.
For the smaller pulley, it does 48 rpm (revolutions per minute) each revolution is 360 degrees. This indicates that the pulley completes one revolution every second .
radians / π = degrees / 180
radians = πx 360 / 180 = 2 π radians per second
The distance covered by both pulleys is equivalent for the larger pulley.
then d1 = d2
every second, small pulley covers a distance of 40π (small pulley circumference) = d1
d2 = 40π = 120π (large pulley circumference) x factor (f)
f = 1/3
a) the revolutions per min by larger pulley=16 rpm
b) the speed of smaller pulley = 3*2π=6π=6rad/sec=360rad/min
c) then speed of the large pulley = 1/3 * 2π = 2/3 π = 0.66 rad/sec=39.6rad/min
d)the speed of smaller pulley=7200 cm/min
Therefore the solution to this question of 2 pulleys is )16 rpm
b)360 rad/min c)39.6 rad/min d) 7200cm/min
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Please help me.
Prove that if a + b > 100, a, b, or both must be greater than 50
Answer:
Step-by-step explanation:
To prove this statement, we can use the contrapositive. The contrapositive of the statement "If a + b > 100, then a, b, or both must be greater than 50" is "If a and b are both less than or equal to 50, then a + b is less than or equal to 100."
To prove the contrapositive, we must show that if a and b are both less than or equal to 50, then a + b is indeed less than or equal to 100. This is easy to do, because if a and b are both less than or equal to 50, then the largest possible value for a is 50 and the largest possible value for b is 50. Therefore, the largest possible value for a + b is 50 + 50, which is equal to 100.
Since the contrapositive is true, it follows that the original statement must also be true. Therefore, we have proven that if a + b > 100, then a, b, or both must be greater than 50.
Select the expressions that are equivalent to 8(5q). 8 + 5g 8(5 + q) 40q (q + 5)8
I don't know what is equivalent to 8(5q) ?
Answer:
the answer is 40q
Step-by-step explanation:
8x5 is 40 when using the distributive property
Your family goes to a Southern-style restaurant for dinner. Some order chicken dinner for $14 each and some order the steak dinner for $17 each. If the total bill came to $99, how many people ordered dinner?
People in my family ordered 1 chicken dinner and 5 steak dinner.
There are total 6 peoples in a family.
Let's x number of people order chicken dinner
and y number of people order steak dinner.
Here we have to use concept of linear equation.
we have to make 2 linear equation and solve them to get the value.
sum of number of people is 6.
[tex]x + y = 6[/tex] --- i
total bill came to $99.
1 chicken dinner takes $14.
So x chicken dinners takes x*14
1 steak dinner takes $17.
So y steak dinners takes y*17.
Sum of both dinners price
[tex]x*14+y*17 = 99[/tex] -- ii
From equation i x = 6 - y.
put value of x in equation ii.
(6-y)*14+y*17 = 99
84-14*y+17*y = 99
3*y = 99-84
3*y = 15
y = 5
x = 6-5 = 1.
So 1 people ordered chicken dinner and 5 people ordered steak dinner.
Given Question is incomplete Complete Question here
Your family goes to a southern style restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14 and some order the steak dinner for $17. If the total bill was $99 l, how many people ordered each dinner?
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Raquel wants to buy a concert ticket online. Raquel has a coupon code to discount the cost of the concert ticket. The cost of the concert ticket online has been found to be t-.25t + 15, where t the cost of the ticket in dollars.
By what percent is the ticket cos being discount ?
How much is the flat booking fee ?
Answer:
the percent being discounted is 25% and the flat booking fee is 15
Step-by-step explanation:
t is the cost of the ticket. -.25t is the 25% coupon being taken off. The 15 is the booking fee.
“The sum of three and a number, divided by three, is five”
I need help again due tomorrow
Answer: The number is 12
Step-by-step explanation:
Let x= the number that is unknown
The sum of three and a "number"= 3+"x"
Divided by three, means that x+3 is divided by 3
Is five, means that (x+3)/3=5
Algebra:
[tex]\frac{x+3}{3}=5[/tex]
Multiply by 3 to arrive at x+3=15
Subtract both sides by 3, then x=12
The radius of a circle is 4.5 cm. Find the circumference
to the nearest tenth
Answer: C≈28.27cm
Step-by-step explanation:
C=2πr=2·π·4.5≈28.27433cm
Answer:
28.3 cm
Step-by-step explanation:
You want the circumference of a circle with radius 4.5 cm.
CircumferenceThe circumference of a circle is given by ...
C = 2πr
For the given circle, the circumference is ...
C = 2π(4.5 cm) = 9π cm ≈ 28.3 cm
The circumference is about 28.3 cm.
<95141404393>
What is the probability of landing on a 5 and then landing on an even number?
Write your answer as a percentage rounded to the nearest tenth.
The probability of landing on a 5 and then landing on an even number is 8.3%.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
The number of 5 on the dice is one.
Probability is the ratio of the number of favorable outcome to the total number of outcome.
The number of faces of dice is 6.
The probability of getting 5 is 1/6.
The even faces on the dice are 2, 4, 6.
The number of even number faces is 3.
The probability of getting even number is 3/6 = 1/2.
The probability of two independent event is the product of the probability of the events.
Therefore, the probability is (1/6) × (1/2)
= 1/12
= 0.083
= 8.3%
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