The standard equation of the circle is x² + y² + 8x - 9 = 0 if the circle with center at (-1,-4) that passes through the point (-4,0).
According to the question,
The circle with center at (-1,-4) that passes through the point (-4,0).
To find the radius of the circle:
Radius r = √[(-4 - (-1))² + (0- (-4))²]
=√(-4+1)² + (4)²
=√9+16
=√25
=5.
In order to find the standard equation of the circle is
(x - (-4))² + (y - (0))² = (5)²
(x + 4)² + (y )² = 25
x² + 8x + 16 + y² = 25
x² + y² + 8x + 16 = 25
x² + y² + 8x = 25 - 16
x² + y² + 8x = 9
x² + y² + 8x - 9 = 0
Hence, the standard equation of the circle is x² + y² + 8x - 9 = 0.
Learn more about circle here
https://brainly.com/question/12238856
#SPJ4
This map of china is 65inches from east to west and 68 from the north to south. if 1 inch is 50 miles, how large is the actual country?
The country is 3250 miles in distance from east to west, and 3400 miles from north to south.
Given Information
It is given that,
The distance of the country on map from east to west, l = 65 inches
The distance of the country on map from north to south, b = 68 inches
As per the given scaling of map, 1 inch = 50 miles
How large is the actual country?
Thus, the actual distance from east to west, L = l × 50 miles
L = 65 × 50 miles
L = 3250 miles
The actual distance from north to south, B = b × 50 miles
B = 68 × 50 miles
B = 3400 miles
Therefore, the actual size of the country is 3250 miles in distance from east to west, and 3400 miles in distance from north to south.
Learn more about distance here:
https://brainly.com/question/15172156
#SPJ4
The triangles are similar. Find the value of the variable.
PLEASE IM BEGGING U so hard to understand T_T
Answer:
[tex]b^{2} +7b+7[/tex] with remainder 1
1. The length of a rectangle is four
times its width. If the area is 100m
what is the length of the rectangle
Answer:
20m
Step-by-step explanation:
write a equation duh
x * 4x = 100
u can split 100 into 5 x 20
x * 4x = 5 * 20
x = 5
and 4x = 20
Some band members have raised much more money than other. which measure can be used to show this?explain.
A ratio measure can be used to show this.
What is a ratio measure?A ratio in mathematics describes how many times one number contains another.The highest (most sophisticated) level of measurement that a variable can have is referred to as a ratio measure.A 3 to 5 ratio (3:5) A 3:5 ratio can be written as 3:5, 3/5, or 3/5. Furthermore, 3 and 5 can represent any number or measurement, including pupils, fruit, weights, heights, speed, and so on. A 3 to 5 ratio simply means that for every three of something, there are five of something else, for a total of eight.Therefore, a ratio measure can be used to show the given situation.
Know more about ratios here:
https://brainly.com/question/2328454
#SPJ4
When rolling a single number cube, what are the odds, in simplest form, in favor of rolling a 4 or a 5?
A. 1:1
B. 1:2
C. 1:3
D. 1:5
Answer:
C
Step-by-step explanation:
You have a total of 6 outcomes (1,2,3,4,5,6). That is your numerator. Out of those numbers, you only want 2 of them (4 or 5), so the fractions would be 2/6 or 1/3 which can also be written 1:3
Find the missing side length of the triangle.
Answer:
c = 10
Explanation:
Use Pythagoras theorem: a² + b² = c²
where 'a' and 'b' are legs and 'c' is the hypotenuse (the longest side)
Here given: a = 8 cm, b = 6 cm, c = ?
Substituting values:
8² + 6² = c²
c² = 64 + 36
c² = 100
c = √100
c = 10
Answer:
10 cm
Step-by-step explanation:
[tex]a^2=b^2+c^2[/tex]
[tex]a^2=6^2+8^2[/tex]
[tex]a^2=100[/tex]
[tex]\sqrt{a^2}=\sqrt{100[/tex]
a=10
Using the unit circle, determine the value of sin(-240°).
Answer:
See my picture below for the answer.
Step-by-step explanation:
If you look at the unit circle and locate 240 degrees. You will see an ordered pair. The first number -1/2 is the cos of 240 and the second number is the sin.
Answer:
it’s the square root of 3, divided by 2 (sorry, can’t type any special characters at the moment)
Step-by-step explanation:
-240 = 120 because you measure negative angles clockwise starting at 0.
Using unit circle, value of sin for an angle is the 2nd number
please help me, i want now
The value of angle C in the triangle is 50°.
How to calculate the triangle?From the information given, the angle A = 60° while B is given as 70° and we are told to calculate the value of C.
It should be noted that the sum of angles on a triangle is 180°. Therefore, the value of C will be:
= 180° - (60° + 70°)
= 180° - 130°
= 50°
Learn more about triangles on:
brainly.com/question/1058720
#SPJ1
which expression uses the associtive property to make it easier to evaluate 8 (1/4 x 3/5)
The value of the expression 8 (1/4 * 3/5) is 6/5
How to evaluate the expression?The expression is given as:
8 (1/4 * 3/5)
The associative property states that:
a * (b * c) = (a * b) * c
Using the above expression, we have:
8 (1/4 * 3/5) = 8 * 1/4 * 3/5
Evaluate the product
8 (1/4 * 3/5) = 2 * 3/5
This gives
8 (1/4 * 3/5) = 6/5
Hence, the value of the expression 8 (1/4 * 3/5) is 6/5
Read more about associative property at:
https://brainly.com/question/5637942
#SPJ1
I was born on saturday. got marries the 10,000 day of my life. what day of the week is it?
Answer:
Tuesday
Step-by-step explanation:
Days of the week repeat every seven days, so Saturday is day (1+7n) for some integer n.
Number of weeksThe value of n that makes the day number just under 10,000 is ...
1 +7n ≤ 10000
7n ≤ 9999
n ≤ 1428 3/7
Day of the weekSo, Day 1 +1428·7 = 9997 is Saturday. Day 10,000 is 3 days later. That makes Day 10,000 a Tuesday.
__
Additional comment
1428 weeks is about 27.5 years. You got married at age 27.
The graph of F(x) shown below resembles the graph of G(x) = x4, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
Using translation concepts, the equation of F(x) is:
A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is:
[tex]G(x) = x^4[/tex]
For function F(x), we have that:
It was shifted down 2 units, hence F(x) = G(x) - 2.It was vertically compressed by a factor of 3, hence [tex]F(x) = \frac{1}{3}G(x) - 2[/tex]Then the equation is:
A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]
More can be learned about translation concepts at https://brainly.com/question/28098112
#SPJ1
A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 3, 6, 9, 12. Column 2 is labeled y with entries 3, 9, 18, 27, 36.
Given that y varies directly with x in the table, find the value of y if the value of x is 5.
Given that y varies directly with x in the above table, if the value of x is 5, the value of y is 15.
How to calculate direct variation?According to this question, a 2-column table with 5 rows is given.
Column 1 is labeled x with entries 1, 3, 6, 9, 12 Column 2 is labeled y with entries 3, 9, 18, 27, 36If y varies directly with x, the mathematical representation is as follows:
y = kx
Since y = 3, when x = 1
3 = k × 1
k = 3
The relationship between x and y is as follows: y = 3x
Therefore, if the value of x is 5, the value of y = 3 × 5 = 15.
Learn more about direct variation at: https://brainly.com/question/14254277
#SPJ1
What is the length of the hypotenuse of the triangle?
Triangle A B C. Side A C is 7 centimeters and side B C is 3 centimeters. Hypotenuse A B is unknown.
StartRoot 20 EndRoot cm
StartRoot 23 EndRoot cm
StartRoot 40 EndRoot cm
StartRoot 58 EndRoot cm
The length of the hypotenuse of the triangle as given is; √58 cm.
What is the length of the hypotenuse of the triangle described?It follows from the task content that the triangle described in the task content is a right triangle with two other side lengths; 7cm and 5cm.
Hence, it follows from Pythagoras theorem that the length of the hypotenuse side of the triangle is;
Hypotenuse = √(5² + 7²)
Hypotenuse = √58 cm.
Read more on hypotenuse;
https://brainly.com/question/6653008
#SPJ1
Use the graph to find the solution.
Given the graph of w(x), w(2) = ?
(the graph is below)
THE FIRST ANSWER WILL GET BRAINLIEST OR 5 STARS! PLEASE ANSWER QUICK :)
Answer:
W(2) = 5
Step-by-step explanation:
Because when you look at the graph, the y value is 5 when the x value is 2.
Answer:
w(2) = 5
Step-by-step explanation:
by using rise over run to find the slope easily, you get a slope of 4 and an equation of w(x) = 4x - 3, -3 being the y-intercept
to calculate w(2):
w(2) = 4(2) - 3
w(2) = 8 - 3
w(2) = 5
or you could just look at when y is 2 and see that the corresponding x value is 5 but i wanted to provide a longer explanation in case :)
2 Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Mr.Royal, tysm for the help!
#6
Yes
Direct variation because Time increases cupcakes increases and vice versa
#B
Constant of proportionality represents the amount of time required per cupcakes
#7
Yes we can find it
We have to check the x and y values of the ordered pairs (x,y)
If y is decreasing with respect to increase in x then it's inverse variation
Find the smallest number by which 1008 must be multiplied to get a perfect square. also, find the square root of the perfect square so obtained
Answer:
7
Step-by-step explanation:
we have 1008=2×2××2×3×3×3
The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.
Now 1008×7=2×2×2×2×3×3×7×7
7056=2×2×3×7
=84
Answer : 7
Answer:
1. 7
2. square root is 84.
Step-by-step explanation:
First find the prime factors:
1008 =2*2*2*2*3*3*7
There's an even number of 2's and 3's but only one 7, so we multiply by 7
Smallest number = 7.
The square number is 1008 * 7
= 7056.
Its square root is 2*2*3*7 = 84.
PLS HELP>>>look at pic
Answer:
3x + 2 >= 0
Step-by-step explanation:
Since this is a 4th root, not a cubic root, the radical can only contain 0 or positive numbers. Therefore there is 3x + 2 >= 0.
Find the magnitude of the
resultant vector.
(8, 10)
W
(7, -1)
[?]
Round to the nearest tenth.
17.49 is the magnitude of the resultant vector. This can be obtained by adding the vectors and finding magnitude.
Calculate the magnitude of the resultant vector:Resultant vector: vector that gives the combined effect of all the vectors. When we add two or more vectors, the outcome is the resultant vector.
For example,
Sum of vector (3,4) and vector (5,7)(3,4) + (5,7) = (3+5,4+7) = (8,11)
(8,11) is the resultant vector of vector (3,4) and vector (5,7)
Magnitude of a vector: the length of the vector. The magnitude of the vector a is denoted as ∥a∥.
Magnitude of a = (a₁, a₂)
∥a∥=[tex]\sqrt{a_{1}^{2} +a_{2}^{2} }[/tex]
In the given question,
v (8,10) and w (7, -1)
Adding the vectors,
resultant vector = (8,10) + (7, -1) = (15, 9)
Magnitude of a vector (a,b) = √a²+b²
Here, magnitude = √15²+9² = √225+81 = √306 ≈ 17.49
Hence 17.49 is the magnitude of the resultant vector.
Learn more about vectors:
brainly.com/question/27870005
#SPJ1
PLEASE ANSWER WILL GIVE YOU ALOT OF POINTS
The theorems that prove that lines are parallel includes:
Alternate interior angle theorem.Converse of corresponding angles postulate.How to prove lines are parallel?Parallel lines are the lines that do not intersect or meet each other at any point in a plane.
Theorems that prove that lines are parallel includes:
Alternate interior angle theorem.Converse of corresponding angles postulate.learn more on parallel lines here:https://brainly.com/question/2437978
#SPJ1
Line segment Z E is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector of AngleYGZ and the perpendicular bisector of Line segment E F. Line segment F Y is the angle bisector of AngleZFX and the perpendicular bisector of Line segment E G. Point A is the intersection of Line segment E Z, Line segment G X, and Line segment F Y.
Triangle G E F has angles with different measures. Point A is at the center. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Z, and A Y.
Which must be true?
Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.
Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z
The correct option that depicts the centroid of the triangle is; C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
How to interpret the segments formed from Triangle Centroid?The center of inscribed circle into the triangle is the point where the angle bisectors of the triangle meet.
The center of the circumscribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.
Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides. Thus, the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle.
Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Thus, the correct option is option C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Read more about Triangle Centroid at; https://brainly.com/question/7644338
#SPJ1
In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?
r > 4 and r ≤ 4.1
r > 4 or r ≤ 4.1
r < 4 and r ≥ 4.1
r < 4 or r ≥ 4.1
The compound inequality represents the situation is r > 4 and r ≤ 4.1
Compound inequalityRadius of the gear = rr must be greater than 4 cmr > 4
r must not exceed 4.1 cmr ≤ 4.1
Therefore, r > 4 and r ≤ 4.1 is the compound inequality which represent the situation.
Learn more about compound inequality:
https://brainly.com/question/234674
#SPJ1
Its A: r > 4 and r ≤ 4.1
I WILL GIVE BRAINLY A dairy farmer wants to mix a 60% protein supplement and a standard 20% protein ration to make 1400 pounds of a high-grade 40% protein ration. How many pounds of each should he use?
The number of pounds of 60% protein and 20% protein supplement used is 700 and 700 pounds respectively.
Simultaneous equationlet
Pounds of 60% protein used = xPounds of 20% protein used = yx + y = 1400
0.60x + 0.20y = 1400×0.40
0.60x + 0.20y = 560
From (1)
x + y = 1400
x = 1400 - y
Substitute into (2)
0.60x + 0.20y = 560
0.60(1400 - y) + 0.20y = 560
840 - 0.60y + 0.20y = 560
- 0.60y + 0.20y = 560 - 840
-0.40y = -280
y = -280/-0.40
y = 700 pounds
Recall,
x + y = 1400
x + 700 = 1400
x = 1400 - 700
x = 700 pounds
Learn more about simultaneous equation:
https://brainly.com/question/16863577
#SPJ1
Maria buys some soft drinks for her friends. she buys a total of 13 drinks for a total of $32. if medium drinks, m, cost $3 and small, s, drinks $2, write a system of equations which can be used to find how many small drinks and medium drinks she bought.
The total number of small drinks 's' bought by Maria is 7.
The total number of medium drinks 'm' drinks bought by Maria is 6.
What is system of linear equations?A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).
Formation of the linear equation for the drinks bought by Maria:
The total number of drinks bought by the Maria is 13.
Lets say 'm' represents the number of medium drink.
's' represents the number of small drink.
Total drinks comprises of medium drinks and small drinks.
Thus,
s + m = 13, is the first linear equation.
Now medium drinks cost $3.
Total cost for purchasing medium drinks = (price of one medium drink)×(total number of medium drinks)
Total price for medium drinks = 3×m
Similarly,
Total cost for purchasing small drinks = (price of one small drink)×(total number of small drinks)
Total price for small drinks = 2×s
Total cost = total cost of medium drink + total cost of small drink
32 = 3×m + 2×s, is second linear equation.
From equation first substitute the value of 'm' in second equation to fine the total number of drink.
32 = 3×(13 - s) + 2×s
32 = 39 - 3s + 22
s = 7
Put s = 7 in first equation and calculate 'm'.
m = 13 -7
m = 6
Therefore, The total number of small drinks 's' bought by Maria is 7.
The total number of medium drinks 'm' drinks bought by Maria is 6.
To know more about system of linear equations, here
https://brainly.com/question/3654260
#SPJ4
Question 5(Multiple Choice Worth 1 points)
(02.01 LC)
Which of the following tables represents a function?
Answer:
(a) see attached
Step-by-step explanation:
A table will represent a function if no input (x) values are repeated.
ChoicesThe offered tables can be evaluated as follows:
(a) x-values {-4, -1, 1, 4}, no repeats. Is a function.
(b) x-values {2, 2, 3, 3}, both values repeated
(c) x-values {-5, -5, 5, 5}, both values repeated
(d) x-values {2, 2, 7, 7}, both values repeated
PLEASE HELP NOW
Which formula can be used to find the volume of the cylinder? Check all that apply. A = ( d )( h ) V = B( h ) V = ( l )( w )( h ) V = 2( r )( h ) V = (pi) (r squared) (h)
Answer:
V= (pi) (r squared) (h)
Step-by-step explanation:
There were only 86 confirmed cases of Measles in the year 2000. In 2019, there was a reported 1,350 % increase in confirmed
cases of Measles. How many cases were there in 2019?
Answer:
1161 confirmed cases
Step-by-step explanation:
In 2000 the number of cases was 86
Percent means out of a hundred, so if we divide 1350 by 100 we get 13.5.
So, we must multiply 13.5 and 86 to get the amount of cases in 2019.
13.5*86 = 1161 confirmed cases in 2019
A set of 5 numbers has an average of 50. The largest element in the set is 5 greater than 3 times the smallest element in the set. If the median of the set equals the mean, what is the largest possible value in the set
Answer:
5×3=15
15×3=45
therefore the largest value is 45
The largest possible value in the set is 92. The set has an equal mean and median. So, the set is {29, 29, 50, 50, 92}.
What are the mean and median of a set of data?Mean:
For a set of data, the average of all the data values is said to be its mean.
Median:
When the set is arranged in ascending order, the middle term is said to be its median (if there are an odd number of data values in the set) or the average value of the two middle terms is the median (if there are an even number of data values in the set).
Calculation:It is given that,
there are 5 numbers in the set
Mean = 50 and Median = Mean
So, Median = 50
Since there are 5 numbers in the set (odd number), the median is the third(middle) number.
Consider the first or smallest number as 's'.
Then the largest number = 3s + 5
By minimizing each term we get,
first term = s
second term = s
third term = 50
fourth term = 50
fifth term = 3s+5
If the mean is 50, then the sum of all the terms = 50 × 5 = 250
So,
s + s + 50 + 50 + 3s + 5 = 250
⇒ 5s + 105 = 250
⇒ 5s = 145
∴ s = 29
Thus, the smallest number is 29
Then, the largest number = 3s + 5 = 3 × 29 + 5 = 92
Therefore, the largest number in the given set is 92.
Learn more about mean and median here:
https://brainly.com/question/14532771
#SPJ4
Which of the following polynomials has a remainder of -7 when divided by x - 2?
ANSWER : -7x + 14
EXPLANATION, to reverse division multiply
The lifetime of a certain type of battery is normally distributed with mean value 13 hours and standard deviation 1 hour. There are nine batteries in a package. What lifetime value (in hours) is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages
The lifetime of the batteries in a package is 14.31 hours which exceeds that value for only 5% of all packages.
Give sample mean of 13 hours and standard deviation of 1 hour and sample size is 9.
We have to apply t test in this because the value of n which is sample size is less than 30.
We have been given the p value of the required mean so we have to find the t value for this with degree of freedom (9-1)=8
t value=2.306.
We know that
t=X bar-μ/s/[tex]\sqrt{n}[/tex]
s/[tex]\sqrt{n}[/tex]=1/[tex]\sqrt{3}[/tex]=0.57
Put all the values in the above formula to calculate required mean.
2.306=X bar-13/0.57
X bar=1.31442+13
=14.31442
after rounding off we get
X bar=14.31
Hence the lifetime of the batteries is 14.31 for which the percentage exceeds 5%.
Learn more about t test at https://brainly.com/question/6589776
#SPJ4