Step-by-step explanation:
[tex] {x}^{2} - 14x - 25 {y}^{2} + 100y = 76[/tex]
Factor by grouping,
[tex]( {x}^{2} - 14x) - (25 {y}^{2} - 100y) = 76[/tex]
Complete the square, with the x variables,
[tex]( {x}^{2} - 14x + 49) - (25 {y}^{2} - 100y) = 125[/tex]
Factor out 25 for the y variables
[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y) = 125[/tex]
Complete the square
[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y + 4) = 25[/tex]
Simplify the perfect square trinomial
[tex](x - 7) {}^{2} - 25(y - 2) {}^{2} = 25[/tex]
Make the right side be 1 so divide everything by 25.
[tex] \frac{(x - 7) {}^{2} }{25} - (y - 2) {}^{2} = 1[/tex]
Here our center is (7,2).
Round to the nearest tenth. B 63 142° 61 A C X x = [?]
The value of x in the triangle is 117.2 units
The missing image is attached with the answer.
What is an Equation?An equation is formed when two expression is equated by an equal sign to a constant , variable or an expression.
Cosine rule of Triangles is used and is given by
c² = a² + b² - 2ab cos C
Where a, b, c are the sides and C is the angle opposite side c.
from the given data in the figure
c = 63
a = 61 and
angle B is 142 degree
x² = 63² + 61² - 2(63)(61) * cos(142)
On solving
x = 117.2
The value of x in the triangle is 117.2 units
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find the value of x in the given figure
To solve this problem, you will first use the Angle Sum Property to determine the value of x after creating an algebraic equation, combining like terms, and subtracting from both sides of an equation.
Use the Angle Sum PropertyThe Angle Sum Property states that all interior angles of a triangle will summate to 180º.
An equation can be created to find this when you are given two angles and missing a third. That third angle can be referred to as x in this scenario.
Adding the two known angles and the unknown angle will result in a sum of 180º. This means that our unknown is x and can therefore be placed in an equation:
[tex]65+42+x=180[/tex]
Combine Like TermsCombine the like terms by combining the constants on the left side of the equation using addition:
[tex]65+42+x=180[/tex]
[tex]107+x=180[/tex]
SubtractAfter combining like terms, subtract 107 from both sides of the equation:
[tex]107 - 107 +x = 180-107[/tex]
[tex]\boxed{x=73}[/tex]
The final answer is x = 73 degrees.
For each expression below, select the letter that corresponds to the equivalent expression from the given list.
is equivalent to expression
is equivalent to expression
is equivalent to expression
Option 1 corresponds to Part B , Option 2 corresponds to Part D , Option 3 corresponds to Part A , Option 4 corresponds to Part C
The complete question is attached in the image
What is an Expression ?An expression corresponds to the mathematical statement that consists of variables , Constants and mathematical operators simultaneously.
Solving the given option will give us the answer.
(x²+15x+65)+(2x-5)*(3x+8)
(x²+15x+65)+(6x²+16x-15x-40)
(7x²+16x+25)
Option 1 corresponds to Part B
(4x+1)*(3x-4)-(5x²-10x-12)
(4x+1)*(3x-4)-(5x²-10x-12)
(12x²-16x+3x-4)-(5x²-10x-12)
(7x²-3x+8)
Option 2 corresponds to Part D
(8x²+19x+4)+(3x+2)*(x-5)
(8x²+19x+4)+(3x²-15x+2x-10)
(11x²+6x-6)
Option 3 corresponds to Part A
(6x+1)*(3x-7)-(7x²-34x-20)
(18x²-42x+3x-7)-(7x²-34x-20)
(11x²-5x+13)
Option 4 corresponds to Part C
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Which two numbers does √√61 lie between on a number line? O 7.7 and 7.8 O 7.8 and 7.9 O 7.9 and 8.0 Stm O 8.0 and Which two numbers does √√61 lie between on a number line ? O 7.7 and 7.8 O 7.8 and 7.9 O 7.9 and 8.0 Stm O 8.0 and 8.1
Answer:
B) 7.8 and 7.9
Step-by-step explanation:
Taking the square root of 61, we can conclude that the decimal form is 7.810, which falls between the range of 7.8 and 7.9
Answer:
√61 lie between 7.8 and 7.9
Evaluate.
{3−[−4−(6+2)]}⋅(−5)
A−75
B−57
C−15
D−9
Step-by-step explanation:
please mark me as brainlest
Suppose y varies inversely with x, and y = a when x = a 2. What inverse variation equation relates x and y ?
a.
y = a2xa2x
b.
y = a 3x
c.
y = a3xa3x
d.
y = ax
The variation equation is xy = a^3
How to determine the equation?An inverse variation is represented as:
xy = k
Where k is the constant of variation
When y = a and x =a^2, we have:
k = a * a^2
Evaluate
k = a^3
Substitute k = a^3 in xy = k
xy = a^3
Hence, the equation is xy = a^3
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1. Kelsey spent 55 hours over 2 weeks working on a ELA project. She worked 32 hours the
Answer:
23
Step-by-step explanation:
If Kelsey spent 32 hours in the first week. We subtract 32 from 55. 55-32=23. That means she worked 23 hours in the second week.
What is the formula for capacity of a prism?
Answer:
The prism volume formula is B*h B (area of one end) =0.5*1000*566 = 283,000 mm 2 (area of a triangle) H (length/height of prism) = 1000 mm
Step-by-step explanation:
Answer:
Step-by-step explanation:
Any prism volume is equal to the area of the base (B) multiplied by the height of prism (H)
V = BH
Now, to find the area of the base you need this formula : B = 1/2 h(b1+b2), then multiply by the height of the prism.
can someone please help mee i need the exact answer(30 points will give brainliest!!!)
Answers:
Domain: [tex]\boldsymbol{(-\infty, \infty)}[/tex]
Range: [tex]\boldsymbol{(-\infty, \infty)}[/tex]
=======================================================
Explanation:
domain = set of all possible x inputs
range = set of all possible y outputs
--------------
In this case, the domain is the set of all real numbers because the graph stretches forever to the left and right. There aren't any gaps, holes, jumps, etc to worry about. Any real number works as an input.
We can say x is between [tex]-\infty[/tex] and [tex]\infty[/tex] and write [tex]-\infty < x < \infty[/tex]
That turns into the interval notation [tex](-\infty, \infty)[/tex]
The curved parenthesis are always used with either infinity because we cannot reach them.
--------------
The range is the same story, but with the y values this time. The graph stretches forever upward and downward due to the arrow.
If it peaked at y = 4, then the range would be [tex](-\infty, 4][/tex], but instead the graph goes beyond y = 4 because of that upward arrow.
PLEASE HELP ME WITH THIS ASAP
Answer:
4 rows
Step-by-step explanation:
First set:
unknown rows, 5 tiles each
meaning old total is divisible by 5
Second set:
3 additional rows, 3 tiles each
meaning that the new total is divisible by 3
so, our total number of tiles is divisible by 5, add 1 and it is divisible by 3 when added 1
{another way I solved it : [and when it is divided by 3, it has 8 that fit into the original pattern; which is another way of knowing that each of the rows of 5 [each have 2 removed when turned into rows of 3] add up to having a remainder of 8 tiles; 8 / 2 = 4; so there were four rows in the original pattern contributing to the change--there were four rows] }
x is divisible by 5, x + 1 is divisible by 3
essentially, we are looking for a number that ends in 5 or 0, and the next number [ending in 6 or 1] is divisible by 3
I know that 5 goes into 20, and that 21 is divisible by 3, so let's test it out:
4 (rows of 5) turns into 7 [4 + 3] rows of 3
because 21 can be split into 7 rows, this number of tiles is possible
so, in the original pattern, there must have been 4 rows
hope this helps!! {so sorry if this confuses you, please let me know if I should explain my reasoning further}
have a lovely day :)
9.
(05.04 MC)
The following data show the prices of different types of hot dogs at a store:
$6, $8, $7, $6, $5, $7, $5, $7, $6, $28, $30
Which statement is correct about the box plot for the data? (1 point)
The box plot will have its right tail longer than the left tail because a few exceptionally high prices make the distribution skewed to the right.
The box plot will have its right tail longer than the left tail because a few exceptionally high prices make the distribution skewed to the left.
The box plot will have its left tail longer than the right tail because a few exceptionally high prices make the distribution skewed to the right.
The box plot will have its left tail longer than the right tail because a few exceptionally high prices make the distribution
The correct statement regarding the box plot of the data-set is given by:
The box plot will have its right tail longer than the left tail because a few exceptionally high prices make the distribution skewed to the right.
What does the box plot a data-set shows?It shows:
On the left-tail, the first quartile.At the center, the median.On the right-tail, the third quartile.In this problem, we have two unusually high values, $28 and $30, hence the right tail is longer than the left tail, hence the box plot is right-skewed, and the correct statement is:
The box plot will have its right tail longer than the left tail because a few exceptionally high prices make the distribution skewed to the right.
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tan A + sin A/tan A-sin A
= sec A +1/sec A-1
We need to prove
[tex]\frac{\tan A+\sin A}{\tan A-\sin A}=\frac{\sec A+1}{\sec A-1}[/tex]
[tex]\text{LHS}=\frac{\tan A+\sin A}{\tan A-\sin A}\\\\=\frac{\frac{\sin A}{\cos A}+\sin A}{\frac{\sin A}{\cos A}-\sin A}\\\\=\frac{\sin A+\sin A \cos A}{\sin A-\sin A \cos A}\\\\=\frac{\sin A(1+\cos A)}{\sin A(1-\cos A)}\\\\=\frac{1+\cos A}{1-\cos A}\\\\=\frac{1+\frac{1}{\sec A}}{1-\frac{1}{\sec A}}\\\\=\frac{\sec A+1}{\sec A-1}\\\\ =\text{RHS}[/tex]
Nick wants to save up enough money to go to Carowinds for the day with a group of his friends. He already has $50 saved up and plans to save $10 each week. Write an expression that represents the total amount Nick will have depending on the number of weeks (w) he saves for.
Answer:
a=10w +50
Step-by-step explanation:
a= amount
w= weeks
please vote brainliest
Which of the following is an example of why irrational numbers are not closed under addition?
√4+√4=2+2=4,
and 4 is not irrational
1/2+1/2=1, and 1 is not irrational
√10+(-√10) = 0, and 0 is not irrational
-3 +3 = 0, and 0 is not irrational
Answer:
√10 + (-√10) = 0, and 0 is not irrational
^ this one
Two boats left a base camp at bearing of S60°E and S50°W at speeds of 50km/h and 70km/h respectively. Find the distance between the both boats after two hours.
Answer:
197.93 kmStep-by-step explanation:
Let the base camp is point A and boats' locations after two hours are points B and C.
By connecting the three points together we get a triangle ABC with sides:
AB = 50*2 = 100 kmAC = 70*2 = 140 kmThe angle between AB and AC is:
60 + 50 = 110 degrees (opposite directions from south)We are looking for the distance BC, which can be found by using the law of cosines:
BC² = AB² + AC² - 2AB*AC*cos ∠BACBC² = 100² + 140² - 2*100*140*cos 110°BC² = 39176.56 (rounded)BC = √39176.56 = 197.93 km (rounded)The distance between the boats is 197.93 km.
Find each difference.
(-6s² + 12s-8) - (3s² +8s - 6) =
O-9s² + 4s-14
O-9s² + 4s-2
O-9s² + 20s - 14
O-9s² +20s-2
DONE ✔
Answer: [tex]-9s^2 + 4s-2[/tex]
Step-by-step explanation:
[tex](-6s^2 +12s-8)-(3s^2 + 8s-6)\\\\=-6s^2 + 12s-8-3s^2 - 8s+6\\\\=\boxed{-9s^2 +4s-2}[/tex]
A gym has 65 members. If 35 are men and the
rest are women, what is the ratio of the female
members to the total members of the gym?
Answer:
Step-by-step explanation:
số nữ là 65- 35= 30
vậy tỷ lệ số tv nữ trên tổng số thành viên của phòng tập là 30/65 = 6/13
Quick
Check
Match each power of a power expression with its simplified expression.
There are 7 pieces of pie over in the cafeteria. If 5 pieces are apple and 2 are cherry, what fraction of the remaining pieces are cherry?
Answer:
No
Step-by-step explanation
because 5+2=7 so I don't have a piece of cake left over
What number is the opposite of -2?
O A. ¹/2
O B. -¹/2
5
O C. - 13/
OD. /
12
Answer: 2
Step-by-step explanation:
The opposite of a negative number is the corresponding positive number.
20 points!!
Flynn is playing with a toy that is tied to his hand by a string. The toy falls toward the floor then rises back toward Flynn's hand, and repeats this motion, following the path illustrated by given graph.
The function is h(t) = 7/4 cos π/3 t + 9/4,
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
As, h(t) = x cos π/3 t +y
when t= 0, h(t) = 4
when t= 3, h(t) = 0.5
So,
x cos π/3 *0 +y=4
x cos π/3 *3 +y=0.5
and, x+ y = 4, -x+ y =0.5
Now,
2y= 4.5
y= 9/4
and, x= 4-9/4= 7/4.
Hence, h(t) = 7/4 cos π/3 t + 9/4
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Answer:got it right
h(t)=1.75, cos(1/3), + 2.25
Step-by-step explanation:
Instructions
For this activity, you will need two different coins. First, you will determine the theoretical probability of events. Then, you will flip the coins 100 times and determine the experimental probability of the events.
Flip two different coins 100 times, and record the results of each coin toss in a table like the one below:
Result Frequency
Two heads
Two tails
One head, one tail
Answer the following questions based on the data you gathered. You must show your work to receive credit.
What is the theoretical probability that a coin toss results in two heads showing?
What is the experimental probability that a coin toss results in two heads showing?
What is the theoretical probability that a coin toss results in two tails showing?
What is the experimental probability that a coin toss results in two tails showing?
What is the theoretical probability that a coin toss results in one head and one tail showing?
What is the experimental probability that a coin toss results in one head and one tail showing?
Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?
The theoretical probability of getting two tails on two coin tosses is 0.25.
How to calculate the probability?The theoretical probability is the ratio of the number of favorable outcomes to the number of possible outcomes. Given a coin is tossed twice.
We have to find the theoretical probability of tossing two tails. The probability of getting tails on the toss of a coin is 1/2 0r 0.5.
Therefore, the probability of getting two tails on two coin tosses is 0.5 × 0.5 or 0.25.
The theoretical probability that a coin toss results in two heads showing is 0.25.
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Marcy and her sister watched a cartoon movie that was 2 hours and 18 minutes long. after the movie, they played a card game for 34 minutes and then played soccer for 1 hour and 12 minutes. when they came in from playing soccer, it was 5:28 p.m. what time did marcy and her sister start watching the movie?
Answer:
1:24pm
Step-by-step explanation:
Couple of ways to solve this. Here is one method
Convert all times to minutes and find the total number of minutes they spent on all 3 activities. Then convert to hours and minutes and subtract from the end time of 5;28 to get the start time of all activities which is also the start time of watching the movie (first activity)
So time spent:
Movie: 2 hours 18 minutes = 2 * 60 + 18 = 120 + 18 = 138 minutes
Card game: 34 minutes
Soccer: 1 hour 12 minutes = 1 * 60 + 12 = 72 minutes
Total time spent = 138 + 34 + 72 = 244 minutes = 4 hours and 04 minutes
Subtract 4:04 from 5:28 to get 1:24pm
Check
Movie watch starts at 4:04, ends at 1:24 + 2:18 or 3:42pm
Card game starts at 3:42pm ends at 3:42+0:34 ==> 4:16pm
Soccer starts at 4:16pm ends at 4:16pm + 1:12 ==> 5;28pm
8y and y are like terms
true
or
false
Answer:
True
Step-by-step explanation:
Hope this helps :)
Help with math work
Answers for different section are given below;
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, given function;
f(x) = -x² - 4x + 6
1. If we take -1 common from the given function, we get
f(x) = -1 (x² + 4x - 6)
f(x) = -1 (x² + 4x) + 6
Thus, first block contains -1 and second block contains 4.
2. Then we add half of the coefficient of x², (b/2)², inside the bracket and subtract it outside a times, a(b/2)².
f(x) = -1 ( x² + 2. 2x + 2²) +2² + 6
f(x) = -1 ( x² + 4x + 2²) +4 + 6
Thus, first block contains -1, second block contains 4, third block contains 4, and fourth block contains 4.
3. Then we factorize the bracket and simplify outside the bracket;
f(x) = -1 (x + 2)² + 10
Thus, first block contains -1, second block contains 2 and third block contains 10.
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What is 9 squared?
Why?
Why do we call this "Squared"?
What is 5 cubed?
Why?
Why do we call this "Cubed"?
Answer:
The squared root of 9 is 3
Why - Half of 9 is 3
Why do we called this squared - It is the positive solution of the equation x2 = 9. The number 9 is a perfect square.
5 Cubed is equal to 125
Why - The number 125 on prime factorization gives 5 × 5 × 5. On combining the prime factors in groups of 3 gives 5
Why do we call this cubed = The cube of a number is that number times itself times itself. 5 cubed, denoted 53, is equal to 5×5×5, or 125.
Expression -2(x + 4)
Sentence
Symbol
operation
Answer:
c
Step-by-step explanation:
Which inequality is shown on this graph?
The inequality which shows the graph is [tex]y\le\ 4x+2[/tex].
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
As, from the inequalities the graph is representing the fourth inequality.
The graph attached below show the graph corresponding to
[tex]y\le\ 4x+2[/tex] is shown.
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What are all the solutions of x² + 3x -4 = 0? Multiple choice
A: -4
B:-2
C:-1
D:0
E:1
F:2
G:4
Answer :
A and E .
Step-by-step explanation:
Is the following relation a function?
Answer: Yes.
Step-by-step explanation: No number in the map is paired to two different, distinct numbers.