After solving, she is 25 years old.
In the given question,
When he asked her age, She replied "If you take my age and square it and then subtract 22 time my age then the result is 75"
We have to find the age of she.
To find the age of she we we firstly simplify the given statement in the form of expression then we solve the expression.
To write the expression we clearly read then sentence and then write the expression.
Let the age of she is x.
So When we take the square of her age, it is x^2.
When we subtract 22 times her age then it is x^2-22x.
Then its is equal to the 75. Now the expression is;
x^2-22x=75
Subtract 75 on both side, we get
x^2-22x-75=0
Now we simplifying the equation by factoring it.
x^2-(25-3)x-75=0
x^2-25x+3x-75=0
x(x-25)+3(x-25)=0
(x+3)(x-25)=0
Now the factor of x is -3 and 25.
Age can not be negative. So the age of she is 25.
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The right question is;
When he asked her age, She replied "If you take my age and square it and then subtract 22 time my age then the result is 75"how old is she?
What happens when the scale factor is negative 1?
The area of a rectangle is 105 sq in and the length of one side is 7 in. What is the length of the perimeter?
Perimeter of Rectangle is 44m
What is Perimeter ?A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape.
According to the given information
Area of Rectangle = l × b
Area of Rectangle = 105 [tex]m^{2}[/tex]
Length of one side = 7 m
Let the length of the adjacent side = b
Area of Rectangle given = 7 × b
105 = 7 × b
b = [tex]\frac{105}{7}[/tex]
b = 15 m
Perimeter of Rectangle given = 2( l + b )
= 2 ( 7 + 15 )
= 2 × 22
= 44m
Perimeter of Rectangle is 44m
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There are 4,500 cities on planet Purple. The planetary government takes a random sample of 350 cities and finds that the average number of complaints about feral cats from the sample was 3.4 ± 0.49. Which of the following is an estimate of the total number of feral cat complaints for planet Purple?
A) Between 1018.5 and 1361.5 complaints B) Between 171.5 and 1190 complaints C)Between 13,095 and 17,505 complaints D) Between 2,205 and 15,300 complaints
Based on the margin of error, an estimate of the total number of feral cat complaints for planet Purple is A. Between 1018.5 and 1361.5 complaints.
What is the error margin?The statistical difference between the predicted or estimated results and the actual results is displayed by the margin of error.The difference between the sample estimate's upper and lower bounds is represented by the margin of error.One defines a degree of confidence or the confidence interval in the sample findings using the margin of error.4,500 cities make up the entire population of planet Purple.
350 cities make up the random sample.
Average complaints are 3.4.
Error or margin = 0.49
[350 x (3.4 + 0.49)] Upper limit = 1,361.5
Lower limit: 1,081.5 (350 times (3.4 - 0.49).
As a result, Option A's estimated number of feral cat complaints floats above the error margin.
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Hi I need help which is the answer ??
Answer:
[tex]b) 5^{\frac{1}{12} }[/tex]
Step-by-step explanation:
∛5 = 5^1/3
⁴√5 = 5^1/4
Then:
∛5 / ⁴√5 = (5^1/3) / (5^1/4)
= 5^(1/3 - 1/4)
1/3 - 1/4 = 4/12 - 3/12 = 1/12
Then:
5^(1/3 - 1/4) = 5^1/12
= [tex]5^{\frac{1}{12} }[/tex]
**** The symbol ^ means that the expression on the right is an exponent.
Example:
5^1/3
means 1/3 is an exponent,
determine the intervals on which the function is increasing decreasing and constant
The interval on which the graph is increasing and decreasing are ( -∞,3] and [3,∞) respectively.
There is no interval where the function is constant.
In order to solve this question we need to study the graph attached,
From the graph, we could see that the plotting of the graph is starting from the negative axes and we could observe an increasing slope in the function, and the increment stopped after reaching point B(3,0), we can also observe that the value of the y-axis increases with that of the x-axis.
The interval at B(0,3) must be wrote down as ( -∞,3]
Again we could see a sudden drop in the slope of the function of the graph as the slope of the graph this time starts decreasing and moves to infinity and again we could observe that the value of the x-axis starts decreasing with the decrease in the value of the y-axis.
The function was constant at a null interval.
Therefore, The interval on which the graph is increasing and decreasing are ( -∞,3] and [3,∞) respectively and there is no interval where the function is constant.
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Pls help rn!
There were 110 people at the concert. If 55% of the seats were filled, how many seats are in the auditorium?
There are seats in the auditorium.
Answer:61
Step-by-step explanation:
Answer:
200
Step-by-step explanation:
Because there were 110 people at the concert, that means only 110 seats were filled. So we can think of the problem as its own equation if we word it like this:
110 is 55% of how many seats
110 = 0.55 x ?
Now to solve by dividing 110 by 0.55
110/0.55 = 200
Help me please raise my grade
Answer:
20% = 20 out of 10080% = 80 out of 10080th percentile = 80% of all the values in the data set are less than or equal to this quantity.20th percentile = 20% of all the values in the data set are less than or equal to this quantity.Which is an example of AAS congruence theorem?
Given ▲ ABC and ▲DEF are the examples of AAS congruence theorem.
According to the AAS, or Angle Angle Side congruence rule, two triangles are said to be congruent if two pairs of corresponding angles and the opposite or non-included sides are equal to one another.
The sides are not included between the angles but rather run in either direction of the angles, whereas the angles are sequential and corresponding in nature.
let's consider 2 triangles ▲ ABC , ▲DEF.
A at top B left C right . D at top E left F right side
∠B = ∠E
∠C = ∠F
AB = DE.
We can see that ∠B = E and ∠C = F if we superimpose the two triangles on top of one another. The lengths of the excluded sides, AB and DE, are also equal. As a result, we can state that ABC ≅ DEF.
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On oct. 15, 2003, yang liwei orbited the earth 14 times in 21 hours for the country of china. How many hours did it take liwei to orbit the earth one time?.
Yang Liwei took 1.5 hours to orbit the earth one time.
What is an Orbit?A route that an object in space follows around another is known as an orbit.. An orbit is a regular, repeating path that one object in space takes around another one.
Given that the Yang Liwei orbited the Earth 14 times in 21 hours for the country of China.
To find the time period in one time,
Required time period = time period of total travel / number of times he orbited
Required time period = 21 / 14
Required time period = 3/2
Required time period = 1.5 hours
Hence, Yang Liwei will take 1.5 hours to orbit the earth one time.
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Find the missing side of the triangle.
X
8.3 m
5.9 m
The missing side of the triangle is approximately 10.2 m. This solution assumes that the given sides form a right triangle.
How to find side of triangle ?To find the missing side of a triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The formula for the Pythagorean theorem is:
a^2 + b^2 = c^2
where a and b are the lengths of the two sides of the triangle and c is the length of the hypotenuse.
The lengths of two sides of the triangle, 8.3 m and 5.9 m, and you need to find the length of the third side (the hypotenuse).
You can use the Pythagorean theorem to solve for the missing side as follows:
c^2 = a^2 + b^2
c^2 = 8.3^2 + 5.9^2
c = sqrt(8.3^2 + 5.9^2)
c = sqrt(69.29 + 34.81)
c = sqrt(104.1)
c = 10.2 m
Therefore, the missing side of the triangle is approximately 10.2 m.
This solution assumes that the given sides form a right triangle. If the triangle is not a right triangle, the Pythagorean theorem may not be applicable and a different method may be needed to find the missing side.
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what is 3.50 divided by 3
Answer:
1.1667
Step-by-step explanation:
Brainliest please!
Choose all of the values that are equivalent to
Answer:
A and B
Step-by-step explanation:
-(5/3) = -1.67
-5/3 = -1.67
5/-3 = -1.67
5/3 ≠ -1.67
-5/-3 ≠ -1.67
-(-5/3) ≠ -1.67
during the first leg of a backpacking trip, a group of hikers covered 10.4 miles in 3 hours and 1 minute. the next day, the group hiked 8.6 miles in 3 hours and 47 minutes. what was the group's average speed over the two days?
Over the two days, the group traveled an average speed of 2.79 miles per hour.
Given:
during the first leg of a backpacking trip, a group of hikers covered 10.4 miles in 3 hours and 1 minute.
he next day, the group hiked 8.6 miles in 3 hours and 47 minutes.
we are asked to find the group's average speed over the two days = ?
average speed = total distance / total time
total distance = 10.4 + 8.6 mi = 19 miles
total time = ( 181 + 227 min ) = 408 min
hence average speed = ( 10.4 + 8.6 mi) / ( ( 181 + 227 min )/60 min/hr) =2.79 mi/hr
Hence we get the average speed as 2.79 miles/hour.
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find the component form of vector v
By using the concept of vector, it can be calculated that
Component form of vector v = (-4 , 5)
What is a vector?
Vector is anything that has magnitude and direction and follow the vector addition law. Vector is a very important tool in mathematics and physics.
Here,
The initial point of vector v is (1, -4) and the terminal point of vector v is (-3, 1)
Component form of vector v = (-3 - 1, 1 - (-4)) = (-4 , 5)
Second option is correct
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2x(4 + 3) + 3x PLEASEE I ALKSO NEED AN EQUATION
Answer:
the answer would be 17x
Step-by-step explanation:
Answer:
17x
Step-by-step explanation:
Simplify 2x times 7 to 14x= 14x+3x
17x
PLS HELP ME ASAP SHOW ME THE MATH PLSSS PLSSS ILL GIVE U BRAINLIEST
Answer: C = 16
Step-by-step explanation:
1. Subtract 9 on both sides
[tex]-1=-\frac{5}{8} c+9[/tex]
[tex]-9[/tex] [tex]-9[/tex]
----
2. Solve [tex]-1 - 9[/tex]
[tex]-10=-\frac{5}{8}c[/tex]
3. Multiply both sides by 8 to remove the fraction
[tex](8)-10=-\frac{5}{8}(8)[/tex]
4. Solve 8 x -10
[tex]-80=-5c[/tex]
5. Divide both sides by -5
[tex]\frac{-80}{-5} =\frac{-5}{-5} c[/tex]
[tex]\frac{-80}{-5} =c[/tex]
[tex]16=c[/tex]
[tex]c=16[/tex]
DONEEEE!!
Does dilation change the shape of the image?
No, The dilation doesn't change the shape of the image
Dilation is a type of a transform where an image size either increase or decrease but has the same shape as the original. In other words, the dilation is similar to the original.
All dilations have a center and a scale factor. The center is the point of reference for the dilation (like the vanishing point in a perspective drawing)
Scale factor tells us how much the figure stretches or shrinks. A scale factor is typically labeled "k" and is always greater than zero. It is the ratio of the sizes of the original figure with the dilated figure
The only change in the dilation process is that the distance between the points changes. It means that the length of the sides of the original image and the dilated image may vary.
Therefore , Dilation doesn't changes the shape
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suppose the scores of a standardized test are normally distributed. if the population standard deviation is 2 points, what minimum sample size is needed to be 90% confident that the sample mean is within 1 point of the true population mean?
The minimum sample size is 11 needed to be 90% confident that the sample mean is within 1 point of the true population mean.
What is the mean?
Mean, in terms of math, is the total added values of all the data in a set divided by the number of data in the set.Given:
Standard deviation, σ = 2points
Confidence level = 90%
Sample mean, ε = 1 point
At 90% confidence level
1 - α = 0.90
α = 1 -0.90
α = 0.10
α/2 = 0.05
Zα / 2 = Z₀.₀₅
= 1.645
To find n
n = (Zα / 2 )*(σ)²
= (1.645)² * (2)² / (1)²
= (2.706) * 4
= 10.8241
n = 11
Hence, the minimum sample size is 11 needed to be 90% confident that the sample mean is within 1 point of the true population mean.
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Jaya is going to invest $8,000 and leave it in an account for 6 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Jaya to end up with $10,900?
The interest rate, to the nearest tenth of a percent, would be required in order for Jaya to end up with $10,900 is 3 %.
What is Compound interest rate?To calculate the future value, we need to use the following formula on each investment:
FV = PV e^(it),
where FV =Future value, PV=Present Value, e =Euler’s number, i =nominal rate per year, t =Number of years.
Given that Jaya is going to invest $8,000 and leave it in an account for 6 years.
FV =PV * e^(i*t),
P = $8,000
t= 6 years
FV = 10,900
10,900 =8,000 e^(i*6)
i = 3%,
Thus, the interest rate, would be required for Jaya to end up with $10,900 is 3 %.
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You deposit $500 into a savings account. You will earn 3% interest per year. If you are earning simple interest, how much money will you have in your bank account after 5 years?
Answer:
$575 after 5 years
Step-by-step explanation
3% of 500= 15
15 × 5= 75
500 + 75= $575
Factorise completely 12 p 2 + 10 p
Answer:
2p(6p + 5)
Step-by-step explanation:
12p² + 10p ← factor out 2p from each term
= 2p(6p + 5)
After 9 years in an account with a 3.9% annual interest rate compounded continuously, an investment is worth a total of $17,757.16. What is the value of the principal investment? Round the answer to the nearest penny. $8,103.08 $5,256.41 $12,500.75 $12,530.37
The principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.
What is continuous compounding?
There is no cap on how frequently interest can accumulate thanks to continuous compounding. A balance can compound continuously an unlimited number of times, which means interest is earned on it constantly.
We have,
9 years in an account with a 3.9% annual interest rate compounded continuously,
an investment is worth a total of $17,757.16.
First, convert R as a percent to r as a decimal
r = R/100
r = 3.9/100
r = 0.039 per year,
Then, solve the equation for P
P = A / ert
P = 17,757.16 / e(0.039*9)
P = $12,500.75
Hence, the principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.
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Answer:
$12,500.75
Step-by-step explanation:
I got it right.
is The number 0.9584584584584584 irrational or rational?
Why
Forces of 34 N and 46 N make an angle of 42° with each other and are applied to the same point. Find the magnitude and direction of the resultant force.
The magnitude and direction of the resultant force are respectively; F = 44.954 N and θ = 36.47°.
How to find the magnitude and resultant of two forces?We are given two forces as;
F₁ = 34 N
F₂ = 46 N
Angle between the two forces; θ = 42°
Now, the formula to find the resultant of the two forces is gotten by using the cosine rule as;
F = √[F₁² + F₂² + 2F₁F₂cos θ]
Where θ represents the angle between the two force vectors
Thus;
F = √[34² + 46² + 2(34 * 46 * cos 42]
F = 44.954 N
the direction will be;
θ = tan⁻¹(34/46)
θ = 36.47°
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If f(x) = -x² - 1, and g(x) = x + 5, then f(g(x)) = [? ]x² + [ ]x + [ ] +[
explanation please
Answer:
-x² -10x -26
Step-by-step explanation:
Substitute x in f(x) with x + 5:
f(g(x)) = - (x+5)² - 1
= - (x² + 10x + 25) -1
= -x² -10x -25 -1
= -x² -10x -26
What does dilating an image do?
After dilation, the size of the image will change and the shape of the image will be same
Dilating an image means the changing the size of the image, but the shape of the image will be same
Dilation is the process of changing the size of the image without changing the shape of the image
The image after the dilation is called as the pre image.
The dilation can be done by using the scale factor or normally increase or decrease the size,
If the dilation of an image done by scale factor, the size is increased or decreased according to the value of scale factor. If it is greater than 1 the size increases and if it is between 0 and 1 the size decreases
Therefore, size of the image will change after the dilation
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What is the past verb of split?
The past verb of the word split is to divide any number or a group into smaller or subgroups.
Explanation:
The past verb of the word split is :
To divide any number or a group into smaller group.Past tense of the word is a word split.Verb represents the action or doing of any given word.It represents the irregular verb.For example split any large number into small ratio of prime numbers.Split group of children into subgroups to make the work easy.Therefore, the past verb of the word split is given to divide a number or any group into smaller parts or subgroups.
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solve the following equation: x/7-6=-x/6+5
By solving the given equation x/7 - 6 = - x/6 + 5 we get x value = 462/13.
What is called the equation?
An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.Given that :
x/7 - 6 = - x/6 + 5
Multiply the denominators with numerator on both sides
x / 7 - 6(7) = - x / 6 + 5(6)
x - 42 / 7 = - x + 30 / 6
Multiply both denominators with numerator on both sides
6 (x - 42) = 7 (- x + 30)
Multiply 6 and 7 inside the bracket
6x - 252 = - 7x + 210
Separate x terms and constant terms
6x + 7x = 210 + 252
13x = 462
x = 462 / 13
Therefore, x = 462 /13
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What do you mean by maximum number?
The maximum number is nothing but a number having the largest value in the data set.
We know that the maximum number is nothing but a number having the largest value in the data set.
To find the maximum number in a list of numbers, we go through the whole list of numbers and compare each values.
The maximum number in the list is the largest value found when all values have been compared.
For example, in the list of numbers 23, 98, 76, 90, 17, 71
the maximum number is 98
Therefore, the maximum number in the list is the largest value found when all values have been compared.
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Change 120 km/h into km/min.
Answer:
Step-by-step explanation:
2 because in a hour there is 60 minutes so you just divide 120 by 6 and you get 2 km per minute