The area of a rectangular plot 24 feet long and 16 feet wide will be doubled by adding an equal distance to each side of the plot. What is the distance added to each side?
24*16 = 384
384*2 = 768
24+d * 16+d =768
384 + 40d+d^2 = 768
d^2 + 40d-384 =0
(d+48) (d-8) = 0
d=-48, d=8 can't use a negative number so d = 8
check:
24+8=32, 16+8=24, 32x 24 = 768
so 8 feet is added to each side
The sum of two numbers, x and y, is 12. The difference of x and two times y is 6. What are the values of x and y? x = 8, y = 4 x = 10, y = 2 x = 18, y = -6 x = 20, y = -8
how do you find the inverse of a 2x2 matrix
To find the inverse of a 2x2 matrix, calculate the determinant (ad-bc), then swap the diagonal elements, change the signs of the off-diagonal elements, and multiply each by the reciprocal of the determinant.
Explanation:To find the inverse of a 2x2 matrix, you must follow a specific procedure. Given a 2x2 matrix A:
\( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \)
The inverse of matrix A, denoted as \( A^{-1} \), is calculated using the formula:
[tex]\( A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} \)[/tex]
Here, \( ad - bc \) is called the determinant of matrix A. For the inverse to exist, the determinant must not be zero. To calculate the inverse, you compute the determinant \( (ad - bc) \), then swap the elements of the diagonal positions (a and d), change the signs of the off-diagonal elements (b and c), and then multiply each element by \( \frac{1}{ad - bc} \).
For example, if you have a matrix:
[tex]\( A = \begin{bmatrix} 4 & 7 \\ 2 & 6 \end{bmatrix} \)[/tex]
The determinant is [tex]\( 4\cdot6 - 7\cdot2 = 24 - 14 = 10 \).[/tex]
The inverse of A is:
[tex]\( A^{-1} = \frac{1}{10} \begin{bmatrix} 6 & -7 \\ -2 & 4 \end{bmatrix} = \begin{bmatrix} 0.6 & -0.7 \\ -0.2 & 0.4 \end{bmatrix} \)[/tex]
Which answer is correct
diagonal is square root of A^2+b^2
so C is the correct answer
John is participating in a marathon that is 26.2 miles. His distance (d, in miles) depends on his time (t, in hours). Which is an appropriate range for this situation?
The appropriate range for John's distance in miles (d) during the marathon is A. [tex]$0 \leq d \leq 26.2$[/tex].
In a marathon, the distance (d) John covers depends on the time (t) he spends running. The distance is fixed at 26.2 miles, so we need to find the appropriate range for the time (t) he spends running.
Let's calculate John's average speed (v) during the marathon. We know that speed is given by:
[tex]\[ v = \frac{d}{t} \][/tex]
Where:
- v = average speed (miles per hour)
- d = distance covered (miles)
- t = time spent running (hours)
Given that John's distance is 26.2 miles, and the marathon covers this distance, we have:
[tex]\[ 26.2 = \frac{26.2}{t} \][/tex]
Solving for t:
[tex]\[ t = \frac{26.2}{26.2} = 1 \][/tex]
So, John takes 1 hour to cover the 26.2 miles.
Now, let's consider the maximum and minimum possible times for John to complete the marathon:
- Minimum time: John completes the marathon in the fastest time possible. Let's say this is 0. This implies he runs the marathon in 0 hours.
- Maximum time: John takes his time and completes the marathon at the slowest pace possible. Let's use the average time for a marathon, which is around 4.5 hours.
Thus, the appropriate range for the time (t) is:
[tex]\[ 0 \leq t \leq 4.5 \][/tex]
This corresponds to option C: [tex]$0 \leq t \leq 4.5$[/tex].
Complete Question:
John is participating in a marathon that is 26.2 miles. His distance (d, in miles) depends on his time (t, in hours) Which is an appropriate range for this situation?
A. [tex]$0 \leq d \leq 26.2$[/tex]
B. [tex]$0 \leq d \leq 4.5$[/tex]
c. [tex]$0 \leq t \leq 4.5$[/tex]
D. [tex]$0 \leq t \leq 26.2$[/tex]
(05.02)
What is the y-intercept of the line shown?
−1
0
0.5
1
In the game of roulette, a player can place a $99 bet on the number 3333 and have a startfraction 1 over 38 endfraction 1 38 probability of winning. if the metal ball lands on 3333, the player gets to keep the $99 paid to play the game and the player is awarded an additional $315315. otherwise, the player is awarded nothing and the casino takes the player's $99. what is the expected value of the game to the player? if you played the game 1000 times, how much would you expect to lose? note that the expected value is the amount, on average, one would expect to gain or lose each game.
Which shows 54^2 − 46^2 being evaluated using the difference of squares method?
54^2 − 46^2 = (2916 + 2116)(2916 − 2116) = 4,025,600
54^2 − 46^2 = (54 + 46)(54 − 46) = (100)(8) = 800
54^2 − 46^2 = 2916 − 2116 = 800
54^2 − 46^2 = (54 − 46)^2 = 8^2 = 64
Which expression is equivalent to (m^5n/pq^2)^4
Answer
Find the expression is equivalent to
[tex](\frac{m^{5}n}{pq^{2}})^{4}[/tex]
To prove
As the expression is given in the question as follow .
[tex]=(\frac{m^{5}n}{pq^{2}})^{4}[/tex]
By using the exponent properties of the raise a power to a power
[tex](x^{a})^{b} = x^{ab}[/tex]
than the above expression becomes
[tex]=\frac{(m^{5}n)^{4}}{(pq^{2})^{4}}\\ =\frac{(m^{5})^{4}n^{4}}{p^{4}(q^{2})^{4}}[/tex]
[tex]=\frac{m^{20}n^{4}}{p^{4}q^{8}}[/tex]
Thus the expression is equivalent to
[tex]=(\frac{m^{20}n^{4}}{p^{4}q^{8}})[/tex]
A quick-loan company charges an 18% fee on any loan that is paid up to one week late. A woman borrowed $400 and paid the loan back 3 days late. What is the total she has to pay, including any fee?
In the diagram, ∠ABC = 90°. What is the radius of the circle?
A. 5.7 in
B. 16.5 in
C. 24.6 in
D. 12.3 in
D. 12.3 in
Explanation and solution;We are give that ∠ABC = 90°; therefore a line from point A to point C is the diameter, this is because a diameter subtends an right angle to the circumference of the circle. Therefore; triangle ABC is a right-angled triangle, thus AC is the hypotenuse.Using the Pythagoras theorem;
AC² = AB² + BC²
= 22.1² + 10.9²
= 607.22
AC = √ 607.22
= 24.64
But, since AC is the diameter and the radius is half of the diameter, then
Radius = 24.64/2
= 12.32
≈ 12.3 (to 1 decimal place)
Students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey.
Approximately what percent of students in the sample were male?
Round your answer to the nearest percent.
%
Preference Male Female TOTAL
Prefers dogs 36 20 56
Prefers cats 10 26 36
No preference 2 6 8
TOTAL 48 52 100
To find the percentage of students in the sample who were male, divide the total number of male students by the total number of students and multiply by 100.
Explanation:To find the percentage of students in the sample who were male, we need to look at the total number of male students and divide it by the total number of students in the sample. From the given two-way table, we can see that the total number of male students is 48. The total number of students in the sample is 100. To find the percentage, we can divide 48 by 100 and multiply by 100 to get:
Percentage of male students = (48/100) * 100 = 48%
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Answer:
36%
Step-by-step explanation:
150 centimeters is equivalent to
If the inflation rate increases faster than their income, people will most likely:
A. use a higher proportion of their incomes on basic needs
B. spend a lower proportion of their incomes on basic needs
C. get more goods and services for less money
D. obtain less goods and services for less money
If the inflation rate increases faster than their income, people will most likely use a higher proportion of their incomes on basic needs
What is inflation rate?Inflation is the rate of increase in prices over a given period of time. Inflation is typically a broad measure, such as the overall increase in prices or the increase in the cost of living in a country.
According to the question
If the inflation rate increases faster than their income, people will most likely:
As
inflation rate increases means increase in prices of goods and services over a given period of time.
i.e
People will use a higher proportion of their incomes on basic needs .
Hence, If the inflation rate increases faster than their income, people will most likely use a higher proportion of their incomes on basic needs.
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What is the solution to the equation below? Log6 4x^2-log6x-2
The logarithmic equation is solved to find x to be equal to 9
How to solve the equation
To solve the equation, we can use logarithmic properties to simplify and solve for x
[tex]\(\log_6(4x^2) - \log_6(x) = 2\)[/tex]
[tex]log_6\left(\frac{4x^2}{x}\right) = 2[/tex]
[tex]log_6(4x) = 2[/tex]
6²= 4x
36 = 4x
x = 9
The solution to the equation [tex]\(\log_6(4x^2) - \log_6(x) = 2\) is \(x = 9\).[/tex]
To solve the equation [tex]\(\log_6(4x^2) - \log_6(x) = 2\)[/tex], you can use the properties of logarithms.
First, apply the quotient rule of logarithms to combine the two logarithms:
[tex]\[ \log_6\left(\frac{4x^2}{x}\right) = 2 \][/tex]
Simplify the expression inside the logarithm:
[tex]\[ \log_6(4x) = 2 \][/tex]
Now, rewrite this equation in exponential form:
[tex]\[ 6^2 = 4x \]\[ 36 = 4x \][/tex]
Now, solve for x:
[tex]\[ x = \frac{36}{4} \]\[ x = 9 \][/tex]
So, the solution to the equation [tex]\(\log_6(4x^2) - \log_6(x) = 2\) is \(x = 9\).[/tex]
Find the surface area of a sphere with a volume of 36π in3.
SHOW WORK
will give medals and mark brainliest
its 113.10 inches squared
To find the surface area of a sphere given the volume, first solve for the radius using the volume formula (4/3πr³). In this case, the radius is 3. Then, use the surface area formula (4πr²), which gives the surface area as 36π square inches, or an approximate value of 113.10 square inches.
Explanation:The volume of a sphere is given by the formula V = 4/3 * π * r³. First, we need to find the radius of the sphere. Set the volume of the sphere (36π in³) equal to the volume formula and solve for r:
36π = 4/3πr³
From this, we find that r = 3. Now, we use the radius to find the surface area with the formula A = 4πr²:
A = 4π * 3² = 36π in²
So, the surface area of a sphere with a volume of 36π in³ is 36π square inches or approximately 113.10 square inches.
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Help asap plz ill give a gold medal. the label on cars antifreeze claims to protect the car between -30celsius and 130celsius. to convert Celsius temperature Fahrenheit temperature, the formula is, c=5/9(F-32). Write an solve and inequality to determine the Fahrenheit temperature range at which antifreeze protects the car.
What is the factorization of 2x²+4x+2
A. (2x+2)(x+2)
B. (2x+1)(x+2)
C. (2x+1)(x+1)
D. (2x+2)(x+1)
How will the circumference of the circle change if it is dilated by a scale factor of 4?
The circumference will be 4 times greater than the original.
The circumference will be 16 times greater than the original.
The circumference will be 1/4 the original.
The circumference will be1/16 the original.
Answer:
The circumference will be [tex]4[/tex] times greater than the original
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
where
r is the radius of the circle
In this problem we have
The radius of the original circle is
[tex]r1=16\ cm[/tex]
The circumference of the original circle is equal to
[tex]C1=2\pi (16)=32\pi\ cm[/tex]
If the circumference is dilated by a scale factor of [tex]4[/tex]
then
the radius of the dilated circle will be
[tex]r2=4*16=64\ cm[/tex]
and the circumference of the dilated circle will be
[tex]C2=2\pi (64)=128\pi\ cm[/tex]
so
[tex]C2=4C1[/tex]
therefore
The circumference will be [tex]4[/tex] times greater than the original
Use the the factor theorem to determine wether the first polynomial is a factor of the second. X-3; 2x^2-4x+30
Michelle found a new violin on sale at 30% off. how much would she pay the cashier if it originally sells for $250 in a city that had no sales tax
100%-30% = 70%
70%=0.70
250*0.70 = 175
she would pay $175
Cost to rent a bicycle is $5 plus $3 per hour for x hours what equation represents the total cost for c hours
You roll two standard number cubes. What is the probability that the sum is odd, given than one of the number cubes shows a 1? Show your work.
Which expression will produce an answer with the fewest significant figures?
a.15.4 - 8.1
b.54.5 30.7
c.4350 - 2210
d.18.8 - 6.5?
The sum of twice a number and a larger number is 145. The difference between the numbers is 55. Let x represent the smaller number and y represent the larger number. Which equations represent the situation? Check all that apply.
A. x-y=55
B. 2(x+y)=145
C. 2x+y=145
D. y-x=55
E. y=x+55
Which theorem could Chelsea use to show the measure of angle KPR is equal to the measure of angle QRL?
What number is 7 units to the left of -1?
Is the coordinate (1, 2) a solution of the system below?
x + 2y = 5
y = x + 1
A. Yes
B. No
Need help on #30 and 31 thanks!!
A carpenter trims a triangular peak of a house with three 7-ft pieces of molding. The carpenter uses 21 ft of molding to trim a second triangular peak. Are the two triangles formed congruent? Explain.
The two triangles formed by trimming the peaks of the house with the 7-ft pieces of molding are congruent.
Explanation:To determine if the two triangles formed by trimming the peaks of the house with the 7-ft pieces of molding are congruent, we can use the concept of the Side-Angle-Side (SAS) congruence criterion.
In the first case, the carpenter uses three 7-ft pieces of molding to trim the first triangular peak. This means that each side of the triangle is 7 feet long.
In the second case, the carpenter uses 21 ft of molding to trim the second triangular peak. Since the total length of molding used is 21 ft, we know that each side of the triangle is still 7 feet long.
So, in both cases, the triangles are formed by sides of the same length, which is 7 feet, and they have a common angle at the peak of the house.
This satisfies the SAS congruence criterion, which states that if two triangles have two sides of equal length and the included angle is the same, then the triangles are congruent.
Therefore, the two triangles formed by trimming the peaks of the house with the 7-ft pieces of molding are congruent.
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