A tree grows 1 3/4 feet per year. How long will it take the tree to grow from a height of 21 1/4 feet to a height of 37 feet?
Is the coordinate (1, 2) a solution of the system below?
x + 2y = 5
y = x + 1
A. Yes
B. No
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.
150 centimeters is equivalent to
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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A ball is thrown from a height of 140 feet with an initial downward velocity of 8 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=140-8t-16t^2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
The time would be 2.71 seconds after the ball is thrown does it hit the ground.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
A ball is thrown from a height of 140 feet with an initial downward velocity of 8 ft/s.
The ball's height h (in feet) after t seconds is given by the following.
⇒ h = 140-8t - 16t²
h = 0 at the ground.
We divide both sides of the equation by (-8) to yield:
⇒ 0 = 2t² + t - 17.5
where a = 2, b= 1, c = -17
[tex]t = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\t = \dfrac{-1\pm\sqrt{2^2-4\times2\times-17.5}}{2\times2}[/tex]
t = [-1 ± √141] / (4)
t = 2.71 and -3.21
For this problem, time can only be positive, so ignore the negative solution.
Therefore, the time would be 2.71 seconds after the ball is thrown does it hit the ground.
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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]
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)
The length of a rectangle is 22 meters longer than the width. if the area is 2626 square meters, find the rectangle's dimensions. round to the nearest tenth of a meter.
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.
Use the the factor theorem to determine wether the first polynomial is a factor of the second. X-3; 2x^2-4x+30
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
What number is 7 units to the left of -1?
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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Use basic identities to simplify the expression. sin^2θ + tan^2θ + cos^2θ
You and six friends play a game where each person writes down his or her name on a scrap of paper, and the names are randomly distributed back to each person. Find the probability that everyone gets back his or her own name.
Answer with explanation:
Total number of different candidates who are playing the game=7
Suppose, Seven candidates are represented by ={A,B,C,D,E,F,G}
Total Possible Outcome =7
→Probability that , "A" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{7}[/tex]
→Now, 6 candidates are left.
Probability that , "B" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{6}[/tex]
→Now, 5, candidates are left.
Probability that , "C" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{5}[/tex]
→Now, 4 candidates are left.
Probability that , "D" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{4}[/tex]
→Now, 3 candidates are left.
Probability that , "E" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{3}[/tex]
→Now, 2 candidates are left.
Probability that , "F" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{2}[/tex]
→Now, a single candidates is left.
Probability that , "G" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{1}=1[/tex]
Required Probability
[tex]=\frac{1}{7} \times\frac{1}{6} \times\frac{1}{5} \times\frac{1}{4} \times\frac{1}{3} \times\frac{1}{2} \times 1\\\\=\frac{1}{5040}[/tex]
An ice cream store sells 2 2 drinks, in 3 3 sizes, and 8 8 flavors. in how many ways can a customer order a drink?
If an ice cream store sells 2 drinks, in 3 sizes, and 8 flavors, the number of ways can a customer order a drink will be 48.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
It given that, An ice cream store sells 2 drinks, in 3 sizes, and 8 flavors.
We have to find the number of ways can a customer order a drink,
It is obtained by multiplying all the possible cases for that event, Multiplication is one type of arithmetic operation. There are basically four types of arithmetic operations.
=2×3×8
=48
Thus, if an ice cream store sells 2 drinks, in 3 sizes, and 8 flavors, the number of ways can a customer order a drink will be 48.
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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:
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
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?
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?
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.
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]
A 31-in. television has a 31 in. diagonal and a 18 in. width. what is the height of the 31-in. television?
Larry travels 60 miles per hour going to a friend’s house and 50 miles per hour coming back, using the same road. he drove a total of 5 hours. what is the distance from larry’s house to his friend’s house, rounded to the nearest mile?
Final answer:
To find the distance from Larry's house to his friend's house, we use the relationship between distance, speed, and time for his trip to and from his friend's house, taking into account the different speeds and total travel time of 5 hours.
Explanation:
The student's question asks to find the distance from Larry's house to his friend's house given his speed and total travel time in both directions. To solve this problem, we use the formula distance = speed × time. Let's call the distance one way d, the time to travel to the friend's house t1, and the time to travel back t2. Larry's speed going to the friend's house is 60 miles per hour and coming back is 50 miles per hour. The total travel time is 5 hours.
So for the trip to the friend's house we have:
d = 60 × t1
And for the trip back:
d = 50 × t2
Since the total travel time is 5 hours:
t1 + t2 = 5
Substituting the expressions for d from the first two equations into the third, we get:
60t1 + 50t2 = 60(5)
Using the fact that t1 + t2 = 5, we solve for either variable, say t1, which gives us t2 as well. After finding t1 and t2, we plug either of those back into the original distance equations to find d, which will be the distance from Larry's house to his friend's house. The answer should be rounded to the nearest mile.
(02.01 LC)
Figure ABCD is transformed to figure A′B′C′D′:
Which angle in Figure A′B′C′D′ is equal to Angle CDA.?
Angle D prime A prime B prime.
Angle A prime B prime C prime.
Angle B prime C prime D prime.
Angle C prime D prime A prime.
Answer:
I think it is Angle B prime C prime D prime
Step-by-step explanation:
A'B'C'D' is a translation so they are congruent.So the figure B'C'D' is congruent or equal to BCD. Please let me know if i'm right
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]
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
Need help on #30 and 31 thanks!!
Probability theory predicts that there is a 22.4% chance of a particular soccer player making four penalty shots in a row. If the soccer player taking four penalty shots is simulated 2500 times, in about how many of the simulations would you expect at least one missed shot?
1940 ~~~~~~~~~~~~ APEX