Answers
keeping in mind that, "x" is just a length unit, and thus it cannot be negative.
Related Questions
Simplify the expression. 3y3 – 2y[4y – y(y – 3)] – [2y(y + 1) – 3y(y2 –1)] =
Answers
Answer:
Step-by-steThe first step for solving this expression is to distribute -y through the parenthesis.
3y³ - 2y × (4y - y² + 3y) - (2y × (y + 1) - 3y × (y² - 1))
Distribute 2y through the parenthesis.
3y³ - 2y × (4y - y² + 3y) - (2y² + 2y - 3y × (y² - 1))
Now distribute -3y through the parenthesis.
3y³ - 2y × (4y - y² + 3y) - (2y² + 2y - 3y³ + 3y)
Collect the like terms in the first set of the parenthesis.
3y³ - 2y × (7y - y²) - (2y² + 2y - 3y³ + 3y)
Collect the like terms in the second set of the parenthesis.
3y³ - 2y × (7y - y²) - (2y² + 5y - 3y³)
Distribute -2y through the parenthesis.
3y³ - 14y² + 2y³ - (2y² + 5y - 3y³)
Remember that when there is a "-" sign in front of the parenthesis,, you must change the sign of each term in the parenthesis. This will change the expression to the following:
3y³ - 14y² + 2y³ - 2y² - 5y + 3y³
Collect the like terms with an exponent of 3.
8y³ - 14y² - 2y² - 5y
Lastly,, collect like terms that have an exponent of 2.
8y³ - 16y² - 5y
Since we cannot simplify the expression any further,, the correct answer is going to be 8y³ - 16y² - 5y.
Let me know if you have any further questions.
M is the midpoint of CF for the points C(1, 2) and F(7, 10). Find MF.
Answers
To calculate the length of MF, find the midpoint M of CF using the midpoint formula, then use the distance formula to determine the length of MF, which is 5.0 cm.
Explanation:To find the length of the segment MF, we must first determine the coordinates of the midpoint M of the segment CF. Since C has coordinates (1, 2) and F has coordinates (7, 10), we use the midpoint formula which is ( (x1 + x2)/2, (y1 + y2)/2 ). Calculating this for C and F gives us the coordinates of M as:
x-coordinate of M = (1 + 7)/2 = 4y-coordinate of M = (2 + 10)/2 = 6Therefore, M has coordinates (4, 6). Now, to find the distance MF, we use the distance formula between points M and F:
MF = √[(x2 - x1)² + (y2 - y1)²] where (x1, y1) are the coordinates of M and (x2, y2) are the coordinates of F.
Replacing with the known values:
MF = √[(7 - 4)² + (10 - 6)²]
MF = √[3² + 4²] = √[9 + 16] = √25 = 5.0 cm
Thus, the length of the segment MF is 5.0 cm.
For f(x)=-3x+6, find f(-4)
Answers
x + y = 12
x - y = 10
What is the value of the x-determinant for the system shown?
(A.) -22
(B.) -12
(C.) -2
Answers
Final answer:
The value of the x-determinant for the system of equations is (C) -2, which is found by evaluating the determinant of the system's coefficient matrix.
Explanation:
To find the x-determinant for the system of equations given below:
x - y = 10
We can set up the coefficient matrix for these equations:
Matrix [A] =
| 1 1 |
| 1 -1 |
The determinant of this matrix is calculated by multiplying the diagonal elements and then subtracting the product of the off-diagonal elements. Hence, the determinant (det A) = (1)(-1) - (1)(1) = -1 - 1 = -2.
Therefore, the value of the x-determinant is (C) -2.
Solve the equation,if possible.
And check the solution.
4/d = 2/6
Check:
Answers
4/d = 2/6
2d = 24
d = 24/2 = 12
Mark draws one card from a standard deck of 52. he receives $ 0.35 for a heart, $ 0.55 for a jack and $ 0.85 for the jack of hearts. how much should he pay for one draw
Answers
To find out how much Mark should pay for one draw, calculate the expected value by multiplying the payouts for a heart, a jack, and the jack of hearts by their respective probabilities. Sum these values to find the amount Mark should pay per draw to make the game fair, which is $0.135.
To determine how much Mark should pay for one draw from the deck of 52 cards, we need to calculate the expected value (EV) of one draw. The EV is calculated by multiplying each outcome by its probability and summing these products.
The deck has 13 hearts, so the probability of drawing a heart (excluding the jack of hearts) is 12/52 or 3/13. Drawing any jack other than the jack of hearts has 3 possible outcomes in the remaining 51 cards; the probability is 3/52. The jack of hearts is a single card with a probability of 1/52. The remaining 36 cards are neither hearts nor jacks and yield no payout.
The EV is calculated as follows:
(12/52 × $0.35) for a heart
(3/52 × $0.55) for a jack
(1/52 × $0.85) for the jack of hearts
Adding these up we get: (3/13 × $0.35) + (3/52 × $0.55) + (1/52 × $0.85) = $0.13538. To ensure the game is fair and the host neither loses nor gains money in the long term, Mark should pay $0.135 per draw.
Let point C be between V and W on VW. Given that VW = 61, VC = z + 13, and CW = z + 8, solve for z. A. 18 B. 19 C. 20 D. 21
Answers
Therefore:
VC + CW = VW
z+13+z+8 = 61
2z+21=61
2z=61-21
2z=40
z=40/2
z=20
At a rate of 36 miles per hour, it takes Henry 15 minutes to drive from the library to his house. Show how to find the distance that Henry traveled. Include units in your calculation.
Answers
[tex]distance=rate*time[/tex]
We have a slight problem, though, because we are measuring rate in miles per hour, and we are measuring time in minutes. To make this problem solvable, we need to convert to either miles per minute or convert the time to hours. I'm going to convert the 15 minutes into hours:
[tex]15min*\frac{1 hour}{60 min}=\frac{1}{4}hour[/tex]
Now that all of the units match, we have:
[tex]distance=36\frac{mi}{hr}*\frac{1}{4}hr[/tex]
You can finish from there I'm sure.
Find a linear function that gives the cost in dollars of buying
Pop tarts on sale two boxes cost four dollars four boxes cost six dollars
Answers
The linear function that gives the cost in dollars of buying Pop tarts can be obtained using the equation of a straight line with passing through points (2, 4) and (4, 6) as follows:
[tex] \frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1} \\ \\ \Rightarrow\frac{y-4}{x-2} = \frac{6-4}{4-2} = \frac{2}{2} =1 \\ \\ \Rightarrow y-4=x-2 \\ \\ \Rightarrow y=x-2+4=x+2[/tex]
Therefore, the linear function that gives the cost in dollars of buying Pop tarts is y = x + 2.
A crane cable can support a maximum load of 20,000 kg. If a bucket has a mass of 4,000 kg and gravel has a mass of 1,500 kg for every cubic meter, how many cubic meters of gravel (g) can be safely lifted by the crane?
Answers
Answer:
10.67 kg of gravel can be safely lifted by the crane
Step-by-step explanation:
Maximum load that a crane can support = 20000 kg.
Bucket has a mass = 4000 kg
Gravel has a mass = 1500 kg for every cubic meter.
Let the volume of gravel is = g cubic meter
Therefore, mass of the gravel = 1500g kg
Now we form an equation to show the weight that the crane cable can support
Mass of Bucket + mass of Gravel = Total mass that a lift can support
4000 + 1500g = 20000
1500g = 20000 - 4000
1500g = 16000
[tex]g=\frac{16000}{1500}[/tex]
g = 10.67 kg
Therefore, 10.67 kg of gravel can be safely lifted by the crane.
A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width. A. 34 inches B. 35 inches C. 23 inches D. 12 inches
Answers
perimeter = 2L +2w
L = w+11
70 = 2(w+11) +2w
70 = 2w+22+2w
70= 4w + 22
48 = 4w
w=48/4 = 12
width = 12
length = 12+11 = 23
2x12 = 24
2x23 = 46
46+24 = 40
length = 23 inches, width = 12 inches
Answer is D
Answer:
The answer is the option D
[tex]12\ inches[/tex]
Step-by-step explanation:
we know that
The perimeter of a rectangle is equal to
[tex]P=2L+2W[/tex]
where
L is the length side of the rectangle
W is the width side of the rectangle
In this problem we have
[tex]P=70\ in[/tex]
so
[tex]70=2L+2W[/tex] ------> equation A
[tex]L=W+11[/tex] ------> equation B
Substitute equation B in equation A and solve for W
[tex]70=2[W+11]+2W[/tex]
[tex]70=2W+22+2W[/tex]
[tex]4W=70-22[/tex]
[tex]W=48/4[/tex]
[tex]W=12\ in[/tex]
Find the inverse of f(x)= -x + 3
Answers
The most important property of g and f being inverses of each other, is that
g(f(x))=x, also f(g(x))=x
so, what one function 'does' to x, the other 'undoes' it.
Thus, we have:
f(g(x))=x and alos f(g(x))= -g(x)+3, from the rule
thus :
-g(x)+3=x
-g(x)=x-3
g(x)=-x+3
check: f(g(x))=f(-x+3)=-(-x+3)+3=x-3+3=x
Answer: the inverse of f is g, such that g(x)=-x+3
The square root of 2.25 is
A.15
B.1.5
C.0.15
D.irrational
Answers
How to put 33 into 4:7
Answers
so
33 / 11 = 3
4 x 3 = 12
7 x 3 = 21
so answer
4:7 = 12:21
In a college of exactly 2740 students, exactly 55 % are male. what is the number of female students? express your answer as an integer.
Answers
In a college of exactly 2740 students, exactly 55 % are male. 1233 is the number of female students.
What is percentage?
A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
In a college of exactly 2740 students,
exactly 55 % are male.
i.e. female students = 45%
so, the number of female students = 2740*45%
=1233
Hence, In a college of exactly 2740 students, exactly 55 % are male. 1233 is the number of female students.
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Justify the last two steps of the proof.
Given MN is congruent to segment PO and MO is congruent to PN
Prove MNO is congruent to PON
Proof:
1. MN is congruent to segment PO _______ 1. Given
2.MO is congruent to PN_______ 2. Given
3. NO is congruent to ON ________ 3. ?
4.MNO is congruent to PON___ 4. ?
*Symmetric Property of congruent to; SAS
*Reflexive Property of congruent to; SAS
*Symmetric Property of congruent to; SSS
*Reflexive Property of congruent to; SSS
Answers
NO and ON are the same line. They are congruent by the reflexive property (a line segment is a reflection of itself).
Statement 4:
Shape MNO and shape PON are congruent by side-side-side since:
side PN = side MO
side MN = side PO
side NO = side ON
Answer: Fourth option
Based on the information, the correct option is 4. Reflexive Property of congruent to; SSS
What is congruence?The reflexive property of congruence states that any geometric figure is congruent to itself. In other words, any shape or object is congruent to itself.
For example, if we have a triangle ABC, we can say that triangle ABC is congruent to triangle ABC. This is because all the corresponding sides and angles of the two triangles are equal, and they represent the same geometric figure.
NO and ON are the same line. They are congruent by the reflexive property (a line segment is a reflection of itself). Shape MNO and shape PON are congruent by side-side-side since:
side PN = side MO
side MN = side PO
side NO = side ON
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Only individuals over the age of 60 need to create an estate plan? True or False
Answers
Answer: False
Step-by-step explanation: People of any age over 21 need to complete an estate plan or a will. If you don't complete an estate plan or a will, anything you have could be left to the government. Regardless of your age or income, you always want to have a plan to distribute your money should you die unexpectedly.
What is the union of the following sets?
G = {12, 14, 16, 18}
H = {13, 15, 17, 18}
A. {18}
B. {12, 13, 14, 15, 16, 17}
C. { }
D. {12, 13, 14, 15, 16, 17, 18}
Answers
I hope this helps
Answer: D. {12, 13, 14, 15, 16, 17, 18}
Step-by-step explanation:
The union of two sets A and B is the set of elements which are in A, in B, or in both A and B, without repetition.
In this case, the union of the sets G and H will be the set of elements in G= {12, 14, 16, 18} and then the set of elements in H= {13, 15, 17, 18}, excluding those that already were in G, which in this case is the number 18.
Then:
G ∪ H={12, 13, 14, 15, 16, 17, 18}
how would you translate this into an equation
"one less than the product of number and 3 is 5 more than the number itself "
Answers
Hope this helps!
A rectangle has perimeter 80 m and length 27 m. What is the width?
Answers
the length is 27
27 x 2 = 54
80 - 54 = 26
26/2 = 13
13 is your answer for the width
hope this helps
A fracture in the left femoral region that is 5 centimeters proximal to the patellar region and 30 centimeters distal to the coxal region will be __________.
Answers
A fracture in the left femoral region that is 5 centimeters proximal to the patellar region and 30 centimeters distal to the coxal region will be located in the midshaft of the femur.
The femur is the long bone in the thigh, and it has distinct regions:
Coxal Region (Hip Region):
This refers to the upper end of the femur, which articulates with the hip bone (coxal bone).
A fracture occurring here would typically be near the hip joint.
Patellar Region (Knee Region):
This refers to the lower end of the femur, where it articulates with the patella (knee cap).
A fracture here would typically involve the knee joint.
Midshaft of the Femur:
This is the region between the coxal and patellar regions.
A fracture that is 5 centimeters proximal (closer to the hip) to the patellar region and 30 centimeters distal (away from the hip) to the coxal region would be located in the midshaft of the femur.
Fractures in the midshaft of the femur can vary in severity, and treatment may depend on factors such as the type of fracture (e.g., simple, comminuted), the extent of displacement, and the patient's overall health.
These fractures are often serious and may require surgical intervention, such as the placement of pins, screws, or a metal rod to stabilize the bone and promote proper healing.
Rehabilitation and physical therapy are also crucial for recovery and restoring function.
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1. The radius, r, of a circle is one-half of the length of its diameter, d.
r = d
2r = d
+ r = d
r=d
r=
Answers
Answer:
2r=d stands as correct
Step-by-step explanation:
what is 3(7x-6)<-81?
Answers
3(7x - 6) < -81
First, we need to apply the Distributive Property to the left side of the inequality.
This mathematical term means to multiply the number or variable outside of the parenthesis to all numbers and/or variables on the inside of the parenthesis.
Here's an example;
3(2 + 1)
Multiply the outside number by all inside numbers.
3(2) + 3(1)
Multiply.
6 + 3
Simplify the expression.
9.
Now that we've explained our concept for distributing, let's apply what we now know to our current problem.
3(7x - 6) < -81
Apply the Distributive Property to the left side of the inequality.
3(7x) + 3(-6)
Multiply.
21x - 18
We now have:
21x - 18 < -81
Now we need to isolate the variable. To do this, we need to make sure that 'x' is by itself. Since x is being subtracted by 18, we need to apply the opposite order of operations to both sides of the inequality.
Add 18 to both sides to isolate the variable.
21x < -63
We now need to solve for x. To solve for x, we need to divide both sides by 21, as iur variable is being multiplied by 21.
We are now left with:
x < -3
This is your final solution to your inequality.
I hope this answer helps you, and feel free to ask me any questions you have in the comments below this answer! Have a great day, and thank you for asking your question here at Brainly!
The store keeper sold 9 1/4 yards from a piece of material containing 53 yards. How much was left in the original piece?
Answers
Find an equation of the sphere with points p such that the distance from p to a(−3, 6, 4) is twice the distance from p to b(5, 3, −2).
Answers
At the half ime show, a marching band marched in formation. the lead drummer started at a point with coordinates (–2, –5) and moved 3 steps up and 1 step right.
a. write a rule to describe the translation.
b. what were the coordinates of the drummer's final position?
Answers
b) (-1, -2)
I thought of a number, multiplied it by 2 1/2 , divided the result by 1 1 /5 , subtracted 7/18 from it, and got 1 5/6 . What was my number?
Answers
The student's original number was 1 3/45. This was obtained by reversing the processes described in the problem and applying them to the final number.
Explanation:
To solve this problem, we basically need to reverse the operations given in the problem and perform them on the final answer 1 5/6. Let's start:
Add 7/18 to 1 5/6. The sum is 2. Multiply 2 by 1 1/5. The product is 2 2/5. Finally, divide 2 2/5 by 2 1/2. The quotient, which is the number the student originally thought of, is 48/45 or 1 3/45.
So the student's original number was 1 3/45.
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what is( ×+4 /6)=(18/12)
Answers
x = 18/12 - 4/6. Simplify each fraction and 18/12 simplified by 6 will be 3/2 and 4/6 simplified by 2 would 2/3. The equation would now be x = 3/2 - 2/3. The least common denominator would be 6 so when converted the equation would now be 9/6 - 4/6 = 5/6 so x = 5/6. You can check your answer by substituting x in the original equation with 5/6 so it would be (5/6 + 4/6) = (18/12) and 5/6 + 4/6 = 9/6 and when expressed as a mixed number and simplified it would equal 1 1/2 and 18/12 simplified as a mixed number and simplified would equal 1 1/2.
1 1/2 = 1 1/2.
Thirty-five states in a country have four-star hotels. Assume the country has 50 states. (a) What fraction of the states can claim at least one four-star hotel? (b) How many states do not have a four-star hotel? (c) Write the fraction of states without a four-star hotel.
a. The fraction of states with a four-star hotel ........ (Simplify your answer.)
Answers
the portion of states that have a four star hotel compared to how many states there are uses the fraction 35/50. You must simplify this, and to do this you find the greatest value with can divide the numerator and the denominator. This is 5. 35/5=7, and 50/5= 10, therefore, 7/10
(b) 15
simply subtract the number of states which have a four star hotel from the total number of states
(c) 3/10
this is the same logic as (a). use the answer you got from part b, and simplify the fractions
The fraction of states with at least one four-star hotel is 7/10, 15 states do not have a four-star hotel, and the fraction of states without a four-star hotel is 3/10.
Answer to Student's Question
(a) To find the fraction of states with at least one four-star hotel, we divide the number of states with a four-star hotel by the total number of states. Therefore, the fraction is 35/50, which simplifies to 7/10.
(b) To determine how many states do not have a four-star hotel, we subtract the number of states with a four-star hotel from the total number of states: 50 - 35 = 15. So, there are 15 states without a four-star hotel.
(c) Finally, the fraction of states without a four-star hotel is the number of states without such hotels divided by the total number of states. This is 15/50, which can be simplified to 3/10.
What is the distributive property of 60 - 50?
Answers
Simple.