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=
Answer:
2r=d stands as correct
Step-by-step explanation:
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
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]
What is the equation of the line, in point-slope form, that passes through the points (-3, -1) and (-6, 8)? open study?
إ
Hello : let A(-3,-1) B(-6,8)
the slope is : (YB - YA)/(XB -XA)
(8+1)/(-6+3) =9/(-3)
the slope is: -3
For f(x)=-3x+6, find f(-4)
Find the values of x and y that make k || j and
m || n.
x =
y =
Answer:
x= 80
y= 130
Step-by-step explanation:
The correct values of x and y that make k || j and m || n are x = 130 and y = 130.
To find the values of x and y, we need to use the fact that if two lines are parallel, their corresponding angles are equal.
Given that k is parallel to j, we have:
x = 50 (corresponding angles)
Since m is parallel to n, we have:
y + 80 = 210 (corresponding angles)
Solving for y:
y = 210 - 80
y = 130
Now, we have the value of x as 50 and the value of y as 130. However, we also know that the angles x and y are supplementary because they form a straight line. Therefore, their sum must be 180 degrees.
x + y = 180
50 + y = 180
y = 180 - 50
y = 130
This confirms that y is indeed 130 degrees. Since x and y are supplementary and both equal to 130 degrees, we have a contradiction because the sum of x and y should be 180 degrees.
To resolve this contradiction, we must re-evaluate our initial assumption that x = 50 degrees. Since x and y are supplementary, and we have correctly determined that y = 130 degrees, we must have:
x + y = 180
x + 130 = 180
x = 180 - 130
x = 50
This is incorrect because we initially assumed x = 50 degrees based on corresponding angles, but we did not consider that the angle adjacent to x on line k is not given and could be different from the corresponding angle of 50 degrees on line j.
To correct this, we should consider the angle adjacent to x on line k, which must sum up with x to 180 degrees because of the straight line. Let's call this angle x'. Since k is parallel to j, x' corresponds to the angle of 130 degrees on line j. Therefore, we have:
x' + x = 180
130 + x = 180
x = 180 - 130
x = 50
Now, considering that x and y are supplementary:
x + y = 180
50 + y = 180
y = 180 - 50
y = 130
Thus, we have x = 50 degrees and y = 130 degrees, which are indeed the values that make k || j and m || n. However, since x and y are supplementary, they must both be 130 degrees to satisfy the conditions of the problem.
Therefore, the correct values are x = 130 degrees and y = 130 degrees.
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}
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}
What is the total surface area of this composite solid ?
Simplify the expression. 3y3 – 2y[4y – y(y – 3)] – [2y(y + 1) – 3y(y2 –1)] =
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.
The data set shows the weights of pumpkins, in pounds, that are chosen for a photograph in a farming magazine. 18 22 14 30 26 (a) What is the mean, x , of the data set? (b) What is the sum of the squares of the differences between each data value and the mean? Use the table to organize your work. (c) What is the standard deviation of the data set? Use the sum from Part (b) and show your work. (d) A second group of pumpkins, with weights of 32, 35, 33, 34, and 36 pounds, are chosen for another photograph. Will the standard deviation of these weights be greater or less than the standard deviation found in Part (c)? Answer this without doing a calculation and explain your reasoning.
M is the midpoint of CF for the points C(1, 2) and F(7, 10). Find MF.
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.
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
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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Solve the equation,if possible.
And check the solution.
4/d = 2/6
Check:
16x^2 = 49 help find x.
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 __________.
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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Suppose you have 19 black socks and 19 green socks in the dryer. 4. without looking, how many socks would you need to pull out of the dryer to be sure you get a black pair?
You would need to pull out 21 socks from the dryer to ensure you have a black pair since you might initially pull out all 19 green socks before getting to the black ones.
To determine how many socks one would need to pull out of the dryer to be sure to get a pair of black socks when you have 19 black socks and 19 green socks, consider the worst-case scenario. In the worst case, you pull out all 19 green socks one by one. Since you have not yet pulled out a single black sock, the 20th sock you pull out has to be black, because there are no more green socks left. However, to ensure you have a pair of black socks, you will need to pull out one more sock. So the answer is that you need to pull out 21 socks to be certain of having a pair of black socks.
The angle of elevation to the sun is 24°. What is the length of the shadow cast by a person 1.82 m tall?
The length of the shadow cast by a person 1.82 m tall is; 4.09m
Angle of ElevationThe angle of Elevation to the sub is 24°.
On this note, the shadow cast on the floor represents the adjacent of the angle of Elevation.
Hence, the length of the shadow cast can be calculated from Tangent identify as follows;
Tan 24° = 1.82/ll = 1.82/Tan 24l = 1.82/0.445Length of shadow = 4.09m
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Olivia's work and solution to the equation -6x + 11=43 is shown. Identify each error in Olivia,s work ad epxplian what she would have done instead.
-6x + 11=43
+11 +11
-6x = 54
-6x/6 = 54/6
X = 9
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
Please help me . I don't get it
How to put 33 into 4:7
what is( ×+4 /6)=(18/12)
In a college of exactly 2740 students, exactly 55 % are male. what is the number of female students? express your answer as an integer.
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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A rectangle has perimeter 80 m and length 27 m. What is the width?
How to write a standard form equation with an undefined slope?
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.
What is the sector area created by the hands of a clock with a radius of 9 inches when the time is 4:00? 6.75π in.2 20.25π in.2 27π in.2 81π in.2?
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
In this problem we have
[tex]r=9\ in[/tex]
substitute in the formula
[tex]A=\pi*9^{2}=81 \pi\ in^{2}[/tex]
The area of the complete circle subtends [tex]360\ degrees[/tex]
When the time is 4:00 the angle formed by the hands of a clock is [tex]120\ degrees[/tex]
so by proportion
Find the area of the sector area
[tex]\frac{81\pi}{360} \frac{in^{2}}{degree} =\frac{x}{120} \frac{in^{2}}{degree} \\ \\x=120*81 \pi /360\\ \\x=27 \pi\ in^{2}[/tex]
therefore
the answer is the option
[tex]27 \pi\ in^{2}[/tex]
Write an equation of the line passing through point P(−8, 0) that is perpendicular to the line 3x−5y = 6
To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope. Substituting the values into the point-slope form, we can find the equation of the perpendicular line.
Explanation:To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The given line has the equation 3x - 5y = 6, so its slope is 3/5. The negative reciprocal of 3/5 is -5/3, so the slope of the line perpendicular to the given line is -5/3.
Since we know a point on the perpendicular line is P(-8, 0), we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting -8 for x1, 0 for y1, and -5/3 for m, we get y - 0 = -5/3(x - (-8)).
Simplifying the equation gives y = -5/3x - 40/3, which is the equation of the line passing through point P(-8, 0) and perpendicular to the line 3x - 5y = 6.
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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?
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.
2007 divided by j = 223
5. 41°F equals how many degrees Celsius?