The circumference of the circle C = 207.24 inches.
The formula for the circumference of circle is,
[tex]C=2\pi r[/tex]Assume the value of pi be 3.14.
Substitute 207.24 for C in the formula to determine the radius of circle.
[tex]\begin{gathered} 207.24=2\pi r \\ r\approx\frac{207.24}{2\cdot3.14} \\ =33 \end{gathered}[/tex]Thus radius of circle is 33 inches.
Given P(A)=0.31P(A)=0.31, P(B)=0.5P(B)=0.5 and P(A\text{ or }B)=0.585P(A or B)=0.585, find the value of P(A\text{ and }B)P(A and B), rounding to the nearest thousandth, if necessary.
Given:
P(A) = 0.31
P(B) = 0.5
P(A or B) = 0.585
To find:
P(A and B)
To determine P(A and B), we will apply the formula:
[tex]P(A\text{ or B\rparen}=\text{ P\lparen A\rparen + P\lparen B\rparen}-\text{ P\lparen A and B\rparen}[/tex][tex]\begin{gathered} substitute\text{ the values:} \\ 0.585\text{ = 0.31 + 0.5 +- P\lparen A and B\rparen} \\ 0.585\text{ = 0.81 - }P(A\text{ and B\rparen} \\ 0.585+\text{ P\lparen A and B\rparen = 0.81} \\ P(A\text{ and B\rparen = 0.81 - 0.585} \end{gathered}[/tex][tex]P(A\text{ and B\rparen = 0.225 }[/tex]What is the distance between the following points?The answer choices areA- 9B- 10C- square root of 21D- square root of 58
Given:
Points: (3, -9) and (6, -2) on a coordinate plane
To find:
The distance between the two points
To determine the distance between the points, we will apply the formula:
[tex]$$dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}$$[/tex][tex]\begin{gathered} x_1=3,y_1=-9,x_2=6,y_2\text{ = -2} \\ dis\tan ce\text{ = }\sqrt{(-2-(-9))^2+(6-3)^2} \\ dis\tan ce\text{ = }\sqrt{(-2+9)^2+(6-3)^2} \\ dis\tan ce\text{ = }\sqrt{(7)^2+(3)^2} \end{gathered}[/tex][tex]\begin{gathered} distance\text{ = }\sqrt{49\text{ + 9}} \\ distance\text{ = }\sqrt{58} \end{gathered}[/tex]For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?
m greater-than StartFraction 25 Over 3 EndFraction
m less-than StartFraction 25 Over 3 EndFraction
m less-than StartFraction 49 Over 12 EndFraction
Value of m for which the graph of y = 3x² + 7x + m have two
x- intercepts is equal to m < 49 /12.
As given in the question,
Given graph equation:
y = 3x² + 7x + m
Graph y = 3x² + 7x + m has two x-intercepts if and only if
3x² + 7x + m<0 __(1)
Formula used to calculate x value is x = -b/2a
Compare with the standard form:
a= 3
b=7
c=m
x= -7/ 2(3)
= -7/6
Substitute x=-7/6 in (1)
3(-7/6)² + 7(-7/6) +m<0
⇒49/12 -49/6 +m <0
⇒-49/12 +m<0
⇒m< 49/12
Therefore, Value of m for which the graph of y = 3x² + 7x + m have two
x- intercepts is equal to m < 49 /12.
The complete question is:
For what values of m does the graph of y = 3x²+ 7x + m have two x-intercepts?
a. m > 25/3
b. m < 25/ 3
c. m < 49 /12
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6. Keaton needs to fill juice cups for her little sister's birthday party. There are 22 juice cups and each juice cup holds 12 fluid ounces. The juice comes in 1-gallon bottles. How many 1-gallon bottles of juice will Debbie need to purchase?
(1 quart = 32 fluid ounces, 1 gallon = 4 quarts)
Answer: she will need about 2 gallons of juice
Step-by-step explanation:
not all tiles would be used, need help solving the steps for a bisecting line statement.
We have different steps for bisecting a line segment using a reflective device, and these steps are as follows:
And we have to select three of them to complete the process.
To determine the steps, we need to remember that the reflective device permits us to see through it, and also see reflections on it. Then the steps for bisecting a line segment AB are:
1. Place the reflective device anywhere on the segment - It does not matter the position at which we need to put the reflective device.
2. Move the reflective device around on the paper until the reflection of point A coincides with point B.
3. Draw the line of the reflection using the edge of the reflective device as a guide.
Therefore, in summary, the three steps are:
• Place the reflective device anywhere on the segment (,first box,).
,• Move the reflective device around on the paper until the reflection of point A coincides with point B (,third box,).
• Draw the line of the reflection using the edge of the reflective device as a guide (sixth box),.
what is the circumference of a circle with a radius of 6cm
The circumferance of a circle with radius of 6cm is 37.68cm
To find:
Circumferance of a circle
Given:
Radius of circle is 6cm
Solution:
Circumference is similar to perimeter as it is the total length required to draw a circle.
Let c be the perimeter.
c = 2πr
or
c = πd
This depends on knowing the radius (r) or diameter (d).
For example, let's calculate it manually.
If r = 6 cm, the circumference in π is c = 2π(6) = 12π cm.
When expressed numerically, it is 37.7 cm after the decimal point is rounded off.
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A Christmas tree is supported by a wire that is 9 meters longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 23 meters shorter than the height of the tree. What is the height of the tree?
Through the given statement measurements we find that the height of the tree is = 33 m.
What is Pythagoras Theorem?The right-angled triangle's relationship between its sides is explained by the Pythagorean Theorem, often known as Pythagoras Theorem, a key concept in mathematics.
The Pythagorean triple describes the sides of the right triangle. For the most part, the Pythagorean theorem is employed to determine a triangle's angle and the length of an ambiguous side.
The base, perpendicular, and hypotenuse formulas are derived by means of this theorem. The perpendicular, base, and hypotenuse of this triangle are its three named sides.
As it is on the other side of the angle of 90 degrees, the hypotenuse in this case is the longest side.
An equation, commonly known as a Pythagorean triple, is created by squared values for the sides of a right triangle that have positive integer values.
Let the Height of the Christmas tree be 'h' meters.
Length of the wire = (h + 9) meters
Distance from the base = (h - 23) meters
This scenario forms a right-angled triangle, with height = h m, base = (h-23) m and hypotenuse = (h+9) m
Now, as this is a right-angled triangle,
h^2 + (h-23) ^2 = (h+9) ^2 (Pythagoras theorem)
⇒ h^2 + h^2 - 46h + 529 = h^2 + 18h + 81
⇒ 2h^2 - h^2 - 46h - 18h = 81 - 529
⇒h^2 - 64h = -448
⇒ h^2 - 64h + 448 = 0
⇒ h^2 - (56 + 8) h + (56 x 8) = 0
⇒ (h - 56) x (h - 8) = 0
⇒ h = 56 or h = 8
Since the distance from the base = (h - 23) m cannot be a negative value,
therefore, h = 56 m
Therefore,
The height of the tree = 56 m,
The length of the wire = h + 9 = 56 + 9 = 65 m
The distance from the base of the tree to the wire = h -23
= 56 - 23 = 33 m
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 A gardener has 1080 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. Find the greatest area of the garden?
which value of y makes the inequality 3y^2+2(y-5)>8 true?
A. y = 0
B. y = –1
C. y = –2
D. y = –3
The captain of a ship at sea sights a lighthouse which is 100 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 26°. How far is the ship from the base of the lighthouse? How many feet?
Answer:
Explanation;
The set will be a right angled triangle as shown;
Mr. Pittman's language arts class participated in a Read-And-Write challenge during April. For each of the first 10 days, Felipe read for x minutes and wrote in his journal for 15 minutes. For each of the last 20 days, Felipe read for x minutes and wrote in his journal for 30 minutes.
The expression representing the time Philip spent in the challenge is 30x+750.
If an expression was created utilizing integer variables, constants, and algebraic operations, it is said to be algebraic (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
Transcendental numbers, like such and e, are not algebraic, though, as they are not produced by the application of algebraic operations and numerical constants.
While it is common to produce with Euclidean expressions, the definition of e requires an unlimited number of algebraic operations.
An expression is considered to be rational if it can be completely reduced to a reasonable fraction using the principles of arithmetic operations ( associative properties and commutative properties of multiplication and addition, distributive property and rules for the operations on the fractions).
For the first 10 days:
read =10 x wrote 15 × 10 = 150
For the last 20 days
read =20 x
wrote = 30×20 = 600
Hence the total expression is 30x+750.
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Please help, I’ll give you 20 pts and 30 later I just don’t want to waste them.
The discriminant and the point of tangency are used to find the values of the variables as follows;
7. The line y = m·x is tangent to the curve x² + 2·x·y + 2·x = 1 when m = 1
8. The line y = 2·x - k is tangent to the curve x² + y² = 5, when k = ±5
Exercise 11.
1. The discriminant of the equation x² - 6·x + y² - 2·y + 2 = 0 is zero when y = x - 6, therefore the line x - y = 6 is tangent to the curve x² - 6·x + y² - 2·y + 2
2. The exact values of k for which the line 2·x + 3·y = k is tangent to the curve C = 4·x² + 9·y² = 36 is k = ±6·√2
What is the discriminant in a quadratic equation?The discriminant is the values which are within the radical sign of the quadratic formula.
7. At the point of tangency, the discriminant is 0
The equation is; x² + 2·x·y + 2·x = 1
The equation of the line is; y = m·x
Rewriting the equation of the curve, we get;
x² + 2·x·y + 2·x = 1
2·x·y = 1 - x² - 2·x
[tex]y = \dfrac{1 - x^2 - 2 \cdot x}{2\cdot x}[/tex]
At the point of tangency, we have;
[tex]y = \dfrac{1 - x^2 - 2 \cdot x}{2\cdot x} = m\cdot x[/tex]
1 - x² - 2·x - 2·m·x² = 0
1 - x² - 2·m·x² - 2·x = 0
1 - x²·(1 - 2·m) - 2·x = 0
The discriminant is zero at the point of tangency, which gives;
((-2²) - 4× (-(1 - 2·m)) × 1) = 0
8 - 8·m = 0
8 = 8·m
m = 8 ÷ 8 = 1
The value of m for which the line y = m·x is tangent to x² + 2·x·y + 2·x = 1 is m = 18. The line y = 2·x - k is tangent to the curve, x² + y² = 5 where we have;
y² = 5 - x²
y² = (2·x - k)²
5 - x² = (2·x - k)²
Which gives;
k² - 4·k·x + 5·x² - 5
5·x² - 4·k·x + k² - 5
At a tangent point the discriminant is therefore;
(-4·k)² - 4 × 5 × (k² - 5) = 100 - 4·k² = 0
100 - 4·k² = 0
4·k² = 100
k² = 100 ÷ 4 = 25
k = √(25) = ±5
The value of k is ± 5Exercise 11
1. The equation of the line is; x - y = 6
The equation of the curve is; x² - 6·x + y² - 2·y + 2 = 0
From the equation, x - y = 6, we get; y = x - 6
Which gives; x² - 6·x + (x - 6)² - 2·(x - 6) + 2 = 0
x² - 6·x + (x - 6)² - 2·(x - 6) + 2 = 2·x² - 20·x + 50 = 0
2·x² - 20·x + 50 = 0
x² - 10·x + 25 = 0
The discriminant is; (-10)² - 4 × 1 × 25 = 0
Therefore;
The number of points at which the line x - y = 6 intersects the curve is one point and the line x - y = 6 is therefore a tangent to the curve x² - 6·x + 2·y² - 2·y + 2 = 0,3. The curve 4·x² + 9·y² = 36 has the tangent line 2·x + 3·y = k, when we have;
4·x² + 9·y² = 36
9·y² = 36 - 4·x²
y² = (36 - 4·x²)/9 = 4 - (4/9)·x²
y² = 4 - (4/9)·x²
2·x + 3·y = k
3·y = k - 2·x
y = (k - 2·x)/3
y² = ((k - 2·x)/3)²
4 - (4/9)·x² = ((k - 2·x)/3)²
4 - (4/9)·x² - ((k - 2·x)/3)² = 0
8·x² - 4·k·x + k² - 36 = 0
(-4·k)² - 4 × 8 × (k² - 36) = 0
1152 - 16·k² = 0
16·k² = 1152
k² = 1152 ÷ 16 = 72
k = √(72) = ±6·√2
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A fair die is rolled two times. What is the probability that both rolls are 3?
A) 0.028
B) 0.083
C) 0.167
D) 0.0046
Answer:
b)
Step-by-step explanation:
this is so becuz a fair die contains or has six parts meaning if its rolled once there are 6 probabilities so if its rolled twice the probabilities increase the chances are (1,1),(1,2),(1,3)... to (1,6) there is only one probability that its(3,3) so giving u 1/12 which when divided hives u b)
a person earns $16,700 one year and gets a 5% raise in salary what is the new salary
Answer: $17, 535
[tex]\begin{gathered} \text{ 5\% raise means an increament on the salary} \\ 5\text{ + 100 = 105\%} \\ \text{The intital salary the person earned = \$16,700} \\ \text{The new salary = percentage increase x the initial salary} \\ \text{The new salary = 105\% x \$16, 700} \\ \text{new salary = }\frac{105}{100}\text{ x \$16, 700} \\ \text{New salary = 1.05 x 16, 700} \\ \text{New salary = \$17, 535} \end{gathered}[/tex]Find the scale factor of the line segment dilation. AB: endpoints (-6, -3) and (-3,-9) to A'B': endpoints at (-2, -1) and (-1, -3). A) -1/3 B) 1/3 C) 3D) -3
we know that the endpoints of AB are
[tex]\begin{gathered} (x_1,y_1)=\mleft(-6,-3\mright) \\ (x_2,y_2)=(-3,-9) \end{gathered}[/tex]and the distance formula is given by
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]By substituying these points, we have that
[tex]d=\sqrt[]{(-3-(-6))^2+(-9-(-3))^2}[/tex]which is equal to
[tex]\begin{gathered} d=\sqrt[]{(-3+6)^2+(-9+3)^2} \\ d=\sqrt[]{3^2+(-6)^2} \end{gathered}[/tex]then
[tex]\begin{gathered} d=\sqrt[]{9+36} \\ d=\sqrt[]{45} \\ d=\sqrt[]{9\cdot5} \\ d=\sqrt[]{9}\cdot\sqrt[]{5} \\ d=3\sqrt[]{5}\ldots..(A) \end{gathered}[/tex]On the other hand, if
[tex]\begin{gathered} (x_1,y_1)=(-2,-1) \\ (x_2,y_2)=(-1,-3) \end{gathered}[/tex]similarly to the previous case, the distance between the endpoint for A'B' is
[tex]d=\sqrt[]{(-1-(-2))^2+(-3-(-1))^2}[/tex]which is equal to
[tex]\begin{gathered} d=\sqrt[]{(-1+2)^2+(-3+1)^2} \\ d=\sqrt[]{1^2+(-2)^2} \\ d=\sqrt[]{1+4} \\ d=\sqrt[]{5}\ldots..(B) \end{gathered}[/tex]Now, by comparing equation A and equation B, we can see that, the scale factor is 1/3.
Then, the answer is B.
The function y=3.75+2.50(x-3) can be used to determine the cost of dollars for a uber ride of x of miles. What is the rate of change of the cost in dollars with respect to the number of miles?
function y = 3.75 + 2.5(x - 3)
dy/dx = 0 + 2.5 - 0
dy/dx = 2.5
The rate of change of the cost in dollars = 2.5
(Combining Equations)What is the result of adding these two equations ? 5x - y = 6 -2x + y = 8
Answer:
3x=14
Explanation:
Given the two equations:
[tex]\begin{gathered} 5x-y=6 \\ -2x+y=8 \end{gathered}[/tex]Adding the two equations gives:
[tex]\begin{gathered} \lbrack5x+(-2x)\rbrack+\lbrack-y+y\rbrack=6+8 \\ \lbrack5x-2x\rbrack+0=14 \\ 3x=14 \end{gathered}[/tex]Identify the number as prime Kompass it or neither if the number is comp is it rated as the product of prime factors 133
Given the number 133, we list the first prime numbers and then look for a possible factor of 133:
Prime_list = {2, 3, 5, 7, 11, ...}
133 is not an even number, so we discard 2. 133 does not end with 0 or 5, so 5 can not be a factor. We evaluate 3, 7, and 11:
The only division with no rest is 133/7 = 19, and we know that 7 and 19 are prime numbers. We conclude that 133 is composite and can be represented as a product of 7 and 19:
[tex]133=7\cdot19[/tex]The height of a building is proportional to the number of floors. The figure shows the height of a building with 7 floors. Complete parts a..
H=119 ft
A. Write the ratio of height of the building to the number of floors. Then, find the unit rate, and explain what it means in this situation. Fill in the correct answers to complete the sentences.
The ratio of height of the building to the number of floors is 119/7 and the unit ratio is 17 which means that the height of each floor is 17 ft.
In the given question,
The height of a building is proportional to the number of floors.
In the building have 7 floors.
That means, n = 7
the height of building H = 119 ft.
Since the height of a building is proportional to the number of floors.
So [tex]\frac{H}{n}=k[/tex] where k = constant.
Firstly we have to find the ratio of height of the building to the number of floors.
As we know, H = 119 ft, n = 7
So the ratio,
[tex]\frac{H}{n}=\frac{119}{7}[/tex]
The ratio of height of the building to the number of floors is 119/7.
Now we have to find the unit rate.
To find the unit rate we have to divide the height of building to the number of floors.
As we know,
[tex]\frac{H}{n}=\frac{119}{7}[/tex]
now simplifying the ratio by dividing the both number by 7
Unit ratio [tex]=\frac{H}{n}[/tex]
Unit ratio [tex]=\frac{119/7}{7/7}[/tex]
Unit ratio [tex]=\frac{17}{1}[/tex]
Unit ratio = 17
Hence, the unit ratio is 17 ft which means that the height of each floor is 17 ft.
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1. On a bookshelf containing 17 novels, 5 of them were written by Stephen King. If Sheri selects one at random, find the probability that she does not choose a Stephen King novel. Give your answer as a reduced fraction.
2. In a company there are 11 executives: six women and five men. Four are selected to attend a management seminar. Find the probability that one woman and three men are selected. Give your answer as a reduced fraction.
The probability that she does not choose a Stephen king novel is 12/17.
What is probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
Given,
1) total books no shelf = 17
Novel of Stephen king = 5
The probability of stephen king = 5/17
The probability of not choosing Stephen novel = 1-5/17
= (17-5)/17
=12/17
2) total number of executives = 11
Number of men = 5
Number of women = 6
probability of a man = 5/11
Probability of a woman = 6/11
Given, one woman and 3 men are selected
therefore, using combination.
Total combinations = n! / (r! x (n - r)!)
n = 4
r = 3
Therefore, probability = n! / (r! x (n - r)!)[tex](5/11)^{1} (6/11)^{3}[/tex]
=4!/3!(1!)(5/11)^{1} (6/11)^{3}
=4(5/11)(216/1331)
=4320/14641
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rewrite 3^15x3^-3/3^-5x3^7 as a single term of the form 3", where n is an integer.
Using the law of indices
[tex]\frac{3^{15-3}}{3^{-5+7}}[/tex]This can further be simplify into;
[tex]\frac{3^{12}}{3^2}[/tex][tex]=3^{12-2}[/tex][tex]=3^{10}[/tex]XB is the angle bisector of ZAXC. MZAXB23А.BVхC с
To obtain x, we can sum the angles < AQB and < BQC
=> 5X + 8X - 24
=> 13X -24
we are also told that that the sum of their angles is 80
13X - 24 = 80
13 X = 24 + 80
13X = 104
Divide both sides by 13
x = 104/13
x = 8
2. Each egg carton holds 12 eggs. The number of eggs is_______
to the number of egg cartons.
Each egg carton holds 12 eggs. The number of eggs is proportional to the number of egg cartons.
What does the word "proportional" mean?
In a proportionate relationship, two amounts fluctuate at the same rate, maintaining the consistency of their relationship.When two ratios are equal, they are said to be in proportion. The time it takes a train to travel 50 kilometers per hour, for instance, is equal to the time it needs to travel 250 kilometers over the course of five hours. e.g., 250km/5 hours at 50 km/h.Comparing the quantity of eggs and egg cartons is what we're attempting to do.
Since each carton contains 12 eggs, we can be certain that there will be 12 times as many eggs as there are cartons. Increases in egg production will follow increases in carton production, and vice versa.
Equal or having the same value are definitions of equivalent. Because 1/4, 2/8, and 0.25 all have the same value, they are all comparable. They are not equal because we only have 12 eggs in a carton.
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- 7 + 4x = - 15The answer
Evaluate the value of expression.
[tex]\begin{gathered} -7+4x=-15 \\ 4x=-15+7 \\ 4x=-8 \\ x=-\frac{8}{4} \\ =-2 \end{gathered}[/tex]Answer is - 2.
Answer: х=-8 gooood luck
Step-by-step explanation:
Find the total amount given the original price and tax rate. Round to the nearest hundredth if necessary.
Original price: $156.67
Tax rate: 6%
Answer:
166.07
Step-by-step explanation:
A manufacturing machine has a 3% defect rate.If 6 items are chosen at random, what is the probability that at least one will have a defect?
Given
defect rate = 3%
Number of items chosen at random = 6
Find
probability that at least one will have a defect
Explanation
Probability of defective items = 3% = 0.03
Probability of non defective items = 1 - 0.03 = 0.97
so ,
probability that at least one will have a defect = 1 - Probability of 0 defects
[tex]\begin{gathered} 1-^6C_0\times(0.03)^0(0.97)^6 \\ 1-(1\times1\times0.83297200492) \\ 1-0.83297200492 \\ 0.16702799508\approx0.167 \\ \end{gathered}[/tex]Final Answer
Hence , the probability that at least one will have a defect is 0.167(approx)
Titus drew circle with his Compass the circle has five central angles for the angles measure 55° 37 degrees 96 degrees and 88 degrees what is the degree measure of a central angle.
The measure of the unknown central angle is 84°.
We are given that Titus drew a circle with the compass. The circle has five central angles, which measure 55°, 37°, 96°, 88°, and one of the angles is unknown.
A circle is a shape formed by all points in a plane that are at a particular distance from the centre. It is the curve sketched out by a point moving in a plane so that its distance from a particular point remains constant.
We know that the measure of the complete angle is 360°. Thus, the sum of all the central angles must be equal to 360°. Let the measure of the unknown angle be "x". The equation is given below :
55° + 37° + 96° + 88° + x = 360°
276° + x = 360°
x = 84°
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if k is the midpoint of CT , CK =3x+23,and KT =5x+7,then find x and CT
Given:
CK = 3x + 23
KT = 5x + 7
If K is the midpoint of CT, then CK = KT. Then,
[tex]3x+23=5x+7[/tex]Finding x:
Subtracting 3x from both sides:
[tex]\begin{gathered} 3x+23-3x=5x+7-3x \\ 23=2x+7 \end{gathered}[/tex]Subtracting 7 from both sides:
[tex]\begin{gathered} 23-7=2x+7-7 \\ 16=2x \end{gathered}[/tex]And dividing both sides by 2:
[tex]\begin{gathered} \frac{16}{2}=\frac{2x}{2} \\ 8=x \end{gathered}[/tex]x = 8.
Finding CT:
K is the midpoint of CT, then CT = CK + KT
[tex]\begin{gathered} CT=3x+23+5x+7 \\ CT=3*8+23+5*8+7 \\ CT=24+23+40+7 \\ CT=94 \end{gathered}[/tex]CT = 94.
Answer:
x = 8
CT = 94
I need help!!!! Please I'm not good at this:(
The values of the numbers will be:
1. 162
2. 162
3. 1 99/100.
4. 11.4
5. 72
How to calculate the values?1. 6³ - 8² + 300 ÷ ( 5 + 5)²
It should be noted that this will follow the rules or PEDMAS. This implies that the parentheses will be solved first and that subtraction comes last.
6³ - 8² + 300 ÷ ( 5 + 5²)
= 216 - 64 + 300 ÷ 30
= 216 - 64 + 10
= 216 - 54
= 162
2. 6³ - 8² + 300 ÷ ( 5 + 5²)
= 216 - 64 + 300 ÷ 30
= 216 - 64 + 10
= 216 - 54
= 162
3. (1/5 + 1/2)² + 3/10 × 5
= (7/10)² + 3/10 × 5
= 49/100 + 1 1/2
= 1 99/100
4. 8.1 ÷ 0.9 + 0.4³ ÷ 0.8 × 30
= 9 + 0.064 ÷ 0.8 × 30
= 9 + 0.08 × 30
= 9 + 2.4
= 11.4
5. (18 - 4² + 2)² / (1 ÷ 4 1/2)
= 4² / 2/9
= 16 × 9/2
= 72
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Which statement BEST describes the effect on the value of y when the value of x isdoubled?
This is a linear function whose graph cuts the origin.
Therefore, any increase in the x axis will lead to a corresponding increase in the y axis by the same factor.
[tex]\begin{gathered} \text{The graph has the equation y =}\frac{x}{2} \\ If\text{ x is doubled, the corresponding value of y is also doubled} \end{gathered}[/tex]Thus, C is the answer
