What is the value of x?
The value of x =20 when the angles given are 3x° and (x+40)°.
Given that,
There a picture with 2 lines.
The angles given are 3x° and (x+40)°.
We have to find the x value.
We the alternative angles are equal in an intersecting angles.
Angles that are in opposition to a transversal connecting two lines are known as alternate angles.
x +40=3x
Taking 40 to right side.
x= 3x-40
Taking 3x to left side.
x-3x=-40
Subtracting x ad 3x
-2x=-40
Divide by -2.
x=20
Therefore, the value of x =20 when the angles given are 3x° and (x+40)°.
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what are the similarities between rate and ratio
A rate is a specific type of ratio. A rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit.
For example, in a bowl, there are 12 fruits: 8 oranges and 4 apples. This means the ratio of oranges to apples is 8:4.
If we simplify the ratio, we can see that the ratio of oranges to apples is 2:1, because:
[tex]\frac{8}{4}=\frac{4\cdot2}{4\cdot1}=\frac{2}{1}=\frac{2}{1}[/tex]Then, there are 2 oranges in the bowl for every apple.
On the other hand, suppose we want to distribute the fruits to 3 people. We can use a rate to find out how many fruits correspond to each person because we have 2 different units:
[tex]\begin{gathered} \frac{12\text{ fruits}}{3\text{ people}}=\frac{x}{1\text{ person}} \\ \text{ Apply cross product} \\ 12\text{ fruits}\cdot1\text{ person}=x\cdot3\text{ people} \\ \text{ Divide by 3 people from both sides} \\ \frac{12\text{ fruits}\cdot1\text{ person}}{3\text{ people}}=\frac{x\cdot3\text{ people}}{3\text{ people}} \\ \frac{12\text{ fruits}}{3}=x \\ 4\text{ fruits }=x \end{gathered}[/tex]Now, we know that each person corresponds to 4 fruits, in other words, the rate is 4 fruits/person.
Therefore, we can see the similarities between rate and ratio are:
• Both are a comparison of two numbers.
,• Both can be written as fractions.
,• Both reduce to the lowest form.
identify the rate, base and portion.17% of what number is 60?
For the given question which is;
17% of what number is 60?
We shall begin by determining the value of the number. Let us call the number a.
We can now set up the following equation;
[tex]\begin{gathered} 17\text{ \% of a}=60 \\ 0.17\times a=60 \end{gathered}[/tex]We now divide both sides by 0.17;
[tex]\begin{gathered} \frac{0.17a}{0.17}=\frac{60}{0.17} \\ a=352.9411 \\ \text{Rounded to the nearest whole number,} \\ a=353 \end{gathered}[/tex]So we now have;
"17% of 353 is 60."
The rate is the variable that represents part of the whole and that is 17
The base is the whole number itself which is a 100% value and that is 353
The portion is that part of the whole (base) made up of 17% and that is 60."
ANSWER:
Rate is 17%
Base is 353
Portion is 60
Question 8 of 10Which of these is a geometric sequence?O A. 2, 3, 5, 9, 17,...O B. 5, 2, 3, 4, ...O C. 2, 4, 6, 8, 10, ...
We have that in a geometric sequence, the common ratio are equal in geometric sequence, this is:
[tex]\frac{second\text{ term}}{first\text{ term}}=\frac{third\text{ term}}{second\text{ term}}[/tex]Next, check options:
A. 2, 3, 5, 9, 17
Common ratio
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What is the conversion factor?
It is a number used to change one unit to another when it is multiplied.
Jenna wants to know how many pounds correspond to 50 tons, she does know that 1 ton = 2,000lb. Then she has the following equivalence:
50 tons ⇄ ??
1 ton ⇄ 2,000 lb
We know that if we divide both sides of the equivalence we will have the same result:
[tex]\frac{50\text{tons}}{1\text{ton}}=\frac{?\text{?}}{2000lb}[/tex]Multiplying both sides by 2000lb we have that
[tex]undefined[/tex]the radius of a circle is 9 feet. what is the diameter? give the exact answer in simplest form.
The diameter of a circle equals twice the radius of that circle.
Then:
[tex]\begin{gathered} D=2\times r \\ =2\times9ft \\ =18ft \end{gathered}[/tex]Therefore, the diameter of the circle is:
[tex]18\text{ feet}[/tex]Answer:
18 feetStep-by-step explanation:
The radius is always 2 times the diameter. Since the radius is [tex]9 ~feet[/tex], the diameter is [tex]9\cdot2=\boxed{18}~feet[/tex]
From the waiting area, they walked another 0.1 miles to board the plane. The plane left the gate 45 min after they arrived at the waiting area. Part C: what was the length from the waiting area to the airplanes takeoff?
C) We have to calculate the distance from the waiting area to the plane.
From the waiting area they walked 0.1 miles to board the plane.
Answer: from the waiting area to the plane there is a distance of 0.1 miles.
If ∠2 = 50° and lines a and b are parallel, which of the following angles cannot be determined? *-∠1-∠3-∠4-∠8-None of the above
If you have the angle 2, you can deduce its the supplement,which is the angle 4. In this case the supplement is equal to 130°.
Angle 2 and angle 6 are corresponding angles, so they have the same measure.
Angle 4 and angle 8 are corresponding, so they have the same measure.
Angle 2 and angle 1 are vertically opposite angles, so they have the same measure.
Angle 5 and angle 6 are vertically opposite angles, so they have the same measure.
Angle 7 and angle 8 are vertically opposite angles, so they have the same measure.
Angle 4 and angle 3 are vertically opposite angles, so they have the same measure.
Therefore the answer is None of the above.
what is the quotient of {24a^4 b^2 + 36a^2 b-36ab^2 +48 ab}÷(12ab)?
To divide this polynomial, we will follow steps below:
Step 1
Arrange
step 2
Divide 24a⁴b² by by 12ab
The result will be 2a³b
Write the result at the top of the root sign
Step 3
Mutiply 12ab by 2a³b, the result will be 24a⁴b²
Write the result in the root sign under 24a⁴b²
step 4
subtract, the result is zero
step 5
Take down 36a²b
Step 6
divide 36a²b by 12ab
The result is 3a
write the result at the top of the root sign
step 7
Multiply 12ab by 3a
The result is 36a²b
Write the result in the root sign under 36a²b
Step8
subtract, the result is 0
step 9
Take down -36ab²
step10
Divide -36ab² by 12ab
The result is -3b
Write the result at the top of the root sign
step11
Multiply 12ab by -3b
The result is -36ab²
Write the result in the root sign under -36ab²
step12
subtract, the result is zero
step 13
Take down 48ab
step 14
divide 48ab by 12 ab
The result is 4
write the result at the top root sign
step 15
Mulltiply 12ab by 4
The result is 48ab
Write the result in the root sign under 48 ab and then subtract
The result is zero
Hence the quotient is : 2a³b + 3a -3b + 4
Please help me solve the following problem:A conic kettle has a cover which height is 30% of its total height. The height is 2 cm less than the diameter of the base, which has an area of 380 squared cm. Which is the volume capacity of the kettle?
If a conical kettles has a solid cover whose volume is 30% of the total volume, and it's height is 2 cm less than the radius of it's base, which has an area of 380cm², then the volume of the kettle is 798.6cm³.
As per the question statement, a conical kettles has a cover whose volume is 30% of the total volume, and it's height is 2 cm less than the radius of it's base, which has an area of 380cm²,
And we are required to calculate the volume capacity of the kettle.
To solve this question, first we need to know the formula to calculate the volume of a cone, which goes as, [Volume (V) = {π * r² * (h/3)}],
Where, "r" is the radius of the base of the cone,
And, "h" is the height of the cone.
Now, the height of our concerned cone is 2 cm less than the radius of it's base, and the area of the base is 380cm². Assuming that the height of the cone be "h" and the radius of it's base be "r", we get that,
[r = (h - 2)]...(i)
And, [(π * r²) = 380]
Or, [{(22/7) * r²} = 380]
Or, [(r²) = {(380 * 7)/22]
Or, [(r²) = 120.9090]
Or, (r = √120.91)
Or, (r = 10.9959)
Or, (r ≈ 11 cm)
Therefore, using the value for "r" in equation (i), we will get,
[h = (11 - 2)cm = 9cm]
And finally substituting these values of "h" and "r" in the above mentioned formula to calculate the volume of a cone,, we get,
[V = {π * (11)² * (9/3)}]
Or, [V = {(22/7) * 121 * 3}]
Or, [V = (7986/7)]
Or, (V = 1140.85714 cm³)
Or, (V ≈ 1140.86 cm³)
Since the cover of the kettle occupies 30% of the volume of the total structure of the conical kettle with it's cover, the volume capacity of the kettle is [(100 - 30)% = 70%] of the volume of the total structure of the conical kettle with it's cover, that is,
[1140.86 * (70/100)]cm³ = (1140.86 * 0.7)cm³ = 798.6cm³
Volume: The volume of any object is the three-dimensional space, occupied by the existence of that very object.To learn more about Volumes of Cones, click on the link below.
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Two dice are rolled. What is the probability that the sum of the numbers rolled is either 3 and 8? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest million
The two dice have 6 numbers each.
Look at the image to find the outcomes:
First, we need to find the total of outcomes with the sum of 3:
T. outcomes with the sum of 3 = 2
Now, find the total of outcomes with the sum of 8 = 5
When we ave in probability the expression "or" we add the probabilities:
In this case,
T. outcomes with the sum of 3 + T. outcomes with the sum of 8.
Replace the values and sum:
P = 2 +5
P = 7
Now, to find the probability divide it by the total of outcomes
Total outcomes= 36. because 6 * 6 = 36
P( sum being 3 or 8) = 7/36
Find 3 ratios that are equivalent to the given ratio. 3 6 Find 3 ratios that are equivalent to the given ratio. g B. 18 9 DA. 24 6 D. 18 C. 6 24 1 F. 2 12 O E. 18 OH. 6 12 g G. 12
Which transformations can be used to carry ABCD ontoitself? The point of rotation is (3, 2). Check all that apply.yB1 23 4 5 6A. Translation four units to the rightB. Dilation by a factor of 2C. Rotation of 180°D. Reflection across the line x = 3
C. Rotation of 180°
D. Reflection across the line x = 3
Explanation:The point of rotation = (3, 2)
From the diagram:
The center of the rectangle = (3, 2)
Note that:
The point of rotation = The center of the rectangle
Therefore, the rectangle ABCD will be reflected across its center, x =3 and y = 2
Also note that ABCD has two lines of symmetry. Therefore, a rotation by 180 degrees will carry ABCD back to itself
Solve for y and show steps 75-3.5y-4y=4y+6
Solve for y;
[tex]\begin{gathered} 75-3.5y-4y=4y+6 \\ \text{Collect like terms, which means the values with y would be moved to one side} \\ \text{And the values without y would be moved to the other side} \\ 75-6=4y+4y+3.5y \\ \text{Note that when a positive value moves to the other side of the equation} \\ It\text{ becomes a negative value, and vice versa} \\ 69=11.5y \\ \text{Divide both sides by 11.5} \\ \frac{69}{11.5}=\frac{11.5y}{11.5} \\ 6=y \end{gathered}[/tex]The answer is y equals 6
question 13Consider the following data: 12, 15, 13, 10, 15, 10. Answer the following questicwrite final answers only. [T/I - 4]#1) What is the mean of the data?#2) What is the median of the data?#3) What is the mode of the data?#4) What is the range of the data?
Solution:
Given:
The data;
[tex]12,15,13,10,15,10[/tex]Question 1:
To get the mean:
The mean of a set of numbers, sometimes simply called the average, is the sum of the data divided by the total number of data.
[tex]\begin{gathered} \text{Mean}=\frac{\text{ sum of data}}{n\text{ umber of data}} \\ \text{Mean}=\frac{12+15+13+10+15+10}{6} \\ \text{Mean}=\frac{75}{6} \\ \text{Mean}=12.5 \end{gathered}[/tex]Therefore, the mean is 12.5
Question 2:
To get the median:
The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest)
If there is an even number of data, the median is the average of the middle two numbers.
[tex]\begin{gathered} R\text{ earranging the data given in rank order,} \\ 10,10,12,13,15,15 \end{gathered}[/tex]
The data indicates an even number of data. There are 6 numbers in the set.
Hence, the median is the mean of the middle two numbers.
[tex]\begin{gathered} \text{The middle two numbers are;} \\ 12\text{ and 13} \\ \text{Hence, the median is the mean of 12 and 13} \\ \text{Median}=\frac{12+13}{2} \\ \text{Median}=\frac{25}{2} \\ \text{Median}=12.5 \end{gathered}[/tex]Therefore, the median is 12.5
Question 3:
To find the mode:
The mode of a set of numbers is the number that occurs the most. Hence, the mode of a set of numbers is the number with the highest frequency.
If a set of data has two modes, the data is said to be bimodal.
[tex]\begin{gathered} 10,10,12,13,15,15 \\ \\ \text{From the above, 10 appears twice} \\ 15\text{ also appears twice} \\ \\ \text{Hence, the mode is 10 and 15. The data has two modes, it is a bimodal data.} \end{gathered}[/tex]
Therefore, the modes are 10 and 15.
Question 4:
The range is the difference between the highest and lowest values in a set of numbers.
[tex]\begin{gathered} 10,10,12,13,15,15 \\ \text{Lowest number=10} \\ \text{Highest number=15} \\ \\ \text{Hence, range=highest number-lowest number} \\ \text{Range}=15-10 \\ \text{Range}=5 \end{gathered}[/tex]Therefore, the range is 5.
Vance bought 2 packages of large beads
and 1 package of medium beads. He
bought 2 packages of large buttons and 2
packages of medium buttons. How many
more beads than buttons did Vance buy?.
The no. of more buttons than beads that Vance bought is 1 (medium package)
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
How to solve algebraic expressions?A General Rule for Equation Solving
B Remove parenthesis from either side of the equation and combine similar phrases to make it simpler.
C To separate the variable term on one side of the equation, use addition or subtraction.
D To find the variable, use division or multiplication.
Given:- The no: of package of large beads is 2
The no: of the package of medium beads is 1
The no: of the package of large buttons is 2
The no: of the package of medium buttons is 2
Hence large packages
2(buttons)-2(beads)=0
For medium packages
2(buttons)-1(beads)=0
therefore, the no of more buttons than beads is 1 medium package
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If Martha is x years old and her mother is 5 times older and the sum of their age is 88, how old is Martha?
Let Martha age = x years old
Since her mother's age is 5 times her age, then
Her mother = 5(x) = 5x years old
Since the sum of their ages is 84, then
Add x and 5x, then equate the sum by 84
[tex]\begin{gathered} x+5x=84 \\ 6x=84 \end{gathered}[/tex]Divide both sides by 6 to find x
[tex]\begin{gathered} \frac{6x}{6}=\frac{84}{6} \\ x=14 \end{gathered}[/tex]Martha is 14 years old
Can you please help me with this question thank youu.The first one.
Given that:
- Tara has 18 pairs of white socks.
- She has 12 pairs of colored socks.
You can state the proportion of those types of socks using ratios.
By definition, a ratio can be written in this form:
[tex]a\colon b[/tex]And it is read "a to b".
In this case, you need to find the ratio of white socks to colored socks, then you have to set up this ratio:
[tex]18\colon12[/tex]You can simplify the ratio dividing both sides by 6:
[tex]\begin{gathered} 18\div6\colon12\div6 \\ \\ 3\colon2 \end{gathered}[/tex]Hence, the answer is: Option B.
The Quadratic f(x)=x^2-2x-15Using the functions of your graphing calculator calculate the coordinates of the following points (as shown in the calculator videos in this lesson). If the parabola doesn't intersect the x-axis then write "none." If necessary, round to the nearest hundredths place (2 decimal places).a. The vertex using the min/max calculate function.b. X-intercept(s) using the zero calculate function.c. Y-intercept using the value calculate function (w/ a value of x=0).d. Now, copy down the t-table generated by your calculator for integer input values from-3≤x≤3.
Given: The function below
[tex]f(x)=x^2-2x-15[/tex]To Determine: The vertex, the x-intercept, the y-intercept, and the table for -3≤x≤3
Solution
The graph of the given function is as shown below
Hence:
The vertex is a minimum value at y = -16 and coordinate (1, -16)
(b) The X-intercepets is x = -3, x = 5, coordinates: (-3, 0) and (5, 0)
(c) The Y-intercept is at y = -15, coordinate: (0, - 15)
(d) The table showing the values of f(x) for -3≤x≤3 is as shown below
x-2Question 8 of 15Use the remainder theorem to find P (2) for P (x)=xª − 3x³ +x−9.-(2,01 mismoSpecifically, give the quotient and the remainder for the associated division and the value of P (2)_Quotient =RemainderP (2)=
8)
The remainder theorem states that when a polynomial P(x) is divided by a linear polynomial x-b, the remainder is given by r=P(b).
Thus, in our case,
[tex]P(2)=2^4-3(2)^3+2-9=16-24+2-9=-15[/tex]Then, the Remainder theorem states that if we divide P(x) by x-2, the remainder will be -15.Calculating the quotient of P(x)/(x-2),
Hence, the answers are[tex]\begin{gathered} Q(x)=x^3-x^2-2x-3 \\ Remainder=-15 \\ P(2)=-15 \end{gathered}[/tex]How many red squares will there be if there are 60 squares?
• There are 3 red squares.
,• There are 4 white squares.
To compare them and get the ratio, we can build the following relation:
[tex]\frac{3}{4}=\frac{x}{60}[/tex]where x is the number of red squares it will be when there are 60 white squares.
Solving for x:
[tex]x=\frac{3}{4}\cdot60[/tex][tex]x=45[/tex]Answer: C. 45
What number is 75% of 96?
Answer
The number is 72
Explanation
75% of 96 is
[tex]\begin{gathered} =\frac{75}{100}\times\frac{96}{1} \\ =\frac{7200}{100} \\ =72 \end{gathered}[/tex]Please Help! Functions and Relations The graph shows the absolute value parent function. which statement best describes the function?
The function is increasing when, if xa > xb, then f(xa) > f(b).
Let's choose values for x < 0 and for x > 0.
First, let's compare x = -2 and x = -1
-1 > -2
f(-1) < f(-2)
Then, the function is decreasing for x < 0.
Second, let's compare x = 1 and x = 2.
2 > 1
f(2) > f(1)
Then, the function is increasing for x > 0.
Answer: c. The function is increasing when x >0.
Find the area of the triangle below. Be sure to include the correct unit in your answer. bu
The area of the triangle = 0.5 x base x height
For the given triangle:
Base = 25 ft
The corresponding height to the base = 7 ft
So, the area =
[tex]0.5\cdot25\cdot7=87.5[/tex]So, the area of the triangle = 87.5 ft^2
[tex](3x^{2} -x+1)-(6x^{2} -x+2)[/tex]
Answer:
−3x2−1
Step-by-step explanation:
−3x2−1 Is the answer to this equatiom
Find the circumference and area of the circle. Express answers in terms of and then round to the nearest tenth. Find the circumference in terms of . C = _
Solution:
Given the circle with its radius, r;
[tex]r=11cm[/tex]Thus, the circumference, C, of a circle is;
[tex]C=2\pi r[/tex]Then;
[tex]\begin{gathered} C=2\pi(11)cm \\ \\ C=22\pi cm \end{gathered}[/tex]ANSWER:
[tex]C=22.0\pi cm[/tex]Also, the area, A, of the circle is;
[tex]A=\pi r^2[/tex]Then;
[tex]\begin{gathered} A=\pi(11)^2 \\ \\ A=121\pi cm^2 \end{gathered}[/tex]ANSWER:
[tex]A=121.0\pi cm^2[/tex]Katie rents a car when spending her vacation in Argentina while she returns the car she has driven 900 miles and used about 36 gallons of gas if you guess cost an average of $4.139 Per gallon estimate how much she spent on fuel
Given that Katie had driven 900 miles and used about 36 gallons of gas.
The average cost of gas per gallon = $4.139
The amount she spent on gas would be:
[tex]\text{ The average cost of gas per gallon x gallons of gas used}[/tex]Hence, the amount Katie spent on gas would be:
[tex]\begin{gathered} \text{ }\frac{\text{\$4.139}}{\text{gallon}}\times\text{ 36 gallons} \\ =\text{ \$149.004} \end{gathered}[/tex]She spent $149.004
Can you pls help me with this question thank you
The Solution:
The difference of c and 7 is either:
[tex]\begin{gathered} c-7\text{ } \\ \text{ or} \\ 7-c \end{gathered}[/tex]Multiplying the result by 10, we get
[tex]\begin{gathered} 10(c-7) \\ \text{ or} \\ 10(7-c) \end{gathered}[/tex]We are asked not to simplify any part of the expression.
So, the correct answer is:
[tex]\begin{gathered} 10(c-7) \\ or \\ 10(7-c) \end{gathered}[/tex]
X = y - 4-2x + 3y= 6Solve each system by equation
Answer: x=-6 and y=-2
Given:
[tex]\begin{gathered} x=y-4 \\ -2x+3y=6 \end{gathered}[/tex]Having these two equations, we can substitute the first equation with the second equation to solve for y:
[tex]\begin{gathered} -2x+3y=6 \\ \end{gathered}[/tex]Since the first equation says that x = y - 4,
[tex]\begin{gathered} -2x+3y=6 \\ -2(y-4)+3y=6 \\ -2y+8+3y=6 \\ -2y+3y=6-8 \\ y=-2 \end{gathered}[/tex]Then, we will substitute this y-value to the first equation to solve for x.
[tex]\begin{gathered} x=y-4 \\ x=-2-4 \\ x=-6 \end{gathered}[/tex]We now have the values x=-6 and y=-2. To check, let us substitute both values to the second equation
[tex]\begin{gathered} -2x+3y=6 \\ -2(-6)+3(-2)=6 \\ 12-6=6 \\ 6=6 \end{gathered}[/tex]Therefore, the answer is correct, and the answer is x=-6 and y=-2
The slope of the line below is 2 Write the point-slope equation of the line using the coordinates of the labeled point.
As per given by the question,
there are given that,
The slope of the line is 2, and the point is (3, 10).
Now,
For finding the point slope equation;
From the formula for point slope equation of the line,
[tex]y-y_1=m(x-x_1)[/tex]Here,
[tex]x_1=3,y_1=10,\text{ and m=2}[/tex]Then put the value in above formula,
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