The key feature is that; The left side continues down, and the right side continues up.
How to describe the behavior of a Polynomial?We are given the polynomial;
Polynomial function;
f(x) = 2x³ + 5x² - 2x - 3
Leading coefficient = 2
Degree of the polynomial = 3
Since, degree of the polynomial given is odd and the leading coefficient is positive.
Therefore, left side of the graph will continue down and the right side continues up.
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The table to the right lists probabilities for the corresponding numbers of girls in three births. What is the random variable, what are its possible values, and are its values numerical?
The true statement is (b) the random variable is x, the possible values are 0 to 3 and the values are numerical
How to determine the true statement?The table is added as an attachment
From the attached image, we have:
Number of girls (x) P(x)
0 0.125
1 0.375
2 0.375
3 0.125
In the above, the random variable is x, while P(x) represents its probabilities.
Also, the possible values are 0 to 3 as shown in the table.
0 to 3 are numerical digits, and the values are numerical
Hence, the true statement is (b)
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Step 3: So, M 12= 60 Degrees
Use the drop-down menus to explain whether or not Stuart is corrrect.
The reasoning that may be used for finding the measure of m∠12, is the
same side interior angles theorem.
The correct options using the drop-down menu are;
The sum of ∠1, ∠7, and ∠8 is 180°
∠8 and ∠12 are the same side interior angles
The measure of ∠12 must be = 120°
Stuart is not correct
The complete question is given below:-
In the diagram, line x is parallel to line y,m21= 65°, and m27 = 55°. Stuart says that m212 = 60°. His reasoning is shown. Step 1: mZ8 = 60°, because m21+ m27 +m28 = 180º. Step 2:28 212, because 28 and 212 are corresponding angles. Step 3: So, mZ12 = 60° Use the drop-down menus to explain whether or not Stuart is correct.
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Given parameters;
Line x ║ line y
m∠1 = 65°, m∠7 = 55°
m∠12 = 60°
Stuart states ∠12 = 60°
The reasoning is presented as follows;
Step 1: m∠8 = 60°, because m∠1 + m∠7 + m∠8 = 180°
Step 2: ∠8 ≅ ∠12, because ∠8 and ∠12 are corresponding angles
Step 3: So, m∠12 = 60°
Using the drop-down menu, we have;
The sum of ∠1, ∠7, and ∠8 is 180° (Sum of angles in the triangle)
∠8 and ∠12 are same side interior angles (by definition)
Same side interior angles are supplementary, therefore;
∠8 +∠12 = 180°
∠12 = 180° - ∠8
Which gives;
The measure of ∠12 must be 180° - ∠8 = 180° - 60° = 120°
The measure of ∠12 must be = 120°
Stuart is not correct
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The directrix and focus of a parabola are shown on the graph. Which is an equation for the parabola?
i would appreciate your help
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[tex]\text{\textbf{Hello!} In this question, we are trying to figure out the \underline{equation} of the line}\\\text{with the given information.}[/tex]
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[tex]\textbf{Explanation:}\\\quad{}\\\text{In the question, we were given our \emph{slope} (gradient) and a \emph{point}. This will help}\\\text{us solve our problem.}\quad{}\\\\\text{Slope: 2 }\\\\\text{Point: (1, 4)}\\\quad{}\\\text{In order to find the equation, we will be using the \underline{point-slope formula:}}\\\quad{}\\y - y1 = m(x - x1)\\\quad{}\\\text{With this equation, we would plug in our given values to its}\\\text{correct variable and solve.}[/tex]
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[tex]\textbf{Solve:}\\\\\text{Use the point-slope formula to solve.}\\\\y - y1 = m(x - x1)\quad{}\\\\\text{Plug in 2 to m, 1 to x1, 4 to y1 and then solve.}\\\\y - 4 = 2(x - 1)\\\\\text{Use the \underline{distributive property} to distribute the 2.}\\\\y - 4 = 2x - 2\\\\\text{Add 4 to both sides to cancel the 4 on the left and move the remainder}\\\text{to the right side of the equal sign.}\\\\y = 2x + 2\\\\\text{Since we can't simplify any further, our answer is: \fbox{y = 2x + 2}}[/tex]
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[tex]\textbf{Answer:}\\\\\text{Therefore, the equation of the line (our final answer) would be \fbox{y = 2x + 2}}[/tex]
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Draw a graph of y=3x-2. Using a scale of 2cm to 5units on both axes for values from x -2 to +2
What is the x-intercept
What is the y- intercept
Find the value of x when y= 5
Find the value of y when x= 0.5
pls pls ASAP
Function: y = 3x - 2
To find x-intercept, set [y = 0]:
[tex]\rightarrow \sf 3x - 2 = 0[/tex]
[tex]\rightarrow \sf 3x = 2[/tex]
[tex]\rightarrow \sf x = \dfrac{2}{3}[/tex]
The x-intercept: (2/3, 0)
To find y-intercept, set [x = 0]
[tex]\rightarrow \sf y = 3(0) - 2[/tex]
[tex]\rightarrow \sf y = - 2[/tex]
The y-intercept: (0, -2)
When [y = 5], x is:
[tex]\rightarrow \sf 3x - 2 = 5[/tex]
[tex]\rightarrow \sf 3x = 5 + 2[/tex]
[tex]\rightarrow \sf 3x = 7[/tex]
[tex]\rightarrow \sf x = \dfrac{7}{3}[/tex]
[tex]\rightarrow \sf x = 2 \dfrac{1}{3}[/tex]
Value of x is 2.33...
When [x = 0.5], y is
[tex]\rightarrow \sf y =3(0.5) - 2[/tex]
[tex]\rightarrow \sf y =-0.5[/tex]
Value of y is -0.5
Graph shown:
find the area of quadrilateral
Answer:
here is answer try this type
One possible integer of x for which 1/4 < k/10 < 1/3 is true?
Answer:
[tex]\fbox {x = 3}[/tex]
Step-by-step explanation:
Decimal form of the lower and higher limits :
1/4 = 0.251/3 = 0.33...Hence, the best one which lies in the middle of the limits would be 0.3.
Now, equate the middle part :
x/10 = 0.3x = 3The Pine Scrub Rail Trail is 126 miles long. If the Willy-Nilly Bike Club rides 18 miles per day, how many days will it take them to ride from one end of the trail to the other?
A. 6 days
B. 9 days
C. 7 days
D. 8 days
PLS HELP
Select the correct answer.
Consider function f.
f(x) = 2x²
What is the value of (f of)(x)?
A.
B.
OC.
D.
8x4
16x4
4x4
4x²
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} [/tex]
[tex] \: [/tex]
[tex] = (f \circ f)(x)[/tex]
[tex] = f(f(x))[/tex]
[tex] = 2 {x}^{2} [/tex]
[tex] = 2 {(2 {x}^{2} )}^{2} [/tex]
[tex] = 2( {2}^{2} {x}^{2 + 2} )[/tex]
[tex] = 2(4 {x}^{4} )[/tex]
[tex] = 8 {x}^{4} [/tex]
The answer is A.
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 37 hours and the median is 33.2 hours. Twenty-four of the families in the sample turned on the television for 22 hours or less for the week. The 10th percentile of the data is 22 hours. Based on the given information, determine if the following statement is true or false. Approximately 120 families turned on their televisions for less than 37 hours.
The statement; Approximately 120 families turned on their televisions for less than 37 hours is true.
What is true about the data?From the task content, since the 10% percentile of the data corresponds to 24 families, it.follws that the total number of families sampled is; 24 × 10 = 240 families.
On this note, after the first 120 data points, the median is determined to be 33.2 hours which is less than the mean. Conclusively, it follows that approximately 120 families turned on their televisions for less than 37 hours.
Hence, the statement is true.
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what is the solution to square root 5x+3= 3 square root x?
A.3/4
B. 3/2
C.-3/4
D.-3/2
Answer:
A. 3/4
Step-by-step explanation:
1. Square both sides:
5x + 3 = 9x
2. Subtract 5x from both sides:
3 = 4x
3. Divide 4 from both sides:
3/4 = x
Answer: A
Answer:
3/4
Step-by-step explanation:
it's correct
What is the area of the trapezoid? If necessary, round your answer to the nearest tenth.
A trapezoid with bottom side length of 8.5 feet, top side length of 5.5 feet, and height of 6.5 feet.
35.8 feet squared
45.5 feet squared
46.8 feet squared
The area of the trapezoid is calculated as 45.5 feet squared.
What does Area of Trapezoid mean?
The entire area occupied by the sides of a trapezoid is its area. It's important to notice that if we know the lengths of all the sides, we can divide the trapezoid into smaller polygons, such as triangles and rectangles, calculate their areas, and then sum them all together to determine the area of the trapezoid.
The formula for Trapezoid Area:If the parallel sides of the trapezoid are known, along with their height, it is possible to determine their area. It is expressed as,
A=[tex]1/2[/tex](a+b) h
where, A= the area of the trapezoid
h= height
'a' & 'b' = parallel side bases
Solution:a=5.5 feet , b= 8.5 feet & h=6.5 feet
A=[tex]1/2[/tex](a+b)h
∴A=[tex]1/2[/tex](5.5+8.5)*6.5
⇒A=[tex]1/2[/tex](14)*6.5
⇒A=7*6.5
⇒A=45.5 feet squared
Therefore, the solution is (b) 45.5 feet squared.
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Find one-third of the sum 9 and 12.
Answer:
7
Step-by-step explanation:
9 plues 12 = 21
21 divide by 3
= 7
Answer:
7
Step-by-step explanation:
9 + 12 = 21
one third of 21 is the same as 21 divided by 3
so 21 divided by 3
= 7
so 7 is the answer
OR
9 divided by 3 = 3
12 divided by 3 = 4
3 + 4 = 7
Given that y varies directly as x², find the percentage increase in y when x doubles.
Answer:400%
Step-by-step explanation: by the commutativity of multiplication we find (2x)^2=4(x^2)=4(y)
What is the slope of the line thatpasses through these two points?(2,3)(2,9)
Answer:
The slope is undefined
Step-by-step explanation:
[tex]m=\frac{9-3}{2-2}[/tex]
The denominator leads to 0 so it would not be possible to find the answer
Answer:
undefined
Step-by-step explanation:
anything divided by zero is undefined since you cant logically give (for example) 2 apples to 0 people.
For slopes not so obvious, the formula is (slope)m= (rise)y/(run)x
(a) By what least number must 27 be divided to make it perfect square
Answer:
3
Step-by-step explanation:
When you divide 27 by 3 it will give you 9 and the square root of 9 gives you a perfect answer indicating that 3 is the least number that must be divided into 27
Answer:
[tex]\fbox {3}[/tex]
Step-by-step explanation:
First, prime factorize 27 :
⇒ 27 = 3 × 3 × 3
If 27 was divided by 3, it would give 3 × 3, which would give 9, a perfect square.
∠C, ∠F are rt. ∠'s; AB = DE; BC = EF
What is 5,435,778 expressed in scientific notation? A. 5.435778 x 10 B. 5.435778 x 10 C. 5.435778 x 10 D. 5.435778 x 10
Answer:
The answer options seem to be missing their exponents for the 10 unit.
Answer is: 5.435778 x [tex]10^{6}[/tex]
Step-by-step explanation:
5,435,778
Move the decimal point to the left until it is between the 5 and 4. Scientific notation means rewriting the number with only one digit to the left of the decimal point and adding the "x [tex]10^{x}[/tex] after to account for the number of positions the decimal point was moved.
Count the number of places required for the move.
5,435,778 0
543577.8 1
54357.78 2
5435.778 3
543.5778 4
54.35778 5
5.435778 6
Each move reduces the number by a factor of 10. This means that the final move to make the number 5.435778 required dividing the original number by 10 a total of 6 times. By multiplying this last number by 10 a total of 6 times, we obtain the original number.
We could write this as: (5.435778)*(10)*(10)*(10)*(10)*(10)*(10)
but that defeats the purpose of scientific notation, which is to simplify the number so that it is 1) easier to read, 2) saves printers paper and ink, and 3) reduces transcription errors.
So scientific notation is the process of writing this as:
5.435778 x [tex]10^{6}[/tex]
Brian ordered 3 large cheese pizzas and a salad. The salad cost $4.95. If he spent a total of $47.60 including the $5 tip, how much did each pizza cost? (Considering there's no tax) Please I really need help
Answer:
Each pizza was $12.55.
Step-by-step explanation:
et's take it piece by piece.
Salad and the tip together is 4.95 + 5 = 9.95, right?
47.60 - 9.95 = 37.65 spent on pizza
37.65/3 = 12.55
Raphael is ordering a scoop of ice cream. For the flavor, he is given the option of chocolate, strawberry, vanilla, cookies ‘n cream, or peanut butter. For the size, he is given the option of small, medium, or large. For the cone, he is given the option of a sugar cone, waffle cone, or cup. How many possible order combinations are there?
Answer: 165
Step-by-step explanation: If you calculate the 3 different choices and the total of 11 different objects, you get 165 total combinations.
Answer:
45 possible combinations
Step-by-step explanation:
since there are 5 options of flavour (chocolate, strawberry, vanilla, cookies 'n' cream, and peanut butter) then you must multiply your flavours by your next option.
the size options come in 3 options (small, medium, and large) therefore we multiply the flavours (5) by sizes (3)
5 * 3 = 15
then multiply the result (15) by the cup options (3)
15 * 3 = 45
your answer is 45
hope this helps:)
In the diagram below, Θ is measured in radians. Which equation represents the relationship between the radius, r, and arc length, s?
Circle O is shown. Line segments A O and B O are radii with length r. Angle A O B has a measure of theta. Arc A B has a measure of s.
s = Θ · r
r = Θ · s
s = Θ + r
r = Θ + s
The equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r
How to determine the arc length?See attachment for the complete question
From the complete question, we have:
Θ represents the central angler represents the circle radiusThe angle is given in radians.
So, the arc length is calculated using
Arc length = Angle * Radius
Substitute known values
s = Θ * r
Hence, the equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r
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Answer:
A
Step-by-step explanation:
On Edge
how many eggs are in 2 3/4 dozen?
please answer this one...i need it today
Step-by-step explanation:
please mark me as brainlest
Answer:
33 eggs
Step-by-step explanation:
1 Dozen = 12 units
2 dozen = 2*12 = 24 units
3/4 dozen = 12*3/4 = 36/4 = 9 units
2 3/4 = 2 + 3/4 = 24 + 9 = 33 units
What type of association does the following scatterplot represent?
Answer:
Positive Linear Association
Step-by-step explanation:
A positive/negative association can be determined by seeing if the slope of the line of best fit is positive or negative. A positive slope indicates a positive relationship and a negative slope indicates a negative relationship.
If y increases as x increases => positive
If y decreases as x increases => negative
In the graph, the line of best fit clearly has a positive slope. I.e. as x increases, y also increases. Therefore, the association is positive.
Next determine if the relationship is linear or nonlinear. A linear relationship can be modeled strongly with a straight line. Anything else is nonlinear. In the graph, a straight line can be draw through the points with a strong correlation, therefore the association is linear.
Therefore, the best answer is Positive Linear Assosciation
Guys, can you please help me write an expression for shaded circle and please expand and simplify for me, guys, please? :)
Answer:
[tex]\sf Shaded \: Area=14 \pi r+49 \pi[/tex]
Step-by-step explanation:
Area of a circle
[tex]\sf A=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
To find the area of the shaded area, subtract the area of the unshaded circle from the larger circle.
Area of the larger circle
[tex]\implies \sf A=\pi (r+7)^2[/tex]
Area of the smaller (unshaded) circle
[tex]\implies \sf A=\pi r^2[/tex]
Therefore, the area of the shaded area is:
[tex]\implies \sf A=\pi (r+7)^2-\pi r^2[/tex]
Expand and simplify the expression:
[tex]\implies \sf A=\pi (r+7)^2-\pi r^2[/tex]
[tex]\implies \sf A=\pi (r^2+14r+49)-\pi r^2[/tex]
[tex]\implies \sf A=\pi r^2 +14 \pi r +49 \pi -\pi r^2[/tex]
[tex]\implies \sf A=14 \pi r+49 \pi[/tex]
OUTER CIRCLE AREA
π(r+7)²Inner circle area
πr²Area of shaded one
π(r+7)²-πr²π(r²+14r+49-r²)π(14r+49)14πr+49πwrite and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
Using proportion, the equivalent units of the following units are as follows:
6km = 3.73 miles2.5 L = 0.66 gallons 90 Ib = 40.82 kgHow to use proportion to find equivalent units?Using proportion,
1.60934 km = 1 miles
6 km = ?
cross multiply
distance(m) = 6 / 1.60934 = 3.7282364199 = 3.73 miles
1 litre = 0.264172 gallons
2.5 litres = ?
volume(gallons) = 2.5 × 0.264172 = 0.66 gallons
1 pounds = 0.453592 kg
90 pounds = ?
weight(kg) = 40.82328 = 40.82 kg
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A rectangular parallelepiped has dimensions a, b and c. The volume is 100cm3. A second parallelepiped has dimensions α, β, γ, where α is 50% of a, β is 20% of b and γ is 10% of c. What is the volume of the second parallelepiped in cubic meters?
The volume of the second parallelepiped will be 1 cm³. According to the given conditions, α is 50% of a, β is 20% of b and γ is 10% of c.
What is volume?The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
Given condition;
α is 50% of a, β is 20% of b and γ is 10% of c
α = a/2
β = b/5
γ = c/10
The volume of the first parallelepiped:
V = abc
100cm³=abc
The volume of the second parallelepiped:
[tex]\rm V'= \alpha \times \beta \times \gamma \\\\ \rm V'= \frac{a}{2} \times \frac{b}{5} \times \frac{c}{10} \\\\ V' = \frac{abc}{100} \\\\ V'=\frac{100}{100} \\\\ V' = 1 cm^3[/tex]
Hence, the volume of the second parallelepiped willl be 1 cubic meter.
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Translate this sentence into an equation. the product of jenny's height and 4 is 52.
Answer:
4J = 52
Step-by-step explanation:
If Jenny's height is J:
4J = 52
A school stores expenses and sales for a three-month period are shown in the table below. Month Expense Sales September $125.00 $47.00 October$0.00 $65.00 November $57.00 $28.00 Based on the data in the table, what is the loss or pro t for the store for the three-month period? A. $182.00 loss B. $42.00 loss C. $15.00 profit D. $140.00 profi
t
The school store is in $42 loss , Option B is the correct answer.
What is Profit and Loss ?When the sales is more than the expenses then it is called profit and vice versa is called Loss.
The sales and expenses for three months are given
To calculate overall Profit/Loss
Total Expenses = $125 + $0 +$ 57 = $182
Total Sales = $47 +$65 + $28 = $140
Therefore as sales is less than the expense , The school is in loss
Loss = $ 182 -$ 140 = $42
Thus Option B is the correct answer.
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Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 polnts)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Horizontal and Vertical translations can transform f(x) to g(x).
Equations to transform f(x) to g(x) are: g(x) = f(x) + k, and g(x) = f(x + k).
In vertical translation k = 18, and horizontal translation k = 6.
SolutionEquations of the two st. lines
Select two points on the line f(x) viz. (1,2), (2,5).
The equation of the line f(x) is
[tex]\frac{y-2}{x-1} = \frac{5-2}{2-1} \Rightarrow \mathbf{y=3x-1}.[/tex]
Select two points on the line g(x) viz. (-5,2), (-4,5).
The equation of the line g(x) is
[tex]\frac{y-2}{x+5} = \frac{5-2}{-4+5} \Rightarrow \mathbf{y=3x+17}.[/tex]
Ways to transform
The two lines, f(x) and g(x), are parallel to each other so their orientation w.r.t. each other is not changed. f(x), thus, can be translated to obtain g(x).
The translation of f(x) can be done in two ways: Vertical translation, and Horizontal translation.
Horizontal translation
f(x) can be translated horizontally to obtain g(x) by the relation of type g(x) = f(x + k).
Using the above relation for the two lines,
3x + 17 = 3(x + k) -1 ⇒ k = 6.
The horizontal translation relation is g(x) = f(x + 6).
Vertical translation
Vertical translation can be done with the relation g(x) = f(x) + k.
Using the above relation for the two lines,
3x + 17 = 3x - 1 + k ⇒ k = 18.
The vertical translation relation is g(x) = f(x) + 18.
The two transformation relations are: g(x) = f(x + 6), and g(x) = f(x) + 18.
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Question 9 of 10
A fellow classmate tosses 3 coins and finds that 2 of them come up tails.
Which of the following is the best conclusion for her to come to?
OA. She needs to keep flipping the coins until she gets 50% heads in
order to determine if they are fair.
OB. If she flips the coins once more, they will all come up heads.
OC. The coins are unfair.
OD. This could easily happen with a fair coin after only 3 flips.
The best conclusion for her to come to: D. this could easily happen with a fair coin after only 3 flips.
What is a fair coin?A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly tossed.
This ultimately implies that, the best conclusion for her to come to is that this could easily happen with a fair coin after only 3 flips considering 2 of the three coins come up tails.
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