Final answer:
The perimeter of the rectangle with given dimensions is represented by the polynomial 8x^2 + 2x + 2, which corresponds to option A.
Explanation:
To determine the perimeter of a rectangle, we need to add up all sides of the rectangle. The formula for the perimeter (P) of a rectangle is P = 2(length) + 2(width). Given the length is x2 + 3x - 5 and the width is 3x2 - 2x + 6, we would calculate the perimeter as follows:
P = 2(x2 + 3x - 5) + 2(3x2 - 2x + 6)
Expanding this expression:
P = 2x2 + 6x - 10 + 6x2 - 4x + 12
Combining like terms gives us:
P = (2x2 + 6x2) + (6x - 4x) + (-10 + 12)P = 8x2 + 2x + 2
So the correct polynomial expression for the perimeter of the rectangle is option A: 8x2 + 2x + 2.
Final answer:
The polynomial expression for the perimeter of the rectangle with given side lengths is 8x^2 + 2x + 2.
Explanation:
The perimeter of a rectangle is given by the formula P = 2l + 2w, where l represents the length and w represents the width. For the lengths provided, the length (l) is x2 + 3x - 5 and the width (w) is 3x2 - 2x + 6. To find the polynomial expression for the perimeter, we will multiply both the length and the width by 2 and then sum them:
Perimeter (P) = 2(x2 + 3x - 5) + 2(3x2 - 2x + 6)
On simplifying:
P = 2x2 + 6x - 10 + 6x2 - 4x + 12
P = (2 + 6)x2 + (6 - 4)x - (10 - 12)
P = 8x2 + 2x + 2
Therefore, the correct polynomial expression for the perimeter is 8x2 + 2x + 2, which corresponds to option B.
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What is the trigonometric ratio for sin S?
Enter your answer, as a simplified fraction, in the boxes.
Answer: [tex]\frac{8}{17}[/tex] or 8:17
Step-by-step explanation:
For any angle x (other than right angle) in a right triangle ,the trigonometric ratio of sin x is given by :-
[tex]\sin x=\frac{\text{side opposite to x}}{\text{Hypotenuse}}[/tex]
Given: A right triangle with hypotenuse = 68 units
The side adjacent to S = 60
Let h be the side opposite to S, then using Pythagoras in the given right triangle, we get
[tex](68)^2=60^2+h^2\\\\\Rightarrow\ h^2=68^2-60^2\\\\\Rightarrow\ h^2=1024\\\\\Rightarrow\ h=\sqrt{1024}=32[/tex]
Thus, the side opposite to S = 32 units
Now, the trigonometric ratio for sin S is given by :-
[tex]\sin S=\frac{\text{side opposite to S}}{\text{Hypotenuse}}\\\\\Rightarrow\sin S=\frac{32}{68}=\frac{8}{17}[/tex]
Hence, the trigonometric ratio for sin S =[tex]\frac{8}{17}[/tex] or 8:17
Omar uses 1/6 of his tickets to ride the water slide. How many tickets does he use he has 24 in total?
Compare the Triangle Proportionality Theorem and the Triangle Midsegment Theorem.
which number is least to greatest 42%,0.43,17/40
The stopping distance s of a car varies directly as the square of its speed v. If a car traveling at 20 mph requires 28 ft to stop, find the stopping distance for a car traveling at 55 mph
solve. -2/5x-9<9/10 show all steps pleaseee!!
A circle has an area 324 pi cm. What is the radius?
The radius of the circle with an area of 324π sq cm is 18 cm.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know, The area of a circle is πr².
So, We can equate the given area with the general formula,
324π = πr².
r² = 324.
r = 18 cm.
A clock can be thought of as a circle having 12 steps and we know that circle is 360°,
So, the measure of each integer step of a clock is 30°.
Also, If we want to find some portion(arc) of the circumference we use the formula, s = rФ.
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Given: ΔXYZ
AB is a midsegment parallel to XZ. The slope of XZ is 4.
What is the slope of AB?
△ABC is reflected to form △A′B′C′ .
The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) .
Which reflection results in the transformation of △ABC to △A′B′C′ ?
A)reflection across the x-axis
B) reflection across the y-axis
C)reflection across y = x
D)reflection across y=−x
Answer:
The correct option is A.
Step-by-step explanation:
The vertices of △ABC are A(−7, 1) , B(−5, −3) , and C(−3, 2) . The vertices of △A′B′C′ are A′(−7, −1) , B′(−5, 3) , and C′(−3, −2) .
The relation between coordinates of preimage and image is defined as
[tex](x,y)\rightarrow (x,-y)[/tex]
Sign of y-coordinate changes but x-coordinate remains the same. It is possible it the figure is reflection across the x-axis.
Therefore the correct option is A.
Find f(1/4) when f(x)=2x^2+9x-7
To find f(1/4) when f(x)=2x^2+9x-7, substitute x=1/4 into the function and simplify.
Explanation:To find f(1/4) when f(x) = 2x² + 9x - 7, we substitute x = 1/4 into the function.
Plugging in the value of x, we have f(1/4) = 2(1/4)² + 9(1/4) - 7.
Simplifying the expression, we get f(1/4) = 2/16 + 9/4 - 7. Evaluating the fractions and subtracting, we find that f(1/4) = -45/16.
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solve equations using addition x+y=5 and x-y=3
Help with this math question please
your water hose is leaking at a rate of 0.25 cups per hour. how many gallons did you hose leak in a full 24 hour day
Solution:
we are given that
water hose is leaking at a rate of 0.25 cups per hour.
We have been asked to find that
how many gallons did you hose leak in a full 24 hour day.
Since water hose is leaking at a rate of 0.25 cups per hour.
It mean the tank will leak by [tex] 0.25*4=1 \ Cup [/tex] in 4 Hours.
So in 24 Hours the tank will leak by [tex] \frac{24}{4}*1=6*1=6 \ Cups [/tex] .
As we know that 1 Gallon=16 Cups.
It mean in 24 Hours the tank leaked by [tex] \frac{1}{16}*6= 0.375 \ Gallon [/tex]
an athlete is training to run a marathon. she plans to run 2 miles the first week. she increases the distance by 8% each week. whixh function models how far she will run in the nth week
Akira Chang's uncle dies without a will, leaving an estate of $945,000. His heirs consist of a wife and two adult children. His state requires that, in the absence of a will, each child is to receive two-thirds as much as a spouse. How much will his wife receive?
These are the first sentences in the short story, “The Gift of the Magi,” by O. Henry: one dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies.” A. Simplify the equation that represents the value of the coins. Make it an equation that expresses the value of quarters, dimes, and nickels. B. Is it possible to have exactly 60 pennies in $1.87? Explain.
Answer:
From the given problem statement of the this question,the amount of the gift is 1 dollar and sixty cents
x=60*B
Yes is it possible to have 60 pennies in $1.87
A box contains 3 red balls, 2 white balls, and 5 black balls. two balls are drawn at random from the box (with replacement of the first before the second is drawn). what is the probability of getting a red ball on the first draw and a white ball on the second?
a leatherback turtle swims at a constant rate of 2.5 kilometers per hour, at its constant rate of speed how long will it take for a leatherback turtle to swim 10 kilometers?
Katie filled a measuring cup with 9/10 of a cup of vegetable oil. Then she poured 1/4 of a cup of the oil into a frying pan. How much oil is left in the measuring cup? Simplify your answer.
help me please show ur work
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides of this triangle?
5 cm and 8 cm
6 cm and 7 cm
7 cm and 2 cm
8 cm and 8 cm
Answer:
D
Step-by-step explanation:
Find the volume of the tetrahedron having the given vertices. (3, −1, 1), (5, −2, 4), (1, 1, 1), (0, 0, 1)
Use the inverse of the function y = x2 − 18x to find the unknown values. y=+/= square root of bx+c+d
The inverse of a function is its opposite
The values of the unknown are: b = 1, c = 81 and d = 9
The function is given as:
[tex]y = x^2 - 18x[/tex]
Rewrite the equation in vertex form as:
[tex]y = (x - 9)^2 - 81[/tex]
Swap the positions of x and y
[tex]x = (y - 9)^2 - 81[/tex]
Add 81 to both sides
[tex](y - 9)^2 = x + 81[/tex]
take the square roots of both sides
[tex]y - 9 = \pm\sqrt{x + 81}[/tex]
Add 9 to both sides
[tex]y = \pm\sqrt{x + 81} + 9[/tex]
By comparison, the values of the unknown are:
b = 1, c = 81 and d = 9
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One side of a square is 2^3 inches.
What would be the area of the square?
*Solve the equation of 2^3 first*
True Or False
The term software refers to everything from the machine’s operating system (OS) to the individual programs and applications you use to write, listen, speak, sing, or learn.
A store sells two kinds of candles, scented and unscented. The scented burns 1/12 inches in 20 minutes and the unscented burns 1/6 inches in 30 minutes. Which type of candle burns in 1 hour and what is its burn rate?
Given :The scented burns [tex] \frac{1}{12} [/tex] inches in 20 minutes
The scented candle will burn [tex] \frac{1}{12} times 3 =\frac{1}{4} [/tex] inches in one hour.
The unscented candle burns [tex] \frac{1}{6} [/tex] inches in 30 minutes
In one hour it will burn [tex] \frac{1}{6} times 2=\frac{1}{3} [/tex] inches .
Burn rate of scented is [tex] \frac{1}{4} [/tex] inches per hour.
Burn rate of unscented is [tex] \frac{1}{3} [/tex] inches per hour.
which of the following statements are true? check all that apply
Answer with explanation:
Mean of this data set
[tex]=\frac{\text{sum of all the observation}}{\text{Total number of observation}}\\\\=\frac{30+37+37+41+22+69+45+64+51+22+63+31+64+65+25+51+26+48+28+49}{20}\\\\=43.4[/tex]
Arranging the data set in ascending order
22, 22,25, 26, 28,30,31,37,37,41,45,48,49,51,51,63,64,64,65,69
Median =Middle observation ,if number of terms is odd
and if number of terms is even, divide number of terms by ,2 and then follow the procedure
[tex]=\frac{10^{th term}+11^{th term}}{2}\\\\=\frac{41+45}{2}\\\\=43[/tex]
To find the Outlier
[tex]Q_{1}=\frac{28+30}{2}=29,Q_{3}=\frac{51+63}{2}=57[/tex]
Interquartile range = 57 - 29=28
Data values are approximately equally distributed on both sides of median.
That is, 43-22=21, and ,69 -43=26
So,we can say that there will be no outliers.
Graph will be positively skewed.
Mean > Median
So,mean will be better measure of central tendency because, 43.4-22=21.4, and 69-43.4=25.6
Option A: There are no outliers.
And, Option C: The Mean is good measure of central tendency.
Write the fraction as money amount 65/100
What is the Pythagorean Theorem and what is the equation for it?
Please help!! Dexter made a frequency distribution, setting up groups for the data shown.
His first group was for 20-24. What was the frequency of his forth group?
42 33 28 27 51 29 31 42 38 49 35 30 22 27 26 41 47 33
The frequency of Dexter's fourth group (35-39) in his frequency distribution is 2. This was determined by counting the numbers within the 35-39 range from the provided data set.
Calculating the Frequency of the Fourth Group:
To calculate the frequency of the fourth group in Dexter's frequency distribution, let's first establish the groups.
First Group: 20-24Second Group: 25-29Third Group: 30-34Fourth Group: 35-39Next, we'll count how many data points fall within each range:
3538Thus, there are 2 data points in the fourth group (35-39).