Answer:
length = 26.6
width = 11.3
Step-by-step explanation:
1. Set up the equation
(2x + 4)(x) = 300
2. Simplify
2x² + 4x = 300
3. Solve by completing the square
Divide by 2 to make "a" equal to 1
x² + 2x = 150
Find term to complete the square by squaring half of "b"
(2/2)² = 1
x² + 2x + 1 = 150 + 1
Factor perfect square trinomial
√x² + 2x + √1 = 151
(x+1)² = 151
Square root each side
x + 1 = ±12.3
Set up two possibilities and solve
x + 1 = 12.3
x = 11.3
x + 1 = -12.3
x = -13.3
The measurement cannot be negative so width is equal to 11.3
4. Use the width to solve for the length
11.3(2) + 4 = 26.6
The length and width is 26.6 and 11.3.
Calculation of the length and width:Since The length of the fence is four more than two times the width.
So here the equation should be
(2x + 4)(x) = 300
[tex]2x^2 + 4x = 300[/tex]
Now
Here we divided by 2
So,
[tex]x^2 + 2x = 150[/tex]
Now we determine the term
[tex](2/2)^2 = 1\\\\x^2 + 2x + 1 = 150 + 1[/tex]
Now applied the Factor perfect square trinomial
[tex]\sqrt x^2 + 2x + \sqrt1 = 151\\\(x+1)^2 = 151[/tex]
Now do the Square root each side
x + 1 = ±12.3
Here we required to set up two possibilities and solve
x + 1 = 12.3
x = 11.3
And,
x + 1 = -12.3
x = -13.3
The measurement should not be negative so the width is equal to 11.3
Now the width is
= 11.3(2) + 4
= 26.6
Therefore, The length and width is 26.6 and 11.3.
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Find the length of, x, of the third side of the triangle.
Answer:
i do not know either so please help me because this is not my level
Answer:
8=x
Step-by-step explanation:
can u give me a 5 star plz ty :)
Find the Probability that a point chosen randomly inside the
rectangle is inside the trapezoid. Enter your answer as a decimal.
10 ft
4 ft
6 ft
4 ft
12 ft
1
2 ft
Answer: 1/5
Step-by-step explanation:
We need to calculate the area of rectangle and trapezium and the Circumference of the circle.
Area of rectangle :
Length(L) = 10 ; width (W) = 6
Area = L * W = (10 * 6)ft = 60ft^2
Area of trapezium :
Height (h) = 4ft ; length(a) = 2ft ; length(b) = 4ft
Area = 0.5 ( a + b) h
Area = 0.5(2 +4) * 4 = 0.5(6)*4 = 12ft^2
Area of circle :
πr^2 ; r = radius of circle ; r= 2ft
3.142 * 2^2 = 3.142 * 4 = 12.568 ft^2
Probability = required outcome / Total possible outcomes.
P(point chosen inside rectangle is inside trapezium) = Area of trapezium / Area of rectangle
= 12/60
= 1/5
How much will Bob need to save each month if he wants to buy a $30,000 car with cash in 5 years? He can earn a nominal interest rate of 10% compounded monthly.
a) $2.50
b) $250.00
c) $25.00
d) $1,862.76
Answer:
B
Step-by-step explanation:
C is too little and D is too much
Which graph represents the function f(x)=−4x−3?
The graph on the top left.
Step-by-step explanation:f(x) = [tex]-4^x - 3[/tex]
That means that when x = 0...
f(0) = [tex]-4^0 - 3[/tex]
f(0) = -1 - 3
f(0) = -4
So, the function will have a point at (0, -4). We can eliminate the two graphs on the right.
When x = 1...
f(1) = [tex]-4^1 - 3[/tex]
f(1) = -4 - 3
f(1) = -7
So, the function will have a point at (1, -7). That corresponds to the graph on the top left.
Hope this helps!Answer:
the top left
Step-by-step explanation:
just took the test
if a student is selected at random find the probability the student is a male given that it's a senior. Round to the nearest whole percent.
Answer: 40%.
Step-by-step explanation:
From the table : Total Seniors = 2+3= 5
Number of male seniors = 2
If a student is selected at random find the probability the student is a male given that it's a senior:
P(Male | senior)[tex]=\dfrac{\text{Number of male seniors}}{\text{Total seniors}}[/tex]
[tex]=\dfrac{2}{5}[/tex]
In percent, [tex]\dfrac{2}{5}\times100=40\%[/tex]
Hence, the probability the student is a male given that it's a senior. =40%.
The probability of the student is a male senior is 7%.
Given, here from the 2- way table the total no. students will be 30.
We have to find out the probability of the student select at random, student is a senior male .
We know that, the probability of an event E, will be
[tex]P(E)=\dfrac{No.\ of \ favaurable\ outcomes}{Total\ outcomes}[/tex]
Now,
[tex]P( Senior\ male)= \dfrac{2}{30} \\\\P( Senior\ male)=0.06\\[/tex]
Representing it in percentage as,
[tex]P( Senior\ male)=0.06666\times100\%\\P( Senior\ male=6.66\%[/tex]
Hence the nearest whole percent will be 7%.
Thus probability of the student is a male senior is 7%.
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ASAP!!! PLEASE help me with this question!!!!!
Answer:
last one
Step-by-step explanation:
3*√(3.5 - 3) -1 = 1.12......
Answer:
[tex]\boxed{-1<F(x)<2}[/tex]
Step-by-step explanation:
x is given the value of 3 1/2 or 3.5.
When x is 3, F(x) is -1.
When x is 4, F(x) is 2.
If x is 3 1/2, then the value of F(x) is between -1 and 2.
The municipal swimming pool in Charlotte, North Carolina has three different ways of paying for individual open swimming. Nick is trying to decide which way to pay. • Early Pay: Pay $38.00 before Memorial Day; swim any number of days • Deposit Plus: $13.00 deposit plus $3.00 per day • Daily Pay: $5.00 per day
Answer:
$13.00 deposit plus $3 per day.
Step-by-step explanation:
Nick is deciding to acquire membership in municipal swimming pool in Charlotte, North Carolina. There are three different ways for the payment. The lump sum initial is $38 which is difficult for Nick to finance. Also if Nick is unable to go for swim he will lose $38. The per day deposit is suitable option for Nick as he will only have to pay when he goes for swim.
Answer:
Table of swimming costs using the three different payment methods
Payment Method Number of days
0 days 5 days 10 days 15 days 20 days
Early Pay $38.00 $38.00 $38.00 $38.00 $38.00
Deposit Plus $13.00 $28.00 $43.00 $58.00 $73.00
Daily Pay $00.00 $25.00 $50.00 $75.00 $100.00
Myra took a picture of the sky one afternoon when two jet airplanes appeared to draw a pair of parallel lines with their vapor trails. The vapor trails from two other jets flying from another direction crossed over the parallel trails. She printed her picture and labeled the angles and lines.
Parallel lines c and d are cut by transversals a and b. All angles are described clockwise, from uppercase left. The intersection of lines c and b form angles: 2, 4, 3, 1. The intersection of lines d and b form angles: 6, 8, 7, 5. The intersection of lines c and a form angles: 10, 12, 11, 9. The intersection of lines a and d form angles: 14, 16, 15, 13.
Assume lines c and d are parallel and Angle2 measures 98°. Which statements are true? Select three options.
Answer:
a, c. d
Step-by-step explanation:
Answer:
a c d
Step-by-step explanation:
Fareeda is researching a paper for her astronomy class and has identified a book of star charts that she feels would be a useful resource. Unfortunately, neither the school nor the local city library has it in their collections, and it would be expensive to purchase. However, there is a copy of the book at another school's library, about 150 miles away. What would be the BEST way for Fareeda to obtain the book for her research
Step-by-step explanation:
I would suggest that she studies or do a cost analysis of what it will cost her to transport to the library to request for the book and return it, if it is not expensive as compared to the cost of the book she should travel down to request for it. else she should purchase the book
Or
Fareeda can simply check if the second library has a distant library services so that the book can be either
1. Sent to her home or placement address, or
2.Scans of book chapters and articles be emailed to her.
Determine the number of terms, n, given the geometric series -1 - 2 - 4 - 8 - ... and Sn=−31.
Answer:
5
Step-by-step explanation:
We are given the geometric series:
-1, - 2, - 4, - 8.......
In the geometric series above, the common ratio = second term/first term = -2/-1
= 2
Where common ratio is greater than 1(r >1)
The sum of a geometric progression =
Sn = a(rⁿ -1)/r - 1
In the question we are asked to find the number of term = n
Sn = -31
a = -1
r = 2
Hence,
-31 = -1(2ⁿ - 1)/2 - 1
-31 = -1(2ⁿ - 1)
-31 = -2ⁿ + 1
2ⁿ = 1 + 31
2ⁿ = 32
2ⁿ = 2^5
n = 5
Therefore, the number of terms(n) = 5
Please answer it now in two minutes
Answer:
8.4 in
Step-by-step explanation:
Solution:-
- We consider the large right angle triangle namely, " XVW "
- We will recall all the trigonometric ratios that are applicable to all right angled triangles.
- While we are dealing with trigonometric ratios we have the following terms that needs to be correlated with the given specific problem:
Hypotenuse ( H ): Side opposite to 90 degrees angle
Base (B): The side adjacent to the available angle ( θ )
Perpendicular (P): The side opposite to the available angle ( θ )
- We will go ahead and mark our respective sides as follows:
Angle ( θ ) : 34°
Hypotenuse ( H ) : XW = 15 in
Base ( B ) : VW
Perpendicular ( P ) : VX
- Now recall all the trigonometric ratios studied:
sin ( θ ) = P / H = VX / XW
cos ( θ ) = B / H = VW / XW
tan ( θ ) = P / B = VX / VW
- Now choose the appropriate trigonometric ratio with two values given and one ( VX ) that needs to be determined as follows:
sin ( θ ) = P / H = VX / XW
sin ( 34° ) = VX / 15
VX = 15*sin ( 34° )
VX = 8.387 .. ( 8.4 ) in
ANSWER FAST A 10 ft long ladder has one end that leans against a wall and another that rests on the ground 6 feet from the wall. How high on the wall does the ladder rest?
Answer:
8 feet
Step-by-step explanation:
[tex]h = \sqrt{10^{2} - 6^{2} } = \sqrt{100 - 36} = \sqrt{64} = 8[/tex]
abby owns a square plot of land. she knows that the area of the plot is between 2200 and 2400 square meters. which of the following answers is a possible value for the side length of the plot of land?
Answer:
48
Step-by-step explanation:
The formula for the area of a square is A = s². Plug in each value and see if is in between 2200 and 2400.
A = s²
A = (46)²
A = 2116
A = s²
A = (48)²
A = 2304
A = s²
A = (50)²
A = 2500
A = s²
A = (44)²
A = 1936
The only value that fits in between 220 and 2400 is 48.
Forty-nine is subtracted from a number. The difference is divided by 11. The quotient is 3. What is the number?
Answer:
N = 82
Step-by-step explanation:
(N - 49)/11 = 3
N - 49 = 33
N = 82
what is the value of the angle marked with x
Answer:
67°Step-by-step explanation:
Given figure is an isosceles trapezoid. Then angles corresponding to equal sides must also be equal. Hence, X = 67°
Theorem: If a quadrilateral ( with one set of parallel sides ) is an isosceles trapezoid, it's legs are congruent.
Hope this helps...
Best regards!!
A trapezoid, square, and semicircle are connected to form a composite figure. Trapezoid M D C K has base lengths of 8 millimeters and 4 millimeters. Square A B C D has side lengths of 2 millimeters. Line A B is the diameter of the semicircle and has a length of 4 millimeters. What is the area of the composite figure if AB ≅ BC ≅ CD ≅ DA ≅ DN? (2π + 28) mm2 (2π + 32) mm2 (2π + 40) mm2 (2π + 48) mm2
Answer:
(2π + 28) mm²
Step-by-step explanation:
The Area of the Composite figure =
Area of the Trapezoid + Area of the Square + Area of the semicircle
a) Area of the Trapezoid
Trapezoid M D C K has base lengths of 8 millimeters and 4 millimeters
Diameter of the semicircle= length of 4 millimeters = height of the trapezoid
Area of trapezoid = 1/2 × h × (b + b)
= 1/2 × 4 × (8 + 4)
= 1/2 × 4 × 12
= 1/2× 48
= 24mm²
b) Area of the square
Square A B C D has side lengths of 2 millimeters.
Area of a square = Side length²
=(2mm)² = 4mm²
c) Area of the semicircle
Line A B is the diameter of the semicircle and has a length of 4 millimeters.
Formula for the Area of a semi circle: πr²/2
Radius = Diameter/2 = 4mm/2 = 2mm
= π × 2²/2
= 4π/2
= 2πmm²
The Area of the Composite figure =
Area of the Trapezoid + Area of the Square + Area of the semicircle
= 24mm² + 4mm² + 2πmm²
= 28mm² + 2πmm²
= (28 + 2π)mm²
Therefore, the Area of the Composite figure = (28 + 2π)mm² or (2π + 28) mm²
Answer:
A- (2π + 28) mm²
Step-by-step explanation:
edge
A: Top 6% of scores B: Scores below the top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answer:
The numerical limits for a B-grade is between 81 and 92
Step-by-step explanation:
Here in this question, our task is to find the numerical limits for B grade. This means the range between a test taker would be scored a B grade
Please check attachment for complete solution and explanation
find the slope and y intercept of the line y=7/5x-3 5/7; 3 3; 7/5 7/5;-3 -3; 7/5
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question
y = 7/5x - 3
Comparing with the above formula
Slope / m = 7/5c/ y intercept = - 3Hope this helps you
The value of the slope of the line is 7/5 and the y-intercept is -3
Given the line equation :
y = 7/5x - 3The general form of the equation is :
y = bx + cslope = b ; intercept = cComparing the equations :
b = 7/5 c = -3Hence, the slope and y-intercept are 7/5 and -3
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Which of the following rational functions is graphed below?
Hey Mate!!
Your answer will be below.
Step-by-step explanation:
The answer is C. Because, There's vertical asymptotes at 1 and -1. Vertical asymptotes are present where the x on the denominator is equal to 0. So, Both the values are 1 and -1 set are equal to the 0 in the denominator, So, They're both horizontal asymptotes. Good Luck!
An athlete runs 100 m each minute.
If she starts running at 10:00 am, how
many kilometres will she have run
by 10:20 am?
Given the sequence -3, 9, -27, 81, -243, ..., find the recursive formula.
Answer:
a(1)= -3
a(n)=a(n-1) (-3)
Step-by-step explanation:
hope this helps
Recursive formula of the given sequence -3, 9, -27, 81, -243, ... , is (-3)^n ; where n = 1,2,3, ...
What is recursive formula?A recursive formula defines any term of sequence with its preceding term.
The given sequence is -3, 9, -27, 81, -243, ... ,
First term = -3
Second term = (-3)^2 = 9
Third term = (-3)^3 = -27
Fourth term = (-3)^4 = 81
Fifth term = (-3)^5 = -243
Hence, the recursive formula of the given sequence -3, 9, -27, 81, -243, ... , is (-3)^n ; where n = 1,2,3, ...
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Give me correct answer and fast
Answer:
r=8.8
Step-by-step explanation:
sin 36=opp/ hyp
sin36=r/15
r= 15 sin36
r=8.8
Helppppppppppppppppp
Answer/Step-by-step explanation:
Surface area of cylinder = 2πrh + 2πr²
Surface area of the cylinder with,
height (h) = 4 ft
radius (r) = 5 ft
Surface area = 2*3.14*5*4 + 2*3.14*5²
= 125.6 + 157
= 282.6 ft²
Surface area of the cylinder with,
height (h) = 12 yd
radius (r) = 3 yd
Surface area = 2*3.14*3*12 + 2*3.14*3²
= 282.74 yd²
What is the range of the function represented by this graph?
Answer: The range is real numbers less than 1
[1, -∞)
Step-by-step explanation: The range is all the y-values. The top of the parabola (vertex) is at 1 above the x-axis. You have to look at the scale and notice that the scale is in increments of 2, The vertex is between 0 and 2. The parabola extends down to negative infinity.
Answer:
y < 1
(the < has a line underneath it)
Step-by-step explanation:
find the zeros or x-intercepts (values of r and s) of a quadratic relation y=x^2-5x+6 by factoring using the sum and product method
Answer:
[tex] y = x^2 -5x +6[/tex]
And for this case we want to find the zeros or x interceps r and s so we want to rewrite the function on this way:
[tex] y = (x-r) (x-s)[/tex]
The reason why we have two zeros is because the degree of the polynomial is 2. If we find two numbers that adding we got -5 and multiplied 6 we solve the problem. For this case the solution is r =3, s =2
[tex] y=(x -2)) (x-3)[/tex]
Step-by-step explanation:
For this problem we have the following polynomial given:
[tex] y = x^2 -5x +6[/tex]
And for this case we want to find the zeros or x interceps r and s so we want to rewrite the function on this way:
[tex] y = (x-r) (x-s)[/tex]
The reason why we have two zeros is because the degree of the polynomial is 2. If we find two numbers that adding we got -5 and multiplied 6 we solve the problem. For this case the solution is r =3, s =2
[tex] y=(x -2)) (x-3)[/tex]
03.07A LC)Which of the following describes a situation in which a basketball player ends up 0 m from his starting point? The player runs 9 meters forward, and then runs 0 meters in the opposite direction. The player runs 5 meters forward, and then runs 6 meters in the opposite direction. The player runs 6 meters forward, and then runs 5 meters in the opposite direction. The player runs 4 meters forward, and then runs 4 meters in the opposite direction.
Answer:
The correct option is;
The player runs 4 meters forward, and then runs 4 meters in the opposite direction
Step-by-step explanation:
From the question relates to the displacement of a body, compared to the distance covered by the body
In the question instance, the situation in which the player displacement will be zero is one where both the players forward and backward displacement are equal such that they cancel each other
We have the instance where the forward and opposite displacement are equal is given by the situation where the player runs 4 meters forward, and then runs 4 meters in the opposite direction.
Answer:
d would be the answer if your so needy
Step-by-step explanation:
If anyone doesn't mind helping may you plz help me
Answer:
SAS
Step-by-step explanation:
Please let me know if this doesn't help. I'm trying my best to relearn this so I can help you.
Instructions: Find the measure of the indicated angle to the
nearest degree
Answer:
x = 60°
Step-by-step explanation:
let the missing angle be = x
Cos x = 8/16
x = Cos-¹ 0.5
x = 60°
The question is in the picture
Answer:
angle B=92
Step-by-step explanation:
cos C= adj/hyp
sin C=12/14=6/7 ( in rad.)
angle C is 31 degree
the sum of angles of triangle =180
angles A+B+C=180
angle B=180-(31+57)=92 degrees
HELP FAST PLEASE
Polygon ABCDE is congruent to polygon TVSRK. VSR corresponds to
a,)
b,)
c,)
d,)
We are given that ABCDE is congruent to TVSRK and want to find what corresponds to VSR.
Look at the ordering of the letters. VSR is the second, third, and fourth letters of TVSRK, respectively.
Thus, we just have to select the second, third, and fourth letters of ABCDE and we get BCD.
Thus, VSR corresponds to BCD. Let me know if you need any clarifications, thanks!