Answer:
The length and the width of the rectangle are 11 units and 5 units
Step-by-step explanation:
Let us use the factorization to find the length and the width of the rectangle
∵ The trinomial is r² - 6r - 55
∵ r² = (r)(r)
∵ -55 = (-11)(5)
- Multiply r by -11 and r by 5, then add the products, the sum
must be equal the middle term of the trinomial
∵ (r)(-11) = -11r
∵ (r)(5) = 5r
∵ -11r + 5r = -6r ⇒ the middle term of the trinomial
∴ r² - 6r - 55 = (r - 11)(r + 5)
- Equate each factor by 0 to find the value of r
∵ r - 11 = 0
- Add 11 to both sides
∴ r = 11
OR
∵ r + 5 = 0
- Subtract 5 from both sides
∴ r = -5 ⇒ rejected because no negative dimensions
∴ The length of the rectangle is 11 units
∵ The area of the rectangle is 55 units²
∵ Area of a rectangle = length × width
∴ 55 = 11 × width
- Divide both sides by 11
∴ 5 = width
∴ The width of the rectangle is 5 units
Rani and her friends are raking leaves as a part of a school service project. The regular price of the supplies they need is 60$,but the store manager is giving them a 20% discount. Rani wants to know the sale price of the supplies.
Rani and her friends can purchase their supplies for $48 after a 20% discount on the original price of $60.
Explanation:Rani and her friends need to calculate the sale price of the supplies after a 20% discount. The original price is $60, and the discounts amount in money can be determined by multiplying this original cost by 20% or 0.20. This gives you a discount amount of $12. To determine the final price after the discount, you subtract the discount amount from the original price. Therefore: $60 - $12 = $48. Hence, the sale price of the supplies that Rani and her friends need is $48.
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A slot machine has 3 dials. Each dial has 30 positions, one of which is "Jackpot". To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot?
1/30 = 0.03 or 3%
3/(30+30+30) = 3/90 = 0.33 or 33%
3/(30×30×30) = 3/27000 = 0.0001 or 0.01%
1/(30×30×30) = 1/27000 = 0.00003 or 0.003%
Answer:
3/(30×30×30) = 3/27000 = 0.0001 or 0.01%
Step-by-step explanation:
Answer:
here we have 3 dials in the slot machines and each dial has 30 position
so probability of getting a number of the each dial =
30
1
since all dials are independent so probability of getting same number would be
P ( getting jack pot) =
30
1
30
1
30
1
=
27000
1
= 0.003% option D is correct.
Step-by-step explanation:
What's the snaller angle?
Answer:
the (2x) obviously because it is close to an acute angle and the (13x) is closer to a right angle
Step-by-step explanation:
Write the equation of the line that passes through the point (-5,5) and has a slope of -8/5
A) y= -8/5 x - 3
B) y= -8/5x+3
C) 3x - 5y =0
D) 5x-3y=0
Answer:
A) y= -8/5x -3
Step-by-step explanation:
This is your current equation: y= -8/5x + b. I would plug in your point to the equation. It should look like this: 5= -8/5(-5)+b. Multiply -8/5 by -5 to get 8. This is what you should have: 5=8+b. Subtract 8 from both sides to get -3=b. So, this is your final answer: y= -8/5x -3. So, A is the correct answer. Hope this helped!
Which statement is not true about the data shown by the box plot below?
a.
The interquartile range is 52.
b.
The median of the upper half of the data is 49.
c.
The median of the data is 37.
d.
Three fourths of the data is less than 49.
The false statement is "the median of the data is 37" because the IQR of the data is 20 option (a) is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
It is given that:
A box plot is shown in the picture;
As we know,
The interquartile range(IQR):
IQR = Q3 - Q1
IQR = 50 - 30
IQR = 20
From the box plot:
The median of the upper half of the data is 49.
The median of the data is 37.
Three-fourths of the data is less than 49.
Thus, the false statement is "the median of the data is 37" because the IQR of the data is 20 option (a) is correct.
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You randomly draw marble from the bag of marbles contains seven blue marbles two Green marbles and one red marble what is P(not draw a blue marble)?
Answer:
3/10 probability as it is the same as getting 2gm +1rm =3m
Step-by-step explanation:
You add up the numbers 7+2+1=10m
Simplify the expression and find the value, if x=2 : 5x-6-x+9
Answer:11
Step-by-step explanation:
5x-6-x+9
When x=2 we have
5(2)-6-2+9
10-6-2+9
10+9-6-2
19-6-2=11
Answer:
11
Step-by-step explanation:
5x - 6 - x + 9
4x + 3
x = 2
4(2) + 3 = 11
Drivers of semitrucks and other large vehicles pay close attention to signs similar to the one below. These signs indicate a change in the grade or slope of the road. Look at the black scalene triangle in the sign. How can the third-angle theorem be applied to find all three angle measurements in the black triangle? (2 points)
Answer:
A triangles angles equal 180 so add 90 and 60 then subtract that from 180. 2) yes. they have same angles so they must be congruent
A triangle with two angles that measure 34°.
Then the correct option is A.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
here, we have,
In triangle ΔABC, the measure of the third angle is calculated as,
∠C + ∠B + ∠A = 180°
∠C + 112° + 34° = 180°
∠C = 34°
The measure of the two angles of the triangle is identical.
Then the triangle will be an isosceles triangle.
A triangle with two angles that measure 34°.
Then the correct option is A.
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Complete Question:
Triangle ABC is shown.
Which triangle listed below must be similar to triangle ABC?
(1 point)
(A) A triangle with two angles that measure 34°
(B) A triangle with angles that measure 34° and 66°
(C) A scalene triangle with only one angle that measures 112°
(D) An isosceles triangle with two angles that measure 56°
Include with your answer choice below, reasoning why your choice is correct.
(2 points)
Use formulas, definitions, or theorems in your reasoning.
- What is it about the angles?
- Anything with the angle sums?
- What about the type of triangles?
Drag & Drop. Thank you to anyone who helps
Answer:
Top Left.) None of these, these are vertical angles.
Top Right.) Alternate Exterior
Middle Left.) None of these
Middle Right.) Corresponding
Bottom.) Alternate interior angles
please help, no spam answers please, I will mark brainleist!
Answer:
D.
Step-by-step explanation:
Its given that the rectangle has a perimeter of 60 units. A rectangle has four sides, and to get the perimeter, you add up all four sides. You are given one side is 20 units, and the other as 'x.'
So,
x + x + 20 + 20 = 60
2x + 40 = 60
Example for *wrong* answer:
Letter C, x + 20 = 60, that would'nt equal 60 because youre only adding two sides instead of all four.
Hopefully this helps :)
I'm trying to figure out question 4 but I don't understand it and neither do my friends.
Answer:
A: 88 — 100B: 85 — 87C: 82 — 84D: 80 — 81F: 0 — 79Step-by-step explanation:
You know the relation between X and Z is ...
Z = (X -μ)/σ
Solving for X, we find ...
Zσ +μ = X
You're trying to find the exam scores that correspond to the Z-values you found in question 3.
A = 90th percentile and above = 1.28(8) +78 = 88.24 ≈ 88
B = 80th percentile and above = 0.84(8) +78 = 84.72 ≈ 85
C = 70th percentile and above = 0.52(8) +78 = 82.16 ≈ 82
D = 60th percentile and above = 0.25(8) +78 = 80
So, your blanks are filled like this ...
A: 88 — 100
B: 85 — 87
C: 82 — 84
D: 80 — 81
F: 0 — 79
_____
Comment on this curve
The setup guarantees that 60% of the class will fail. It is more common to have those below Z = -2 get an F, and those above Z = 2 get an A.
Find f(t-3) for f(×)=4x^2-8×+4
Answer:
4t^2-32t+64=4(t^2-8x+16)
Step-by-step explanation:
f(x)=4x^2-8x+4
f(t-3)=4(t-3)^2 - 8(t-3)+4=
4(t^2-2*t*3+9)-8t+24+4=
4(t^2-6t+9)-8t+28=
4t^2-24t+36-8t+28=
4t^2-32t+64=4(t^2-8x+16)
Why is the reference angle the angle
the terminal side and the x-axis instead of the y-axis?
Answer:
If necessary, first "unwind" the angle: Keep subtracting 360 from it until it is lies between 0 and 360°. (For negative angles add 360 instead).
Sketch the angle to see which quadrant it is in.
Depending on the quadrant, find the reference angle:
A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can travel on 7 gallons of gas?
Answer:Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps
Step-by-step explanation:
Answer:
147 miles
Step-by-step explanation:
Let x be the number of miles travelled on 7 gallons, then proportion is of the form
[tex]\frac{miles}{gallons}[/tex], thus
[tex]\frac{63}{3}[/tex] = [tex]\frac{x}{7}[/tex] ( cross- multiply )
3x = 63 × 7 = 441 ( divide both sides by 3 )
x = 147
Thus the car can travel 147 miles on 7 gallons
Solve the provides equation verify the solution and state the answer using solution set notation. 126= w+38
Answer:
88
Step-by-step explanation:
126=w+38
w=126-38
=88
One step equations
6r=42
R=7
I hope that help you! :)
If the base angle of the cone needs to measure 60° and the cone needs to be 24 inches tall, approximately how wide will the base of the resulting cone need to be?
A.
27.72 inches
B.
13.86 inches
C.
41.57 inches
D.
83.14 inches
Final answer:
Using the base angle and the height of the cone, we can use trigonometry to find that the width of the base of the cone needs to be approximately 41.57 inches, making option C the correct answer.
Explanation:
The question asks for the width of the base of a cone given that its base angle is 60° and its height is 24 inches. To solve this, we need to understand that the base angle of 60° creates a right-angled triangle when a line is drawn from the apex of the cone to any point on the base's circumference, with the height of the cone being one side of this triangle and half of the cone's base width being the other side.
Using trigonometry, specifically the tangent function, which is the opposite side (half the base width) over the adjacent side (height), we can solve for the base width. Given that tan(60°) = √3 and the height is 24 inches, the formula becomes √3 = (base width/2) / 24, solving for the base width gives us roughly 41.57 inches, which makes option C correct.
Write the point-slope form of the line passing through (2, -12) and parallel to y=3x.
y - 12 = -(x + 2)
y + 12 = -(x - 2)
y + 12 = 3(x - 2)
y + 12 = -3(x - 2)
Answer:
y + 12 = 3(x-2)
Step-by-step explanation:
To start, you want the slope of the other line. Well, the slope of a parallel line is the same, so since the first line's slope is 3, so will the other one. then, because there is no other answer with a slope of 3, you automatically know it is the third answer. you don't need to work this problem further, but if you need to in the future, just comment and I will help you.
This describes the relationship between one set of data that increases as another set of data increases. This is synonymous with directly related.
Answer:
Positive correlation
Step-by-step explanation:
Correlation:
Correlation is a technique that help us to find or define a linear relationship between two variables.It is a measure of linear relationship between two quantities. A positive correlation means that an increase in one quantity leads to an increase in another quantity A negative correlation means with increase in one quantity the other quantity decreases.Positive correlation means that the data sets are directly related with each other.Thus, the correct answer is
Positive correlation
Answer:
Negative Correlation
Step-by-step explanation:
if cos x=2/3 and x is in quadrant 4 then sin x/2=
A. 1/3
B. Sqrt 1/6
C. -Sqrt 1/6
D. -1/3
Options are above will mark brainliest
Answer: B, [tex]\sqrt{\frac{1}{6} }[/tex]
Step-by-step explanation:
Using half-angle identities
Using half angle identities, we know that
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1-cosx}{2} }[/tex]
Plug in 2/3 for cosx
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1-2/3}{2} }[/tex]
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1/3}{2} }[/tex]
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1}{6} }[/tex]
Determining sign
Since the angle x is in quadrant 4 from 270 to 360 degrees, if we divide the angle by 2, the angle x should be somewhere from 135 to 180 degrees, which would all fall in quadrant 2
all sin values in quadrant 2 are positive
Final answer
[tex]sinx = \sqrt{\frac{1}{6} }[/tex]
If cos x=2/3 and x is in quadrant 4 then value of sin x/2 is -√(1/6), option C is correct.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To find sin(x/2), we can use the half-angle formula for sine:
sin(x/2) = ±√[(1 - cos x)/2]
Since x is in quadrant 4, cosine is positive and sine is negative. We are given that cos x = 2/3
so we can substitute this value into the formula:
sin(x/2) = -√[(1 - 2/3)/2]
sin(x/2) = -√(1/6)
Hence, if cos x=2/3 and x is in quadrant 4 then sin x/2 is -√(1/6)
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Aldon and Jamal raised the same amount of money for the school fundraiser. Aldon
donated $40 and sold 12 tickets for the school raffle. Jamal donated $25 and sold
15 tickets for the raffle. What was the cost of each raffle ticket?
The cost of each raffle ticket was $5.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
Amount donated by Aldon = $40
Number of tickets sold by Aldon = 12
Amount denoted by Jamal = $25
Number of tickets sold by Jamal = 15
Let x be the cost of each raffle ticket.
So, Cost of tickets sold by Aldon = 12x
Cost of tickets sold by Jamal = 15x
So, Total amount raised by Aldon = 12x + 40
Total amount raised by Jamal = 15x + 25
∵ Aldon and Jamal raised the same amount of money for the school fundraiser
⇒ 12x + 40 = 15x + 25
Taking aliketerms together we get,
15x - 12x = 40 - 25
⇒ 3x = 15
Dividing both side by 3 we get,
x = $5
which is the required cost of each raffle ticket.
Thus, the cost of each raffle ticket was $5.
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A cubic box that holds 125 units
Answer: 5 units
Step-by-step explanation:
what is the square root of -25
Answer:
the square root of -25 is 5i
Answer:
5i
Step-by-step explanation
All negative roots have i, which is an imaginary number.
i^2=-1.
Following this, the square root of -25 is 5i.
To double check:
5i*5i=5*5*i*i
25*-1=-25
How much money invested at 5% compounded continuously for 3 years will result in $852
Answer:
Step-by-step explanation:
Rate of interest is 5%.
Time =3years
Amount =$852
Then, we need to find P
Generally compound interest is given as
A=P(1+r/n)^nt
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period=12
t=number of time periods elapsed
A=P(1+r/n)^nt
852=P(1+0.05/12)^(12×5)
852=P(1+0.004167)^60
852=P(1.004167)^60
852=1.2834P
Then, P=852/1.2834
P=$663.88
Then the principal amount invested is $663.88
Approximately $664
Which is the length of the arc MPN expressed in terms of pie?
The calculated length of the arc MPN is 79/9π units
Finding the length of arc MPN
From the question, we have the following parameters that can be used in our computation:
Central angle = 360 - 44 = 316 degrees
Radius = 5 units
Using the above as a guide, we have the following:
arc MPN = central angle/180 * π * Radius
Substitute the known values in the above equation, so, we have the following representation
arc MPN = 316/180 * π * 5
Evaluate
arc MPN = 79/9π
Hence, the length of the arc is 79/9π units
The lengths of two sides of a triangle are 26
meters and 48 meters. What is the range of
possible lengths, in meters, for the third side,
x, of this triangle? Write your answers in the
boxes.
Answer:
[tex]22\ m < x < 74\ m[/tex]
Step-by-step explanation:
Let
x ----> the length for the third side
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) [tex]26+48> x[/tex]
solve for x
[tex]74> x[/tex]
Rewrite
[tex]x < 74\ m[/tex]
2) [tex]26+x>48[/tex]
solve for x
subtract 26 both sides
[tex]x> 22\ m[/tex]
therefore
The range of possible lengths, in meters, for the third side is equal to
[tex]22\ m < x < 74\ m[/tex]
The range of the possible length of the third side of the triangle is 22 to 74 (exclusive)
Assume the lengths of a triangle are x, y and z.
The following are the possible inequalities that relate the side lengths
[tex]x + y > z[/tex]
[tex]y + z > x[/tex]
[tex]x + z > y[/tex]
The unknown side length is x.
So, we have:
[tex]x + 26 > 48[/tex]
[tex]48 + 26 > x[/tex]
[tex]x + 48 > 26[/tex]
Solve for x in the three inequalities
[tex]x + 26 > 48[/tex]
[tex]x > 22[/tex]
[tex]48 + 26 > x[/tex]
[tex]74 > x[/tex]
[tex]x + 48 > 26[/tex]
[tex]x > -22[/tex]
The values of x cannot be negative.
So, we ignore the inequality [tex]x > -22[/tex]
We are left with
[tex]74 > x[/tex] and [tex]x > 22[/tex]
Combine the inequalities
[tex]74 > x > 22[/tex]
Rewrite as:
[tex]22 < x < 74[/tex]
Hence, the range of the possible length is 22 to 74 (exclusive)
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What is the perimeter of a square with an area of 441 cm2?
Area of the square = side x side = side ^2
therefore to find a length of one side = Square root of the 441
sqrt of 441 = 21 cm
so the perimeter of a square is 21 x 4 = 84 cm
(a+1)+(b-2)i=6+7i Solve for a and b
Answer:
a = 5 and b = 9Step-by-step explanation:
(a+1)+(b-2)i=6+7i
⇔
a + 1 = 6
and
b - 2 = 7
⇔
a = 5
and
b = 9
21 3/4 as a improper fraction
Answer:
87/4
Step-by-step explanation:
Step 1: Convert 21 3/4 into an improper fraction
21 3/4 is same as 21 * 4/4 + 3/4
21 * 4/4 = 84/4
Step 2: Add them up
84/4 + 3/4
87/4
Answer: 87/4
Answer: 87/4
Step-by-step explanation:
Multiply:
21*4=84
Add:
84+3=87
Your answer should be: 87/4
The denominator stays the same
estimated a 3 out of every 25 men are left handed
what percent of men are left ahnded
Answer:
12
Step-by-step explanation:
Percent means out of 100
We have 3/25
Multiply the top and bottom by 4
12/100
The percent is 12
Final answer:
Based on the estimate provided, 12% of men are left-handed, which is calculated by dividing 3 by 25 and then multiplying the result by 100.
Explanation:
To calculate the percentage of men who are left-handed based on the estimate that 3 out of every 25 men are left-handed, you can use the following steps:
Divide the number of left-handed men by the total number of men. In this case, 3 divided by 25 equals 0.12.Multiply the result by 100 to convert it to a percentage. So, 0.12 multiplied by 100 equals 12%.Therefore, based on the given estimate, 12% of men are left-handed.