The length of the rectangle is 11 units
The width of the rectangle is 5 units.
Explanation:
The equation of the trinomial is [tex]r^{2}-6 r-55[/tex]
We need to find the length and the width of the rectangle.
The length and width of the rectangle can be determined by factoring the trinomial [tex]r^{2}-6 r-55=0[/tex]
Factoring using the quadratic formula, we have,
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
where [tex]a=1, b=-6[/tex] and [tex]c=-55[/tex]
Substituting these in the above formula, we have,
[tex]r=\frac{-(-6) \pm \sqrt{(-6)^{2}-4 \cdot 1(-55)}}{2 \cdot 1}[/tex]
[tex]r=\frac{6\pm \sqrt{36+220}}{2}[/tex]
[tex]r=\frac{6\pm \sqrt{256}}{2}[/tex]
[tex]r=\frac{6\pm 16}{2}[/tex]
Hence, the two roots of the trinomial are
[tex]r=\frac{6+ 16}{2}[/tex] and [tex]r=\frac{6- 16}{2}[/tex]
Solving [tex]r=\frac{6+ 16}{2}[/tex] , we get,
[tex]r=\frac{22}{2}[/tex]
[tex]r=11[/tex]
Solving [tex]r=\frac{6- 16}{2}[/tex] , we get,
[tex]r=\frac{-10}{2}[/tex]
[tex]r=-5[/tex]
Thus, the solutions of the trinomial are 11 and -5
Since, the length of the rectangle is larger than the width, the length of the rectangle is 11 units.
Also, the width of the rectangle cannot be negative.
Thus, ignoring the negative sign, we have, [tex]r=5[/tex]
Hence, the width of the rectangle is 5 units.
A cone with height 8 and radius 2 is sliced halfway along its height by a plane that is parallel to the base of the cone. What is the radius of the circle at the intersection of the plane and the cone?
Answer:
1
Step-by-step explanation:
The cone is sliced by a plane, which produces a smaller cone on top. This cone is similar to the original cone. Therefore:
R / H = r / h
2 / 8 = r / 4
r = 1
The radius of the circle at the intersection of the plane and the cone is 1.
To find the radius of the circle at the intersection of the plane and the cone, we start by understanding the geometry of the cone and the slicing plane.
Given:
- Cone height ( h = 8 )
- Cone radius ( r = 2 )
- The plane slices the cone halfway along its height, so the distance from the vertex to the plane is [tex]\( \frac{8}{2} = 4 \)[/tex].
Let's denote:
- ( R ): Radius of the circle at the intersection of the plane and the cone.
At height ( h ) from the vertex of the cone, the radius ( R ) of the circle formed by the intersection with the plane is related to the similar triangles formed by the cone and the slice plane.
The ratio of corresponding sides of similar triangles gives us:
[tex]\[ \frac{R}{r} = \frac{h - 4}{h} \][/tex]
Substitute the given values:
[tex]\[ \frac{R}{2} = \frac{8 - 4}{8} = \frac{4}{8} = \frac{1}{2} \][/tex]
Now, solve for ( R ):
[tex]\[ R = 2 \cdot \frac{1}{2} = 1 \][/tex]
Therefore, the radius of the circle at the intersection of the plane and the cone is [tex]\( \boxed{1} \).[/tex]
Divide the number in the thousands place by itself and then multiply the answer by 0. Write your answer in the tenths place
To divide the number in the thousands place by itself and then multiply the answer by 0, we can follow a simple process. Let's consider an example where the number in the thousands place is 5. Dividing 5 by 5 gives us 1. Multiplying 1 by 0 gives us 0, which is the answer in the tenths place.
Explanation:To divide the number in the thousands place by itself, we can consider a specific number for better understanding. Let's say the number in the thousands place is 5. Dividing 5 by 5 gives us 1. To find the answer in the tenths place, we need to multiply 1 by 0. The product of 1 and 0 is 0. Therefore, the answer in the tenths place is 0.
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six episodes of a tv series last total of five hours, How many minutes on average does an episode last
Step-by-step explanation:
[tex]5 \: hours \: = 5 \times 60 = 300 \: min \\ minutes \: per \: episode = \frac{300}{6} \\ = 50 \\ [/tex]
Hence, each episode lasted for 50 minutes on an average.
On average, each episode of the TV series lasts 50 minutes, calculated by converting the total viewing time of five hours to 300 minutes and dividing that by the number of episodes, which is six.
To calculate the average duration of an episode, we need to convert the total time of all episodes from hours to minutes and then divide by the number of episodes.
There are 60 minutes in one hour, so five hours equates to 300 minutes (5 hours × 60 minutes/hour = 300 minutes). With six episodes in total, we divide the total minutes by the number of episodes to find the average length of one episode.
300 minutes / 6 episodes = 50 minutes per episode.
Therefore, on average, each episode of the TV series lasts 50 minutes.
Mrs.Roberts charges 25 for a basic cake that serves 12 people. If you want a large cake, it costs an additional $1.25 per serving. Write equation for the total cost or a cake, where y represents total cost and x represents the number of additional servings. How much would a cake that serves 20 people cost?
The total cost of a cake that serves 20 people is $35.
Step-by-step explanation:
Total cost = yNumber of additional servings = xThe number of additional servings = 20 - 12 = 8. (x=8)The equation can be formed as:
Total cost = basic cost + (No. of additional serving [tex]\times[/tex] cost per additional serving)y = 25 + x1.25Substitute x=8 in the above equationy = 25 + 8(1.25)y =25+10y = 35Therefore, the total cost of a cake that serves 20 people is $35.
a mechanical engineer designs a robotic rm to be used in an assembly line. one portion of the arm is 5/12 yard long, and the length of the second portion of the arm is 3/12 yard long.What wouldbe the length, in yards, of the robotic arm if the two portions of the arm were measured end to end?
Answer:
8/12 yard or 2/3 yard
Step-by-step explanation:
The sum of the two lengths is ...
5/12 yd + 3/12 yd = (5+3)/12 yd = 8/12 yd
This fraction can be reduced by removing a factor of 4 from numerator and denominator.
8/12 yd = 2/3 yd
If the arm portions are end-to-end, the total length is 2/3 yard.
genas new outfit originally cost 75. she received 20% off how much did genas outfit cost
Answer:
$75 x .20=$15
75-15=$60
To find out how much Gena's outfit cost after the 20% discount, subtract the discount amount from the original price.
Explanation:To find out how much Gena's outfit cost after the 20% discount, we can use the formula:
The discount amount = original price x discount percentage
In this case, the discount amount = $75 x 0.20 = $15.
Therefore, Gena's outfit cost after the discount is:
Original price - discount amount = $75 - $15 = $60.
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A tetrahedron has 4 sides. If the numbers 1, 2, 3, and 4 are on the faces of the tetrahedron, what
is the probability of randomly rolling a 3?
Probability of randomly rolling a 3 is 1/4
Step-by-step explanation:
Step 1:
It is given that a tetrahedron has 4 sides with 1,2,3 and 4 and is randomly rolled. We need to compute the probability of randomly rolling a 3.
Step 2:
Probability of an event = (Favorable outcomes) / (Total outcomes).
There are 4 total outcomes when the tetrahedron is rolled, these are the values 1 to 4.
The only favorable outcome is getting a 3
Probability of getting a 3 when the tetrahedron is randomly rolled = 1/4
Step 3:
Answer:
Probability of randomly rolling a 3 is 1/4
Answer:
3/4
Step-by-step explanation:
Which expression is equivalent to (18x + 9k) + (2x + 6k)? 16 x + 3 k 20 x + 15 k 20 x + 16 k 36 x + 54 k. Need it soon. Thx!
Answer: 20x + 15k
Step-by-step explanation:
Lose the parentheses and add the like terms. Add 18x and 2x, then add 9k and 6k. That's all there is to it.
The equivalent expression of (18x + 9k) + (2x + 6k) is 20x + 15k.
The correct option is A.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
We have an expression,
(18x + 9k) + (2x + 6k).
To find the equivalent expressions:
Simplifying,
(18x + 9k) + (2x + 6k),
= 20x + 15k
This is the equivalent expression.
Therefore, 20x + 15k is the equivalent expression.
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Why do you have to use the formula a=l×w
Answer:
This formula corresponds to find the area of a rectangle/square. You multiply one side by the other to get the area.
Example: The sides of a rectangle are 6 in and 14 in. Find the area.
A = l * w
A = 6 * 14
A = 84
A carpet installer charges a flat rate of $40, plus $1.50 per square foot for labor. So, the total cost for labor depends on the amount of carpet installed. The relationship between the total cost for labor and the amount of carpet installed is . The domain of the relation is x ≥ . The range of the relation is y ≥ .
Answer:
[tex]x\geq 0[/tex] Domain
y = 40+1.5x relationship
[tex]y \geq 40[/tex] range
Step-by-step explanation:
The domain is the amount of carpet installed. We can install zero carpeting or any positive amount of carpeting.
[tex]x\geq 0[/tex]
Now writing the equation for the cost
They charge 40 flat rate plus 1.50 per square foot
y = 40+1.5x
Let x = 0
y = 40+0
Even if they do not install anything, they still charge 40 dollars flat rate. That is the minimum amount we have to pay. As x increases, the cost will increase.
That is the range, or the values of y
[tex]y \geq 40[/tex]
We want to get the equation for the total cost and its domain and range.
The equation is:
c(x) = $40 + $1.50*x
domain: x > 0ft^2
range: y > $40.
First, let's get the equation.
We know that the carpet installer charges a flat rate of $40 plus $1.50 per square feet.
So if he/she works for x square feets, the cost is:
c(x) = $40 + $1.50*x
This is the cost equation.
Now we want to find the domain and range of this. The domain is given by the possible values of x that we can input in the function. Here we know that x must represent the number of square feet that are worked on, so it only must be a number larger than zero.
x > 0ft^2.
While the range is the set of the possible outputs.
The smallest possible output is the one we get when we evaluate the function in the smallest value of the domain, so we get:
y > $40.
These two define the domain and range.
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How long is AB please explain how you answered
Answer:
AB = [tex]4\sqrt{3}[/tex]
Step-by-step explanation:
30-60-90 theorem, usually x is used to explain but I will use y since x is in your problem, just substitute any variable for y
in a 30 -60 -90 triangle
the length opposite the 30 degrees is y
the length opposite the 60 degrees is y[tex]\sqrt{3}[/tex]
the length opposite the 90 degrees is 2y
since y[tex]\sqrt{3}[/tex] = 6
y = 6/[tex]\sqrt{3}[/tex]
rationalizing the denominator
[tex]\frac{6}{\sqrt{3} } *\frac{\sqrt{3}}{\sqrt{3}}[/tex] = [tex]\frac{6\sqrt{3} }{3} = 2\sqrt{3}[/tex]
if y = [tex]2\sqrt{3}[/tex], 2y = [tex]4\sqrt{3}[/tex]
Samantha and her children went into a grocery store and she bought $7 worth of bananas and peaches. Each banana costs $0.40 and each peach costs $0.50. She bought a total of 15 bananas and peaches altogether. Determine the number of bananas and the number of peaches that Samantha bought.
Answer:
10 peaches and 5 bananas
Step-by-step explanation:
To solve the problem increase the cost by adding more peaches and less by adding more bananas
7 peaches = 3.50
8 bananas = 3.20 + 3.50 = 6.70
We need 30 more cents so add three more peaches
10 peaches = 5
5 x 0.4 = 2
2 + 5 = 7
Final answer:
To determine the number of bananas and peaches Samantha bought, we can set up a system of equations and solve for the variables. By using substitution, we find that Samantha bought 5 bananas and 10 peaches.
Explanation:
To determine the number of bananas and peaches that Samantha bought, we can set up a system of equations. Let x represent the number of bananas and y represent the number of peaches. From the given information, we know the cost of each banana is $0.40 and the cost of each peach is $0.50. We can write two equations to represent the total cost of the bananas and peaches:
$0.40x + $0.50y = $7 (equation 1)
x + y = 15 (equation 2)
To solve this system of equations, we can use substitution or elimination. Let's use substitution:
From equation 2, we know that x = 15 - y. We can substitute this value of x into equation 1:
$0.40(15 - y) + $0.50y = $7
Simplifying the equation, we get:
$6 - $0.40y + $0.50y = $7
Combining like terms, we have:
$0.10y = $1
Dividing both sides by $0.10, we get:
y = 10
So, Samantha bought 10 peaches. Substituting this value of y back into equation 2, we can solve for x:
x + 10 = 15
Subtracting 10 from both sides, we get:
x = 5
Therefore, Samantha bought 5 bananas and 10 peaches.
The perimeter of a rectangle is 15x + 17y
If the length is 7/2x + 7y then find the width of the rectangle.
Answer choices:
A. 4x + 3/2y
B. 8x + 3y
C. 8x + 10y
D. 4x + 3y
The width of the rectangle, given its perimeter and length, is calculated using the formula for the perimeter of a rectangle. By reorganizing the terms and isolating the width, we find that the width is 4x + 3/2y, which is Answer Choice A.
Explanation:The perimeter of a rectangle is given as 15x + 17y. The length is provided as 7/2x + 7y. To find the width, we need to remember that the perimeter of a rectangle is twice the sum of its length and width (P = 2l + 2w). Let's denote the width of the rectangle as 'w'.
So, the equation representing the perimeter is:
15x + 17y = 2(7/2x + 7y) + 2w
Now let's multiply out the factors on the right side:
15x + 17y = 2(7/2x) + 2(7y) + 2w
15x + 17y = 7x + 14y + 2w
To find 'w', we need to move all terms involving 'w' to one side of the equation and all other terms to the other side:
2w = 15x + 17y - (7x + 14y)
2w = 15x - 7x + 17y - 14y
2w = 8x + 3y
Divide throughout by 2 to find 'w':
w = 4x + 3/2y
The width of the rectangle is 4x + 3/2y, which corresponds to Answer Choice A.
Last week Geraldo bought 7 pounds of apples for $5.95. This week apples are the same price, and he buy 4 pounds. How much will he pay?
Answer:
$3.40
Step-by-step explanation:
Final answer:
To determine the cost Geraldo will pay for 4 pounds of apples, we find the cost per pound from his previous purchase and multiply by the desired weight. At $0.85 per pound, Geraldo will pay $3.40 for 4 pounds of apples.
Explanation:
Last week, Geraldo bought 7 pounds of apples for $5.95. To find out how much he will pay for 4 pounds of apples this week at the same price, we first need to calculate the cost per pound of the apples. We do this by dividing the total cost by the total weight in pounds from the previous purchase.
The cost per pound is $5.95 divided by 7 pounds, which equates to approximately $0.85 per pound (rounding to two decimal places).
So, for 4 pounds of apples, Geraldo will pay 4 times $0.85, which results in a total of $3.40.
Therefore, Geraldo will pay $3.40 for 4 pounds of apples.
Find the quotient of 85 and 4find the quotient of 85 and4
Quotient is 21
Step-by-step explanation:
Step 1:
Divide 85 by 4. Using long division method, find the quotient.
21
4|85
8
-------
5
- 4
--------
1
solve the equation : -20=-4x-6x
Answer: 2
Step-by-step explanation:
So first combine like terms, -4x-6x= -10x. Then to isolate x by itself, divide both sides by -10 and get 2=x.
Answer:
x=2
Step-by-step explanation:
-20=-4x-6x
In this kind of question, ensure that you collect like terms especially when they are scattered that is not well arranged...
But the question given is straight forward so there is no need to collect like terms...but to solve directly,
-20=-4x-6x
-20=-10x
Divide both sides by -10
x=2
What is the unit rate 1/2÷$1.25
Answer:
0.4 U.S dollars-4 I guess
Students visited a zoo where they learned that a large white rhinoceros could weigh as much as 6,000 pounds. How many tons is this?
I need dis by 7:00
Answer:
Step-by-step explanation:
Information: 1 ton = 2000 lb
Step one:
Do problem:
6000lb divides by 2000lb.
The answer is 3 tons.
Wayne is 37 years old and has his retirement savings in a
401(k). If he makes $110,000 annually, what is the maximum
percentage of his income that he can contribute to his 401(k)
plan per year?
A. 12%
B. 30%
C. 15%
D. 16.5%
ANSWER: C. 15%
Answer:
15%Step-by-step explanation:
15Answer:
Step-by-step explanation:
Ture or False
The median better represents
the data than the mean.
Answer:
False
Step-by-step explanation:
Which expression is equivalent to 30 divided by (3+x )
The expression 30 divided by (3+x) is already presented in its simplest form which is 30 / (3 + x).
The question which expression is equivalent to 30 divided by (3+x) pertains to the simplification of algebraic expressions, a basic concept in algebra. To solve or simplify this expression directly, it remains 30 / (3 + x), as there is no further simplification that can be done without additional context or constraints on the variable x. In algebra, expressions are simplified or manipulated using algebraic rules, but in this case, the expression is already in its most simplified form unless specific values are provided for x.
The formula for the surface area of a cube is S 5 6x2
where x is the length of one side. Find the length of the
side of a cube with a surface area of 150 square inches.
Which number line best shows how to solve -4-(-8)
Answer:
The first point should be plotted at -4, then there should be a line that goes up 8 units and gives us a final destination of 4.
A farmer uses 1/3 of his land to plant cassava, 2/5 of the remaining and to plant maize and the rest vegetables .if vegetables cover an area of 10acres,what is the total area of the farmers land.
Simplify the expression by combining like terms.
16+8−3+6−9
Answer:
18
Step-by-step explanation:
Step 1: Combine
16 + 8 - 3 + 6 - 9
24 - 3 + 6 - 9
21 + 6 - 9
27 - 9
18
Answer: 18
Answer: 1
Step-by-step explanation:
16+8
23 - 3
2 + 6
8 - 9
1
Tamiko got a check for 109.60 and a small bonus check for 34.15.What is the net result of her transactions using the result from part A.She wants to save 3/5 of this amount.How much will she save?
a) Net result of Tamiko's transactions = $143.75
b) Total amount she can save = $86.25
Step-by-step explanation:
Step 1 :
Given,
Amount Tamiko got in her first check = $109.60
Amount of the bonus check = $34.15
Fraction of the amount she wants to save = [tex]\frac{3}{5}[/tex]
We need to find the net results of her transactions and the amount she will save
Step 2 :
The new result of her transactions can be computed by adding the amount she has received through both the check.
Total amount she received = 109.60 + 34.15 = 143.75
Total amount she can save = [tex]\frac{3}{5}[/tex] × 143.75 = 86.25
Step 3 :
Answer :
a) Net result of Tamiko's transactions = $143.75
b) Total amount she can save = $86.25
Solve.
The answer must be a fraction. Solve by substituting.
Answer: x = -14/5
Step-by-step explanation: We shall begin by expanding the brackets for both sides of the equation
-2/3 (x + 2) = 1/6 (x + 6)
(-2x/3) -4/3 = (x/6) + 1
By collecting like terms we now have
(-2x/3) - (x/6) = 1 + 4/3
(-4x - x)/6 = 7/3
-5x/6 = 7/3
By cross multiplication we now have
-5x (3) = 7 (6)
-15x = 42
x = -(42/15) {simplify further by dividing the RHS by 3}
x = -14/5
Therefore x equals, minus fourteen over five (-14/5)
What is the volume of the pyramid shown, in cubic units? Round to the nearest whole number if necessary.
there are no answer choices. btw
Answer:
1904 units^3
Step-by-step explanation:
multiply all of the sides by each other. 17 X 14 X 8 =
Answer:
the answer is 317
Step-by-step explanation:
I did the test
Angle m and angle n are supplementary angles. If the measure of angle M= 5x+18 and the measure of angle N= 3x+2, find the value of x, and the measure of angle M
Answer:
Step-by-step explanation:
∠ M + ∠N = 180 {supplementary}
5x+18 + 3x + 2 = 180 {Now add the like terms}
8x + 20 = 180
8x = 180 - 20
8x = 160
x = 160/8
x = 20
∠M = 5x + 18 = 5*20 + 18 = 100 + 18 = 118
∠N = 3x + 2 = 3*20 + 2 = 60 + 2 = 62
In a random sample, 3 out of 400 computer chips are defective. How many chips out of 100000 would be defective?
Answer: x =750
Step-by-step explanation:
Well you just make 3 and 400 a fraction 3/400 and 100,000 and the unknown number a fraction x/100,000. Now you do :
3/400=x/100,000
and figure that out :
3/400=x/100,000
3/400=x/100,000
(3)*(100000)=x*(400)
300000=400x
400x=300000
400x/400=300000/400
x=750 is your answer.
3/400=750/100,000.
Hoped I helped!