Answer: D. an angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive x-axis.
D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive [tex]x-[/tex]axis.
A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.
An angle can be defined as the figure formed by two rays meeting at a common end point.
D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive [tex]x-[/tex]axis.
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If two sides of a triangle are 3cm and 5cm in length, which could not be the measure of the third side ?
Answer: c-5 cm, 2 cm, 2 cm.
Gene paid $171 to keep his dog at the kennel for 12 days. What was the unit rate, r, per day to keep the dog at the kennel?
Final answer:
The unit rate, r, per day to keep the dog at the kennel is $14.25.
Explanation:
To find the unit rate, we need to divide the total cost by the number of days. In this case, Gene paid $171 to keep his dog at the kennel for 12 days. So the unit rate, which represents the cost per day, is calculated as:
Unit rate = Total cost / Number of days
Unit rate = $171 / 12
Unit rate = $14.25 per day which is the required answer
Therefore, unit rate to keep the dog at the kennel is $14.25 per day.
a company a company paid $48 for two cases of printer paper each case contains 12 packages of paper next month the company office manager needs a order of 180 packages of the same paper of the same paper if the price per package does not change what would be the total cost of next month order
Answer:
$360
Step-by-step explanation:
So for 2 cases that have 12 packs its $48 which means each case cost $24, so keep that for later now look closely, they need 180 PACKAGES not cases so if there are 12 packages in one case divide 180/12 and you will get 15, so that means you need 15 cases, so take the $24 per case and multiply that by the 15 cases you need and boom...it will cost the company $360 for next months order :)
A person standing close to the edge on top of a 112-foot building throws a ball vertically upward. The quadratic function h ( t ) = − 16t^2 + 96t + 112 models the ball's height about the ground, h ( t ) , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball?
b) How many seconds does it take until the ball hits the ground?
Answer:
the maximum height of the ball= 256 feet
7 seconds
Step-by-step explanation:
The quadratic function h ( t ) = − 16t^2 + 96t + 112 models the ball's height about the ground, h ( t ) , in feet, t seconds after it was thrown.
a= -16 , b= 96 and c= 112
To find maximum height , we find vertex
[tex]x= \frac{-b}{2a}=\frac{-96}{2(-16)}= 3[/tex]
Now plug in 3 for 't' in h(t)
[tex]h(t) = -16t^2 + 96t + 112[/tex]
[tex]h(t) = -16(3)^2 + 96(3)+ 112=256[/tex]
Hence vertex is (3, 256)
the maximum height of the ball= 256 feet
(b) when the ball hits the ground then height becomes 0
so we plug in 0 for h(t) and solve for t
[tex]0 = -16t^2 + 96t + 112[/tex]
Apply quadratic formula
[tex]t=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
Plug in all the values a= -16 , b= 96 and c= 112
[tex]t=\frac{-96+-\sqrt{96^2-4(-16)(112)}}{2(-16)}[/tex]
t= -1 and t= 7
time cannot be negative. So it will take 7 second to hit the ground.
The maximum height of the ball is 160 feet and it takes 4 seconds for the ball to hit the ground.
Explanation:The quadratic function h(t) = -16t^2 + 96t + 112 represents the height of the ball above the ground (h(t)) in feet after t seconds since it was thrown. To find the maximum height of the ball, we need to determine the vertex of the quadratic function. The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula x = -b/2a, where x represents the time and a and b are coefficients in the quadratic equation.
In this case, the coefficient a = -16 and b = 96. Plugging these values into the formula, we get t = -96/(2 * -16) = 3 seconds. Substituting this value into the quadratic function, we find h(t) = -16(3^2) + 96(3) + 112 = 160 feet. Therefore, the maximum height of the ball is 160 feet.
To determine how many seconds it takes until the ball hits the ground, we need to find the time when h(t) = 0. Setting the quadratic equation equal to zero and solving for t, we get -16t^2 + 96t + 112 = 0. This equation can be solved using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula.
Applying the quadratic formula, we have t = (-b ± √(b^2 - 4ac)) / 2a. Plugging in the values of a = -16, b = 96, and c = 112, we get t = (-96 ± √(96^2 - 4(-16)(112))) / (2 * -16). Evaluating this expression, we get two solutions: t = 4 and t = 7. Therefore, the ball takes 4 seconds to reach the ground after being thrown.
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find the value of x.
a) 18
b) 6
c) 15
d) 7
Answer:
b) 6
Step-by-step explanation:
Since this is an isosceles triangle, the two sides are equal and the two angles are equal.
That means
5x-3 = 2x+15
Subtract 2x from each side.
5x-2x-3 = 2x-2x+15
3x-3 = 15
Add 3 to each side.
3x-3+3 = 15+3
3x =18
Divide each side by 3
3x/3 = 18/3
x =6
Answer: the answer to this question is A because the angle is acute angle and when you solve (5x-3) it equals up to 18 when you finish figureing it out.
Step-by-step explanation:
In right △ABC with right angle B, m∠A=(3x−8)° and m∠C=(x−2)°.
What is m∠A?
Question Options:
47°
67°
25°
92
Answer:
<A = 67
Step-by-step explanation:
The three angles of a triangle add up to 180 degrees. We know a right angle is 90 degrees.
<A + <B + <C = 180
3x-8 + 90 + x-2 =180
Combine like terms
4x-10+90 = 180
4x+80 =180
Subtract 80 from each side
4x+80-80=180-80
4x=100
Divide each side by 4
4x/4 = 100/4
x=25
But we want to know <A
<A = 3x-8
Substitute x=25
=3(25) -8
=75-8
= 67
Answer:
67°
Step-by-step explanation:
In a right triangle, the acute angles are complementary. That means that the sum of their measures is 90 deg.
m<A + m<C = 90
3x - 8 + x - 2 = 90
4x - 10 = 90
4x = 100
x = 25
m<A = 3x - 8
m<A = 3(25) - 8
m<A = 75 - 8
m<A = 67
∆ABC is transformed with the center of dilation at the origin.
Pre-image: ∆ABC with vertices A(−3, 4), B(−1, 12), C(4, −2)
Image: ∆A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4), C' (0.8, −0.4)
What is the scale factor of the dilation that maps the pre-image to the image?
Answer:
1/5
Step-by-step explanation:
We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−3, 4), B(−1, 12) and C(4, −2) to the image triangle A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4) and C' (0.8, −0.4).
Center of dilation is at the origin.
To find the scale factor, we will divide the corresponding vertices of the image and pre-image.
A (−3, 4) ---> A' (−0.6, 0.8) = [tex]\frac{-0.6}{-3} , \frac{0.8}{4}=(\frac{1}{5} , \frac{1}{5})[/tex]
B(−1, 12) ---> B' (−0.2, 2.4) = [tex]\frac{-0.2}{-1} , \frac{2.4}{12} = (\frac{1}{5} , \frac{1}{5})[/tex]
C(4, −2) ---> C' (0.8, −0.4) = [tex]\frac{0.8}{4} , \frac{-0.4}{-2} = (\frac{1}{5} , \frac{1}{5})[/tex]
Therefore, the scale factor of the dilation is 1/5.
Homer Simpson finds himself in a panic attempting to meet the April 15th tax deadline. If Homer and his wife have an income of $60,000, earned $1200 in interest, invested $2500 in a tax-deferred savings plan, and have a total of $12,000 in exemptions and deductions, what would be his taxable income
After all the deductions and exemptions, the total taxable income of Homer Simpson is $46,700.
Given that, income of Homer and his wife = $60000 and interest earned = $1200.
In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.
Adding this to total income, we have total taxable amount = 60000+1200 = $61200
Now, investment in tax deferred savings plan = $2500
This amount will be subtracted from total taxable income, so amount becomes = 61200-2500 = $58700
Subtract the exemptions and deductions = $12000
That is, amount becomes = 58700-12000 = $46700
Hence, the net taxable income is $46,700.
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Homer Simpson's taxable income is determined by subtracting his tax-deferred savings and total deductions from his total income. His taxable income comes to $46,700. The percentage of tax he pays depends on the U.S income tax bracket he falls under.
Explanation:To calculate Homer Simpson's taxable income, we need to consider their total income, deductions, and investments. Homer's total income is the sum of his salary, $60,000 and the interest earned, $1200. So, the total income equals $60,000 + $1200 = $61,200.
Next, we subtract the total deductions which include the tax-deferred savings plan and the total deductions and exemptions they have, from the total income. Thus, the taxable income equals $61,200 - $2,500 (savings plan) - $12,000 (deductions and exemptions) = $46,700.
The U.S income tax code is based on a progressive system, so knowing the taxable income can help determine the income tax bracket Homer falls under. Given the figures, Homer's income is in the bracket that is taxed at 22% as per the 2020 basic tax tables from the Internal Revenue Service. However, it is important to take into consideration any changes in tax laws or additional deductions they might have.
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If she completely guesses on all of the questions, what is the probability that she gets two of the four questions correct?
Answer:
D) 0.211
Step-by-step explanation:
The probability of getting a correct answer is 1/4, so the probability of an incorrect answer is 3/4.
The probability of 2 correct and 2 incorrect is (1/4)(1/4)(3/4)(3/4) = 9/256.
There are C(4,2) = 4·3/(2·1) = 6 ways to have some combination of 2 correct and 2 incorrect out of 4 questions. So, the probability of that result is ...
... 6 · 9/256 = 27/128 =0.2109375 ≈ 0.211
The sale tax on the purchase of a refrigerator that cost 695 is 7 percent.What is the amount of sales tax
What is the solution to the equation x+3/x+2=3+1/x
Answer:
x=-1
Step-by-step explanation:
x+3
------- = 3 + 1/x
x+2
Get a common denominator on the right
3*x/x + 1/x
3x/x + 1/x = (3x+1)/x
x+3 3x+1
------- = ---------
x+2 x
We can use cross products to solve
(x+3) *x = (3x+1) * (x+2)
x^2+3x = 3x*x +x + 3x*2 +2
Simplifying
x^2 + 3x = 3x^2 +7x+2
Subtract x^2 from each side
x^2 -x^2 + 3x = 3x^2-x^2 +7x+2
3x = 2x^2 +7x+2
Subtract 3x from each side
3x-3x = 2x^2 +7x -3x+2
0 = 2x^2 +4x +2
Divide by 2
0 = x^2 +2x +1
Factor
0 = (x+1) (x+1)
Using the zero product property
x+1 =0
x=-1
Answer:
The solution set is { -1 }.
Step-by-step explanation:
If we multiply each term by the LCM of x and x+ 2 ( = x(x + 2)) we get:-
x(x + 3) = 3x(x + 2) + x + 2
x^2 + 3x = 3x^2 + 6x + x + 2
0 = 3x^2 - x^2 - 3x + 6x + x + 2
2x^2 +4x + 2 = 0
2(x^2 + 2x + 1) = 0
2( x + 1)(x + 1) = 0
x = -1 Multiplicity 2
The solution set only contains 1 * -1 . Elements in a set are not repeated
So its {-1} (answer)
50 points Hannah is 2 times her sister’s age. The sum of their ages is no more than 18 years.
1) Write an inequality that can be used to represent this situation.
2) Using the inequality you just found, solve it to find the oldest age Hannah's sister can be.
Answer:
Step-by-step explanation:
Let "Hannah" = h, and her sister = s
h = 2s
h + s ≤ 18
Plug in 2s for h in the second equation.
(2s) + s ≤ 18
Simplify
2s + s ≤ 18
3s ≤ 18
Isolate the variable (s). Divide 3 from both sides
(3s)/3 ≤ (18)/3
s ≤ 18/3
s ≤ 6
2) The oldest Hannah's sister can be is 6 years
~
Answer:
12 years old
Step-by-step explanation:
1) 2x+x=18
2) Now solve 2x+x=18
Add alike terms
3x=18
Now divide both sides by 3 (3x/3 and 18/3)
x=6
So Hannah is 6 years old. Her sister must be 12.
Anja divides (8x3 – 36x2 + 54x – 27) by (2x – 3) as shown below. What error does Anja make? 2x-3sqrt 4x^-12x+9/8x-36x^2+54x-27
THE ANSWER IS C
Answer:
c
Step-by-step explanation:
A bag contains 4 green, 3 blue, and 5 yellow marbles. What is the probability of selecting a green marble, replacing it, then selecting a yellow marble?
Answer:
5/36
Step-by-step explanation:
Total number in the universe = 4 + 3 + 5 = 12Probability of selecting a green (first time) = 4/12Probability of selecting a yellow (2nd time) = 5/12P(gr then yellow) = 4/12 * 5/12 = 20 / 144This reduces to 5/36Matt is making a scale model of a building the model is 3.4 feet tall the actual building is 41.848 ft tall.How many times as great is the actual building as the model
41.848/3.4=12.308
The actual building is 12.306 times larger than the model.
I need help please Algebra two
Answer:
Odd
Step-by-step explanation:
The graph intersects the x-axis three times. These three intercepts are the roots of the function and form the factors or solutions for x. They also represent the degree. This is an odd degree because there are 3 roots and 3 is odd. It is at least 3 but could be higher. All odd degree polynomials have the shape of a sideways s.
A pro basketball player has a vertical leap of 3333 in. What is his hang time? (Use V=48T2.)
Answer:
Hang time of the basketball player is 0.83 sec.
Step-by-step explanation:
A pro basketball player has a vertical leap of 33 in.
His hang-time can be calculated by the function given by,
[tex]V=48t^2[/tex]
Where,
V = vertical leap (vertical leap is the act of raising itself in the vertical plane)
t = the time for which the object stays in the air
Putting all the values,
[tex]\Rightarrow 33=48t^2[/tex]
[tex]\Rightarrow t^2=\dfrac{33}{48}[/tex]
[tex]\Rightarrow t=\sqrt{\dfrac{33}{48}}[/tex]
[tex]\Rightarrow t=0.83\ sec[/tex]
Therefore, hang time of the basketball player is 0.83 sec.
Below is a graph of exponential functions label I though VI.
Answer:
option-C
Step-by-step explanation:
We are given
graphs -- I , V , VI have same starting point
it means that it has same initial values
Suppose, we are given exponential function as
[tex]f(x)=a(b)^x[/tex]
Here , 'a' is initial value
we can see that initial value of graph-I is 30
so, all other graphs must also have 30 initial value
so, graphs
[tex]e,\delta , \phi[/tex] have same initial value =30
so, option-C.......Answer
The baseball team sold $1,340 in tickets one Saturday. The number of $12 adult tickets was 15 more than twice the number of $5 child tickets. How many of each were sold?
Final answer:
40 child tickets and 95 adult tickets were sold.
Explanation:
Let's assume the number of child tickets sold is x.
According to the problem, the number of adult tickets sold is 15 more than twice the number of child tickets. So the number of adult tickets sold is 2x + 15.
The total income from ticket sales is $1,340. The income from child tickets is $5 times the number of child tickets and the income from adult tickets is $12 times the number of adult tickets.
Therefore, we can express the total income as the sum of the income from child tickets and adult tickets:
$5x + $12(2x + 15) = $1,340
Simplifying the equation:
$5x + $24x + $180 = $1,340
$29x = $1,340 - $180
$29x = $1,160
Dividing both sides by 29:
x = $1,160/$29
x = 40
So, the number of child tickets sold is 40, and the number of adult tickets sold is 2x + 15 = 2(40) + 15 = 80 + 15 = 95.
Therefore, 40 child tickets and 95 adult tickets were sold.
11) Flowers grow rapidly. A flower is 60 inches tall. Tomorrow it will be 71 inches tall. The next day it will be 82 inches tall, and on the next day it will be 93 inches tall. Write a rule to represent the height of the flower as an arithmetic sequence. How tall will the plant be in 12 days?
Answer:
you add 11 inches each day
Step-by-step explanation:
Which of the following are remote interior angles of one check all that apply?
Answer:
<4 and <3
Step-by-step explanation:
The remote interior angles are the two angles that are inside the triangle and away from the angle adjacent to the exterior angle.
5 is adjacent to 1
so 3 and 4 are the remote interior angles
What is the solution set of the equation 8/q+2= q+4/q-1?
q=4,-1
you need to isolate q
The solution set of the equation is {-4, 2}
Given expression:
[tex]\frac{8}{q} +2=\frac{q+4}{q-1}[/tex]
Solve for q: simplify
[tex]\frac{8}{q} +2=\frac{q+4}{q-1}\\\frac{8+2q}{q}=\frac{q+4}{q-1}\\(8+2q)(q-1)=(q(q+4)\\8q-8+2q^{2} -2q=q^{2} +4q\\2q^{2} +6q-8 =q^{2}+4q\\q^{2} +2q-8=0[/tex]
Factorize the quadratic equation to solve q
[tex]q^{2} +4q-2q-8=0\\q(q+4)-2(q+4)=0\\(q+4)=0, (q-2)=0\\q= -4, 2[/tex]
Therefore, The solution set of the equation is {-4, 2}
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The selling price of an item is ?$ 440 440. It is marked down by 20?%, but this sale price is still marked up from the cost of ?$ 320 . Find the markup from cost to sale price.
To find the markup from cost to sale price, calculate the original sale price by dividing the selling price by (1 - discount percentage) which is 230
Explanation:To find the markup from cost to sale price, we first need to calculate the cost price.
The item is marked down by 20% from the selling price of $440.
So, the original sale price before the discount would be $440 / (1 - 0.20) = $550.
Since the sale price is still marked up from the cost of $320, we can calculate the markup as:
$550 - $320 = $230.
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In triangle ABC, m<A=80, m<B=50, AB=4x-4, AC=2x+16, BC=5x+4. Find BC
Answer:
BC - 54 units
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
∠C = 180° - (∠A + ∠B) = 180° - (80 + 50)° = 180° - 130° = 50°
Since ∠B = ∠C = 50° then the base angles of the triangle are equal hence the triangle is isosceles with
AB = AC, that is
4x - 4 = 2x + 16 ( subtract 2x from both sides )
2x - 4 = 16 ( add 4 to both sides )
2x = 20 ( divide both sides by 2 )
x = 10
⇒ BC = 5x + 4 = (5 × 10) + 4 = 50 + 4 = 54
ahhhh please help! T.T
Answer: 70
=====================================
Explanation:
The exterior angles (2x+12) and (2x) have corresponding interior angles 180-(2x+12) and 180-(2x)
Triangle ABC has the following interior angles
A = 112
B = 180 - 2x
C = 180 - (2x+12) = 180-2x-12 = 168-2x
Add up the interior angles for A,B,C and set the result equal to 180. Solve for x
A+B+C = 180
(112)+(180-2x)+(168-2x) = 180
112+180-2x+168-2x = 180
460-4x = 180
-4x = 180-460
-4x = -280
x = -280/(-4)
x = 70
---------------
Side note:
2x = 2*70 = 140 is the exterior angle for B, so 180-140 = 40 is the interior angle for angle B
2x+12 = 2*70+12 = 152 is the exterior angle for C, so 180 - 152 = 28 is the interior angle for C
Add up the interior angles to find that A+B+C = 112+40+28 = 180, so this helps confirm we have the right x value.
Find all the zeros of the equation
-3x^4+27^2+1200=0
if you could show yourworkthat would be great :3
Divide both sides by -3, and replace [tex]x^2[/tex] with [tex]y[/tex]. Then
[tex]-3x^4+27x^2+1200=0\iff y^2-9y-400=0[/tex]
Factorize the quadratic in [tex]y[/tex] to get
[tex]y^2-9y-400=(y+16)(y-25)=0\implies y=-16,y=25[/tex]
which in turn means
[tex]x^2=-16,x^2=25[/tex]
But [tex]x^2\ge0[/tex] for all real [tex]x[/tex], so we can ignore the first solution. This leaves us with
[tex]x^2=25\implies x=\pm\sqrt{25}=\pm5[/tex]
If we allow for any complex solution, then we can continue with the solution we ignored:
[tex]x^2=-16\implies x=\pm\sqrt{-16}=\pm i\sqrt{16}=\pm4i[/tex]
The numbers 4, 5, 6, and 7 are on a spinner. You spin the spinner twice. Which calculation proves that landing on an even number for the first spin and the second spin are independent events?
Answer:
As long as the numbers are in equal proportion on the spinner, the probabilty of landing on an even number for the first and second spin is 1/4, or 25%.
Step-by-step explanation:
If there are four numbers on a spinner, all in equal proportion, than the probability of getting an even number (either 4 or 6) on any spin is 2/4, or 1/2, which is also 50%. Since the results of the first spin do not influence the results of the second spin, then they are independent events. So, if the likelihood of landing on even each time is 1/2, then we would mutliply 1/2 by 1/2 in order to find the probability that landing on an even number would happen in both spins. Our result would be 1/4, or 25%.
Not sure what that dude is even saying. The answer is C- P(A and B)=2/4*2/4
Hope this helped.
A six-sided number cube labeled from 1 to 6 is rolled. What is the probability of getting a multiple of 2 or a multiple of 3?
Answer:
2/3
Step-by-step explanation:
A six-sided number cube labeled from 1 to 6 is rolled.
Total outcomes = 1,2,3,4,5,6= 6 outcomes
multiple of 2 are 2,4,6 so 3 outcomes
multiple of 3 are 3,6 so 2 outcomes
multiply of 2 or 3 are 2,4,3,6 so 4 outcomes
the probability of getting a multiple of 2 or a multiple of 3
= possible outcomes / total outcomes
= 4/6
now reduce the fraction, divide by 2 on both sides
the probability of getting a multiple of 2 or a multiple of 3 = 2/3
Tthe probability of rolling a multiple of 2 or a multiple of 3 on a six-sided die is [tex]\(\frac{5}{6}\)[/tex].
To find the probability of getting a multiple of 2 or a multiple of 3 when rolling a six-sided number cube, we can list out the possible outcomes and identify which ones satisfy our conditions.
The possible outcomes when rolling six-sided die are: 1, 2, 3, 4, 5, and 6:
Multiples of 2 on the die are: 2, 4, 6.
Multiples of 3 on the die are: 3, 6.
We can see that there is an overlap with the number 6, which is both a multiple of 2 and a multiple of 3. To avoid counting this outcome twice, we use the principle of inclusion-exclusion.
First, we add the number of multiples of 2 to the number of multiples of 3
- There are 3 multiples of 2.
- There are 2 multiples of 3.
So, without considering the overlap, we would have [tex]\(3 + 2 = 5\)[/tex] favorable outcomes.
However, since the number 6 has been counted twice, we subtract one instance of it from our total:
[tex]\(5 - 1 = 4\) unique favorable outcomes (2, 3, 4, 6)[/tex]
Since there are 6 possible outcomes in total when rolling a six-sided die, the probability of rolling a multiple of 2 or a multiple of 3 is the number of favorable outcomes divided by the total number of possible outcomes [tex]\(\frac{4}{6}\)[/tex].
This fraction simplifies to [tex]\(\frac{2}{3}\)[/tex]. However, we have overlooked the fact that every number on a six-sided die is a multiple of 1, and since 1 is neither a multiple of 2 nor of 3, it does not contribute to favorable outcomes. Therefore, the only outcome that is not a multiple of 2 or 3 is number 1.
Thus, the correct probability is [tex]\(1 - \frac{1}{6} = \frac{5}{6}\)[/tex], since there is only 1 unfavorable outcome out of 6 possible outcomes.
In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, AE=x2−16 , and CE=6x .
What is AC ?
Enter your answer in the box.
_______units
Answer:
AC is 96 units
Mario is setting up a new tent during a camping trip. The tent came with 7 feet of rope. The instructions are to use 34.5 inches of rope to tie a tarp on top of the tent. Then the remaining rope should be cut into 8 1/4 inches sections to tie a tent to states in the ground. Mario will use all the rope as instructed. Determine the number of 8 1/4 inch sections of rope mario can cut from the rope.
Answer: There are 6 sections of [tex]8\frac{1}{4}\ inches[/tex] of rope Mario can cut from the rope .
Step-by-step explanation:
Since we have given that
Length of the rope for the tent = 7 feet
As we know that
[tex]1\ feet=12\ inches\\\\7\ feet=12\times 7=84\ inches[/tex]
Length of rope is used to tie a tarp on top of the tent = 34.5 inches
Remaining length of rope is given by
[tex]84-34.5=49.5\ inches[/tex]
According to question, the remaining rope should be cut into
[tex]8\frac{1}{4}\ inches\\\\=\frac{33}{4}\ inches[/tex]
So, Number of [tex]8\frac{1}{4}\ inches[/tex] sections of rope Mario can cut from the rope is given by
[tex]\frac{49.5}{8\frac{1}{4}}\\\\=\frac{49.5}{\frac{33}{4}}\\\\=\frac{49.5\times 4}{33}\\\\=6[/tex]
Hence, there are 6 sections of [tex]8\frac{1}{4}\ inches[/tex] rope Mario can cut from the rope .
Answer:
6
Step-by-step explanation:
Mario has 7 feet of rope. Since there are 12 inches in every foot, this means he has
7(12) = 84 inches of rope.
34.5 inches of the rope must be used to tie the tarp to the top; this leaves Mario with
84-34.5 = 49.5
This remaining rope will be cut into 8 1/4 inch sections. We can also write 8 1/4 as 8.25. To find the number of sections this length he can cut, we divide:
49.5/8.25 = 6
He can cut 6 sections this length.