Answer:
12 ft - 2 ft = 10 ft
The rope is 10 feet long.
10 · cos 30° = 10 · √3 / 2 = 8.66 ft
x = 12 - 8.66 = 3.34 ft
Answer:
A ) 3.34 feet
7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0
Answer:
x = 2, - 4
Step-by-step explanation:
The factors of 8 are:
1, 8
2, 4
You can combine 2 and 4 to create 2.
( x - 2 ) ( x + 4 ) = 0
0 can either be x - 2 or x + 4
Therefore, x = 2 or - 4
Hey there!
Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0
Answer :x = -4 or x = 2 ✅
Explanation :Quadratic formula : ax² + bx + c = 0 where a ≠ 0
The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :
If b² - 4ac > 0 , There are 2 real-number solutionsIf b² - 4ac = 0 , There is 1 real-number solution.If b² - 4ac < 0 , There is no real-number solution.The roots of the equation are determined by the following calculation:
[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
Here, we have :
a = 1b = 2c = -81) Calculate the discriminant :
b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36
b² - 4ac = 36 > 0 ; The equation admits two real-number solutions
2) Calculate the roots of the equation:
▪️ (1)
[tex]x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}[/tex]
▪️ (2)
[tex]x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}[/tex]
>> Therefore, your answers are x = -4 or x = 2.
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pls help find the lateral surface area of this prism in square centimeters, i give brainliest!! :)
Answer:
1232 square meters
Step-by-step explanation:
The lateral surface area are all the rectangles.
1st rectangle:
A = lw
A = 25(22)
A = 550
2nd rectangle:
A= lw
A = 7(22)
A = 154
3rd rectangle:
A = lw
A = 24(22)
A = 528
Add the areas together.
550 + 154 + 528 = 1232
please help! the questions are in the photo.
The diameter of a circle is 16 centimeters. How would you calculate the area?
A. TT. 82 cm.
B. 28 cm.
C. TT 162 cm.2
D. 2. T. 16 cm.
factor 6x(x + 12) – 15(x + 12)
ac/b−(a+d) if a=−2 , b=3 , c=−12 , and d=−4 .
Answer:
the answer is 14 hopes this helps
Step-by-step explanation:
Ac/b=?
-2(-12)=24/3
24/3=8
8-(a+d)=?
8-(-2(+-)4)=?
8-(-2-4)=?
8+2+4=?
10+4=?
14
The equation 6 = 2x2 – 11x has two solutions, p and q, with p being greater than q.
What is the value of p – q?
[tex]~~~~~~6=2x^2 -11x\\\\\implies 2x^2 -11x -6 = 0\\\\\implies 2x^2 -12x +x-6=0\\\\\implies 2x(x-6) +(x-6) = 0\\\\\implies (2x+1)(x-6) = 0\\\\\implies x = -\dfrac 12,~~ x= 6\\\\\text{Since }~p > q,}~~ p =6~ \text{and}~ q = -\dfrac 12\\ \\\text{So,}~ p-q = 6 -\left(- \dfrac 12 \right)\\\\~~~~~~~~~~~~~=6+\dfrac 12 \\\\~~~~~~~~~~~~~=\dfrac{13}2\\\\~~~~~~~~~~~~~=6.5[/tex]
The value of p -q is 6.5.
How to find the roots of a quadratic equation?Suppose that the given quadratic equation is
ax^2 + bx + c = 0
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The equation 6 = 2x^2 - 11x has two solutions, p and q, with p being greater than q.
[tex]6 = 2x^2 - 11x \\\\ 2x^2 - 11x - 6 = 0\\\\ 2x^2 - 12x + x- 6 = 0\\[/tex]
(2x + 1) (x-6) = 0
Thus, x = -1/2 , 6
Since p>q
p = 6 , q = -1/2
So, p -q = 6 - (-1/2)
= 6 + 1/2
= 13/2
= 6.5
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How is the graph of the parent function y=x² transformed to produce the graph of y=3(x+1)²?
O It is translated 1 unit right and compressed vertically by a factor of 3.
OIt is translated 1 unit left and compressed vertically by a factor of 3.
O It is translated 1 unit right and stretched vertically by a factor of 3.
OIt is translated 1 unit left and stretched vertically by a factor of 3.
The graph of the parent function y = x² transformed to produce the graph of y = 3(x+1)². It is translated 1 unit left and stretched vertically by a factor of 3.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
The graph of the parent function y = x² transformed to produce the graph of y = 3(x+1)²
We need to find how the parent function transformed to produce the graph of y = 3(x+1)².
The parent graph is shifted 1 unit towards the left by the rule of transformation.
[tex]f(x) = f(x+1)[/tex]
By applying this rule then,
[tex]y(x) = f(x+1)^2[/tex]
Now, the parent function stretched vertically 3 times the previous graph by the rule
[tex]f(x) = 3f(x)[/tex]
Apply this rule then, we get
[tex]y(x) = 3(x+1)^2[/tex]
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A fair coin is flipped 120 times. Estimate the expected number of ‘heads’.
Answer:
76.47
How I did it(using a specific range)
(n, 54, 66 (120 C)) 2¹²⁰ = 0.76 × 100 ≈ 76.47
Tickets to the play cost $5.00 for adults and $3.00 for kids. The play sold 20 tickets for a total of $76. How many kids and adults attended the play?
The number of adults =16 and the number of kids =4
Paul went to a blackjack table at the casino. at the table, the dealer has just shuffled a standard
deck of 52 cards.
paul has had good luck at blackjack in the past, and he actually got three blackjacks with kings in a
row the last time he played. because of this lucky run, paul thinks that kings are the luckiest card.
the dealer deals the first card to him. in a split second, he can see that it is a black card, but he is
unsure if it is a king.
what is the probability of the card being a king, given that it is a black card? answer choices are
in a percentage format, rounded to the nearest whole number.
Using it's concept, it is found that there is a 8% probability of the card being a king, given that it is a black card.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In a standard deck, there are 26 black cards, of which 2 are kings, hence the probability is given by:
p = 2/26 = 0.0769 = 7.69%.
Rounded to the nearest whole number, 8% probability of the card being a king, given that it is a black card.
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The catalog is advertising a stack of these cups that is 95 cm tall. Lori says, “That must be a misprint because a stack of that height is not possible.”
Do you agree or disagree with Lori? Explain your reasoning.
Answer:
in particular, the relationship between height of stack and number of cups yields a non-whole number of cups, corresponding to a height of 95 cm. In this context, that is not possible because we do not allow for parts of cups.
Step-by-step explanation:
It is possible for a stack of cups to be 95 cm tall depends on the size and shape of the cups and how they are stacked.
What is Area of Rectangle?The area of Rectangle is length times of width.
Assuming the cups are all the same size and shape, the height of the stack would depend on the number of cups in the stack.
if each cup is 5 cm tall, a stack of 19 cups would be 95 cm tall (19 x 5 = 95).
If the cups are irregularly shaped or have varying sizes, it may be more difficult to stack them in a way that reaches 95 cm in height.
It is possible for a stack of cups to be 95 cm tall depends on the size and shape of the cups and how they are stacked.
It is possible for some stacks of cups to reach this height, but not necessarily all stacks of cups.
Hence, it is possible for a stack of cups to be 95 cm tall depends on the size and shape of the cups and how they are stacked.
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Evan places a rectangular birdbath in his garden. The dimensions are 24, 8, and 11
2
in. Explain how to find the maximum amount of water the birdbath can hold. Then find the amount.
The maximum amount of water the birdbath can hold is 288 cubic in which is the volume of the cuboid.
What is a cuboid?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
We have a rectangular birdbath in his garden. The dimensions are 24, 8, and [tex]1\dfrac{1}{2}[/tex] inches
The maximum amount of water in the birdbath = volume of the birdbath
[tex]\rm = 24 \times 8 \times 1\dfrac{1}{2}[/tex]
[tex]\rm = 24 \times 8 \times \dfrac{3}{2}[/tex]
= 288 cubic in
Thus, the maximum amount of water the birdbath can hold is 288 cubic in which is the volume of the cuboid.
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A circle is placed in a square with a side length of 4 yards as shown below find the area of the shaded region use the value 3.14 for π and do not round your answer be sure to include the correct unit in your answer
Answer:
If the circle touches all 4 sides, the diameter is 2 so the area us 3.14(4) = 12.56.
16 - 12.56 = your answer
Mark brainliest if I am right pls
A marathon swim follows a triangular course marked with three buoys, A, B, and C. The distance from buoy A to B is 400 meters, B to C is 500 meters, and C to A is 600 meters. What is the smallest angle the swimmers must turn between the buoys
By applying the law of cosine, the smallest angle which the swimmers must turn between the buoys is 41.4°.
How to determine the smallest angle?In order to determine the smallest angle which the swimmers must turn between the buoys, we would apply the law of cosine.
Given the following data:
Side AB = c = 400 meters.Side BC = a = 500 meters.Side CA = b = 600 meters.
Form the law of cosine, we have:
[tex]CosC =\frac{a^2 + b^2 - c^2}{2ab} \\\\CosC =\frac{500^2 + 600^2 - 400^2}{2 \times 500 \times 600}\\\\CosC =\frac{450000}{600000}\\\\C = cos^{-1} 0.75\\\\[/tex]
C = 41.4°.
For angle B, we have:
[tex]CosB =\frac{a^2 + c^2 - b^2}{2ac} \\\\CosB =\frac{500^2 + 400^2 - 600^2}{2 \times 500 \times 400}\\\\CosB =\frac{1}{8}\\\\B = cos^{-1} 0.125\\\\[/tex]
B = 82.8°.
For angle A, we have:
[tex]CosA =\frac{b^2 + c^2 - a^2}{2bc} \\\\CosA =\frac{600^2 + 400^2 - 500^2}{2 \times 600 \times 400}\\\\CosA =\frac{9}{16}\\\\A = cos^{-1} 0.5625\\\\[/tex]
A = 55.8°.
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For what real values of $c$ is $4x^2 + 14x + c$ the square of a binomial?
Only for c = 49 the given expression is the square of a binomial.
For which values of c is the given expression the square of a binomial?We want to find the values of c such that:
[tex]4x^2 + 14x + c[/tex]
Is the square of a binomial.
Remember that:
[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
Now we can rewrite our expression as:
[tex](2x)^2 + 2*7*x + c[/tex]
If you compare that with the general binomial expansion, we can see:
[tex]a = 2x[/tex]
[tex]b = 7[/tex]
Then c must be equal to 7 squared:
[tex]7^2 = 49 = c[/tex]
Only for c = 49 the given expression is the square of a binomial.
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please help me solve this
Answer:
It's 5/30 Seniors. As a fraction, it would be 16.7 % of the seniors take the bus. Hope this helps!!!!!
Answer:
5/35=1/7=0.14
Step-by-step explanation:
35 in total for Senior
5 take bus
5/35=1/7
The midpoint of overline AB is M(4, -5). If the coordinates of A are (6, -4)what are the coordinates of B?
Img attached
[tex]\huge\mathfrak\colorbox{white}{}[/tex]
5. Which theorem justifies the statement in No. 4?
A. Exterior Angle Inequality theorem B. Triangle Inequality Theorem 1(Ss-Aa)
C. Triangle Inequality Theorem 2(Aa-Ss)
D. Triangle Inequality Theorem 3(S₁ + S₂ > S3)
Answer:
D
Step-by-step explanation :
Three trains are made of identical train cars, so each car has the same number of seats. The first train has 418 seats, the second train has 456 seats, and the third train has 494 seats. How many cars are in each train if no train has more than 25 seats
If no train has more than 25 seats. Then the number of cars in the first, second, and third train will be 17, 18, and 20 respectively.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Three trains are made of identical train cars, so each car has the same number of seats.
The first train has 418 seats, the second train has 456 seats, and the third train has 494 seats.
If no train has more than 25 seats.
Then the number of the cars on each train will be
Let x, y, and z be the number of the cars in the first, second, and third train.
Then we have
x = 418 / 25
x = 16.75
x ≅ 17
y = 456 / 25
y = 18.24
y ≅ 18
z = 294 / 25
z = 19.76
z ≅ 20
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Answer:
11 cars in the 1st train, 12 cars in the 2nd train and 13 cars in the 3rd train
Step-by-step explanation:
There is a difference of 38 between the numbers 418, 456 and 494.
[tex]418/38=11\\456/38=12\\494/38=13[/tex]
Trust me, this is 100% the correct answer!
hope this helps!
factor the expression using the gcf 25+50
Answer:
25(1+2)
Step-by-step explanation:
25 goes into 25 once and 50 twice.
The circle graph shows the results of a survey by a bakery on which of their new products 71 customers preferred most. How many customers preferred cake? Round your answer to the nearest whole number. show work and explain to your best ability please and thank you.
Answer:
25 customers
Explanation:
To find the number of people preferred cake, multiply the percentage by total customers.
People who preferred cake:
⇒ 35% × 71
⇒ 24.85
⇒ 25 (rounded to nearest whole number)
The guidance department conducted a random survey of the student body and found that 16% of the students plan to volunteer at the school festival. Predict how many volunteer positions they should plan for a population of 950 students.
Answer:
152
Step-by-step explanation:
950 x 16% simple as that
3 If f(x) = x2 and g(x) = x + 6, find g(f(0)). A. -6 B. 6 C. 12 D. 36
Answer:
6
Step-by-step explanation:
g(f(0)) means that the input of f(x) is 0 and this value of f(x) found is the input of g(x). This is known as composite functions.
Let's find the value of f(0).
f(x)= x²
f(0)= 0²
f(0)= 0
Now, we can find the value of g(f(0)).
g(x)= x +6
g(f(0))
= g(0)
= 0 +6
= 6
somebody please help me?
The events A and B are independent events, and the values of P(A) and P(B) are 7/12 and 1/2, respectively
The value of P(A)The event A is given as:
A : Sum greater than 6
In the sample space of a roll of two dice, there are 21 outcomes that are greater than 6, out of a total of 36 outcomes
This means that:
P(A) = 21/36
Simplify
P(A) = 7/12
The value of P(B)The event B is given as:
B : Sum is divisible by 2
In the sample space of a roll of two dice, there are 18 outcomes that are divisible by 2, out of a total of 36 outcomes
This means that:
P(B) = 18/36
Simplify
P(B) = 1/2
Hence, the probability values of P(A) and P(B) are 7/12 and 1/2, respectively
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The polar equation r = 8 cos (30) graphs as a rose.
What is the length of the petals of the rose?
The length of the petals of the rose is 8 units
How to determine the length of the petals?The polar equation is given as:
r = 8 cos(30)
The amplitude of the above equation is:
A = 8
This is the same as the length of the petals
i.e.
Length = 8
Hence, the length of the petals of the rose is 8 units
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Factor
Please help me I will mark as brainliest
Answer:
hope this will help you
Step-by-step explanation:
[tex]b { }^{2} - 81 = 0 \\ b {}^{2} = 81 \\ b = \sqrt{81} \\ b = 9[/tex]
Answer: Heyaa! :D
Your Answer Is... 9
Step-by-step explanation:
Since both terms are perfect squares, factor using the difference of squares formula,
a²−b²=(a + b)(a − b) where a = B and
b = 9.
(B + 9)(B − 9)
-
I
The shaded area shows a patio that Rudy built. He covered the shaded area with square tiles.
1 tile = 1 square foot
What is the area of the patio?
O A. 15 square feet
O B. 18 square feet
OC. 21 square feet
OD. 25 square feet
Answer:In the diagram, there are 28 tiles. You can do that with easy multiplication or just counting. Each square length is 1.5 feet, or 18 inches. You get that by multiplying 12 by 1.5. The area of a square is 324 inches, found by multiplying 18 by 18. Divide 324 by the area of a tile, 36 (6*6), to get 9. There are 9 tiles in each square. Multiply 9 by 28 to get... 252
Step-by-step explanation:
Find the length of the third side. If necessary, write in simplest radical form.
2741
8
Answer:
10
Step-by-step explanation:
Let the missing side be 'x'.
Using Pythagorean Theorem, we can find the missing side.
x² + 8² = (2√41)²x² + 64 = 4(41)x² + 64 = 164x² = 100x = 10Quick please!!
Tell whether a triangle with the given side lengths is a right triangle.
14 cm, 23 cm, and 25 cm