Answers
[tex]\Delta ADC\ and\ \Delta CDB\ are\ similar\ therefore\\\\\dfrac{y}{4}=\dfrac{9}{y}\ \ \ \ |cross\ multiply\\\\y\cdot y=4\cdot9\\\\y^2=36\to y=\sqrt{36}\to y=6[/tex]
Related Questions
The total price of an article is $7.02, including tax. If the tax rate is 8%, what is the retail price of the article?
Answers
Tax is 8% of article = 0.08x
x+0.08x=7.02
1.08x=7.02
x=7.02/1.08
x=6.5
The retail price is $6.50.
The solution is: The retail price is $6.50.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Here, we have,
given that,
The total price of an article is $7.02, including tax.
If the tax rate is 8%
Lets price of article = x
Tax is 8% of article = 0.08x
so, we get,
x+0.08x=7.02
1.08x=7.02
x=7.02/1.08
x=6.5
The retail price is $6.50.
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What is the value of x? x = 2 x = 3 x = 4 x = 6
Answers
Answer:
The answer is 3
Step-by-step explanation:
The value of x is 3.
The correct option is B.
Use one of your formulas from the figure we can write
x(x+21) = (x+1)(x+1+14)
Now, solving for x we get
x² + 21x = (x+1)(x+15)
x² + 21x = x² + 15x + x + 15
x² + 21x= x² + 16x+ 15
21x = 16x+ 15
21x - 16x = 15
5x= 15
x= 15/5
x= 3
Thus, the value x is 3.
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A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = −16t2 + 32t + 6. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
Answers
We find the maximum by finding the vertex. We first find the axis of symmetry, whose equation is
x = -b/2a
x = -32/2(-16)
x = -32/-32 = 1
This gives us that it reaches the maximum in 1 second.
To find the y-coordinate, the maximum height, we substitute this into the equation:
h(1) = -16(1²)+32(1)+6
h(1) = -16+32+6 = 22
It reaches a height of 22 feet.
The ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.
To find the time at which the ball reaches its maximum height, we can first determine the vertex of the quadratic function [tex]\( h(t) = -16t^2 + 32t + 6 \),[/tex] where t represents time in seconds and h represents height in feet.
The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is given by the formula:
[tex]\[ t_{\text{max}} = \frac{-b}{2a} \][/tex]
For the function [tex]\( h(t) = -16t^2 + 32t + 6 \)[/tex], we have a = -16 and b = 32 . Plugging these values into the formula:
[tex]\[ t_{\text{max}} = \frac{-32}{2(-16)} \]\[ t_{\text{max}} = \frac{-32}{-32} = 1 \][/tex]
So, the ball reaches its maximum height at t = 1 second.
To find the maximum height, we substitute t = 1 into the function h(t) :
[tex]\[ h(1) = -16(1)^2 + 32(1) + 6 \]\[ h(1) = -16 + 32 + 6 \]\[ h(1) = 22 \][/tex]
Therefore, the ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.
A triangular flag has an area of 187.5 square inches. The base of the flag measures 25 inch How tall is the triangular flag?
Answers
Answer:
To find the height, you would do the area divided by the base, or in this case,187.5 / 25 which equals 7.5 inches
Step-by-step explanation:
The next stop on the road trip is the zoo! jacob goes to find his favorite animal, the giraffe. jacob wonders how tall the tallest giraffe at the zoo is. if jacob is 5 feet 6 inches and his shadow at the time is 3 feet long, find the height of the giraffe whose shadow is 5 feet 9 inches at the same time.
Answers
The height of the giraffe whose shadow is 5 feet 9 inches at the same time will be 10 feet and 6.5 inches.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
The next stop on the road trip is the zoo.
Jacob goes to find his favorite animal, the giraffe.
Jacob wonders how tall the tallest giraffe at the zoo is.
If Jacob is 5 feet 6 inches and his shadow at the time is 3 feet long.
Then the height of the giraffe whose shadow is 5 feet 9 inches at the same time will be
Let x be the hieght of the giraffe. Then we have
The ratio will remain constant.
x / 5.75 = 5.5 / 3
x = 10.54
x = 10 feet 6.5 inches
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Guys I need help with this question, I have some marked but i have no idea which ones are the correct ones to begin with...
Answers
The first two are the same, and both are correct.
A vertical directrix means that the parabola is opening around an axis of symmetry that is parallel to the x axis. In this case it is the x axis. The minus sign indicates that it opens left.
Which measure is of an angle that is coterminal with a 425 degree angle
A. 425 degree-(1,000n)degree, for any integer n
B.425 degree-(840n)degree, for any integer n
C. 425 degree+(960n)degree, for any integer n
D. 425 degree+(1,440n)degree, for any integer n
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We know that co terminal angles are those angles which have a difference equal to a multiple of 360 degrees. For example co terminal angle of 45 degrees is 76 degrees because their difference is equal to 720 degrees, which is a multiple of 360.
We have been given an angle 425 degrees.
From the given choices, we need to check if angles being added or subtracted to 425 degrees are multiples of 360 or not.
Let us check each of the options one by one.
(A) The angle being subtracted is [tex]1000n[/tex]. Therefore, we have [tex]\frac{1000n}{360}=2.77n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(B)
The angle being subtracted is [tex]840n[/tex]. Therefore, we have [tex]\frac{840n}{360}=2.33n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(C)
The angle being added is [tex]960n[/tex]. Therefore, we have [tex]\frac{960n}{360}=2.67n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(D)
The angle being added is [tex]1440n[/tex]. Therefore, we have [tex]\frac{1440n}{360}=4n[/tex], which is an integer for all values of n. Therefore, angle given in this option is indeed a co terminate angle to 425 degrees.
Hence, correct answer is option (D).
Box a is by 2 lb lighter than box b and 5 times lighter than box
c. boxes a and c together are 4 times heavier than box
b. find the weight of each box.
Answers
----------------------------------------------------------------------------------------------------
Box A = x
Box B = x+2
Box C = 5x
----------------------------------------------------------------------------------------------------
Now Using The Rest Of The Information Make An Equation Like So.
----------------------------------------------------------------------------------------------------
4(x+2) = 5x + x
4x + 8 = 6x
8 = 2x
x = 4
---------------------------------------------------------------------------------------------
Now Go Back To The Top And Insert x
---------------------------------------------------------------------------------------------
Box A = x = 4
Box B = x+2 = 6
Box C = 5x = 20
Answer:
Box A: 4
Box B: 6
Box C: 20
Step-by-step explanation:
Because 4+2 = 6
4 x 5 = 20
How many combinations with 3 numbers 0-6?
Answers
6x7x7=294
In how many different ways can someone arrange 6 books on a shelf
Answers
Number of ways = 6 x 5 x 4 x 3 x 2 x 1
Number of ways = 720
------------------------------
Answer: 720 ways
------------------------------
6x5x4x3x2x1---- this equals 720.
So, there are 720!
Find g(x), where g(x) is the translation 9 units up of f(x)=x2. write your answer in the form m(x+a)2+b, where m, a, and b are integers.
Answers
Look at the picture.
Answer:
(x+9)^2
Step-by-step explanation:
The combined cost of one advance ticket and one same-day ticket to a show was $50. it is known that 17 advance tickets were sold and 48 same-day tickets were sold, for total receipts of $1842. what was the price of each kind of ticket?
Answers
17 advance + 17 same-day = $50 x 17 = $850
$1842 - $850 = $992
48 - 17 = 31 same-day
31 same-day = $992
1 same-day = $32
1 advance + 1 same-day = $50
1 advance + $32 = $50
1 advance = $50 - $32 = $18
Answer: same day ticket costs $32 and advance-day ticket costs $18.
At bonnie's bagels, you can choose from five different types of bagels, four different spreads, and four different toppings. how many different bagel combinations are possible?
Answers
ABCD is an isosceles trapezoid with legs AB and CD, and base BC. If the length of AB = 6y +5, the length of BC= 4y - 6, and the length of CD= 2y +1, what is the value of y?
Answers
To find the value of y in the given isosceles trapezoid ABCD, we can set up an equation AB = CD and solve for y.
Explanation:To find the value of y in the given isosceles trapezoid ABCD, we can set up the equation AB = CD and solve for y.
Given that AB = 6y + 5 and CD = 2y + 1, we have the equation 6y + 5 = 2y + 1.
Simplifying this equation, we can subtract 2y from both sides to get 4y + 5 = 1.
Finally, subtracting 5 from both sides gives us 4y = -4.
Dividing both sides of the equation by 4, we find that y = -1.
To find the value of y in an isosceles trapezoid ABCD with given side lengths in terms of y, we set the equations for the congruent legs, AB = 6y + 5 and CD = 2y + 1, equal to each other and solve for y, arriving at y = -1.
Explanation:To find the value of y in an isosceles trapezoid where the lengths of the sides are given in terms of y, we can utilize the properties of an isosceles trapezoid. In an isosceles trapezoid, the legs (non-parallel sides) are congruent. Given that AB = 6y + 5 and CD = 2y + 1, and these lengths must be equal for ABCD to be an isosceles trapezoid, we can set up the following equation:
6y + 5 = 2y + 1
Solving for y, we subtract 2y from both sides to get:
4y + 5 = 1
Now, subtract 5 from both sides:
4y = -4
And finally, divide by 4 to find y:
y = -1
Thus, the value of y is -1.
Rearrange the formula to calculate the diameter of a circle.
Answers
a=1/4pid^2
4a=pid^2
4a/pi=d^2
square both sides to get d
Answer: Square root of 4a over pi equals d.
1) Start by multiplying both sides by 4 to get rid of the 4 in the denominator on the right. bringing it to the other side:
[tex]A = \frac{1}{4} \pi d^{2} \\ 4(A) = 4(\frac{1}{4} \pi d^{2} )\\ 4A = \pi d^{2} [/tex]
2) Divide both sides by π to move the π to the other side of the equation (I put the d squared on the left, but you can keep it on the right):
[tex]4A = \pi d^{2} \\ d^{2} = \frac{4A}{ \pi } [/tex]
3) Finally, take the square root of both sides to get the value of d:
[tex]d^{2} = \frac{4A}{ \pi } \\ d = \sqrt{\frac{4A}{ \pi } } [/tex]
-----
Answer: [tex]d = \sqrt{\frac{4A}{ \pi } } [/tex]
a drainage pipe 66 in. tall measures 25.12 in. around.
Using the formula for the volume of a cylinder, what is the volume of the drainage pipe rounded to the nearest hundredth of a cubic inch?
(Pi = 3.14)
Answers
C= 3.14(2r)
25.12=2r divide each by 2
12.56=r
now use this in the volume formula:
V= 12.56^2(3.14)(66)
V=32,692.86 cubic inches
The central angle of a circle is equal in measure to one radian when the corresponding arc length is equal to which of the following? A) The radius of the circle B) Any chord of the circle C) The diameter of the circle D) One-half the circumference of the circle
Answers
L = r*theta
where r is the radius and theta is the central angle in radians (this formula will not work if theta is in degrees)
If the central angle is 1 radian, then theta = 1 and
L = r*theta
L = r*1
L = r
So the arc length is the same as the radius
Answer: Choice A) The radius of the circle
40 POINTS!
Any help would be greatly appreciated!
Answers
Look at the picture.
[tex]x=0\ \vee\ x=\pi\ \vee\ x=\dfrac{3\pi}{2}[/tex]
how do we find the volume ?
Answers
The volume of figure is 877.876 yd³
1. Volume of Cone
= 1/3πr²h
= 1/3 x 3.14 x 2 x 2 x 4
= 16.746
2. Volume of cylinder
= 3.14 x 2 x 2 x 8
= 100.48
3. Volume of Hemisphere
= 2/3πr³
= 7.065
4. Volume of cylinder
= 3.14 x 1.5 x 1.5 x 9
= 63.585
5. Volume of prism
= 1/2 x ( 6 x 6) x 12
= 216
6. Volume of Cuboidal prism
= l w h
= 6 x 6 x 12
= 432
7. Volume of pyramid
= 1/3 x 3 x 2
= 2
8. Volume of cuboidal prism
= 10 x 2 x 2
= 40
So, the volume of figure is
= 16.746 + 100.48 + 7.065 + 63.585 + 216 + 432 + 2 + 40
= 877.876 yd³
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What is the interval for the number of people who are likely to want this restaurant in their city?
Answers
112,483 * 0.24 = 26,996
112,483 * 0.38 = 42,744
Answer: (26996, 42744)
Factor the polynomial: x(5x-8)-2(5x-8)
A. -2x(5x-8)
B. 2x(5x-8)
C. (5x-8)(x-2)
D. (5x-8)(x+2)
Answers
Answer is C. (5x-8)(x-2)
The polynomial x(5x-8)-2(5x-8) is factored by identifying the common factor (5x-8) and simplifying to get (5x-8)(x-2), which corresponds to option C.
The question asks to factor the polynomial: x(5x-8)-2(5x-8). To factor this polynomial, observe that the term (5x-8) is common in both parts of the expression. This allows us to apply the factorization method by taking out the common factor. The steps are as follows:
Identify the common factor in both terms, which is (5x-8).
Factor out the common factor: (5x-8)(x-2).
This simplification shows that the polynomial can be written as the product of (5x-8) and (x-2), matching option C: (5x-8)(x-2).
A cone-shaped hole is drilled into a solid cube of metal as shown. If the cube has sides of length 9 cm, what is the volume of the metal after the hole is drilled? Let π ≈ 3.14 and round your answer to the nearest tenth.
Answers
The volume of the cube after drilling hole is 538.24 cu.m, the correct option is D.
What is a Cube?A three dimensional figure that has all faces of a square, it has total 6 faces of equal length, height and width.
The Side of the cube is 9 cm.
The volume of the metal = Volume of the cube - Volume of cone
Volume of the cube = a³
Volume of cone = πr²h/3
Volume of metal = (9)³ - πr²h/3
The radius of the cone is half of the side length = 9/2 =4.5 cm
The height of the cone is 9 cm
Volume of metal = (9)³ - 3.14 * 4.5 ² * 9 /3
Volume of metal = 538.24 cu. cm
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10PTS!!!!!! UGRENT WILL MARK BRAINLYEST, THANK AND 5 STARS!!
Find the volume of the tank below.
could't inbed the image but it a cylindar 5m tall and has a radius of 2m
96 m3
78 m3
54 m3
63 m3
Answers
Cylinder Volume = PI * 2^2 * 5
Cylinder Volume = 62.8318530718 cubic meters
Correct answer is the last one.
Express each product in the simplest form. 3wx\6x * 3wx\9w
Answers
Answer: xw/6
Anyone know the answer?
Answers
an initial deposit of $200 is made into an account that pays 4.2% annual interest. What is a model to represent the balance in the account after x years?
Answers
A = Original amount = 200
r = interest rate = 0.042 (when converted from percent to decimal)
t = time = x
Plug them in and you get the model: y = 200(1+0.042)^x
or just simplify the parentheses to (1.042)
The model to represent the balance in an account from an initial deposit of $200 at an annual interest of 4.2% is given by the formula A = 200(1.042)^x. Here A is the amount accrued after x years.
Explanation:The subject of the given problem is related to exponential growth as it involves the growth of a principal amount in a bank account accruing annual interest. The model to represent the balance in the account after x years can be described by the formula A = P(1 + r/n)^(nt). Where, A represents the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, t is the time the money is invested for in years.
In this case, P = $200, r = 4.2/100 = 0.042 (converted percentage to decimal), n = 1 (since it is compounded annually), and t = x (number of years). Substituting these values into the formula, we obtain the model: A = 200 (1 + 0.042) ^ (1*x) simplified to, A = 200(1.042)^x. Which is used to represent the balance in the account after x years.
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Need help please ASAP!!
Answers
Good Luck C:
Alexandra rented a costume for $39 per day.
She knows there was a deposit for the costume, but she cannot remember the amount of the deposit.
If she rented the costume for 3 days and paid a total of $167, the deposit must have been $____
Answers
3 days = $39 x 3 = $117
Deposit = $167 - $117 = $50
Answer: Deposit = $50
Answer:
$50
Step-by-step explanation:
because I know :p
Have a good day!
He shorter leg of a 30°-60°-90° triangle is 6. what is the length of the hypotenuse?
Answers
If line segment ab is defined by the endpoints a(4,2) and b(8,6) , write an equation of a line that is the perpendicualr bisector line segment ab
Answers
So the slope of the perpendicular line is -1/1 = -1
This line passes through the midpoint of ab
The midpoint of ab = ( 8+4 / 2 , 2+6 / 2) = (6, 4)
Finding the equation of the perpendicular line:-
y - y1 = -1(x - x1) where x1 = 6 and y1 = 4:-
y - 6 = -1(x - 4)
y = -x + 10 is the answer
An equation of a line that is the perpendicular bisector line segment AB is y=-x+10.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, line segment AB is defined by the endpoints A(4,2) and B(8,6).
Midpoint of line AB is (x, y) =[(x₂+x₁)/2, (y₂+y₁)/2]
= [(8+4)/2, (6+2)/2]
= (6, 4)
Slope of line AB is (y₂-y₁)/(x₂-x₁)
= (6-2)/(8-4)
= 4/4
= 1
The slope of a line perpendicular to given line is m1=-1/m2
So, the slope of a line is -1
Now, substitute m=-1 and (x, y)=(6, 4) in y=mx+c, we get
4=-1(6)+c
c=10
Substitute m=-1 and c=10 in y=mx+c, we get
y=-x+10
Therefore, an equation of a line that is the perpendicular bisector line segment AB is y=-x+10.
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