Answer:
Step-by-step explanation:
The shadow length will be proportional to height
12 / 60 = h / 32
h = 12(32)/60 = 6.4 ft or 6 ft 4.8 inches
Solve the inequality and express your answer in interval notation.
x2 - 12x + 5 <0
Answer:
([tex]6 - \sqrt{31}[/tex], [tex]6 + \sqrt{31}[/tex])
Step-by-step explanation:
[tex]x^{2}-12x+5 < 0[/tex]
To solve this inequality, we can start by completing the square. To do this, we divide the x coefficient (-12) by 2 and then square it. We then add the result to the left side of the equation. To ensure the inequality remains true, we also subtract it.
[tex]x^{2}-12x+(-6^{2})-(-6^{2}) + 5 < 0\\x^{2}-12x+36-36 + 5 < 0\\[/tex]
We can then express the first trinomial as a perfect square.
[tex](x-6)^{2} - 31 < 0[/tex]
Add 31 to both sides:
[tex](x-6)^{2}< 31[/tex]
Then take the square root of both sides:
[tex]x-6<[/tex] ± [tex]\sqrt{31}[/tex]
Finally, add 6 to both sides:
x < 6 + [tex]\sqrt{31}[/tex]
x > 6 - [tex]\sqrt{31}[/tex]
The solution to the inequality in interval notation is shown by option A
What is inequality?
An inequality in mathematics describes how two expressions relate to one another by indicating whether one expression is greater, smaller, equal to, or not equal to the other. Inequalities are denoted by symbols.
We have to use the quadratic formula that states that;
x < (-b ± √([tex]b^2[/tex] - 4ac)) / 2a
So we have that;
x < [12 ± √([tex](-12)^2[/tex] - 4 * 1 * 5)] / 2 * 1
Thus we would obtain in the end;
6 - √31 < x < 6 + √31
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#SPJ3
Anyone able to help with this?
Answer:
20.1°
Step-by-step explanation:
Put the given numbers into the given formula and do the arithmetic.
∆L = 1050/(60·cos(29.5°)) ≈ 20.1°
The change in longitude is about 20.1 degrees.
__
Additional comments
A degree is 60 minutes: 1° = 60', so 30' = 0.5°.
This formula is accurate when the distance units are nautical miles.
find the value of x for which f(x)=4
[tex] \: \: \: [/tex]
[tex]f(x) = 4[/tex]
The domain of a constant function is the set of all real numbers[tex]x = R[/tex]
hope it helps[tex] \: \: \: [/tex]
Find all solutions to below and explain why it must be constant coefficient.
The solution to the differential equation will be expressed as [tex]y_c=Ce^{2x}[/tex]
Given the differential equation;
[tex]\frac{d^2y}{dx^2}+2y \frac{dy}{dx} =0[/tex]
Since the right-hand side of the homogenous equation is zero, the differential equation is a homogenous equation
Let [tex]D=\frac{dy}{dx}[/tex]
The differential equation becomes;
[tex]D^2y-2Dy=0\\(D^2-2D)y=0[/tex]
Factorizing the auxiliary equation m² - 2m = 0
m² = 2m
m = 2
Since the auxiliary solution is real and distinct, the solution to the differential equation will be expressed as [tex]y_c=C_1e^{m_1x} + C_1e^{m_2x} \\[/tex]
Given that m =2, the solution will be expressed as [tex]y_c=Ce^{2x}[/tex]
b) Most linear differential equations have a constant coefficient because they are mostly solved using the quadratic method which is also called the method of quadrature. This means that the solution maybe expressed in integral form.
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PLEASE HELP WITH THIS ONE QUESTION
Answer:
g(x) = x(x-2)^2(x-3) -3
Step-by-step explanation:
the translation from f(x) to g(x) is right 1 down 3.
vertical translations are easier since you just add the amount to everything. so we have f(x) - 3 = (x-1)^2(x-2)(x+1) -3.
for the horizontal translation, we make every x into x-1, so now we have (x-1-1)^2 (x-1-2) (x-1+1) - 3 or (x-2)^2(x-3)x -3
looking at the answers it is g(x) = x(x-2)^2(x-3) -3
A. 48 inches
B. 4 feet
Explain why length A is equivalent to length B. Use your knowledge of converting inches to feet in your answer.
Answer:
As 1 feet = 12 inches
Therefore, 4 feet = 48/12
= 4
Answer = 4 feet
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
URGENT PLEASE
Heron's Formula:
In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square centimeters, of ΔABC.
Question 6 options:
A)
16.541
B)
15.612
C)
14.704
D)
24.708
[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=7.2\\ b=6.7\\ c=4.5\\ s=\frac{7.2+6.7+4.5}{2}\\[0.5em] \qquad 9.2 \end{cases} \\\\\\ A\sqrt{9.2(9.2-7.2)(9.2-6.7)(9.2-4.5)}\implies A=\sqrt{9.2(2)(2.5)(4.7)} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 14.704~\hfill[/tex]
Answer:
The answer is C. 14.704
Step-by-step explanation: I just took the test
Solve for x. x+12√=x√+2
[tex]x = - \frac{2 \sqrt{3} + 12 }{11} [/tex]
hope it helps
see the attachment for explanation
[tex] \: [/tex]
Isosceles triangle has , and a circle with radius is tangent to line at and to line at . What is the area of the circle that passes through vertices , , and
The circle that passes through the vertices of triangle ΔABC (A, B, C) is the
circumscribing circle of triangle ΔABC.
The area of the circle that passes through vertices A, B, and C, is (C) 26·π
Reasons:
The given parameters are;
Side length of isosceles triangle ΔABC; [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex] = 3·√6
Radius of circle tangent to [tex]\overline{AB}[/tex] at B and [tex]\overline{AC}[/tex] at C = 5·√2
Required:
Area of the circle that passes through vertices A, B, and C
Solution:
Angle ∠BAO is given as follows;
[tex]\angle BAO = arctan\left(\dfrac{5 \cdot \sqrt{2} }{3 \cdot \sqrt{6}} \right) = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]
Therefore;
[tex]\angle BOA = 90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]
[tex]\overline{BC} = 2 \times 5 \cdot \sqrt{2} \times sin\left(90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right) = 15\cdot \sqrt{\dfrac{6}{13} }[/tex]
∠ABO' = ∠BAO' (Base angles of isosceles triangle ΔABO')
[tex]\angle BAO' = \angle BAO = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]
Therefore;
[tex]\angle BO'A = 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]
From sine rule, we have;
[tex]\dfrac{\overline{AB}}{sin \left(\angle BO'A \right)} = \mathbf{\dfrac{\overline{BO'}}{sin \left(\angle BAO' \right) \right)}}[/tex]
Which gives;
[tex]\mathbf{\dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)}} = \dfrac{\overline{BO'}}{sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right)}[/tex]
Using a graphing calculator, we get;
[tex]\overline{BO'} = \dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)} \times sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right) = \sqrt{26}[/tex]
The radius of the circumscribing circle [tex]\overline{BO'}[/tex] = √(26)
Therefore, area of the circumscribing circle, [tex]A_{O'}[/tex] = π·(√(26))² = 26·π
The area of the circle that passes through vertices A, B, and C, is (C) 26·π
Learn more here:
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The possible question options obtained from a similar question online are;
(A) 24·π (B) 25·π (C) 26·π (D) 27·π (E) 28·π
what is the definition of fixed percent?
Answer:
the quotient, fixed as a percentage
Step-by-step explanation:
Answer:
Fixed Percentage means, the quotient, expressed as a percentage, obtained by dividing the unexpended and not withdrawn amount of the Allocated Amount, at the time a Net Profits Interest is assigned by the total of (i) the unexpended and not withdrawn amount of the Allocated Amount and (ii) the unexpended and not.
The product of two positive odd consecutive integers is 1599. What is the larger integer?
Answer:
800
Step-by-step explanation:
800+799=1599
Find the odds for and the odds against the event rolling a fair die and getting a 1,a4,a3 or 5
Answer:
Step-by-step explanation:
Assuming we're rolling a cube die with 6 sides.
Odds for rolling any of 1, 4, 3, or 5 has four possible successes
4/6 = 2/3
Odds for NOT rolling any of 1, 4, 3, or 5 has two possible successes, 2 and 6
2/6 = 1/3
1) f(x) = x² + 2x + 1
2) g(x) = x² + 6x + 5
3) h(x) = x² - 12x + 36
4) g(x) = 9x² + 6x + 2
5) g(x) = x² + 6x + 4
Answer:
(X+1)(X+1) (X+5)(X+1)3. (X-6)(X-6)
Find the measure of each interior angle of a polygon having 9 sides
Answer:
Sum of the interior angles = 1260°.
Step-by-step explanation:
Sum of the interior angles = (n - 2)180° where n= number of sides
Sum of the interior angles = (9-2)180
Sum of the interior angles = 1260°
Solve the equation for y. 5x+2Y=9
Answer:
y = 9/2 - 5/2(x)
Step-by-step explanation:
I think this is right
What is the distance between points (8, 3) and (3, 1) on the coordinate plane?
???????????????????? :((
Step-by-step explanation:
1. Not all rational numbers are whole numbers. Whole numbers can be rational numbers, if expressed in fraction form. For example, 1 can be expressed as [tex]\frac{1}{1}[/tex]. A set of rational numbers consists of a set of numbers written as a quotient of two integers, a and b, in the form [tex]\frac{a}{b}[/tex] , where b ≠ 0. The reason why b ≠ 0 because division by zero is an undefined mathematical operation.
2. Irrational numbers differ from rational numbers in terms of its representation: while the rational numbers can be expressed as a ratio or in fraction form, irrational numbers cannot be expressed in fraction form.
Irrational numbers are a set of numbers for which its decimal representations is neither terminating, nor repeating. A couple examples of irrational numbers are: π and [tex]\sqrt{2}[/tex], as their decimal representations do not come to an end and doesn't have a block of repeating digits.
3. All real numbers are rational numbers. Real numbers comprise of natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
Solve: (4x^2-3x+7)-(x^2+8x-5)
Given polynomial:
(4x²-3x+7) - (x²+8x-5)
⇛ 4x²-3x+7-x²-8x+5
⇛ (4x²-x²) +(-3x-8x)+(7+5)
⇛ (4-1)x²+(-3-8)x+12
⇛ 3x²+(-11)x+12
⇛ 3x²-11x+12
(4x²-3x+7) - (x²+8x-5) = 3x²-11x+12Note:-
When subtracting two polynomials,change the symbols of the each term in the second polynomial which is subtracted from the first polynomial.
Read more:
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Answer:
[tex]3x^2-11x+12[/tex]
Step-by-step explanation:
First, distribute the negative:
[tex]4x^2-3x+7-x^2-8x+5[/tex]
Then combine like terms:
[tex]3x^2-11x+12[/tex]
which number is not a member of the solution set of the inequality 4x ≥ 18
A. 4.4
B. 4.5
C. 4.6
D. 4.7
Answer:
4.4
Step-by-step explanation:
4 (4.4) ≥ 18 does not make sense. 4 x 4.4 = 17.6, which is not more than or equal to 18.
Answer:
Step-by-step explanation:
PLEASE HELP WITH THIS ONE QUESTION
Answer:
D. -3
Step-by-step explanation:
g(x) moved 3 units to the right
A game designer is creating a computer animation of a rectangle with sides that vary in size. The length of the rectangle in centimeters after t seconds is given by the expression 2t-9, while the width is given by the expression 1 + t. After how many seconds is the rectangle a square?
Answer:
Step-by-step explanation:
Squares have equal length and widths
2t - 9 = 1 + t
2t - t - 9 + 9 = 1 + 9 + t - t
t = 10 s
3/2 x -1/9
-5/4 divided by 1 3/7
Show your work please
Answer:
3/2 x -1/9= -1/6
-5/4 divided by 1 3/7=-7/8
Step-by-step explanation:
Anyone know the answer to this plz
Answer:
Domain: -10 < x < 10
Range: -2 < y < 8
Step-by-step explanation:
Hope this helps!
Please Help!! I can"t solve this ! Kendrick had 2/3 of an ice cream cake left. Each piece on the ice cream cake is 1/ 12 of the entire cake. How many pieces are left?
Answer:
8
Step-by-step explanation:
is -1/8 greater than -1/10
Answer:
false
Step-by-step explanation:
-1/8 = -0.125
-1/10 = -0.100
as it is negative
-0.125 < -0.1
so it is false
pls help with khan academy
Answer:
c
Step-by-step explanation:
because the rest are just way off
Answer:
The answer is C, bro
Step-by-step explanation:
hope this helped.
The graph below represents the function f(x) and the translated function g(x).
AVA
2x
/g(x)
a
If f(x) = x, which of the following functions could be an algebraic representation of g(x)?
Solve for x:
Yeah can't come in3x+7x=10x
Answer:
#happy learningStep-by-step explanation:
#brainly ph9.091 as a mixed number
Secondary succession occurs following triggers such as logging, mining, wildfires, or
drought. The presence of soil nutrients allows for a faster recovery.
Hardwood trees
Pine trees
Perennials
and
grasses
Shrubs
Answer:7777
Step-by-step explanation: