Step-by-step explanation:
we have a rectangle, that is then cut in half diagonally into 2 right-angled triangles.
in our problem it does not matter which side is the larger and which is the shorter one, because the distance calculation for both cases involve one short and one long side. the sequence does not matter.
Mary walks one short and one large side to get to the opposite corner (from D to F) :
264 + 900 = 1,164 ft
Kate walks diagonally. and that diagonal is the Hypotenuse of the right-angled triangle with a short and a long side of the rectangle.
so, Pythagoras applies :
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), and a and b are the legs.
in our case that means
diagonal² = 264² + 900² = 69,696 + 810,000 =
= 879,696
diagonal = sqrt(879,696) = 937.9211054... ft ≈ 938 ft
so, Kate walked
1,164 - 938 = 226 ft
less than Mary.
what is 687/4 equal to
Answer: 171.75
Step-by-step explanation:
a basic operation of arithmeticwhere numbers are broken up into equal parts687 will need to be split evenly into 4 groups[tex]687/4 = 171.75[/tex]
Answer:
To find the result we have to divide, in a fraction the numerator is always divided by the denominator and the final result is 171.75
---
Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
Question 3 Now change the central angle, ∠CAB, and see how it affects the inscribed angle, ∠CDB. To do this, move point B around the circle without crossing points D and C, and do the same for point C without crossing points B and D. Record five data sets for m∠BAC and m∠BDC in the table.
ANSWER FAST!
By changing the central angle, ∠CAB, the inscribed angle, ∠CDB has the following data sets:
m∠BAC (β) m∠BDC (α)
42° 84°
40° 80°
45° 90°
35° 70°
52° 104°
What is a circle?A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
In Geometry, a circle is considered to be a conic section which is formed by a plane intersecting a double-napped cone that is perpendicular to a fixed point (central axis) because it forms an angle of 90° with the central axis.
What is the inscribed angle theorem?The inscribed angle theorem states that the measure of an inscribed angle is one-half the measure of the intercepted arc in a circle. Thus, this is given by this mathematical expression:
m∠BDC = ½ × m∠BAC.
For this exercise, we would change the central angle, ∠CAB, so that the inscribed angle, ∠CDB can have the following data sets:
m∠BAC (β) m∠BDC (α)
42° 84°
40° 80°
45° 90°
35° 70°
52° 104°
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Answer:
plato
Step-by-step explanation:
m∠BAC m∠BDC
50° 25°
70° 35°
90° 45°
125° 62.5°
150° 75°
will give brainliest
The possible rational roots of the given equation are 1 and -3
Solving polynomial equationsFrom the question, we are to determine all the possible rational roots of the given equation
The given equation is
x⁴ -2x³ -6x² +22x -15 = 0
To determine the rational roots, we will test for values that make the equation equal to zero
Test for -1(-1)⁴ -2(-1)³ -6(-1)² +22(-1) -15
1 + 2 - 6 - 22 -15
= -40
∴ -1 is not a root of the equation
Test for 1(1)⁴ -2(1)³ -6(1)² +22(1) -15
1 - 2 - 6 + 22 -15
= 0
∴ 1 is one of the roots of the equation
Test for -2(-2)⁴ -2(-2)³ -6(-2)² +22(-2) -15
16 + 16 - 24 - 44 -15
= -51
∴ -2 is not a root of the equation
Test for 2(2)⁴ -2(2)³ -6(2)² +22(2) -15
16 - 16 - 24 + 44 -15
= 5
∴ 2 is not a root of the equation
Test for -3(-3)⁴ -2(-3)³ -6(-3)² +22(-3) -15
81 + 54 - 54 -66 -15
= 0
∴ -3 is one of the roots of the equation
Test for 3(3)⁴ -2(3)³ -6(3)² +22(3) -15
81 - 54 - 54 + 66 -15
= 24
∴ 3 is not a root of the equation
The other roots of the equation are irrational roots.
Hence, the possible rational roots of the given equation are 1 and -3
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Which pair of angles are vertical angles? AngleWRU and AngleSRT AngleWRS and AngleVRT AngleVRU and AngleTRS AngleVRT and AngleSRT
Step-by-step explanation:
important of festival in nepali languages for class seven
Answer:
b
Step-by-step explanation:
Find the value of x
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
x = 35°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:4x + 1 + x + 4 = 180[/tex]
[ by linear pair ]
[tex]\qquad❖ \: \sf \:5x + 5 = 180[/tex]
[tex]\qquad❖ \: \sf \:5(x + 1) = 180[/tex]
[tex]\qquad❖ \: \sf \:x + 1 = 180 \div 5[/tex]
[tex]\qquad❖ \: \sf \:x + 1 = 36[/tex]
[tex]\qquad❖ \: \sf \:x = 36 - 1[/tex]
[tex]\qquad❖ \: \sf \:x = 35[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
x = 35°5. Compound Interest - Single Payment: $5000 was invested at 5.2%, compounded semi-annually, for 3 years. What was the investment worth at its maturity? (3)
Answer:
78000
Step-by-step explanation:
5000/1 times 52/10 times 3)1
E4.2 Simplify the following using suitable properties (a) 109x 50
109×50
100×50+9×50=5000+450
5450
Answer:
5450
Step-by-step explanation:
You can just use a caculater to get the answer.
Pls help answer this before 8pm
Answer:
Step-by-step explanation:
16 + 12 + 5 + 3 = 36
16 prefer email, 36 total students surveyed
16:36 / 4 = 4:9
4 out of 9 students prefer email
4:9 x 680 = 302.222
302 students can be expected to prefer email.
Fill in the blank with the correct response.
Twenty-one is 20% of
Answer: 105
Step-by-step explanation:
105 * .2 = 21 :)
216 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.
Answer:
The no. of student failed is 36.
Step-by-step explanation:
Given, the number of student enrolled= 216
Let us suppose number of student failed = x
Given,
no. of student passed is 5 times no. of student failed.
Then, no. of student passed = 5x
x +5x = 216
6x = 216
x = 216/6
x = 36
Thus, the no. of student failed is 36.
Study the spinner below. If wedges 2 and 5 are each twice the area of one of
the other wedges, what is the likelihood of landing on 2 or 3?
Using the probability concept, the likelihood of landing on 2 or 3 is given by:
[tex]p = \frac{3}{8}[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, considering the areas of 2 and 5 counting twice, the spinner has 8 areas, out of which 3 are 2 or 3, hence the probability is given as follows:
[tex]p = \frac{3}{8}[/tex]
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please help :,)
(geometry involving arc lengths)
Answer:
bx/a (3rd choice)
Step-by-step explanation:
The length of an arc, s, in a circle of radius r, and central angle Θ given in radians is
s = rΘ
Circle M has radius a. The central angle in radians of the sector is Θ. The length of the arc is x.
x = aΘ
Solve for Θ:
Θ = x/a Eq. 1
Circle N has radius b. The central angle in radians of the sector is Θ. The length of the arc is s.
s = bΘ
Solve for Θ:
Θ = s/b Eq. 2
Since Θ = Θ, then equate the right sides of Equations 1 and 2 above.
x/a = s/b
Multiply both sides by ab.
abx/a = abs/b
bx = as
as = bx
s = bx/a
Answer: bx/a
Assume that a sample is used to estimate a population proportion p. Find the 95% confidence for a sample of size 246 with 52% successes. Enter your answer as an open -interval using decimals
Using the z-distribution, the 95% confidence interval for the proportion is given as follows:
(0.4576, 0.5824).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The other parameters for the interval are given as follows:
[tex]n = 246, \pi = 0.52[/tex].
The lower and upper bound of the interval, respectively, are given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 - 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.4576[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 + 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.5824[/tex]
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I need help with the question
Answer:
B
Step-by-step explanation:
Comment
√15 = 3.87
√12 = 3.46 Subtract these 2
Difference = 0.41
f(x) = x². What is g(x)?
5
g(x)
A. g(x)=x²-4
OB. g(x)=x2-4
C. g(x)=-4x2²
OD. g(x)=x²+4
+
f(x)=x²
The function f(x) = x² then the required function exists g(x) = -x²- 4.
What is a function?The function exists described as y = f(x).
In mathematics, a function from a set X to a set Y allocates to each element of X exactly one element of Y. The set X exists named the domain of the function and the set Y exists named the codomain of the function. Functions stood originally for the idealization of how a variable quantity relies on another quantity.
For every x there exists a certain value of y.
From the graph g(x) exists reflection of f(x) at y = -4.
So g(x) = -f(x) - 4, the negative sign for reflection.
g(x) = -x² - 4
The required function exists g(x) = -x² - 4.
Therefore, the correct answer is option D. g(x) = -x² - 4.
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The complete question is:
F(x) = x². What is g(x)?
A. g(x) = x² - 4
B. g(x) = x² + 4
C. g(x) = -4x²
D. g(x) = -x² - 4
PLEASE HELP!!!!! ASAP
The absolute value equation that satisfies the solution set shown on the number line is given by:
|x| = 1/2
What is the absolute value function?The absolute value function is defined by:
[tex]|x| = x, x \geq 0[/tex]
[tex]|x| = -x, x < 0[/tex]
It measures the distance from a point x to the origin at x = 0. In this problem, the solution set has a distance to the origin of [tex]\frac{1}{2}[/tex], as |-0.5 - 0| = |0.5 - 0| = 0.5, hence the equation is:
|x| = 1/2
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David signed up to provide snacks for his daughter and her school group's camping trip. He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days. He also wanted to buy some boxes of fruit snacks, which were $4 each. He just needed to decide how many to buy, and then figure the total cost.
Select the expression that will help him to determine the total cost.
The expression that will help him to determine the total cost is as follows:
y = 60 + 4x
How to construct an expression?He signed up to provide snacks for his daughter and her school group's camping trip.
He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days.
He also wanted to buy some boxes of fruit snacks, which were $4 each.
The number to buy and the total cost can be expressed as follows:
let
y = total cost
x = number of boxes of fruit juice.
Therefore, the expression that will help him to determine the total cost is as follows:
y = 60 + 4x
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how to find h’(3)
base on the graph
By the quotient rule for differentiation,
[tex]\displaystyle h'(x) = \dfrac{g(x)f'(x) - f(x)g'(x)}{g(x)^2}[/tex]
According to the plots of [tex]f[/tex] and [tex]g[/tex], we have [tex]f(3)=2[/tex] and [tex]g(3)=3[/tex].
On the interval [2, 4], [tex]f[/tex] is a line through the points (2, 5) and (4, -1), and hence has slope (-1 - 5)/(4 - 2) = -3, so [tex]f'(3)=-3[/tex]. We can similarly find [tex]g'(3)=2[/tex].
Then
[tex]h'(3) = \dfrac{3\cdot(-3)-2\cdot2}{3^2} = \boxed{-\dfrac{13}9}[/tex]
2. What is the solution for the system of equations?
16x - 32y = 27
8x - 16 = 16y
a) Use the linear combination (elimination) method to solve the system of equations.
b) What does the solution tell you about the two lines of the system?
Answer:
no solution
Step-by-step explanation:
16x - 32y = 27 → (1)
8x - 16 = 16y ( subtract 16y from both sides )
8x - 16 - 16y = 0 ( add 16 to both sides )
8x - 16y = 16 → (2)
multiply (2) by - 2 and add to (1)
- 16x + 32y = - 32 → (3)
add (1) and (3) term by term
0 + 0 = - 5
0 = - 5 ← not possible
this indicates the system has no solution
(b)
the solution to a system is the point of intersection of the 2 lines
since there is no solution, no point of intersection, then
this indicates the lines are parallel and never intersect
Answer:
a) no solution
b) the two lines never intersect
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases} 16x-32y=27\\8x-16=16y \end{cases}[/tex]
Part (a)To solve by linear combination (elimination):
Step 1
Write both equations in standard form: Ax + By = C
[tex]\implies 16x-32y=27[/tex]
[tex]\implies 8x-16y=16[/tex]
Step 2
Multiply one (or both) of the equations by a suitable number so that both equations have the same coefficient for one of the variables:
[tex]\implies 16x-32y=27[/tex]
[tex]\implies 2(8x-16y=16) \implies 16x-32y=32[/tex]
Step 3
Subtract one of the equations from the other to eliminate one of the variables:
[tex]\begin{array}{l r l}& 16x-32y & = 32\\- & 16x-32y & = 27\\\cline{1-3}& 0 & =\:\: 5\end{array}[/tex]
Therefore, as 0 ≠ 5, there is no solution to this system of equations.
Part (b)
The solution to a system of equations is the point(s) of intersection.
As there is no solution to the given system of equations, this tells us that the two lines never intersect.
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If f ( x ) = 3x 2 - 6x + 2 and g ( x ) = 2x 2 + 2x - 11,
then find f ( x ) + g ( x ).
Answer:
[tex]5x^{2} -4x-9[/tex]
Step-by-step explanation:
f(x)+g(x)
[tex](3x^{2} -6x+2) + (2x^{2} +2x-11)\\3x^{2} -6x+2 + 2x^{2} +2x-11\\[/tex]
combine like terms --
[tex]5x^{2} -4x-9[/tex]
The sum of the given two functions f(x) = 3x² -6x + 2 and g(x) = 2x²+ 2x -1 is: f(x) + g(x) = 5x² - 4x - 9
Given that:
Functions, f ( x ) = 3x² - 6x + 2
And g ( x ) = 2x² + 2x - 11.
Then find f ( x ) + g ( x ).
To find the sum of two functions, f(x) + g(x), simply add the corresponding terms together.
To find f(x) + g(x), add the coefficients of the corresponding terms:
f(x) + g(x) = (3x² + 2x²) + (-6x + 2x) + (2 - 11)
Now, combine like terms:
f(x) + g(x) = 5x² - 4x - 9
So, the sum of the two functions is:
f(x) + g(x) = 5x² - 4x - 9
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Simplify.
x to the 4 power x z to the 5 power over xz to the 6 power
The expression which represents the simplified form of the given expression; x to the 4 power x z to the 5 power over xz to the 6 power as in the task content is; 1/x²z.
What expression represents the simplified form of the given expression?According to the task content, it follows that the given expression in the task content is; x⁴z⁵/(xz)⁶.
Hence, the expression can be simplified by means of the laws of indices as follows;
x^(4-6) z^(5-6)
= x-²z-¹
= 1/x²z.
Ultimately, the expression which represents the simplified form of the given expression; x to the 4 power x z to the 5 power over xz to the 6 power as in the task content is; 1/x²z.
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Rhombus BCDE is shown below. Give the coordinates of C and D.
The coordinates of C - (2n, 0) and the coordinates of D - (n, -p). The diagonals of a rhombus are perpendicular and bisect each other.
What are the properties of a rhombus?The properties of a rhombus are:
All the sides of a rhombus are congruent and equalOpposite sides are parallelOpposite angles are equalThe adjacent angles add up to 180°Diagonals perpendicularly bisect each otherDiagonals bisect opposite anglesCalculation:The given rhombus BCDE has B(n, p) and E(0, 0).
Since the diagonals of a rhombus are perpendicular bisectors,
EO = OC or BO = OD
Where O is the midpoint of EC and BD.
In the given diagram, points B and D are opposite each other. They are reflecting each other over the x-axis.
So, if B has coordinates (n, p) then its reflection over the x-axis is (x, -y) i.e., (n, -p).
Thus, we have B(n, p), D(n, -p), and E(0, 0)
Consider the coordinates of C as (x, y).
The midpoint of BD = ([tex]\frac{n+n}{2}[/tex], [tex]\frac{p-p}{2}[/tex])
⇒ coordinates of O = (n, 0)
So,
The midpoint of EC = ([tex]\frac{0+x}{2}[/tex], [tex]\frac{0+y}{2}[/tex])
⇒ coordinates of O = (x/2, y/2)
⇒ (n, 0) = (x/2, y/2)
∴ x = 2n and y = 0
Then, the coordinates of C are (2n, o)
Therefore, the required coordinates of the given rhombus are C(2n, 0) and D(n, -p).
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Which expression shows the factored form of 49x² - y²?
Step-by-step explanation:
49x^2-y^2=(7x)^2-(y)^2
=(7x+y) (7x-y)
Therefore, a^2-b^3
=(a+b) (a-b)
what is 4.685 in expanded form
Answer:
4*1/1000+6*100+8*10+5*1
Step-by-step explanation:
Because of stormy weather a pilot flying at 35,000 ft descends 8,000 ft.
What is his new altitude
Answer:
35,000 - 8000=27,000 altitude
please help!!!
Using long division, what is the quotient of this expression?
3x42x³-x-4
x²+2
OA. 3x²
3x - 4
OB. 3x² + 2x + x² + 2
O C.
3x² 2x
O D.
-
2x
3x² + 2x
- 6 +
-
- 5+
-
3x + 8
x² + 2
-
3x+6
x²+2
5x8
x² + 2
Rese
Check the picture below.
notice, the dividend and divisor must be in descending order, and when one of the variables is "missing", is really not missing, it simply has a coefficient of 0.
Here is the solution process:
3 x² - 2 x - 6
x² + 0x + 2 | 3 x⁴ - 2 x³ + 0 x² - x - 4
3 x⁴ + 0 x³ + 6 x²
- 2 x³ - 6 x² - x - 4
- 2 x³ + 0 x² - 4 x
- 6 x² + 3 x - 4
- 6 x² + 0 x - 12
3 x + 8
Long division:
Standard: [tex]\sf{3x^{2} -2x-6+\dfrac{3x+8}{x^{2} +2} \ \ \to \ \ \ Option \ "A" }[/tex]Quotient: 3x² - 2x - 6Rest: 8 + 3xTherefore, the correct option is "A".
Suppose that $17,699 is invested at an interest rate of 6.6% per year, compounded continuously
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
[tex]s(t) = 17699(1 .066) {}^{t} [/tex]
b)[tex]s(1) = 17699(1.066) = 18867.13 \\ s(2) = 17699(1.066) {}^{2} = 20112.36 \\ s(5) = 17699(1.066) {}^{5} = 24363.22 \\ s(10) = 17699(1.066) {}^{10} = 33536.73[/tex]
c)[tex]s(t) = 2 \times initial \: capital \: \\ s(t) = 2 \times 17699[/tex]
[tex]17699(1.066) {}^{t} = 2 (17699) \\ 1.066 {}^{t} = 2 \\ t = log¹°⁰⁶⁶(2) = 10.84511 \: years[/tex]
if 6m of a uniform iron rod weighs 21 kg what will be the weight of 16 m of the same rod?
Answer:
56kg
Step-by-step explanation:
If 6m of a rod is 21 kg, then 21/6 will give us the weight of 1m of the rod. 21/6 = 3.5 kg
16*3.5 = 56 kg
cos 90 - 2sin45 + 2tan180
Answer:
- [tex]\sqrt{2}[/tex]
Step-by-step explanation:
cos90° - 2sin45° + 2tan180°
= 0 - ( 2 × [tex]\frac{\sqrt{2} }{2}[/tex] ) + 2(0)
= 0 - [tex]\sqrt{2}[/tex] + 0
= - [tex]\sqrt{2}[/tex]
can I return notebooks to target?
Answer: yes, as long as you haven't used them. :)
Step-by-step explanation: