Answer:
0.971
Step-by-step explanation:
Given the expression (cos (arctan √3/7)) which all lies in the first quadrant. Note that all the trigonometry identities (sin, cos and tan) are all positive in the first quadrant.
From the expression given
(cos (arctan √3/7)), we need to get the expression in parenthesis first.
Let y = (cos (arctan √3/7))
If u = arctan √3/7
Then y = cos(u) .... 1
Let's get the value of u first
u = arctan √3/7
u = arctan(0.2474)
u = 13.896°
Substituting u = 13.896° into equation 1, we will have;
y = cos(u)
y = cos13.896°
y = 0.971.
Hence the expression (cos(arctan√3/7)) is equivalent to 0.971
Answer:
y = 0.971.
Step-by-step explanation:
Given the expression (cos (arctan √3/7)) which all lies in the first quadrant. Note that all the trigonometry identities (sin, cos and tan) are all positive in the first quadrant.
From the expression given
(cos (arctan √3/7)), we need to get the expression in parenthesis first.
Let y = (cos (arctan √3/7))
If u = arctan √3/7
Then y = cos(u) .... 1
Let's get the value of u first
u = arctan √3/7
u = arctan(0.2474)
u = 13.896°
Substituting u = 13.896° into equation 1, we will have;
y = cos(u)
y = cos13.896°
y = 0.971.
Ami buys x apples and y bananas. The apples cost 15p each and the bananas cost 20p each. The total cost of Ami's apples and bananas is £1.80. a Write an equation for the total cost of Ami's apples and bananas.
Answer:
0.15x + 0.20y = 1.80
Step-by-step explanation:
Here, we are interested in writing an equation for the total cost of the apples and bananas
before we write , kindly understand that 100p = £1
So the cost of apple which is 15p will be 15/100 =£ 0.15
The cost of bananas which is 20p will be 20/100 = £0.2
Thus, the total cost of the apples bought will be number of apples bought * price of apple bought = 0.15 * x = £0.15x
The cost of bananas = number of bananas bought * price of bananas = 0.2 * y = £0.2y
So the total cost of the apples and bananas will be;
0.15x + 0.20y = 1.80
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each figure with the number of edges it has.
Answer:
Rectangular pyramid 8 edges
Rectangular prism 12 edges
Triangular Prism 9 edges
Triangular Pyramid 6 edges
Step-by-step explanation: Faces connected at edges
Rectangular pyramid 1 Base and 4 slanted triangular sides
Rectangular prism 2 top and bottom bases and 4 sides
Triangular Prism 2 top and bottom triangular bases 3 rectangular sides
Triangular Pyramid 1 triangular base, 3 slanted triangular sides
The matching is as follow:
Rectangular pyramid: 8 edges
Rectangular prism: 12 edges
Triangular Prism: 9 edges
Triangular Pyramid: 6 edges
What is Pyramid and Prism?A pyramid is a triangular-sided, single-polygonal base, three-dimensional polyhedron-shaped construction. A prism is a three-dimensional polyhedron with rectangular sides that are perpendicular to the base and two polygonal bases.
Rectangular pyramid have one Base and 4 slanted triangular sides
Rectangular prism have 2 top and bottom bases and 4 sides
Triangular Prism have 2 top and bottom triangular bases 3 rectangular sides.
Triangular Pyramid have 1 triangular base, 3 slanted triangular sides.
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Given $m\geq 2$, denote by $b^{-1}$ the inverse of $b\pmod{m}$. That is, $b^{-1}$ is the residue for which $bb^{-1}\equiv 1\pmod{m}$. Sadie wonders if $(a+b)^{-1}$ is always congruent to $a^{-1}+b^{-1}$ (modulo $m$). She tries the example $a=2$, $b=3$, and $m=7$. Let $L$ be the residue of $(2+3)^{-1}\pmod{7}$, and let $R$ be the residue of $2^{-1}+3^{-1}\pmod{7}$, where $L$ and $R$ are integers from $0$ to $6$ (inclusive). Find $L-R$.
[tex](2+3)^{-1}\equiv5^{-1}\pmod7[/tex] is the number L such that
[tex]5L\equiv1\pmod7[/tex]
Consider the first 7 multiples of 5:
5, 10, 15, 20, 25, 30, 35
Taken mod 7, these are equivalent to
5, 3, 1, 6, 4, 2, 0
This tells us that 3 is the inverse of 5 mod 7, so L = 3.
Similarly, compute the inverses modulo 7 of 2 and 3:
[tex]2a\equiv1\pmod7\implies a\equiv4\pmod7[/tex]
since 2*4 = 8, whose residue is 1 mod 7;
[tex]3b\equiv1\pmod7\implies b\equiv5\pmod7[/tex]
which we got for free by finding the inverse of 5 earlier. So
[tex]2^{-1}+3^{-1}\equiv4+5\equiv9\equiv2\pmod7[/tex]
and so R = 2.
Then L - R = 1.
What is the x-intercept of the line 4x - 3y = 16?
What is the x-intercept of the line 10x - 5y = 40?
What is the x-intercept of the line y = -3x - 9?
Answer:
1.
[tex](x , y) = (4 ,\: 0)[/tex]
2.
[tex](4,0) = (x,y)[/tex]
3.
[tex](x,y) = ( - 3,0)[/tex]
I hope it helps :)
Given the function, f (x) = sq3x+3+3, choose the correct transformation.
Answer:
B.
Step-by-step explanation:
First, let's start from the parent function. The parent function is:
[tex]f(x)=\sqrt{x}[/tex]
The possible transformations are so:
[tex]f(x)=a\sqrt{bx-c} +d[/tex],
where a is the vertical stretch, b is the horizontal stretch, c is the horizontal shift and d is the vertical shift.
From the given equation, we can see that a=1 (so no change), b=3, c=-3 (negative 3), and d=3.
Thus, this is a horizontal stretch by a factor of 3, a shift of 3 to the left (because it's negative), and a vertical shift of 3 upwards (because it's positive).
If f(x) = 2x2 - 5 and g(x) = x2 - 4x - 8, find (f - g)(x).
O A. (f- g)(x) = x2 - 4x - 3
O B. (f- g)(x) = x2 + 4x + 3
O C. (f- g)(x) = 3x2 - 4x - 13
O D. (f - g)(x) = -x2 - 13
The value of (f - g)(x) is x² + 4x + 3 if f(x) = 2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
f(x) = 2x² - 5
g(x) = x² - 4x - 8
(f - g)(x) = f(x) - g(x)
= (2x² - 5) - (x² - 4x - 8)
= 2x² - 5 - x² + 4x + 8
= x² + 4x + 3
(f - g)(x) = x² + 4x + 3
Thus, the value of (f - g)(x) is x² + 4x + 3 if f(x) = 2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.
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Which equation is perpendicular to y= 3/4x + 4 and passes through the point (0,2)
A. Y= 3/4x + 2
B. Y= -3/4x + 2
C. Y= -4/3x + 2
D. Y= 4/3x + 2
Determine the parent function.
Answer:
y= [tex]\sqrt{x}[/tex]
Step-by-step explanation:
2. A vertical stick 10 cm long casts a shadow 8 cm long. At the same time a tower casts a
shadow 30 m long. Determine the height of the tower.
Answer:
The height of the tower is:
24 meters
Step-by-step explanation:
1 meter = 100 centimeters
10 centimeters = 10/100 = 0.1 meters
8 centimeters = 8/100 = 0.08 meters
On a three rule:
0.1 meters is to 0.08 meters
30 meters is to A meters
A = 30*0.08/0.1
A = 24 meters
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combine like terms: 3p2q2-3p2q3+4p2q3-3p2q2+pq PLEASE HELP!!! ASAP!!!
Answer:
p²q³ + pq and pq(pq² + 1)
Step-by-step explanation:
Given
3p²q² - 3p²q³ +4p²q³ -3p²q² + pq
Required
Collect like terms
We start by rewriting the expression
3p²q² - 3p²q³ +4p²q³ -3p²q² + pq
Collect like terms
3p²q² -3p²q² - 3p²q³ +4p²q³ + pq
Group like terms
(3p²q² -3p²q²) - (3p²q³ - 4p²q³ ) + pq
Perform arithmetic operations on like terms
(0) - (-p²q³) + pq
- (-p²q³) + pq
Open bracket
p²q³ + pq
The answer can be further simplified
Factorize p²q³ + pq
pq(pq² + 1)
Hence, 3p²q² - 3p²q³ +4p²q³ -3p²q² + pq is equivalent to p²q³ + pq and pq(pq² + 1)
¡Ayuda!
1. Método del Triángulo: Una embarcación navega a una distancia de 800 km hacia el Oeste y después avanza 1400 km a 135 °. ¿Cuál es la magnitud, dirección y sentido del desplazamiento resultante? R /. 2,080 km, 155 ° NO.
Answer:
La magnitud del desplazamiento resultante es 2045.463 kilómetros. La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.
Step-by-step explanation:
En primer lugar, se construye el triángulo. La figura resultante se encuentra incluida como archivo adjunto. La magnitud del desplazamiento resultante se determina mediante la Ley del Coseno:
[tex]r = \sqrt{(800\,km)^{2}+(1400\,km)^{2}-2\cdot (800\,km)\cdot (1400\,km)\cdot \cos 135^{\circ}}[/tex]
[tex]r \approx 2045.463\,km[/tex]
La magnitud del desplazamiento resultante es 2045.463 kilómetros.
La dirección del desplazamiento resultante es hallada por medio de la Ley del Seno, sabiendo que el ángulo del desplazamiento resultante a la recta de 1400 kilómetros:
[tex]\frac{1400\,km}{\sin \alpha} = \frac{2045.463\,km}{\sin 135^{\circ}}[/tex]
Se despeja el ángulo correspondiente:
[tex]\alpha = \sin^{-1}\left(\frac{1400\,km}{2045.463\,km}\times \sin 135^{\circ} \right)[/tex]
[tex]\alpha \approx 28.945^{\circ}[/tex]
La dirección absoluta del desplazamiento resultante es:
[tex]\alpha' = 180^{\circ}-\alpha[/tex]
[tex]\alpha' = 180^{\circ}-28.945^{\circ}[/tex]
[tex]\alpha' = 151.055^{\circ}[/tex]
La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.
Martin sent 3 emails on Wednesday 9 emails on Tuesday 27 emails on Friday 81 emails on Saturday 243 emails on Sunday. If the pattern continues how many emails will Martin sent on Monday...
Answer:
729 emails
Step-by-step explanation:
The pattern is to multiply by 3
3*3 = 9
9*3 = 27
27*3 = 81
81*3 = 243
If the pattern continues, Martin will sent on monday:
243*3 = 729
729 emails
Answer:
729
Step-by-step explanation:
Plz help urgently i dont know how to do it
Answer:
11
Step-by-step explanation:
1650/15/10 = 11
So the polynomial 24r squared represents the surface are of a cube a : determine the polynomial that represents the area of one face of the cube b: use this answer to determine a polynomial that represents the length of an edge of the cube c: what is the length of an edge of the cube when r = 3 cm
Answer:
a. 4r² b. 2r c. 6 cm
Step-by-step explanation:
The surface area A of the cube is A = 24r². We know that the surface area, A of a cube also equals A = 6L² where L is the length of its side.
Now, equating both expressions, 6L² = 24r²
dividing both sides by 6, we have
6L²/6 = 24r²/6
L² = 4r². Since the area of one face is L², the polynomial that determines the area of one face is A' = 4r².
b. Since L² = 4r² the rea of one face of the cube, taking square roots of both sides, we have
√L² = √4r²
L = 2r
So, the polynomial that represents the length of an edge of the cube is L = 2r
c. The length of an edge of the cube is L = 2r. When r = 3 cm.
L = 2r = 2 × 3 cm = 6 cm
So, the length of an edge of the cube is 6 cm.
find the 10th term of the following sequences T(2)=20 and the term-to-term rule is subtract 6
==================================================
Work Shown:
T(2) = 20 means the second term is 20
T(1) = 26 because we go backwards from what the rule says (subtract 6) to step back one term. Going forward, 26-6 = 20.
Since a = 26 is the first term and d = -6 is the common difference, the nth term is
T(n) = a + d*(n-1)
T(n) = 26 + (-6)(n-1)
T(n) = 26 - 6n + 6
T(n) = -6n + 32
Plugging n = 1 into the equation above leads to T(1) = 26. Using n = 2 leads to T(2) = 20.
Plug in n = 10 to find the tenth term
T(n) = -6n + 32
T(10) = -6(10) + 32
T(10) = -60+32
T(10) = -28
Answer:
-28.
Step-by-step explanation:
T(1) = 20 + 6 = 26.
This is an arithmetic series with:
nth term T(n) = 26 - 6(n - 1).
So T(10) = 26 - 6(10-1)
= 26 -54
= -28.
the shape of a piece is pallelogram whose adjacent side are 12m and 9 m and the corresponding diagonal is 15 .find the area of land
Answer: The area of land =108 m²
Step-by-step explanation:
In the given piece of land is in the shape of a parallelogram.
Diagonals divide it into 2 equal parts.
So, area of parallelogram = 2 x (Area of triangle with sides 12m and 9 m and 15 m)
Heron's formula :
Area of triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\dfrac{a+b+c}{2}[/tex]
Let a= 12 , b= 9 and c = 15
[tex]s=\dfrac{12+9+15}{2}=18[/tex]
Area of triangle = [tex]\sqrt{18(18-12)(18-9)(18-15)}[/tex]
[tex]=\sqrt{18\times6\times9\times3}=\sqrt{2916}=54\ m^2[/tex]
Then, area of parallelogram= 2 x 54 = 108 m²
Hence, the area of land =108 m²
Convert 125 degrees into radians. (NEED ASAP)
Answer:
[tex]\boxed{\frac{25\pi }{36}}[/tex]
Step-by-step explanation:
Use the formula to convert from degrees to radians: [tex]x * \frac{\pi }{180}[/tex], where x is the value in degrees.
[tex]125 * \frac{\pi }{180}[/tex] = [tex]\frac{125\pi }{180}[/tex]
Then, simplify your fraction ⇒ [tex]\frac{125\pi }{180} = \boxed{\frac{25\pi}{36} }[/tex]
Solve and CHECK the following: 2(a−3)/3=4
Answer:
2(a - 3). = 4
_______
3
Cross multiply.
2(a- 3) = 12
2a - 6 = 12
2a = 12 + 6
2a = 18
a = 18 ÷ 2
a = 9
Answer:
a = 9
Step-by-step explanation:
Given
[tex]\frac{2(a-3)}{3}[/tex] = 4 ( multiply both sides by 3 to clear the fraction
2(a - 3) = 12 ( divide both sides by 2 )
a - 3 = 6 ( add 3 to both sides )
a = 9
As a check substitute a = 9 into the left side of the equation and if equal to the right side then it is the solution.
[tex]\frac{2(9-3)}{3}[/tex] = [tex]\frac{2(6)}{3}[/tex] = [tex]\frac{12}{3}[/tex] = 4 = right side
Thus solution is a = 9
The Free Food Club holds weekly meetings. In chronological order, they've ordered 12, 9, 11, 10, 13, 8, 7, and 13 pizzas over the last two months. What is the median number of pizzas that they ordered?
NEED ASAP
Answer:
10.375
Step-by-step explanation:
1.) Add up all the amount of pizzas | 12 + 9 + 11 +10+13+8+ 7,+ 13=83
2) Divide the total amount of pizzas by the amount of pizzas/amount of numbers of pizzas. | 83 divided by 8 =
10.375
Factorise (7x+19)/(x+1)(x+5)
Answer:
[tex] \frac{7x + 19}{ {x}^{2} + 6x + 5 } [/tex]Step-by-step explanation:
[tex] \frac{7x + 19}{(x + 1)(x + 5)} [/tex]
Multiply each term in the first parentheses by each term in second parentheses ( FOIL)
[tex] \frac{7x + 19}{x(x + 5) + 1(x + 5)} [/tex]
Calculate the product
[tex] \frac{7x + 19}{ {x}^{2} + 5x + x + 5} [/tex]
Collect like terms
[tex] \frac{7x + 9}{ {x}^{2} + 6x + 5 } [/tex]
Hope this helps...
Best regards!!
Factor x2 - 2x + 3
I have no idea and no one else has done it
Answer:
prime
Step-by-step explanation:
x^2 - 2x + 3
What two numbers multiply to 3 and add to -2
There are none so this cannot be factored in the real numbers
Please help me, I'm so confused
Answer:
C
Step-by-step explanation:
x+4> 8
Subtract 4 from each side
x+4-4>8-4
x > 4
Open circle at 4, line going to the right
━━━━━━━☆☆━━━━━━━
▹ Answer
[tex]Solved - x > 4\\Graphed - C[/tex]
▹ Step-by-Step Explanation
x + 4 > 8
x > 8 -4
x > 4
When graphing inequalities, you have less than, greater than, less than or equal to, and greater than or equal too. When graphing an inequality with less than or greater than, you use an open circle. When graphing an inequality with less than or equal too or greater than or equal too, you used a closed circle.
Since the numbers are positive, we are going to move up the number line therefore leaving us with the answer of C.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
The level of water in a dam was decreasing by 20% each day. If the level of water was 1500cm,what was the level after two days?
Answer:
[tex] L_o= 1500 cm[/tex]
And we know that the level is decreasing 20% each day so then we can use the following model for the problem
[tex] L_f = L_o (1-0.2)^t[/tex]
Where t represent the number of days and L the level for this case we want to fnd the level after two days so then t =2 and replacing we got:
[tex] L_f = 1500cm(0.8)^2 = 960cm[/tex]
Step-by-step explanation:
For this case we know that the initial volume of water is:
[tex] L_o= 1500 cm[/tex]
And we know that the level is decreasing 20% each day so then we can use the following model for the problem
[tex] L_f = L_o (1-0.2)^t[/tex]
Where t represent the number of days and L the level for this case we want to fnd the level after two days so then t =2 and replacing we got:
[tex] L_f = 1500cm(0.8)^2 = 960cm[/tex]
In the article, Attitudes About Marijuana and Political Views (Psychological Reports, 1973), researchers reported on the use of cannabis by liberals and conservatives during the 1970's. To test the claim (at 1% significance) that the proportion of voters who smoked cannabis frequently was lower among conservatives, the hypotheses were
Answer:
Option B.
Step-by-step explanation:
According to the question, the data provided is as follows
[tex]H_o : p_1 - p_2 = 0\ (p_1 = p_2)\\\\ H_\alpha : p_1 - p_2 < 0\ (p_1 < p_2)[/tex]
Based on the above information,
The type ii error is the error in which there is an acceptance of a non rejection with respect to the wrong null hypothesis. The type I error refers to the error in which there is a rejection of a correct null hypothesis and the type II refers that error in which it explains the failure of rejection with respect to null hypothesis that in real also it is wrong
So , the type II error is option B as we dont create any difference also the proportion is very less
Can someone tell me the answer?
Answer:
the first one has one solution because eventually they will cross
It is 64º F at the 5000-foot level of a mountain, and 48º F at the 10,000-foot level of the mountain. Write a linear equation, in slope-intercept form, to find the temperature T at an elevation e on the mountain, where e is in thousands of feet.
Answer:
T = - 3.2e + 80
Step-by-step explanation:
Given the following :
e = elevation in thousands of feets
T = temperature (°F)
e1 = 5 ; e2 = 10 (in thousands of feet)
T1 = 64° ; T2 = 48°
y = mx + c ; T = me + c
y = ; m = slope, c = intercept
64 = m5 + c - - - - (1)
48 = m10 + c - - - - (2)
From (1)
c = 64 - m5
Substitute c = 64 - m5 into (2)
48 = m10 + c - - - - (2)
48 = m10 + 64 - m5
48 - 64 = 10m - 5m
-16 = 5m
m = - 16 / 5
m = - 3.2
Substitute the value of m into c = 64 - m5
c = 64 - 5(-3.2)
c = 64 - (-16)
c = 64 + 16
c = 80
Inserting our c and m values into T = me + c
T = - 3.2e + 80
Where e is in thousands of feet
T is in °F
For the following systems of equations, match each diagram on the left with its solution on the right.
Answer:
1. (2,1)
2. (6,-1)
3.(-2,3)
Answer:
1. (2,1)
2. (6,-1)
3. (-2,3)
Step-by-step explanation:
Each of the answer is consistent system because the lines intersect at one point, which is one solution.
Choose the best estimate for the division problem below
6.7 /0.6
A. 16
B. 15
C. 11
Answer:
11
Step-by-step explanation:
6.7 / .6
Multiply top and bottom by 10
67/6
66/6 = 11 so this is close to 11
Consider this system of equations. Which equation represents the first equation written in slope-intercept form? 5 x minus 2 y = 10. Y = one-fourth x + 1.
Answer:
[tex]y = \frac{5x}{2} - 5[/tex]
Step-by-step explanation:
Given the equation 5x - 2y = 10, to write the equation in slope-intercept form, we need to write it in the standard format y = mx+c where m is the slope/gradient and c is the intercept.
From the equation given 5x - 2y = 10, we will make y the subject of the formula as shown;
[tex]5x - 2y = 10\\\\subtract \ 5x \ from \ both \ sides\\\\5x - 2y - 5x = 10 - 5x\\\\-2y = 10-5x\\\\Dividing \ both \ sides\ by \ -2;\\\\\frac{-2y}{-2} = \frac{10-5x}{-2}\\ \\[/tex]
[tex]y = \frac{10}{-2} - \frac{5x}{-2} \\\\y = -5 + \frac{5x}{2}\\\\y = \frac{5x}{2} - 5[/tex]
Hence the equation that represents the first equation written in slope-intercept form is [tex]y = \frac{5x}{2} - 5[/tex]
Is it possible to draw a triangle whose sides are as follows? 6 cm, 7 cm, 17 cm. Give reasons to support your answer.
Answer:
No
Step-by-step explanation:
The sum of two random sides of a triangle must be bigger than the third side and their differences must be smaller than the third side
For example
3 - 4 - 5 can be made into a triangle because 3 + 4 > 5 and 4 - 3 < 5