Answers
Answer:
A
Step-by-step explanation:
The line from the vertex to the base is a perpendicular bisector and divides the isosceles triangle into 2 right triangles.
Using Pythagoras' identity in either of the 2 right triangles, then
([tex]\frac{1}{2}[/tex] x )² + 3² = ([tex]\sqrt{45}[/tex] )²
[tex]\frac{1}{4}[/tex] x² + 9 = 45 ( subtract 9 from both sides )
[tex]\frac{1}{4}[/tex] x² = 36 ( multiply both sides by 4 to clear the fraction )
x² = 144 ( take the square root of both sides )
x = [tex]\sqrt{144}[/tex] = 12 → A
Related Questions
find the 10th term of the following sequences T(2)=20 and the term-to-term rule is subtract 6
Answers
==================================================
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.
What is 1/9 of 63% of 6000?
Answers
Answer:
420
Step-by-step explanation:
To find 63% of 6000, we can do 0.63 * 6000 = 3780 because 63% = 0.63.
1/9th of that is 1/9 * 3780 = 420.
Answer:
420
Step-by-step explanation:
Let's first start by finding 63% of 6000 so we can later find 1/9 of that number.
We can set up a percentage proportion.
[tex]\frac{x}{6000} = \frac{63}{100}[/tex]
[tex]6000\cdot63=378000\\378000\div100 = 3780[/tex]
Now to find 1/9 of 3780.
[tex]\frac{1}{9} \cdot \frac{3780}{1}\\\\\frac{3780}{9} = 420[/tex]
So, the answer is 420.
Hope this helped!
Find the midline for f(x)=2cos(3x−5π6)−2
Answers
Answer: y = -2
Step-by-step explanation:
f(x) = A cos (Bx - C) + D
↓
center line (aka midline)
f(x) = 2 cos (3x - 5π/6) - 2
↓
midline = -2
The midline of the cos function f(x) = 2cos(3x − 5π/6) − 2 is y = -2 after comparing with standard cos function f(x) = Acos(Bx - C) + D
What is cos function?It is defined as a function that is sin-cos wave in nature, and it has a domain of all real numbers and lies between the [a, a] where is the amplitude of the function.
It is given that the cos function is:
f(x) = 2cos(3x - 5π/6) - 2
As we know, the standard form of the cos function is:
f(x) = Acos(Bx - C) + D
Here, A is the amplitude
B is the period of the cos function
C is the phase shift of the cos function
D is the vertical shift of the cos function/midline
On comparing:
D = -2
The midline:
y = -2
Thus, the midline of the cos function f(x) = 2cos(3x − 5π/6) − 2 is y = -2 after comparing with standard cos function f(x) = Acos(Bx - C) + D
Learn more about the cos function here:
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30% of a number is 45 what is the number ?
Answers
Hey there! I'm happy to help!
When talking about percents, the word "is" usually means equals. Let's use this to solve an equation! We will call our number n. Note that 30% is equal to 0.3 in decimal form because 0.3 is 30% of one! :D
0.3n=45
To solve, we need to isolate the n. To do this, we divide both sides by 0.3 because this cancels out the 0.3 that is being multiplied by n and it shows us what n will then equal.
0.3n÷0.3=45÷0.3
n=150
Therefore, 30% of 150 is 45. Try multiplying 0.3 by 150 and you will get 45!
Have a wonderful day! :D
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
Answers
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
Can someone tell me the answer?
Answers
Answer:
the first one has one solution because eventually they will cross
Show that (a - b)+(b-c)+(c -a)3 = 3 (a - b) (b -c) (c-a)
Answers
Answer:
I think that it should be
[tex] {(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]
Step-by-step explanation:
Here,
we take , a - b = A,b-c = B , c - a= C
A+B+C = 0
we know that,
[tex] {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)[/tex]
Here , A+B+C = 0
so,
A^3 +B^3 + C^3 = 3 ABC
now we put the values
[tex]{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]
I am done .
I think that it should be
{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)
Step-by-step explanation:
Here,
we take , a - b = A,b-c = B , c - a= C
A+B+C = 0
we know that,
{a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)
Here , A+B+C = 0
so,
A^3 +B^3 + C^3 = 3 ABC
now we put the values
{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)
I am done .
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
Answers
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.
Determine the parent function.
Answers
Answer:
y= [tex]\sqrt{x}[/tex]
Step-by-step explanation:
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
Answers
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.
Answers
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
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
Answers
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
Please answer this question now
Answers
Answer:
36°
Step-by-step explanation:
<U + < V + <W = 180° (sum of angles in a triangle)
<W = 54°
The tangent is always perpendicular to the radius drawn to the point of tangency...
therefore,
<U = 90°
90° + <V + 54° = 180°
144° + <V = 180°
<V = 180° - 144°
<V = 36°
Answer:
V=36
Step-by-step explanation:
tangent makes rigt angle with radius angle U=90
W+V+U=180
V=180-90-54
V=36
Sketch the graph of y=-3(x-3)2+4 and identify the axis of symmetry.
Answers
Answer:
The axis of symmetry of parabola is the equation where it cuts the middle of the graph.
So the axis of symmetry is x = 2 .
What are the square roots of; (note: i think there are supposed to be 2 each) 36 12 1.96 0.64 400 25/36
Answers
Answer:
36 : 6 and -6
12 = [tex]2\sqrt{3} , -2\sqrt{3}[/tex]
1.96 =1.4 and -1.4
0.64 : 0.8 and -0.8
400 : 20 and -20
25/36 = 5/6 and -5/6
Step-by-step explanation:
we know that
(-x)^2 = x^2
ALSO
(x)^2 = x^2
thus, square of both negative and positive number is same positive number.
_________________________________________________
36 = 6*6
36 = -6*-6
hence
square roots of 36 is both -6 and 6
12 = 4*3 = [tex]2^2*\sqrt{3} *\sqrt{3}[/tex]
[tex]\sqrt{12} = 2\sqrt{3}[/tex]
also
12 = [tex]-2\sqrt{3} *-2\sqrt{3}[/tex]
[tex]\sqrt{12} = -2\sqrt{3}[/tex]
___________________________________
1.96 = 196/100 = (14/10)^2
1.96 = 196/100 = (-14/10)^2
hence
[tex]\sqrt{1.96} = 14/10 \ or -14/10[/tex]
_______________________________
0.64 = 64/100 = (8/10)^2 = 0.8^2
0.64 = 64/100 = (-8/10)^2 = (-0.8)^2
Thus, square root of 0.64 = 0.8 and -0.8
_________________________________
400 = 20^2
400 = (-20)^2
[tex]\sqrt{400} = 20\\\sqrt{400} = -20\\[/tex]
__________________________________
25/36 = (5/6)^2
25/36 = (-5/6)^2
[tex]\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6[/tex]
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.
Answers
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
The first three steps in determining the solution set of the system of equations algebraically are shown.
y = x2 − x − 3
y = −3x + 5
What are the solutions of this system of equations?
(−2, −1) and (4, 17)
(−2, 11) and (4, −7)
(2, −1) and (−4, 17)
(2, 11) and (−4, −7)
Answers
Answer:
(2, −1) and (−4, 17)
Step-by-step explanation:
I used a graphing tool to graph the systems of equations. The parabola and line pass at points (2, -1) and (-4, 17).
Answer:(2, −1) and (−4, 17) Its C on Edge 2023
Step-by-step explanation: Its (C) after an extensive research
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.
Answers
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]
This is Algebra 1 functions and I'm struggling with this one function-
-1•f(-9)+7•g(6)=_____
Answers
Answer:
38
Step-by-step explanation:
f(-9) is the value of f(x) when x = -9. Therefore, f(-9) = 4 from the graph. Doing the same with g(6), we can see that g(6) = 6. Our expression becomes:
-1 * 4 + 7 * 6
= -4 + 42
= 38
y=8-2x. What is the value of y when x = 8?
Answers
Because the math problem is y=8-2x8
You multiple 2x8 which equals 16
You are then left with y=8-16
And 8-16 = -8
Answer:
y = -8
Step-by-step explanation:
Start by filling 8 in place of x
y = 8 - 2(8)
Multiply -2(8)
y = 8 - 16
Subtract 16 from 8
y = -8
The time between failures for an electrical appliance is exponentially distributed with a mean of 25 months. What is the probability that the next failure will not occur before 30 months have elapsed
Answers
Answer:
The probability that the next failure will not occur before 30 months have elapsed is 0.0454
Step-by-step explanation:
Using Poisson distribution where
t= number of units of time
x= number of occurrences in t units of time
λ= average number of occurrences per unit of time
P(x;λt) = e raise to power (-λt) multiplied by λtˣ divided by x!
here λt = 25
x= 30
P(x= 30) = 25³⁰e⁻²⁵/ 30!
P (x= 30) = 8.67 E41 * 1.3887 E-11/30! (where E= exponent)
P (x=30) = 1.204 E31/30!
Solving it with a statistical calculator would give
P (x=30) = 0.0454
The probability that the next failure will not occur before 30 months have elapsed is 0.0454
The diameter of a circle is 3.5 inches. What is the circumference of the circle?
Answers
Answer:
About 11 (10.9955742876...)
Step-by-step explanation:
Circumference=(pi) (diameter) or C=πd
Hope this helps!
The circumference of the circle is about 11 inches.
We are given that the diameter of a circle is 3.5 inches.
Noted that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
Therefore circumference of the circle = 2πr
Circumference=(2πr)
The diameter or C = πd
diameter = 3.5 inches
Circumference=(3.5 x 3.14)
Circumference = (10.99) inches
Learn more about circumference here;
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Please help me as fast as you can. thanks
Answers
Answer:
<DEF = 40<EBF = <EDF = 56<DCF = <DEF =40<CAB = 84Step-by-step explanation:
In triangle DEF, we have:
Given:
<EDF=56
<EFD=84
So, <DEF =180 - 56 - 84 =40 (sum of triangle angles is 180)
____________
DE is a midsegment of triangle ACB
( since CD=DA(given)=>D is midpoint of [CD]
and BE = EA => E midpoint of [BA] )
According to midsegment Theorem,
(DE) // (CB) "//"means parallel
and DE = CB/2 = FB =CF
___________
DEBF is a parm /parallelogram.
Proof: (DE) // (FB) ( (DE) // (CB))
AND DE = FB
Then, <EBF = <EDF = 56
___________
DEFC is parm.
Proof: (DE) // (CF) ((DE) // (CB))
And DE = CF
Therefore, <DCF = <DEF =40
___________
In triangle ACB, we have:
<CAB =180 - <ACB - <ABC =180 - 40 - 56 =84(sum of triangle angles is 180)
[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK! [/tex]
Factor x2 - 2x + 3
I have no idea and no one else has done it
Answers
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 answer this question now
Answers
Answer:
541.4 m²
Step-by-step Explanation:
Step 1: find m < V
V = 180 - (50+63) (sum of the angles in ∆)
V = 67
Step 2: find side length of XW using the law of sines
[tex] \frac{XW}{sin(V)} = \frac{XV}{sin(W)} [/tex]
Where,
V = 67°
W = 63°
XV = 37 m
XW
[tex] \frac{XW}{sin(67)} = \frac{37}{sin(63)} [/tex]
Multiply both sides by sin(67) to solve for XW
[tex] \frac{XW}{sin(67)}*sin(67) = \frac{37}{sin(63)}*sin(67) [/tex]
[tex] XW = \frac{37*sin(67)}{sin(63)} [/tex]
[tex] XW = 38.2 m [/tex] (to nearest tenth)
Step 3: find the area using the formula, ½*XW*XV*sin(X)
area = ½*38.2*37*sin(50)
Area = 541.4 m² (rounded to the nearest tenth.
the hypotnuse of a 45 -45 -90 triangle measures 22√2 units. what is the length of the leg of the triangle?
Answers
Answer:
22 units.
Step-by-step explanation:
In 45- 45- 90 triangles, there is a 1 to 1 to the square root of 2 formula. Each side length measures 1x, while the hypotenuse measures x times the square root of 2.
In this case, the hypotenuse measures 22 and the square root of 2 units. To find the value of x, simply divide that by the square root of 2 units, and you get x = 22 units. Multiply that by 1, and you get 22 units, which is the length of the leg of the triangle.
Hope this helps!
Area of a triangle is 1400 cm² the base of the triangle is 5 times the height what is the height of the triangle
Answers
Answer:
≈23.66
Step-by-step explanation:
Height ---> x
base ---> 5x
Formula for area of triangle: (base*height)/2
((5x)(x))/2 = 1400
[tex]5x^{2}[/tex]/2 = 1400
[tex]5x^{2}[/tex] = 1400 · 2 = 2800
[tex]x^2[/tex] = 2800/5 = 560
x= √560 ≈ 23.66
Given the coordinate points of the preimage, use the transformation given to provide the points of the image. E(−5,−1) D(−5,1) C(−1,0) B(−2,−3) Rotation: 180∘ about the origin
Answers
Answer:
The points of the image are;
E'(5, 1), D'(5, -1), C'(1, 0), E'(-2, -3)
Step-by-step explanation:
The coordinates of the preimage are E(-5, -1) D(-5, 1) C(-1, 0) B(-2, -3)
Rotation of a point 180° about the origin gives;
Coordinates of the point of the preimage before rotation = (x, y)
The coordinates of the image after rotation = (-x, -y)
Therefore, the coordinates of the points EDCB after 180° rotation about the origin are;
E(-5, -1) rotated 180° becomes E'(5, 1)
D(-5, 1) rotated 180° becomes D'(5, -1)
C(-1, 0) rotated 180° becomes C'(1, 0)
B(-2, -3) rotated 180° becomes E'(-2, -3).
¡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.
Answers
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.
Solve and CHECK the following: 2(a−3)/3=4
Answers
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