Answer:
1. 12 + x = 20 2. x + 8 = 4x + 6
Step-by-step explanation:
problem 1 :
12 + x = 20
problem 2:
x + 8 = 4x + 6
ASAP!!! PLEASE
A pair of equations is shown below: y = 2x − 1 y = 4x − 5 Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points) Part B: What is the solution to the pair of equations? (4 points)
Step-by-step explanation:
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Change 300mm into cm
Answer:
30 centimeters
Step-by-step explanation:
true
What is an equation of the line that passes through the points (0, 8) and (-8, -4)?
Answer:
y = 1.2x + 2
Step-by-step explanation:
slope = (8 - 2)/(5 - 0) = 6/5y-intercept = (0, 2)y = (6/5)x + 2y = 1.2x + 2
Answer:
y=1.5x +8
Step-by-step explanation:
which of the following represents…
Let the lengths of each side of △ABC having area equal to 1 be as follows: AB = 2, BC = a and CA = b. Let CD be a perpendicular line from point C to AB. Answer the following questions.
(1) Given AD = x, write a²+(2√3-1)b² in the form of x.
(2) Find the value of x at which a²+(2√3 - 1)b² is the lowest and the magnitude of ∠BAC.
Need help! Please show your work too. Thanks!
Answer:
Part 1)
[tex]\displaystyle \left((2-x)^2 + 1)\right) + (2\sqrt{3} - 1 ) \left(x^2 + 1\right)[/tex]
Or simplified:
[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]
Part 2)
The value of x for which the given expression will be the lowest is:
[tex]\displaystyle x = \frac{\sqrt{3}}{3}\approx 0.5774[/tex]
And the magnitude of ∠BAC is 60°.
Step-by-step explanation:
We are given a ΔABC with an area of one. We are also given that AB = 2, BC = a, and CA = b. CD is a perpendicular line from C to AB.
Please refer to the diagram below.
Part 1)
Since we know that the area of the triangle is one:
[tex]\displaystyle \frac{1}{2} (2)(CD) = 1[/tex]
Simplify:
[tex]\displaystyle CD = 1[/tex]
From the Pythagorean Theorem:
[tex]\displaystyle x^2 + CD^2 = b^2[/tex]
Substitute:
[tex]x^2 + 1 = b^2[/tex]
BD will simply be (2 - x). From the Pythagorean Theorem:
[tex]\displaystyle (2-x)^2 + CD^2 = a^2[/tex]
Substitute:
[tex]\displaystyle (2-x)^2+ 1 = a^2[/tex]
We have the expression:
[tex]\displaystyle a^2 + (2\sqrt{3} - 1) b^2[/tex]
Substitute:
[tex]\displaystyle = \boxed{\left((2-x)^2 + 1)\right) + (2\sqrt{3} - 1 ) \left(x^2 + 1\right)}[/tex]
Part 2)
We can simplify the expression. Expand and distribute:
[tex]\displaystyle (4 - 4x + x^2 + 1)+ (2\sqrt{3} -1)x^2 + 2\sqrt{3} - 1[/tex]
Simplify:
[tex]\displaystyle = ((2\sqrt{3} -1 )x^2 + x^2) + (-4x) + (4+1-1+2\sqrt{3})[/tex]
Simplify:
[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]
Since this is a quadratic with a positive leading coefficient, it will have a minimum value. Recall that the minimum value of a quadratic always occur at its vertex. The vertex is given by the formulas:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 2√3, b = -4, and c = (4 + 2√3).
Therefore, the x-coordinate of the vertex is:
[tex]\displaystyle x = -\frac{(-4)}{2(2\sqrt{3})} = \frac{1}{\sqrt{3}} =\boxed{ \frac{\sqrt{3}}{3}}[/tex]
Hence, the value of x at which our expression will be the lowest is at √3/3.
To find ∠BAC, we can use the tangent ratio. Recall that:
[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]
Substitute:
[tex]\displaystyle \tan \angle BAC = \frac{CD}{x}[/tex]
Substitute:
[tex]\displaystyle \tan \angle BAC = \frac{1}{\dfrac{\sqrt{3}}{3}} = \sqrt{3}[/tex]
Therefore:
[tex]\displaystyle\boxed{ m\angle BAC = \arctan\sqrt{3} = 60^\circ}[/tex]
giá tiền cước của một hãng taxi được tính như sau :giá mở đến 1km đầu là 12000 đồng ; 10500 đồng/km cho 20 km tiếp theo và 99000 đồng/km cho những km còn lại . Hỏi ông sáu đi từ nhà đến khu du lịch sinh thái Bò Cạp Vàng với quãng đường 62km bằng taxi của hãng đó hết bao nhiêu
Answer:
Ông sáu sẽ mất 4281000 đồng
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNKW THE ANSWER!!
Answer: will be D
Step-by-step explanation:
The lengths of the sides of a triangle are 4,5 and 6 if the length of the longest side of a similar triangle is 15,what is the length of the shortest side of the triangle
Answer:
The length of the shortest side of the triangle is 10.
Step-by-step explanation:
Given that the lengths of the sides of a triangle are 4, 5 and 6, if the length of the longest side of a similar triangle is 15, to determine what is the length of the shortest side of the triangle, the following calculation must be performed :
6 = 15
4 = X
4 x 15/6 = X
10 = X
Therefore, the length of the shortest side of the triangle is 10.
what is the equation of the line written in general form?
Answer:
option 2 or y + x -2 = 0
Step-by-step explanation:
Given a line on a graph, it is easiest to start with point-slope form.
y = mx + b
where m is the slope (rise/run) and b is the y-axis intercept.
From the plot m = -2/2 = -1 and b = 2 SO
y = mx + b
y = -x + 2
Then the general form is
y + x -2 = 0
log 55 is the power to which ---- must be raised in order to produce a value of 55
Answer:
10
Step-by-step explanation:
just took the quiz
a student walks 50m on a bearing 0.25 degrees and then 200m due east how far is she from her starting point.
Answer:
Step-by-step explanation:
I'm going to use Physics here for this concept of vectors. Here are some stipulations I have set for the problem (aka rules I set and then followed throughout the problem):
** I am counting the 50 m as 2 significant digits even though it is only 1, and I am counting 200 as 3 significant digits even though it is only 1. 1 sig dig doesn't really give us enough accuracy, in my opinion.
** A bearing of .25 degrees is measured from the North and goes clockwise; that means that measured from the x axis, the angle is 89.75 degrees. This is the angle that is used in place of the bearing of .25 degrees.
** Due east has an angle measure of 0 degrees
Now let's begin.
We need to find the x and y components of both of these vectors. I am going to call the first vector A and the second B, while the resultant vector will be C. Starting with the x components of A and B:
[tex]A_x=50cos(89.75)[/tex] so
[tex]A_x=.22[/tex]
[tex]B_x=200cos(0)[/tex] so
[tex]B_x=200[/tex] and we need to add those results together. Due to the rules for adding significant digits properly, the answer is
[tex]C_x=200[/tex] (and remember I am counting that as 3 sig fig's even though it's only 1).
Now for the y components:
[tex]A_y=50sin(89.75)[/tex] so
[tex]A_y=50[/tex] (which I'm counting as 2 sig fig's)
[tex]B_y=200sin(0)[/tex] so
[tex]B_y=0[/tex] and we need to add those results together.
[tex]C_y=50[/tex]
Now for the resultant magnitude:
[tex]C_{mag}=\sqrt{(200)^2+(50)^2}[/tex] and that gives us a final magnitude of
[tex]C_{mag}=206[/tex] m
Now for the angle:
Since both the x and y components of the resultant vector are in quadrant 1, we don't need to add anything to the angle to get it right, so
[tex]tan^{-1}(\frac{50}{200})=14[/tex]
The girl is 206 meters from her starting point at an angle of 14 degrees
Write and algebraic expression:
The tens digit of a number is b and the units digit is twice as big. What is the value of the number in terms of b if the digits are reversed?
Answer:
21b
Step-by-step explanation:
Factor the expression
Thank you so muchh
Answer:
(x+8)(x-5)
Step-by-step explanation:
x^2 +3x-40
What two numbers multiply to -40 and add to 3
8 * -5 = -40
8+-5 = 3
(x+8)(x-5)
Answer:
(x + 8)(x - 5)
Brainliest, please!
Step-by-step explanation:
(x + )(x - )
Factors of 40: 1 and 40, 2 and 20, 4 and 10, 5 and 8
(x + 8)(x -5)
Find the number of bit strings that satisfies the given conditions. The bit strings of length 11 having at least four 1s
Answer:
Step-by-step explanation:
[tex] \frac{5}{5 \sqrt{6 + 2 \sqrt{3} } } \times ( \frac{1}{5 \sqrt{3} } + \frac{3 \sqrt{2} }{2 \sqrt{3} } - \frac{2 \sqrt{3} }{3 \sqrt{2} } ) = [/tex] ....................
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
Enter the location of the point as an ordered pair.
5
-5
-6
Answer:
(4,1)
Step-by-step explanation:
(4,1) is the correct answer. Answered by Gauthmath
Answer the question
Answer:
1,041,958.5, or 104,195 1/2
Step-by-step explanation:
All you have to do is 15787.25 times 66, because 15787.25 is the price for on acre, so 66 acres will be 15787.25 times 66. If you want to put it in fraction form, you can do 15787 1/4 times 66. I hoped you liked this answer!
What is the value of the expression 3.9x10^5/1.3x10^2?
I will mark Brainliest whoever person I actually trust.
Answer:
3 * 10 ^3
Step-by-step explanation:
Divide the numbers
3.9 / 1.3
3
Subtract the powers of 10
10^5 / 10^2 = 10 ^ (5-2) = 10^3
The result is 3 * 10 ^3
[tex] \frac{3.9 \times {10}^{5} }{1.3 \times {10}^{2} } \\ = \frac{3.9}{1.3} \times {10}^{5 - 2} \\ = 3.0 \times {10}^{3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
In the circle below, if arc AC = 66°, and arc BD = 146, find the measure of
Select one:
a. 146
b. 212
C. 66
d. 106
Answer:
D. 106°Step-by-step explanation:
m∠BPD = m∠APC = 1/2(mAC + mBD) = 1/2(66° + 146°) = 1/2(212°) = 106°Answer:
By applying intersecting chords angle theorem:-
[tex]m\angle BPD= 106[/tex]° [tex]=1/2(BD+AC)[/tex]
[tex]=1/2(146+66)[/tex]
[tex]=1/2\time(212)[/tex]°
[tex]m\angle BPD=106[/tex]°
Answer:- D) 106°
OAmalOHopeO
What is the volume of the solid? Let π=3.14
.
The volume of the solid as shown in the task content is; 2786.2cm³.
What is the volume of the solid?It can be obtained from the task content that the solid given is a Cone.
On this note, the volume of the cone can be evaluated by means of the formula;
V = (1/3)π r²h where(r =22/2 = 11 and h=22).
Hence, Volume, V = (1/3) ×3.14× (11)²×22 = 2786.2cm³.
Read more on volume;
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What is the value of the expression below when z=10z=10 and w=4w=4? 2z-3w 2z−3w
Answer:
8
Step-by-step explanation:
more details
2(10)-3(4)
20-12
8
Write the digits used in binary number system
Answer:
Binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2.
The price of a hamburger is 3 dollars. what is the price of 90 hamburgers?
Cost of each Hamburger = $3
Cost of 90 Hamburgers = 3×90
= $270
Therefore cost of 90 hamburgers is $270
Must click thanks and mark brainliest
One number is three times another number. If the sum of the numbers is 36, determine the two numbers.
Step-by-step explanation:
A=3B
A+B=36
3B+B=36
4B=36
B=36/4
Step-by-step explanation:
let x represent the smaller number
3x is the second number
x+3x=36
4x=36
4x/4=36/4
x=9
the second number is 3(9)
=27
What is the midpoint of segment AB?
Answer:
(-1, -3.5)
Step-by-step explanation:
Use the midpoint formula by finding the points of A and B.
A = (-5, -4)
B = (3, -3)
Add the x-values of both coordinates to get the following:
[tex]3_{1} + -5_{2} = -2\\-2/2 = -1[/tex]
Midpoint = (-1, y)
Now we find the y-value by doing the same as we did to the x-coordinates of A and B.
[tex]-3_{1} + -4_{2} = -7\\-7/2 = -3.5[/tex]
Midpoint = (-1, -3.5)
Find the length of the side labeled 2. Round intermediate values to
the nearest tenth. Use the rounded values to calculate the next
value. Round your final answer to the nearest tenth. PLEASE HELP ASAP!
A. 11.6
B. 13
C. 16.6
D. 22.4
Answer:
B
Step-by-step explanation:
The perpendicular is sin(43)*39=21.82. Next tan(32)=x/21.82. x=21.82*tan(32)=13.6
The value of x in the given question is 16.6
What are trigonometric ratios in a right angle triangle ?A right angle triangle has 3 sides opposite is the side opposite to the angle formed by two adjacent sides.hypotenuse is the largest side and adjacent is the remaining side.
Assuming height of the triangle = y
Sin∅ = opposite/hypotenuse
sin43° = y/39
y= 39sin43°
y = 26.6
From this we will solve the value of x
tan∅ = opposite/adjacent
here adjacent = 26.6 and opposite = x
tan32° = x/26.6
x = 26.6tan32°
x = 16.6
Learn more about Trigonometric ratios here :
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Can someone answer this pls
Answer:
maximum/minimum value for f(x) = ax2 + bx + c: Put the quadratic in standard form f(x) = a(x − h)2 + k, and the absolute
Step-by-step explanation:
maximum/minimum value is k and it occurs at x = h. If a > 0, then the parabola opens up, and it is a minimum functional value of f.
What is a simplified form of 1 − sin^2 θ?
Answer:
cos^2(θ)
Step-by-step explanation:
32 x square Y - 2 y cube
Answer:
207y
Step-by-step explanation:
I need help on this asap please!
Answer:
-8 5/20 , 4/25 , 9/20
Step-by-step explanation:
If there are negative numbers, those are the least. Let's say the number was -2 and -1. With a positive integer, 2 would be greater, but since it's negative, it's the least. SO -8 and 5/20 would be the least. Then putting the other two fractions into decimal form, or you can find the greatest common denominator, you'll find that 9/20 is greater than 4/25.
