Answer:
lines 1 and 3
Step-by-step explanation:
y = 2 is a horizontal line parallel to the x- axis
x = - 4 is a vertical line parallel to the y- axis
Then these 2 lines are perpendicular to each other
y = 15x - 3 ( in the form y = mx + c ) with m = 15
y + 1 = - 5(x + 2) ( in the form y - b = m(x - a) with m = - 5
For the lines to be perpendicular the product of their slopes = - 1
However
15 × - 5 = - 75 ≠ - 1
The 2 lines 1 and 3 are perpendicular
what is the length of the third side triangle?
Answer:
x = 8cm
Step-by-step explanation:
17² = 15² + x²
289 = 225 + x²
- x² = 225 - 289
x² = 64
x = √64
x = 8
Good Luck! :)[tex]{ \boxed{ \sf \color{blue}{answer}}}[/tex]
x = 8 cm
Step-by-step explanation:
17² = 15² + x²
289 = 225 + x²
x² = 225 - 289
x² = 64
x = √64
x = 8
___________________Teorema pythagoras
Can someone answer all these questions
If the perimeter is 16' the sum of the length and width must be 8'. Assuming that area is non 0 possible dimensions are:
1x7 2x6 3x5 4x4 5x3 6x2 7x1
What are the solutions to the equation 3(x – 4)(x + 5) = 0
Answer:
x=4
x=-5
Step-by-step explanation:
in order for this to be equal to 0, 1 or both of the factors has to be 0, because anything multiplied by 0 is 0.
123 * 29382 * 8139* 0 = 0
x-4 = 0
x = 4
x+5 = 0
x=-5
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]
What is the probability that you roll at least one 3 in your dice? Convert your answer to
decimal form, then round to 3 decimal places,
Answer:
0.167
Step-by-step explanation:
1 dice has 6 faces, 2 dice will have a total of 12 faces
1 dice has 1 face with a 3 on it, so 2 dices will have 2 total 3s on them.
2 /12 = 1/6 = 0.16666666666
Rounded to 3 d.p = 0.16666
= 0.167
Answered by Gauthmath
How is karl Pearson coefficient of skewness is differ from bowley's coefficient?
Answer:
where is the rest of the question??
Step-by-step explanation:
A
D
С
B
If mZABD = 60°, then mZDBC = [?]°
Answer:
60
Step-by-step explanation:
Since the angles are shown equal in the diagram, ABD=DBC=60
sin 0=20/29. Find tan 0.
Mrs brown designed a rug if it cost $22 per square foot to make how much will Mrs brown pay if the square feet is 31.25
Answer:
$687.5
Step-by-step explanation:
Cost of the rug per square foot = $22
Length of the rug = 31.25 feet
Total amount Mrs brown will pay = Cost of the rug per square foot × Length of the rug
= 31.25 × 22
= $687.5
Total amount Mrs brown will pay = $687.5
find the surface area of this cylinder??
Answer:
4
Step-by-step explanation:
A=ch
then,
2ft×2ft
4ft
Someone please help! I have spent lots of time on this and I’m still confused
Answer:
its the 3rd choice.
Step-by-step explanation:
Firstly, we find angle BDC (180-90-30=60)
Now that we found it we can use the sine rule to find DB (which i put as an x), which is sin60/14=sin30/x, by cross multiplication, we find that its equal to a decimal number, i will use its root version to this easier, its equal to 14sqrt3/3 inches.
And now we use the pythagorean theorem to find DC, we find that it is equal to 28sqrt3/3
Now, we find angle BAC (180-90-(30+15)=45)
Again, we use the sine rule to find AB (whom i will refer to as x and from whom we will subtract DB to find the length of AD), so we cross multiply in sin45/14=sin(30+15)/x, it is equal to 14.
So since AB-DC=AD
14-(14sqrt3/3)= 5.917096231 (and we ound that to a 5.9)
find the missing side lengths
Answer:
b = 2√3
a = 4
Step-by-step explanation:
Here taking 60 as reference angle
so
tan60 = p/b
[tex]\sqrt{3}[/tex] = p/2
so p = 2√3
so
b = 2√3
so
[tex]h^2 = p^2 + b^2\\h^2 = (2\sqrt{3})^2 + 2^2\\h^2 = 12 + 4\\h^2 = 16\\h = \sqrt{16} \\h = 4[/tex]
a = 4
in a data ,range is 17 and coefficient of range is 0.2 find the smallest term of the data.
I will make brainelist to the best answer
Answer:
Step-by-step explanation:
Let largest value of data be L
and smallest value of data be S.
We are given that the range and coefficient of range of the data are 17 and 0.2 respectively.
Range formula is given by = Largest value - Smallest value
17 = L - S
L = 17 + S ---------- [Equation 1]
Coefficient of range formula = (Largest - Smallest) ÷ (Largest + Smallest)
0.2 = l-s/l+s
0.2 = 17/l+s
L + S = 17/0.2 = 85
So, L + S = 85
17 + S + S = 85 {using equation 1}
2*S = 80
S = 80/2 = 40
Putting value of S in equation 1, we get L = 20 + 40 = 60
Therefore, Largest value, L = 60
smallest value, S = 40
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Step-by-step explanation:
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I need help to find m =
Answer:
hlo buddy
are u free now.. nhjm....
Phythagorean theorem HELPPPP PLSSSSS ASAPPP
Answer:
5
Step-by-step explanation:
We know that we can use the Pythagorean theorem
a^2 + b^2 =c^2
where a and b are the legs and c is the hypotenuse
one of the legs is 12 and the hypotenuse (diagonal) is 15
a^2 + 12^2 = 15^2
a^2 +144 = 169
a^2 +144-144 =169-144
a^2 = 25
Taking the square root of each side
sqrt(a^2) = sqrt(25)
a = 5
Answer:
l = 9 cm
Step-by-step explanation:
Using Pythagoras' identity in one of the right triangles with legs width w, length l and hypotenuse h , then
l² + w² = h²
l² + 12² = 15²
l² + 144 = 225 ( subtract 144 from both sides )
l² = 81 ( take the square root of both sides )
l = [tex]\sqrt{81}[/tex] = 9
Find the length of PR from the given figure ( step by step ).
Answer:
PR = 39 cm
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
PR² + PQ² = QR² , that is
PR² + 80² = 89²
PR² + 6400 = 7921 ( subtract 6400 from both sides )
PR² = 1521 ( take the square root of both sides )
PR = [tex]\sqrt{1521}[/tex] = 39
Answer:
[tex]PR=39[/tex]
Step-by-step explanation:
The triangle (PQR) is a right triangle. This means the triangle has a (90) degree angle, such is indicated by the box around one of the angles in the triangle. One of the properties of the sides of a right triangle is the Pythagorean theorem. The Pythagorean theorem states the following:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs of the right triangle, or the sides adjacent to the right angle. (c) is the side opposite the right angle of the triangle triangle, in other words, the hypotenuse. Substitute the respective legs into the formula for the Pythagorean theorem and solve for the unknown,
[tex]a^2+b^2=c^2[/tex]
Substitute,
[tex]a^2+b^2=c^2[/tex]
[tex]PQ^2+PR^2=QR^2[/tex]
[tex]80^2+PR^2=89^2\\[/tex]
Simplify,
[tex]80^2+PR^2=89^2\\[/tex]
[tex]6400+PR^2=7921[/tex]
Inverse operations,
[tex]6400+PR^2=7921[/tex]
[tex]PR^2=1521\\\\PR=39[/tex]
Write the solution set of the inequality graphed below as a com-
pound inequality using the variable g.
Answer:
-17 < g [tex]\leq[/tex] 8
Step-by-step explanation:
'g' is within the range of numbers that are greater than -17 and less than or equal to 8. we know that it is less than or equal to because the circle is closed or filled in, at 8.
Identify the correct explanation and the similarity statement for the similar triangles.
A: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅, m∠B = m∠A.
This gives m∠A = 75° by Substitution.
Then, by the Δ Subt. Thm., m∠C = 30°.
Now apply the Isosc. Δ Thm. and the Δ Subt. Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by SSS ~.
B: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅ , m∠B = m∠C.
This gives m∠C = 75° by substitution.
Then, by the Δ Sum Thm., m∠A = 30°.
Now apply the Isosc. Δ Thm. and the Δ Sum Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by AA ~.
C: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅, m∠B = m∠C.
This gives m∠C = 30° by Substitution.
Then, by the Δ Subt. Thm., m∠A = 75°.
Now apply the Isosc. Δ Thm. and the Δ Subt. Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by SSS ~.
D: By the Isosc. Δ Thm., ∠B ≅ ∠C, so by the Def. of ≅, m∠B = m∠A.
This gives m∠A = 75° by Substitution.
Then, by the Δ Sum Thm., m∠C = 30°. Now apply the Isosc. Δ Thm. and the Δ Sum Thm. to ΔPQR to find that m∠P = m∠Q = 75°.
Therefore ΔABC ~ ΔPQR by AA ~.
Answer:
Option B
Step-by-step explanation:
From the picture attached,
In ΔABC,
m∠B = m∠C = 75° [Isosceles triangles]
By applying triangle sum theorem,
m∠A + m∠B + mC = 180°
m∠A + 75° + 75° = 180°
m∠A = 180° - 150°
m∠A = 30°
In triangle PQR,
m∠P = m∠Q [Isosceles triangle]
By applying triangle sum theorem,
m∠P + m∠Q + m∠R = 180°
2(m∠P) + 30° = 180°
m∠P = 75°
m∠P = m∠Q = 75°
In ΔABC and ΔRPQ,
m∠B ≅ m∠Q [Given]
m∠C ≅ m∠R [Given]
Therefore, by AA property of similarity of two triangles, both the triangles will be similar.
ΔABC ~ ΔRPQ
Option B will be the answer.
The data set represents the total number of pencils each student in a class needs to sharpen.
0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9
Which box plot correctly represents the data?
A number line goes from 0 to 10. The whiskers range from 0 to 9, and the box ranges from 2 to 6. A line divides the box at 3.
A number line goes from 0 to 10. The whiskers range from 0 to 9, and the box ranges from 2 to 6. A line divides the box at 4.
A number line goes from 0 to 10. The whiskers range from 0 to 9, and the box ranges from 1 to 6. A line divides the box at 4.
A number line goes from 0 to 10. The whiskers range from 0 to 9, and the box ranges from 1 to 6. A line divides the box at 3.
Given:
The data set is:
0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9
To find:
The correct statement that represents the box plot of the data correctly.
Solution:
We have,
0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9
Divide the data in 2 equal parts.
(0, 1, 1, 1, 2), 3, (4, 4, 6, 6, 9)
Divide each parenthesis in 2 equal parts.
(0, 1), 1, (1, 2), 3, (4, 4), 6, (6, 9)
Here,
Minimum value = 0
First quartile = 1
Median = 3
Third quartile = 6
Maximum value = 9
A number line goes from 0 to 10. The whiskers range from 0 to 9, and the box ranges from 1 to 6. A line divides the box at 3.
Therefore, the correct option is D.
Answer:
its d
Step-by-step explanation: my yt Tray Clayps
Find SP where MP=Rs875 and discount =Rs75
Answer:
SP is Rs 800.
Step-by-step explanation:
MP = Rs 875
Discount = Rs 75
so
SP = MP - discount
= Rs 875 - Rs 75
= Rs 800
If p:q=3:4 and q:r=14:9, find p:r
Answer:
7/6
Step-by-step explanation:
p=3/4*q
q=14/9*r
so p=3/4*14/9r=7/6r
Find the surface areas of each figure. Round your answers to the nearest tenth, if necessary
Find an equation in slope-intercept form of the line that has slope –7 and passes through point A(8,-4)
a.) y = 52x + 7
b.) y = 7x + 52
c.) y = -7x - 52
d.) y = -7x + 52
Answer:
y = -7x + 52
Step-by-step explanation:
y = -7x - b
-4 = -7(8) + b
-4 = -56 + b
52
Hey can anyone help me pls
Answer:
6.8=6 8/5
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hope it help
29. If (x, 5) is a solution to the equation 3x + 5y = -5, what is the value of x?
A.-10
B.-4
C. 2
D. 6
Answer:
the answer is -10
Step-by-step explanation:
x=x
y=5
then
3x+5y=-5
3x+5*5=-5
3x=-5-25
3x=-30
x=-30/3
•°•x=-10
Answer:
A
Step-by-step explanation:
3x+5*5=-5
x=-10
Translate the following into an expression 45% of a
Answer:
Step-by-step explanation:
ok so this is pretty simple,
Imagine a was the number 1
45% of 1, which would obviously be
45/100 * 1
Same thing here but for the variable a.
45/100 * a!
That would be the algebraic expression for 45% of a!
Cheers! I hope you can understand the problem better now.
Kyle brough a case of 24 12 ounce bottles of water.He drank the same amount of water each day and finished the case after 3 days.How many onces of water did kyle drink each day?
Answer:
96 ounces each day
Step-by-step explanation:
Divide the 24 bottles by 3
24/3 = 8
8bottles per day
8 bottles *12 ounces per bottle
96 ounces each day
The value of a gold coin picturing the head of the Roman Emperor Vespasian is increasing at the rate of 11% per year. If the coin is worth $135 now, what will it be worth in 12 years?
Answer:
[tex]A = 135(1.11)^{12}[/tex]
A= $472.29
Step-by-step explanation:
Put the steps In order
What is the perimeter of the following figure
Answer:
13
Step-by-step explanation:
7 cm +1 cm +2cm +2cm :12cm
