Solve for x.
13(x-3) = 39
x=1
x=4
x=6
x= 10
Answer:
x=6
Step-by-step explanation:
13(x-3) = 39
Divide each side by 13
13/13(x-3) = 39/13
x-3 = 3
Add 3 to each side
x-3+3 = 3+3
x = 6
Answer:
x=6 ,is right.
6-3=3&multiply 13=39
so answer is x=6
mark brainleast plz
Which expression represents the prime factorization of 243?
Answer:
[tex]\boxed{3^5}[/tex]
Step-by-step explanation:
Hey there!
Look at the image below↓
By looking at the image we can tell the PR expression is [tex]3^5[/tex].
Hope this helps :)
Answer:
Below in bold.
Step-by-step explanation:
Dividing by primes:
3 ) 243
3 ) 81
3 ) 27
3) 9
3.
So the prime factors of 243 are 3 * 3 * 3 * 3 * 3 or 3^5.
40 POINTS!!!!
ANSWER ASAP!!!
What is the value of y?
O 3 sqrt 3 units
O 6 sqrt 3 units
O 9 sqrt 3 units
O 12 sqrt 3 units
Answer:
6 sqrt(3) = y
Step-by-step explanation:
We can use the leg rule to find y
hyp leg
----- = -------
leg part
9+3 y
----- = -------
y 9
Using cross products
12*9 = y^2
108 = y^2
Taking the square root of each side
sqrt(108) = sqrt(y^2)
sqrt(36 *3) = y
6 sqrt(3) = y
Answer: B) 6/3 units
Step-by-step explanation:
7. Verify the following: i) (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0 ii) (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc iii) (p – q) (p² + pq + q²) = p³ – q³. EXPLAIN
1. (ab + bc) (ab – bc) + (bc + ca) (bc – ca) + (ca + ab) (ca – ab) = 0
We know that (a+b)(a-b) = a²-b²
(ab + bc)(ab -bc) can be written as a²b² - b²c²
(bc + ca)(bc -ca) can be written as b²c² - c²a²
(ca + ab)(ca - ab) can be written as c²a² - a²b²
→ a²b² - b²c² + b²c² - c²a² + c²a² - a²b²
→ a²b² - a²b² - b²c² + b²c² - c²a² + c²a²
→ 0
2. (a + b + c) (a² + b² + c² – ab – bc – ca) = a³ + b³+ c³ – 3abc
→ a³ + ab² + ac² -a²b - abc -ca² + a²b + b³ + bc² - ab² - b²c - abc + a²c + b²c + c³ - abc - bc² - c²a
→ a³ + b³+ c³ + (- abc - abc - abc) + (ab² - ab² )+ (ac² - ca² ) -(a²b + a²b )+ (bc² - bc² )+ (a²c - c²a) + (b²c - b²c)
→ a³+b³+c³ - 3 abc .
3. (p – q) (p² + pq + q²) = p³ – q³.
→ p³ + p²q + pq² - p²q - pq² - q³
→ p³ - q³ +(p²q - p²q) + (pq² - pq²)
→ p³ - q³
In the figure above, O is a circle. What is the
measure of obtuse angle AOB, in degrees?
Answer:
An obtuse angle is an angle that is bigger than 90° degrees, but doesn’t reach a straight line at 180°.
Step-by-step explanation:
i didnt see a figure above but this is the answer to "what is the measure if obtuse angle in degrees?"
Dtermine the answer to (−5) + 4 and explain the steps using a number line
Answer:
Step-by-step explanation:
=-5 +4
= -1
put a dot on -1 and go from -5 to -1 and then from -1 to -5
Function g can be thought of as a scaled version of f(x)=|x| what is the equation for g(x)?
Answer:
A
Step-by-step explanation:
Khan academy
The equation for the g(x) is g(x) = -4|x| if function g can be thought of as a scaled version of f(x)=|x| 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:
Function g can be thought of as a scaled version of f(x)=|x|
The function f(x):
f(x) = |x|
The blue lines represent the function f(x)
First reflect the function f(x) around the x-axis
F(x) = -|x|
Multiply by the factor 4 to stretch the function:
g(x) = -4|x|
Thus, the equation for the g(x) is g(x) = -4|x| if function g can be thought of as a scaled version of f(x)=|x| option (B) is correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ5
What is the sum of the complex numbers
9- i and – 5 – i?
[tex]9-i+(-5-i)=9-i-5-i=4-2i[/tex]
Solve for g.
-3+5+ 6g = 11 – 3g
g =
Answer:
g = 1
Step-by-step explanation:
-3 + 5 + 6g = 11 - 3g
Move the variables to one side and the numbers to the other:
9g = 9
Simplify:
g = 1
Answer:
g=1
Step-by-step explanation:
-3+5=2
2+6g=8
11-3g=8
makes sense that g will have to be 1
Celine is Drake’s granddaughter. Her age is 4 years greater than of Drake’s age. If Celine is 28 years old, how old is Drake?
Answer:32
Step-by-step explanation:
if selling is 28 and she is 4 years greater than Drake then that is 28-4 which is 32 so Drake is 32 years old
Answer:
The answer is 32.
Step-by-step explanation:
If Celine is 28 and Drake is four years older than her, we do 28+4.
Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-Intercept, and vertex of the function.
f(x)= x^2- 4x-5
+
10-
Line
8
6
4
2-
-10
-8
Answer:
1) Please find attached the graph sowing the line of symmetry
The symmetry line is a vertical line passing through (2, -9)
2) The x-intercept are (5, 0) and (-1, 0)
The y-intercept is (0, -5)
The vertex is (2, -9)
Step-by-step explanation:
The given function is;
f(x) = x² - 4·x - 5
The data values are generated as follows;
x, f(x)
-1, 0
-0.8, -1.16
-0.6, -2.24
-0.4, -3.24
-0.2, -4.16
0, -5
0.2, -5.76
0.4, -6.44
0.6, -7.04
0.8, -7.56
1, -8
1.2, -8.36
1.4, -8.64
1.6, -8.84
1.8, -8.96
2, -9
2.2, -8.96
2.4, -8.84
2.6, -8.64
2.8, -8.36
3, -8
3.2, -7.56
3.4, -7.04
3.6, 6.44
3.8, -5.76
4, -5
4.2, -4.16
4.4, -3.24
4.6, -2.24
4.8, -1.16
5, 0
The minimum is found from differentiating the function, f(x), with respect to x and looking for the zeros of the result as follows;
f'(x) = 2·x -4
f'(x) = 0 = 2·x -4
x = 2
The y-coordinate gives; f(2) = 2² - 4×2 - 5 = -9
Therefore, the symmetry line is a vertical line passing through (2, -9)
The x-intercept is the point at which y = 0, therefore, from f(x) = x² - 4·x - 5, we have;
0 = x² - 4·x - 5 = (x - 5)·(x + 1)
Therefore, the x-intercept are x = 5 or -1
The x-intercept are (5, 0) and (-1, 0)
The y-intercept occur at the point where the x value = 0, therefore, we have;
The y-intercept occur at y = f(0) = 0² - 4·0 - 5 = -5
The y-intercept is (0, -5)
Re-writing the equation in vertex form y = a(x - h)² + k gives;
f(x) = x² - 4·x - 5 = 1·(x - 2)² - 9
Therefore, the vertex is (2, -9)
Answer:
see attached graph
The x-intercept are (5, 0) and (-1, 0)
The y-intercept is (0, -5)
The vertex is (2, -9)
Step-by-step explanation:
Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $65 . For one performance, 25 advance tickets and 35 same-day tickets were sold. The total amount paid for the tickets was 1875 . What was the price of each kind of ticket?
Answer:
same day = 25
advanced = 40
Step-by-step explanation:
Let a = advanced tickets
s = same day tickets
s+a = 65
25a+35s = 1875
Multiply the first equation by -25
-25s -25a = -1625
Add this to the second equation
25a+35s = 1875
-25a -25s= -1625
---------------------------
10s = 250
Divide each side by 10
10s/10 = 250/10
s =25
Now find a
s+a = 65
25+a = 65
a = 40
Answer: same day = 25
advanced = 40
what is this equation in simplest form? 9x + 26 + 7x - 17 = 2x + (-3x) + 5x
Answer:
4x+3=0 or x=-3/4
Step-by-step explanation:
9x+26+7x-17=2x-3x+5x
arrange all numbers with coefficient x at one side let's say the left hand side and constant or real numbers at the right hand side in doing that we get
9x+7x-2x+3x-5x=17-26
12x=-9
(12x)/3=-9/3
4x=-3
x=-3/4
whats the squareroot of 144 needs to be simplified
Answer:
12
Step-by-step explanation:
The square root of any number is basically asking "what number multiplied by itself will equal this number?"
Usually you memorize these, but there's also a quick way to do it.
We know that [tex]10\cdot10=100[/tex], so the square root must be greater than 10.
We also know that [tex]15\cdot15=225[/tex], so the square root must be less than 15.
A good mid point between these numbers is 13. Let's see what 13 squared is:
[tex]13\cdot13=169[/tex]
So it's a bit less than 13. Let's try 12.
[tex]12\cdot12=144[/tex]
So 12 is the square root of 144.
Hope this helped!
Answer:
[tex]\huge\boxed{\sqrt{144}=12}[/tex]
Step-by-step explanation:
[tex]\begin{array}{c|c}144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\\\\144=2\cdot2\cdot2\cdot2\cdot3\cdot3=2^2\cdot2^2\cdot3^2\\\\\sqrt{144}=\sqrt{2^2\cdot2^2\cdot3^2}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{3^2}=2\cdot2\cdot3=12\\\\\text{Used}\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\sqrt{a^2}=a\\\\\text{for}\ a\ge0,\ b\geq0[/tex]
The Cartesian coordinate system can be applied to three-dimensional solids. Instead of two axes, the coordinate system has three. What are the labels? Check all that apply.
A. z
B. y
C. a
D. x
E. w
Answer:
its z y and x
Step-by-step explanation:
can i pls get brainliest
What is the slope of the line between (3, −4) and (−2, 1)?
Answer:
Slope = -1
Step-by-step explanation:
To find the slope of the line between two points, we simply need to take the difference of the y-coordinates over the difference of the x-coordinates.
(-2, 1) and (3, -4)
Slope = (-4 - 1) / (3 - (-2) )
Slope = -5 / ( 5 )
Slope = - 1
Cheers.
help please, got a little lost in everything
Answer:
375 mm cubed
Step-by-step explanation:
The volume would stay the same because the same number of the same pennies are being used.
If the question was asking for the surface area, then the answer would be different.
Hope that helped!!! k
Answer: 375 mm cubed
One leg of a right triangle measures 8 units and the hypotenuse measures 12 units. The perimeter of the triangle is irrational. True False
Answer:
TRUE
Step-by-step explanation:
Length of other leg [tex]= \sqrt {12^2 - 8^2} \\
= \sqrt {144 -64} \\
= \sqrt {80} \\
= 4\sqrt {5} \\[/tex]
Since, [tex] \sqrt 5[/tex] is an irrational number, hence Perimeter of triangle will also be irrational.
TRUE
Answer:
True.
Step-by-step explanation:
The length of the other side = sqrt ( 12^2 - 8^2)
= sqrt (144 - 64)
= sqrt ( 80) which is irrational so the perimeter is also irrational.
(The sum of a rational number and an irrational is irrational).
y=2/5x-12 is it liear or nolinear or both
Answer:
Step-by-step explanation:
y=2/5x-12 it is a linear equation in the form of y=mx+b
the best way to know is to graph the function
Consider a triangle ABC like the one below. Suppose that b=27, c=66, and B=130º. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or".
Answer:
The remaining dimensions of the triangle are [tex]A \approx 31.7368^{\circ}[/tex], [tex]C \approx 18.2632^{\circ}[/tex] and [tex]a \approx 45.3201[/tex].
Step-by-step explanation:
As angle B is an obtuse angle, Angle C can be obtained by means of the Law of Sine:
[tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
[tex]\sin C = \frac{b}{c}\cdot \sin B[/tex]
[tex]C = \sin^{-1}\left(\frac{b}{c}\cdot \sin B \right)[/tex]
Where:
[tex]b[/tex], [tex]c[/tex] - Measures of triangle sides, dimensionless.
[tex]B[/tex], [tex]C[/tex] - Measures of angles, measured in degrees.
If [tex]b = 27[/tex], [tex]c = 66[/tex] and [tex]B =130^{\circ}[/tex], then:
[tex]C = \sin^{-1}\left(\frac{27}{66}\cdot \sin 130^{\circ} \right)[/tex]
[tex]C \approx 18.2632^{\circ}[/tex]
Given that sum of internal angles in triangles equals to 180º, the angle A is now determined:
[tex]A = 180^{\circ}-B-C[/tex]
[tex]A = 180^{\circ}-130^{\circ}-18.2632^{\circ}[/tex]
[tex]A \approx 31.7368^{\circ}[/tex]
Lastly, the length of the side [tex]a[/tex] is calculated by Law of Cosine:
[tex]a = \sqrt{b^{2}+c^{2}-2\cdot b\cdot c\cdot \cos A}[/tex]
[tex]a =\sqrt{27^{2}+66^{2}-2\cdot (27)\cdot (66)\cdot \cos 31.7368^{\circ}}[/tex]
[tex]a \approx 45.3201[/tex]
The remaining dimensions of the triangle are [tex]A \approx 31.7368^{\circ}[/tex], [tex]C \approx 18.2632^{\circ}[/tex] and [tex]a \approx 45.3201[/tex].
Vince went on a 333 day hiking trip. Each day, he walked 3\4 the distance that he walked the day before. He walked 83.2583, point, 25 kilometers total in the trip.
Answer:
x= 36 km
Step-by-step explanation:
Vince went on a 3 day hiking trip. Each day, he walked 3/4 the distance that he walked the day before. He walked 83.25 kilometers total in the trip. How far did Vince walk on the 1st day of the trip?
Assume vince walked x km on the first day .
The following equation can be formed
x + 3/4 x + (3/4)^2 x = 83.25
x + 0.75x + 0.5625x = 83.25
Add the like terms
2.3125x = 83.25
Divide both sides by 2.3125
x = 36 km.
Answer:
36
Step-by-step explanation:
ASAP!!!!!!!!! PLEASE help me with this question! This is really urgent! No nonsense answers please.
==========================================================
Explanation:
Let point A be the center of the circle.
Arc DCF is 316 degrees. Arc FG is 20 degrees. Subtracting the arc measures gives 316-20 = 296 which is the measure of arc DCG, and by extension, it is the measure of reflex angle DAG. The acute angle DAG is 360-296 = 64 degrees
Triangle DAG is isosceles with AD = AG, so the base angles are ADG and AGD. Let's call each of these angles x for now. The sum of the three angles add to 180
x+x+64 = 180
2x+64 = 180
2x = 180-64
2x = 116
x = 116/2
x = 58
Therefore angle ADG is 58 degrees. It adds to angle ADB = 90 to get 90+58 = 148, which is the measure of angle BDG.
Note: angle ADB is 90 because tangent BD forms a right angle with the radius AD.
Another note: angle ADG is half that of the arc it cuts off, so in a sense it's similar to an inscribed angle
Simplify 3 x times the fraction 1 over x to the power of negative 4 times x to the power of negative 3.
Answer:
3x^2
Step-by-step explanation:
Given:
(3x) * {(1/x)^-4 }* (x^-3)
=(3x) * {1 ÷ (1/x)^4} * {1/x^3}
=(3x) * {1(x/1)^4} * (1/x^3)
=(3x) * (x^4) * (1/x^3)
=(3x) (x^4) (1) / x^3
Multiply the denominators
=3x^5 / x^3
Can also be written as
=3*x*x*x*x*x / x*x*x
Divide the x
= 3*x*x / 1
=3x^2
2) In 1000 sq. meter of land a farmer cultivated 765 kg of rice with the wastage of 23.5%. I) Find the weight of the wastage. II) Find the weight and percentage of rice cultivated. 3) If the area has been increased 40 times in size, how much rice will be cultivated (excluding the wastag
Answer:
Weight of wastage=179.775kg
weight of rice cultivated= 585.225 kg
percentage of rice cultivated=76.5%
Step-by-step explanation:
Area of land=100 square meters
Cultivated rice=765kg
Wastage=23.5%
1) Weight of the wastage=23.5% of 765kg
=23.5/100 × 765
=17977.5 / 100
=179.775 kg
2) Weight and percentage of rice cultivated.
weight of rice cultivated = 765 kg - 179. 775 kg
= 585.225 kg
percentage of rice cultivated = 100 - 23.5
= 76.5%
3) if area is increased 40 times in size
New area=1000 square meters × 40
=40,000 square meters
Cultivated rice= 765kg × 40
=30,600 kg
Cultivated rice excluding wastage=585.225 kg × 40
=23,409 kg
Tori and Gavin were trying to solve the equation: (x+1)^2-3=13(x+1) 2 −3=13left parenthesis, x, plus, 1, right parenthesis, squared, minus, 3, equals, 13 Tori said, "I'll add 333 to both sides of the equation and solve using square roots." Gavin said, "I'll multiply (x+1)^2(x+1) 2 left parenthesis, x, plus, 1, right parenthesis, squared and rewrite the equation as x^2+2x+1-3=13x 2 +2x+1−3=13x, squared, plus, 2, x, plus, 1, minus, 3, equals, 13. Then I'll subtract 131313 from both sides, combine like terms, and solve using the quadratic formula with a=1a=1a, equals, 1, b=2b=2b, equals, 2, and c=-15c=−15c, equals, minus, 15."
The other answer is correct, its both !<3
Answer:
Both
Step-by-step explanation:
Both Tori and Gavin are correct, the two methods work. Completed this in Khan Academy, it's correct.
f(x) = x2. What is g(x)?
Answer:
-x^2 - 3
Step-by-step explanation:
SO we know f(x); x^2
when you place a (-), it flips teh image across the x-axis.
Finally, we see that the line is at (0,-3). To get it there, we need to go down 3, which gives us the -3 in the equation.
So we have -x^2-3
(rember the - sign is to flip it across the x-axis, and the -3 is to move the line 3 down the y-axis)
I checked my answer on a calculator btw lol.
How many more festivals had 18 to 23 countries represented than 0 to 5 countries represented?
Answer:
3
Step-by-step explanation:
Here, by reading the histogram, we will provide answer for the question asked.
We want to know how many more festivals had 18 to 23 countries represented than 0 to 5 countries.
Checking the histogram, we can see the 0-5 countries having a value of 1, while the 18-23 has a value of 4.
So, the number of more countries will be simply 4-1 = 3
Answer:
3
Step-by-step explanation:
Factor completely 2c5 + 44c4 + 242c3. 2c3(c + 11)2 2(c + 11)2 2c3(c + 11)(c − 11) 2c3(c2 + 22c + 121)
Answer:
2c^3(c+11)^2
Step-by-step explanation:
2c^5 + 44c^4 + 242c^3
Factor out the greatest common factor
2c^3(c^2+22c+121)
Recognizing inside the parentheses is (a+b) ^2 where a =c and b = 11
2c^3(c+11)^2
how many are 3 raised to 2 ???
Answer:
[tex]\huge \boxed{9}[/tex]
Step-by-step explanation:
3 raised to 2 is 3 to the power of 2.
[tex]3^2 =3 \times 3 = 9[/tex]
3 is multiplied by itself.
The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units. Which expression represents the height of the triangular base of the pyramid? Five-halves StartRoot 2 EndRootunits Five-halves StartRoot 3 EndRootunits 5 StartRoot 2 EndRootunits 5 StartRoot 3 EndRootunits
Answer:
The height of the triangular base of the pyramid is s√3/2 units
Step-by-step explanation:
Here in this question, what we are concerned with is to calculate the height of the equilateral-triangle base of the oblique pyramid.
From the question, we are told that the equilateral triangle has a length of a units.
Let’s have a recall on some of the properties of equilateral triangles;
a. All sides are of equal lengths. Meaning side s is the length of all the sides in this case.
b. All angles are equal, meaning they are 60 degree each.
c. Dropping a perpendicular line from the top vertex to the base length will split the equilateral triangle into two right-angled triangles of angles 60 and 30 each.
So to find the height of this triangular base, we can use any of the two right angled triangles.
Kindly recall that the properties of each would be angles 30, 60 and side length s
so to calculate the height h, we can use trigonometric identities
Mathematically, the trigonometric identity we can use is the sine( side length s represents the hypotenuse, while the height h represents the opposite facing the angle 60 degrees)
Thus; we have
Sine of an angle = length of the opposite/length of hypotenuse
sin 60 = h/s
h = s sin 60
In surd form,
sin 60 = √3/2
Thus;
h = s * √3/2 = s√3/2 units
Answer:
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
Step-by-step explanation:
