Answer:
a) If order matters, choices the player have = 5040
b) If order does not matter, choices the player have = 210
Step-by-step explanation:
n = 10, r = 4
When the order matters, its permutation.
permutation without repetition = P(n, r) = [tex]\frac{n!}{(n - r)!}[/tex]
= [tex]\frac{10!}{(10 - 4)!}[/tex]
= [tex]\frac{10!}{6!}[/tex]
= 5040
When the order doesn't matter, its combination.
combination without repetition= C(n, r) = [tex]\frac{n!}{r!(n - r)!}[/tex]
= [tex]\frac{10!}{4!(10 - 4)!}[/tex]
= [tex]\frac{10!}{4! × 6!}[/tex]
= 210
If order matters, there are 5,040 different choices. If order does not matter, there are 210 different choices.
Explanation:a) If order matters, the player has 10 choices for the first number, 9 choices for the second number (since it cannot be the same as the first), 8 choices for the third number, and 7 choices for the fourth number. Therefore, the total number of different choices is 10 * 9 * 8 * 7 = 5,040.
b) If order does not matter, the player is selecting a combination rather than a permutation. The number of combinations of four numbers chosen from a set of ten is given by the formula nCr = n! / (r!(n-r)!). In this case, n = 10 and r = 4, so the number of different choices is 10! / (4!(10-4)!) = 210.
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solve for x X - 47 = 192
Answer: x = 239
Step-by-step explanation:
You need to get rid of everything else except the x = #
So, to do that you need to take the -47 and add 47 on each side.
That would get you x = 239
Answer:
239
Step-by-step explanation:
X - 47 = 192
X = 192 + 47
X = 239
Graph f(x)=x2 +2x-3 label x and y intercept and vertex with their coordinates and draw axis of symmetry
Answer:
f(x) = x² + 2x - 3 ..….equation1
The graph of function will be a parabola
Standard form of parabola:
y=ax²+bx+c
x-coordinate of the vertex can be found using
x = [tex]\frac{−b}{2a}[/tex]
from equation 1 find values for a, b, and c.
a = 1, b = 2, c = -3 ⇒ x=−2/2(1) ⇒ x = -1
substitute the value of x into equation 1 for y-coordinate
f(-1) = (-1)² + 2(-1) – 3 ⇒ −4
vertex =(-1,−4)
Axis of symmetry = x = -1,
Axis of symmetry is vertical and passes through the vertex with equation
x = -1
For x-intercept, put y = 0
x² + 2x - 3=0 ⇒ x² + 3x -x - 3=0 ⇒ x( x + 3 ) -1 ( x + 3 ) ⇒ ( x − 1 )( x + 3 ) = 0
equate each factor to zero and solve for x
x − 1 = 0 ⇒ x = 1, x + 3 = 0 ⇒ x = -3
x-intercept = { 1, -3 }
For y-intercepts put x = 0
y = (0)² + 2(x) - 3
y = -3
y-intercept = ( 0 , -3 )
The points for the vertex, x-intercepts, and y-intercept and axis of symmetry are plotted on the graph.
So I need to determine what he did wrong is this problem and what the correct step would be?
WORTH 59 POINTS
The top line has 4x^-2, they needed to move the x^-2 to the denominator using the negative exponent rule, so in line 1 instead of 1/y^-2, it should be 1/x^-2
Then the answer would become 4y^3 / x^3
Tickets to the concert cost $5.00 for adults and $2.50 for children. A group of 17 people went to the concert and paid $57.50 for tickets. How many adult tickets were purchased? How many children's tickets were purchased?
6 adults and 11 children.
In order to solve this problem we going to use linear equations.
A group of 17 people went to the concert. There are adults and children in that group x + y = 17 where x are adults and y are children. That group pay $57.50 for tickets, if tickets cost $5.00 for adults and $2.50 for children, then 5.00x + 2.50y = 57.50.
x + y = 17 ----------> y = 17 - x
Substituting the value of y in the equation 5.00x + 2.50y = 57.50:
5.00x + 2.50(17 - x) = 57.50 solving
x = 6
Substituting x = 6 in the equation x + y = 17
6 + y = 17 solving
y = 11
From a group of 17 people who went to the concert 6 are adults and 11 are children.
After eliminating radicals, what quadratic equation can you solve to find the potential solutions of sqrt 2x+3 - sqrt x+1 = 1
Answer:
Step-by-step explanation:
We have given:
√2x+3 - √x+1 = 1
First of all isolate the square root of the left hand side:
√2x+3 = √x+1 +1
Now take square on both sides.
(√2x+3)^2 = (√x+1 +1)^2
Open the R.H.S by squaring formula.
∴(a+b)^2 = a^2+2ab+b^2
2x+3 = (√x+1)^2 + 2(√x+1)(1)+(1)^2
2x+3 = x+1 +2√x+1 +1
2x+3 = x+2 +2√x+1
Combine the like terms:
2x-x+3-2 = 2√x+1
x+1 = 2√x+1
Take square on both sides
(x+1)^2 = (2√x+1)^2
x²+2x+1 = 4x+4
x²+2x-4x+1-4 = 0
x²-2x-3 = 0
Now solve the quadratic equation:
a = 1 , b= -2 , c = -3
x = -b+/-√b²-4ac/2a
x = -(-2)+/-√(-2)² - 4(1)(-3) / 2(1)
x = 2 +/- √4+12 / 2
x = 2+/- √16/2
x = 2+/- 4 /2
x = 2+4/2 , x = 2-4/2
x = 6/2 , x = -2/2
x = 3 , x = -1
The solutions we get is (3, -1).
Answer:
Quadratic Equation: x²-2x-3 = 0
Solutions (Next Question): (3, -1)
Step-by-step explanation:
Absor201 is correct! (look at the BOLDED text in their answer)
if f(x)=x^2 - 12, solve for f (x+4)
Answer:
f(x + 4) = x² + 8x + 4Step-by-step explanation:
Instead of x substitute (x + 4) to f(x) = x² - 12
f(x + 4) = (x + 4)² - 12 use (a + b)² = a² + 2ab + b²
f(x + 4) = x² + 2(x)(4) + 4² - 12
f(x + 4) = x² + 8x + 16 - 12
f(x + 4) = x² + 8x + 4
3 tons of dirt cost $360.00. What is the price per pound
Answer: $0.12 per pound
Step-by-step explanation:
divide $360.00 by 3, then divide it by 1000, because 1000 lbs is 1 ton
Final answer:
To calculate the price per pound of dirt, divide the total cost of $360.00 by the total weight of 6000 pounds, resulting in a cost of $0.06 per pound.
Explanation:
The student asked how much it would cost per pound if 3 tons of dirt cost $360.00. First, it's essential to know how many pounds are in a ton. There are 2000 pounds in one ton. So for 3 tons, there would be 6000 pounds (3 tons x 2000 pounds/ton).
Next, to find the price per pound, you would divide the total cost by the total weight in pounds. That's $360.00 divided by 6000 pounds, which equals $0.06 per pound.
Therefore, the price per pound of dirt is $0.06.
the length of a slide at a water park is 50 feet from the top of the slide to ground level the top of the slide is 20 feet above the ground what is the approximate measure of the angle formed by the top of the slide and vertical support
Answer:
66
Step-by-step explanation:
cos 0=20/50
The approximate measure of the angle formed by the top of the slide and the vertical support is approximately 21.8 degrees.
In trigonometry, the tangent function can help us find the angle in a right-angled triangle. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. In this case, the side opposite the angle is the height of the slide (20 feet), and the adjacent side is the length of the slide (50 feet).
Now, we can use the tangent function to find the angle (θ):
tan(θ) = Opposite / Adjacent
tan(θ) = 20 feet / 50 feet
tan(θ) = 0.4
To find the value of θ, we can take the inverse tangent (also known as arctan or tan⁻¹) of 0.4:
θ ≈ arctan(0.4) ≈ 21.8 degrees
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Which graph shows the graph of a circle with equation x^2+(y-4)^2=16
Answer:
The option on the top left
Step-by-step explanation:
As the equation is [tex]x^2+(y-4)^2=16[/tex]
We know that the circle will have a radius of 4 and will be shifted 4 units up
The center and radius of given circle equation are (0, 4) and 6√6 units respectively.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²
The given circle equation is x²+(y-4)²=216.
Find the properties of the conic section
Center: (0,4)
Radius: 6√6
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
Domain:
[−6√6,6√6],{x∣∣−6√6≤x≤6√6}
Range: [4−6√6,4+6√6],{y∣∣4−6√6≤y≤4+6√6}
Therefore, the center and radius of given circle equation are (0, 4) and 6√6 units respectively.
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Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1?
5,–1, –7, –13, –19
Answer:
[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]
Step-by-step explanation:
The terms of the sequence are:
[tex]5,-1,-7,-13,-19[/tex]
The first term of this sequence is [tex]f(1)=5[/tex].
There is a constant difference among the terms.
This constant difference can determined by subtracting a previous term from a subsequent term.
[tex]d=-1-5=-6[/tex]
The general term of this arithmetic sequence is given recursively by [tex]f(n)=f(n-1)+d[/tex]
We substitute the necessary values to obtain:
[tex]f(n)=f(n-1)+-6[/tex]
Or
[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]
Answer:
C
Step-by-step explanation:
Hillary joins a gym. She pays $15 per month plus $13.75 for each personal training session she does. If her monthly bill is $125, how many personal training sessions did she get that month?
Subtract the monthly fee from the total, then divide by the price of each session.
125 - 15 = 110
110 / 13.75 = 8
She got 8 sessions.
The ordered pair (-9, 1) is a solution to the inequality y ≤ 2x - 7
Replace x in the equation with the x value from the ordered pair and see if the y value meets the inequality.
y ≤ 2(-9) -7
y ≤ -18 - 7
y ≤ -25
The y value in the ordered pair is 1, so replace y with 1 and see if the inequality is true:
1 ≤ -25
1 is a positive value and the equation equals a negative value, so this is not true, because 1 is greater than -25.
What is the value of -6x3-y2-3xy if x=-2 and y=4
The answer is:
The value of the given expression evaluated with x equals to -2 and y equals to 4, is equal to 56 units.
Why?To solve the problem, we need to evaluate both variables for the given values:
[tex]x=-2[/tex]
and
[tex]y=4[/tex]
So, we are given the expression:
[tex]-6x^{3}-y^{2}-3xy[/tex]
Then, evaluating the given values for both variables, we have:
[tex]-6*(-2)^{3}-(4)^{2}-3*(-2)*(4)=(-6*-8)-(16)+24=48-16+24=56[/tex]
Hence, we have that the answer is:
The value of the given expression evaluated with x equals to -2 and y equals to 4, is equal to 56 units.
Have a nice day!
Answer:
The value of given expression = 56
Step-by-step explanation:
It is given an expression in variable x and y
-6x³ - y² - 3xy
To find the value of given expression
Let expression be,
-6x³ - y² - 3xy
When x = -2 and y =4
-6x³ - y² - 3xy = -6(-2)³ - 4² - (3 * -2 * 4)
= -6*-8 - 16 + 24
= 48 - 16 + 24
= 56
Therefore the value of given expression is 56
My teacher dis the first one
Answer:
x² + 11x + 30
Step-by-step explanation:
Solve using the FOIL method. The FOIL method is:
FOIL =
First
Outside
Inside
Last
, and is the order in which you do the problem.
(x + 5)(x + 6)
Follow FOIL. First, solve First (multiply x with x)
(x)(x) = x²
Next, multiply Outside (multiply x with 6)
(x)(6) = 6x
Then, multiply Inside (multiply 5 with x)
(5)(x) = 5x
Finally, multiply Last (multiply 5 with 6)
(5)(6) = 30
Combine like terms (terms with the same amount of variables, and the same variables)
x² + 6x + 5x + 30
x² + (6x + 5x) + 30
x² + 11x + 30
x² + 11x + 30 is your answer.
~
A cylindrical-shaped cup has a height of 7 centimeters and a volume of 112 cubic centimeters. Henry fills the cup completely full of water. He then pours the water from the cup and completely fills a cone. If the cone has the same radius as the cup, what is the height of the cone?
let's bear in mind that the cylinder and the cone both have the same volume of 112 cm³, and the same radius, but different heights.
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} V=112\\ h=7 \end{cases}\implies 112=\pi r^2(7)\implies \cfrac{112}{7\pi }=r^2\implies \cfrac{16}{\pi }=r^2 \\\\\\ \sqrt{\cfrac{16}{\pi }}=r\implies \cfrac{\sqrt{16}}{\sqrt{\pi }}=r\implies \cfrac{4}{\sqrt{\pi }}=r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\qquad \qquad \begin{cases} r=\frac{4}{\sqrt{\pi }}\\ V=112 \end{cases}\implies 112=\cfrac{\pi \left( \frac{4}{\sqrt{\pi }} \right)^2(h)}{3} \\\\\\ 336=\pi \left( \cfrac{4^2}{(\sqrt{\pi })^2} \right)h\implies 336=\pi \cdot \cfrac{16h}{\pi }\implies 336=16h \\\\\\ \cfrac{336}{16}=h\implies \blacktriangleright 21=h \blacktriangleleft[/tex]
Calculate the radius of the cup using its volume and height. Determine the cone's height by applying the cup's height to the volume formula for a cone after elimination.
The volume of the cup:
The formula for the volume of a cylinder: V = πr²h.
The formula for the volume of a cone: V = (π/3)r²h.
(πr²h)cylinder = ((π/3)r²h)cone
Since the cone has the same radius as the cylindrical cup and given h = 7 cm
Finding the height of the cone by eliminating:
[tex]h_{cylinder}[/tex] = [tex]h_{cone}[/tex]×(1/3)
[tex]h_{cone}[/tex] = 3 × 7 = 21
Therefore, height of cone is 21 cm.
Carlos is half as old as Andre Andre is 15 years older than Carlos how old is Andre
Carlos is 15 years old and Andre is 30 years old.
Explanation:Let's represent Carlos' age as 'x', and Andre's age as 'y'.
We are given that Carlos is half as old as Andre, so we can write the equation:
x = (1/2)y
We are also told that Andre is 15 years older than Carlos, so we can write the equation:
y = x + 15
Substituting the value of y from the second equation into the first equation, we get:
x = (1/2)(x + 15)
Now, we can solve for x:
2x = x + 15
x = 15
Therefore, Carlos is 15 years old. Andre's age can be found by substituting the value of x into the second equation:
y = 15 + 15
y = 30
So, Andre is 30 years old.
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Amira is solving the equation x2 – 6x = 1. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?
–9
8
9
36
Answer:
9
Step-by-step explanation:
When the leading coefficient (the coefficient of the x² term) is 1, we can complete the square by taking the b coefficient (coefficient of the x term), dividing it by 2, squaring the result, and adding it to both sides.
b = -6
b/2 = -3
(b/2)² = 9
Add 9 to both sides to make the left side a perfect-square trinomial.
To form a perfect square trinomial from the equation x²-6x, add 9 to both sides. This is achieved by halving the coefficient of x and squaring the result.
Explanation:Amira can make the left side of the equation, x² - 6x, a perfect-square trinomial by adding 9 to both sides. The process for this involves completing the square. Half of the coefficient of x, which is -6, is -3. Squaring -3 gives 9. Therefore, Amira should add 9 to both sides of the equation to get x² - 6x + 9 = 1 + 9, simplifying to (x-3)² = 10. This results in a perfect-square trinomial on the left.
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The Finest Hour department store wants to run a special ad this week in The Country Times. It wants to run a half-page ad on Friday, and a full-page ad on Saturday and Sunday. How much will it cost the Finest Hour for the ads?
Sorry this took awhile.
So for Friday, it would be $550
Saturday, $895
Sunday, 1,095
So the total is $2540 if you add the numbers up. Hope this helps!
If y varies directly as x and y=4 when x=-2 find y when x=30
Answer:
Step-by-step explanation:
y=kx
4=k(-2)
k=-2
y=-2x
when x=30
y=-2*30=-60
Write the slope-intercept form of the equation for the line.
let's use those two endpoints in the line of (-5 , 2) and (5 , -1)
[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-2}{5-(-5)}\implies \cfrac{-3}{5+5}\implies -\cfrac{3}{10}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=-\cfrac{3}{10}[x-(-5)]\implies y-2=-\cfrac{3}{10}(x+5) \\\\\\ y-2=-\cfrac{3}{10}x-\cfrac{3}{2}\implies y=-\cfrac{3}{10}x-\cfrac{3}{2}+2\implies y=-\cfrac{3}{10}x+\cfrac{1}{2}[/tex]
Answer:
y=-(3/10)x+(1/2)
Step-by-step explanation:
Let
A(-5,2),B(5,-1)
step 1
Find the slope m
m=(-1-2)/(5+5)
m=-3/10
step 2
Find the equation of the line into slope point form
we have
m=-3/10
point A(-5,2)
y-2=(-3/10)(x+5) ----> equation of the line into slope point form
Convert to slope intercept form -----> isolate the variable y
y=-(3/10)x-(15/10)+2
y=-(3/10)x+(5/10)
simplify
y=-(3/10)x+(1/2)
Someone left me a ______ message on my voicemail; I had no idea what it meant.
Cryptic
Boisterous
Petulant
Jovial
Answer:
It is cryptic
Step-by-step explanation:
It is cryptic bc it means secretive and with hidden meaning
Answer:
Cryptic
Step-by-step explanation:
Cryptic means "having a meaning that is mysterious or obscure," so this would be the right answer
Why the others aren't correct:
Boisterous- Noisy, energetic, cheerful, rowdy [This doesn't fit the sentence]
Petulant- Childishly sulky [pouty] or bad tempered [This doesn't fit the sentence]
Jovial- Cheerful and friendly [This doesn't fit the answer]
Thus, the answer is cryptic.
I hope this helps!
A cone-shaped dispenser is filled with cereal. The cone has a radius of 1.5 inches and a height of 5 inches. Which measurement is closest to the volume of cereal that the cone-shaped dispenser holds?
Possible Answers:
A - 3.75
B - 11.78
C - 141.37
D - 47.12
Answer:
Option B. [tex]11.78\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3} \pi r^{2}h[/tex]
we have
[tex]r=1.5\ in[/tex]
[tex]h=5\ in[/tex]
substitute
[tex]V=\frac{1}{3} \pi (1.5)^{2}(5)[/tex]
[tex]V=3.75\pi\ in^{3}[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]V=3.75(3.14)=11.78\ in^{3}[/tex]
A rectangle is 7 cm Long and 6 cm wide what is it's area
Answer:
A = 42 cm^2
Step-by-step explanation:
To find the area of a rectangle , multiply the length and the width
A = lw
A = 7cm * 6 cm
A = 42 cm^2
3. I need help with question in the attached picture!
ANSWER
p
[tex]{f}^{ - 1} (x) = 3x + 4[/tex]
EXPLANATION
The line r has equation,
[tex]f(x) = \frac{x - 4}{3} [/tex]
The line that represents
[tex] {f}^{ - 1} [/tex]
is p.
To find the equation of p, we let
[tex]y = \frac{x - 4}{3} [/tex]
We now interchange x and y.
[tex]x= \frac{y - 4}{3} [/tex]
We solve for y,
[tex]3x=y - 4[/tex]
[tex]y = 3x + 4[/tex]
Therefore
[tex] {f}^{ - 1} (x) = 3x + 4[/tex]
You are riding your bike and notice the square sign above. You mentally draw a straight line from point A to C.
1. Describe the angle relationship between ∠DCA and ∠BCA
2. Your sister says that the angles ∠DCA and ∠BCA are supplementary angles. Is she correct? Explain your reasoning
(both questions are separate)
1. The angles DCA and BCA are the same.
2. Angles DCA and BCA are not supplementary. Since the both of them add up to 90° (we know that angle c is equal to 90° because in a right square all angles are 90°) the angles would be complementary, not supplementary. Supplementary angles add up to 180°
The angle relationship between ∠DCA and ∠BCA are equal and they are complementary angles.
What is a square?A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.
Given that, ABCD is a square.
Here, a straight line from point A to C.
1) AC is diagonal, ∠DCA and ∠BCA are equal.
2) ∠DCA and ∠BCA are equal and added to 90°.
Therefore, the angle relationship between ∠DCA and ∠BCA are equal and they are complementary angles.
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Given: is a diameter
m 1 = 100°
m BC= 30°
m AD=
50
80
100
Answer:
100
Step-by-step explanation:
1=ad=100
and I need more characters so don't mind me.
Answer:
The correct option is 3. The measure of arc AD is 100°
Step-by-step explanation:
Given information: BD is a diameter, ∠1 = 100° and arc BC=30°.
The central angle of an arc is the measure of arc.
From the given figure it is clear that the central angle of arc AD is equal to the angle 1.
[tex]Arc(AD)=\angle 1[/tex]
It is given that ∠1 = 100°
[tex]Arc(AD)=100^{\circ}[/tex]
The measure of arc AD is 100°, therefore the correct option is 3.
which sampling method starts with a random number and then selects every “k”th number thereafter?
A. simple random sampling
B. systematic random sampling
C. stratified random sampling
D. Cluster sampling
Answer:
B. Systematic Random Sampling
Step-by-step explanation:
The process of systemic random sampling involves randomly selecting the starting point but the succeeding points will be based on the interval in between each point. The interval is computed by dividing the population by the sample size.
Answer:
B. Systematic Random Sampling
Step-by-step explanation:
none that i can explain
This consists of more than one answer. Please read carefully!! Use the first attachment for the two questions.
**Part A**
Write a simplified equation to solve for x in terms of AT, the area of the tile. If necessary, use rational coefficients instead of root symbols.
**Part B**
If the tile is a square with a length of b centimeters, what would AT be in terms of b?
Answer:
Part A)AT=16x^2
Part B)AT=4b^2 +12x^2
Step-by-step explanation:
Part A:
length of each side of square in tile=x
length of each small base side of trapezoid in tile=x
length of each large base side of trapezoid in tile=2x
height of each trapezoid in tile=x
Area of each square in tile= x^2
Area of each trapezoid in tile= x(x+2x)/2
= (3x^2)/2
area of squares inside tile= 4(x^2)
area of trapezoids inside tile= 8[(3x^2)/2]
Area of tile, AT= area of squares inside tile+area of trapezoids in tile
AT= 4(x^2) + 8[(3x^2)/2]
= 4x^2 + 12x^2
= 16x^2
Part B)
if If the tile is a square with a length of b centimeters then AT
= 4b^2 +12x^2 !
30 POINTS,NEED HELP ASAP !!!
Which rule yields the dilation of the figure CDEF centered at the origin?
A) (x, y) → (4x, 4y)
B) (x, y) → (0.25x, 0.25y)
C) (x, y) → (x + 4, y + 4)
D) (x, y) → (x + 0.25, y + 0.25)
Answer: OPTION A.
Step-by-step explanation:
You can observe that in the figure CDEF the vertices are:
[tex]C(-2,-1),\ D(-2,0),\ E(2,2)\ and\ F(2,1)[/tex]
And in the figure C'D'E'F' the vertices are:
[tex]C'(-8,-4),\ D'(-8,0),\ E'(8,8)\ and\ F'(8,4)[/tex]
For this case, you can divide any coordinate of any vertex of the figure C'D'E'F' by any coordinate of any vertex of the figure CDEF:
For C'(-8,-4) and C(-2,-1):
[tex]\frac{-8}{-2}=4\\\\\frac{-4}{-1}=4[/tex]
Let's choose another vertex. For E'(8,8) and E(2,2):
[tex]\frac{8}{2}=4\\\\\frac{8}{2}=4[/tex]
You can observe that the coordinates of C' are obtained by multiplying each coordinate of C by 4 and the the coordinates of E' are also obtained by multiplying each coordinate of E by 4.
Therefore, the rule that yields the dilation of the figure CDEF centered at the origin is:
[tex](x, y)[/tex]→[tex](4x, 4y)[/tex]
Answer:
A. (x, y) => (4x, 4y) this will help you out ;-)
x^y=p
Express in logarithmic form for the base.
ANSWER
[tex]y= log_{x}(p)[/tex]
EXPLANATION
The given expression is
[tex] {x}^{y} = p[/tex]
We take logarithm of both sides to base x.
[tex] log_{x}( {x}^{y} ) = log_{x}(p) [/tex]
Apply the power rule of logarithms to get:
[tex]ylog_{x}( {x}) = log_{x}(p)[/tex]
Logarithm of the base is 1.
This implies that,
[tex]y( 1) = log_{x}(p)[/tex]
[tex]y= log_{x}(p)[/tex]