Answer:
x^2 = 12 y equation of the directrix y=-3x^2 = -12 y equation of directrix y= 3y^2 = 12 x equation of directrix x=-3y^2 = -12 x equation of directrix x= 3Step-by-step explanation:
To find the equation of directrix of the parabola, we need to identify the axis of the parabola i.e, parabola lies in x-axis or y-axis.
We have 4 parts in this question i.e.
x^2 = 12 yx^2 = -12 yy^2 = 12 xy^2 = -12 xFor each part the value of directrix will be different.
For x² = 12 y
The above equation involves x² , the axis will be y-axis
The formula used to find directrix will be: y = -a
So, we need to find the value of a.
The general form of equation for y-axis parabola having positive co-efficient is:
x² = 4ay eq(i)
and our equation in question is: x² = 12y eq(ii)
By putting value of x² of eq(i) into eq(ii) and solving:
4ay = 12y
a= 12y/4y
a= 3
Putting value of a in equation of directrix: y = -a => y= -3
The equation of the directrix of the parabola x²= 12y is y = -3
For x² = -12 y
The above equation involves x² , the axis will be y-axis
The formula used to find directrix will be: y = a
So, we need to find the value of a.
The general form of equation for y-axis parabola having negative co-efficient is:
x² = -4ay eq(i)
and our equation in question is: x² = -12y eq(ii)
By putting value of x² of eq(i) into eq(ii) and solving:
-4ay = -12y
a= -12y/-4y
a= 3
Putting value of a in equation of directrix: y = a => y= 3
The equation of the directrix of the parabola x²= -12y is y = 3
For y² = 12 x
The above equation involves y² , the axis will be x-axis
The formula used to find directrix will be: x = -a
So, we need to find the value of a.
The general form of equation for x-axis parabola having positive co-efficient is:
y² = 4ax eq(i)
and our equation in question is: y² = 12x eq(ii)
By putting value of y² of eq(i) into eq(ii) and solving:
4ax = 12x
a= 12x/4x
a= 3
Putting value of a in equation of directrix: x = -a => x= -3
The equation of the directrix of the parabola y²= 12x is x = -3
For y² = -12 x
The above equation involves y² , the axis will be x-axis
The formula used to find directrix will be: x = a
So, we need to find the value of a.
The general form of equation for x-axis parabola having negative co-efficient is:
y² = -4ax eq(i)
and our equation in question is: y² = -12x eq(ii)
By putting value of y² of eq(i) into eq(ii) and solving:
-4ax = -12x
a= -12x/-4x
a= 3
Putting value of a in equation of directrix: x = a => x= 3
The equation of the directrix of the parabola y²= -12x is x = 3
PLZ HELP IM ON A TIMELINE HURRY
Answer:
5 x 5, 2 raised to the fifth power, 25
6 x 6 x 6, six cubed, 216
1/5 2, one fifth cubed, 1/5
62, 6 x 6, 36
hope this helped please give me the brainliest answer?
Have a good day ma dude!!! <3
5. Solve the equation. 8/x+3 = 1/x+1
Answer:
x = -5/7
Step-by-step explanation:
8 1
---------- = ----------
x+3 x+1
Using cross products
8 (x+1) = 1 (x+3)
Distribute
8x+8 = x+3
Subtract x from each side
8x-x +8 = x-x+3
7x+8 =3
Subtract 8 from each side
7x +8-8 =3-8
7x = -5
Divide each side by 7
7x/7 = -5/7
x = -5/7
Which expression has a value of 36?
A. 9/12 x 48
B. 6/7 x 21
C. 10/13 x 39
D. 3/7 x 42
The expression that has a value of 36 is A. 9/12 x 48
Which expression has a value of 36?
From the question, we have the following parameters that can be used in our computation:
A. 9/12 x 48
B. 6/7 x 21
C. 10/13 x 39
D. 3/7 x 42
Evaluating the expressions, we have
A. 9/12 x 48 = 36
B. 6/7 x 21 = 18
C. 10/13 x 39 = 30
D. 3/7 x 42 = 18
Hence, the expression that has a value of 36 is A. 9/12 x 48
8 * 4.9999a(345.5 x .98)^9
Answer:
Step-by-step explanation:
Always do what is inside the brackets first.
345.5 * 0.98 = 338.59
Now raise this to the 9th power.
338.58^9 = 5.8488*10^22
You are now finished with the brackets.
8*4.9999a = 39.9992a
Now multiply by 5.84 * 10^22
2.3395 * 10^24
If cos0= -5/13 and sin 0<0, what is tan 0
Answer:
12/5
Step-by-step explanation:
I doubt that you actually meant If cos0= -5/13 and sin 0<0. Please use a Greek letter, such as Ф, to represent the angle.
If you'd do this, you'd have:
If cosФ= -5/13 and sin Ф<0
cos Ф and sin Ф are both negative in Quadrant III.
Recall that cos Ф = adj / hyp, and that hyp is always +. Thus, adj = -5 and hyp = +13. Using the Pythagorean Theorem to find opp:
opp² + adj² = hyp², or:
opp² = hyp² - adj². Applying this, we find that opp = -12.
Recall that tan Ф = opp / adj.
Here,
tan Ф = -12 / (-5) = +12/5
Sam has 2/3 of a piece of poster board. He cuts the poster board into 6 equal size pieces. What part of the whole poster board is each smaller piece?
2/3 divided by 6
2/3 times 1/6
1/9
Both circles have the same center. The circumference of the inner circle is 77.872 centimeters. What is the area of the shaded region?
Answer:
The area of the shaded region is [tex]875.68\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the large circle minus the area of the inner circle
step 1
Find the radius of the inner circle
we know that
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=77.872\ cm[/tex]
substitute and solve for r
[tex]77.872=2(3.14)r[/tex]
[tex]r=77.872/[2(3.14)]=12.4\ cm[/tex]
step 2
Find the radius of the large circle
[tex]r=12.4+8.4=20.8\ cm[/tex]
step 3
Find the area of the shaded region
[tex]A=(3.14)[20.8^{2} -12.4^{2}]= 875.68\ cm^{2}[/tex]
The area of the shaded region is: 875.60 square centimeters
What is the area of the shaded region?The formula for the circumference of a circle is:
C = 2πr
where:
C is Circumference
r is radius
We are told the the circumference of the inner circle is 77.872 cm
Thus:
2πr = 77.872
r = 77.872/2π
r = 12.39 cm
Total radius of larger circle = 12.39 + 8.4 = 20.79 cm
Area of larger circle = π * 20.79²
Area of larger circle = 1357.87 cm²
Area of smaller circle is: π * 12.39²
Area of smaller circle is: 482.27 cm²
The area of the shaded region = 1357.87 cm² - 482.27 cm²
The area of the shaded region = 875.60 square centimeters
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Back side lateral area and surface area
This is a regular pyramid. A regular pyramid is a right pyramid whose base is a regular polygon and whose apex is directly above the centre of the base. The lateral surface area is the sum of the areas of all the lateral faces while the surface area is the sum of all the lateral faces plus its base. In this exercise, the base is a square so this is also a square pyramid. Next, we have:
LATERAL SURFACE AREA:
For the lateral sides, we have four identical triangles, so the area of a triangle can be found as:
[tex]A=\frac{bh}{2} \\ \\ Where: \\ \\ b:base \\ \\ h:height[/tex]
and the lateral surface will be four times this value:
[tex]S_{L}=4A[/tex]
The base of the triangle is the same as the base of the square. So:
[tex]b=9yd[/tex].
On the other hand, the height of the triangle is the slant height of the pyramid, which is:
[tex]h=10yd[/tex]
So the area of a triangle is:
[tex]A=\frac{(9)(10)}{2} \\ \\ A=45yd^2[/tex]
Therefore:
[tex]S_{L}=4(45)\\ \\ \boxed{S_{L}=180yd^2}[/tex]
SURFACE AREA:
The surface area can be found as:
[tex]S=S_{L}+A_{b} \\ \\ Where: \\ \\ A_{b}: Area \ of \ the \ base \\ \\ S_{L}: Lateral \ surface[/tex]
Calculating the area of the base, which is a square, we have:
[tex]A_{b}=b^2 \\ \\ A_{b}=9^2 \\ \\ A_{b}=81yd^2[/tex]
Therefore:
[tex]S=180+81 \\ \\ \boxed{261yd^2}[/tex]
8. Find the lateral and surface area.In this case, we have another similar pyramid compared to the previous one, but we are given the height of the pyramid and we'll name it [tex]H[/tex] in capital letter. We know that the area of a triangle is:
[tex]A=\frac{bh}{2} \\ \\ Where: \\ \\ b:base \\ \\ h:height[/tex]
and the lateral surface will be:
[tex]S_{L}=4A[/tex]
To find [tex]h[/tex], which is the slant height of the pyramid, we need to use the Pythagorean theorem. Next, it is true that:
[tex]h=\sqrt{\left(\frac{b}{2}\right)^2+H^2} \\ \\ b=14 \\ H=12 \\ \\ h=\sqrt{\left(\frac{14}{2}\right)^2+12^2} \therefore h=\sqrt{193}[/tex]
So the area of a triangle is:
[tex]A=\frac{(14)(\sqrt{193})}{2} \\ \\ A=7\sqrt{193}ft^2[/tex]
Therefore:
[tex]S_{L}=4(7\sqrt{193})\\ \\ S_{L}=28\sqrt{193}ft^2 \approx 388.9884[/tex]
Rounding to the nearest tenth:
[tex]\boxed{S_{L}=389.0ft^2}[/tex]
SURFACE AREA:
We know that the surface area can be found as:
[tex]S=S_{L}+A_{b} \\ \\ Where: \\ \\ A_{b}: Area \ of \ the \ base \\ \\ S_{L}: Lateral \ surface[/tex]
Calculating the area of the base, which is a square, we have:
[tex]A_{b}=b^2 \\ \\ A_{b}=14^2 \\ \\ A_{b}=196ft^2[/tex]
Therefore:
[tex]S=28\sqrt{193}+196 \\ \\ S \approx 584.9884ft^2[/tex]
Rounding to the nearest tenth:
[tex]\boxed{S=585ft^2}[/tex]
9. Lateral surface area.Here Patrick is making a paper model of castle. He has a net, so he can fold it to build up a pyramid. That's amazing, right? Well, recall that for a pyramid like that the lateral surface area is the area of the lateral faces, that are all triangles. Thus, for a triangle:
[tex]A=\frac{bh}{2} \\ \\ Where: \\ \\ h: \ slant \ height \ of \ the \ pyramid \\ \\ b: base \ of \ the \ pyramid[/tex]
The slant height of the pyramid is [tex]h=20cm[/tex] because this is the same height of the triangle. On the other hand, the base is [tex]b=15cm[/tex]. So:
[tex]A=\frac{15(20)}{2} \\ \\ h=150cm^2[/tex]
Next the lateral surface area is:
[tex]S_{L}=4(150) \\ \\ \boxed{S_{L}=150cm^2}[/tex]
________________
THE OTHER ANSWERS HAVE BEEN ATTACHED BELOW.what is the value of x?
•4
•4√3
•8
•8√3
Answer:
4√3Step-by-step explanation:
Look at the picture.
We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
Therefore we have the equation:
[tex]x=\dfrac{8\sqrt3}{2}\\\\x=4\sqrt3[/tex]
two times a number plus 8 is the same as 20 minus the number
Answer:
2x+8=20-x
Step-by-step explanation:
if it is an equation you are asking that will be it
2x + 8=20 - x
That is the equation. As you are reading the sentence try writing down exactly what it says. “2 times a number” We know that “times” means multiply, but what are we multiplying. It says to multiply 2 and a number, but we don’t know that number so we call it “x.” Then, it says “plus 8” or add 8. From that information we should come up with the expression 2x + 8. Then, it states “is the same as” which basically means equal to or =. Finally, it states “20 minus the number.” We subtract 20 and the number which can be shown as 20 - x.
All together the equation is written as 2x + 8=20 - x
We can simply do this by writing exactly what the sentence states in the order that it is written.
Identify the terms, coefficients, and constants in the expression 3x+10.
Answer:
Terms (in BOLD) : 3x+10
two terms
Coefficients (in BOLD) : 3x+10
one coefficient
Constants (in BOLD) : 3x+10
one constant
Step-by-step explanation:
Terms are the contents in the equation of such. For example, 10+4n. There are two terms. Coefficients are the number next to a variable. For example, 9x. 9 is the coefficient. Constants are numbers without a variable. Numbers like 7, 8, 9, 10-- they don't have variables so they are constants in an equation. Now, knowing this information lets get to work!
The equation: 3x+10
Terms (in BOLD) : 3x+10
two terms
Coefficients (in BOLD) : 3x+10
one coefficient
Constants (in BOLD) : 3x+10
one constant
Hope this helps!!
-Ketifa
Final answer:
The expression 3x+10 consists of two terms: 3x (with the coefficient 3) and 10 (the constant).
Explanation:
In the expression 3x+10, there are two terms: 3x and 10. The term 3x consists of a variable (x) and a coefficient (3), which is the number multiplying the variable.
The term 10 is a constant because it does not contain any variables and its value does not change. The coefficients in this expression are therefore the number 3, and the constant is 10.
The function below describes the population of caribou in a tundra, where f(t) represents the number of caribou, in hundreds, and t represents the time, in years.
f(t)=1.8(1.2)^t
Initially, the tundra has _____ caribou, and every ____ , the number of caribou increases by a factor of ____ .
Answer:
Initially, the tundra has 180 caribou, and every year , the number of caribou increases by a factor of 1.2 .
Step-by-step explanation:
"Initially" generally means "when t=0." Put 0 where t is in the function and evaluate it:
f(0) = 1.8(1.2)^0 = 1.8(1) = 1.8 . . . . . hundreds
1.8 hundreds is 1.8×100 = 180.
__
t is in years, so the simplest choice for the second blank in the statement is "year".
__
The exponent of 1.2 is t, which means that 1.2 is a factor of the expression the number of times specified by t.
for t=0, f(0) = 1.8
for t=1, f(1) = 1.8(1.2)
for t=2, f(2) = 1.8(1.2)(1.2)
for t=3, f(3) = 1.8(1.2)(1.2)(1.2)
Perhaps you can see that every year, the number increases by a factor of 1.2.
_____
You could put "3 years" in the second blank, then the third blank would be 1.2³ = 1.728. While correct, it is probably not what is expected by your answer checker.
Answer:
180
1 year
1.2
Step-by-step explanation:
got it correct on edmentum
Solve for p.
2(p + 1) = 18
Answer:
p = 8
Step-by-step explanation:
Subtract 18 from behind the equal sign to cancel it out. This leaves you with 2(p+1)- 18= 0.
Next you'll need to pull out the terms to work with the beginning of the problem. 2(p+1)- 18= 0 would turn into 2p - 16 = 2(p - 8).
This would leave you with 2= 0, but that's not true so continue on to the variable.
So p - 8= 0 making the answer p = 8
In triangle XYZ, angle Z is a right angle. If sinX = 3/4, find tan Y.
ANSWER
[tex]{ \tan(y) } = \frac{ \sqrt{7} }{3}[/tex]
EXPLANATION
If
[tex] \sin(X )= \frac{3}{4} [/tex]
[tex] \sin(X )= \frac{opposite}{hypotenuse} [/tex]
This implies that the opposite is 3 units and the hypotenuse is 4 units.
We now find the adjacent side using the Pythagoras Theorem.
[tex] {a}^{2} + {o}^{2} = {h}^{2} [/tex]
[tex] {a}^{2} + {3}^{2} = {4}^{2} [/tex]
[tex]{a}^{2} + 9 =16[/tex]
[tex] {a}^{2} =16 - 9[/tex]
[tex]{a}^{2} = 7[/tex]
[tex]{a}= \sqrt{7} [/tex]
[tex] { \tan(y) } = \frac{opposite}{adjacent} [/tex]
The side opposite to Y is √7 and the side adjacent to Y is 3.
[tex] { \tan(y) } = \frac{ \sqrt{7} }{3} [/tex]
You invest $5,175 in a stock plan. It increases 9% the first year then loses 5% of its value the second year. What is your gain compared to your original investment?
A. 183.71
B. 195.65
C. 201.14
D. 185.21
Answer:
A. 183.71
Step-by-step explanation:
Original investment in stock plan = $5175
Increase in the first year of investment in stock plan = 9% of $5175
= 0.09 ( $5175)
= $465.75
then new value of investment in stock plan = $5175 + $465.75 = $5640.75
Loss in the investment of stock plan = 5% of $5640.75
= 0.05 ( $5640.75)
= $282.0375
then new value of investment in stock plan = $5640.75 - $282.0375 = $5358.7125
Now let's find difference between latest value and the original value of investment
$5358.7125 - $5175 = $183.7125
Hence choice A. 183.71 is correct.
identify the frequency of the graph
ANSWER
[tex] \frac{1}{2} [/tex]
EXPLANATION
The frequency of a wave function refers to the number of times the graph repeats its cycle within the interval [0,2π]
We can observe explicitly from the graph that the frequency is half.
The period of the given function is 4π
[tex] \frac{2\pi}{b} = 4\pi[/tex]
[tex]b = \frac{2\pi}{4\pi} = \frac{1}{2} [/tex]
Hence the frequency is half.
I need help with this question on USA Test Prep
Answer choice C, 1.5 x 3= 4.5
your correct answer would be c. 3
Use the substitution method to solve the system of equations 3x+2y=13 y=x-1
Answer:
b
Step-by-step explanation:
The solution of the equations 3x + 2y = 13 y = x - 1 will be (3, 2). Then the correct option is B.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equations are given below.
3x + 2y = 13 ...1
y = x - 1 ...2
Then from the equations 1 and 2, we have
3x + 2(x - 1) = 13
5x - 2 = 13
5x = 15
x = 3
Then the value of y will be
y = x - 1
y = 3 - 1
y = 2
More about the linear system link is given below.
https://brainly.com/question/20379472
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How to find the area of a polygon
The method of calculating the area of a polygon depends on the type of polygon. Rectangles and triangles have straightforward calculations, however complex polygons might need to be divided into simpler figures. Certain figures such as circles and ellipses have unique formulas.
Explanation:Calculating the area of a polygon depends on the type of polygon. For simple regular polygons like a rectangle, area can be found by length x width, for triangles it's base x height / 2. In particular complex polygons, the shape might need to be divided into simpler shapes, and the areas calculated separately.
For a circle, the area A = πr², where r is the radius. If you're trying to find the area of an ellipse, it can be calculated by A = πab, with a and b being half the long and short axis respectively.
The process to determine the area of a frequency polygon is little complex. First, the range of each class interval must be determined, and then multiplied by the frequency of that interval, with these values then being added together.
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To find the area of a polygon, you can divide it into smaller shapes with known area and add them up. Alternatively, you can use the formula for the area of a regular polygon.
Explanation:To find the area of a polygon, you can use different formulas depending on the type of polygon. One general method is to divide the polygon into smaller shapes whose area you know how to calculate, such as triangles or rectangles, and then add up the areas of those shapes. For example, to find the area of a rectangle, you multiply its length by its width.
Another method is to use the formula for the area of a regular polygon, which is given by the formula: Area = 1/2 * ap, where 'a' is the apothem (the distance from the center of the polygon to the middle of one of its sides) and 'p' is the perimeter of the polygon.
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Which is equivalent to (9y2-4x)(9y2+4x) , and what type of special product is it?
Answer:
81y^4 - 16x^2, difference of squares.
Step-by-step explanation:
So we need to expand the following product:
(9y2-4x)(9y2+4x) = 9y2*9y2 + 4x*9y2 - 4x*9y2 -4x*4x = 81y^4 - 16x^2
And this type of product is the difference of squares.
Answer:
Step-by-step explanation:
The given expression is ( 9y² - 4x) (9y² + 4x)
We will simplify the given expression
(9y² - 4x) (9y² + 4x) = 9y² (9y² + 4x) - 4x (9y² + 4x) [Distributive property]
= 81y⁴ + 36xy² - 36xy² - 16x²
= (81y⁴ - 16x²)
This simplified form is the difference of squares of terms (9y²) and (4x)
What is the value of x in the equation -x =4 -3x +6?
A. 5
B. 10
C. -5
D. -10
Worth 10 points
Answer:
A.5
Step-by-step explanation:
-x = 4 - 3x + 6
-x+3x = 4 + 6
2x =10
x=5
Someone plz explain!
Answer:
18° and 72°
Step-by-step explanation:
Complimentary angles form 90°
We have an angle (x) 4 times larger than the other (y).
Well actually, a system of equations isn't required, so forget about x and y, just divide 90 by 5. This gives you 18, one of the angle's measurements is 18°. Multiply 18 by 4 and get 72. The other angle's measurement is 72°.
Here's an easy one for you! Change £x to pence.
Answer:
£x = 100x pence
Step-by-step explanation:
£1 = 100 pence
£x = 100x pence
Answer:
100x pence
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
We know that £1 = 100 pence so from this knowledge we can
£x = 100 p
A- 43
B- 48
C- 37
D- 24
A circle has 360°
Each percent of a circle represents 3.6°
Faucets contributed to 12% of the used water.
12 * 3.6° = 43.2°
What’s the answe please
Answer:
C - a line segment and a ray are both two-dimensional. Already has one endpoint and extends and One Direction indefinitely.
Step-by-step explanation:
Well, A ray is and endpoint with an indefinite line coming out of it.
(·--------------------->)
A line segment ends like this:
(·---------------------·)
They are both 2-dimensional. :)
Plz help me with this
Answer: [tex]\bold{y=sin(4x)+3}[/tex]
Step-by-step explanation:
[tex]\text{The standard form of a sine equation is: y=A cos(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]
The given information is:
A (amplitude) = 1[tex]Period\bigg(\dfrac{2\pi}{B}\bigg)=\dfrac{\pi}{2}}\qquad \implies B=4[/tex]D (Vertical shift) = +3[tex]\implies \large\boxed{y=sin(4x)+3}[/tex]
Select the correct product.
(5m 2 - 2m + 1)(3m - 4)
15m3 - 26m2 + 5m - 4
15m3 - 26m2 + 11m - 4
15m3 - 14m2 + 11m + 4
15m3 - 14m2 - 5m - 4
Answer: 15m3 - 26m2 + 11m - 4
Simplify the variable expression by evaluating it's numerical part m-8+143-5 and how did get m
m - 8 + 143 - 5
Answer: m + 130
Final answer:
To simplify the expression m - 8 + 143 - 5, combine the numerical parts to get 130, then the simplified expression is m + 130.
Explanation:
To simplify the variable expression m - 8 + 143 - 5, you must combine the numerical parts of the expression and keep the variable part as is. The numerical parts are -8, +143, and -5.
First, simplify the numerical parts by addition and subtraction:
143 - 8 - 5 = 130.
Next, keep the variable m in the expression, so the simplified form of the expression is:
m + 130
This is straightforward numerical evaluation, where units are not involved and thus can be worked out easily without mathematical complexity.
HELP ASAP!
Mr. Ray had $400. He spent 2/5 of it on a vacuum cleaner and 1/4 of the remainder on a fan. How much money did he have left?
WILL MARK AS BRAINLEST
and also remember to add ur step by step exclamation.
Answer:
180
Step-by-step explanation:
Ok first lets find out what 1/5 of 400 dollars is: 400/5= 80
So 1/5 of 400 is 80, now lets see what 2/5 is= 80 * 2= 160
Then subtract: 400 - 160= 240
we have 240 left. If he spent 1/4 of that on a vacuum cleaner then we have to: 240/4=60
He spent 60 dollars, now to find the remaining we must subtract: 240-60=180
Hope this helped ;)
So 2/5 is 0.4
0.4 of 400=160
400-160=240
240 is the remainder(what is left)
He used 1/4
1/4=0.25
240*1/4 =60
So 240-60=180
So your answer is: Mr.Ray will have $180 left.
if f(x)=4x+7, which if the following is the inverse of f(x)?
Answer:f
1/4y +-7/4 is your answer hope this help if it did mark me brainliest
Step-by-step explanation: