Answer:
(-3, 1), 5
Step-by-step explanation:
x² + y² + 6x - 2y - 15 = 0
Rearrange:
x² + 6x + y² - 2y = 15
Complete the square:
x² + 6x + 9 + y² - 2y + 1 = 15 + 9 + 1
(x + 3)² + (y - 1)² = 25
Therefore, the center is (-3, 1) and the radius is 5.
The center of the circle is (-3, 1), and the radius is 5.
To find the center and radius of the circle described by the equation[tex]x^2 + y^2 + 6x - 2y - 15 = 0,[/tex] we'll first rewrite the equation in standard form, which has the general form:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where (h, k) represents the center of the circle, and r represents the radius.
Let's complete the square to rewrite the given equation in standard form:
[tex]x^2 + 6x + y^2 - 2y = 15[/tex]
Now, we'll complete the square for both the x and y terms.
To complete the square for the x terms, we add and subtract [tex](6/2)^2 = 9:x^2 + 6x + 9 + y^2 - 2y = 15 + 9[/tex]
Now, complete the square for the y terms by adding and subtracting (-2/2)^2 = 1:
[tex]x^2 + 6x + 9 + y^2 - 2y + 1 = 15 + 9 + 1[/tex]
Now, we have:
[tex](x^2 + 6x + 9) + (y^2 - 2y + 1) = 25[/tex]
Next, we can rewrite this as two perfect square trinomials:
[tex](x + 3)^2 + (y - 1)^2 = 25[/tex]
Now, the equation is in standard form. Comparing it to the standard form, we can see that:
h = -3 (opposite sign in the equation)
k = 1 (opposite sign in the equation)
[tex]r^2 = 25[/tex] (radius squared)
To find the radius (r), take the square root of 25:
r = √25 = 5.
For similar question on center of the circle.
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NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! DUE TODAY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(1) -3x+6=-9
show work
( 2) 5m+4m=72
show work
( 3 ) 6d-10d=40
show work
( 4) 2(x+4)=30
show work
( 5)78=-2(m+3)+m
show work
Answer :
1. -3x + 6 = -9
-3x = -9 - 6
-3x = -15
x = -15 / -3
x = 5
2. 5m + 4m = 72
9m = 72
m = 72 / 9
m = 8
3. 6d - 10d = 40
-4d = 40
d = 40 / -4
d = -10
4. 2(x + 4) = 30
2x + 8 = 30
2x = 30 - 8
2x = 22
x = 22 / 2
x = 11
5. 78 = -2(m + 3) + m
78 = -2m - 6 + m
78 = -m - 6
78 + 6 = -m
84 = -m
m = -84
x − 78 = −42
x = 78 − 42
x = −36
Answer:
x= 36
(it is positive since 78 is larger than 42, everything else is correct)
Step-by-step explanation:
If a baseball player hits a baseball from 4 feet off the ground with an initial velocity of 64 feet per second, how long will it take the baseball to hit the ground? Use the equation h = −16t2 + 4t + 4. Round your answer to the nearest hundredth.
0.36
0.39
0.61
0.65
Answer:
0.64 seconds.
Step-by-step explanation:
When it hits the ground h(t) = 0.
0 = -16t^2 + 4t + 4
-4(4t^2 - t -1) = 0
t = [-(-1) +/- sqrt (1 - 4*4*-1)] / 8)
t = 0.64, -0.39
answer is 0.64 seconds.
it will take the baseball 0.64 seconds to hit the ground.
The equation representing the height is:
h = -16t² + 4t + 4
When the baseball hits the ground, the height will be 0. That is,h =0
Substitute h =0 into the equation above
0 = -16t² + 4t + 4
Rearrange the given equation to be:
16t² - 4t - 4 = 0
Solving the quadratic equation above:
t = -0.39 and 0.64
Since time cannot be negative, it will take the baseball 0.64 seconds to hit the ground.
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Each letter of the alphabet is printed on an index card. What is the theoretical probability of randomly choosing any letter except Z? Write your answer as a fraction or percent rounded to the nearest tenth.
The theoretical probability of choosing a letter other than Z is
for z the fraction value is 1/26 and for other letters then Z is 25/26
What is 3 3/4 ft = in yd?
Answer: 1.25
Step-by-step explanation:
Because...
All you have to do is divide the length value by 3
and your answer will be 1.25.
* Hopefully this helps:) Mark me the brainliest:)!!!
Answer:
1.25yd
Step-by-step explanation:
couted through table
Which polynomial is a perfect square trinomial?
9x2 − 12x + 4
36b2 − 24b + 16
16x2 − 24x − 9
4a2 − 10a − 25
Answer:
Step-by-step explanation:
Eliminate the last two possible answers immediately, because their constants are negative. A perfect square trinomial MUST have a positive constant.
If we factor the first answer choice, we get (3x - 2)(3x - 2) = 9x^2 - 12x + 4. This is a perfect square trinomial.
Looking at the second answer choice: (4x - 3)(4x - 3) = 36b² - 24x + 9. This is also a perfect square trinomial.
Please note: Please use " ^ " to indicate exponentiation:
9x^2 is correct; 9x2 is incorrect.
Answer:
its C 16x2 + 24x + 9
Step-by-step explanation:
17 points
please show your work
Solve. x^2+5x+6=0
Answer:
x = -2 or x = -3Step-by-step explanation:
[tex]x^2+5x+6=0\\\\x^2+2x+3x+6=0\\\\x(x+2)+3(x+2)=0\\\\(x+2)(x+3)=0\iff x+2=0\ \vee\ x+3=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3[/tex]
If you make $15 per hour and you receive a 10% raise, how much will you be earning after the raise?
Answer:
$16.50/hr
Step-by-step explanation:
Current pay is 1.00($15/hr).
Current pay plus a 10% raise is 1.10($15/hr) = $16.50/hr
After receiving a 10% raise on a $15 per hour wage, you would be earning $16.50 per hour.
If you are currently making $15 per hour and you receive a 10% raise, you can calculate your new hourly wage by first determining the amount of the raise and then adding it to your current wage. To find the raise amount, you multiply your current wage by the raise percentage expressed as a decimal. In this case:
Amount of raise = Current hourly wage imes Raise percentage
Amount of raise = $15 per hour imes 0.10 (since 10% = 0.10)
Amount of raise = $1.50 per hour
Now, you add this raise to your current hourly wage to find your new hourly wage:
New hourly wage = Current hourly wage + Amount of raise
New hourly wage = $15 per hour + $1.50 per hour
New hourly wage = $16.50 per hour
To give an example for comparison, if your job pays $10 per hour and your boss gives you a $2 per hour raise, that is a 20% increase because the percentage change is calculated as $2/$10 = 0.20 or 20%. In your case, the 10% raise increases your wage by $1.50, making it $16.50 per hour after the raise.
Factor 2x^2 + 7x + 3
Answer: (x - 3) (2x-1)
Answer:
(x+3)(2x+1)
Step-by-step explanation:
I got it right on khan academy.
Consider the combined function
Given:
f(x)=4x-3
f(x) +g(x) =9x +4
To find:g(x)
Solution:
f(x) + g(x) =9x +4
Replacing f(x) with its value.
4x -3 +g(x) = 9x +4
=> g(x) = 9x+ 4 -(4x-3)
=> g(x) = 9x+4 -4x +3
=> g(x) = 5x +7
Hence;
Option A g(x)=5x+7 is the answer.
Hope it helps...
Regards;
Leukonov/Olegion.
Use the zero product property to find the solutions to the equation x^2-15x-100=0
Answer:
[tex]x = 20[/tex] or [tex]x = -5[/tex]
Step-by-step explanation:
To solve the quadratic equation we must factor the expression
Look for 2 numbers that when you multiply them, obtain the result -100 and when you add them, obtain the result -15.
You can verify that these numbers are -20 and 5
[tex]-20 +5 = -15\\\\-20 * 5 = -100[/tex]
Then the polynomial factors are
[tex](x-20) (x + 5) = 0[/tex]
The zero product property says that if two terms [tex]a * b = 0[/tex] then
[tex]a = 0[/tex] or [tex]b = 0[/tex]
So
[tex](x-20) = 0[/tex] or [tex](x + 5) = 0[/tex]
[tex]x = 20[/tex] or [tex]x = -5[/tex]
Answer:
x = -5 or x = 20
Step-by-step explanation:
There fore the answer is C
Which company’s tower holds the most water?
Answer: First Option
Step-by-step explanation:
The formula to calculate the volume of a cylinder is:
[tex]V = \pi(\frac{d}{2})^2*h[/tex]
Where d is the diameter of the cylinder and h is the height.
Notice that the term d is squared. This means that to increase the volume of a cylinder it is more efficient to increase its diameter as well. Therefore, look for the cylinder with the largest diameter among the options.
The first cylinder is 90 ft in diameter and 40 ft in height and its volume is
[tex]V = \pi(\frac{90}{2})^2*40[/tex]
[tex]V=254469\ ft^3[/tex]
You can verify that it is the tank that has the highest volume
Question 3
(Score for Question 3: _of 6 points)
3. In a game, if you roll a 6 on a 6-sided number cube, you lose a turn.
(a) What is the probability that you roll a 6? Explain your reasoning.
(b) What is the probability that you either roll a 6 or do not roll a 6? Explain your reasoning.
(c) What is the probability that you don't roll a 6? Explain your reasoning.
Answer.
Answer:
(a) What is the probability that you roll a 6?
1/6
(b) What is the probability that you either roll a 6 or do not roll a 6?
1
(c) What is the probability that you don't roll a 6?
5/6
Step-by-step explanation:
(a) What is the probability that you roll a 6?
In a 6- sided cube, a 6 occurs only once. That is only one face is labelled 6. Therefore, the probability that you roll a 6 is;
(number of faces labelled 6)/(totals number of sides) = 1/6
(b) What is the probability that you either roll a 6 or do not roll a 6?
The probability of rolling a 6 was found to be, 1/6.
On the other hand, the probability of not rolling a 6 is;
(number of faces not labelled 6)/(totals number of sides) = 5/6
Therefore, the probability that you either roll a 6 or do not roll a 6 is;
1/6 + 5/6 = 1
These two events are mutually exclusive and exhaustive.
(c) What is the probability that you don't roll a 6?
The probability of not rolling a 6 is;
(number of faces not labelled 6)/(totals number of sides) = 5/6
We have 5 faces not labelled 6 out of 6 possible faces or outcomes
Which are the solutions of x2 = -5x + 8?
- 5
-
7
-5 + 17
0 -5 -157 -5 + 157
0-5=17-57 v7
o S-x57.5+, 187
05-55+
IN
SEN
5 -
57
5 + 57
N
Answer:
1.27, -6.27 to the nearest hundredth,
or if you require it in exact form,
-2.5 + √14.25, -2.5 - √14.25.
Step-by-step explanation:
x^2 = -5x + 8
x^2 + 5x = 8
Competing the square:
(x + 2.5)^2 - 6.25 = 8
(x + 2.5) = 14.25
x + 2.5 = +/-√14.25
x = -2.5 + √14.25, -2.5 - √14.25
x = -2.5 + 3.77, -2.5 - 3.77
= 1.27, -6.27.
Find the surface area of a square pyramid whose base edge is 6cm and whose slant edge is 5cm
Check the picture below.
so let's notice, the base is a 6x6 square, and triangular faces have a base of 6 and an altitude/height of 5. So we can just get the area of the square and the triangles and sum them up and that's the area of the pyramid.
[tex]\bf \stackrel{\textit{triangles' area}}{4\left[ \cfrac{1}{2}(6)(5) \right]}+\stackrel{\textit{square's area}}{(6\cdot 6)}\implies 60+36\implies 96[/tex]
For this case we have that by definition, the surface area of a regular pyramid, is given by:
[tex]SA = \frac {1} {2} p * l + B[/tex]
Where:
p: Represents the perimeter of the base
l: The inclination height
B: The area of the base
Now, since the base is square we have:
[tex]B = 6 ^ 2 = 36 \ cm ^ 2\\p = 6 + 6 + 6 + 6 = 24 \ cm\\l = 5 \ cm[/tex]
Then, replacing the values:
[tex]SA = \frac {1} {2} 24 * 5 + 36\\SA = 60 + 36\\SA = 96 \ cm ^ 2[/tex]
ANswer
[tex]96 \ cm ^ 2[/tex]
y = x2 + 11x + 24 is equivalent to the graph of which equation? y = (x + 8)(x + 3) y = (x + 4)(x + 6) y = (x + 9)(x + 2) y = (x + 7)(x + 4)
Answer:
First option: [tex]y=(x + 8)(x + 3)[/tex]
Step-by-step explanation:
Given the quadratic equation [tex]y = x^2 + 11x + 24[/tex], you need to factor it.
To do this, you need to find two number that when you add them you get 11 and when you multply them you get 24. These numbers are: 8 and 3.
Therefore, knowing this, you can factor the quadratic equation:
[tex]y = x^2 + 11x + 24\\\\y=(x + 8)(x + 3)[/tex]
Then, [tex]y = x^2 + 11x + 24[/tex] is equivalent to the graph of the equation [tex]y=(x + 8)(x + 3)[/tex], which matches with the first option.
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
well, let's grab a couple of points off the line hmmmm let's see, the lines runs through (0, 4) and also (3,5), so let's use those to get its slope and thus its function.
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) ~\hfill slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-4}{3-0}\implies \cfrac{1}{3}[/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-4=\cfrac{1}{3}(x-0)\implies y-4=\cfrac{1}{3}x \\\\\\ y=\cfrac{1}{3}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
(HELP ASAP PLEASE!!)
Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent $79 on 4 new shirts and 3 pairs of shorts. The older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185. How much did each item cost?
Each shirt cost $ ___ and each pair of shorts cost $ ___ .
Answer:
Each shirt cost $7 and each pair of shorts cost $17 .
Step-by-step explanation:
let shirts be represented as x
let shorts be represented as y
Younger brother spent $79 on 4 new shirts and 3 pairs of shorts.
4 x + 3 y = $79 .......equation 1
Older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185.
7 x + 8 y = $185 .......equation 2
multiply equation 1 by 7 and equation 2 by -4 and add both equations to get the value of y.
7 × (4 x + 3 y = $79) ⇒ +28 x + 21 y = $553
-4 × (7 x + 8 y = $185) ⇒ -28 x - 32 y = - $740
0 - 11 y = - $187 ⇒ -11 y = - $187
y = [tex]\frac{- $187}{- 11}[/tex] ⇒ y = $17
shorts = y = $17
put value of y in equation 1
4 x + 3 ( $17 ) = $79 ⇒ 4x + $51 = $79 ⇒ 4x = $79 - $51
4x = $28 ⇒ x = [tex]\frac{$28}{4}[/tex] ⇒ x = $7
Shirts = x = $7
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar. Let x = the number of packages of pasta and y = the number of jars of pasta sauce. Identify each point as either a solution to the system or not a solution to the system of inequalities. (1, 12) (2, 10) (4, 5) (6, 10) (12, 8) (18, 6) .
Answer:
Solutions: (2,10), (4,5)
Not solutions: (1,12), (6,10), (12,8), (18,6)
Step-by-step explanation:
Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.
1. Tyler has $36, then
[tex]x+3y\le 36.[/tex]
2. Tyler can carry up to 20 pounds of food in his backpack, then
[tex]x+1.5y\le 20.[/tex]
You get the following system of inequalities:
[tex]\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.[/tex]
Now substitute the coordinates of each point:
(1,12):
[tex]\left\{\begin{array}{l}1+3\cdot 12=37> 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.[/tex]
False, because first inequality doesn't hold.
(2,10):
[tex]\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.[/tex]
True, both inequalities hold.
(4,5):
[tex]\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.[/tex]
True, both inequalities hold.
(6,10):
[tex]\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21> 20\end{array}\right.[/tex]
False, because secondt inequality doesn't hold.
(12,8):
[tex]\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24> 20\end{array}\right.[/tex]
False, because second inequality doesn't hold.
(18,6):
[tex]\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27> 20\end{array}\right.[/tex]
False, because second inequality doesn't hold.
A company owns two manufacturing
plants with daily production levels of
8x + 17 widgets and 5x - 7 widgets,
where x represents a minimum
quantity. How many more items does
the first plant produce daily than the
second plant?
Answer:
3x+24 more widgets
Step-by-step explanation:
A company owns two manufacturing plants:
1st plant: 8x+17 widgets;2nd plant: 5x-7 widgets.To find how many more items the first plant produces daily than the second plant, we have to subtract from the number of widgets the first plant produces the second plant produces. So,
[tex](8x+17)-(5x-7)\\ \\=8x+17-5x+7\ [\text{Eliminate brackets}]\\ \\=(8x-5x)+(17+7)\ [\text{Combine the like terms}]\\ \\=3x+24[/tex]
Answer:
3x + 24
Step-by-step explanation:
The question simply requires us to find the difference between the daily production levels of the two plants;
The first plant produces 8x + 17
The second plant produces 5x - 7
The difference between these two expressions will be our required solution;
(8x + 17) - ( 5x - 7) = 8x + 17 - 5x + 7
= 8x - 5x +17 + 7 = 3x + 24
If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a _
If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a parallelogram.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a quadrilateral, specifically a parallelogram.
The two identical triangles, when combined in this way, will have their bases aligned and their vertices opposite each other, forming two pairs of parallel sides.
A parallelogram, which is a quadrilateral with opposite sides that are parallel and congruent.
Hence, If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a parallelogram.
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Factorise completely 9a^2-1
Answer:
(3a-1)(3a+1)
Step-by-step explanation:
This is the difference of two squares so we can factorise using the rules
x^2-y^2 = (x-y)(x+y)
In this case x = 3a and y = 1 since (3a)^2 = 9a^2 and 1^2 = 1
1. m’+9 = 58
m
=
2. 7e² = 28
er
d=
3. d? + 6 = 70
4 n - 10 = 62
N=
For this case we must solve each of the equations proposed:
A) [tex]m ^ 2 + 9 = 58[/tex]
Subtracting 9 from both sides of the equation we have:
[tex]m ^ 2 = 49[/tex]
Applying root to both sides of the equation:
[tex]m = \sqrt {49}\\m = \pm7[/tex]
B) [tex]7e ^ 2 = 28[/tex]
We divide between 7 on both sides of the equation:
[tex]e ^ 2 = \frac {28} {7}\\e ^ 2 = 4[/tex]
We apply root to both sides of the equation:
[tex]e = \pm \sqrt {4}\\e = \pm2[/tex]
C) [tex]d ^ 2 + 6 = 70[/tex]
Subtracting 6 on both sides of the equation:
[tex]d ^ 2 = 64[/tex]
We apply root to both sides of the equation:
[tex]d =\pm \sqrt {64}\\d = \pm8[/tex]
D) [tex]\frac {1} {2} n ^ 2-10 = 62[/tex]
We add 10 to both sides of the equation:
[tex]\frac {1} {2} n ^ 2 = 72[/tex]
We multiply by 2 both sides of the equation:
[tex]n ^ 2 = 144[/tex]
We apply root to both sides of the equation:
[tex]n = \pm \sqrt {144}\\n =\pm12[/tex]
Answer:
[tex]m = \pm7\\e = \pm2\\d = \pm8\\n = \pm12[/tex]
Find the circumference of the following
Pythagorean Theorem
[tex]7^2 + 24^2 = x^2[/tex]
[tex]49 + 576 = x^2[/tex]
[tex]x^2=625[/tex]
[tex]x = 25[/tex]
Circumference
1. Since the diameter is 25 the formula to find the circumference is [tex]c = d\pi[/tex]
2. Plug in 25 into the formula
3. [tex]c = 25\pi[/tex]
Answer
[tex]25\pi[/tex]
The circumference of the circle is approximately 78.54 cm.
To find the circumference of the circle, we first need to find the length of the hypotenuse (which is also the diameter of the circle) using the Pythagorean theorem. Then, we can use the formula for the circumference of a circle, which is C = π * d, where C is the circumference and d is the diameter.
Let's calculate it step by step:
Step 1: Find the length of the hypotenuse using the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
where a and b are the lengths of the chords (24 cm and 7 cm, respectively), and c is the length of the hypotenuse (diameter).
[tex]24^2 + 7^2 = c^2\\\\576 + 49 = c^2\\\\625 = c^2[/tex]
c = √625
c = 25 cm
Step 2: Calculate the circumference using the formula C = π * d:
C = π * 25 cm
C ≈ 78.54 cm
The circumference of the circle is approximately 78.54 cm.
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The price, p, for different size orders of custom printed shirts, n, is given in the table.
Can a linear equation be used to model the situation? If it can, what is the slope and the y-intercept of the equation?
Answer:
linear: slope =10,y-intercept=25
Step-by-step explanation:
Yes, a linear equation can be used to model the situation because for any two given pints, there is a constant value of 10 for change in (p) over change in (n).
The slope is given by:
[tex]m=\frac{Change\:in\:p}{Change\:in\:n}[/tex]
Using (1,35) and (5,75) from the table, we have:
[tex]m=\frac{75-35}{5-1}[/tex]
[tex]m=\frac{40}{4}=10[/tex]
Therefore the slope is 10.
Using the formula
[tex]y=mx+b[/tex], and the point (1,35) we have:
[tex]35=10(1)+b[/tex]
[tex]\implies 35-10=b[/tex]
[tex]\implies 25=b[/tex]
Therefore the y-intercept is 25.
A monument has the shape of a square pyramid. The base has a length of 6ft. The height of a face is 13ft. What is the surface area of the pyramid
The answer is:
The total surface area of the pyramid is:
[tex]TotalSurfaceArea=192ft^{2}[/tex]
Why?To calculate the surface area of a square pyramid, we need to use the following formula:
[tex]TotalSurfaceArea=\frac{1}{2}pl+BaseArea[/tex]
Where,
p, is the perimeter of the base.
l, is the slant of the pyramid.
Base area, is the area of the square base.
Now, from the statement we know that the base has a length of 6 feet, and the height of a face (slant) is 13 feet.
So, calculating, we have:
[tex]BaseArea=BaseLength^{2}=(6ft)^{2} =36ft^{2}[/tex]
[tex]Perimeter=4*side=4*6feet=24feet[/tex]
The total surface area will be:
[tex]TotalSurfaceArea=\frac{1}{2}l+BaseArea[/tex]
[tex]TotalSurfaceArea=\frac{1}{2}*24ft*13ft+36ft^{2}[/tex]
[tex]TotalSurfaceArea=156ft^{2}+36ft^{2}=192ft^{2}[/tex]
Hence, we have the total surface area of the pyramid is:
[tex]TotalSurfaceArea=192ft^{2}[/tex]
Have a nice day!
Need major help with this problem!!
Rel. Max:
-1 , x=0
Rel. Min:
-6 ,x=5
Increasing in the interval(s)
(-infinty ,0) U (5, infinity)
[ i doubt the above answer]
Decreasing in the interval(s)
(0,5)
Domain
it could be R
Range
R
Step-by-step explanation:
Look at the picture.
The function has a realtive maximum of -1 at x = 0.
The function has a realtive minimum of -6 at x = 5.
The function is increasing on the intervals: (-∞, 0> and <5, ∞).
The function is decreasing on the interval: <0, 5>.
The domain of the function is: (-∞, ∞) = R
The range of the function is: (-∞, ∞) = R
Which function has the same y intercept as the function y = 2/3x - 3 ?
(1) x + 4y = 12
(2) 2/3x + 3y = -3
(3) -2/3x + 3y = 6
(4) 6x - 7y = 21
[tex]\bf y=\cfrac{2}{3}x\stackrel{\stackrel{b}{\downarrow }}{-3}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf 6x-7y=21\implies -7y=-6x+21\implies y=\cfrac{-6x+21}{-7}\implies y=\cfrac{6x-21}{7} \\\\\\ \stackrel{\textit{distributing the denominator}}{y=\cfrac{6x}{7}-\cfrac{21}{7}}\implies y=\cfrac{6}{7}x\stackrel{\stackrel{b}{\downarrow }}{-3}[/tex]
y=mx+b
b=y intercept
get into this form with no coefficient to y
Original: yint: -3
1)x+4y=12
4y=-x+12
y=-.25+3
b=3
2)2/3x+3y=-3
3y=2/3x-3
y={doesn't matter}x-1
b=-1
3)-2/3x+3y=6
3y=-2/3x+6
y={doesn't matter} +2
b=2
4) 6x-7y=21
-7y=-6x+21
y=6/7-3
b=-3
4 is the answer
Simplify:
Simplity: – V2.25
It is best to consider the radicand as a fraction,
Start by entering 2.25 as an improper fraction in simplest form in the
box
Convert the decimal number to a fraction by placing the decimal number over a power of ten. So convert the mixed number which is 2 1 /4 into an improper fraction first by multiplying the denominator which is (4)(4) by the whole number part which is (2)(2) and add the numerator (1)(1) to get the new numerator.
Place the new numerator (9)(9) over the old denominator (4)(4).94
What is the equation of line l?
Answer:
y = 3x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (1, 0) ← 2 points on the line
m = [tex]\frac{0+3}{1-0}[/tex] = 3
The line crosses the y- axis at (0, - 3) ⇒ c = - 3
y = 3x - 3 ← equation of line
The equation of line l will be;
⇒ y = 3x - 3
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (1, 0) and (0, -3).
Now,
Since, The equation of line passes through the points (1, 0) and (0, -3).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 3 - 0) / (0 - 1)
m = - 3 / - 1
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - 0 = 3 (x - 1)
⇒ y = 3x - 3
Therefore, The equation of line passes through the points (1, 0) and
(0, -3) will be;
⇒ y = 3x - 3
Learn more about the equation of line visit:
https://brainly.com/question/18831322
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