Answer:
(0, 7)Step-by-step explanation:
The equation of a circle in the standard form:
[tex](a-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the equation:
[tex]x^2+y^2-12y-15=0[/tex]
Convert into a standard form using
[tex](a-b)^2=a^2-2ab+b^2\qquad(*)[/tex]
[tex]x^2+\underbrace{y^2-2(y)(7)+7^2}_{(*)}-7^2-15=0\\\\(x-0)^2+(y-7)^2-49-15=0[/tex]
[tex](x-0)^2+(y-7)^2-64=0[/tex] add 64 to both sides
[tex](x-0)^2+(y-7)^2=64[/tex]
The center (0, 7)
The radius: r = √64 = 8
write 169=13^2 in logarithmic form
Answer:
[tex]\log_{13}(169)=2[/tex]
Step-by-step explanation:
The given exponential form is:
[tex]169=13^2[/tex]
The base of the given expression on the right is 13 and the exponent is 2.
The number is 169.
In terms of logarithms, the base still remains the base and the exponent becomes the result of the logarithm of the number 169 to the given base 13.
[tex]\log_{13}(169)=2[/tex]
somebody i need help please
OK so first you find the square root of 363 which is 19.05255888325765 then you find the square root of 27 which is 5.196252422706632 then times that by 3 you get 15.5884572681199 so then you have 19.05255888325765 subtract 15.5884572681199 which equals 3.46410161513775
Hope this helped!
Mrs. Rodriguez has a blueprint of her new house. The actual living room has a width of 20 feet and a length of 24 feet. If the scale
used to make the blueprint is inch = 4 feet, what is the length of the living room on the blueprint?
12 inches
3 inches
5inches
6 inches
Answer:
D) 6 in
Step-by-step explanation:
The length is 24 feet. The blueprint scales 1 ft : ¹/₄ in.
So, we can set up a proportion: 1 ft / ¹/₄ in = 24 ft / x in
Cross-multiply: 24 * ¹/₄ = x
Multiply: x = 6 in
meg has 47 baby carrots to share equally with 6 friends. she puts an equal number of carrots on 6 plates.how manycarrots are left?
Answer:
5 carrots
Step-by-step explanation:
Since there are 6 friends, find the factor closest to 47. The closest one would be 6*7=42. Thus, the answer is 5 because every friend gets 7 carrots.
Which two values are solutions to the inequality r ≤ 5?
Answer:
Step-by-step explanation:The solution is x > 3
60 POINTS!!! CAN SOMEBODY PLEASE HELP ME!! I DONT WANT TO FAIL THIS!
3. A rocket is launched vertically from the ground with an initial velocity of 64 .
(a) Write a quadratic function that shows the height, in feet, of the rocket t seconds after it was launched.
(b) Graph on the coordinate plane.
(c) Use your graph from Part 3(b) to determine the rocket’s maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air.
Answer:
(A): The equation is h(t)= -16t^2 + 64t
(B): The vertex points are (2,64) and the t intercepts are 0 and 4
(C): I dont know c!! i need help!
PLEASE EXPLAIN WELL!!!
a) The graph of the function is illustrated below.
b) The rocket's maximum height is 64 feet, it takes 2 seconds to reach this height.
c) The total time it was in the air is 4 seconds.
(A) Quadratic Function: To model the height of the rocket as it moves upward, we use a quadratic function in the form h(t) = at² + bt + c, where h(t) represents the height of the rocket at time t seconds. Since the rocket is moving vertically, we consider the acceleration due to gravity, which is -32 feet per second squared. The initial velocity of the rocket is 64 feet per second, so the coefficient of the linear term, b, is 64.
The equation for the height of the rocket is: h(t) = -16t² + 64t
(B) Graphing on the Coordinate Plane: To graph the quadratic function, we plot points on a coordinate plane. The vertex of the parabola represents the maximum height of the rocket, and the t-intercepts correspond to the times when the rocket hits the ground. The vertex of a quadratic function in the form h(t) = at² + bt + c is given by the coordinates (t_v, h(t_v)), where
t_v = -b / 2a.
In this case,
t_v = -64 / 2(-16) = 2 seconds.
(C) Finding Rocket's Maximum Height and Time in the Air: The vertex point we found earlier is (2, 64). This means that the rocket reaches its maximum height of 64 feet after 2 seconds of flight. To find the maximum height, we plug the value of t_v back into the equation:
h(t_v) = -16(2)² + 64(2) = -16(4) + 128 = 64 feet.
The rocket's maximum height is 64 feet, and it takes 2 seconds to reach this height. To find the total time the rocket is in the air, we look at the t-intercepts on the graph, which correspond to the times when the rocket hits the ground. From the equation h(t) = -16t² + 64t, we set h(t) to 0 and solve for t:
0 = -16t² + 64t t(0) = 0 (corresponding to the initial time of launch) t(4) = 4 seconds.
The rocket is in the air for 4 seconds.
To know more about function here
https://brainly.com/question/28193995
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A falcon flying at a height of 200 yards spots a sparrow flying at a height of 150 yards. The location of the sparrow makes an angle of 40° from the horizontal line through the falcon's location. What is the distance x between the falcon and the sparrow? Assume that the ground beneath the birds is level.
Answer:
77.79 yard
Step-by-step explanation:
Given in the question that,
falcon flying at a height of 200 yards
sparrow flying at a height of 150 yards
Suppose, distance between Falcon and Sparrow = x yards
Step 1
Difference between the height of falcon and sparrow = 200-150 = 50 yards
Step 2
We will use Trigonometry Identity to find the distance between Falcon and Sparrow
SinФ = opposite / hypotenuse
Sin(40) = 50 / x
x = 50 / Sin(40)
x = 77.79 yard
Answer:
78
Step-by-step explanation:
The amount Mike gets paid weekly can be represented by the expression 2.50a + 290, where a is the number of cell phone accessories he sell that week.
What is the constant term in this expression and what does it represent?
Answer:
The 2.50a is the constant. He's getting paid 2.50 dollars weekly
Step-by-step explanation:
When theres a variable next to a number, that means that's the constant.
Answer:
no. Hes getting paid 290, guaranteed.
Step-by-step explanation:
...
If the measure of arc AD = (6x – 80)° and 2G = (x + 2)°, what is the measure of G?
Answer:
The measure of G = 9.2°
Step-by-step explanation:
From the figure we can write,
The measure of <G is half the the measure of arc AD
To find the value of x
We have AD = (6x - 80)° and 2G = (x + 2)°
6x - 80 = (x + 2)
6x - 80 = x + 2
6x - x = 82
5x = 82
x = 82/5 = 16.4
To find the measure of <gG
m<G = (x + 2 )/2
= (16.4 + 2)/2 = 18.4 = 9.2
Therefore the measure of <G = 9.2°
HELPPPPPPPPP PLZ ASAP 50. SHOW ALL WORK if not your answer will be deleted.
A set of equations is given below: Equation C: y = 6x + 9 Equation D: y = 6x + 2 How many solutions are there to the given set of equations? One solution No solution Two solutions Infinitely many solutions
Answer:
[tex]\large\boxed{\bold{No\ solution}}[/tex]
Step-by-step explanation:
[tex]C:\ y=6x+9\\\\D:\ y=6x+2\\\\\left\{\begin{array}{ccc}y=6x+9&(1)\\y=6x+2&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\6x+9=6x+2\qquad\text{subtract 6x from both sides}\\\\9=2\qquad\bold{FALSE}\\\\\text{Therefore the answer is:}\ \bold{no\ solution}[/tex]
What are the excluded values?
x-7 / x+9 ( /) represents the line between a fraction in case u didn't know
a. x=7
b.x=9
c.x=-9
d. none of the above
Answer:
c. x = -9.
Step-by-step explanation:
The excluded value is the value of x which gives a value of 0 to the denominator, so that value would be x = -9.
Note: (x - 7) / 0 is undefined.
Could the lengths 18 in., 80 in., and 82 in. be the side lengths of a right triangle?
Answer:
yes
Step-by-step explanation:
The formula to finding the hypotenuse of a right triangle is a^2+b^2=c^2. So since the longest side is the hypotenuse, the 82 in. is the hypotenuse. 18^2+80^2= 6724, then we square root it, square root of 6725 is 82.
Answer:
This is a right triangle
Step-by-step explanation:
We can check this using the Pythagorean theorem
a^2 +b^2 = c^2
where a and b are the legs and c is the hypotenuse
18^2 + 80^2 = 82^2
324+6400=6724
6724 = 6724
True, so this is a right triangle
A parallelogram has symmetry with respect to the point of intersection of its diagonals.
True
False
what is the slope of (1,-3) and(-1,-3)
Answer:
slope = 0
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, - 3) and (x₂, y₂ ) = (- 1, - 3)
m = [tex]\frac{-3+3}{-1-1}[/tex] = [tex]\frac{0}{-2}[/tex] = 0
mia mowed 6 lawns in 2 hours. what was her rate of mowing in lawns per hour
Answer:
3 lawns per hour
Step-by-step explanation:
Divide the lawns by the time: 6/2=3
6/2 = 3
So, Mia mowed 3 lawns in an hour.
Answer: 6 divided by 2 equals 3
what is the factored form of 11x-x^2=0
Answer: [tex]x(11-x)=0[/tex]
Step-by-step explanation:
Given the quadratic equation [tex]11x-x^2=0[/tex], you need to factor it.
In order to find the form asked of the given equation, you need to factor out the common factor of the terms.
You can observe that the common factor of the terms of the equation is: [tex]x[/tex]
Now, knowing this, you must factor out [tex]x[/tex]. Then you get the following form:
[tex]x(11-x)=0[/tex]
Therefore, the factored fom of the equation [tex]11x-x^2=0[/tex] is:
[tex]x(11-x)=0[/tex]
The general term for the sequence 3,9,27,81,243, .... is
Answer:
[tex]a_n=3(3)^{n-1}[/tex]
Step-by-step explanation:
We have the following sequence
3,9,27,81,243
Note that if you divide each term of the sequence between the previous term you get:
[tex]\frac{9}{3} = 3\\\\\frac{27}{9} = 3\\\\\frac{81}{27} = 3[/tex]
then the radius of convergence of the series is r.
therefore this is a geometrical series.
The formula to find the general term [tex]a_n[/tex] of the geometric sequence is:
[tex]a_n=a_1(r)^{n-1}[/tex]
Where
[tex]a_1[/tex] is the first term of the sequence
Then the general term for this sequence is:
[tex]a_n=3(3)^{n-1}[/tex]
12
Which polynomial function has zeros at -3, 0, and 4?
1 f(x) = (x + 3)(x2 + 4)
2 f(x)=(x2 – 3)(x – 4)
3 F(x) = x(x + 3)(x – 4)
4 f(x) = x(x - 3)(x +4)
Answer:
3
Step-by-step explanation:
Given a polynomial with zeros x = a, x = b, x = c
Then the factors are (x - a), (x - b) and (x - c)
and the polynomial is the product of the factors
f(x) = k(x - a)(x - b)(x - c) ← k is a multiplier
here the zeros are x = - 3, x = 0, x = 4, thus the factors are
(x - (- 3)), (x - 0) and (x - 4), that is
(x + 3), x and (x - 4)
let k = 1, then
f(x) = x(x + 3)(x - 4) → 3
Answer:
F(x) = x(x + 3)(x – 4)
Step-by-step explanation:
The polynomial function has zeros at -3, 0, and 4 is F(x) = x(x + 3)(x – 4)
x(x + 3)(x – 4), set each part = 0 to find the solutions
x(x + 3)(x – 4) = 0
x = 0
x + 3 = 0; x = -3
x - 4 = 0; x = 4
The surface area of a right cone which has a base diameter of six units and a height of eight units is:
Answer: [tex]A = 108.80\ units^2[/tex]
Step-by-step explanation:
The surface area of right cone is calculated by the following formula
[tex]A = \pi r *\sqrt{r^2 +h^2}+\pi r^2[/tex]
Where r is the radius of the cone and h is the height
In this case we know that the diameter d of the base is:
[tex]d=2r[/tex]
So the radius is:
[tex]r=\frac{d}{2}\\\\r=\frac{6}{2}\\\\r=3\ units[/tex]
and
[tex]h=8\ units[/tex]
So the area is:
[tex]A = \pi*3 *\sqrt{3^2 +8^2}+\pi(3)^2[/tex]
[tex]A = 108.80\ units^2[/tex]
Answer:
[tex]SA=108.8 units^2[/tex]
Step-by-step explanation:
The surface area of a right cone is given by
[tex]S.A=\pi r^2+\pi rl[/tex]
The relation between the slant height l, the radius r, and the height h, is
[tex]l^2=r^2+h^2[/tex]
[tex]l^2=3^2+8^2[/tex]
[tex]l^2=9+64[/tex]
[tex]l^2=73[/tex]
[tex]l=\sqrt{73}[/tex]
[tex]S.A=\pi \times 3^2+\pi \times3\times\sqrt{73}[/tex]
[tex]S.A=\pi \times 3^2+\pi \times3\times\sqrt{73}[/tex]
[tex]SA=108.8 units^2[/tex]
Multiply this problem
12(17q+19)
Answer:
204q+228
Step-by-step explanation:
ANSWER
[tex]12(17q + 19) = 204q + 228[/tex]
EXPLANATION
The given expression is:
[tex]12(17q + 19)[/tex]
Recall the distributive property,
If a, b, and c are real numbers, then
a(b+c)=ab+ac
We apply this property to expand the parenthesis and obtain:
[tex]12(17q + 19) = 12 \times 17q + 12 \times 19[/tex]
[tex]12(17q + 19) = 204q + 228[/tex]
What’s the answer ?
Answer:
10
Step-by-step explanation:
Answer:
Slope = 0
Step-by-step explanation:
(y2 - y1) ÷ (x2 - x1) = (-3 - [-3]) ÷ (1 - [-9]) = 0 ÷ 10 = 0
Jenny, who rides a moped, takes 2 hours less to travel 60 miles than Maureen takes to travel 50 miles on her bicycle. Jenny travels 10 miles per hour faster than Maureen. (Hint: speed = distance ÷ time.)
Answer:
See below
Step-by-step explanation:
Givens
Jenny's Stats
t = m - 2
d = 60 miles
r = r1 + 10
Maureen's stats
d = 50 miles
t = m
r = r1
=======
60 = (r1 + 10) * (m - 2)
50 = r1 * m
m = 50/r1
60 = (r1 + 10)* (50/r1 - 2)
60 = 50 + 500/r1 - 2r1 - 20
60 = 30 + 500/r1 - 2r1
60r1 = 30r1 + 500 - 2*r1^2
30r1 = 500 - 2r1^2
2r1^2 + 30r1 - 500
This quadratic factors into
2 (r1 - 10)(r1 + 25)
r1 = 10 mph The 25 has no meaning.
m = 50/r1
m = 50/10
m = 5 hours
m - 2 = 3 hours.
Find the slope.
A 2
B -1/2
C -2
D 1/2
Answer:
-2
Step-by-step explanation:
I believe its -2 :) :3
The number of sports drinks in a cooler during practice is modeled by the equation y=648-24x where y is the number of ounces in the cooler after practice and x is the number of players at the practice who take drinks from the cooler.
Part A
Based on the information in the equation, press the hotspots of three statements that are true.
Hint: 648 is the starting point.
-24 is the slope (rate of change).
The answers are:
B. Before practice, there are 648 ounces of sports drink in the cooler.
C. Each plater drinks approximately 24 ounces of sports drink at practice.
E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice.
Why?We are given the equation:
[tex]y=f(x)=648-24x[/tex]
Let's discard each of the given options in order to find the three correct options.
A. The cooler is meant to be used only by 24 players: False.
If we want to calculate how many players can use the cooler, we need to isolate "x" (rate of change) from the given equation, so, isolating we have:
[tex]f(x)=648-24x[/tex]
[tex]0=648-24x[/tex]
[tex]648=24x\\\\24x=648\\\\x=\frac{648}{24}=27[/tex]
We have that the cooler can be used by 27 players, so, the first option that states that "The cooler is meant to be used only by 24 players" is false.
B. Before practice, there are 648 ounces of sports drink in the cooler: True.
We have that before the practice when the cooler is not being used by any player (or there is no any player) has 648 ounces (full), we can calculate it making the variable "x" equal to 0, so, calculating we have:
[tex]f(x)=648-24x[/tex]
[tex]f(0)=648-24*(0)=648[/tex]
Therefore, we have that the statement "Before practice, there are 648 ounces of sports drink in the cooler." is true.
C. Each plater drinks approximately 24 ounces of sports drink at practice: True.
From the statement, we know that the rate of change is equal to (-24), and it's equal to the number of ounces that each player drinks.
Hence, we have that the statement "Each plater drinks approximately 24 ounces of sports drink at practice." is true.
D. If 24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink: False.
If we want to calculate the number of ounces that 24 players will drink, we need to use the slope value. If we know that each player drinks 24 ounces, so, to calculate how many ounces of sports drink will 24 players drink, we need to use the following equation:
[tex]DrankOunces=24oz*Players\\\\DrankOunces=24oz*24=576oz[/tex]
We have that 24 players will drink a total of 576 ounces, so, the statement "If 24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink." is false.
E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice: True.
From the statement and the equation, we know that the slope (rate of change) is negative, meaning that for each player (x) it will be 24 fewer ounces of sports drink after practice, for example, calculating for 1 and 2 players, we have:
[tex]f(1)=648-24*1=624[/tex]
[tex]f(x)=648-24*2=600[/tex]
We can see that for each player, it will be 24 fewer ounces of sports drink after practice.
Hence, we have that the statement "For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice." is true.
Therefore, the correct options are:
B. Before practice, there are 648 ounces of sports drink in the cooler.
C. Each plater drinks approximately 24 ounces of sports drink at practice.
E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice.
Have a nice day!
Calculate Medicare tax (1.45% of gross pay
Gross Pay: $576.00
Answer: $8.35
Step-by-step explanation:
Given: The amount as gross pay= $576.00
The rate of Medicare tax =1.45% = 0.0145
Now, to calculate the medicare tax we need to multiply the rate of Medicare tax with the gross pay , we get
[tex]\text{Medicare tax=0.0145*Gross Pay}\\\\\Rightarrow\ \text{Medicare tax}=0.0145\times576.00\\\\\Rightarrow\ \text{Medicare tax}=\$8.352\approx\$8.35[/tex]
What would the answer for this question be
Answer:
A
Step-by-step explanation:
The only one you can eliminate on sight is C. You are going to get an x^3 somewhere along the line.
You can eliminate D on sight as well. The x^3 term is 12x^3 not 7x^3
Doesn't leave much does it?
(3x + 2)(4x^2 - 2x - 7)
3x: 12x^3 - 6x^2 - 21x
2 : 8x^2 - 4x - 14
======================= Add
12x^3 + 2x^2 - 25x - 14
Answer: A
[tex](3x + 2)(4x^{2} - 2x - 7) \\ \: a. = 12 {x}^{3}+ 2x^{2} - 25x - 14[/tex]
10 Points! Drag each value or expression to the correct location on the equations and sentences. Each value and expression can be used more than once, but not all values and expressions will be used.
Gary works at a bakery, and he needs to select a rectangular cookie sheet with an area of 192 square inches. The area of the cookie sheet is represented by the expression given below.
[tex]x^{2} + 4x[/tex]
Complete the given statements, and find the width of the cookie sheet.
The answers are:
Second step:
First box, 4
Second box,
The width is:
[tex]x+4[/tex]
Fourth step:
Box, 16
The length cant be -16in, the length is 12in, and the width is 16in.
Why?To solve the problem, we are using the formula to calculate the area of a rectangle, however, since the dimensions of the rectangle are not constant numbers, we will work with the variable "x", also, we know that the area of the cookie sheet is equal to 192 square inches.
So, solving we have:
First step:
We have the expression:
[tex]x^{2} +x[/tex]
Which is equal to: [tex]192in^{2}[/tex]
So,
[tex]x^{2} +4x=492[/tex]
Second step:
We have that the common factor of the left side of the equation is "x", so, we can simplify the expression in the following way:
[tex]x(x+4)=492[/tex]
Now, using the formula to calculate the area of a rectangle, we have:
[tex]length*width=Area\\\\length*width=92in^{2}\\\\x(x+4)=192in^{2}[/tex]
Where,
The length of the rectangle is "x"
The width of the rectangle is "x+4"
Third step:
Rewriting the expression, we have:
[tex]x^{2} +4x-192=0[/tex]
We need to find the roots (zeroes) of the quadratic function, in order to find the width of the rectangle without using the variable "x".
So, finding the values of "x" (roots or zeroes of the expression), we have:
[tex]x^{2} +4x-192=0[/tex]
Fourth step:
We need to find two numbers which it product gives as result the number -192 (including its sign) and their algebraic sum gives as result "4", those numbers are, -12 and 16,
[tex]-12*(16)=-192\\-12+16=4[/tex]
Then, rewriting the equation, we have:
[tex](x+16)(x-12)=0[/tex]
So, we that the expression is equal to 0 for two values of "x", these values are:
[tex]x_1=-16\\x_2=12[/tex]
Now, since the length can't be -16in, its equal to 12in.
[tex]length=x=12in[/tex]
[tex]length=12[/tex]
Then, from the second equation, we have that:
[tex]width=x+4[/tex]
Substituting "x" we can find the value of the width, so:
[tex]width=x+4=\\\\width=12+4=16in[/tex]
Hence, we have:
[tex]length=12in\\width=16in[/tex]
Have a nice day!
someone please help me choose all answers that apply
First you must combine like terms (x and x)
2y + 2 + (x + x)
2y + 2 + 2x
^^^All have the number two in common so we can take a two out like so...
2 (y + 1 + x)
or
2(x + y + 1)
There fore the answer is A!
Hope this helped!
~Just a girl in love with Shawn Mendes
What value can be written on the blank line to make the expressions equivalent?
48 + 54 = x(8+9)
Answer:
x=6
Hope This Helps! Have A Nice Day!!
Answer:
x=6
Step-by-step explanation:
[tex]48+54=x(8+9)\\\\102=8x+9x\\\\102=17x\\\\6=x[/tex]
CAN ANYONE HELP ME ANSWER THIS
Answer:
9/100
Step-by-step explanation:
There are 10 marbles in the bag
There are 3 pink marbles.
P (1st marble pink) = pink marbles/ total marbles
= 3/10
We put the marble back.
There are 10 marbles in the bag
There are 3 pink marbles.
P (2nd marble pink) = pink marbles/ total marbles
= 3/10
Multiply the probabilities together
P (pink, then pink) = 3/10 * 3/10 = 9/100