Answer:
B.(4,20)
Step-by-step explanation:
Given: [tex]x^2 -24x = -80[/tex]
To solve the quadratic equation by completing the square, we follow these steps.
Step 1: Divide the coefficient of x by 2
[tex]-\dfrac{24}{2}=-12[/tex]
Step 2: Square your result fro Step 1
[tex](-12)^2[/tex]
Step 3: Add the result form step 2 to both sides of the equation
[tex]x^2 -24x+(-12)^2 = -80+(-12)^2[/tex]
Step 4: Rewrite the Left hand side in the form [tex](x+k)^2[/tex]
[tex](x-12)^2=-80+144\\(x-12)^2=64[/tex]
Step 5: Take square roots of both sides
[tex]x-12=\pm \sqrt{64}[/tex]
Step 6: Solve for x
[tex]x=12\pm \sqrt{64}\\=12\pm8\\x=12+8$ or x=12-8\\x=20 or x=4.[/tex]
Therefore, the solution set of the equation is (4,20).
A concrete planter is formed from a square-based pyramid that was inverted and placed inside a cube.
This question is incomplete and it lacks the attached diagram of the square based pyramid. Find attached to this answer, the square based pyramid.
Correct Question
A concrete planter is formed from a square-based pyramid that was inverted and placed inside a cube.
A. What is the slant height of the pyramid?
B. What is the surface area of the composite figure?
HINT: The surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.
C. How many cubic yards of concrete are needed to make the planter?
Answer:
A. The slant height of the pyramid = 2.24 yards.
B. The surface area of the composite figure = 12.94 square yards.
C. The cubic yards of concrete are needed to make the planter = 2.67 cubic yards.
Step-by-step explanation:
A. What is the slant height of the pyramid?
To calculate the Slant height of a pyramid we make use of the Pythagoras Theorem which is given as:
a² + b² = c²
Where a = Height of the square pyramid represent by h
b = radius of the square pyramid represented by r
c = Slant height of the square pyramid represented by s
Therefore, we have
h² + r² = s²
Looking at the attached diagram, we are given the side length = 2 yards.
The radius of the square based pyramid = side length ÷ 2
= 2÷ 2 = 1 yard.
The height of a square based pyramid = 2 yards
Since , h² + r² = s²
The slant height of the square pyramid is calculated as :
√h² + r² = s
√(2² + 1²) = s
√5 = s
s = 2.24 yards
B. What is the surface area of the composite figure?
We were given hints in the question that the the surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.
Step 1
We find the Lateral area of the faces of the insides of the inverted pyramid
We have 4 faces, Hence,
The formula is given as
a × √( a² + 4h²
a = 2 yards
h = 2 yards
So, = 2 × √( 2² + 4 ×2²
The Lateral area of the faces = 8.94 square yards.
Step 2
Area of the 5 faces of the cube
= a²
Where a = side length = 2 yards
= 2²
= 4 square yards.
Step 3
Therefore, surface area of the composite figure = 8.94 square yards + 4 square yards
= 12.94 square yards.
C. How many cubic yards of concrete are needed to make the planter?
This is calculated by find the Volume of the Square based pyramid.
The formula is given as :
V = (1/3)a²h
Where a = side length = 2 yards
h = height of the square based pyramid = 2 yards
V = 1/3 × 2² × 2
V = 2.67 cubic yards
Mrs. Rodriguez bought 3 tickets for a concert. She also paid for a poster at the concert. Mrs. Rodriguez paid a total of $102 for the tickets and the poster. The equation 3t + p = 102 can be used to find p, the amount Mrs. Rodriguez paid for the poster. If Mrs. Rodriguez paid $29 for each ticket, t, then how much did she pay for the poster
Answer:
15
Step-by-step explanation:
102-(29 x 3)
Answer:
p=15
Step-byexplanation:
3t+p/102
3(29)+p=102
87+p=102
p=15
Select all the equations where =3 is a solution.
Choose 2 answers
Help?
Answer:
A and C
Step-by-step explanation:
Please help, it’s a math question
Answer:
the answer is B
Step-by-step explanation:
hope it help
On a coordinate plane, a circle has a center at (4, 5) and a radius of 3 units.
Which equation represents a circle with the same center as the circle shown but with a radius of 2 units?
(x – 4)2 + (y – 5)2 = 2
(x – 4)2 + (y – 5)2 = 4
(x – 5)2 + (y – 4)2 = 2
(x – 5)2 + (y – 4)2 = 4
Answer:
(x - 4)² + (y - 5)² = 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (4, 5) and r = 2, thus
(x - 4)² + (y - 5)² = 2², that is
(x - 4)² + (y - 5)² = 4 ← second option on list
The required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x-4)^2 + (y-5)^2 = 4
Equation of a circleThe standard equation of a circle is expressed as:
(x-a)^2 + (y-b)^2 = r^2
where:
(a, b) is the centre = (4, 5)
r is the radius = 3 units
Substitute to have;
(x-4)^2 + (y-5)^2 = 2^2
(x-4)^2 + (y-5)^2 = 4
Hence the required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x-4)^2 + (y-5)^2 = 4
Learn more on equation of circle here: https://brainly.com/question/14150470
Mark recently took a road trip across the country. The number of miles he drove each day was normally distributed with a mean of 450. If he drove 431.8 miles on the last day with a z-score of -0.7, what is the standard deviation?
Answer:
The (population) standard deviation is 26 miles or [tex] \\ \sigma = 26[/tex] miles.
Step-by-step explanation:
We can solve this question using the concept of z-score or standardized value, which is given by the formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
[tex] \\ z[/tex] is the z-score.
[tex] \\ x[/tex] is the raw score.
[tex] \\ \mu[/tex] is the population's mean.
[tex] \\ \sigma[/tex] is the population standard deviation.
Analyzing the question, we have the following data to solve this question:
The random variable number of miles driven by day is normally distributed.The population's mean is [tex] \\ \mu = 450[/tex] miles.The raw score, that is, the value we want to standardize, is [tex] \\ x = 431.8[/tex] miles.The z-score is [tex] \\ z = -0.7[/tex]. It tells us that the raw value (or raw score) is below the population mean because it is negative. It also tells us that this value is 0.7 standard deviations units (below) from [tex] \\ \mu[/tex].Therefore, using all this information, we can determine the (population) standard deviation using formula [1].
Then, substituting each value in this formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
Solving it for [tex] \\ \sigma[/tex]
Multiplying each side of the formula by [tex] \\ \sigma[/tex]
[tex] \\ \sigma*z = (x - \mu) * \frac{\sigma}{\sigma}[/tex]
[tex] \\ \sigma*z = (x - \mu) * 1[/tex]
[tex] \\ \sigma*z = x - \mu[/tex]
Multiplying each side of the formula by [tex] \\ \frac{1}{z}[/tex]
[tex] \\ \frac{1}{z}*\sigma*z = \frac{1}{z}*(x - \mu)[/tex]
[tex] \\ \frac{z}{z}*\sigma = \frac{x - \mu}{z}[/tex]
[tex] \\ 1*\sigma = \frac{x - \mu}{z}[/tex]
[tex] \\ \sigma = \frac{x - \mu}{z}[/tex]
Then, this formula, solved for [tex] \\ \sigma[/tex], will permit us to find the value for the population standard deviation asked in the question.
[tex] \\ \sigma = \frac{431.8 - 450}{-0.7}[/tex]
[tex] \\ \sigma = \frac{-18.2}{-0.7}[/tex]
[tex] \\ \sigma = 26[/tex]
Thus, the (population) standard deviation is 26 miles or [tex] \\ \sigma = 26[/tex] miles.
Tamara received a gift card with a $200 balance for her birthday she buy several video games for $45 each write an equation to help find how many video games she brought if she has $20 left on her card
someone be a real one and finish this... plz
Answer:
y + 21 = - 4(x - 7)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (7, - 21) and (x₂, y₂ ) = (- 4, 23)
m = [tex]\frac{23+21}{-4-7}[/tex] = [tex]\frac{44}{-11}[/tex] = - 4
Using m = - 4 and (a, b) = (7, - 21), then
y - (- 21) = - 4(x - 7), that is
y + 21 = - 4(x - 7)
A rectangular prism has a length of 12in, a height of 5in, and a width of 8in. What is its volume, in cubic in?
Answer: 480 in^3
Step-by-step explanation:
v= l * w*h
v = 12 * 8 * 5
v= 480
Solve x2 - 8x + 15 <0.
Recall that the quadratic factors as:
(x - 3)(x - 5) <0
Therefore, the intervals that must be tested are
x<3,3 5.
The solution set for the quadratic inequality is:
Answer:
x<3 and x<5Step-by-step explanation:
Given the quadratic inequality x² - 8x + 15 <0, to get the solution set for the inequality, the following steps must be followed;
Step 1: Factorize the quadratic expression
x² - 8x + 15 <0
x² - 3x - 5x + 15 <0
x(x - 3) - 5(x - 3) <0
(x -3)(x -5)< 0
x -3<0 and x -5<0
x< 3 and x< 5
Therefore, the solution set for the quadratic inequality are x<3 and x<5
Answer:
(3, 5)
Step-by-step explanation:
Correct on e2020
Mark walked 15 miles in 6 hours
Calculate his average speed
Average speed = 2.5 miles
Divide 6 from both sides.
6/6 = 1
15/6 = 2.5
So, overall Mark walks 2.5 miles per hour.
hope it helps!
What is the value of x in the equation
7 (4x + 1) – 3x = 5x – 13?
T =
Answer:
x = - 1
Step-by-step explanation:
7 (4x + 1) – 3x = 5x – 13
28x + 7 - 3x = 5x - 13
25x + 7 = 5x - 13
25x - 5x = -13 - 7
20x = -20
x = -20/20
x = -1
Answer: x = -1
Step-by-step explanation:
[tex]7 (4x + 1) -3x = 5x-13[/tex]
Distribute 7.
[tex]28x+7-3x=5x-13[/tex]
Subtract 7.
[tex]28x-3x=5x-13-7[/tex]
Subtract 5x
[tex]28x-3x-5x=-13-7[/tex]
Combine like terms;
[tex]20x=-20[/tex]
Divide by 20.
[tex]x=\frac{-20}{20}\\ x=-1[/tex]
It costs 31.25 for 1 box of candy and 4 large bags of popcorn at a movie theatre. For 3 boxes of candy and 5 large bags of popcorn it costs 46.50 how much does 1 bag of popcorn cost
Answer:
$6.75
Step-by-step explanation:
$31.25 = C + 4B C for box of candy and B for large bags of popcorn
$46.50 = 3C + 5B
3($31.25 = C + 4B)
$93.75 = 3C + 12B
-46.50. -3C. -5B
$47.25 = 7B
÷7. ÷7
$6.75. = B
A pilot is flying a plane 20000 ft above the ground.The pilot begins a 2 descent to an airport runway.How far is the airplane from the start of the runway(in ground distance)
Answer:
381623 ft
Step-by-step explanation:
Since the airport altitude is 20000 ft and the pilot needs a 2° descent, to calculate the distance of the airplane at the start of this approach, first this is represented in the diagram attached. The distance from the runway at the start is x.
[tex]tan(3) = \frac{20000}{x} \\x=\frac{20000}{tan(3)} \\x=381623ft[/tex]
The airplane is at a distance of 381623 ft away from the airplane runaway at the start of the descent.
Ana dives into a pool off of a springboard high dive. Her height (in meters above the water), xxx seconds after diving, is modeled by h(x)=-5(x+1)(x-3)h(x)=−5(x+1)(x−3), What is the height of Ana above the water at the time of diving?
Answer:
15m
Step-by-step explanation:
When Ana is diving the time=0 therefore just substitute x=0 into h(x) and it will give you 15m
what are the first 100 hundred digits of pi?
Answer: first 1000 digest
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989
Step-by-step explanation:
Answer:
you aren't ready for this!!!!
Step-by-step explanation:
And now
AsapSCIENCE presents-
100 digits of π
3.14159, this is π
Followed by 2-6-5-3-5-8-9
Circumference over diameter
7-9, then 3-2-3
OMG! Can't you see?
8-4-6-2-6-4-3
And now we're on a spree
38 and 32, now we're blue
Oh, who knew?
7, 950 and then a two
88 and 41, so much fun
Now a run
9-7-1-6-9-3-9-9
Then 3-7, 51
Half way done!
0-5-8, now don't be late
2-0-9, where's the wine?
7-4, it's on the floor
Then 9-4-4-5-9
2-3-0, we gotta go
7-8, we can't wait
1-6-4-0-6-2-8
We're almost near the end, keep going
62, we're getting through
0-8-9-9, on time
8-6-2-8-0-3-4
There's only a few more!
8-2, then 5-3
42, 11, 7-0 and 67
We're done! Was that fun?
Learning random digits
So that you can brag to your friends
wserdtcfvygbuhnjkml,;kmojnihbugvyf
Answer:
taco
Step-by-step explanation:
20POINTS AND I WILL MARK BRAINLIEST!!!! ANSWER AND EXPLAIN
Answer:
72 degrees
Step-by-step explanation:
A pentagon has five lines of symmetry. For rotation symmetry, the order of any regular polygon is the number of sides. The angle of rotation would be 360 degrees divided by that order. Therefore, the answer is 72 degrees.
Write the equation of the line with the following characteristics: A slope of 4 through the origin.
Answer:
Payton, our equation looks like y = mx + b with m being the slope and b being the y-intercept. We are given a slope of 3, and if the graph passes through the origin, the y-intercept is 0.
Step-by-step explanation:
Find the Equation of a Line Given That You Know a Point on the Line And Its Slope. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you a point that a line passes through, and its slope, this page will show you how to find the equation of the line.
Tristan and Anthony go to the movie theater and purchase refreshments for their friends. Tristan spends a total of $132.00 on 10 drinks and 7 bags of popcorn. Anthony spends a total of $102.00 on 2 drinks and 14 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answer:
Popcorn=$6
Step-by-step explanation:
1) Setting variables
d= price of drinks
p= price of popcorn
2) Writing the system of equations
10d+7p=132
2d+14p=102
3) Simplifying one equation
2d=102-14p
d=51-7p
4) Solving the other equation by plugging the first equation in
d=51-7p
10d+7p=132
10(51-7p)+7p=132
510-70p+7p=132
510-63p=132
63p=378
p=6
5) Substituting p=6 into the first equation
d=51-7p
d=51-42
d=9
The number y of raccoons in an area after x years can be modeled by the function y= 0.4x^2+2x+2. When were there about 45 raccoons in the area? Round your answer to the nearest year
Answer:
A timeframe of 8 years is when there were 45 raccoons in the area.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityStandard Form:
[tex]\displaystyle ax^2 + bx + c = 0[/tex]
Quadratic Formula:
[tex]\displaystyle x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \begin{aligned}y & = 0.4x^2 + 2x + 2 \\y & = 45 \ \text{raccoons} \\\end{aligned}[/tex]
Step 2: Find Specific Year
We are trying to find the year when there were 45 raccoons present in the area. From first glance, we see we probably can't factor the quadratic expression, so let's set up to use the Quadratic Formula:
[Model Equation] Substitute in y:Now that we have our variables from Standard Form, we can use the Quadratic Formula to find which years when there were 45 raccoons present in the area:
[Quadratic Formula] Substitute in variables:Since time cannot be negative, we can isolate the other root to obtain our final answer:
[tex]\displaystyle\begin{aligned}x & = 8.16536 \ \text{years} \\& \approx \boxed{ 8 \ \text{years} } \\\end{aligned}[/tex]
∴ we have found the approximate amount of years to be 8 years when there were 45 raccoons in the area.
___
Learn more about Algebra I: https://brainly.com/question/16442214
___
Topic: Algebra I
Helppppppppppppppppppppppp
Answer:
JK
Step-by-step explanation:
Answer:it might be the last on if right please mark as brainliest
Step-by-step explanation:
PLEASE INCLUDE ALL STEPS! BRAINLIEST GETS 25+ POINTS!!
During a canoe trip, Roberto paddled twice as many hours as Edward, and Jim paddled for one hour. If the three of them paddled less than a total of ten hours, what is the number of hours that Roberto could have paddled?
Answer:
Roberto did 4 or 5 hours
Step-by-step explanation:
r- Roberto
e- Edward
j- Jim
j = 1 hr. paddled
r= 2e for the number of hours, r, robert paddled.
r+ e+ j < 10 Substitute in for r and j.
2e+ e+ 1 < 10
3e <9
e< 3
r = 2*e
r < 2*3 I Changed it to less than, so because edward has to do less than 3 hours, so now im finding the number of hours that he has to be below.
r<6
Roberto did less than 6 hours.
Edward did less than 3 hours.
Jim did 1 hour.
Possible Combination of hours that satisfies all the criteria and is below 10 total hours:
Jim Does 1 hour, Edward does 2 hours, and Roberto does 4 hours.
Another Possibility is
Jim does 1 hours, Edward does 2.5 hours and Roberto does 5 hours.
(Edward has to do 2.5 hours for Roberto to do 5 hours, because it states that Roberto does twice as many hours as Edward, it does not state that he did more than twice as many hours so it is necessary for Edward to do 2.5 hours for Roberto to do 5.)
hey can anyone help me in dis pls!!!!!!!!
Answer:
1. the blue one 2. because the blue one have more length.
good luck.
Answer:
1. Blue
2. blue, because i measured both lines with a ruler
3. This one is harder to decide because the blue line was barely longer than the red line
Step-by-step explanation:
I measured the lines with a ruler for this one too.
what will happen to the volume of a cylinder if the length if the height is tripled?
A. Double
B. Stay the same
C. Triple
D. 9 times as large
Answer:
Triple
Step-by-step explanation:
V = π * r^2 *h
h is directly proportional to V so when h increases V increases.
This is a linear relationship so if h is tripled the volume will be tripled as well.
if r tripled then V would be 9 times as large since r has a square relationship with V.
If you're unsure about these just plug in number r= 2, h= 4, and perform the operation they ask you to do (triple or double) and you'll always get it right.
If f(x) = x2 + 2x – 10, what is f(-2)?
Answer:
The answer is -18
Step-by-step explanation:
Actually if the x2 is supposed to be x^2 then it's -10
Answer: -18
Step-by-step explanation:
What is the length c of the right triangle, rounded to the nearest
tenth?
Answer:
6.1
Step-by-step explanation:
we will name the length in front of the angle , y :
tan(71°)≅2.904= y ÷2
⇒ y= 5.8
and we know that
c = [tex]\sqrt{2^{2} + y^{2} }[/tex]
then
c = 6.14
and if we round it to the nearest tenth :
c = 6.1
Si al numerador de una fraccion se añade 5, el valor de la fraccion es 2, y si al numerador se resta 2, al valor de la fraccion es 1.Hallar la fraccion.
Answer:
Respuesta.- La fracción es 9/7
Step-by-step explanation:
1) Llamando X e Y a la fracción, tenemos: X/Y
Si al numerador se le añade 5, es decir X+5, el valor de la fracción es 2, luego:
(X+5)/Y = 2
Y si al numerador se le resta 2, es decir X-2, el valor de la fracción es 1, luego:
(X-2)/Y = 1
Juntando amabas ecuaciones:
(X+5)/Y= 2
(X-2)/Y = 1
Despejando Y en ambas:
Y = (X+5)/2
Y = (X-2)..........(1)
Igualandolas:
(X+5)/2= (X-2)
De donde:
X+5 = 2X-4
X = 9
Y finalmente, sustituyendo el valor de X = 9 en la ecuaión (1), tendremos:
Y = (X-2)
Y = (9-2)
Y = 7
Respuesta.- La fracción es 9/7
The thickness of a protective coating applied to a conductor designed to work in corrosive conditions follows a uniform distribution over the interval [20;40] microns. Find the probability that the coating is between 24 and 38.
Answer:
[tex] P(24< X<38)= P(X<38) -P(X<24)= F(38) -F(24)[/tex]
And replacing we got:
[tex] P(24< X<38)=\frac{38-20}{40-20}-\frac{24-20}{40-20}= 0.9-0.2= 0.7[/tex]
Step-by-step explanation:
We can define the random variable X as the thickness of a protective coating applied to a conductor designed to work in corrosive conditions. And the distribution for X is given by:
[tex] X \sim Unif (a = 20, b=40)[/tex]
And we want to find this probability:
[tex] P(24< X<38) [/tex]
And in order to find this probability we can use the cumulative distribution function given by:
[tex] F(x) = \frac{x-a}{b-a} , a\leq X \leq b[/tex]
And if we use this formula for the probability desired we have:
[tex] P(24< X<38)= P(X<38) -P(X<24)= F(38) -F(24)[/tex]
And replacing we got:
[tex] P(24< X<38)=\frac{38-20}{40-20}-\frac{24-20}{40-20}= 0.9-0.2= 0.7[/tex]
hey can anyone pls help me out in dis!!!!!!!!!
Answer:
Look at the attachment