Answer:
Statements 3, 4 and 5 are true.
Step-by-step explanation:
x^2 - 8x + 4
Using the quadratic formula:
x = [ -(-8) +/- √((-8)^2 - 4*1*4)] / 2
= (8 +/- √(64 - 16)) / 2
= 4 +/- √48 / 2
= 4 +/- 4√3/2
= 4 +/- 2√3.
So the third statement is true.
Converting to vertex form:
x^2 - 8x + 4
= (x - 4)^2 - 16 + 4
= (x - 4)^2 -12
So the extreme value is at (4, -12)
So the fourth statement is true.
The coefficient of the term in x^2 is 1 (positive) so the graph has a minimum.
Correct answers only!
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
$39
Step-by-step explanation:
Using the given formula :
I = P × R × T
I = 30 × 10/100 × 3
I = $9
She have = 30 + 9 = $39
helppppppppppppppp meeeeeee
1x1x1. That's pretty much the definition of
Answer: 1 cubic foot, last choice
Select all ratios equivalent to 16:4.
12:3
1:2
24:6
can you show me a picture then maybe i can help you
Arthur is cutting construction paper into rectangles for a project. He needs to cut one rectangle that is 16 inches × 12 1 4 inches. He needs to cut another rectangle that is 10 1 2 inches by 10 1 4 inches. How many total square inches of construction paper does Arthur need for his project?
Answer:
303.63 sq inches
Step-by-step explanation:
We need to find the area of the two rectangles he cuts and add them together.
The area of a rectangle is given as:
A = L * B
The first rectangle is 16 inches × 12 1/4 inches. Its area is:
A = 16 * 12 1/4 = 16 * 49/4 = 196 sq inches
The second rectangle is 10 1/2 inches by 10 1/4 inches. Its area is:
A = 10 1/2 * 10 1/4 = 21/2 * 41/4 = 107.63 sq inches
The total square inches of construction paper that he needs is:
196 + 107.63 = 303.63 sq inches
Halla el término trigésimo de la progresión aritmética de diferencia 3 y primer término 11. Halla el término general de la progresión y la suma de los cuarenta primeros términos
Answer:
13th term = 47
General term: Tn = 11 + 3(n-1)
Sum of the first 40 terms = 2780
Question:
Find the thirtieth term of the arithmetic progression of difference 3 and the first term 11. Find the general term of the progression and the sum of the first forty terms.
Step-by-step explanation:
Common difference (d)= 3
First term = a = 11
Find attached the solution of problem.
Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state who paid more to fill her pool. [ 1 ft3 water = 7.48 gallons]
Answer:
Step-by-step explanation:
Both pools were filled 6 inches from the top.
12 inches = 1 feet
6 inches = 6/12 = 0.5 foot
Considering Theresa's pool, it is rectangular. The formula for determining the volume if the rectangular pool is
Volume = length × width × height
Height filled is 4 - 0.5 = 3.5 feet
Volume = 30 × 15 × 3.5 = 1575 ft³
Recall, 1 cubic feet = 7.48 Us gallons
Therefore,
1800 cubic feet = 1575 × 7.48 = 11781 gallons of water
Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water. It means that the amount she paid to fill her pool is
3.95 × 11781/100 = $465.35
Considering Nancy's pool, it is cylindrical. The formula for determining the volume if the cylindrical pool is
Volume = πr²h
Diameter = 24
Radius = diameter/2 = 24/2 = 12 ft
Volume = 3.14 × 12² × 3.5 = 1582.56 ft³. Converting to gallons, it becomes
1582.56 × 7.48 = 11837.55 gallons of water.
Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.
It means that the amount she paid to fill her pool is
200 × 11837.55/6000 = $394.59
Therefore, Theresa paid more to fill her pool.
find the total surface area of a right cone with a base diameter of 10cm and a height of 12cm. give your answer in terms of pie.
Answer:
The total surface area is 90π cm²
Step-by-step explanation:
To find the total surface area of his cone, we will follow the steps below;
write the formula for finding the total surface area of a cone
Total surface area = πrl + πr²
where r is the radius and l is the slant height
from the question, diameter = 10 cm, diameter = 2r this implies that r = d/2 = 10/2 = 5 cm
Also from the question given to us, height h = 12 cm, but what we want is slant height l. We can find this by using the Pythagoras theorem to find the slant height using the height giving to us and the radius.
opposite² + adjacent² = hypotenuse²
where radius is the adjacent, height is the opposite and the slant height is the hypotenuse
5² + 12² = l²
25 + 144 = l²
169 = l²
13 = l
l= 13 cm
hence slant height =13 cm
We can now proceed to insert the values into the formula
Total surface area = πrl + πr²
= π×5×13 + π×5²
=65π + 25π
=90π cm²
The total surface area is 90π cm²
How many times larger is the volume of a sphere if the radius is multiplied by 5?
Answer:
Brainliest please
The Volume is 125 times bigger.
Step-by-step explanation:
V = [tex]\frac{4}{3}*\pi *r^{3}\\[/tex] is the normal formula.
If you multiply the radius by 5 the it changes to
V = [tex]\frac{4}{3}*\pi *(5r)^{3}[/tex]
And when you simplify you get
V = [tex]\frac{4}{3} * \pi * 125r^3[/tex]
And the only difference between the inital equation and this one is *125 and so the volume is 125 bigger if the radius is multiplied by 5.
I need help preciate it
Answer: x=1
They all have 1 for their x coordinate; 'nuff said.
Find the height of a prism with volume 720cm3 and base area 45cm2
Answer:
The height is 16 cm
Step-by-step explanation:
It's just v/b
720/45=16
The height is 16 cm
solve 25+8m =73 M=....
Answer:
25+8m=73
We move all terms to the left:
25+8m-(73)=0
We add all the numbers together, and all the variables
8m-48=0
We move all terms containing m to the left, all other terms to the right
8m=48
m=48/8
m=6
Answer:
[tex]m = 6[/tex]
Step-by-step explanation:
[tex]25 + 8m = 73 \\ 8m = 73 - 25 \\ 8m = 48 \\ \frac{8m}{8} = \frac{48}{8} \\ m = 6[/tex]
A new park in the shape of a hexagon will have 6 sides of equal length. On a scale drawing, the coordinates of the vertices of the park are:
(-2.5, 3), (2.5, 3), (6.5, 0), (2.5, -3), (-2.5, -3), (-6.5, 0). How long is each side of the park?
Answer:
5 unit
Step-by-step explanation:
by taking the two points and calculating their distance
length of each side of the park=
sq.rt[(6.5-2.5)^2 + (0-3)^2]
=5
Solve for x: 4(x + 2) = 3(x − 2) PLEASE HURRY
Answer:
X= -14
Step-by-step explanation
4(x + 2) =3(x-2)
4x + 8 = 3x - 6
4x - 3x= - 8 - 6
X = - 14
Help me pleasee for this equation
Answer:
11.3 (C)
Step-by-step explanation:
sqrt(12^2 - 4^2) =
sqrt(144 - 16) =
sqrt(128)-->
11.3 (C)
Answer:
11.3 ft
Step-by-step explanation:
We have a right triangle with the hypotenuse of 12 and a leg of 4
Using the pythagorean theorem
a^2 +b^2 = c^2
4^2 + b^2 = 12^2
16 +b^2 = 144
Subtract 16 from each side
b^2 =144-16
b^2 =128
Taking the square root of each side
sqrt(b^2) = sqrt( 128)
b =11.3137085
Replace A with a number to make A/24 ≥ 1/4 a true statement.
Answer:
B. 7
Step-by-step explanation: 6/24= 1/4 so 7/24>1/4
I need help with number 2 name the radii of the circle
Answer:
AO and OB
Step-by-step explanation:
The radii are radiuses and in this case you have two. They radius half of the circle and the diameter is the whole length. Hope this was helpful.
What is the slope of the line x= -1
plz help
who ever answers first will get brainliest
Answer:
Step-by-step explanation:
If the line has an equation of x = (some number), this is a vertical line. The slope is undefined and all the points on the line have an x-coordinate of that (some number). For example, if x = -2, then all points along this line will have an x-coordinate of -2, making it a vertical line.
Answer:
its undefined, since its a vertical line and is parallel to the y-axis it is passes though all points with a x-axis of -1
Step-by-step explanation:
If sin x= (sqrt 2)/2 and tan x=-1 what is sec x
Answer:
[tex]-\frac{2}{\sqrt{2}}[/tex] or [tex]-\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sec{x}[/tex] is the reciprocal of [tex]\cos{x}[/tex], or in symbols: [tex]\sec{x}=\frac{1}{\cos{x}}[/tex]. [tex]\tan{x}[/tex] is also the ratio of [tex]\sin{x}[/tex] to [tex]\cos{x}[/tex], and we can multiply both sides of the equation [tex]\tan{x}=\frac{\sin{x}}{\cos{x}}[/tex] by [tex]\frac{1}{\sin{x}}[/tex] to get the equation [tex]\frac{\tan{x}}{\sin{x}}=\frac{1}{\cos{x}}[/tex]. Of course, this is just the definition of [tex]\sec{x}[/tex], so we can rewrite this fact as [tex]\sec{x}=\frac{\tan{x}}{\sin{x}}[/tex].
In this problem, we're given that [tex]\sin{x}=\frac{\sqrt{2} }{2}[/tex] and [tex]\tan{x}=-1[/tex], so plugging those two values into our equation gives us
[tex]\sec{x}=\dfrac{-1}{\frac{\sqrt{2}}{2}} =-\frac{2}{\sqrt{2}}[/tex]
We could leave our solution as [tex]-\frac{2}{\sqrt{2}}[/tex], or we could rationalize the denominator to get a solution of
[tex]-\frac{2}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=-\frac{2\sqrt{2}}{2}=-\sqrt{2}[/tex]
3x-y=8 in slope intercept form
Answer:
y=3x−8
Step-by-step explanation:
Which angle is coterminal to 2pi/3
the correct answer is -4π/3.
Which function represents the graph of y=x^2 after it has been translated 4 units to the left?
options:
y=(x-4)^2 or y=(x+4)^2
Answer:
oh.. maybe you can install photomath
Answer:
y=(x+4)^2
Step-by-step explanation:
A trick I use is if it is a plus sign then it goes left, if it is a minus sign then it goes right.
i am having trouble i need help.
Answer:
A. y=2x-2
Step-by-step explanation:
Answer:
the answer is A
Step-by-step explanation:
to find the slope intercept formula u need the slope, the y-intercept, and the X and Y
1st step: find the slope and to find the slope, pick any two points from the line
point 1: (2,2)
point 2: (3,4)
slope= y2-y1/x2-x1
4-2/3-2=2/1 or 2
the slope intercept form is y=mx+ b, so now substitute the variables for the known
y=2
x=2
m=2
2=2(2)+b
solve the equation
2=4+b
subtract 4 on both sides
b=-2
the slope intercept form is y=2x-2
Solve 3.4 [ 6 ( 4) +6^2]
Please show your work! <3
Answer:
204
Step-by-step explanation:
3.4[6(4)+6^2]=
3.4[24+36]=
3.4[60]=
204
Hope this helps!
Lee has a bag with 500 quarters. Some are the older eagle quarters, and others are the
newer state quarters. She pulls out 10 quarters at random. Four are eagle quarters, and 6 are
state quarters. Based on this sample, how many of the quarters in the full bag were likely to
be eagle quarters?
300
100
400
200?
Answer:
400
Step-by-step explanation:
The 200 quarters in the full bag were likely to be eagle quarters.
What is the ratio?In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.
Given that:-
Lee has a bag with 500 quarters. Some are the older eagle quarters, and others are thenewer state quarters. She pulls out 10 quarters at random. Four are eagle quarters, and 6 arestate quarters. Based on this sample, how many of the quarters in the full bag were likely tobe eagle quartersWe can conclude from the given data that the ratio of the Eagle and state quarters is 4:6 or 2:3 suppose the common factor is a so the value will be calculated as:-
E + S = 500
2a + 3a = 500
5a = 500
a = 100
E = 2a
E = 2 x 100 = 200
Therefore 200 quarters in the full bag were likely to be eagle quarters.
To know more about ratios follow
https://brainly.com/question/2328454
#SPJ2
factorise :x^2y^2-16
Answer:
(xy - 4)(xy + 4).
Step-by-step explanation:
The is the difference of 2 squares.
a^2 - b^2 = (a - b)(a + b: so we have:
x^2y^2 - 16 = (xy - 4)(xy + 4)
Samantha’s mom has a koi fish pond at the corner of her backyard. Samantha wanted to install a brick walkway on two sides of the pond. Below is a picture of the pond.
a. Create an equation that can be used to solve for the width, x, of the walkway.
b. Use any method (other than graphing) to figure out how much the width, x, of the walkway will be.
Answer:
A- 3x2= 6
6 divided by 2 is 3
B- flip it around with division first
Step-by-step explanation:
36x^2 + 84xy + 49y^2 = ?
A. (6x + 7y)(6x - 7y)
B. (12x + 7y)(3x - 7y)
C. (6x + 7y)^2
D. (6x - 7y)^2
Answer:
The answer is C
Step-by-step explanation:
Place parentheses around one operation and two numbers to make this equation true. Then solve it, showing all of your steps. 64 - 8 + 12 x 2 + 9 = 188
Answer:
64 - 8 + 12 x (2 + 9) = 188
Step-by-step explanation:
64 - 8 + 12 x 2 + 9 = 188
Putting parentheses around two numbers and one operation:
64 - 8 + 12 x (2 + 9) = 188
Following the BODMAS principle
Solving the bracket or parentheses first
(2 + 9) = 11
64 - 8 + 12 × 11
Then multiplication:
12 × 11 = 132
64 - 8 + 132
Then addition:
-8 + 132 = 124
64 + 124 = 188
Hence the proof
Chuck says that he can draw a cylinder on his polyhedron poster because it has a pair of base that are congruent.Is chuck correct?Explain your reosining.
Answer:
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
Please have a look at the attached photo.
My answer:
1. Chuck wants to draw three-dimensional figures whose lateral faces are rectangles. He says he can draw prisms and pyramids. Do you agree
No, I do not agree because:
The lateral faces of a pyramid are triangles The lateral faces of a prism are rectangles2. Part B. Chuck says that he can draw a cylinder on his polyhedron poster because it has a pair of bases that are congruent.
No, do not agree because:
A cylinder has two congruent bases but it is not a polyhedron while a cylinder has a curved surface when a polyheron has faces that are polygons
Hope it will find you well.
Please Help!!!! ASAP!! I will mark Brainliest!!! Please awnser CORRECTLY!! No guessing.
Answer:
C
Step-by-step explanation:
f(5) means we must plug in 5 wherever we see an x in the function.
[tex]f(x) = \frac{1}{9} 3^{x}[/tex]
[tex]f(5) = \frac{1}{9} 3^{5}[/tex]
[tex]f(5) = \frac{1}{9} * 243[/tex]
[tex]f(5) = \frac{243}{9} = 27[/tex]
So f(5) = 27! The answer is C.