Answer:
50.24inches
Step-by-step explanation:
Your diameter is 8 inches so divide that by two to get a radius of 4 multiply 4 by itself and multiply that (16) by pi.(it gives you 50.24)
Find the focus and the directrix of the parabola with the equation y = –1∕2 (x – 8)2 – 6.
A) Focus = (–8,–61∕2), directrix is y = –51∕2
B) Focus = (–8,–51∕2), directrix is y = –61∕2
C) Focus = (8,–61∕2), directrix is y = –51∕2
D) Focus = (8,–51∕2), directrix is y = –61∕2
Answer:
c
Step-by-step explanation:
The focus of the parabola is (–8,–51∕2), directrix is y = –61∕2 option (C) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
We have an equation for the parabola:
The parabolic equation also in the form of quadratic equation.
Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
y = (-1∕2)(x – 8)² – 6
The vertex of the parabola is (h, k)
h = 8, k = -6
The focus of the parabola:
(c, d)
c = -6
d = -6 - 1/2 = -13/2 = -6 1/2
Directrix of the parabola:
y = -6 - (-1/2)
y = -6 + 1/2
y = -11/2 = -5 1/2
Thus, the focus of the parabola is (–8,–51∕2), directrix is y = –61∕2 option (C) is correct.
Learn more about the parabola here:
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The amount of money 'y' made at a laundromat after 'x' months can be represented by the linear function: y = 8.50x - 5. After 2 months, the laundromat made 20 dollars, but the linear function predicted they would make 12 dollars. What is the residual value for this data?
Answer:
[tex] \hat y = 8.5*2 -5 = 12[/tex]
And the residual is defined as:
[tex] e_ i = y_i -\hat y_i [/tex]
And replacing we got:
[tex] e_i = 20-12 = 8[/tex]
Step-by-step explanation:
For this case we know that the amount of money 'y' made at a laundromat after 'x' months can be represented by the linear function:
[tex] y = 8.50 x -5[/tex]
And fter two months we know that the laundromat made 20 dollars. And if we use the linear function we got:
[tex] \hat y = 8.5*2 -5 = 12[/tex]
And the residual is defined as:
[tex] e_ i = y_i -\hat y_i [/tex]
And replacing we got:
[tex] e_i = 20-12 = 8[/tex]
Solve the following inequality
2(x – 3) – 5x < 9
Answer:
Step-by-step explanation:
hello : here is an solution
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Answer:
u = 11
Step-by-step explanation:
6(u+5)=96
Divide both sides by 6
u+5=16
Subtract 5 from both sides
u=11
The variable, u, is equivalent to 11
Answer:
u=11
Step-by-step explanation:
If you multiply the parentheses by the outside number (6) it will bring you
6u+30=96 then take away 30 from each side to get
6u=66 last step is to divide by six
u=11
Find the length of the diagonal of an 8cmx 6cmx 10cm rectangular prism. Round to the nearest tenth. (HELP PLEASE!!)
Answer:
14.1 cm
Step-by-step explanation:
first find the base diagonal :
base di = Square root (8^2 + 6^2) = 10cm
so,
diagonal = Square root (10^2 + 10^2) = 14.1 cm (ANS)
Which ratio is equivalent to 7:3
Answer:
14:6
3.5:1.5
21:9
Answer:
14/6
Step-by-step explanation:
How many x-intercepts does the graph of y = 4x2 + 5x + 2 have?
Answer:
Step-by-step explanation:
hello : y= 4x² + 5x + 2
the x-intercepts when y=0 means : 4x² + 5x + 2=0
a=4 b= 5 c=2
∆ = b²- 4ac ∆ = (5)²- 4(4)(2) =25-32 = -7
∆ < 0 no reals solutions no x-intercepts
The radius of a circle is 5 m. Find its area in terms of .
Answer:
78.5 m²
Step-by-step explanation:
Area formula: πr²
Plug it in: (3.14)(5m)²
Answer: 78.5 m²
Someone help pleaseee
Answer:
38°
Step-by-step explanation:
All triangles have a sum of 180°
180 - (119 + 23) = missing angle
180 - (142) = missing angle
38 = missing angle
So, the missing angle has a measurement of 38°
Help Me
I don't quite understand this...
Answer:
(x-3)^2 = 4
Step-by-step explanation:
2 (x-3)^2 + 6 = 14
Subtract 6 from each side
2 (x-3)^2 = 8
Divide each side by 2
2/2 (x-3)^2 + 6 = 8/2
(x-3)^2 = 4
Emma Punch with 3/4 gallons of pineapple juice 1 1/2 gallons of orange juice and 7/8 gallons of apple juice how much gallons of Ginger ale does she need to add to make the total of 4 gallons of punch
Answer:
7/8 gallons of Ginger aleStep-by-step explanation:
Total gallons of punch mixture = gallons of pineapple juice + orange juice + gallons of apple juice + gallons of Ginger ale
Given gallons of pineapple juice = 3/4 gallons
Orange juice = 1 1/2 gallons
Gallons of apple juice = 7/8
Total gallons of punch = 4 gallons
On substituting into the formula above:
4 = [tex]\frac{3}{4} +\frac{3}{2}+\frac{7}{8}+Gallons\ of\ ginger\ ale[/tex]
[tex]4=\frac{6+12+7}{8} + Gallons\ of\ ginger\ ale[/tex]]
gallons of ginger ale = [tex]4-\frac{25}{8}[/tex]
gallons ginger ale = [tex]\frac{7}{8}[/tex]
She needs 7/8 gallons of Ginger ale to make the total of 4 gallons of punch
Answer:
Emma would need 7/8 gallons of Ginger Ale to make the total of 4 gallons of punch.
Step-by-step explanation:
In the question, Emma used different quantities of juice to make a punch. To find the remainder, needed to make 4 gallons, we sum up the given quantities, and subtract it from the expected amount.
The summation of the given quantities of juice is as follows;
3/4 + 1 1/2 +7/8 = 25/8
We no subtract the quantity we already have from the expected amount, which is 4 gallons, thus;
4 - 25/8 = 7/8 gallons of Ginger Ale.
To confirm the answer, we sum up all the given quantities. Therefore;
3/4 + 1 1/2 + 7/8 + 7/8 = 4 gallons of punch.
A math teacher randomly selects one student in a class to write a probability question on a chalkboard. The teacher then randomly selects a different student to answer the probability question. There are 18 boys in the class, and the ratio of boys to girls is 3:5. Find the probability that the teacher selects a girl first and a girl second. Write your answer as a decimal rounded to the nearest thousandth.
Answer:
The probability to the nearest thousandth is 0.386
Step-by-step explanation:
Firstly, we will need to know the number of girls and the total number of students in the class.
We have the ratio as 3:5 for boys and girls with the number of boys being 18
What we have is thus;
3:5 = 18:g
3/5 = 18/g
3g = 90
g = 90/3
g = 30 girls
Thus, we have 18 boys and 30 girls with a total of 48 students.
The probability that the teacher selects a girl to write the question on the board is 30/48 = 5/8
Now, we intend selecting another girl to answer the question. This is like a probability without replacement. So this means that the number of girls we have now is 29 and the number of students we are selecting from is 47 students
Thus, the probability of selecting a girl to answer the question becomes 29/47
The joint probability is thus; 29/47 * 5/8 = 145/376 = 0.3856
To the nearest thousandth, we have 0.386
Pengelola layanan air minum di desaku membuat tempat penampungan air di dataran tinggi agar air dapat menjangkau seluruh desa. Tempat penampungan tersebu berbentuk kubus dengan panjang rusuk 8 meter. Jika tempat penampungan itu penuh, berapa liter air yang tertampung?
Answer:
The shelter can contain 512 cubic meters of water.Step-by-step explanation:
This question can be translated to:
"The manager of the drinking water service in my town creates a water tank in the highlands so that the water can reach the entire town. The cube-shaped shelter is 8 meters long. If the shelter is full, how many liters of water can it contain?"
As you can observe, the volumetric form is a cube with 8 meters long each edge.
We know the volume of a cube is defined as
[tex]V=l^{3}[/tex]
Where [tex]l=8 \ m[/tex], replacing this value, we have
[tex]V=(8 \ m)^{3} \\V=512 \ m^{3}[/tex]
Therefore, the shelter can contain 512 cubic meters of water.
How many points of intersection are on the graph?
y=x2+3x-7
y - X=9
The linear-quadratic system has (select) points of intersection.
Answer:
2 and 1
Step-by-step explanation:
[tex]y = {x}^{2} + 3x - 7 \: will \: have \: two \: points \: of \: \\intersection \\ \\ y - x = 9 \: will \: have \:only \: one\: point \: of \:\\ intersection[/tex]
The leaning Tower of Pisa was completed in 1372 and makes 86 degree angle with the ground. The tower is 50 meters tall, measured vertically from the ground to the highest point. If you were to climb to the top then accidentally drop your keys, where would you start looking for them?
How far from the base of the tower would they land?
I made having no luck in figuring this out.
Answer:
The distance where the keys would drop from the base is 3.5m
Step-by-step explanation:
Height of the tower = 50m
Angle it makes to the ground = 86°
To solve this question, you have to understand that the tower isn't vertically upright and the height of the tower is different from the distance from the top of the tower to the ground.
The tower makes an angle 86° to the ground and that makes it not vertically straight because a vertically straight building is at 90° to the ground.
See attached document for better illustration.
The distance from where the keys drop to the base of the tower can be calculated using SOHCAHTOA
We have to use cosθ = adjacent / hypothenus
θ = 86°
Adjacent = ? = x
Hypothenus = 50m
Cos θ = x / hyp
Cos 86 = x / 50
X = 50 × cos 86
X = 50 × 0.06976
X = 3.488 = 3.5m
The distance where the keys would drop from the base of the tower is approximately 3.5m
How many solutions are there to the equation below? 12x+32=12x-7
Answer:
I think it's no solutions
Step-by-step explanation:
12x+32=12×-7
-12 -12
32=-7
no solutions
simplify 5x+5(2x+2)+7
Answer:
12x+14
Step-by-step explanation:
5x+5(2x+2)+7
5x+7x+7+7
12x+7+7
12x+14
PLZZZZZZZZZZ HELP MEEEEEEEE
Answer:
D
Step-by-step explanation:
[tex]2x^2+2x+12=3x^2-x+2\\2x+12=x^2-x+2\\x^2-3x-10=0\\(x-5)(x+2)=0\\x=5, -2[/tex]
The correct answer is choice D. Hope this helps!
Answer:
{-5, 2}
Step-by-step explanation:
[tex]2x^{2} + 2x + 12 = 3x^{2} -x + 2[/tex] move everything to the right side
[tex]-2x^{2} -2x-12=-2x^{2} -2x-12[/tex] add line 1 and 2 to get the below equation
[tex]0 = x^{2} -3x -10[/tex] find multiples of -10 that add to give you -3
to get -10 we have to have (+)(-)
{-5, 2}
What type of sequence is 0,12,24,36,48 geometric or arithmetic?
Answer:
Arithmetic
Step-by-step explanation:
Since each number is 12 larger than the last, this is an arithmetic sequence. A geometric sequence is one in which each next number in the sequence is the previous one multiplied by a certain set coefficient, while in an arithmetic sequence it's a certain number added. Hope this helps!
Answer:
It is arithmetic because to get from one term to the next, you add 12, and in an arithmetic sequence, you add/subtract a common difference to get from one term to the next. Hope this helps!
A swimming pool is in the shape of a right rectangular prism. The base of the pool has an area of 216 square feet. When the pool is completely filled, it holds 1,944 cubic feet of water. What is the depth of the water when the pool is completely full?
Answer:
Just divide
1944/216=9
9 feet deep
Hope this helps
Step-by-step explanation:
PLZ HELP ME MY ASSIGNMENT IS DUE IN THE NEXT FEW MINUTES AND I HAVEN’T‘ DONE ANYTHING YET PLZ HELP ME
Answer:
C y=3x
Step-by-step explanation:
1 x 3 = 3
2 x 3 = 6
3 x 3 =9
Answer:
C. Y=3x i believe
Step-by-step explanation:
hope this helps
what is 3.39 as a fraction
Answer:
339/100
Step-by-step explanation:
the answer is 339/100
The chart shows rate of decay.
Which value is being measured in the columns labeled "Fraction remaining” and "Percentage remaining”?
years of decay
quantity of energy
number of stable atoms
amount of material that has not decayed
Years of decay...
It takes around 4 years for something to go through their half life (depending on the thing). This chart is showing the years go by (half lives that occur within the years) while the decaying is happening.
Answer: year of decay
Step-by-step explanation:
Consider circle C with angle ACB measuring 3 pi/4 radians if minor arc AB measures 9 pi inches what is the length of the radius of circle C if necessary round your answer to the nearest inch
Answer:
r = 12 inches
Step-by-step explanation:
In this question, we are asked to calculate the length of the radius of the circle.
This is accessible from using the length of an arc.
Mathematically, the length of an arc can be calculated using the formula;
Theta/360 * 2 * pi * r
Where Theta is the angle subtended at the center and r is the radius of he circle.
According to the question, Theta is 3pi/4 radians or let’s just say 0.75pi . This to degrees will be 135 degrees ( pi = 180 degrees)
Thus we have;
9 pi = 135/360 * 2 * pi * r
divide through by pi
9 = 270r/360
360 * 9 = 270r
r = (360 * 9)/270
r = 12 inches
Answer:
b
Step-by-step explanation:
A store employee counts 285 different lawn decorations. He wants to organize them and place the lawn decorations on 9 shelves. About how many lawn decorations will go on each shelf? A About 30 B About 40 C About 50 D About 90
Answer: C) About 30
Step-by-step explanation: 285/9= 31.6666666667 which rounded to the nearest ten is equal to 30
There should be about 30 decorations on each shelf.
What is division?The opposite of multiplication is division. Assuming that 3 gatherings of 4 make 12 in augmentation, 12 isolated into 3 equivalent gatherings give 4 in each gathering in division.
The primary objective of partitioning is to perceive the number of equivalent gatherings that are shaped or the number of are in each gathering while sharing decently.
Given total lawn decorations = 285
and to arrange in 9 shelves
each shelves will have
285/9 = 31.6667
the nearest ten is 30.
Hence each shelf have about 30 decorations.
Learn more about division;
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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.
Identify the outlier of the data set.
3,4,4,5,5,6,6,7,7,7,8,20
a
20
b
8
oooo
C
6.8
d
3
Answer:
a.20
Step-by-step explanation:
20 is standing out from the rest of the numbers
A 21-foot flagpole casts a shadow. The distance along the ground from the base of the pole to the top of the shadow is 11 feet. What is the distance from the top of the pole to the tip of the shadow?
Answer:
Step-by-step explanation:
.
A cereal box has the dimensions shown. A drawing of a rectangular prism shaped cereal box with length 9 inches, width 4 inches and height 12 inches. a. Find the surface area of the cereal box.
Answer:
surface area of the rectangular shaped cereal box = 384 ft²
Step-by-step explanation:
The cereal box is a rectangular prism . The rectangular prism has a length of 9 inches, height of 12 inches and width of 4 inches . The surface area can be computed below .
Surface area of the prism is the sum of the area of all the faces. Therefore,
surface area = 2wl + 2lh + 2hw
where
l = length
w = width
h = height
surface area = 2wl + 2lh + 2hw
l = 9 inches
w = 4 inches
h = 12 inches
surface area = 2(4 × 9) + 2(9 × 12) + 2(12 × 4)
surface area = 2(36) + 2(108) + 2(48)
surface area = 72 + 216 + 96
surface area of the rectangular shaped cereal box = 384 ft²
Answer:
The cereal box is a rectangular prism . The rectangular prism has a length of 9 inches, height of 12 inches and width of 4 inches . The surface area can be computed below .
Surface area of the prism is the sum of the area of all the faces. Therefore,
surface area = 2wl + 2lh + 2hw
where
l = length
w = width
h = height
surface area = 2wl + 2lh + 2hw
l = 9 inches
w = 4 inches
h = 12 inches
surface area = 2(4 × 9) + 2(9 × 12) + 2(12 × 4)
surface area = 2(36) + 2(108) + 2(48)
surface area = 72 + 216 + 96
surface area of the rectangular shaped cereal box = 384 ft
Step-by-step explanation:
Subtract 6
24
18
12
?
DONE
Answer
6
we keep subtracting by 6
12-6 = 6
A = 6
