Answer:
Pyramid
Step-by-step explanation:
[tex]\text{Volume of a Square Pyramid }=\frac{1}{3} \times l^2 \times Height\\\\ \text{Volume of a Cone }=\frac{1}{3} \pi r^2 \times Height[/tex]
Given that the two solids have the same volume
[tex]\frac{1}{3} \times l^2 \times Height=\frac{1}{3} \pi r^2 \times Height[/tex]
If the length of a side of the square base of pyramid A is the same as the base radius of cone B. i.e l=r
[tex]\frac{1}{3} \times l^2 \times $Height of Pyramid=$\frac{1}{3} \pi l^2 \times $Height of cone$\\\\$Cancel out $ \frac{1}{3} \times l^2$ on both sides\\\\Height of Pyramid= \pi \times $ Height of cone$[/tex]
If the height of the cone is 1
[tex]H$eight of Pyramid= \pi \times 1 \approx 3.14$ units[/tex]
Therefore, the pyramid has a greater height.
A contractor can spend at most $250 a day on operating costs and payroll. It costs $45 each day to operate the forklift and $60 a day for each crew member. Write an inequality to represent the contractor's budget for the day.
Answer: [tex]45+65x\leq250[/tex] .
Step-by-step explanation:
Given: Cost to operate the forklift per day = $45
Cost for each crew member per day = $65
Let x be the number of crew members.
Then, we have
Total cost = (Cost to operate the forklift per day)+(Cost for each crew member per day)×(number of crew members)
= 45+65x
Since, the contractor can spend at most $250.
Then, the required inequality: [tex]45+65x\leq250[/tex] .
if the pattern continued,what value of y would be associated with x=6? y=
Answer: the answer would be 24
Step-by-step explanation: just did the assignment
Answer:
24
Step-by-step explanation:
Just got it right on edge 2020
John is planning a party. There are 28 pieces of carrot cake and 7 pieces of marble cake. He wants to create plates with the same number of each type of cake. What is the greatest number of plates he can create?
Answer:
Hey there!
He can create 7 plates at most, with one carrot cake and one marble cake on each plate.
Hope this helps :)
Kaylee has $4,500 for a down payment and thinks she can afford monthly payments of $300. If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate), what is the maximum amount Kaylee can afford to spend on the car? [use the calculation in the text or the online calculators in the resource section]
Answer:
$17,028.06
Step-by-step explanation:
Given that :
Kaylee's down payment = $4500
monthly payment = $300
If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate).
the maximum amount Kaylee can afford to spend on the car is being calculated as the present value for all the payments.
= [tex]=\$4,500 +\dfrac{\$300}{(1+\frac{0.07}{12})} + \dfrac{\$300}{(1+\frac{0.07}{12})^2} +\dfrac{\$300}{(1+\frac{0.07}{12})^3} + ....+ \dfrac{\$300}{(1+\frac{0.07}{12})^{46}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{47}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{48}}[/tex]
Using the online desmos calculator to determine the maximum amount Kaylee can afford to spend on the car; we have:
= $17,028.06
Where is the function increasing?
A)1
B)3< X
C)-infinity < x < 1
D)-infinity
Answer:
A) [tex]1<x<\infty[/tex]
Step-by-step explanation:
Given:
A graph of a function.
When we analyze the given graph, it is of a parabola.
To find:
The interval of values of [tex]x[/tex] where the function is increasing.
Solution:
First of all, let us learn about the meaning of increasing and decreasing functions.
1. A function [tex]y=f(x)[/tex] is known as increasing in an interval [tex]a<x<b[/tex] when
Value of y keeps on increasing when we move from the value of x from a to b.
2. A function [tex]y=f(x)[/tex] is known as decreasing in an interval [tex]a<x<b[/tex] when
Value of y keeps on decreasing when we move from the value of x from a to b.
On analyzing the given graph , we can see that the graph is decreasing on the interval: [tex]-\infty<x<1[/tex]
and is increasing on the interval: [tex]1<x<\infty[/tex]
When we choose from the options,
The correct answer is option A) [tex]1<x<\infty[/tex]
Given that C is at (-6, -1) and D (4, 8), find the point P that partitions CD into the ratio of 1:3.
Answer:
The coordinates of point P are (-7/2, 5/4)
Step-by-step explanation:
Here, we want to give the coordinates of the point P that divide CD in the given ratio
To do this , we shall be making use of a mathematical formula;
Let’s say the ratio 1:3 represents a:b, our formula those becomes
{(bx1 + ax2)/(a + b) ,( by1+ay2)/a+b}
From the question, we can identify that
(x1,y1) = (-6,-1)
(x2,y2) = (4,8)
a = 1 and b = 3
Plugging these values into the formula we have
3(-6) + 1(4)/(1+3) , 3(-1) + 1(8)/(1+3)
= (-18 + 4)/4 , (-3+ 8)/4
=-14/4, 5/4
= (-7/2, 5/4)
The diagonals of a rhombus are 12cm and 16cm.Find the length of each side.
Answer:Let PQRS to be the rhombus where PQ=12cm and RS = 16cm
step 1:let,PQ and RS intersect each other at O.Now, diagonals of rhombus bisect each other at right angles.
STEP 2:Since POQ is a right angled triangle, by pythagoras theoram.
STEP 3:After applying formula , PQ =10cm .length of each side of rhombus is 10cm.
Step-by-step explanation:
Answer:
10cm
Step-by-step explanation:
As you can see in the first image is a rhombus with its diagonals 12cm and 16cm
You can see that the diagonals divide the rhombus into four right triangles and that the hypotenuse of each triangle is one side of the rhombus.
In the second image I picked out one triangle from the rhombus and slashed the length of the diagonals of the rhombus in half to get the sides of the triangle.
Now all you have to do is use the Pythagorean theorem to find the hypotenuse of the triangle which will give you the length of side of rhombus
6² + 8² = hypotenuse²
36 + 64 = h²
100 = h²
h = √100
h = 10
All the side of the rhombus are equal so all the sides of the rhombus are 10cm
Amy gets a new kennel for her dog. A sketch of the kennel is shown here. If the roof is in the shape of a triangular prism (bottom face included), what is the surface area of the roof of the kennel, including the bottom face?
Answer:
Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2
Step-by-step explanation:
The image is attached below
For the triangular sides of the roof, area is
A = [tex]\frac{1}{2}bh[/tex]
where b is the base = 4 ft
h is the vertical height = 2.24 ft
A = [tex]\frac{1}{2}*4*2.24 =[/tex] 4.48 ft^2
for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2
For the rectangular sections of the roof, area is
A = [tex]lh[/tex]
where [tex]l[/tex] is the length of the rectangle = 5 ft
h is the height of the rectangle = 3 ft
A = 5 x 3 = 15 ft^2
For the two rectangular faces, we have 2 x 15 ft^2 = 30 ft^2
For the bottom face, area is
A = [tex]lw[/tex]
where [tex]l[/tex] is the length of the house = 5 ft
w is the width of the house = 4 ft
A = 5 x 4 = 20 ft^2
Surface area of the roof of the dog kennel is
8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2
I'LL GIVE BRAINLIEST AND THANKS -SOLVE THE QUADRATIC EQUATION
Answer:
x = -1.47, 1.14
Step-by-step explanation:
Quadratic Formula: [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
We are given a = 3, b = 1, and c = -5. Simply plug it into the Quadratic Formula:
Step 1: Plug in variables
[tex]x=\frac{-1+/-\sqrt{1^2-4(3)(-5)} }{2(3)}[/tex]
Step 2: Solve
[tex]x=\frac{-1+/-\sqrt{1+60} }{6}[/tex]
[tex]x=\frac{-1+/-\sqrt{61} }{6}[/tex]
Step 3: Plug into calculator to evaluate into decimals
You should get x = -1.46837 and 1.13504
Answer:
1.13 and -1.46
Step-by-step explanation:
Our quadratic equation is: 3x²+x-5=0
The method we will use is te dicriminant method
let Δ be the discriminant:
a= 3b= 1c= -5Δ = b²-4*a*c
Δ= 1²-4*3*(-5)Δ= 1+60Δ=6161 is a positive number so we have solutions x and x':
x= (-b-√Δ)/2*a = (-1-√61)/2*3 = [tex]\frac{-1-\sqrt{61} }{6}[/tex] = -1.46 x'= (-b+√Δ)/2*a = (-1+√61)/2*3 =[tex]\frac{-1+\sqrt{61} }{6}[/tex] = 1.13so the two solutions are :
-1.46 and 1.13
Triangle ABC is isosceles with AB = AC.
Angle BAC = 110° and the area of the triangle is 85cm^2
Calculate AC.
Answer:
22.5 cm
Triangle area is (L x W) / 2
7.5 x 6 = 45
45 / 2 = 22.5
Step-by-step explanation:
brainlist plzzzz
What is the center of the circle with the equation (x-1)^2 + (y+3)^2= 9? a (1,3) b (-1,3) c (-1,-3) d (1,-3)
Answer:
The center is ( 1,-3) and the radius is 3
Step-by-step explanation:
The equation of a circle can be written in the form
( x-h)^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
(x-1)^2 + (y+3)^2= 9
(x-1)^2 + (- -3)^2= 3^2
The center is ( 1,-3) and the radius is 3
The price of sugar increased by 20%. What percent of sugar would the family have to stop using so that they pay the same amount of money each month?
Answer:
9.16
Step-by-step explanation:
We know that
Total expense = price of sugar * consumption
let price of sugar was 100
So total expense = 100*10=1000
But now new expense =1100 (I,e.10% more than 1000)
and new price =120(i,e. 20% more than 100)
So new consumption = new expense/ new price=
1100/120
=110/12
=9.16
HOPE IT HELPS :)
PLEASE MARK IT THE BRAINLIEST!
Answer:
16 2/3 % or approx. 16.67%
Step-by-step explanation:
Original price = 100%
New price = 100+20% = 120%
To reduce back to 100%
we need to reduce 20% from 120 % = 20/120 = 1/6 = 16 2/3 % = 16.7% approx.
Write these series with summation notation. 1,4,9,16...
Answer: [tex]\sum\limits_{i=1}^{n} n^2[/tex] , where n is a natural number.
Step-by-step explanation:
A series can be represented in a summation or sigma notation.
Greek capital letter, ∑ (sigma), is used to represent the sum.
For example: [tex]\sum\limits_{n=1}^{\infty} n=1+2+3+4+5+...[/tex], where n is a natural number.
The given series : 1,4,9,16 which can be written as [tex]1^2, 2^2, 3^2,...[/tex] .
So , we can write it as
[tex]\sum\limits_{n=1}^{\infty} n^2[/tex] , where n is a natural number.
Answer:
B=6
C=n^2
Just did the test
Step-by-step explanation:
What the answer now and answer fast correct answer
Answer:
[tex] f = 12.7 [/tex]
Step-by-step explanation:
Given:
<H = 94°
FG = h = 15
<F = 58°
GH = f = ?
Use the law of sines to find f:
[tex] \frac{f}{sin(F)} = \frac{h}{sin(H)} [/tex]
[tex] \frac{f}{sin(58)} = \frac{15}{sin(94)} [/tex]
[tex] \frac{f}{0.848} = \frac{15}{0.998} [/tex]
[tex] \frac{f}{0.848} = 15.03 [/tex]
Multiply both sides by 0.848
[tex] \frac{f}{0.848}*0.848 = 15.03*0.848 [/tex]
[tex] f = 15.03*0.848 [/tex]
[tex] f = 12.74544[/tex]
[tex] f = 12.7 [/tex] (nearest tenth)
I need help with this!
Part A
Answer: 33.2 degrees F
Explanation: Adding on a negative is the same as subtracting. So 72.3 + (-39.1) = 72.3 - 39.1 = 33.2
================================================
Part B
Answer: 70 + 2 + 0.3 + (-30) + (-9) + ( -0.1 )
Explanation:
Think of 72 as 70+2. Furthermore, think of 72.3 as 70+2+0.3; we just break the number up into its corresponding digits (adding zeros when needed). The 7 is in the tens place, the 2 is in the units or ones place, and the 3 is in the tenths place.
Similarly, we have 39.1 break down into 30+9+0.1, in which all three terms are made negative to represent -39.1
================================================
Part C
Answer: 70 + (-30) + 2 + (-9) + 0.3 + ( -0.1 )
Explanation: Arrange the tens place value items to be next to each other. Same goes for the units place value, and also the tenths place value.
================================================
Part D
Answer: [70 + (-30)] + [ 2 + (-9) ] + [ 0.3 + ( -0.1 ) ]
Explanation: Take the result of part C and surround each pair of terms in square brackets to show how the terms pair up.
A play school is designing two sand pits in ts play area . Each must have an area of 36 m2 . However , one of the sand pits must be rectangular , and the other must be square haped . What might be the dimensions of ach of the sand pits ?
Answer:
Dimensions of square shaped pit = 6m [tex]\times[/tex] 6m
Dimensions of rectangular pit = 1m [tex]\times[/tex] 36m or 2m [tex]\times[/tex] 18m or 3m [tex]\times[/tex] 12m or 4m [tex]\times[/tex] 9m
Step-by-step explanation:
Given:
Two pits in the school playground area (one square shaped and one rectangular shaped).
Each pit must have an area = 36 [tex]m^2[/tex]
To find:
Dimensions of each pit = ?
Solution:
First of all, let us have a look at the formula for area of a square and a rectangle:
[tex]Area_{square} = (Side)^2[/tex]
[tex]Area_{Rectangle} = Length\times Width[/tex]
Now, let us try to find out dimensions of square:
[tex]36 = Side^2\\\Rightarrow Side = 6\ m[/tex]
So, dimensions of Square will be 6m [tex]\times[/tex] 6m.
Now, let us try to find out dimensions of rectangle.
[tex]36 = Length\times Width[/tex]
We are not given any restrictions on the Length and Width of the rectangle.
So, let us explore all the possibilities by factorizing 36:
[tex]36 = 1 \times 36\\36 = 2 \times 18\\36 = 3 \times 12\\36 = 4 \times 9[/tex]
6 [tex]\times[/tex] 6 factors not considered because then it will become a square and which is not the required case.
Dimensions of rectangular pit = 1m [tex]\times[/tex] 36m or 2m [tex]\times[/tex] 18m or 3m [tex]\times[/tex] 12m or 4m [tex]\times[/tex] 9m
what is the area of the triangle in the diagram?
Answer:
area=17.5
Step-by-step explanation:
area=1/2(base*height)
area=1/2(3*7)
are=17.5
Which lists all of the y-intercepts of the graphed function? (0, –3) (–1, 0) and (3, 0) (0, –1) and (0, 3) (–1, 0), (3, 0), and (0, –3)
Answer:
The correct option is;
(0, -3), (-1, 0) and (3, 0)
Step-by-step explanation:
From the given graph of the function we have the following observations;
There are two x-intercepts which are;
1) To the left of the vertical y-axis having coordinates (-1, 0)
2) To the the right of the y-axis having coordinates (3, 0)
There is only one y-intercept having coordinates, (0, -3)
Therefore, all the intercepts of the function are, (0, -3), (-1, 0) and (3, 0).
Answer:
(0, -3), (-1, 0) and (3, 0)
Step-by-step explanation:
PLEASE help me with this question!!! I really need help...
Answer:
The last option
Step-by-step explanation:
The centroid is the point that is equidistant from all the vertices, not the incenter. Furthermore, the incenter is formed by finding the point of concurrency (intersection) of the angle bisectors.
Find the surface area of the regular pyramid shown to the nearest whole number
Answer:
740 m^2
Step-by-step explanation:
please help :) Which number is less than 2.167 × 10 to the 4 power? A. 9,978 B. 1.1 x 10 to the 6 power C. 56,344,000 D. 2.468 × 10 to the 5 power
Answer: A
Step-by-step explanation
2.167x10^4 = 21,670
= 9,978
1.1x10^6 = 1100,000
= 56,344,000
2.468x10^5 = 246,800
Answer: A. 9,978
Based on the power, move the decimal point that many spaces to the right. (E.g., If it's 4.2 × 10^3, then move the decimal three spaces to the right, and you'd get 4200.)
2.167 × 10^4 = 21670
1.1 × 10^6 = 1100000
2.468 × 10^5 = 246800
Out of all the numbers mentioned in the question, 9,978 is the only one that's less than 2.167 × 10^4 = 21670.
PLEASE HELP!!
Factor the polynomial [tex]x^2+6x+5[/tex]. Your answer can be written as [tex](x+A)(x+B)[/tex] where A
Step-by-step explanation:
[tex]a + b = 6[/tex]
[tex]ab = 1 \times 5 = 5[/tex]
[tex]a = 1 \: \: \: \: \: \: \: \: b = 5[/tex]
[tex]( {x}^{2} + x) + (5x + 5)[/tex]
[tex]x(x + 1) + 5(x + 1)[/tex]
[tex](x + 1)(x + 5)[/tex]
Hope this is correct and helpful
HAVE A GOOD DAY!
A hair color manufacturer performed a survey which was normally distributed. They found that the average age at which a person's hair starts turning gray is 32 years, with a standard deviation of 4 years. Which of the following graphs displays the normal distribution of the average age at which a person's hair starts turning gray?
W.
X.
Y.
Z.
Answer: X
Step-by-step explanation:
Write the number in scientific notation.
a) 423.6
b) 7,194,548
c) 500.23
d) 71.23884
e) .562
f) .0348
g) .000123
h) .5603002
Answer:
a) 4.236 x 10^2
b) 7.194548 x 10^6
c) 5.0023 x 10^2
d) 7.123884 x 10^1
e) 5.62 x 10^-1
f) 3.48 x 10^-2
g) 1.23 x 10^-4
h) 5.603002 x 10^-1
Hopefully this helps :)
Answer:
a) 423.6=4.236*10^2
b) 7,194,548=7.194548*10^6
c) 500.23=5.0023*10^2
d) 71.23884=7.123884*10^1
e) 0.562=5.62*10^-1
f) 0.348=3.48*10^-1
g) 0.000123=1.23*10^-3
h) 0.5603002=5.603002*10^-1
Step-by-step explanation:
The numbers in which the point lies must be between 0 and 10
Hope this helps ;) ❤❤❤
Convert -(3)^1/2 - i to polar form
Answer:
2(cos30°+isin30°)
Step-by-step explanation:
Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
On converting the rectangluar to polar form of the complex number;
x = rcosθ and y = rsinθ
Substituting in the rectangular form of the comlex number above;
z = rcosθ + irsinθ
z = r(cosθ+isinθ)
r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Given the complex number in rectangular form z = -(3)^1/2 - i
z = -√3 - i
x = -√3 and y = -1
r = √(-√3)²+(-1)²
r = √3+1
r = √4
r = 2
θ = tan⁻¹ (-1/-√3)
θ = tan⁻¹ (1/√3)
θ = 30°
Hence the complex number in polar form will be z = 2(cos30°+isin30°)
This is the last one but how do you find y ? what do I subtract 5 from ?
Answer:
y = 250
Step 1:
To solve, we plug in 50x for y.
[tex]50x=200+10x[/tex]
Then, we subtract the 10x from the right side. Our goal is to get the x by itself first.
[tex]40x=200[/tex]
Then, we divide both sides by 40, since we have to get the x by itself.
[tex]\frac{40x}{40}=x\\\\\frac{200}{40} =5[/tex]
x = 5
Step 2:
Now that we found x, we plug in 5 to the original equation and solve from there.
[tex]y=200+10(5)\\y=200+50\\y=250[/tex]
y = 250
Which values for h and k are used to write the function f of x = x squared + 12 x + 6 in vertex form?
h=6, k=36
h=−6, k=−36
h=6, k=30
h=−6, k=−30
Answer:
h=−6, k=−30
Step-by-step explanation:
did on edge
Considering the equation of the parabola, the coefficients of the vertex are:
h=−6, k=−30
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](h,k)[/tex]
In which:
[tex]h = -\frac{b}{2a}[/tex]
[tex]k = -\frac{b^2 - 4ac}{4a}[/tex]
In this problem, the equation is:
[tex]f(x) = x^2 + 12x + 6[/tex]
Hence the coefficients are a = 1, b = 12, c = 6, thus:
[tex]h = -\frac{12}{2} = -6[/tex]
[tex]k = -\frac{120}{4} = -30[/tex]
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
URGENT!!! Please help me with this question!!!!!! I will not accept nonsense answers!
Answer:
B
Step-by-step explanation:
The inscribed angle's arc measures 36°, and central angle's arc measures 72°.
Answer:
the answer is B
Step-by-step explanation:
what is x if x(x+3)(x+3)=0
Answer:
hello :
Step-by-step explanation:
x(x+3)(x+3)=0 means : x=0 or x+3=0 or x+3=0
x=0 or x=-3 or x=3
54x^3y+ 81x^4y^2 factorise
Answer:
I hope it helps you......