Use an equation to write 2 x (2/3) as a multiple of a unit fraction.
A toy is being constructed in the shape of a pyramid. the maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters. the height of the toy is double the side length. what are the maximum dimensions to the nearest square centimeter for a square base and for a hexagonal base? shape of base side length height square cm cm regular hexagon cm cm
The side of the hexagonal pyramid will be 3.81 cm and the height of the toy will be 7.62 cm.
The length of the side of the square and the height will be
6.98 cm and 13.96 cm.
What is a Pyramid ?
Pyramid is a three dimensional Structure ,having square , rectangle , hexagonal base , the faces for a square pyramid and hexagonal pyramid are triangle meeting at one point .
It is given in the question that
A toy is being constructed in the shape of a pyramid.
the maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters.
the height of the toy is double the side length
Let us assume the side length to be x
and therefore the height of the toy is 2x
The surface area of the toy is given = 250 sq.cm
First let us consider for a square base
The surface area of a square pyramid is given by
[tex]\rm A = a^2 + 2 a\sqrt {\dfrac{a^2}{4}+h^2}[/tex]
Here a is the side length which x for us and h = 2x
[tex]\rm 250 = x^2 + 2 x\sqrt {\dfrac{x^2}{4}+(2x)^2}\\\\ 250 = x^2 + 2 x\sqrt {\dfrac{x^2}{4}+4x^2}\\\\\\ 250 = x^2 + 2 x\sqrt {\dfrac{17 x^2}{4}}\\\\\\250 = x^2 + x^2 \sqrt{17}\\\\\\250 = 5.132 x^2\\\\\\48.71 = x^2\\\\\\x = 6.98 cm .[/tex]
Therefore the length of the side of the square and the height will be
6.98 cm and 13.96 cm.
For a hexagonal base
The total surface area is given by
[tex]A =6ah + 3 \sqrt{3}a^2\\\\\\A = 6 \times x \times 2x + 3\sqrt{3} (x)^2\\\\250= 12x^2 + 3\sqrt{3} x^2\\\\\\250 = 17.196 x^2\\\\\\14.54 = x^2\\\\x = 3.81 cm\\\\[/tex]
Therefore the side of the hexagonal pyramid will be 3.81 cm and the height of the toy will be 7.62 cm.
To know more about Pyramid
https://brainly.com/question/13057463
#SPJ1
find the slope using the following points: (20,-10)(6,-20)
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
Find the slope using the following points:
(20, -10) (6, -20)
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
Use the slope formula:-
[tex]\LARGE\text{$\displaystyle\frac{y_2-y_1}{x_2-x_1}$}[/tex]
Replace letters with numbers as follows:-
[tex]\Large\text{$\displaystyle\frac{-20-(-10)}{6-20}$}[/tex]
On simplification,
[tex]\Large\text{$\displaystyle\frac{-20+10}{-14}$}[/tex]
On further simplification,
[tex]\Large\text{$\displaystyle\frac{-10}{-14}$}[/tex]
Reducing the fraction,
[tex]\large\text{$\displaystyle\frac{10}{14}$}[/tex]
[tex]\large\text{$\displaystyle\frac{5}{7}$}\leftarrow\:slope[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
On Monday, Peter ran 20 minutes and walked 20 minutes and he burnt 500 calories. On Tuesday, Peter ran 10 minutes and walked 35 minutes and he burnt, again, 500 calories.
a) Create two equations based on the situation.
b) Determine the value of the variables.
c) How many calories can peter burn with one hour of running?
Answer:
a) 20r + 20w = 500, 10r + 35w = 500
b) r = 15, w = 10
c) 900 calories
Explanation:
Let running time be r, walking time be w
a) Hence, make equation's:
20r + 20w = 500... equation 1
10r + 35w = 500... equation 2
b) Determine the value of the variables by solving simultaneously.
⇒ (500 - 20w)/20 = (500 - 35w)/10
cross multiply
⇒ 10(500 - 20w) = 20(500 - 35w)
multiply
⇒ 5000 - 200w = 10000 - 700w
shift sides
⇒ -200w + 700w = 10000 - 5000
simplify
⇒ 500w = 5000
divide both sides by 500
⇒ w = 10
Now find the value of variable r,
⇒ r = (500 - 20w)/20
insert w = 10
⇒ r = (500 - 20(10))/20
simplify
⇒ r = 15
Hence the value of r is 15 and w is 10
c) Find calories burnt after one hours of running: [1 hours = 60 minutes]
calories = 60r = 60(15) = 900 calories
Hence, he can burn 900 calories after one hours of running.
Which of the following units could be used to measure Area? Select all that apply.
a) m2
b) in
c) cm2
d) sq. ft
e) mm
f) yd3
All the area measure units should have square above them.
For example:mm²cm²yd²in²m²km²ft²Hence, option A, C, D is correct.
Answer:
a) c) d)
Step-by-step explanation:
Length is a one-dimensional measure, therefore it is measured in single units.
⇒ m
⇒ cm
⇒ ft
The area of a shape is a two-dimensional quantity (e.g. length × width), therefore it is measured in square units.
⇒ m × m = m²
⇒ cm × cm = cm²
⇒ ft × ft = ft²
The volume of a shape is a three-dimensional quantity (e.g. length × width × height), therefore it is measured in cubic units.
⇒ m × m × m = m³
⇒ cm × cm × cm = cm³
⇒ ft × ft × ft = ft³
Therefore,
length = options b) e)area = options a) c) d)volume = option f)which of the following plotted points on the graph represent the zeros of the function g(x) = (x^2 - 3x - 10)(x + 4)
Answer: The answer would be (-2,0),(-4,0), and (5,0)
Step-by-step explanation:
Guessing the answer choices are
(-2,0)
(4,0)
(0,10)
(-4,0)
(0,-2)
(0,-10)
(5,0)
The top of the table can be modeled with a cylinder, and the legs can be modeled with rectangular prisms.
Estimate the amount of paint needed to cover all parts of the table, to the nearest square inch.
A.2,375
B.3,703
C.2,707
D.4,014
The amount of paint needed to cover all parts of the table will be 3703 square inches. Then the correct option is B.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The top of the table can be modeled with a cylinder, and the legs can be modeled with rectangular prisms.
The table is shown below.
The surface area of the cylinder will be
SA of cylinder = 2πr² + 2πrh
SA of cylinder = 2π (18² + 18 × 3)
SA of cylinder = 2375 square inches
Then the surface area of the prism will be
SA of prism = 4 [WL + 2(WH + LH)]
SA of prism = 4 [2 x 6 + 2 (2 x 20 + 6 x 20)]
SA of prism = 4 [12 + 2 x 160]
SA of prism = 4 [12 + 320]
SA of prism = 1328 square inches
Then the total surface area of the table will be
Total surface area = SA of prism + SA of cylinder
Total surface area = 1328 + 2375
Total surface area = 3703 square inches
Thus, the amount of paint needed to cover all parts of the table will be 3703 square inches.
Then the correct option is B.
More about the geometry link is given below.
https://brainly.com/question/7558603
#SPJ2
Which of the following equations represents a line that is parallel to the line with equation y = 3/2*x-7/4?
(A) 6x+4y=8
(B) -6x + 4y = 11
(C) x-2y=-4
(D) 3x+2y=7
Answer:
(B) -6x + 4y = 11
Step-by-step explanation:
Two lines are parallel if they have the same slope
In the line equation, y = mx + b, m = slope
For y = 3/2*x - 7/4, slope = 3/2
(B) can be written as
4y = 6x +11
Dividing by 4 on both sides gives y = 6/4*x + 11/4 which is 3/2*x + 11/4 so the coefficient of x (the slope) is 3/2 which is the slope of the line in the question
Using same strategies for the other lines, you will see
(A) has slope -3/2
(C) has slope 1/2
(D) has slope -3/2
which of the following is equivalent to 10x+15
10(x+5)
10(x+15)
5(2+3)
5(2x+3)
Answer:
The last one 5(2x + 3)
Step-by-step explanation:
5 × 2x = 10x
5 × 3 = 15
10x + 15
The area of a rectangle is 48 cm². If its width is 6 cm, what is its length?
================================
[tex] \large \sf \underline{Question:}[/tex]
The area of a rectangle is 48 cm². If its wdth is 6 cm, what is its length================================
[tex] \large \sf \underline{Answer:}[/tex]
[tex] \qquad \qquad \qquad \huge \bold{8cm}[/tex]
To solve for the area of rectangle, you use this formula A = length × width. But we're doing it reversal, we will divide the width to the area
[tex]\large\tt{A \: = \: l \: \times \: w}[/tex][tex]\large\tt{48cm^{2} \: = \: l \: \times \: 6cm}[/tex][tex]\large\tt{48cm^{2} \: \div \: 6cm \: = \: l}[/tex][tex]\large\tt{48cm^{2} \: \div \: 6cm \: = \: \pmb{8cm}}[/tex]Therefore, The length is 8cm.
================================
Hey ! there
Answer:
Length of rectangle is 8 cm .Step-by-step explanation:
In this question we are provided with a rectangle having area 48 cm² and width 6 cm . We are asked to find the length of rectangle .
We know that ,
[tex] \qquad \qquad\underline{\boxed{\frak{Area_{(Rectangle)} = l \times w}}}[/tex]
Where ,
l refers to Lengthw refers to WidthSOLUTION : -
We are finding value of length by substituting value of width as 6 cm and area as 48 cm² in the formula . So ,
[tex] \quad\longmapsto \qquad \:48 = 6 \times l[/tex]
or ,
[tex] \quad\longmapsto \qquad \:48 = 6l[/tex]
Dividing with 6 on both sides :
[tex] \quad\longmapsto \qquad \: \cancel{\dfrac{48}{6}} = \dfrac{ \cancel{6}l}{ \cancel{6}} [/tex]
We get ,
[tex] \quad\longmapsto \qquad \: \orange{\underline{\boxed{ \frak{l = 8 \: cm}}}} \quad \bigstar[/tex]
Henceforth , Length of rectangle having area 48 cm² and width 6 cm is ❝ 8 cm ❞Verifying : -
We are verifying our answer by substituting value of length and width in formula and equating it with given area . So ,
[tex] 8 \times 6 = 48[/tex][tex]48 = 48[/tex][tex] \rm{L.H.S = R.H.S}[/tex][tex] \rm{Hence , \: Verified .}[/tex]Therefore , our answer is correct .
#Keep LearningExpand the binomial using the Binomial Theorem.
(3c − d)^3
Answer:
[tex]27c^3-27c^2d+9cd^2-d^3[/tex]
Step-by-step explanation:
Binomial Theorem
[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]
[tex]\textsf{If }(a+b)^n=(3c-d)^3 \: \textsf{ then}:[/tex]
a = 3cb = -dn = 3Substitute the given values into the formula:
[tex]\begin{aligned}(3c-d)^3 & =(3c)^3+\dfrac{3!}{1!(3-1)!}(3c)^{3-1}(-d)+\dfrac{3!}{2!(3-2)!}(3c)^{3-2}(-d)^2+(-d)^3\\\\& =(3c)^3+3(3c)^2(-d)+3(3c)^1(-d)^2+(-d)^3\\\\& =27c^3-27c^2d+9cd^2-d^3\end{aligned}[/tex]
What is the measure of angle D?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
29.05°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and side lengths in a right triangle. In your triangle, the sides adjacent and opposite angle D are given. The relevant relation is ...
Tan = Opposite/Adjacent
__
Using the given values, we have ...
tan(D) = (25 ft)/(45 ft) = 5/9
The value of the angle is found using the inverse tangent function.
D = arctan(5/9) ≈ 29.05°
The measure of angle D is about 29.05°.
6. The ages of some children from a church were recorded. How many children were there in total?
Answer:
15
Step-by-step explanation:
Just add the number of kids disregarding their age
Answer:
The correct answer is 15.
Step-by-step explanation:
To get this answer, all we have to do is add up the data from the graph.
3 + 4 + 2 + 5 + 1 = 15
Hope this helps:) Goodluck!
The Earth's diameter is 8,000 miles. A satellite
orbits 140 miles above the Earth. An astronaut
works on the satellite and sees the sun rise over
Earth. Rounded to the nearest mile, the
distance from the astronaut to the horizon is
type your answer...
miles.
Applying the Pythagorean theorem, the distance between the Earth's horizon and the satellite would be 5756.70 miles.
How to calculate the distance from the satellite to the Earth's horizon?To calculate the distance from the satellite to the Earth's horizon, it is necessary to use the Pythagorean Theorem as follows:
We must identify the data we have:
Distance from Earth to satellite 140 miles.Earth diameter 8000 miles.To calculate the distance from the satellite to the Earth's horizon, we must first establish the distance from the center of the Earth to the satellite, for this we calculate the radius of the Earth and add the distance to the satellite:
Radius of Earth = 8000 miles / 2Radius of Earth = 4000 miles4,000 miles + 140 miles = 4,140 milesWith these data we can draw an imaginary triangle from the center of the Earth, one of its legs would be the distance between the center of the Earth and the satellite, the other leg would be the distance between the center of the Earth and the Earth's horizon (at 90° to the other leg).
Now, to identify the distance between the horizon and the satellite, we apply the Pythagorean Theorem:
a² + b² = c²4140² + 4000² = c²17139600 + 16000000 = c²33139600 = c²5756.70 = cAccording to the above, the distance between the satellite and the horizon would be 5756.70 miles.
Learn more about Pythagorean Theorem in: https://brainly.com/question/15190643
#SPJ1
Anna paid € 2800 for a dress. Payment was made after the price of the dress was reduced by 30%. What was the starting price?
Answer:
$4000
Step-by-step explanation:
so $2800 was the starting price
100%-30%=70%
So 2800=70%
2800/7=400
400=10%
400*10=$4000
pls answer!!! will mark brainliest!! 60 POINTS
The balance of the loan at 14 months= $10,561.25
It would take a total 23 months to pay off the loan.
The total amount of money paid for the car is = $9,052.5
Calculation of loan compounded monthlyThe total loan for the car = $8,500
The rate at which the loan is compounded monthly is
= 6.5%
The monthly payment for the loan = $390
To calculate the balance of the loan at 14 months;Find the simple interest
= P×T×R/100
= 8,500 × 1 × 6.5/100
= 55,250/100
= $552.5
If 12 months = 8,500 + 552.5
14 months = X
make X the subject of formula,
X = 14 × 9052.5/12
X= 126,735/12
X = $10,561.25
To calculate the period of time it will take to pay off the loanThe amount paid monthly = $390
The amount to be paid for the loan with interest = 8,500 + 552.5 = $9,052.5
If 1 month = $390
× month = $9,052.5
Make X the subject of formula,
X = $9,052.5/$390
X= 23 months
The total amount of money paid for the car is already calculated which is through the simple interest
= P×T×R/100
= 8,500 × 1 × 6.5/100
= 55,250/100
= $552.5
Total amount of money paid for the car= 8,500 + 552.5
= $9,052.5
Learn more about simple interest here:
https://brainly.com/question/20690803
#SPJ1
PLSS HELP ASAPP!! ILL GIVE BRAINLIEST!What is the point slope form of the line with slope -3/2 that passes through
the point (1, -3)?
Answer:
y= -3/2x - 3/2
Step-by-step explanation:
So you know the gradient of the line is -3/2x since that is the gradient.
So the equation so far is y=-3/2x +c
Then, substitute the co-ordinates to find c so:
-3 = -3/2 +c
-3/2 = c
The equation is y = -3/2x -3/2
50. Mrs. Lopez made decorative candles in different
sizes for sale at her church. All of the candles are in
cylindrical jars. The size of the largest candle was bigger
than the smallest candle by a scale factor of two. If the
height and radius of the smallest candle are 5 cm and
1.7 cm, respectively, calculate the volume of the biggest
candle. Use 3.14 for T. Round to the nearest hundredth.
The volume of the biggest candle given the volume of the smallest candle is 90.75cm³.
What is the volume of the largest candle?A cylinder is a three-dimensional object. It is a prism with a circular base.
Volume of a cylinder =πr²h
π = 3.14r = radiusVolume of the smallest candle = 3.14 x 5 x 1.7² = 45.37 cm³
Volume of the largest candle = 45.37 cm³ x 2 = 90.75cm³
To learn more about to determine the volume of a cylinder, check: https://brainly.com/question/9624219
#SPJ1
What is the volume?
Bernice made a rectangle wooden toolbox that has a base of 50 square cm and a height of 15 cm.
Answer:
750 cm^3
Step-by-step explanation:
VOLUME = base * height = 50 cm^2 x 15 cm = 750 cm^3
The measures of the angles of a triangle are shown in the figure below solve for X
Answer:
36
Step-by-step explanation:
We know all angles in a triangle must add up to 180°
The square in the triangle that angle is equal to 90°
We can now solve for x
90 + 54 + x = 180
144 + x = 180
x = 36
That is your answer
- Kan Academy Advance
help pls pls my math needs to be good grade pls pls no summer school pls pls
Which inequalities are true when x equals -8 ?
Answer:
I think it's just water bro
Answer:
B & C
Step-by-step explanation:
Use the information in the diagram to find the length of segment AD. Round your answer to the nearest hundredth.
Two triangles, A B C and C B D, with segment C D connecting vertex C with a point D on side A C. Angle C D B is a right angle. Segment C B is 23.2, segment B D is 14.6 and segment C A is 28.6.
Group of answer choices
36.83
22.20
18.03
7.20
Based on the lengths of the given triangles and the length of segment BD, the length of segment AD is 22.20.
What is the length of segment AD?The triangle ABC is a right angled triangle with segment AB being the hypothenuse.
We can therefore find this length using the Pythagoras Rule:
Hypothenuse ² = a² + b²
Hypothenuse ² = 28.6² + 23.2²
Hypothenuse ² = 1,356.20
Hypothenuse = √1,356.20
= 36.83
Length of AD:
= AB - BD
= 36.83 - 14.60
= 22.2
Find out more on the Pythagorean theorem at https://brainly.com/question/343682.
#SPJ1
Someone please help me!?
Answer:
rise is 11 and run is 2
Step-by-step explanation:
i believe but not fully sure
Answer:
5.5
Step-by-step explanation:
Line is passing through the points (1, 0) and (3, 11)Slope of line [tex]=\frac{11 -0}{3-1}[/tex]Slope of line [tex]=\frac{11}{2}[/tex]Slope of line [tex]=5.5[/tex]In a survey of adults, 18% lift weights regularly, 32% run regularly, and 7% lift weights and run regularly. What is the conditional probability that an adult who lifts weights regularly, also runs regularly?
The conditional probability that an adult who lifts weights regularly, also runs regularly is 0.219 or 21.9% if the 18% lift weights regularly, 32% run regularly, and 7% lift weights and run regularly.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
Let's suppose P(A) is the probability of adults who lift weights regularly.
P(A) = 18% = 0.18
Similarly,
P(B) = 32% = 0.32
P(A∩B) = 0.07
We know:
[tex]\rm P(A|B) = \dfrac{P(A\cap B)}{P(B)}[/tex]
[tex]\rm P(A|B) = \dfrac{0.07}{0.32}[/tex]
P(A|B) = 0.219 or
P(A|B) = 21.9%
Thus, the conditional probability that an adult who lifts weights regularly, also runs regularly is 0.219 or 21.9% if the 18% lift weights regularly, 32% run regularly, and 7% lift weights and run regularly.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ1
what equations will give me this
Answer:
2[tex]n[/tex] = [tex]\alpha n[/tex] and [tex]n + n[/tex] = [tex]\alpha n[/tex]
Step-by-step explanation:
Pythagorean Theorem (Radical Answers)
May 12, 8:47:08 AM
Find the length of the third side. If necessary, write in simplest radical form.
7
412
8
c=√a2+b2 I really hope this helps
The triangles are similar by the AA Similarity Postulate. Find the value of x.
Me dicen plis 2 multiplicaciones que den de resultado 139.
Plis
Doy coronita‼
Answer:
Claro esta:
139 x 1
Pero tambien
69.5 x 2
Y
46.3 x 3
Y muchos mas
first correct answer gets brainleist pls help asap
Answer:
21 m^2
Step-by-step explanation:
0.5 x 14 x 3
hope this helps
have a good day
Answer:
The answer is 21 m^2
cmiller did it first so giver her brainlliest if you were going to do it to me.
What is the volume of the cylinder below? a cylinder with a height of 12 millimeters and diameter of 18 millimeters. 108 pi mm3 216 pi mm3 648 pi mm3 972 pi mm3
The volume of a cylinder with a height of 12 millimeters and diameter of 18mm is 972π mm^3
Volume of a cylinderThe formula for calculating the volume of a cylinder is expressed as:
V = πr²h where:
r is the radius
h is the height
Given the following parameters
h = 12mm
r = 18/2 = 9mm
Substitute
V = π(9)²(12)
V = 972π mm^3
Hence the volume of a cylinder with a height of 12 millimeters and diameter of 18mm is 972π mm^3
Learn more on volume of a cylinder here: https://brainly.com/question/9554871
#SPJ4