The length side of equilateral triangle is 8.08 units
What is Altitude?The altitude or height of an equilateral triangle is the line segment from a vertex that is perpendicular to the opposite side.
Here, let the side of the equilateral triangle be x units
given altitude of the equilateral triangle = 7 units
we know,
Altitude = √3/2 X side
7 = √3/2 X x
x = 7 X 2 / √3
x = 14/√3
x = 8.08 units
Thus, the length side of equilateral triangle is 8.08 units.
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A region with a 10-mile radius has a population density of about 1500 people per square mile. Find the number of people who live in the region to the nearest ten thousand.
The number of people who live in the region is about
.
The number of people who live in the region to the nearest ten thousand will be 942000.
What is population density?
The number of the people live in the given volume is known as the population density.
(r)Region radius= 10 miles
Population density= 1500 per square mile
The area of the region is found as;
A=2πR²
A= 2π(10 x 10)
A=2(3.14) (100)
A= 628 square miles
Population density= Population/Area
1500= Population / 628 square miles
Population = 1500 x 628
Population = 942000
Hence,the number of people who live in the region to the nearest ten thousand will be 942000.
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What is the answer F, G, H or J
Answer:
G its G
Step-by-step explanation:
QUESTION 3 Simplify the following expression 3.1.1 Add:-4
x+6+11x - 5
Answer:
-24 + (-55) = -79
Step-by-step explanation:
-4x+6+11x - 5
Step-by-step explanation:
[tex] = x + 6 + 11x - 5[/tex]
Organize the expression....
[tex] = x + 11x + 6 - 5[/tex]
Simplify the expression...
[tex] = 12x + 1[/tex]
...
Put the numbers from least to greatest: .3, 2/3, .36, 35%, 1/3
Answer:
0.3, 1/3, 35%, 0.35, 2/3
Step-by-step explanation:
Verify if x > 1 is the solution to the inequality 7 - 4x > −2 (3x - 5).
Answer:
No, x>3/2
Step-by-step explanation:
Too lazy sorry.
1. Adrian invests $10,000 in an account that increases by 8% each year. What is the balance in the account after 15 years?
Answer:
$162000
Step-by-step explanation:
8% of 10000
10000÷100=100×8=800
10000+800=10800
10800×15=162000
Please help me with these questions. Thank you.
Answer:
36 x⁸y⁶
√2/2
Step-by-step explanation:
Factor 1296 into its prime factors
1296 = 24 • 34
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
1296 = 24 • 34
No factors remain inside the root !!
To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
36 = 22 • 32
At the end of this step the partly simplified SQRT looks like this:
36 √(x¹⁶y¹²)
STEP2:Simplify the Variable part of the SQRT
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
√(x⁸)=x⁴
√(x^-6)=x^-3
Applying these rules to our case we find out that
SQRT(x¹⁶y¹²) = x⁸y⁶
Combine both simplifications
sqrt (1296x¹⁶y¹²) = 36 x⁸y⁶
Simplified Root : 36 x⁸y⁶
number 2)
3√2/3√4=
=3√2/3×2
=3√2/6
=3√2/6 ×3/3
=1√2/2
=√2/2
What is the value of the dot shown on the number line below? If the answer is not an integer, enter it as a fraction or mixed number.
A cube has a surface area of 96 square inches. If 16 cubes are combined to make a rectangular prism, what is the volume of the rectangular prism?
Answer:
1536
Step-by-step explanation:
The table below represents the function f, and the following graph represents the function g. x -6 -5 -4 -3 -2 -1 0 1 f(x) 8 -2 -8 -10 -8 -2 8 22 Complete the following statements. The functions f and g have . The y-intercept of f is the y-intercept of g. Over the interval [-6, -3], the average rate of change of f is the average rate of change of g
Answer:
Complete the following statements.
The functions f and g have the same axis of symmetry.
The y-intercept of f is greater than the y-intercept of g.
Over the interval [-6, -3], the average rate of change of f is less than the average rate of change of g.
Using the image above, what is the measure of Angle J? Round to the nearest hundredth
Answer:
∠J = 31.06°
Step-by-step explanation:
Taking the inverse sin function :
sin ∠J = 1.6/3.1J = sin⁻¹ (0.516)∠J = 31.06°One a 570-mile trip, George spent two more hours on the Interstate than on the highway. He averaged 75 mph on the Interstate and 65 mph on the highway. How many hours did he spend driving on the Interstate
George spend 5 hours driving on the Interstate if George spent two more hours on the Interstate than on the highway.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the George spend x hours on the interstate and (x+2) hours on the highway.
570 = 75x + 65(x-2)
570 = 75x + 65x -130
700 = 140x
x = 5 hours
Thus, George spend 5 hours driving on the Interstate if George spent two more hours on the Interstate than on the highway.
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An open box is to be made out of a 6-inch by 18-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. find the dimensions of the resulting box that has the largest volume.
dimensions of the bottom of the box:
height of the box:
An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.
Dimensions of the bottom of the box: L x W
Height of the box:
SOLUTION
Diagram
Cardboard with x2 area cutouts...
··················14 - 2x
···x··¦¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¦···x··
¦——¦·······························¦——¦
¦·············································¦
¦·············································¦ 6 - 2x
¦·············································¦
¦——¦·······························¦——¦
···x··¦___________________¦··x···
Volume = l·w·h
After cutouts:
l = 14 - 2x
w = 6 - 2x
h = x
V = (14 - 2x)(6 - 2x)(x) in3
V = 4x3 - 40x2 + 84x in3
To maximize the volume, take the derivative of V with respect to x, set it equal to zero, and solve for x:
dV/dx = 0 = 12x2 - 80x + 24
x2 - (20/3)x + 7 = 0
x = (10 ± √37)/3 in
Since (6 - 2x) yields a negative number for x = (10 + √37)/3 we use only x = (10 - √37)/3
Thus, the dimensions are:
l = 14 - 2x = 11.39 in
w = 6 - 2x = 3.39 in
h = x = 1.31 in
Base = l·w = 38.59 in2
Volume = 50.39 in3
ok im super confused bc like it ask me put i dont know what to put.............pls help me
Answer:
u drag the green dot thing over to the coordinate (6,8)
Step-by-step explanation:
i put a black dot where i think ur supposed to drag the green dot to
x² + y² = 8
x - y = 0
Select all of the following that are solutions to the system shown.
O (2, 2)
O (2,-2)
O (-2,2)
0 (-2,-2)
Answer:
[tex](2,2)~ \text{and}~ (-2,-2)[/tex]
Step by step explanation:
[tex]x^2 +y^2 =8~~~~~~...(i)\\\\x-y=0~~~~~~~~~...(ii)\\\\\text{From (ii):}\\\\x-y = 0 \implies x = y\\\\\text{Substitute x = y in eq (i):}\\\\~~~~~~y^2 +y^2 =8\\\\\implies 2y^2 = 8\\ \\\implies y^2 = \dfrac 82\\\\\implies y^2 = 4\\\\\implies y = \pm\sqrt 4\\\\\implies y = \pm 2\\\\\text{Substitute y = x in equation (i):}\\ \\~~~~~~x^2 +x^2 = 8\\ \\\implies 2x^2 = 8\\\\\implies x^2 = \dfrac 82\\\\\implies x^2 = 4\\\\\implies x = \pm\sqrt 4\\\\\implies x = \pm2\\\\[/tex]
[tex]\text{Hence,}~ (x,y) = (\pm2, \pm 2)[/tex]
You decide that you will only sell two different types of frozen treats in your
ice-cream cart. You use the following criteria to help you make your decision:
• You will purchase 550 frozen treats for your cart.
• You have a budget of $450.
• Your goal is to make a profit of at least $700.
Which two frozen treats will you sell in your ice-cream cart, and how many of
each treat will you purchase? Show that your combination of frozen treats
meets the criteria.
Based on the given scenario above, the purchase decision will be I will chose Ice cream bar fruit and frozen bar fruit.
What is Purchase decision?This is know to be the thought method or act that helps a consumer to identify a need, gather options, and choosing a given product and brand.
Note that Based on the given scenario above, the purchase decision will be I will chose Ice cream bar fruit and frozen bar fruit.
If I am to purchase 550 frozen treats, I will buy:
Ice cream bar fruit = 300
Frozen bar fruit = 250
Therefore, for Ice cream bar fruit , it will be = amount x cost price
300 x 0.85 = 255
For Frozen bar fruit = 250 x 0.50
= 125
Add up the total cost= 255 + 125
Total amount spent will be= 380
Therefore we can see that the total price spent falls within the budget allocated and so I will choose both Ice cream bar fruit and frozen bar fruit.
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Find the volume of the figure
Answer:
[tex]800\pi yd^3[/tex]
Step-by-step explanation:
[tex]A = 10\pi ^2(8)\\= 800\pi yd^3[/tex]
Answer: 2513.27 yd³
Step-by-step explanation:
Volume of a cylinder:
-> This formula means we are finding the area of the base circle and multiplying it be the height
V = πr²h
V = πr²h
V = π(10)²(8)
V ≈ 2513.27 yd³
The volume of the figure is about 2513.27 yd³.
whats 6 divided by 161?
Answer:
0.03
Step-by-step explanation:
You can do this on a calculator.
6 ÷ 161 = 0.0372670807
Hope this helped
!!100!! POINTS PLEASE HELP!!
Answer:
x = 5
Step-by-step explanation:
The triangles are similar by AA similarity.
They share a common angle (∠A) and have an angle of 90°.
Since they are similar, we can takes the sides in proportion.
[tex]\frac{BC}{DE} = \frac{AB}{BD}[/tex]8/16 = x/10x/10 = 1/2x = 10/2x = 5Answer:
x = 10.
Step-by-step explanation:
Triangles ABC and ADE are similar so their corresponding sides are in the same ratio.
So we have:
8/16 = x / (x + 10)
16x = 8(x + 10)
16x - 8x = 80
8x = 80
x = 10
Helloppp i need hwlp with this plllss
Jayne stacked 2 cubes on top of each other as shown. The edge length of the smaller cube is half the edge length of the cube below it. What is the surface area of the new figure?
Considering the surface area of a cube, and that the figure has two cubes, the total surface area is of 1470 m².
What is the surface area of a cube?The surface area of a cube of edge length a is given by:
S(a) = 6a².
In this problem, we have two cubes, one with a = 14 m and the other with a = 7 m. Hence, the total surface area, in m², is given by:
S(a) = 6 x 14² + 6 x 7² = 1470.
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Option 1: use the applet to construct circles for problems 1 & 2 or 3 & 4.
take a screenshot and insert them into your student companion.
1. circle a, with a diameter of
6 cm.
2. circle c, with a radius that is
equal to circle a's diameter.
3. circle b, with a radius of 5
cm.
4. circle d, with a diameter
that is equal to circle b's
radius.
Answer:
9
Step-by-step explanation:
Option 1: use the applet to construct circles for problems 1 & 2 or 3 & 4.
take a screenshot and insert them into your student companion.
1. circle a, with a diameter of
6 cm.
2. circle c, with a radius that is
equal to circle a's diameter.
3. circle b, with a radius of 5
cm.
4. circle d, with a diameter
that is equal to circle b's
radius.
The exchange rate of mexican pesos for u.s. dollars is approximately 10 pesos for 1 dollar. if lynn exchanged 4,000 pesos for u.s dollars, what was the approximate value in u.s.dollars
400 dollars
4000/10=400 dollars
Learn with an example
on the last day of a shakespeare class, an english teacher asked her students which play
they liked most. out of the 12 students, 3 liked macbeth best.
what is the probability that a randomly selected shakespeare student likes macbeth best?
write your answer as a fraction or whole number.
p(macbeth) =
i don't know exactly what to do
Answer:
Step-by-step explanation: Just relax effortlessly. Communion Kant be for All unless we are primed for purpose...
At Everyday Donuts, 3 of the last 6 donuts sold had sprinkles. Considering this data, how many of the next 10 donuts sold would you expect to have sprinkles?
__5___Sprinkles
THAT IS THE ANSWER
If 10 donuts are sold. Then the expected value of the number of sprinkles will be 5.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
The expected value will be given as
E(X) = np
At Everyday Donuts, 3 of the last 6 donuts sold had sprinkles. Considering this data.
If 10 donuts are sold.
Then the number of the sprinkles will be
The probability will be
p = 3/6
p = 0.5
n = 10
Then the expected value of the number of the sprinkles will be
E(x) = 10 x 0.5
E(x) = 5
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Which expression represents the volume, in cubic units, of empty space in the cube? four-thirdsπ(4.53) – (4.5)3 (9)3 – four-thirdsπ(4.52) four-thirdsπ(4.53) – (9)3 (9)3 – four-thirdsπ(4.53)
The expression that represents the volume of the empty space is 9³ - 4 / 3 π(4.5)³ cubic units.
How to find the expression for volumes?
The volume of the empty space can be represented as follows
volume of the empty space = volume of cube - volume of sphere
Therefore,
volume of sphere = 4 / 3 πr³
where
r = radiusVolume of cube = L³
where
L = side lengthTherefore,
volume of cube = 9³
volume of sphere = 4 / 3 π(4.5)³
Hence,
volume of the empty space = 9³ - 4 / 3 π(4.5)³
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Answer:
D
Step-by-step explanation:
other dude typed too much lam
None shall sleep ellie marney theme
Answer:
“teenager protagonists confronting horror”
Step-by-step explanation:
Marney herself said that she wrote the story specifically about “teenager protagonists confronting horror” for a teenage audience to give them “comfort” and impart a powerful message: “you are strong enough to deal with this. You have been in far worse situations and survived.
Answer:
I love sleep
Step-by-step explanation:
Which is the length of the hypotenuse of the triangle? Triangle A B C. Side A C is 12 feet and side C B is 35 feet. StartRoot 94 EndRoot ft
Answer:37
Step-by-step explanation:
just took the test
Find the value of x.
11.4
12.6
18.9
15.3
