The scale from a playground to this drawing is 5 ft to 1 cm. The scale from the same playground to another drawing is 8 ft to 1 cm. What are the side lengths of the playground in the other scale drawing?
The side lengths of the playground in the other scale drawing is [tex]\frac{5a}{8}[/tex].
By using geometry we answer this question.
Geometry is nothing but the branch of mathematics which deals with measurements of shapes.
Here, we take the scale from a playground to this drawing as "a" and The scale from the same playground to another drawing as "b".
First, we see the scale from a playground to this drawing.
[tex]\frac{a}{l}= \frac{1}{5}[/tex]
[tex]l=5a[/tex]
Now we see the scale from the same playground to another drawing.
[tex]\frac{b}{l} =\frac{1}{8}[/tex]
[tex]b=\frac{l}{8}\\[/tex]
Here, l=5a then
[tex]b=\frac{5a}{8}[/tex]
Therefore, the side lengths of the playground in the other scale drawing is [tex]\frac{5a}{8}[/tex].
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This is confusing me I'd appreciate some help
Answer:
d equals to -3, so in every expression we substitute d with -3.
2d(-3d)
2(-3) x (-3x-3)
-6 x 9 = -54
12d - 28
12(-3) - 28
-36-28 = -64
-3d
-3x(-3) = 9
-5d-8
-5x(-3)-8
15-8 = 7
8d+14
8x(-3) + 14
-24 + 14 = -10
hope it helps.
Help
Please help
I appreciate it
Step-by-step explanation:
f(g(x)) means g(x) is embedded in f(x) as the argument or input value for f(x).
therefore,
f(g)x)) = 4(x² - 1) - 7 = 4x² - 4 - 7 = 4x² - 11
c. is the right answer
g(f(x)) is now the other way around. now f(x) is the only value for g(x) :
g(f(x)) = (4x - 7)² - 1 = 16x² - 56x + 49 - 1 = 16x² - 56x + 48
a. is the right answer
1.76 x 105
5.8 x 10³
It's a little hard to determine what the picture says considering it is slightly blurred, however if you are trying to subtract the following, then after simplifying the expression, the solution written in Scientific Notation would be:
[tex]1.702[/tex] × [tex]10^5[/tex]
Hope this helps!
a rectangular field 50m wide and ym long requires 260m fencing. find y
The value of y such that the amount of fencing needed is 260 meters is 80 meters
What are perimeters?The perimeter of a rectangular field is the sum of the side lengths of the field
For all regular quadrilaterals, you add up the side lengths to determine the perimeter
How to determine the length y?The given parameters are
Width = 50 m
Amount of fencing = 260 m
Length = y
The amount of fencing is the perimeter of the fence
And perimeter is calculated as
P = 2 * (Length + Width)
So, we have
2 * (y + 50) = 260
Divide both sides by 2
So, we have
y + 50 = 130
Subtract 50 from both sides
So, we have
y = 80
Hence, the value of y such that the amount of fencing needed is 260 meters is 80 meters
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what is the quotation of -80 and -16
Based on the given task content, the quotient of - 80 and - 16 is 5
What is quotient?Quotient refers to the number resulting from the division of one number by another. Such as: the quotient of 12 divided by 4 is 3.
The divisor
The number or expression that another is to be divided by.
In "42 ÷ 3" the divisor is the 3.
The dividend
These refers to numbers or expressions that is to be divided by another.
In "42 ÷ 3" the dividend is the 42.
Quotient of -80 and -16= - 80 / - 16
= 5
Therefore, the quotient of -80 and -16 is 5
Complete question:
what is the quotient of -80 and -16
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How do you
Work this equation 5/16 + (-7/16)=
Answer:
-1/8
Step-by-step explanation:
So to start you already have the denominator equal, which helps a lot. So you do whatever operation is on top which in this case would be 5 + -7. Which you end up with -2/16. Then you simplify and end up with -1/8. Hope this helps. Have a great night. :)
Students put 2 1/4 pounds of trail mix into bags that each weigh 3/8 pounds. They bring 2/3 of the bags of trail mix on a hiking trip. Can you determine how many bags of trail mix are left by just completing one step?
There are 4 bags left after completing one step
The number of bags left after completing one step can be calculated as follows
The amount of trail mix into the bags is 2 1/4
= 9/4
The total amount of trail mix in the bag is 2/3
The first step is to calculate the number of bags
= 9/4 ÷ 3/8
= 9/4 × 8/3
= 36/12
= 6
There are 2/3 bags of trail
= 2/3 × 6
= 4
Hence 4 bags of trail mix are left after completing one step
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State of the following Conjecture is true or false
Given X is not a negative number
Conjecture X is a positive number
True or false?
The given conjecture X is a positive number is not always correct. Therefore, the given conjecture is false.
Given X is not a negative number and conjecture X is a positive number.
What is a conjecture?A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases.
Given X is not a negative number
Conjecture X is a positive number
If X is 0, which is neither positive nor negative.
So, the statement is false.
The given conjecture X is a positive number is not always correct. Therefore, the given conjecture is false.
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The distance in feet that a ball rolls down an incline is modeled by s(t) = −2t^2 − 2 , where t is seconds after the ball begins rolling. Find its instantaneous velocity at t = 4 seconds.
v(4) = ____
Answer:
-16
Step-by-step explanation:
pretty sure its the right answer, we did this a week ago in class so it may be wrong.
so first u gotta find the derivative of s(t) to get the vel equation. the derivative of s(t):
s(t)'= -4t, which is the vel equation
s(t)'=v(t)
v(4)=-4(4)
which equals -16
The instantaneous velocity of the ball at t = 4 seconds is -16 feet per second.
To find the instantaneous velocity of the ball at t = 4 seconds, we need to calculate the derivative of the given function s(t) with respect to t, and then evaluate it at t = 4.
Given that s(t) = -2t² - 2, we can find the velocity function v(t) by taking the derivative of s(t):
v(t) = d/dt (-2t² - 2)
v(t) = -4t
Now, we can find the instantaneous velocity at t = 4 by substituting t = 4 into the velocity function:
v(4) = -4(4)
v(4) = -16
This means that at that specific moment, the ball is moving downward with a velocity of 16 feet per second. The negative sign indicates the direction of motion.
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On a plane trip to Hawaii, the baggage weight projected was 2,182 1/4 lbs. The actual weight of all bags totaled 2,095 1/3 lbs. By how much was the projected weight overstated?
The projected weight of baggage overstated on a plane trip to Hawaii is 86(11/12) lbs.
What is an expression?
Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
It is given that : the baggage weight projected was 2,182 1/4 lbs and the actual weight of all bags totaled 2,095 1/3 lbs.
Now, to find out by how much was the projected weight overstated we subtract weight projected with actual weight of baggage :
weight overstated = weight projected - actual weight
weight overstated = 2,182 1/4 lbs - 2,095 1/3 lbs
weight overstated = 87 - 1/12 lbs
weight overstated = 86(11/12) lbs
Therefore, the projected weight of baggage overstated on a plane trip to Hawaii is 86(11/12) lbs.
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What is the solution to the equation?
√x-1= -4
Answer:
x=25
Step-by-step explanation:
√x−1−4=0
√x−5=0
√x=5
√x^2=5^2
x= 25
The base of a square pyramid has side lengths of 4.8 m. The height of each triangular face of the pyramid is 6 m. Do you have enough information to find the surface area of the pyramid? Explain.
There is enough information to find the surface area of the pyramid
What is a pyramid?A polyhedron formed by connecting a polygonal base and a point, called the ape-x is known as a pyramid.
The formula for calculating the volume of a pyramid is expressed as:
Volume = BH/3
B is the base areaH is the height of the pyramidFrom the given question, the pyramid is square based. Since we are given the length of the base to be 4.8m and the height of each triangular face of the pyramid is 6m, we can simply determine the height of the pyramid using Pythagoras theorem and then calculate the volume.
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The product of four times a number an 1
Answer:Let x = the unknown number
The product of a number and 5: 5x
is =
four times the sum of that number and 10: 4*(x+10)
5x = 4(x+10)
5x = 4x + 40
Step-by-step explanation:
Identify the coefficient of 6x3
Answer:
you to get my number 3 whole thing together
JUST LOOK AT THE PICTURE THE QUESTION IS THERE ALREADY JUST GIVE ME THE RIGHT ANSWER PLEASE
Area of rectangle is length times of width. Thomas is painting the wall at a warehouse blue. He painted in 6 hours of area 240 square feet.
What is area of rectangle?Area of rectangle is length times of width.
Area=Length*width.
From the given figure the length is 12 ft and width is 5 ft in 1.5 hrs.
area he covered painting= 12ft*5ft
=60 square feet.
In 1 and half hour he painted 60 square feet.
Now for 6 hours we have to calculate.
4*(1 and half hrs)=6 hrs
So we have to multiply 4 with 60 to get the area in 6 hours.
4*60=240square feet.
Therefore 240 square feet area Thomas painted.
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PLEASE HELP
A weatherwoman is on the news explaining that there will be high winds on the central coast coming in from the ocean. Using Bernoulli's principle, what do we know about the ocean and the coast?
A. The air over the ocean has more volume than the air over the coast
B. The air over the ocean has more mass than the air over the coast
C. There is less air pressure over the ocean than over the coast
D. The air over the ocean has less mass than the air over the coast
E. There is more air pressure over the ocean than over the coast
F. The air over the ocean has less volume than the air over the coast
Using Bernoulli's principle, the thing that we know about the ocean and the coast is that E. There is more air pressure over the ocean than over the coast.
What is Bernoulli's principle?According to Bernoulli's principle, which governs fluid dynamics, a fluid's speed increases concurrently with a reduction in pressure or potential energy.
The Bernoulli principle establishes a connection between a fluid's elevation and speed and its pressure. In water, air, or any other fluid with a very low viscosity, these characteristics can be approximated using Bernoulli's equation.
Since the weatherwoman is on the news explaining that there will be high winds on the central coast coming in from the ocean, it implies that there is more air pressure over the ocean than over the coast.
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Simple Math Range and domain help Part 4
will mark brainliest 15 points
Based on the product rule of exponents, a^4 * a^6 = [tex]a^{10}[/tex]
What is the Product Rule of Exponents?The product rule of exponents says that if two quantities that are multiplied together have the same base, we will add their exponents together to get the product.
Given the following:
a^4 * a^6
Applying the product rule of exponents, we will have:
a^4 * a^6 = a[tex]^{(4 + 6)}[/tex]
a^4 * a^6 = [tex]a^{10}[/tex].
Therefore, based on the product rule of exponents, a^4 * a^6 = [tex]a^{10}[/tex].
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And please show the work plsss help
Answer:
7
Step-by-step explanation:
3 goes into 21 7 times leaving no remainder which means: 3 x 7 = 21
Solve the equation, |2x−6|=8. Enter the answers in the boxes as integer values or simplified improper fractions. x = and x =
Answer:
x = 7
x = -1
Step-by-step explanation:
2x - 6 = 8 Add 6 to both sides
2x = 14 Divide both sides by 2
x = 7
2x -6 = -8 Add 6 to both sides
2x = -2 Divide both sides by 2
x = -1
A child sitting 1.70 m from the center of a merry-go-round moves with a speed of 1.65 m/s.
Calculate the centripetal acceleration of the child
Calculate the net horizontal force exerted on the child
a: The centripetal acceleration of the child = 1.60 m/s².
b: The net horizontal force exerted on the child = 40N.
What is defined as the centripetal acceleration?The acceleration of such a body traveling in a circular path is known as centripetal acceleration. Since velocity is a vector quantity (it has a magnitude, a speed, as well as a direction), when a body moves on a circular path, its direction changes and consequently its velocity changes, resulting in acceleration.The parameters provided;
merry-go-round radius, r = 1.70 m child's speed, v = 1.65 m/s child's mass = 25 kg.Part a: The child's centripetal acceleration is calculated as follows:
a = v²/r
Put the values;
a = 1.65²/1.7
a = 1.60 m/s²
Thus, the child's centripetal acceleration is 1.60 m/s².
Part b: The child's net horizontal force is calculated as follows:
F = ma
F = 25×1.60
F = 40 N
Thus, child's net horizontal force is 40 N.
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The complete question is-
A child sitting 1.70 m from the center of a merry-go-round moves with a speed of 1.65 m/s.
a. Calculate the centripetal acceleration of the child
b. Calculate the net horizontal force exerted on the child
Mass of child = 25 kg.
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
The equation in slope-intercept form is y = x - 6.
What is in slope-intercept form?
Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line p is
y = 8x + 2
Comparing with the slope intercept form, slope = 8
If two lines are parallel, it means that they have the same slope. Therefore, the slope of line q passing through ( -1 , -2 ) is 8
To determine the y intercept, we would substitute m = 8, x = - 1 and
y = -2 into y = mx + c. It becomes
-2 = 8 × - 1 + c
-2 = - 8 + c
c = - 8 + 2 = -6
The equation becomes
y = x - 6
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: The table below shows the cost of buying and shipping boxes of shirts. The variable, b, represents the number of boxes of shirts the client ordered. Which expression best represents the cost of the shirts plus shipping?
The expression that best represents the cost of shirts plus shipping is 20b + 5.
What is the expression that represents the cost of shirts plus shipping?An expression is a statement that is made up of at least two numbers or variables and at least one mathematical operation. An expression usually does not have an equal to sign.
The first step is to determine the cost of a shirt and the cost of shipping.
a + b = 25 equation 1
a + 2b = 45 equation 2
Where:
a = cost of shipping
Subtract equation 1 from equation 2
b = 20
a = 25 - 20
a = 5
Thus, the cost of one shirt is 20. The cost of shipping is 5. The cost of shirts increases with the number of shirts bought while the cost of shipping remains constant.
The expression is: 20b + 5
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For each function, find f(-2), f(0), and f(3)
The values of the functions are:
f(-2) = -6
f(0) = 0
f(3) = 9
How to Find the value of a Function?Given the function, f(x) = 3x, to find the values of f(-2), f(0), and f(3), solve as shown below.
Find f(-2) by substituting x = -2 into the function, f(x) = 3x:
f(-2) = 3(-2)
f(-2) = -6
The value of f(-2) for the given function is: -6
Find f(0) by substituting x = 0 into the function, f(x) = 3x:
f(0) = 3(0)
f(0) = 0
The value of f(0) for the given function is: 0
Find f(3) by substituting x = 3 into the function, f(x) = 3x:
f(3) = 3(3)
f(3) = 9
The value of f(3) for the given function is: 9
Thus, the values of the functions are:
f(-2) = -6
f(0) = 0
f(3) = 9
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Answers these please
A scientist needs 10 liters of a 20% acid solution for an-experiment, but she has only a 5% solution and a 40% solution. To the nearest tenth of a liter, about how many liters of the 5% and the 40% solutions should she mix to get the solution she needs?
The liters of the 5% and the 40% solutions is
x= 4.3L
This is further explained below.
How many liters of the 5% and the 40% solutions should she mix to get the solution she needs?You have been tasked with creating a solution with a concentration of 20% in a volume of 10 liters by combining solutions of 5% and 40%. It seems as if there may be more than one response to this question. If you assume that the combined volume of the 5% and 40% solutions equals 10L, then you may calculate the required volume of solution. The formula ought to go as follows:
10 L= 40% solution volume+ 5% solution volume
10 L= x + 5% solution volume
5% solution volume= 10l-x
In conclusion, The formula for calculating volume would look like this then:
Volume 0.2*concentration 0.2= volume 0.4*concentration 0.4 + volume 0.05*concentration 0.05
10 * 0.2= x *0.4 + (10- x) *0.05
10l * 0.20= x * 35% + 10*0.05
x *35 = 10l * 20 - 10 *5= 10 *15
x = 10l *15/35
x= 4.28 L
x= 4.3L
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Find the set A n B, all the information is on the picture!:)
Answer:
Step-by-step explanation:
I would have to go with b
Drag the tiles to the correct boxes to complete the pairs.
Match each list of numbers with the rule that describes its pattern.
Tiles
multiply by -1
add 2
add -20
multiply by 5
Pairs
5, 7, 9, 11, . . .
arrowBoth
100, 80, 60, 40, . . .
arrowBoth
10, 50, 250, 1,250, . . .
arrowBoth
2, -2, 2, -2, . . .
arrowBoth
- Six inches more than 3 times the height, h
Answer:
3h+6 inches
Step-by-step explanation:
Trymaine is 7 years older than Sunny. In 3 years the sum of their ages will be 39. How old is Trymaine now?
Trymaine is 20 years old and Sunny is 13 years old.
GIven, Trymaine is 7 years older than Sunny.
In 3 years the sum of their ages will be 39.
Let the age of Trymaine be a and age of Sunny be b.
we have,
a = b ₊ 7
a ₊ 3 ₊ b ₊ 3 = 39
a ₊ b = 39 ₋ 6
a ₊ b = 33 .... eq(2)
therefore a = b ₊ 7
a ₋ b = 7 ....eq(1)
solve eq (1) and eq(2)
2a = 40
a = 20
and a ₋ b = 7
20 ₋ b = 7
₋b = 7 ₋ 20
₋b = ₋13
b = 13
hence Trymaine is 20 years old , whereas Sunny is 13 years old.
hence we get the ages of Trymaine and Sunny as 20 and 13 respectively.
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