The length of seesaw will be equal to 11 feet.
It is given that midpoint of the seesaw is 13.5 feet from the swing set and swing set is 8 feet from the edge of the seesaw.
We have to find out the length of seesaw.
What do you mean by midpoint of a line segment ?
The midpoint is halfway between the two end points , whose x value is halfway between the two x values and y value is halfway between the two y values.
As per the question ;
The midpoint of the seesaw is 13.5 feet from the swing set.
and
The swing set is 8 feet from the edge of the seesaw.
So ;
The distance from the midpoint to the edge will be ;
13.5 – 8 = 5.5.
And
The length of the seesaw will be ;
= 2× (5.5)
= 11 feet
Thus , the length of seesaw will be equal to 11 feet.
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Please help!!
1.The height of a projectile is a function of the time it is in the air. The height in feet for t seconds is given by the function h(t) = -16t2 + 96t . What is the domain of the function? What does the domain mean in the context of the problem?
2.Use the graph at right to answer the following question.
Solve for f(x) = -3
Problem 1
The domain is [tex]0 \le t \le 6[/tex] which in interval notation is [0, 6]
This is the set of t values where h(t) is positive or zero. Any other t values will make h(t) to be negative. So we ignore those t values. A negative height makes no sense.
The domain in the context of the problem means that the projectile is in the air from the time markers of t = 0 and t = 6. In short, the object is in the air for 6 seconds. It takes 6 seconds for it to hit the ground.
Here's how we can determine those t values. We plug in h(t) = 0 and solve for t.
h(t) = -16t^2 + 96t
-16t^2 + 96t = 0
-16t(t - 6) = 0
-16t = 0 or t - 6 = 0
t = 0/(-16) or t = 6
t = 0 or t = 6
======================================================
Problem 2
Draw a horizontal line through -3 on the y axis.
This horizontal line touches the blue graph at the points (-2,-3) and (2,3)
This means the inputs x = -2 and x = 2 lead to the output of y = -3
Therefore f(-2) = -3 and f(2) = -3
Answer: The solutions are x = -2 and x = 2
A trapezoid has a height of 12 inches, a base length of 9 inches, and an area of 150 square inches. What is the length of the other base?
The length of other base is 16 inch.
The area of trapezoid is given by the formula -
Area = 1/2×(a+b)×height, where a and b represents the two different bases. Let a be the length of 9 inches and b be the length of other base.
150 = 1/2×(9 + b)×12
Shifting 2 to Left Hand Side and performing multiplication on both sides.
150×2 = (9 + b)×12
300 = 108 + 12b
12b = 300 - 108
12b = 192
Shifting 12 to Right Hand Side of equation to find the other base
b = 192 ÷ 12
Performing division
b = 16 inch
Hence, the length of other base is 16 inch.
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Out of 30 candidates applying for a post, 17 have degrees, 15 diplomas and 4 neither degree nor diploma. How many of them have both.
Answer:
the answer is 6.
Step-by-step explanation:
solution is given in the photo
hi
let's rule ot first candidate with nothing :
as they are 4 , remains : 30 -4 = 26
Now let call X number of candidate with both degrees and diplomas
we have : 17+15 -X = 26
-X = 26 - 32
-X = -6
x = 6
We have to withdraw from categorie degree and diplomas 6 people who have both and then counted twice.
So figues goes as follow :
nothing : 4
degrees only : 11
diplomas only : 9
both degree and diplomas : 6
total : 4 +11 +9 +6 = 30
State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
A ₋trigonometric ratio is a ratio of the lengths of two sides of a right triangle.
Given statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle' is True.
In this question,
We have been given a statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle'
Sometimes, trigonometric ratios used to find the measures of acute angles in a right triangle.
To find the measures of acute angles in a right triangle, you need to know the measures of the two sides of the right triangle.
We determine which ratio to use depending on which sides are given. And we also use the inverse trigonometric functions to find the angle.
Trigonometric ratios are: sine, cosine, tangent, cotangent, secant, cosecant.
These ratios are abbreviated as, sin, cos, tan, cot, sec, cosec.
Therefore, given statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle' is True.
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How many solutions does the equation 12(2x+6)=6−x have?
Answer:x=0
Step-by-step explanation:
f(x)=6^x and g(x)=14^x labeled on graph
f(x)=6ˣ and g(x)=14ˣ on the graph are shown (refer to the graph given below).
What do we mean by the graph?While many people use the terms "graph" and "chart" interchangeably, they are not the same thing. Charts are tables, diagrams, or pictures that clearly and concisely organize large amounts of data. Charts are used to interpret current data and make predictions. Graphs, on the other hand, concentrate on raw data and show trends over time. A graph is defined as a diagram that depicts the relationships between two or more things. A pie chart is an example of a graph. Bar graphs, circle graphs, and line graphs are the three most common types of graphs. Each type of graph is appropriate for displaying a different type of data.So, f(x)=6ˣ and g(x)=14ˣ on graph as:
Refer to the graph given below.Therefore, f(x)=6ˣ and g(x)=14ˣ on the graph are shown (refer to the graph given below).
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Evaluate each expression for x=-2,0,1 , and 4.
(3/5)x-2
The value for x=-2,0,1 and 4 are -16/5, -2, -2/5, 2/5 respectively.
What does solving for x means?Find the value of x that would make the equation you see true is what it means to "solve for x." Consider the following formula: x + 1 Equals 3. If you were to attempt to solve it, you would need to identify a value for x such that it yields three when one is added.
Given expression is -
(3/5)x-2
For x = -2
The value of expression will be = (3/5)(-2) - 2
= -16/5
For x = 0
The value of expression will be = (3/5)(0) - 2
= -2
For x = 1
The value of expression will be = (3/5)(1) - 2
= -2/5
For x = 4
The value of expression will be = (3/5)(4) - 2
= 2/5
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What is the equation 2n x 2m equal to?
Answer: 2n x 2m
Step-by-step explanation:
Since the variables are different, you cannot do anything.
Given two terms of each arithmetic sequence, find a₁ and d . a₄=-34.5 and a₅=-12.5
The two terms of each arithmetic sequence [tex]a_{4}[/tex] = 34.5, [tex]a_{5}[/tex] =12.5 are d = 47 and a = -106.5.
What is sequence?[tex]a_{4}[/tex] = 34.5
34.5 = a +3d.............1
[tex]a_{5}[/tex] =12.5
-12.5 = a + 4d...........2
equating equation 1 and 2
34.5 = a +3d
-12.5 = a + 4d
d = 47
d = 47 ..............3
from equation 3
a = -106.5
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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-6x+6=4x-24
with work, if that's alr
Answer:
x = 3
Step-by-step explanation:
-6x+6-6=4x-24-6
-6x=4x-30
-6x-4x=4x-30-4x
-10x=-30
-10x/-10=-30/-10
Need help please asap
Step-by-step explanation:
the circle standard form is
(x - h)² + (y - k)² = r²
(h, k) are the coordinates of the center of the circle.
r is the radius of the circle.
I cannot draw here, but I can describe the details.
9.
the center is therefore at (-1, 2). and the radius is 5.
to graph the circle mark the 4 points with radius distance up, down, left and right of the center.
up : (-1, 2 + 5) = (-1, 7)
down : (-1, 2 - 5) = (-1, -3)
left : (-1 - 5, 2) = (-6, 2)
right : (-1 + 5, 2) = (4, 2)
10.
the center is therefore at (3, 0). and the radius is 4.
to graph the circle mark the 4 points with radius distance up, down, left and right of the center.
up : (3, 0 + 4) = (3, 4)
down : (3, 0 - 4) = (3, -4)
left : (3 - 4, 0) = (-1, 0)
right : (3 + 4, 0) = (7, 0)
11.
we have the h, k coordinates of the center.
for the radius we need to find the distance between the center and the given point.
remember, this is via Pythagoras in a right-angled triangle
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
for the distance between 2 points the direct distance is the Hypotenuse, and the x and y coordinate differences are the legs.
distance² = r² = (7 - 2)² + (-1 - -1)² = 5² + 0² = 5² = 25
so, the equation is
(x - 2)² + (y + 1)² = 25
12.
we have the h, k coordinates of the center.
for the radius we need to find the distance between the center and the given point.
distance² = r² = (4 - 1)² + (6 - 2)² = 3² + 4² = 9 + 16 = 25
so, the equation is
(x - 1)² + (y - 2)² = 25
Jackson asked a representative sample of 30 of his classmates about their favorite arctic animal for an upcoming science project.
Fill in the table to show reasonable predictions for the whole class.
His class has a total of 240 students.
Favorite Arctic Animal
Polar Bear 12
Reindeer 9
Seal 3
Walrus 6
Answer:
These are the estimates:
Polar Bear: 96
Reindeer: 72
Seal: 24
Walrus: 48
Step-by-step explanation:
240/30=8
Multiply the amount of people that like each animal by 8 to estimate how many out of 240 like that animal.
12*8=96
9*8=72
3*8=24
6*8=48
1) 28/z - z/4 + 1 1/8, when z = 4
A) 7 1/8
B) 4 7/8
C) 9 1/8
D) -5 7/8
2) n+23.1/ 3n - 8n, when n = 2.1
A) -12.8
B) -8.4
C) 20.8
D) -20.8
Answer:
Step-by-step explanation:
9 + 11 = 10 so 120=69 69-5 = 13 answer is 13
What is an equation of the line that passes through the point (4,1)(4,1) and is perpendicular to the line 2x-y=42x−y=4?
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3.
What is the equation of a perpendicular line?The equation of the line is given below.
2x - y = 4
Then the slope of the perpendicular line will be
y = 2x - 4
m = 2
Then the equation of the line will be
y = -(1/2)x + d
Then the line is passing through (4, 1), then we have
1 = -(1/2)4 + d
3 = d
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3.
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Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth.
C=18 in.
A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 2.8648 inches and 5.7296 inches, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that circumference of the circle is 18 inches. Therefore, the radius and the diameter of the circle can be written as,
Circumference of circle = 2 × π × (Radius of the circle)
18 inches = 2 × π × (Radius of the circle)
(Radius of the circle) = 18 in/ (2 × π)
The radius of the circle = 2.8648 inches
Diameter of circle = 2 × (Radius of the circle)
= 2 × 2.8648 inches
= 5.7296 inches
Hence, the radius and the diameter of the circle are 2.8648 inches and 5.7296 inches, respectively.
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Slope
1/5
y-intercept = -2
I need this in slope intercept form. Can someone help?
Answer:
y= 1/5x + (-2)
Step-by-step explanation:
2 ___ =4
- _.
3. 9????
How can you tell that the student made an error when factoring? Explain the error.
Factor:
6x²-x-12
6x²9x + 8x - 12
3x(2x-3)-4(-2x +3)
Step-by-step explanation:
For a polynomial of the form
a
x
2
+
b
x
+
c
, rewrite the middle term as a sum of two terms whose product is
a
⋅
c
=
6
⋅
−
12
=
−
72
and whose sum is
b
=
−
1
.
−
1
out of
−
x
.
6
x
2
−
(
x
)
−
12
Rewrite
−
1
as
8
plus
−
9
6
x
2
+
(
8
−
9
)
x
−
12
Apply the distributive property.
6
x
2
+
8
x
−
9
x
−
12
Factor out the greatest common factor from each group.
Tap for more steps...
2
x
(
3
x
+
4
)
−
3
(
3
x
+
4
)
Factor the polynomial by factoring out the greatest common factor,
3
x
+
4
.
(
3
x
+
4
)
(
2
x
−
3
)
Fit for Family offers a membership fee of
$450 for the year or the option to pay $41
per
month. How much do you save each month by
choosing the annual membership fee?
We save $3.5 each month and in total $42 by giving the annual membership fees.
What are mathematics operations?An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations. A zero-arity operation, also known as a nullary operation, is a constant. The mixed product is an example of an arity 3 operation, also known as a ternary operation.
So,
The yearly pay is $450.The monthly payment is $41.Then, Monthly pay for a whole year:
$41 × 12 = $492Now,
$492 - $450 = $42Saving each month by giving the annual fees:
$42 ÷ 12 = $3.5
Therefore, we save $3.5 each month by giving the annual fees.
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A Dutch company built a submarine that can hold 10 passengers and 1 pilot. The submarine has a safety feature that will automatically raise the submarine if it goes below the certified depth of −650feet. To show this feature to a buyer the submarine dove to a depth of −872[tex]\frac{5}{12}[/tex]feet. The automatic feature then raised the submarine 50[tex]\frac{3}{5}[/tex]feet per minute. How much time, in minutes, does it take for the submarine to reach the certified depth? Round your answer to the nearest tenth of a minute.
The time, in minutes that it take for the submarine to reach the certified depth is 12.85 minutes.
How to illustrate the information?From the information, the submarine has a safety feature that will automatically raise the submarine if it goes below the certified depth of −650feet.
It should be noted that the automatic feature then raised the submarine 50 3/5 feet per minute.
Therefore, the time needed to reach the depth will be:
= 650 / 50 3/5
= 650 / 50.6
= 12.85 minutes
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(4x^2y)(8x^5y^3 find product of monomials
The product of the monomials is 32x^7y4
What is a monomial?A monomial is said to be a product of powers of variables with a non-negative integer exponents, or a product of variables.
Monomials include numbers, variables or multiple numbers or variables multiplied together.
Given the monomials;
(4x²y)(8x^5y³)
Finding the product is simply done by multiplying the two expressions, we have
The product of the numbers = 4 × 8 = 32
The product of the 'x' variables = x^2 + 5 = x^7
The product of the 'y' variables = y^1 + 3 = y^4
32x^7y4
Thus, the product of the monomials is 32x^7y4
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I need help with the problem 5/6 ÷ 3/4
Answer:
10/9 or 1 1/9
Explanation:
Multiply by the reciprocal
cancel out the greatest common factor
multiply the fractions
and you get 10/9 or 1 1/9
Explain the difference between a constant and a coefficient.
The constant is the number that includes in the expression and the coefficient is the number that write along with the variable in the expression.
Here,
The constant is the number that includes in the expression. It is a fixed value that does not change over time
Example : 2x+5
Where 5 is the constant
The coefficient is the number that write along with the variable in the expression
Example : 2x+5
Where 2 is the coefficient.
Hence, the constant is the number that includes in the expression and the coefficient is the number that write along with the variable in the expression.
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A bookcase had nine shelves each shelf had exactly 23 books
___= Books
Answer:
207 book
Step-by-step explanation:
9 shelves x 23 books per shelve=207 books
You stand on a street corner and record the gender of the first twelve people who pass by. if the city is half male and half female, what is the probability that you will record all females?
The probability is 6.
Probability is the possibility of an event occurring. We can scale the probability of an event between 0 and 1. 0 refers to an improbable event, and one refers to an event with the highest possibility. The type of probability we will use to solve this problem is the geometric distribution.
The geometric distribution is defined as a discrete probability distribution representing the probability of consecutive failures before success in a Bernoulli trial. There could be only two possible outcomes; either True (1) or False (0).
Bernoulli's trial is an experiment in which we have only two possible outcomes, success or failure. In other words, the geometric distribution repeats Bernoulli trials until it succeeds, then stops. So, achieving success is the ultimate goal and is the point that stops Bernoulli's trials from happening further.
Geometric distribution, the class of probability distributions, is based on three key assumptions, and these assumptions are defined as:
The studies conducted are independent. Each event is independent of the other.Each attempt has only two outcomes: success or failure. If an event has any other possible outcome other than 0 and 1, it can not be classified as a Bernoulli trial.The probability of success, indicated by p, is the same for each trial.Now for our given problem, we stand on a street corner and record the gender of the first twelve people who pass by. The condition here is the city is half male and half female. Now to find the probability, we will consider the possibility of each of the twelve events. Since half of the population is Female, the probability of one single event is;
p = 1/2 (50 %)
The overall probability is the sum of all the individual probabilities:
P ( ALL FEMALE)
= 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2
= 6
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A rectangle has a perimeter of 15 inches. If the length is two times the sum of 3 and the width find the dimensions of the rectangle.
Answer:
See below
Step-by-step explanation:
Perimeter = 2( L + W ) L = 2 (3+W) <==== given
15 = 2 ( 2(3+W) + W)
15 = 2 ( 6 +3W)
15 = 12 + 6W
3 = 6W
W = 1/2 inch L = 2(3+W) = 7 inches
What are the domain and range of this relation? (-3,14),(0,7),(2,0),(9,-18),(23,-99)
The range and domain of the relation (-3,14),(0,7),(2,0),(9,-18),(23,-99) are {-3, 0, 2, 9, 23} and {14, 7, 0, -18, -99} respectively.
According to the given question.
We have a relation (-3,14),(0,7),(2,0),(9,-18),(23,-99).
As we know that, the set which contains all the first elements of all the ordered pairs of relation R is known as the domain of the relation.
And, the set which contains all the second elements of all the ordered pairs of relation R is known as the range of the relation.
Therefore, the domain of the given relation is {-3, 0, 2, 9, 23}.
And the range of the given relation is {14, 7, 0, -18, -99}.
Hence, the range and domain of the relation (-3,14),(0,7),(2,0),(9,-18),(23,-99) are {-3, 0, 2, 9, 23} and {14, 7, 0, -18, -99} respectively.
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21. A scuba diver dives to a depth of 50 feet,
then rises 15 feet, then rises 20 feet. Write an
addition expression to describe this situation.
Then determine the sum and explain its
meaning.
Answer:
73
Step-by-step explanation:
Based on the given conditions, formulate: 20+50+15-12
Calculate the sum or difference:70+15-12
Calculate the sum or difference:85-12
Calculate the sum or difference:73
get the result:73
Answer:
50 - 15 = 35
35 + 20 = 55
Total amount of feet diven : 55 feet
I forgot how to do these, and i don’t remember whether they have two answers or not.
Solve for d.
-7| d - 1 | = -11
Answer:
=18/7
=−4/7
Step-by-step explanation:
Divide both sides by -7
−7|−1|=−11
The negatives are canceled.
Simplify
|−1|=11/7
Split the problem into two cases: one positive and one negative
=18/7
=−4/7
A random survey was conducted to determine where families vacationed. The results indicated that P(B)=0.6, P(B ^M)=0.2 , and the probability that a family did not vacation at either destination is 0.1 .
b. What is the probability that a family visiting the beach will also visit the mountains?
The probability that a family to visit the beach also will travel the mountains is 0.33.
What exactly is a Venn diagram?A Venn diagram is a graph that uses circles to represent relationships between objects or finite groups of objects. Circles that intersecting share properties, but circles that do not overlap do not.
Please see the Venn diagram.
P(B) [the entire blue circle] = 0.6 is the probability of such a family vacationing there at beach.
P(B∩M) [the red/blue intersecting intersection of two circles] = 0.2 is the possibility of a family taking a vacation in both locations.
Using the property of independent event: Two events are considered independent if the incidence of one does not affect the likelihood of occurrence of the other.
As, occurrence of family visiting the beach will also visit the mountains is an independent event. Thus,
The formula for the independent event is;
P(B | M) = P(B∩M)/P(B)
P(B | M) = 0.2/0.6
P(B | M) = 0.33
Therefore, the probability of the occurrence that family visiting the beach will also visit the mountains is 0.33.
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