In the figure below, a surveyor put stakes at the lettered points. He used string to determine lengths of line segments and a transit to check that the angles at D and B were both right angles.
If CD = 3, CE = 5, DE = 4 and DB = 18, and:
AB/DB=BC/CD
AB =
units.
Answers
The length of segment AB is given as follows:
AB = 20 units.
What are similar triangles?Similar triangles are triangles that share these two features given as follows:
Congruent angle measures.Proportional side lengths.The similar triangles for this problem are given as follows:
ABD and CDE.
Hence the proportional relationship that can be established between the side lengths is given as follows:
AB/DE = BC/CD = AC/CE.
The side lengths are given as follows:
CD = 3, CE = 5, DE = 4, DB = 18.
As CD = 3 and DB = 18, using the segment addition postulate, we have that:
BC = BD - CB
BC = 18 - 3
BC = 15 units.
Hence the length AB is obtained as follows:
AB/4 = 15/3
AB/4 = 5
Applying cross multiplication, we have that:
AB = 4 x 5
AB = 20 units.
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Related Questions
what is schur polynomial in numerical analysis.
Answers
Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials.
What is Schur polynomial?Issai Schur gave the name Schur to a class of symmetric polynomials in n variables that generalize both the complete homogeneous symmetric polynomials and the elementary symmetric polynomials. They are the features of polynomial irreducible representations of the generic linear groups in representation theory. For the space of all symmetric polynomials, the Schur polynomials provide a linear basis. Any Schur polynomial product can be expressed as a linear combination of Schur polynomials with non-negative integral coefficients; these coefficients' values are supplied combinatorially by the Littlewood-Richardson rule. More generally, skew Schur polynomials are connected to pairs of partitions and share Schur polynomials' characteristics.To learn more about Schur polynomial refer to:
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Use the graphs of f and g to graph h(x)=(f+g)(x). (Graph segments with closed endpoints).
Answers
The required graph of the function of h(x) is shown, where h(x) = |x| + |x + 2|.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
In the graph, functions f and g are absolute functions,
f = |x|
g = |x + 2|
So,
h(x) = f + g
Now substitue the functions,
h(x) = |x| + |x + 2|
Thus, the required graph of the function of h(x) is shown.
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Round 0.295833333 to the nearest hundredth
Answers
Answer:
The answer is 0.30.
I wish you luck in your assignments.
Answer:
0.3
Step-by-step explanation:
Since 5 rounds up, that would cause the 0.09 to become a 0.1, so it would be 0.3
Natalie is driving on the freeway. She just passed mile marker 290. The markers have
been increasing as she drives by them. The fastest Cameron will drive is 80 miles per
hour. However, there is a bit of traffic that might slow her down, but she doesn't know
exactly how much it will slow her down.
a. Write an inequality to represent Natalie's position relative to the mile markers
three hours from now.
b. Rewrite this inequality to reveal Natalie's speed.
Need help with this ASAP
Answers
On solving the provided question we can say that - the inequality equation which will be formed is 290x [tex]\geq[/tex] -23 + y
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.
here,
we have 290x
so the inequality equation which will be formed is
-y + 290x [tex]\geq[/tex] -23
290x [tex]\geq[/tex] -23 + y
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What value for the
constant, h, in the equation
shown below will result in an infinite number of
solutions?
6t + 18 = h(3x + 9)
Answers
Therefore , As a result, h = 2 is the answer to the equation in the given question.
Explain equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra is the fundamental foundation of mathematics.
Here,
The formula is as follows: 6x + 18 = h(3x + 9)
To ensure that the expression has an unlimited number of answers, h's value must be determined.
Take the expression now and continue solving it.
=> 6x + 18 = h(3x + 9)
=>3hx + 9h= 6x +8
The expression will have an endless number of solutions if the coefficients of the left-hand side and the right-hand side are equal.
Therefore, 3h = 6 and h = 2
As a result, h = 2 is the answer to the equation in the given question.
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A 969 acre wildlife preserve has 19 cheetahs. About how many acres does each cheetah have to itself, if each cheetah roams the same number of acres?
Answers
By taking a quotient, we will see that each cheetah has around 51 acres for itself.
About how many acres does each cheetah have to itself?If we assume that the cheetahs are evenly distributed along the whole area, then the number of acres that each cheetah has to itself is equal to the quotient between the total area, and the total number of cheetahs.
There are 969 acres and 19 cheetahs, then the quotient is:
969/19 = 51
That is the number of acres that each cheetah has for itself.
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please help fast for my math project and its due today !!!!!!! fasttttb pleaseeee
Answers
1) Note that in the problem above, the complete table is given as:
Team Number: 1 2 3 4 5
Best Jump (ft) 20.6 21.5 20.9 19.4 20.2
2) If Best Jump is denoted as y and Team number as x then, Best Jump is the Range while Team Number is the Domain.
3) For each element of the domain, there is a corresponding element of the range. So this relation is a function.
Why are the Domain and Range Important?Domain and range are crucial characteristics that aid in the definition of a relationship. The domain is a collection of input values.
The independent variable represents these values, which are graphed on the axis of a coordinate graph. A function's range is its collection of output values.
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the cost,y, of red grapefruit can be represented by the equation y=2x, where x is the number of pounds of red grapefruit. the graph shows the cost of pink grapefruit. which type of grapefriut costs more per pound?
Answers
We can conclude that, if --
m{pink} > 2 : The cost (y) of red grapefruit is less than cost (y) of pink grapefruit.m{pink} < 2 : The cost (y) of red grapefruit is greater than cost (y) of pink grapefruit.What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that the cost (y) of red grapefruit can be represented by the equation y = 2x, where {x} is the number of pounds of red grapefruit. Also the graph shows the cost of pink grapefruit.
The cost (y) of red grapefruit can be represented by the equation y = 2x. So, we can write that the cost per unit pound of red grape is $2. The graph of the pink grapefruit is not given, but its slope {m} will tell us its costs per pound.
Now, if -
m > 2 : The cost (y) of red grapefruit is less than cost (y) of pink grapefruit.m < 2 : The cost (y) of red grapefruit is greater than cost (y) of pink grapefruit.Therefore, we can conclude that, if -
m{pink} > 2 : The cost (y) of red grapefruit is less than cost (y) of pink grapefruit.m{pink} < 2 : The cost (y) of red grapefruit is greater than cost (y) of pink grapefruit.To solve more questions on straight lines, visit the link below -
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Find the missing numbers 46 62 87 123 ---- 236
Answers
Answer:
The missing numbers are 74, 105, and 178.
Ann 's car can go 132 miles on 4 gallons of gas. During a drive last weekend, Ann used 5 gallons of gas. How far did she drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ann drove last weekend instead of how much gas she used.
Answers
Answer:
Ann traveled 165 miles on 5 gallons of gas
Step-by-step explanation:
First we must know how many miles are in a gallon (in this situation). Last weekend Ann drove 132 miles with 4 gallons of gas, we can divide to find out how many miles she drove on 1 gallon. 132/4 = 33. This means Ann drove 33 miles on 1 gallon of gas. To get your answer, simply multiply 5 and 33. 5 times 33 = 165.
if molly needs to cross a river 16 feet wide how long does she have to walk
Answers
Molly has to walk for 16/x minutes where x is the speed of molly.
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here molly needs to cross a river 16 feet then let her speed be x and t be the time taken to cross the river
Then we have x=16/t
t=16/x
Hence, Molly has to walk for 16/x minutes where x is the speed of molly.
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Help desperatlu6(5x-3)
Answers
[tex]6(5x-3)[/tex]
Distribute:
[tex](6)(5x)+(6)(-3)[/tex]
[tex]=\fbox{30x - 18}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6(5x - 3)}[/tex]
[tex]\text{DISTRIBUTE 6 WITHIN the PARENTHESES}[/tex]
[tex]\mathsf{= 6(5x) + 6(-3)}[/tex]
[tex]\mathsf{= 30x - 18}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\mathsf{30x - 18}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
If g(x) = x³ - 2x, find the value of g(2+h)-g(2)dividebyh answer is h square plus six h plus ten
Answers
Answer: To find the value of g(2+h)-g(2) divided by h, we can use the definition of the derivative. The derivative of a function at a point is a measure of the slope of the function at that point, and it can be calculated by taking the limit of the difference quotient as h approaches 0.
The difference quotient is defined as:
[g(2+h) - g(2)] / h
So, to find the derivative of g at x=2, we can substitute the value of x in the function g(x) and take the limit as h approaches 0:
lim h→0 [g(2+h) - g(2)] / h
Substituting the value of x in the function g(x), we get:
lim h→0 [(2+h)³ - 2(2+h) - (2² - 2*2)] / h
This simplifies to:
lim h→0 [8+6h+h²-2h - 4] / h
Which simplifies to:
lim h→0 [h²+6h+4] / h
And, finally:
lim h→0 [h(h+6)] / h
The limit of a quotient is equal to the quotient of the limits, as long as the limit of the denominator is not 0. In this case, the limit of the denominator (h) is 0, but the limit of the numerator (h(h+6)) is not. Therefore, we can safely take the limit:
h+6
So, the derivative of g at x=2 is h+6. When h=0, the derivative is equal to the function's value at that point, so the value of g(2) is 6.
Therefore, the value of g(2+h)-g(2) divided by h is:
(h+6) - 6 / h
Which simplifies to:
h / h
Which is equal to:
1
So, the final answer is 1.
Step-by-step explanation:
A store is having a sale on almonds and jelly beans. For 5 pounds of almonds and 2 pounds of jelly beans, the total cost is $12. For 3 pounds of almonds and 8 pounds of jelly beans, the total cost is $31. Find the cost for each pound of almonds and each pound of jelly beans.
Answers
To find the cost of each pound of almonds, we need to find the difference in the cost of the almonds between the two purchases and divide it by the difference in the number of pounds of almonds. In this case, the difference in the cost of the almonds is $31 - $12 = $19 and the difference in the number of pounds of almonds is 3 - 5 = -2 pounds. Dividing the difference in the cost by the difference in the number of pounds gives us $19/-2 = $-9.50 per pound. This means that the cost of each pound of almonds is $-9.50.
To find the cost of each pound of jelly beans, we can use a similar process. In this case, the difference in the cost of the jelly beans is $31 - $12 = $19 and the difference in the number of pounds of jelly beans is 8 - 2 = 6 pounds. Dividing the difference in the cost by the difference in the number of pounds gives us $19/6 = $3.17 per pound. This means that the cost of each pound of jelly beans is $3.17.
TEXT ANSWER
How can you use the unit price to find the cost of 10
pounds of tomatoes? Please help
Answers
To find the cost of 10 pounds of tomatoes, multiply 10 by the unit cost of tomatoes.
What is the unit cost?
The cost a business incurs to create, store, and sell one unit of a specific product is known as the unit cost. All fixed and variable production expenses are included in unit costs. Cost units are a way to measure the quantity of a good or service.
Unitary method: The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
The unitary method is used to find the unit cost of an object.
To find the cost of a unit object, multiply a by unit cost.
Given that, the unit cost of a unit pound of tomatoes.
The cost of 10 pounds of tomatoes is 10 × unit price of tomatoes.
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What is the solution of the inequality shown
below?
a+5>-7
Answers
The required solution for the inequality a + 5 > -7 is (-12, ∞).
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
a + 5 > -7
To find the solution for the inequality,
Simplify the inequality,
a + 5 > - 7
a > - 7 - 5
a > -12
The value of a is greater than -12, implies that,
The solution for the value of the given inequality is (-12, ∞).
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I eh need the Answer to this please i am timed!!
Answers
Answer:
pro tip: crop your screen before you post it....
I think it's B
I did this 2 years ago in middle school
"-12<-3x-15" less than or equal to 36
Answers
Answer:
-17 ≤ x < 1
Step-by-step explanation:
-12 < -3x - 15 ≤ 36
Add 15 to all 3 "sides."
-12 + 15 < -3x - 15 + 15 ≤ 36 + 15
3 < -3x ≤ 51
Divide all 3 "sides" by -3. Remember that when you multiply or divide an inequality by a negative number, you much change the direction of the inequality sign.
3/(-3) > -3x/(-3) ≥ 51/(-3)
-1 > x ≥ -17
Rewrite in standard order.
-17 ≤ x < 1
What is the value of x? Show your work in arriving at your answer.
Answers
The value of x is 18.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
First, both angles shown are equal to each other.
5x + 5 = 95
Next, the opposite side of the equation to isolate x value (5x).
5x + 5 (-5) = 95 (-5)
5x = 90
Finally, we need to divide both sides of the equation by 5.
5x / 5 = 90 / 5
x = 18
The final answer: x = 18
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The midpoint of JK is point L at (–1, 8). One endpoint is J(4, –15). Which equations can be solved to determine the coordinates of the other endpoint, K? Select two options. = –1 = 4 –15 + y1 =16 = y1
Answers
Using the formula of midpoint of a line, the coordinate of the endpoint k is (-6, 31)
What is Midpoint of a LineThe midpoint of a line is the point that is halfway between the two end points of the line. It can be found by taking the average (mean) of the x-values and the average (mean) of the y-values of the two endpoints.
The formula of midpoint of a line is given as;
M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2
Since we have the midpoint and one endpoint, we can use the coordinate to find the missing coordinate.
The x - coordinate is calculated as;
-1 = (4 + x₁) / 2
-2 = 4 + x₁
x₁ = -2 - 4
x₁ = -6
The y - coordinates is calculated as;
8 = (-15 + y₁) / 2
16 = -15 + y₁
y₁ = 16 + 15
y₁ = 31
The coordinates of k is (-6, 31)
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The population of North Carolina was approximately 9.5 million in 2010. The population has increased by about 1.3% per year. If the population continues to grow at this rate, in what year will North Carolina’s population reach 12 million?
Answers
The population of North Carolina will reach 12 million in the year 2028.
What is Population Growth?Population growth is defined as the increase in the number of people which is calculated using population growth rate.
Given that,
Population in 2010 = 9.5 million
Population is increasing to 1.3% per year.
Annual growth rate = 1.3% = 1.3/100 = 0.013
We have the population growth formula,
P = P₀ e^(r t)
Here, P₀ = 9.5 million = 9,500,000
and P = 12 million = 12,000,000
r = 0.013
We have to find t.
12,000,000 = 9,500,000 e^(0.013t)
120 / 95 = e^(0.013t)
Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,
㏑(12/9.5) = 0.013t × ㏑e
[㏑(12/9.5) ÷ 0.013] = t [since ln e = 1]
t = 17.97 ≈ 18 years
The year is 2010 + 18 = 2028
Hence in the year 2028, the population will be 12 million.
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Which segment is parallel
Justify the answer with a converse theorem
Answers
Answer:
Ah and mc are parallel segments
I put “H?” because the last point is not visible, but here’s a picture of the parallel segments. The orange marking highlights the parallel segments.
In 1965, the population of a country was 192 thousand to 3 significant figures.
In 2020, the population of that country was 366 thousand to 3 significant figures.
Work out the percentage increase in population. Give your answer correct to 2 significant figures.
Answers
The percent change in population is 90.65%.
What is percent?A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".
Given population of country in 1965 = 192 thousand = 1,92,000.
population of country in 2020 = 366 thousand = 3,66,000
the increase in population is = 366000 - 192000 = 1,74,000
the percentage increase = (100)(increase in population)/(1965 population)
the percentage increase = (100) (174000)/(192000)
the percentage increase = 90.625%
Hence the percent increase is 90.62%.
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evaluate 5² + 7 - 3 +4
Answers
The value of the numerical expression 5² + 7 - 3 + 4 will be 33.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 5² + 7 - 3 + 4
Simplify the expression, then we have
⇒ 5² + 7 - 3 + 4
⇒ 25 + 7 - 3 + 4
⇒ 36 - 3
⇒ 33
The value of the numerical expression 5² + 7 - 3 + 4 will be 33.
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What are terms and common rations ? Can someone explain to me how to solve
Answers
For the arithmetic sequence 4 - 2(n - 1), we have that:
The first term is 4.The second term is 2.The third term is zero.The fourth term is -2.The fifth term is -4.The common difference is -2.For the geometric sequence 6 x 3^(n - 1), we have that:
The first term is 6.The second term is 18.The third term is 54.The fourth term is 162.The fifth term is 486.The common ratio is 3.How to model the arithmetic sequence?An arithmetic sequence is a sequence of numbers in which there is a common difference of the numbers, that is, the subtraction between consecutive terms of the sequence is always constant.
The nth term of an arithmetic sequence is given by the equation presented as follows:
[tex]a_n = a_1 + d(n - 1)[/tex]
In which:
[tex]a_1[/tex] is the first term.d is the common difference.The sequence in this problem is defined as follows:
4 - 2(n - 1)
Which has first term 4 and common difference -2, hence the terms are:
4, 2, 0, -2, -4, -6 and so on...
What is a geometric sequence?A geometric sequence is a sequence of numbers in which there is a common ratio of the numbers, that is, the quotient between consecutive terms of the sequence is always constant.
The nth term of a geometric sequence is given by the equation presented as follows:
[tex]a_n = a_1 \times q^{n - 1}[/tex]
In which:
[tex]a_1[/tex] is the first term.q is the common ratio.The sequence for this problem is given as follows:
6 x 3^(n - 1)
Which has first term of 6 and common ratio of 3, hence the terms are given as follows:
6, 18, 54, and so on...
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Please solve the ques. below
Answers
The velocity of the train is given as follows:
900 m / min.
How to obtain the velocity of the train?To obtain the velocity of the train, we must understand the relation between velocity, distance and time, which is given as follows:
v = d/t.
In which the parameters are given as follows:
v is the velocity.d is the distance.t is the time.The train took a difference of 200 m in 15 seconds = 0.25 minutes, hence the difference in velocities is given as follows:
200/0.25 = 800 m / min.
(the difference in velocity is the distance covered divided by the time).
As Uncle Tony is walking at a rate of 100 m / min, the velocity of the train is calculated as follows:
800 + 100 = 900 m / min.
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3
Use the drawing tool(s) to form the correct answer on the provided graph.
The function f(x) is shown on the provided graph.
Graph the result of the following transformation on f(x).
Drawing Tools
Select
Line
Click on a tool to begin drawing
-10
-8
f(z) + 6
-6
4
-2
10-
8-
6
Delete
Undo
Reset
10 i need help with this
Answers
Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.
what is transformation ?Four various modifications that can be made to a point, line, or geometric object are referred to as transformations collectively. You must be able to identify which changes have been made and that each alteration has been made. The following guidelines for function translation and transformation: The function is shifted up by b units by F (x) + b. F (x) b causes the function to move downward. The expression f (x + b) causes the function to be moved left b units. Translation, reflection, rotation, and dilation are the four different types of transformations. Transform, reflect, or rotate the geometric shapes that are displayed on a coordinate plane. The transformation, often known as f: X X, is the name given to a function, f, that maps to itself.
given
-1 on the left x-axis and 4 on the right y-axis
Start at -2 on the y-axis, move up the y-axis six times, and you should arrive at 4. However, you must identify the first line in order to complete the puzzle.
Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.
Since you should be at 4, apply the formula rise/run 4/1 to ascend 6 on the y-axis.
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42. Let f be a function from the set A to the set B. Let S and T be subsets of A. Show that
a) f(S ∪ T)=f(S) ∪ f(T).
b) f(S ∩ T) ⊆ f(S) ∩ f(T).
Answers
Start with any random elements of sets and compute LHS and RHS individually.
a) The proof of f(S ∪ T) = f(S) ∪ f(T) is explained below.
b) The proof of f(S ∩ T) ⊆ f(S) ∩ f(T) is expliane dbelow.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Let, The set A = {1, 2, 3, 4, 5} and B = {2, 4, 5}.
Therefore, S = {1, 2, 3} and T = {1, 4, 5}.
Now, f(S ∪ T) = {1, 2, 3, 4, 5} and f(S) ∪ f(T) = {1, 2, 3} ∪ {1, 4, 5}.
Hence, f(S ∪ T)=f(S) ∪ f(T).
Now, f(S ∩ T) = {1} and f(S) ∩ f(T) = {1, 2, 3} ∩ {1, 4, 5} = {1}.
Therefore, f(S ∩ T) ⊆ f(S) ∩ f(T). (⊆ implies improper subset)
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1
Multiple Choice Question
What type of number is 105?
Choose all that apply
Whole number
Integer
Rational
Irrational
Answers
Analyzing the options given in the question, the options that satisfy for the number 105 are: Integer, Rational, Whole number.
What are whole numbers?All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions.
What are rational numbers?A rational number is a number which is in the form of p/q where p and q are both integers and q is not equal to zero.
The number 105 is , Whole number since it falls between all the numbers between 0 to positive infinity. Similarly, the number is an Integer since it does not contain any fractions or decimals. And, the number 105 is rational number since it can be expressed in the form of 105/1.
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find x
y=\frac{1}{4} x+3
Answers
Work Shown:
[tex]\text{y} = \frac{1}{4}\text{x}+3\\\\\text{y}-3 = \frac{1}{4}\text{x}\\\\\frac{1}{4}\text{x}=\text{y}-3\\\\\text{x}=4(\text{y}-3)\\\\\text{x}=4\text{y}-12\\\\[/tex]