We must first plot the given linear equation before we can draw the graph for it. Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.
How do you deduce roots?link the points that lie on it to form a straight line.
Y = 2x - 1 is the first equation.
Calculate the corresponding values of y by substituting various values of x into the equation.
X Y = 2x-1 point (x, y)
0 -1 (0, -1)
2 3 (2, 3)
4 7 (4, 7)
-1 -3 (-1, -3)
-3 -7 (-3, -7)
On the graph paper, place these points and draw a straight line connecting them.
Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.
In order to determine the critical point, we will set the first derivative of the function to zero and solve for x. We may determine whether this point will be a maximum or minimum by taking the second derivative, or f"(x). It will be a minimal value if the second derivative is positive.
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3/4 + 1/3 what is it
Answer:
[tex] \frac{3}{4} + \frac{1}{3} \\ \frac{ \: \: 9 \: \: + \: \: 4 \: \: }{12} \\ \frac{13}{12} [/tex]
a college has 10 time slots for its courses, and blithely assigns courses to completely random time slots, independently. the college offers exactly 3 statistics courses. what is the probability that 2 or more of the statistics courses are in the same time slot?
Probability that 2 or more of the statistics courses are in same slot is 0.28.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
probability that 2 or more of the statistics courses are in same slot
=1-P(all 3 are in different slots)
=1-P(select 3 from 10 slots and arrange them)
=1-(10*9*8)/10^3
=0.28
Therefore, probability that 2 or more of the statistics courses are in same slot is 0.28.
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The temperature of one furnace is 1,200°C and cools at a rate of 3.5°C per minute. The temperature of another furnace is 900°C and is heated at a rate of 0.5°C per minute. After how many minutes will the furnaces be the same temperature?
Answer:
525 minutes
Step-by-step explanation:
Let us find the temperature of each furnace after 't' minutes.
Furnace1:
Temperature in furnace1 is reducing at rate of 3.5°C per minute.
Rate of cooling after t minute = 3.5*t = 3.5t
We have to subtract 3.5t from 1200°C as it is cooling.
Temperature of furnace1 after 't' minutes = 1200 - 3.5t
Furance2:
Temperature in furnace2 is increasing at rate of 0.5°C per minute.
Rate of heating after t minute = 0.5*t = 0.5t
We have to add 3.5t from 900°C as it is getting heated.
Temperature of furnace1 after 't' minutes = 900 +0.5t
After some minutes, both furnace reach the same temperature.
900 + 0.5t = 1200 - 3.5t
900 + 0.5t + 3.5t = 1200
4t = 1200 + 900
4t = 2100
t = 2100 ÷ 4
[tex]\boxed{t = 525 \ minutes}[/tex]
Carver's Auto Custom has two potential retail spaces to choose from.
Warehouse Space A: Includes 8000 sq. Ft. Of showroom and workshop space. It rents for. 85 cents
ar safl per month and an additional 25. Cents per sq. Ft, per month for operations expenses. One
half of this warehouse space will be used to stock paint cans and rims.
According to the area value, the amount required to be paid for the showroom is $2000.85
The term area in math is known as the region bounded by the shape of an object or it is the space covered by the figure or any two-dimensional geometric shape.
Here we have know that Warehouse Space A Includes 8000 sq. Ft. Of showroom and workshop space and it rents for. 85 cents per month and an additional 25. Cents per sq. Ft, per month for operations expenses.
While we looking into the question, we know that the following are known,
Area = 8000 square feet.
Rent = 85 cents.
Additional expenses = 25 cent per square feet.
Then the total expense is calculated as,
=> 85 + (8000 x 25)
=> 200085 cents.
When we convert into dollars, then we get,
=> One dollar = 100 cents.
Then the resulting value is
=> $2000.85
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Tim went 8 mile eat and 15 mile north. Jan went 5 mile wet and 12 mile north. How far apart are they? Round your anwer to the nearet tenth. How do we get the anwer to thi
The distance between Tim and Jan rounded to the nearest tenth is 21.4 miles.
The formula used in this problem is the Pythagorean Theorem. The Pythagorean Theorem states that the square of the hypotenuse (the longest side of a right triangle) is equal to the sum of the squares of the other two sides. This can be shown as A2 + B2 = C2.
In this problem, we need to find the hypotenuse, which is the distance between Tim and Jan. To do this, we will use the Pythagorean Theorem. First, we need to find the sum of the squares of the distances traveled by Tim and Jan.
For Tim, the square of 8 miles plus the square of 15 miles equals 289. For Jan, the square of 5 miles plus the square of 12 miles equals 169. Adding these together gives a total of 458. We then take the square root of 458 and get 21.38. This is the answer we are looking for, the distance between Tim and Jan rounded to the nearest tenth is 21.4 miles.
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HELP!!!!!!
50 POINTS
Answer:
see explanation
Step-by-step explanation:
1
20% of 35
= [tex]\frac{20}{100}[/tex] × 35
= 0.2 × 35
= 7
(2)
60% of 70
= [tex]\frac{60}{100}[/tex] × 70
= 0.6 × 70
= 42
(3)
45% of 80
= [tex]\frac{45}{100}[/tex] × 80
= 0.45 × 80
= 36
Answer:
busy work lol. its = not smart
Step-by-step explanation:
Given the scatter plot, choose the function that best fits the data.
f(x) = 2^x
f(x) = 2x
f(x) = −2x
f(x) = 2x^2
The given scatter plot depicts the exponential function. Therefore, option 1 f(x) = 2ˣ is the correct one.
A scatter plot is a particular kind of graphic diagram that uses Cartesian coordinates to show the values of two variables for a collection of data.
We write y as the function of x as y=f(x). Here, f is considered the name of the function and x is the value of the function. To check which function depicts the given scatter plot, we have to substitute the values for x and find the function. Then, plot the graph.
By doing we get, the plot for f(x) = 2ˣ is equivalent to the given scatter plot. Because this graph depicts the exponential function where the graph passes through the point (0,1). Therefore, option 1 correctly depicts the given plot. Option 2 depicts the identity function and 4 depicts squaring or quadratic function.
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why use the sum function with a range of cells when adding the values together accomplishes the same thing?
It saves time, doesn't need to be changed if a row or column is added to the range, and adjusts the range when the function is copied to another cell.
Based on the values in another column, we'll discover how to add up a column of numerical data. We are attempting, for instance, to assess product sales based on the typical customer rating. Thus, each of our products has an average rating of 9.8, 7.2, 6.1, and so on because customers score our products on a scale of 1 to 10. The sales totals for goods with ratings of 9 to 10, 7 to 8, and so forth should be calculated.
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A 5. 5kg bowling ball initially at rest is dropped from the top of a 12 m building. It hits the ground 1. 75s later. Find the net external force on the falling ball?
The net external force acting on the freely falling ball is 43.12 N.
We are provided with the following information:
Mass of bowling ball (m) = 5.5kg
Distance travelled by the ball (h) = 12m
Time taken by the ball = 1.75 s
To calculate the net force acting on the ball, we first need to calculate the acceleration experienced by the ball under free fall.
We can determine the acceleration using the formula,
d= ut + (1/2)at^2
since, the ball was initially at rest, u=0.
Thus, formula becomes,
d= (1/2)at^2.
Therefore, a= 2d/t^2
=> a= 2*12/(1.75)^2
=> a=24/ 3.0625
=> a= 7.84 m/s^2
Now, according to Newton's 2nd law of Motion,
[tex]F_{net} = mass * acceleration[/tex]
[tex]F_{net}[/tex] = 5.5 * 7.84 N = 43.12 N
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−9(5 − 6x)
answers:
A 45 − 54x45 − 54x
B −45 − 54x−45 − 54x
C 45 + 54x45 + 54x
D −45 + 54x
Answer:
[D] -45 + 54x
Step-by-step explanation:
Base on the given we can use the distributive property to solve this:
Distributive property ⇒ Multiply outside numbers with each term inside the parenthesis.
-9 (5 - 6 x ) → {-9 × 5 = -45 } {-9 × -6x = 54x}
Now let's put it together;
-45 + 54x
Hence, [D] -45 + 54x is the correct answer.
RevyBreeze
Consider the equations f(x)=1/x and g(x) = (x-1)^2-1. To the nearest tenth, what is the solution of f(x)=g(x)?
The solution of equation f(x)=g(x) is 2.
How do equations work?a formula that illustrates the relationship between the two expressions on either side of a sign. Usually, it has one variable and an equal sign. similar to 2. 2x - 4 = 2. The equals sign (=) in equations indicates that two expressions are equal. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.
The "left hand side" and "right hand side" of the equation refer to the expressions on each side of the equals sign. The right side of an equation is frequently thought of as zero.
Given : f(x)=g(x)
1/x = (x-1)^2-1
1 = x (x-1)² - 1
x (x-1)² = 2
x ( x² + 1 - 2x ) = 2
x³ + x - 2x² = 2
x³ + x - 2x² - 2 = 0
x³ - 2x² + x - 2= 0
x²(x-2) + 1(x-2) = 0
(x² +1) + (x-2) = 0
So, x = 2 .
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A group of randomly selected Gamin Middle School athletes were asked to pick their favourite sport. Number of athletes Sport Sport Based on the data, what is the most reasonable estimate for the number of Gamin Middle School athletes whose favourite sport is hockey?
92 is the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey.
A reasonable estimate does not exceed the original numbers in a problem.
Reasonableness can be defined as checking to verify that the result of the solution or the calculation of the problem is correct or not, either estimating or plugging in your result to check it
The most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey.
Estimate= population size x sample proportion.
population size=114
sample proportion=10/45
Estimate=114*10/45
Estimate=92.
Therefore, 92 is the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey.
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Your cousin is building a new house. The layout of the first floor is shown in the diagram above. Using the
diagram and knowledge of polynomials find the following:
1. Write a polynomial that represents the length of the north side of the house. Then simplify the
expression.
2. Write a polynomial expression that represents the area of the kitchen. Then multiply to put the
polynomial in standard form.
3. Write a polynomial expression that represents the area of the bedroom. Then multiply to put the
polynomial in standard form.
4. Find the dimensions of the bathroom in terms of x. (Hint the west and east side of the house
should be equal.)
The polynomial for the north side of the house will be 2x^2+9x-32.
What are polynomials?
Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.
Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.
Now,
As the north side will be the sum of 5x-4,x^2-23 and 4x-5
so the polynomial for north will also be the sum of 5x-4,x^2-23 and 4x-5.
Hence,
Polynomial for north side= 5x-4 + x^2-23 + 4x-5
Polynomial for north side =2x^2+9x-32
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Which number is less than 5/8 but greater than 1/9?
A number that is less than 5 / 8 but is greater than 1 / 9 is A. 0. 5.
How to find the number ?To find the number that is less than 5 / 8 but greater than 1 / 9, first convert both fractions to decimals.
5 / 8 in decimals is:
= 5 / 8
= 0. 625
1 / 9 in decimals is:
= 1 / 9
= 0. 111
The number from the given options that is less than 5/8 but greater than 1/9 is therefore 0. 5 as it is less than 5 / 8 but more than 1 / 9.
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The options for the question include:
0.50.80.90.05substitute 6x-5y=-1 and 6x+4y=-10
Answer:
x=-1 y=-1
Step-by-step explanation:
i am lazy to type
Answer:{x = -1}{y = -1}
Step-by-step explanation:
subtract the two equations
{6x - 5y = -1 ^
{6x + 4y = -10 ^
determine the sign
6x - 5y - (6x +4y) = -1 - (-10) ^
simplify
6x - 5y - 6x - 4y = -1 + 10 ^
substitute
y = -1 ^
solve the equation
6x + 4 x (-1) = -10 ^
write the solution
x = -1 ^
Please help like ASAP find the value of X please ASAP
The value of x is 15 and the angles in the pentagon are 105,49,90,33,83
What is interior angles in a pentagon ?
The interior angles in a pentagon are the angles which are inside the pentagon and sum of the interior angles in a pentagon is 540 degrees.
Given ,
From the figure we can say that it is pentagon.
And the sum of exterior angles in a pentagon is always 360 degrees.
SO,
7x+49+6x+33+83 = 360
13x + 165 = 360
13x = 360 - 165
13x = 195
x = 195 / 13
x = 15
So, the angles could be 7x = 7*15 = 105 and 6x = 6*15 = 90
Therefore, The value of x is 15 and the angles in the pentagon are 105,49,90,33,83 .
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Prove that circle A with center (1, 1) and radius 4 is similar to circle B with center (–4, –2) and radius 3
Since they are not the same, they are not the exact same circles. In other words they are similar.
Since the center point does not affect the size of the circle.
Now, According to the question:
Figures can be proven similar if one, or more, similarity transformations
reflections, translations, rotations, dilations can be found that map one
figure onto another.
To prove all circles are similar, a translation and a scale factor from a
dilation will be found to map one circle onto another
Lets solve the problem
Circle A has center (1 , 1) and radius 4
The standard form of the equation of the circle is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex] , where (h , k) are the coordinates the center
and r is the radius
Equation circle A is [tex](x -1)^2 + (y - 1)^2 = (4)^2[/tex]
Equation circle A is : [tex](x -1)^2 + (y - 1)^2 = 16[/tex]
[tex]x^{2} +1-2x+y^2+1-2y=16\\\\x^2 +y^2-2x-2y+2=16\\\\x^2 +y^2-2x-2y-14=0\\\\x^2+y^2= 14+2x+2y[/tex]
Circle B has center (-4 , -2) and radius 3
Equation circle B is [tex](x - (-4))^2 + (y - (-2))^2 = (3)^2[/tex]
Equation circle B is [tex](x +4)^2 + (y +2)^2 = 9[/tex]
[tex]x^2+16+8x+y^2+4+4y=9\\\\x^{2} +y^2+20+8x+4y=9\\\\x^2+y^2+8x+4y+11=0[/tex]
By comparing between the equations of circle A and circle B
As you can see, if we try to equate the [tex](x^2 + y^2)'s[/tex], the values of them are not the same. Since they are not the same, they are not the exact same circles. In other words they are similar.
You can also compare the radii as well, since the center point does not affect the size of the circle.
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[tex]\frac{1}{4}b[/tex]+ [tex]\frac{1}{4}[/tex]=[tex]-\frac{1}{2}[/tex]
Solve for bb. Express your answer as a proper or improper fraction in simplest terms.
The fraction 1/4b + 1/4 = -1/2 is simplified to b = -12/4
What is a fraction?
A fraction can be defined as the part of a whole variable, or number.
The types of fractions are;
Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
1/4b + 1/4 = -1/2
Now, collect iike terms
1/4b = -1/2 - 1/4
find the lowest common denominator
1/4b = -2 -1 /4
Add the numerators
1/4b = -3/4
Now, divide both sides by the coefficient of b
b = -3/4 × 4/1
Multiply the values
b =-12/4
Hence, the value is - 12/4
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Select one or more expressions that together represent all solutions to the equation. Your answer should be in degrees.
Assume
�
nn is any integer.
7
cos
(
9
�
)
−
1
=
1
7cos(9x)−1=17, cosine, left parenthesis, 9, x, right parenthesis, minus, 1, equals, 1
The trigonometric equation 7cos(9x) - 1 = 17 has an undefined solution.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
7cos(9x) - 1 = 17
Isolating the cosine, we have that:
7cos(9x) = 18
cos(9x) = 18/7
Now we isolate x applying the arc cosine, which is the inverse of the cosine, as follows:
9x = arccos(18/7)
9x = undefined.
The solution is undefined because the arccosine only exists for values between -1 and 1, as the cosine of an angle is always going to assume a value between -1 and 1.
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100 POINTS! How many roots does the polynomial equation have?
0=x^3(x+3)(x−1)^2
Answer: There are none
Step-by-step explanation:
-(-8.2w+10) Im confused about this problem can you help me
Reason:
The negative out front is distributed to each term inside the parenthesis.
This will flip the sign of each term.
The -8.2 flips to +8.2w which is the same as 8.2wThe +10 flips to -10For more information, search out "distributive property".
You spent $250 on your credit card. It has been 5 years and you have a 3.75% interest rate. How much interest do you owe?
Answer:
1050$
Step-by-step explanation:
A persons blood has a pH of 7.371 and a carbonic acid concentration of 1.5, Approximate the concentration of bicarbonate in the persons blood.
Answer: The pH of blood is a measure of its acidity or basicity and is related to the concentration of hydrogen ions (H+) in the blood. The pH of 7.371 indicates that the blood is slightly basic. Carbonic acid (H2CO3) is a weak acid that dissociates into bicarbonate (HCO3-) and hydrogen ions (H+) in water. The carbonic acid concentration of 1.5 indicates the concentration of H2CO3 in the blood.
The concentration of bicarbonate (HCO3-) in the blood can be approximated by using the relationship between the pH, carbonic acid concentration and the bicarbonate concentration. The Henderson-Hasselbalch equation, which relates the pH and the pK of a buffer, to the ratio of the buffer's conjugate base to its acid form is:
pH = pK + log [HCO3-]/[H2CO3]
The pK of carbonic acid is 6.1 and the concentration of H2CO3 is given as 1.5.
Plugging these values into the Henderson-Hasselbalch equation,
7.371 = 6.1 + log [HCO3-]/1.5
Solving for [HCO3-],
[HCO3-] ≈ 25.8 mM
The approximate concentration of bicarbonate (HCO3-) in the person's blood is 25.8 mM.
Please note that this is an approximation, the actual value may vary depending on the person's health condition.
Step-by-step explanation:
A number of major tructural repair completed at the beginning of the current fical year at a cot of $1,000,000 are expected to extend the life of a building 10 year beyond the original etimate. The original cot of the building wa $6,552,000, and it ha been depreciated by the traight-line method for 25 year. Etimated reidual value i negligible and ha been ignored. The related accumulated depreciation account after the depreciation adjutment at the end of the preceding fical year i $4,550,000.
The total cot of the building (original cot of $6,552,000 le the Accumulated Depreciation of $4,550,000 pre-adjutment) divided by the new life of 35 year equal the annual depreciation amount of $188,514.29. The econd journal entry would therefore debit Building for $5,552,000 ($188,514.29 x 10 year) and credit Accumulated Depreciation for the same amount.
The journal entry to record the tructural repair and the related adjutment i:
Debit: Accumulated Depreciation $1,000,000
Credit: Building $1,000,000
Debit: Building $5,552,000
Credit: Accumulated Depreciation $5,552,000
The first journal entry record the cot of the tructural repair. The $1,000,000 tructural repair cot reduce the value of the building, and therefore the amount debited to Accumulated Depreciation will equal the amount credited to Building.
The econd journal entry adjust the Accumulated Depreciation for the change in the life of the building. Since the life of the building wa extended 10 year, the Accumulated Depreciation need to be reduced by 10 year of depreciation. The total cot of the building (original cot of $6,552,000 le the Accumulated Depreciation of $4,550,000 pre-adjutment) divided by the new life of 35 year equal the annual depreciation amount of $188,514.29. The econd journal entry would therefore debit Building for $5,552,000 ($188,514.29 x 10 year) and credit Accumulated Depreciation for the same amount.
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Factored form of 6+27 using GCF
The factored form of 6 + 27 is 3(2 + 9) using GCF.
What is GCF?The greatest common factor, which is the product of two or more numbers, is the biggest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's components have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF)
The given expression is:
6 + 27
Take the factors of the individual numbers:
6 = 1, 2, 3, 6
27 = 1, 3, 9, 17
Take the common factor from both the numbers, in this case it is 3.
Now, factor out the number from the given expression:
6 + 27
3(2 + 9)
Hence, the factored form of 6 + 27 is 3(2 + 9) using GCF.
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how do you prove an angle is a right angle when the other 2 angles are complementary in a triangle theorem
The two non-right angles in a right angled triangle balance each other out because the right angle already takes up 90 degrees of the triangle's 180 total angles. We refer to two angles as complementing each other when their sums equal 90 degrees.
The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The sum of the other two inner angles is 90 degrees. Base and perpendicular are the names of the other two sides that are close to the right angle. The Pythagorean Theorem is a triangle formula.
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a couple has three children. assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl? a. .5 b. .125 c. .875 d. 1
The probability of the couple having at least one girl is 0.875 0r 87.5 % by probability method. So, the option C is correct.
Having at least 1 girl out of 3 children means that there can be 1, 2 or 3 girls out of the 3 children.
So having at lest 1 girl out of 3 children is the same as saying that all 3 children are not boys.
The probability that all 3 children are boys would be
chance that child 1 is a boy * chance that child 2 is a boy * chance that child 3 is a boy = 0.5 * 0.5 * 0.5 = 0.125
since given that there is equal chance of both.
And the probability that NOT all 3 children are boys would be
100% - probability that all 3 children are boys = 1 - 0.125 = 0.875.
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Brad is standing on a hill which places him at the same height as a nearby flagpole.
The flagpole is 15 ft. High and Brad is 20 ft. Horizontally from the top of the pole.
Brad can see the bottom of the flag pole.
What is the length in feet of Brad's "line of sight" to the base of the flagpole?
As per the Pythagoras theorem the length in feet of Brad's "line of sight" to the base of the flagpole 25 feet².
In math the term called Pythagoras theorem is states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
The standard form of the Pythagoras theorem is written with the help of the triangle ABC as,
=> AC² = AB² + BC²
where AC refers the hypotenuse and AB and BC refers the sides of the triangle.
Here we know that it follows from the task content that the length in feet of Brad's line of sight to the base of the flag pole is to be determined.
And here we also know that the flag pole in discuss is said to be 15 feet high.
And here we have also identified that Brad is at the same height as the pole and is at a horizontal distance of 20 feet from the top of the pole.
Then the length is calculated as,
=> l² = 15² + 20²
=> l² = 225 + 400
=> l² = 625
=> l = 25.
Hence the length of the line of sight is 25 feet.
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a pitcher won 75%of the games she pitched. she pitched 60 games. how many games did she win
= 75
75 ___ × 60
75 ___ × 60 100
75 ___ × 60 100= 3
75 ___ × 60 100= 3 ___ × 60
75 ___ × 60 100= 3 ___ × 60
75 ___ × 60 100= 3 ___ × 60 4
75 ___ × 60 100= 3 ___ × 60 4= 45
The population of alaska is approximently 6. 5 x 10^5 people. The population of illinois is about 1. 3 x 10^7 people. How many times greater is the population of illinois than alaska
After finding the ratio, the population of Illinois than Alaska is 20 times greater.
The population of Alaska is approximately 6.5 x [tex]10^5[/tex] people.
The population of Illinois is about 1.3 x [tex]10^7[/tex] people.
We have to find how many times greater is the population of Illinois than Alaska.
We will use their population ratio to determine how many times the population of Illinois is greater than the population of Alaska.
Ratio = Population of Illinois's /Population of Alaska
Ratio = 1.3 x [tex]10^7[/tex]/6.5 x [tex]10^5[/tex]
Now simplifying.
Ratio = 0.2 x [tex]10^2[/tex]
Ratio = 20
To learn more about ratio link is here
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