The height of the building is 315 feet because the ratio of the building's height to the post's height is equal to the ratio of the building's shadow length to the post's shadow length.
How to find height?This problem can be solved using the concept of proportionality.
The height of the building is proportional to the length of its shadow, and the height of the post is proportional to the length of its shadow.
Express this mathematically as follows:
Building height / Post height = Shadow length / Post shadow length
Substituting the known values:
Building height / 3 feet = 105 feet / 4 inches
Convert 105 feet to inches first. 105 feet is equal to 105 × 12 = 1260 inches.
Rewrite the equation as follows:
Building height / 3 feet = 1260 inches / 4 inches
The units cancel out, and are left with:
Building height = 1260 / 4 = 315 feet
Therefore, the height of the building is 315 feet.
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Final answer:
To calculate the building's height, we set up a proportion using similar triangles. With the shadow of the building being 105 feet and the shadow of a 3-foot post being 4 inches (1/3 feet), we solve the proportion to find that the building is 315 feet tall.
Explanation:
To determine the height of the building, we can use similar triangles. The method involves setting up a proportion based on the principle that similar triangles have corresponding sides that are in the same ratio. Given the length of the building's shadow and the length of the shadow cast by a known post, we can find the building's height.
Let's define the following variables: B for the height of the building, Sb for the length of the building's shadow, P for the height of the post, and Sp for the length of the post's shadow. From the problem, Sb = 105 feet, P = 3 feet, and Sp = 4 inches, which is 1/3 feet since there are 12 inches in a foot.
Using these variables, the proportion can be set up as follows:
B/Sb = P/SpPlugging in the known values, we get:
B/105 = 3/(1/3)By solving this proportion for B, we find that:
B = (3 × 105) × 3B = 315 feetTherefore, the height of the building is 315 feet.
I need help ‼️ #10, #11 & #13.
Answer: 10 : t = 16 11 : x = -8 13 : x = 0
Step-by-step explanation: Im sure about 10 and 11 but not too sure about 13 and explanations are too hard for me to explain
Which of the following is(are)the solution(s) to |x+3|=12?
A line has a slope of 2/3 and a y-intercept of 4.
Which of the following is the equation of the line?
The equation of the line with a slope of 2/3 and y-intercept of 4 is y = 2/3x + 4.
Explanation:The equation of a line in slope-intercept form (which is the most common form we deal with in algebra) is y = mx + b, where m is the slope and b is the y-intercept.
In this case, you're given that the slope (m) is 2/3 and the y-intercept (b) is 4. Substituting these values into the equation gives you the equation of the line: y = 2/3x + 4.
This is the equation that represents the given line
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Final answer:
The equation of the line with a slope of 2/3 and a y-intercept of 4 is y = 2/3x + 4.
Explanation:
To find the equation of a line with a slope of ⅓ and a y-intercept of 4, we can use the slope-intercept form of a line, which is y = mx + b where m is the slope and b is the y-intercept.
The given slope is ⅓, so m = ⅓. Given that the y-intercept is 4, b = 4.
Plugging these values into the slope-intercept equation, we get y = ⅓x + 4, which is the equation of the desired line.
The equation of a line is a mathematical expression that describes the relationship between the independent variable (x) and the dependent variable (y) for points on that line in a Cartesian coordinate system. It allows you to represent a straight line graphically on a two-dimensional plane.
For each of the hypothetical data sets, determine whether a bar graph or a pie chart would be an appropriate way to display the data. In some cases, both types of graphs may be appropriate.
the percent of individuals with each of the following natural eye colors:
brown, blue, green, hazel, and other
the population density of each of the 50 states in the United States
the number of college students who play basketball, baseball, or soccer
the proportion of traditional public schools in a region compared to
the proportion of charter and private K–12 schools in that region.
choices: Bar graph Pie chart
The final answers of four different parts of the question can be concluded in the following bulletin points.
Both the charts can be used to represent the above condition but the better way to represent it is Pie chart.Bar Graph is the better way to represent the above scenario, because the higher data entry may result in a very huge pie chart to understand it properly.The pie chart is the better way to represent the above situation.The pie chart is the better way to represent the above situation.1). The percent of individuals with each of the following natural eye colors:
brown, blue, green, hazel, and others.
Both the charts can be used to represent the above condition but the better way to represent it is Pie chart.2). The population density of each of the 50 states in the United States.
Bar Graph is the better way to represent the above scenario, because the higher data entry may result in a very huge pie chart to understand it properly.3). The number of college students who play basketball, baseball, or soccer.
The pie chart is the better way to represent the above situation.4). The proportion of traditional public schools in a region compared to
the proportion of charter and private K–12 schools in that region.
The pie chart is the better way to represent the above situation.To know more about graphs, please refer to the link:
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For the percent of individuals with each natural eye color and the population density of each state in the United States, a bar graph is appropriate. For the number of college students who play different sports, a bar graph is also appropriate.
Explanation:A bar graph would be an appropriate way to display the percent of individuals with each natural eye color. Each bar in the graph would represent a different eye color, and the length of the bar would represent the percentage of individuals with that eye color. This would allow for easy comparison of the different eye colors.
For the population density of each state in the United States, a bar graph would also be appropriate. Each bar in the graph would represent a different state, and the height of the bar would represent the population density of that state. This would allow for easy comparison of the population densities between states.
For the number of college students who play basketball, baseball, or soccer, a bar graph would be the most appropriate choice. Each bar in the graph would represent a different sport, and the height of the bar would represent the number of students who play that sport. This would allow for easy comparison of the number of students playing each sport.
Which compound inequality is represented by the graph?
x<-40x2>3
x<-4 and 2>3
x<-4 or x <3
x<-4 and x <3
Explain how you can use a quick picture to find 3× 2.7
Answer:
see the picture 8.1 is answer
3. What is the name of a symbol that is used to
represent a quantity that can change?
Answer:
Variable
Step-by-step explanation:
A Variable is a letter or symbol used to represent a quantity that can change.
The symbol used to represent a quantity that can change is called a variable.
We have,
The symbol that is commonly used to represent a quantity that can change is called a variable.
In mathematics and algebraic equations, variables are often represented by letters such as x, y, or z.
Variables are placeholders for unknown or changing values that can be assigned different numerical or algebraic values during calculations or problem-solving.
They allow for the generalization and manipulation of mathematical expressions and equations.
Thus,
The symbol used to represent a quantity that can change is called a variable.
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A student missed
15 problems on a Chemistry test and received a grade of
52 %. If all the problems were of equal value, how many problems were on the test? Round off your answer to the nearest integer.
Answer:
x = 31
Step-by-step explanation:
Let x: total amount of questions in the Chemistry test.
Then 52% represents the ratio of questions properly answered vs total questions:
[tex]\frac{Correct}{Total} = 52%[/tex]
The number of correct questions is the number of total questions take the number of missed questions.
[tex]Correct questions = Total questions - missed questions[/tex]
Since, missed questions = 15
[tex]\frac{x-15}{x} = 52%[/tex]
Also, 52% can be expressed as 0.52. Then, the expression can be rewritten as:
[tex]\frac{x-15}{x} = 0.52[/tex]
Then, rearranging:
[tex] x - 15 = 0.52x [/tex]
[tex] x - 0.52x = 15 [/tex]
[tex] 0.48x = 15 [/tex]
[tex] x = 15/0.48 [/tex]
[tex] x = 31.25 [/tex]
Rounding to the nearest unit: x = 31
a fraction that is a repeating decimal between 0.25 and 0.5
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
3 divided by 1 is 0.33 repeating
1. Is the equation true, false or open? Explain. 8 + 4 = -5 + 7
2. Which ordered pair is a solution of the equation y = -11x + 4? Make sure you show work! a.
(0,-7) b.(-1, -7) c, (1, -7) d. (2,26)
3. Complete the table and state the rule.
Answer:
1. False
2. c. (1, -7)
3. Input= 1 and 4; Output=6, 12 and 18. The rule is the input×3
Step-by-step explanation:
1. 8+4=±5+7
8+4= 12 & ±5+7= 2
The left side 12 does not equal to the right side 2 , which means that the given statement is false.
2. I'm not sure how to show my work.
3.
Input: 0, 1, 2, 3, 4, 5, 6
Output: 0, 3, 6, 9, 12, 15, 18
0×3=0; 1×3=3; 2×3=6; 3×3=9; 4×3=12; 5×3=15; 6×3=18
1. The equation is false.
2. The ordered pair that is a solution of the equation y = -11x + 4 is (-1, -7).
3. The rule for the table is to square the input and add 3.
Why is the equation false?1. Given
8 + 4 = -5 + 7
12 = 2
The left side of the equation is 12, and the right side of the equation is 2. 12 is not equal to 2, so the equation is false.
2. The ordered pair that is a solution of the equation y = -11x + 4 is (-1, -7).
To see this, we can substitute the x-value of -1 into the equation and solve for y:
y = -11(-1) + 4
y = 11 + 4
y = 15
We can also substitute the y-value of -7 into the equation and solve for x:
-7 = -11x + 4
-11x = -11
x = 1
Therefore, the ordered pair (-1, -7) satisfies both sides of the equation, so it is a solution.
The other ordered pairs do not satisfy both sides of the equation. For example, if we substitute the x-value of 0 into the equation, we get y = 4, which does not equal -7.
3. The rule for the table is square the input and add 3.
To see this, we can look at the first few rows of the table:
Input | Output
-------|--------
0 | 3
3 | 12
9 | 28
We can see that squaring the input and adding 3 gives us the output for each row. For example, squaring the input of 0 gives us 0, and adding 3 gives us 3, which is the output for the first row.
We can also see that this rule works for all of the rows in the table. Therefore, the rule for the table is to square the input and add 3.
Here is the completed table:
Input | Output
-------|--------
0 | 3
3 | 12
9 | 28
16 | 45
25 | 64
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CORRECT GETS BRAINLIEST A pizzeria delivered p pizzas on Thursday. On Friday, it delivered 3 more
than twice the number of pizzas delivered on Thursday. Write an
expression to show the number of pizzas delivered on Friday.
Answer:
(p×2)+3
Step-by-step explanation:
I'm not too sure, I've only just started practicing this stuff?
what is 3w + 5 =23 it's a two step equation
Answer:
w=6
Step-by-step explanation:
3w+5=23
3w=23-5
3w=18
w=6
The solution to the equation 3w + 5 = 23 is w = 6.
The given equation is 3w + 5 = 23.
We need to solve for w.
Subtract 5 from both sides of the equation to isolate the term with 3w:
3w + 5 - 5 = 23 - 5
3w = 18
Divide both sides of the equation by 3 to solve for w:
(3w) / 3 = 18 / 3
This simplifies to:
w = 6
Therefore, the solution to the equation 3w + 5 = 23 is w = 6.
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what is the square root of 109
[tex] \sqrt{ 109 } [/tex]
Consider the equation 5y = 2x +4. Select all the equations that are perpendicular to the given equation.
None of the given equations are perpendicular to the equation '5y = 2x +4'. This is because perpendicular lines have reciprocal, negative slopes and none of the given lines meet this criteria.
Explanation:To find the equations that are "perpendicular" to the given equation 5y = 2x +4, we first need to find out the slope of the given equation. The slope of the equation is obtained by rearranging it into the y=mx+b form where m stands for the slope. Thus, y=(2/5)x+4/5, which gives us a slope (m) of 2/5.
Perpendicular lines have slopes that are negative reciprocals of each other. So, for a line to be perpendicular to the given line, it should have a slope of -5/2.
Given the equations 7 y = 6x + 8, 4y = 8, and y + 7 = 3x, let's find out their slopes. The slope for the first equation is 6/7, for the second equation is undefined as it's a horizontal line, and for the third equation is 3. Hence, none of these lines are perpendicular to the given line. Similarly, none of the lines Y2 = -173.5+ 4.83x − 2(16.4) and line Y3 = -173.5+ 4.83x + 2(16.4) don't have a slope of -5/2 and hence, are not perpendicular to the given line.
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What is the answer to 10h - 4h
Answer:
Step-by-step explanation:6 hours because 10-4=6
Explain how you could write the mixed number 45 3/8 in
scientific notation.
Answer:
[tex]4.5375*10^1[/tex]
Step-by-step explanation:
we know that
[tex]45\frac{3}{8}=45+\frac{3}{8}=45+0.375=45.375[/tex]
Convert decimal number in scientific notation
A number expressed in scientific notation has the form
[tex]a*10^{n}[/tex]
where
[tex]1\leq a < 10[/tex]
n is a integer
Expressing 45.375 in this form means writing the number as a value between 1 and 10
so
For a=4.5375,n=1
[tex]45.375=4.5375*10^1[/tex]
Final answer:
The mixed number 45 3/8 can be expressed in scientific notation as 4.5375 *[tex]10^2[/tex] by first converting it to an improper fraction, then to a decimal, and finally moving the decimal point two places to the left.
Explanation:
To write the mixed number 45 3/8 in scientific notation, let's first convert it into an improper fraction and then into a decimal. The mixed number 45 3/8 is equivalent to (45 * 8 + 3) / 8, which simplifies to 363/8 or 45.375 as a decimal.
Now, to express this in scientific notation, we move the decimal point two places to the left so that the number falls between 1 and 10. As a result, we get 4.5375. Since we moved the decimal two places to the right, we multiplied by 10 to the power of 2([tex]10^2[/tex])
Finally, 45 3/8 in scientific notation is 4.5375 *( [tex]10^2[/tex] ).
5. Margaret is making fudge for a
party. The recipe calls for
| 1 1/4 cups of sugar and 1 1/4cups of
chocolate chips. How many cups
of sugar and chocolate chips does
Margaret need to make the
fudge?
Margaret needs 2 1/2 cups of sugar and chocolate chips to make the fudge.
Explanation:To make the fudge, Margaret needs 1 1/4 cups of sugar and 1 1/4 cups of chocolate chips.
To find the total number of cups needed, add the amounts of sugar and chocolate chips: 1 1/4 + 1 1/4 = 2 1/2 cups.
Therefore, Margaret needs 2 1/2 cups of sugar and chocolate chips to make the fudge.
Please help me and this question
Answer: 12 inches cubed
Step-by-step explanation:
volume=length x width x height
volume=1.5 in x 2 in x 4 in
volume=12 in^3
Can someone help me, I have no idea how to do this :(
2. A company manufactures tote bags. The company spends $1200 each day for overhead
expenses plus $9 per tote bag for labor and materials. The tote bags sell for $25 each. How
many tote bags must the company sell each day to equal its daily costs for overhead, labor,
and materials?
Answer:
75
Step-by-step explanation:
1200+9X=25X
1200=25X-9X
1200=16X
X=1200/16
X=75
To find the number of tote bags a company needs to sell in order to cover its costs, we need to set its daily costs equal to its daily revenue and solve for the number of bags. In this case, the solution to the equation indicates that the company needs to sell 80 tote bags each day to break even.
Explanation:The subject of this question is business mathematics, specifically the mathematical concept of break-even point. The break-even point is the point at which total revenue equals total expenses, and the business is neither losing nor making money. In this case, the fixed costs, or overhead expenses, total $1200 per day, while the variable costs are $9 per tote bag. We can express daily costs, C, as C = $1200 + $9x, where x represents the number of tote bags. The daily revenue, R, is R = $25x. To find the number of tote bags needed to break even, you set C equal to R and solve the resulting equation $1200 + $9x = $25x. Solving this equation yields x = 80. Therefore, the company needs to sell 80 tote bags each day in order to break even.
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I am thinking of a number. If you triple my number and subtract 11, you get my number plus 33. What's my number?"
Answer:
22
Step-by-step explanation:
22 x 3 = 66
66- 11 = 55
55-33 = 22
The number of boys in the tennis club is 10 more than half the number of girls. There are 30 boys in the tennis club. All together, how many boys and girls are in the club.
Answer:
36
Step-by-step explanation:
Number of boys = 30
also, Number of boys = 10(number of girls/2)
∴ 30 = 10(number of girls/2)
30×2 = 10(number of girls)
⇒ number of girls = [tex]\frac{60}{10}[/tex]
⇒ number of girls = 6
Total number of girls and boys = 30 + 6 = 36
Find −9/14 + 2/7. Write your answer as a fraction in simplest form.
Answer:
[tex]-\frac{5}{14}[/tex]
Step-by-step explanation:
When you add fractions, sometimes you have to raise a number to make it more easier for you.
As in this case, we have two fractions in which seem to not be the same, but note this.
7 is multiple of 14, meaning to make our life easier, we can do this method:
[tex]\frac{2 * 2}{7 * 2} = \frac{4}{14}[/tex]
Whoa! Now we have the same denominator for both fractions, now we made this problem way more easier than it was before.
Do the math:
[tex]\frac{-9 }{14} + \frac{4}{14}[/tex]
==> [tex]-\frac{5}{14}[/tex]
The fraction in the simplest form is -5/4.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Operators who let do a basic mathematical calculation.
* Multiplication operation: Multiplies values on either side of the operator
For example 12*2 = 24
We have been given that expression of fraction as
⇒ -9/14 + 2/7
We have to determine the fraction in the simplest form.
⇒ -9/14 + 2/7
Take the LCM,
⇒ (-9 + 2×2)/7
⇒ (-9 + 4)/7
⇒ -5/4
Therefore, the fraction in the simplest form is -5/4.
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5x+34=-2+14x i need the individual steps
Answer: x = 4
Step-by-step explanation:
5x + 34 = -2 + 14x
5x - 5x + 34 = -2 + 14x -5x Remove 5x from both sides
34 = -2 +9x
34 + 2 = -2 + 2 + 9x Add 2 to both sides (remove constant)
36 = 9x
36/9 = 9x/9 Divide both sides by 9 to isolate the variable
4 = x
or
x = 4
What is the value of y if 6y-2=34
Answer:
6
Step-by-step explanation:
6y - 2 = 34
6y = 36
y = 6
Answer:
y = 6
Step-by-step explanation:
6y - 2 = 34
+2 +2
6y = 36
[tex]\frac{6y}{6} = \frac{36}{6}[/tex]
y = 6
What is 64x + 27 written as a sum of cubes?
Answer:
see explanation
Step-by-step explanation:
64x + 27 ← is not a sum of cubes. We would require
64x³ + 27 ← sum of cubes and factors as
64x³ + 27 = (4x + 3)(16x² - 12x + 9)
Simon used these steps to solve an equation:
Step 1: -6(x + 7) = 2(x − 11)
Step 2: -6x − 42 = 2x − 22
Step 3: -8x − 42 = -22
Step 4: -8x = 20
Which property did he use to get from step 3 to step 4?
A. addition property of equality
B. distributive property
C. subtraction property of equality
D. transitive property
A. Addition Property of Equality. The property that states that if you add the same number to both sides of an equation, the sides remain equal. Which as we see the equation still remains equal.
To go through Step 3 to Step 4 he used the addition property of equality. Option A is correct.
Given that,
Simion used steps to solve the equation,
To determine which property did he use to get from step 3 to step 4.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Step 1: -6(x + 7) = 2(x − 11)
Distributive property
Step 2: -6x − 42 = 2x − 22
Addition property of equality
Adding 2x on both side
Step 3: -8x − 42 = -22
Addition property of equality
Adding 42 on both sides
Step 4: -8x = 20
Thus, to go through Step 3 to Step 4 he used the addition property of equality. Option A is correct.
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10. 4(x - 1) - 5 = 3x + 7
how do i Distribute
Answer:
x=16
Step-by-step explanation:
The Distributive property says a(b+c) = ab+ac
1) You have 4(x-1)... This can be simplified to 4x-4
4x-4-5=3x+7
2) Combine alike terms:
4x-9=3x+7
3) add a 9 to both sides:
4x=3x+16
4) subtract a 3x from both sides:
x=16
Use the graph that shows the solution to f(x)=g(x) . (Images below)
f(x)=7/3x−3
g(x)=2^x−4
What is the solution to f(x)=g(x) ?
Select each correct answer.
−1/2
0
2
3
Here's my step-by-step explanation:
Let's get two facts straight: f(x) is a linear function. It's a line. g(x) is an exponential function. It's a curve.
Method 1: Elimination using f(x)
For f(x), the y-intercept (where on the y-axis it coincides with) in {f(x) = 7/3x - 3} is -3. And the only graph that has that is Graph 2.
Alright, so the first obvious solution, according to that graph, is (0, -3). And since we're speaking in terms of x (thus f(x) and g(x)), we pick the x-value from that coordinate and get 0.
The second solution is not as obvious; it's supposed to be (3,4) but the graph is kinda off. I attached a Desmos graph so you can see what I'm talking about a little more clearly.
Anyway, since we're speaking in terms of x we pick the x-value from that coordinate and get 3. Nice, we've got the solutions 0 and 3.
Hope this helps, let me know if I made a mistake.
X^2- 4y² = 9
3x + 4y = 7
Answer:
[3⅖, -⅘], [5, -2]
Step-by-step explanation:
I could not do any more, but I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.