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For the right traiangle, it is given that
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The base of a 14 foot ladder is 6 feet from a building if the ladder reaches the flat roof how tall is the building? The height of the building is_ ftThe height of the building is approximately_ft
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Step 1. Gather the information that we have and make a diagram.
The length of the ladder is 14 ft, the distance from the base of the ladder to the building is 6 ft and the height of the building is unknown.
We will call this unknown height ''a''.
The following diagram represents the situation:
Step 2. The triangle formed between the floor, the building, and the ladder is a right triangle (it has a 90° angle), this means that we can use the Pythagorean theorem to solve this and find ''a''.
The Pythagorean theorem is represented by the equation:
[tex]a^2+b^2=c^2[/tex]where a and b are the legs of the triangle, and c is the hypotenuse of the triangle (the side opposite to the 90° angle)
In our case,
[tex]\begin{gathered} c=14ft \\ b=6ft \end{gathered}[/tex]And we need to find a.
Step 3. Substituting the known values into the Pythagorean theorem:
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2+(6ft)^2=(14ft)^2 \end{gathered}[/tex]Solving the exponential terms:
[tex]a^2+36ft^2=196ft^2[/tex]And solving for a^2 by subtracting 36ft^2 to both sides of the equation:
[tex]\begin{gathered} a^2=196ft^2-36ft^2 \\ a^2=160ft^2 \end{gathered}[/tex]Taking the square root of both sides and simplifying:
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{160ft^2} \\ \\ a=\sqrt[]{16\cdot10}ft \\ \\ a=4\sqrt[]{10}ft \end{gathered}[/tex]This result can also be represented as a decimal number:
[tex]a=4\sqrt[]{10}ft\approx12.65ft[/tex]Answer:
The height of the building is
[tex]4\sqrt[]{10}ft[/tex]The height of the building is approximately
[tex]12.65ft[/tex]88,826.564 The 6 in the ones place is ___ the value of the 6 in the hundredth place
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Given the question:
88,826.564
The 6 in the ones place is 100 times (greater than) the value of the 6 in the hundredth place, since:
6/0.06 = 100.
Help. I need to be freed from the curse of math homework.
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ANSWER ; On average, Bailey reads 5/7 books per week
EXPLANATION;
Here, we want to get the average number of books per week Bailey reads
To get this, we simply have to divide the number of books she read by the number of weeks it took her to read them
Mathematically, we proceed as follows;
[tex]2\frac{1}{2}\text{ }\div\text{ 3}\frac{1}{2}[/tex]Now, to proceed with the division, we have to turn each of the mixed fractions to improper fraction ( a fraction that has its numerator greater than its denoinator)
To do this, we multiply the denominator by the stand alone number, then add the numerator; after which we place the sum over the denominator
We have an example as follows;
[tex]a\text{ }\frac{b}{c}\text{ = }\frac{(a\times c)+b}{c}[/tex]Applying this to the fractions, we have;
[tex]2\frac{1}{2}\text{ = }\frac{5}{2}\text{ and 3}\frac{1}{2}\text{ = }\frac{7}{2}[/tex]Finally, we proceed with the division;
[tex]\frac{5}{2}\text{ }\div\text{ }\frac{7}{2}\text{ = }\frac{5}{2}\times\frac{2}{7}\text{ = }\frac{5}{7}[/tex]Solve for x143x = 46
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You have the following equation:
14 - 3x = 46 - x
In order to solvet the previous equation for x, you proceed as follow:
14 - 3x = 46 - x subtract 14 and sum x both sides
-3x + x = 46 - 14 simplify similar terms
-2x = 32 divide by -2 both sides
x = 32/(-2) = -16
x = -16
Hence, the solution of the given equation is x = -16
what is the slope of the line?
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You can find the slope using the following formula:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ where\colon \\ (x1,y1)=(0,2) \\ (x2,y2)=(1,0) \\ m=\frac{0-2}{1-0}=\frac{-2}{1}=-2 \end{gathered}[/tex]I don’t think I did this correctly. How would I be able to solve this?
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In a function, every input value can be related to only one output.
In each table, the inputs are in the first column and the outputs in the second column.
In consequence, the first two tables show functions.
In the case of the third table, the input of 2 is related to two different outputs, then this table is not a function.
In the case of the fourth table, the input of 1 is related to two different outputs, then this table is not a function.
What is the equation of a line that passes through the point (1, -10) and is perpendicular to the equation y
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The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
The given equation is expressed as
y = - x/3 + 5
By comparing with the slope intercept equation,
slope, m = - 1/3
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. The negative reciprocal of - 1/3 is 3. Thus, the slope of the line passing through the point, (1, - 10) is 3
We would determine the y intercept, c by substituting x = 1, y = - 10 and m = 3 into the slope intercept equation. It becomes
- 10 = 3 * 1 + c
- 10 = 3 + c
c = - 10 - 3
c = - 13
We would substitute m = 3 and c = - 13 into the slope intercept equation. Thus, the equation of the line is
y = 3x - 13
Option D is correct
The rectangle has an area of 144 square centimeters. which is the perimeter?
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The formula to find the area of a rectangle is:
[tex]\begin{gathered} A=L\cdot W \\ \text{ Where} \\ A\text{ is the area} \\ L\text{ is the length} \\ W\text{ is the width} \end{gathered}[/tex]Then, let it be:
• L: The length of the rectangle.
,• W: The width of the rectangle.
So, we have:
[tex]\begin{gathered} A=144cm^2 \\ L=? \\ W=8cm \end{gathered}[/tex]Now, we can write and solve for L the following equation:
[tex]\begin{gathered} A=L\cdot W \\ 144cm^2=L\cdot8cm \\ \text{ Divide by 8}cm\text{ from both sides} \\ \frac{144cm^2}{8cm}=\frac{L\cdot8cm}{8cm} \\ 18cm=L \end{gathered}[/tex]The following is the procedure for dividing 144 by 8.
On the other hand, the perimeter is the sum of the measures of all sides of a polygon. Then, we have:
[tex]\begin{gathered} \text{Perimter}=L+W+L+W \\ \text{Perimter}=18cm+8cm+18cm+8cm \\ \text{Perimter}=52cm \end{gathered}[/tex]Therefore, the perimeter of the rectangle is 52 cm.
Find the coordinates of the center C of a circle if the endpoints of itsdiameter are A(8,-4) and B(-3, 2).C(x, y) =
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C(2.5,-1)
Explanation
Step 1
if the points A and B are the endpoints of the diameter, we can find the midpoint to find the coordiantes of the center, the midpoint of P1 and P2 is given by:
[tex]\begin{gathered} \text{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_1}{2}) \\ \text{ where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \\ \end{gathered}[/tex]Let
P1=A(8,-4) P2=(-3,2)
midpoint C
Step 2
replace
[tex]\begin{gathered} \text{c}=\text{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_1}{2}) \\ \text{midpoint}=(\frac{8-3}{2},\frac{-4+2}{2}) \\ \text{midpoint}=(\frac{5}{2},\frac{-2_{}}{2}) \\ \text{midpoint}=(2.5,-1) \\ \end{gathered}[/tex]so, the answer is C(2.5,-1)
How to write, Twice the difference of 3 and a
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Answer:
2*(3 - x)
Step-by-step explanation:
We don't know what the number is, so i am going to call it x.
Difference of 3 and a number.
The number is x.
Difference of 3 and x is 3 - x.
Twice
We multiply 2. So
2*(3 - x)
What is the length (magnitude) of the vector (2,-1)? O A. 1 B. -2 O C. 2 D. D. 5
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We are given the following vector
[tex]v=(2,-1)[/tex]The magnitude of a 2-dimensional vector is given by
[tex]|v|=\sqrt{x^2+y^2}[/tex]Substitute the given points into the above formula
[tex]\begin{gathered} |v|=\sqrt{(2)^2+(-1)^2} \\ |v|=\sqrt{4+1} \\ |v|=\sqrt{5} \end{gathered}[/tex]Therefore, the magnitude of the vector (2, -1) is √5
[tex]|v|=\sqrt{5}[/tex]Jade this information to answer the questions below. If not enough information is given to answer a question, write not enough information
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Answer
• a) 3
,• b) 21
,• c) Not enough information
Explanation
Given
• 28 seniors
,• 24 students went to the trip, where 7/8 were seniors.
Procedure
• a)
We are given the proportion of seniors, if we want to know the proportion of juniors we have to subtract it from 8/8 (whole):
[tex]\frac{8}{8}-\frac{7}{8}=\frac{1}{8}[/tex]Next, we have to multiply the students that went times the proportion:
[tex]24\cdot\frac{1}{8}=3[/tex]3 juniors went on the trip.
• b)
Now we have to multiply the proportion given times the students that went:
[tex]24\cdot\frac{7}{8}=21[/tex]Thus, 21 seniors went on the trip.
• c)
As we are not given the juniors that are in the class, we cannot answer this one.
=Knowledge CheckD and E are sets of real numbers defined as follows.
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By definition, we know that:
[tex]\begin{gathered} D\cup E=\mleft\lbrace w\mright|w\in D\text{ or }w\in E\} \\ =\lbrace w|w\le2\text{ or }w<5\} \end{gathered}[/tex]Since 2<5, then the only way w can be out of this union is if 5≤w. Then:
[tex]\begin{gathered} D\cup E=\mleft\lbrace w\mright|w<5\} \\ =(-\infty,5) \end{gathered}[/tex]On the other hand:
[tex]\begin{gathered} D\cap E=\mleft\lbrace w\mright|w\in D\text{ and }w\in E\} \\ =\lbrace w|w\le2\text{ and }w<5\} \end{gathered}[/tex]Since 2<5, then w is in the intersection only if w≤2. Then:
[tex]\begin{gathered} D\cap E=\lbrace w|w\le2\} \\ =(-\infty,2\rbrack \end{gathered}[/tex]Therefore, the answers are:
[tex]\begin{gathered} D\cup E=(-\infty,5) \\ D\cap E=(-\infty,2\rbrack \end{gathered}[/tex]Solve for p in the equation 7p = -63.
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Use the following property of equations to solve the given equation.
Let a, b and c be real numbers, such that c is different from 0. Then:
[tex]a=b\Leftrightarrow\frac{a}{c}=\frac{b}{c}[/tex]On the given equation:
[tex]7p=-63[/tex]Divide both sides of the equation by 7 (as the property says):
[tex]7p=-63\Leftrightarrow\frac{7p}{7}=\frac{-63}{7}[/tex]Simplify the fraction 7p/7:
[tex]\begin{gathered} \frac{7p}{7}=p \\ \Rightarrow p=\frac{-63}{7} \end{gathered}[/tex]Divide -63 by 7. Since -63 is negative and 7 is positive, the result should be negative. Additionally, 63/7 = 9, so:
[tex]\begin{gathered} \frac{-63}{7}=-9 \\ \therefore p=-9 \end{gathered}[/tex]Therefore, the solution for the equation 7p=-63 is p=-9.
Calculate the acelerationof a car (in kmlhis) that can gofrom rest to 100 km/h in 10 seconds
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the aceleration is calculated as:
Ron runs a computer repair company out of his home. He usually gets 4 salescalls and 7 tech support calls each weekday. How many calls does he get in aweek?
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Given:
There are given that they get 4 sales calls and 7 tech support calls each weekday.
Explanation:
According to the concept:
The total number of days in a week is 7.
Then,
From the question:
They get a total number of calls are:
[tex]4\text{ sales + 7 tech = 11}[/tex]Now,
The number of calls in a week will be:
[tex]7\times11=77[/tex]Final answer:
Hence, the total numbers of calls he gets in a week are 77.
Find the area of the figure. (Sides meet at right angles.)5 yd5 yd2 yd2 yd3 yd5 yd
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We need to find the area for the given figure.
Now, we can divide the figure into two rectangles:
Then, we need to find each area. The area for a rectangle is given by the next formula:
[tex]A=Length\cdot\text{ width}[/tex]For the largest rectangle:
Lenght = 2yd + 5yd + 2yd
Lenght = 9yd
Width = 5yd
Therefore, the area for the largest rectangle is:
[tex]A=9yd\cdot5yd[/tex][tex]A=45yd^2[/tex]For the small rectangle:
Length = 5yd
Width = 3yd
Therefore, the area for the small rectangle is:
[tex]A=5yd\cdot3yd[/tex][tex]A=15yd^2[/tex]Now, to find the total area of the figure, we need to add up to both rectangles areas:
[tex]A_t=small\text{ rectangle +largest rectangle}[/tex]Then:
[tex]A_t=60yd^2[/tex]Hence, the total area for the figure is 60yd²
I will send a picture of the equation because it won't make sense if I type it here.
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To find the answer, we will need to replace the population P by 50,000 and solve the initial equation for t because t is the number of years after 2012.
So, we get:
[tex]50,000=25,000e^{0.03t}[/tex]Now, we need to remember some properties of the logarithms:
[tex]\ln e^a=a[/tex]Then, we can solve for t as:
[tex]\begin{gathered} 50,000=25,000e^{0.03t} \\ \frac{50,000}{25,000}=\frac{25,000e^{0.03t}}{25,000} \\ \\ 2=e^{0.03t} \end{gathered}[/tex]So, using the property, we get:
[tex]\begin{gathered} \ln 2=\ln e^{0.03t} \\ \ln 2=0.03t \end{gathered}[/tex]Finally, dividing by 0.03 into both sides, we get that the number of years after 2012 that the population will be 50,000 is:
[tex]\begin{gathered} \frac{\ln 2}{0.03}=\frac{0.03t}{0.03} \\ \frac{\ln 2}{0.03}=t \end{gathered}[/tex]Answer: t = ln2/0.03
Ms. Juhal was making t-shirts. One of the designs had these coordinate points: A (-5, 5), B (-5, 3), C (-5, 1), and D (2, 1). Plot the points on graph paper in the order they are given and connect them. What shape is made?
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Given data:
The given coordinates are A (-5, 5), B (-5, 3), C (-5, 1), and D (2, 1).
The below figure shown the graph of the above coordinate.
Thus, the above figure represents the right angle triangle.
A total of $9500 is invested, part at 10% simple interest and part at 8%. If the total annual return from the two investments is $ 878.00, how much is invested at each rate?
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Answer:
• The amount invested at 10% = $5,900
,• The amount invested at 8% =$3600
Explanation:
[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]Let the amount invested at 10%=y
[tex]\begin{gathered} \text{Simple Interest}=\frac{y\times10\times1}{100} \\ =0.1y \end{gathered}[/tex]Then, the amount invested at 8% =$(9500-y)
[tex]\begin{gathered} \text{Simple Interest}=\frac{(9500-y)\times8\times1}{100} \\ =0.08(9500-y) \\ =760-0.08y \end{gathered}[/tex]The return from the two investments is $ 878.00, thus:
[tex]\begin{gathered} 0.1y+(760-0.08y)=878 \\ 0.1y-0.08y=878-760 \\ 0.02y=118 \\ y=\frac{118}{0.02} \\ y=5,900 \end{gathered}[/tex]We conclude that:
• The amount invested at 10% = $5,900
,• The amount invested at 8% =9500-5900=$3600
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 30 N acts on a certain object, the acceleration of the object is 10 m/s. If the acceleration of the object becomes 3 m's>, what is the force? > Х 5 ? I Don't Know Submit Access 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center 44°F Claudy
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The Solution:
We are required to find the force.
[tex]\begin{gathered} F\propto a \\ \text{This implies that:} \\ F=ka \end{gathered}[/tex]In this case,
F= force=30 N
a = acceleration = 3m/s
k = constant of proportionality = ?
We shall find the constant k by substituting the above values in the formula.
[tex]\begin{gathered} F=ka \\ 30=k(10) \end{gathered}[/tex]Dividing both sides by 10, we get
[tex]k=\frac{30}{10}=3[/tex]So,
The formula for finding Force is:
[tex]F=3a[/tex]To find the Force when a = 3m/s, we shall substitute 3 for a in the formula.
[tex]F=3\times3=9N[/tex]Therefore, the correct answer is 9 N
Solve for x:1/2(2-4x)+2x=13
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Answer:
Explanation:
Given the equation:
[tex]\frac{1}{2}\mleft(2-4x\mright)+2x=13[/tex]First, we open the bracket:
[tex]\frac{1}{2}(2)-\frac{1}{2}(4x)+2x=13[/tex]i can’t find anything to help me with this one
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The formula for simple interest is I = Prt where I is the interest earned, P is the Principal, r is the interest, and t is the number of years. Solve the formula for "t" in terms of P, i, and r. t = ?
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To solve "t", simply divide both sides by Pr.
[tex]\begin{gathered} \frac{I}{Pr}=\frac{Prt\text{ }}{Pr} \\ \frac{I}{Pr}=t \\ t=\frac{I}{Pr} \end{gathered}[/tex]Therefore, the formula for t is t = I/Pr as shown above.
I need to convert the following equation Demonstrating the identity Property of Multiplication
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The identity property of multiplication simply states that a number equals itself when multiplied by 1.
So:
[tex]7y\cdot1=7y[/tex]going to send you pictures
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Answer: We have to find the probablity that a registered voter votted in the election
[tex]\begin{gathered} \text{Voters = 3072757} \\ \text{Not-Voted = 3481030 } \\ \text{Total registered=3,072,757+3,481,030=}6,553,787 \end{gathered}[/tex]Therefore, the probability that a registered voter voted is:
[tex]P_r=\frac{3072757}{6553787}=46.56\text{ percent}[/tex]Likewise, the probablity that a registered voter did not vote is:
[tex]53.11\text{ percent }[/tex]
suppose that the heights of adult men in th united states are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What proportion of the adult men in the united states are less than 6 feet tall?
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Proportion of the adult men less than 6 feet tall = 74.857%
Explanations:The mean height, μ = 70 inches
The standard deviation in height, σ = 3 inches
Proportion of the adult men less than 6 feet
1 foot = 12 inches
6 feet = 12 x 6 = 72 inches
x = 72 inches
Calculate the z-value using the formula below:
[tex]\begin{gathered} z\text{ = }\frac{\text{x -}\mu\text{ }}{\sigma} \\ z\text{ = }\frac{72-70}{3} \\ \text{z = }\frac{2}{3} \\ \text{z = }0.67 \end{gathered}[/tex]Probability that an adult men will be less than 72 inches (6 feet) tall
P(x < 72) = P(z < 0.67) = 0.74857
Therefore, proportion of adult men less than 72 inches (6 feet) tall = 0.74857 x 100% = 74.857%
Find the slope of the graph using two of the points marked in the slope formula?
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Given:
There is a geaph given in the question
Required:
We need to find the slope of given graph
Explanation:
Take two points from graph
[tex]\begin{gathered} (x_1,y_1)=(0,40) \\ (x_2,y_2)=(10,60) \end{gathered}[/tex]formula to find the slope m is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]substitute the values
[tex]m=\frac{60-40}{10-0}=\frac{20}{10}=2[/tex]Final answer:
Slope m of given graph is 2
May I please get help with this. I have tried multiple times but still could not get the correct answers. I would appreciate it so much if I could get help
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To answer this question we need to remember some properties for any parallelogram:
• Two pairs of opposite sides are equal in length.
,• Two pairs of opposite angles are equal in measure.
,• The diagonals bisect each other.
We notice that in the figure QSRP opposite sides are equal in length then we conclude that this is a parallelogram.
In figure RSUT we notice that the diagonals bisect each otherm then we conclude that this is a parallelogram.
In figure KLNM we notice that none of the properties stated before are fullfill, then this is not necesarrily a parallelogram.
In figure BDCA we notice that alternate interior angles are equal, this means that segments BD and CA are parallel, we also notice that the other segments are parallel; therefore this is a parallelogram.
One exploratory mapping session for a 1m by 1m can last 5 minutes. This new mapping system should be able to handle absolute coordinates in space, but the compass directions might not be available. Given: This mapping system uses cartesian system using as origin (0,0,0) the landing site. The robot starts the exploration at the point (1, 2, -3) and ends the exploration at the point (2, 0, 1). Find: Describe the trajectory of the move using the equation of line between the starting and the final location of the robot.
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We have to find the line between the starting and the final location. We have that the parametrics equations of the line are
[tex]\begin{gathered} x=1+t \\ y=2−2t \\ \begin{equation*} z=−3+4t \end{equation*} \end{gathered}[/tex]The symmetric equations are
[tex]x−1=\frac{y−2}{-2}=\frac{z+3}{4}[/tex]