A ladder leans against the side of a house. The top of the ladder is 10 ft from the ground. The bottom of the ladder is 9 ft from the side of the house. Find thelength of the ladder. If necessary, round your answer to the nearest tenth.х5?9ExplanationCheck
Answers
Given:
Distance of top of ladder to the ground = 10 ft
Distance of bottom of ladder from the side of the house = 9 ft
Let's find the length of the ladder.
Since the ladder forms a right triangle with the house, to find the length of the ladder apply Pythagorean Theorem.
[tex]c^2=a^2+b^2[/tex]Where:
a = 10 ft
b = 9 ft
c = length of ladder
Thus, we have:
[tex]\begin{gathered} c^2=10^2+9^2 \\ \\ c^2=100+81 \\ \\ c^2=181 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{c^2}=\sqrt[]{181} \\ \\ c=13.5 \end{gathered}[/tex]Therefore, the length of the ladder rounded to the nearest tenth is 13.5 ft
ANSWER:
13.5 ft
Related Questions
On a circle of radius 9 feet, what angle would subtend an arc of length 7 feet?
_____ degrees
Answers
The angle subtend an arc length of 7 feet is 44.56°
Given,
Radius of a circle = 9 feet
Arc length of a circle = 7 feet
Arc length :
The distance between two places along a segment of a curve is known as the arc length.
Formula for arc length:
AL = 2πr (C/360)
Where,
r is the radius of the circle
C is the central angle in degrees
Now,
AL = 2πr (C/360)
7 = 2 × π × 9 (C/360)
7 = 18 π (C/360)
7/18π = C/360
C = (7 × 360) / (18 × π)
C = (7 × 20) / π
C = 140 / π
C = 44.56°
That is,
The angle subtend an arc length of 7 feet is 44.56°
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Mrs. Smith stores water in different size bottles. she has 4 containers that are 2 1/2 quarts each and 3 containers that are 425 cups each. how many fluid ounces of water does she have?
Answers
Answer:
The total volume of fluid ounces of water she have is;
[tex]422\text{ ounces}[/tex]Explanation:
Given that she has 4 containers that are 2 1/2 quarts each
[tex]\begin{gathered} V_1=4\times2\frac{1}{2}\text{ quarts} \\ V_1=10\text{ quarts} \end{gathered}[/tex]Recall that to convert quarts to ounce;
[tex]1\text{ quart }=32\text{ ounces}[/tex][tex]\begin{gathered} V_1=10\text{ quarts }=10\times32\text{ ounces} \\ V_1=320\text{ ounces} \end{gathered}[/tex]Also, she has 3 containers that are 4.25 cups each;
[tex]\begin{gathered} V_2=3\times4.25\text{ cups} \\ V_2=12.75\text{ cups} \end{gathered}[/tex]To convert cups to ounces;
[tex]1\text{ cup}=8\text{ ounces}[/tex]So;
[tex]\begin{gathered} V_2=12.75\text{ cups }=12.75\times8\text{ ounces} \\ V_2=102\text{ ounces} \end{gathered}[/tex]The total volume of fluid ounces of water she have is;
[tex]V=V_1+V_2[/tex]substituting the values;
[tex]\begin{gathered} V=320+102\text{ ounces} \\ V=422\text{ ounces} \end{gathered}[/tex]Therefore, the total volume of fluid ounces of water she have is;
[tex]422\text{ ounces}[/tex]PLEASE HELP
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, the team observes that the angle of elevation to the top of the mountain is 25o. From a point 1,000 feet closer to the mountain along the plain, the team finds that the angle of elevation is 29o. How tall (in feet) is the mountain? Round to two decimal places.
Answers
The height of the mountain is 2936.39 feet.
Given,
In the question:
The angle of elevation to the top of the mountain is 25°.
To find the height of the mountain, we can draw triangles as in the image attached.
Now, According to the question:
Let's call the height of the mountain 'h', and the distance from the first point (25degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(29) = h/x
tan(25) = h/(x+1000)
tan(25) is equal to 0.4663, and tan(29) is equal to 0.5543, so:
h/x = 0.5543 -> x = h/0.5543
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.5543 + 1000) = 0.4663
h = 0.4663 * (h/0.5543 + 1000)
h = 0.8412h + 466.3
0.1588h = 466.3
h = 466.3 / 0.1588 = 2936.39 feet
Hence, the height of the mountain is 2936.39 feet.
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Solve the quadratic equation by completing the square.x^2+18x+75=0First choose the appropriate form and fill in the blanks with the with the correct numbers. Then solve the equation. If there is more than one solution, separate them with commas.
Answers
we have the quadratic equation
x^2+18x+75=0
complete the square
x^2+18x=-75
x^2+18x+81=-75+81
x^2+18x+81=6
rewrite as perfect squares
(x+9)^2=6
Find out the solutions
square root both sides
[tex]x+9=\pm\sqrt[\square]{6}[/tex][tex]x=-9\pm\sqrt[\square]{6}[/tex]The first solution is
[tex]x=-9+\sqrt[\square]{6}[/tex]The second solution is
[tex]x=-9-\sqrt[\square]{6}[/tex]Please help this is due tomorrow!!
Answers
The expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The given polynomial expression below is:
⇒ 10x⁵y⁷/5x⁵y · 3x⁴y⁸/3x⁻³y¹⁰
Apply the division operation in the constant terms
⇒ 2x⁵y⁷/x⁵y · x⁴y⁸/x⁻³y¹⁰
Apply the arithmetic operation in the Exponents of the same base variables
⇒ 2y⁶ · x⁷y⁻²
⇒ 2y⁶⁻² · x⁷
⇒ 2y⁴ · x⁷
⇒ 2x⁷· y⁴
Therefore, the expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
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Which of the following would be a good name for the function that takes the length of a race and returns the time needed to complete it?
Answers
In general, a function f(x) means that the input is x and the output is f(x) (or simply f).
Therefore, in our case, the input is the length of the race and the outcome is the time.
The better option is Time(length), option A.Using solving systems using elimination addition method3x-7y=5-3x+7y=-9help
Answers
In the elimination method, we need to eliminate one of the variables using addition or subtraction.
In this case, if we add both equations, we have that:
Since we obtained a FALSE result, we can say that this system of linear equations has NO SOLUTIONS.
In summary, using the elimination method, we add both equations. The result for that was a false r
[tex]6x - 9y - 7x + - 6y[/tex]simplify please
Answers
6x - 9y - 7x + -6y
To simplify the expression add the like terms
The like terms are the terms which have the same variable and same degree
6x, -7x are like terms
-9y, -6y are like terms
So let us add them
(6x + -7x) + (-9y + -6y)
6 + -7 = -1
6x + -7x = -x
-9 + - 6 = -15
-9y + -6y = -15y
(6x + -7x) + (-9y + -6y) = -x + -15y
Remember (+)
Rierda Elwynn Garvey takes home $1250 each month. In addition to other expenses, she also makepayments to her debt of $230 per month. What is her Debt Payments to Income Ratio?
Answers
The debt payments to income ratio is the amount that Rierda spend paying her debt each mount divided by her monthly income:
[tex]\text{Ratio}=\frac{230}{1250}=\frac{23}{125}=0.184[/tex]in a 30 60 90° triangle giving the short leg equals 5 find a hypotenuse of the triangle
Answers
To answer this question we need to remember that the longest and shortest side in any triangle are always opposite to the largest and smallest angle, respectively.
With this in mind we can draw the triangle:
Now, we need to find the hypotenuse. To do this we can use the cosine function for the angle 60. Remember that the cosine function is given as:
[tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex]In this case we have that:
[tex]\begin{gathered} \cos 60=\frac{5}{\text{hyp}} \\ \text{hyp}=\frac{5}{\cos 60} \\ \text{hyp}=10 \end{gathered}[/tex]Therefore the hypotenuse is 10.
Find the slope of the line defined by each pair of points.:( points :(-1,4). Points. (-1,-5)
Answers
Notice that the x coordinate of both points is the same, therefore the line is a vertical line.
Answer: The slope is undefined.
Solve x^2 - 3x - 10 = 0 by factoring. *Mark only one oval.O {-5,2}O (-2,-5)O {-2,5}○ {-10,1}
Answers
In order to solve this quadratic equation by factoring, we can do the following steps:
[tex]\begin{gathered} x^2-3x-10=0\\ \\ x^2-3x-5\cdot2=0\\ \\ x^2+2x-5x-5\cdot2=0\\ \\ x(x+2)-5(x+2)=0\\ \\ (x-5)(x+2)=0\\ \\ \begin{cases}x-5=0\rightarrow x=5 \\ x+2=0{\rightarrow x=-2}\end{cases} \end{gathered}[/tex]Therefore the solution is {-2, 5}. Correct option: third one.
Which equation is equivalent to StartRoot x EndRoot + 11 = 15?
Answers
Answer:
x+121=225
Step-by-step explanation:
√x+11=15
to find the equivalent let's square both sides
(√x)²+11²=15²
x+121=225
This answer is the only one that matches the question
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Lne segment AC and BD are parallel, what are the new endpoints of the line segments AC and BD if the parallel lines are reflected across the y-axis?
Answers
Given a point P = (x, y) a reflection P' alongside the y axis of that point follows the rule:
[tex]P=(x,y)\Rightarrow P^{\prime}=(-x,y)[/tex]We need to multiply the x coordinates of the points by (-1)
The cordinates of the points in the problem are:
A = (2, 5)
B = (2, 4)
C = (-5, 1)
D = (-5, 0)
Then the endpoints of the reflection over the y axis are:
A' = (-2, 5)
B' = (-2, 4)
C' = (5, 1)
D' = (5, 0)
Which is the second option.
Find the value of z that makes quadrilateral EFGH a parallelogram.2zz+10FEHGz=Submit
Answers
In a parallelogram opposite sides have the same length therefore, for figure EFGH to be a parallelogram we must have that:
[tex]GF=HE[/tex]Substituting we get:
[tex]z+10=2z[/tex]Now, we solve for "z". First, we subtract "z" from both sides:
[tex]\begin{gathered} z-z+10=2z-z \\ 10=z \end{gathered}[/tex]Therefore, the value of "z" is 10.
Solve the following compound inequalities. Use both a line graph and interval notation to write each solution set.
t+1-5 ort+1> 5
Answers
The value of the inequality expression given as t + 1 < -5 or t + 1 > 5 is (-oo, -6) u (4, oo)
How to determine the solution to the inequality?The inequality expression is given as
t + 1 < -5 or t + 1 > 5
Collect the like terms in the above expressions
So, we have
t < -5 - 1 or t > 5 - 1
Evaluate the like terms in the above expressions
So, we have
t < -6 or t > 4
Hence, the solution to the inequality is t < -6 or t > 4
Rewrite as an interval notation
(-oo, -6) u (4, oo)
See attachment of the number line
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Simplify. 3 6 4 2m n 4 6m Write your answer using only positive exponents. . X Х ?
Answers
we have the expression
[tex](\frac{2m^6n^4}{6m^4})^3[/tex][tex](\frac{2m^6n^4}{6m^4})^3=\frac{(2^3)(m^{(18)})(n^{(12)})}{(6^3)(m^{(12)})}[/tex]simplify
[tex]\frac{(8)(m^{(18-12)})(n^{(12)})}{216}=\frac{(m^6)(n^{(12)})}{27}[/tex]Lee Ann is planning a bridal shower for her best friend. At the party, she wants to serve 3 beverages, five appetizers, and three desserts, but she doesn't not have time to cook. She can choose from 9 bottle drinks, 9 Frozen appetizers, and 12 prepared desserts at the supermarket. How many different ways can lie and pick up the food and drinks to serve at the bridal shower?
Answers
2328480 ways
ExplanationWe want to find out how many ways there are to select an item. The combination formula is a formula to find the number of ways of picking "r" items from a total of "n" items.
This number is given by:
[tex]undefined[/tex]At a local market, 3 apples and 2 pears cost $2.70. Three apples cost the same as 4 pears. Type a system of equations to find the cost for one apple and the cost for one pear.
Answers
Data:
Apple: A
Pears: P
3A+2P=$2.70
3A=4P
to find the cost for one apple:
assume the rate of inflation is 7% per year for the next 2 years. what will be the cost of goods 2 years from now adjusted for inflation if the goods cost $330.00 today? round to the nearest cent
Answers
To find the cost of the goods after two years we are going to use the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where P is the cost now, r is the inglation rate in decimal form, n is the number of times the interest is taken per year and t is the time.
In this case we have P=$300.00, r=0.07, n=1 (once per year) and t=2 (two years). Plugging this values we have:
[tex]A=330(1+\frac{0.07}{1})^{1\cdot2}=377.82[/tex]Therefore after two years the cost will be $377.82
CRITICAL THINKING Describe two different sequences of transformations in which the blue figure is the image of the red figi 1 1 2 B I y ET
Answers
1) rotation 90° clockwise over the origin and a reflection over the x-axis
2) rotation 90° counter clockwise over the origin and reflection over y-axis
Simplify the expression.9n+ 18(2n-6)
Answers
The given expression is,
[tex]\begin{gathered} 9n+18(2n-6) \\ 9n+36n-108 \\ \\ 45n=108 \end{gathered}[/tex]Find the equation of the linear function represented by the table below in slope-intercept form.xy1-82-123-164-20
Answers
Given :
The table for y and x is given as
Explanation :
The slope-intercept form is determined as
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]First find the slope of the equation using the coordinates from the table.
[tex]m=\frac{-12-(-8)}{2-1}=\frac{-12+8}{1}=-4[/tex]Now substitute the values in the slope-intercept form.
[tex]\begin{gathered} y-(-8)=-4(x-1) \\ y+8=-4(x-1) \\ y=-4x+4-8 \\ y=-4x-4 \end{gathered}[/tex]Answer:
Hence the equation of line is determined as
[tex]y=-4x-4[/tex]Finding Slope
HELP ME PLS
Answers
The slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
The first point = (-5,6)
The second point = (-9,-6)
The slope of the line defined as the change in y coordinates with respect to the change in x coordinates.
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = [tex]\frac{-6-6}{-9-(-5)}[/tex]
= -12/-4
= 3
Hence, the slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
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hi, can you help me answer this question please, thank you!
Answers
The correct option is B
Explanation:The given statement shows that there is a 95% chance that the mean of a sample of 29 gadgets will be between 12.8 and 34.9
Solve 7x-2y = 17 for y
Answers
hello
the question here is an equation and we are asked to solve for y
we'll follow some steps here
[tex]7x-2y=17[/tex]step 1
take y to the left side of the equation and bring 17 to the right hand side of the equation
note: the sign changes once they cross equality sign
[tex]\begin{gathered} 7x-2y=17 \\ 7x-17=2y \end{gathered}[/tex]step 2
divide both sides by the coeffiecient of y which is 2
[tex]\begin{gathered} 2y=7x-17 \\ \frac{2y}{2}=\frac{7x-17}{2} \\ y=\frac{7x-17}{2} \end{gathered}[/tex]from the calculations above, the value of y = (7x - 17)/2
There are two points (-7,6) and (7,2) the upper part is a shaded circle the ordered pairs that are solutions to the inequality on the graph.This is the line -- - - - - - - -- - -- - - - - - - -- - - - - - --- - - - - - -You can use DESMOS(6,3)(-6,6)(5,0)(2,4)
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SOLUTION
Incomplete question
Choose the correct equation in point slope form for the line through the given points or through the given point with the given slope
Answers
Answer:
[tex]y-3=-1(x+2)[/tex]Explanation:
The point-slope form of the equation of a line is generally given as;
[tex]y-y_1=m(x-x_1)[/tex]where m = the slope of the line
y1 = y-coordinate of the one point
x1 = x-coordinate of the one point
Given the slope of the line as m = -1 and the point (-2, 3) where x1 = -2 and y1 = 3, let's go ahead and substitute these given values into the point-slope formula to obtain the required equation as seen below;
[tex]\begin{gathered} y-3=-1\lbrack x-(-2)\rbrack \\ y-3=-1(x+2) \end{gathered}[/tex]O EQUATIONS AND INEQUALITIESSolving a decimal word problem using a linear equation with th.
Answers
Given:
[tex]PlanA=0.16\text{ for each minutes of calls}[/tex][tex]PlanB=25\text{ monthly fee plus 0.12 for each minute of calls}[/tex]To Determine: The numbers of calls for the which the two plans are equal
Solution
Let x be the number of minutes of calls for which the two plans are equal
The cost of plan A is
[tex]C_{ost\text{ of plan A}}=0.16x[/tex]The cost of plan B
[tex]C_{ost\text{ of plan B}}=25+0.12x[/tex]If the cost for the two plans are equal, then
[tex]0.16x=25+0.12x[/tex]Solve for x
[tex]\begin{gathered} 0.16x-0.12x=25 \\ 0.04x=25 \\ x=\frac{25}{0.04} \\ x=625 \end{gathered}[/tex]Hence, the number of minutes of calls for which two plans are equal is 625 minutes
If f (x) = 4x^3 - 25x^2 – 154x+ 40 and (x - 10) is a factor, what are the remaining factors?
