Final answer:
Using the Pythagorean theorem, it is determined that the ladder reaches 12 feet up the side of the house when the base is placed 5 feet away.
Explanation:
To solve for the height at which the ladder reaches the house, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.
In this scenario, the ladder represents the hypotenuse (c), the distance from the base of the ladder to the house gives one leg of the triangle (a), and the height the ladder reaches up the side of the house is the other leg (b).
Let a = 5 ft (distance from the ladder's base to the house).Let c = 13 ft (length of the ladder).We need to find b (the height the ladder reaches the house).According to the Pythagorean theorem, a² + b² = c². Plugging in our known values allows us to solve for b²:
a² = 5² = 25.c² = 13² = 169.Subtract a² from c² to get b²: 169 - 25 = 144.Take the square root of b² to find b: √144 = 12.Therefore, the top of the ladder will be 12 feet above the ground.
vivien's handspan measure 18.5 centimeters.estimate the number of times Vivien uses her handspan to measure a length of 1 meter 75 centimeters
Final answer:
Vivien would use her handspan, which measures 18.5 centimeters, approximately 9 times to measure a length of 1 meter 75 centimeters. This estimate assumes precision in her handspan measurement.
Explanation:
To estimate the number of times Vivien uses her handspan to measure a length of 1 meter 75 centimeters, we need to divide the total length by the length of her handspan. Since Vivien's handspan measures 18.5 centimeters, and the total length to measure is 1 meter 75 centimeters (which equals 175 centimeters), we perform the following calculation:
Convert 1 meter 75 centimeters to all centimeters: 1 meter = 100 centimeters, so 1 meter 75 centimeters = 100 + 75 = 175 centimeters.Divide the total length by the length of Vivien's handspan: 175 cm/18.5 cm =9.45945945945946Round the result to the nearest whole number to estimate the number of handspans: approximately 9 times (since we typically round down when the decimal is less than 0.5).This is an estimation technique that assumes Vivien's measurement with her handspan is accurate. The accuracy of this measurement can vary based on several factors, including the precision of Vivien's handspan and the method used for measuring.
What is the area formula for a cylinder
Estimate the quotient of 239.63 ÷ 7.51
assume that y varies directly with x, then solve if y=12 when x=15, find x when y=21
and can someone explain to me how they got the answer because i got 16.8
Determine the exact value of cos (11pi/6)
The value of cos (11pi/6), is -sqrt(3)/2.
To determine the exact value of cos (11π/6), we first need to understand the trigonometric values at certain angles. In this case, 11π/6 radians is equivalent to 330 degrees. Using the unit circle, we know that at 330 degrees, cosine is equivalent to -√3 / 2.
List all subsets of the following set: {dog, cat, fish}
What number is equivalent to: 4 x 1,000,000,000 + 5 x 1,000,000 + 9 x 10,000 + 8 x 100 + 7 x 1?
A. 45,987
B. 459,871
C. 4,509,807
D. 4,005,090,807
Find the sum. 13(9−6m)+14(12m−8)
Final answer:
To solve the expression 13(9−6m)+14(12m−8), distribute the numbers and combine like terms to get the sum, which is 90m + 5.
Explanation:
To find the sum of the expression 13(9−6m)+14(12m−8), we need to distribute the numbers outside the parentheses across the terms inside the parentheses and then combine like terms.
Distribute the numbers:
13 × 9 = 117
13 × (−6m) = −78m
14 × 12m = 168m
14 × (−8) = −112
Now we combine like terms:
117 (−78m) + (168m − 112)
Simplifying this we get:
−78m + 168m = 90m
−112 + 117 = 5
So the sum is 90m + 5.
Maria would like to leave a tip (t) of at least 15% of her dinner bill (b). Which inequality best could be used to find the amount of the tip Maria would like to leave?
Beth created this design to cover a rip in her jacket. It took half an hour toplan the design and two and a quarter hours to cut and sew the frabric to the jacket. How much time did it take Beth to save her favorite jacket?
Rewrite the following equation in slope-intercept form. 19x − 20y = -13 Write your answer using integers, proper fractions, and improper fractions in simplest form.
Final answer:
To rewrite the equation 19x - 20y = -13 in slope-intercept form, you subtract 19x on both sides and then divide by -20 to isolate y. The resulting equation is y = (19/20)x + 13/20.
Explanation:
To rewrite the equation 19x - 20y = -13 in slope-intercept form, follow these steps:
Move 19x to the other side by subtracting it from both sides: -20y = -19x - 13
Divide by -20 to isolate y: y = (19/20)x + 13/20
Therefore, the equation in slope-intercept form is y = (19/20)x + 13/20.
Please help and for number 2
The answers are
1.362.24mm
2.20.55mm
3.181.12mm
4.41.1mm
A wire is stretched from the top of an 8 ft. pole to a bracket 5 ft. from the base of the pole. How long is the wire?
The length of the stretched wire is required.
The length of the wire is 9.43 feet.
Pythagoras theoremb = Length of the pole = 8 ft
a = Distance between bracket and base of pole = 5 ft
c = Length of wire
The two lengths form a right triangle.
From the Pythagoras theorem we have
[tex]c^2=a^2+b^2\\\Rightarrow c=\sqrt{a^2+b^2}\\\Rightarrow c=\sqrt{8^2+5^2}\\\Rightarrow c=9.43\ \text{feet}[/tex]
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If RS=59 AND ST=10x-31,find x
Answer: x=9
Step-by-step explanation:
In the given picture, we have a circle in which we have given two congruent arcs [tex]\overarc{RS}\text{ and }\overarc{TS}[/tex]
And [tex]\overline{RS}=59\text{ and }\overline{ST}=10x-31[/tex]
Since, we know that congruent arcs have congruent chords.
Therefore, [tex]\overline{RS}=\overline{ST}[/tex]
[tex]59=10x-31\\\\\Rightarrow\ 10x=59+31\\\\\Rightarrow 10x=90\\\\\Rightarrow x=\frac{90}{10}\\\\\Rightarrow x=9[/tex]
To solve the problem we must know the Chord's Equidistant From The Center Of A Circle Theorem.
Equidistance chordsIf two chords of a circle are equidistant from the center then they are congruent to each other and their corresponding arcs are also congruent.
The value of x is 9.
Given to usRS = 59,ST = 10x-31,In circle,Chord RS and chord ST are equidistant from the center. therefore,
RS = ST
[tex]59 = 10x-31\\ 59+31 = 10x\\ 90 = 10x\\\\ x= \dfrac{90}{10}\\\\ x= 9[/tex]
Hence, the value of x is 9.
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Leon works at a grocery store for $8 an hour. He also mows lawns for $10 an hour. He needs to earn at least $120 per week, but he does not want to work more than 20 hours per week. Use a system of inequalities to find a possible combination of hours he can work at the grocery store and mowing lawns in order to meet his goal.
Answer:
The data we have is:
He works for $8 an hour.
He mows lawns for $10 an hour.
He wants to work no more than 20 hours per week, and wants to hearn at least $120 week.
So if S is the number of hours he works in the store, and M is the number of hours that he mowns lawns, we have the inequalities:
S + M ≤ 20
S*$8 + M*$10 ≥ $120
So let's choose a possible solution:
Let's select M = 12 and S = 0
in this way, he worsk
0h + 12 h = 12 h that is less than 20 hours, and he wins:
0*$8 + 12*$10 = $120, which is the minimum amount of money that he wants to win.
and we have a lot of other possible solutions:
S= 1, M = 12
S = 2, M= 12.. and so on.
The population of a city in 2005 was 18000. By 2010, the city’s population had grown to 45,000. Economists have determined that the growth is exponential. If they are correct, what is the projected population for 2015?
Solution:
we are given that
The population of a city in 2005 was 18000.
By 2010, the city’s population had grown to 45,000.
Economists have determined that the growth is exponential.
As we know the exponential growth is defined by the relation
[tex]P=p_0e^{rt}\\ \\ \text{where P is the population at time t and initial population is } p_0\\[/tex]
Here we have [tex]p_0=18000, P=45000, t=5[/tex]
substitute these values we get
[tex]45000=18000e^{5r}\\ \\ r=0.183[/tex]
So we get
[tex]P(t)=18000e^{0.183t}[/tex]
So For population is 2015 substitute t=10
[tex]P(10)=18000e^{0.183*10}[/tex]
[tex]P(10)=112209.9598 [/tex]
The projected population for 2015 is 112210
four less than 5 times a number is equal to 6 more than 3 times a number
You have to formulate an equation for this problem.
Let x = the number asked in the problem
5x – 4 = 3x + 6
Solve the equation.
5x – 3x = 6 + 4
2x = 10
X = 5
Therefore, the number is 5.
Which angles are verticle? PLEASE HELP!!!
how about the grand opening at Frankie's Burger every fourth person gets a free Sunday how many Sunday's of the first 150 dinners will receive a free Sunday?
find the zeros x^2+5x-24
Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length, x, of its square base. Nathan uses the formula for the volume of a pyramid to determine the dimensions of the sculpture:
Here, a is the side length of the pyramid’s square base and h is its height.
If 162 cubic centimeters of clay were used to make the sculpture, the equation x3 +
x2 +
= 0 can be used to find that the length of the sculpture’s base is
centimeters.
The student needs to apply the formula for the volume of a pyramid, V = 1/3 * a² * h. Since the height is 3 cm less than the side length, this introduces a variable in the equation, (x - 3), to solve for x.
Explanation:The question relates to pyramid volume and the formulation of mathematical equations. First, it requires understanding that the volume of a pyramid is derived using the formula V = 1/3 * a² * h, where V is the volume, a is the length of the side of the square base, and h is the height of the pyramid. Since the height is stated as 3 cm less than the base (x), we can interpret this in the formula as h = x - 3.
Replacing these values in the volume formula gives us V = 1/3 * x² * (x-3). As the volume given is 162 cubic centimeters, this forms the equation: 162 = 1/3 * x² * (x-3). Simplifying this equation would provide the base length x in cm.
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Your supervisor has asked you to help build the raised platform for the food court. The base needs to be made of pairs of parallel lines. Select the parallel lines from the choices below.
Suppose one third of each of 5 same sized posters is covered with opaque paper.What fraction of the posters are Not covered by opaque paper?Explain how to use multiplication to find what part of the posters are not covered by opaque paper?
Final answer:
Two-thirds of each poster are not covered with opaque paper. Multiplying (2/3) by 5 gives us 10/3, which can be converted to 3 and 1/3, indicating that three whole posters plus one-third of another are not covered.
Explanation:
If one third of each of 5 same sized posters is covered with opaque paper, then two thirds of each poster are not covered. To find what fraction of the posters are not covered by opaque paper, you apply multiplication. You start with one poster: one-third covered means two-thirds are not covered. Represent this as 2/3. Since the question concerns 5 identical posters, you multiply the fraction of one poster (2/3) by the number of posters (5).
Mathematically, this looks like:
(2/3) × 5 = 10/3
However, 10/3 represents more than one whole, and it can be converted into a mixed number to represent the total unobstructed fraction of the posters. This is 3 and 1/3, meaning that in total, you have three whole posters and one-third of another poster not covered by opaque paper.
Use log2 3 =1.5850 and log2 2 =1 to approximate the value of the expression log2 2,304
solve for x. 4x+28° x+19° 3x+13°
For the following ,ignore leap year and assume that births on the 365 different days are equally likely.what is the probability that two people are born in the same day
The sum of the x-coordinates of the vertices of a triangle in the Cartesian plane equals 10. Find the sum of the x-coordinates of the midpoints of the sides of the triangle.
Mrs. Bowen told Mr. Bowen that there is no way he is way he is spending that much money on golf clubs. instead she wants to buy a new flat screen television for the living room. Walmart has a 55 inch ultra slim HDTV flat screen that is normally $1099.99 but its on sale for 42% off. The sales tax on the TV will be 6.5%. How much will the final price of the TV be?
Can you please explain how to do it?
an angle whose measure is 50 degrees is in standard position. in which quadrant does the terminal side of the angle fall?
A bag contains 9 marbles: 4 are green, 2 are red, and 3 are blue. Lisa chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that the first marble is red and the second is blue? Write your answer as a fraction in simplest form.