A ladder leans against a wall. The foot of the ladder is 8 feet from the wall, and the top of the ladder is pulled 1 foot away from the wall. How far will the top of the ladder slide down the wall? (HINT: Draw the coordinate axes and place the
ladder up against the y-axis.)
Answers
Using Pythagoras theorem, the top of the ladder will slide down the wall 1.64 ft
What length will the ladder slide down the wall?The ladder leaning against the wall forms a right-angled triangle of sides 8 ft and 6 ft.
The length of the ladder is y.
Using Pythagoras theorem:
[tex]y = \sqrt{8^{2} + 6^{2}} = 10 \:ft[/tex]
When the ladder is pulled 1 foot away from the wall, the new height, h the ladder rises up the wall is given below:
[tex]h = \sqrt{10^{2} - 9^{2}} = 4.36 \:ft[/tex]
The top of the ladder will slide 6 - 4.36 ft = 1.64 ft
In conclusion, the length the ladder will slide down is obtained using Pythagoras theorem.
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Related Questions
4 rows with circles and triangles, left to right. Row 1, circle, triangle, 2 circles, triangle. Row 2, triangle, circle, 2 triangles, circle, triangle. Row 3, circle, 2 triangles, circle, triangle. Row 4, triangle, 2 circles, 2 triangles. The ratio of the number of circles to the number of triangles in simplest form is . The number of circles that need to be added to make the ratio 1 : 1 is .
Answers
The ratio of circle to triangles is; 3:4 and the number of circles which should be added to make the ratio 1:1 is; 3.
What is the ratio of circles to triangles?It follows from the task content that the total number of circles and triangles in all 4 rows and can be counted and concluded as; 9 and 12 respectively.
Hence, the ratio of circles to triangles is 9 to 12 and in its simplest form is; 3:4.
However, to make the ratio 1:1, the number of circles and triangles must be equal. Hence, 3 circles must be added to make the ratio 1:1.
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Choose the graph of y = |x – 5| by translating the parent function.
Answers
Answer:
x y
3 2
4 1
5 0
6 1
7 2 (There is a line between the x and y that goes all the way down the numbers so they are seperated)
Step-by-step explanation
Answer:
esa respuesta está difícil pero si calculamos la creta de tu mamá con la semilla mía xrei que puede dar tu maldita madre
Could someone help me out?
Answers
What is limit?
Limit, can be defined as the every nearby the value of a variable for a function exists, is called limits|
⇒ [tex]\lim_{h \to0 \zero} 46x^11+32xh^3+6x^15h+23[/tex]
When putting h = 0
⇒ [tex]46x^11+23[/tex]
Thus, the value of a function of its limit is given by [tex]46x^11+23[/tex]
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answers
Answer:
(2^3t•2^t)/16 isn't a not equivalent
the data represented by the following stem-and-leaf plot range from to .
4|578
5|14
6|023
7|69
A. 45,76
B. 48,79
C. 45,79
D. 48,76
Answers
Considering the stem-and-leaf plot, the range of the data-set is given as follows:
C. 45,79
What is an stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
Considering the key format, the smallest value in this problem is 4|5 = 45, and the highest is 7|9 = 79, hence the range is given by:
C. 45,79
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What is the solution to the system of equations?
y= 2/3x + 3
X=-2
Answers
Answer:
(x, y) = (-2, 5/3)
Step-by-step explanation:
The system of equations is easily solved by substitution.
SolutionUsing the given value of x, substitute for x in the first equation to find y.
y = 2/3(-2) +3
y = -4/3 +9/3 = 5/3
The solution is (x, y) = (-2, 5/3).
PLS ANSWERS QUCIK THANK YOU
Answers
Answer:
394.13cm²
Step-by-step explanation:
Formula: The area of a circle is found by A = πr²
Given:
radius is 11.2cm (shown in circle)π = 3.142Plug in:
A = πr² → A = (3.142)(11.2)²
→ A = (3.142)(125.44)
→ A = 394.13248
"2 decimal places", round up to 394.13
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What is the value of x in the triangle?
Answers
The value of x in the right triangle is 4 units.
How to find the side of a right triangle?The side x of the right triangle can be found using trigonometric ratios.
Therefore,
sin 30° = opposite / hypotenuse
sin 30 = x / 8
1 / 2 = x /8
cross multiply
8 = 2x
divide both sides by 2
8 / 2 = 2x / 2
x = 4
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HELP! ASAP!
F is a right angle, and segment (a)(f), BG, and CH are all parallel. Use this information to explain why ∆AFD ~ ∆BGD ~∆CHD. Support your answer using a postulate or theorem.
Use the diagram to answer each part of the question
Answers
By the corresponding angles theorem,
∠AFG, ∠BGD, and ∠CHD are congruent∠BAF, ∠CBG, and ∠DCH are congruentThus, triangles AFD, BGD, and CHD are similar by AA.
Given the figure, triangles AFD, BGD, CGD are similar by Angle-Angle-Angle (AAA) criterion for the similarity.
The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.
In the given question,
∠F = ∠G = ∠H = 90°
Let ∠D = x°
In triangle CHD,
∠H = 90°
∠D = x°
∠C = 180 - 90 - x = (90-x)°
In triangle BGD,
∠G = 90°
∠D = x°
∠B = 180 - 90 - x = (90-x)°
In triangle AFD,
∠F = 90°
∠D = x°
∠A = 180 - 90 - x = (90-x)°
In triangle AFD and BGD and CHD,
∠A = ∠B = ∠C
∠F = ∠G = ∠H
∠D = ∠D =∠D
triangle AFD and BGD and CHD are similar.
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The graph of a system of inequalities is shown.
195
554-3-2-1
4
(5
-5-
-6
-7
-8
9
23 x
Which system is represented by the graph?
O
O
y> 2x
x+2y≤-8
y≥ 2x
x+2y<-8
y< 2x
x+2y²-8
y≤2x
x+2y>-8
Answers
Answer: Option (1)
Step-by-step explanation:
The line y = 2x is shaded above and is dotted, so it represents [tex]y > 2x[/tex].
This eliminates all the options except for option (1).
The graph of a system of inequalities is shown. The following system of inequations represents the graph:
y ≥ 2x;
x + 2y ≤ -8:
Inequality refers to a condition in which there's a lack of equivalency or aesthetics, frequently panning out in disparities or differences in chances, resources, treatment, or outcomes among individuals, groups, or associations. It encompasses various forms, including economic inequality, colonial inequality, and political inequality.
The blue region is on the left of the blue line of equation y = 2x so the region is represented by the line y ≥ 2x. The equality holds in this inequality as the region also includes the origin (0, 0).
The second option only has the inequality y ≥ 2x in its system of inequalities.
So, the correct answer is the second one. The system of inequation is
y ≥ 2x;
x + 2y ≤ -8:
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please help me with this math problem
will mark brainiest
Answers
Using the given exponential function, the age of the skull is 6,733 years old.
What is the exponential function for the skull's amount?It is given by:
[tex]N(t) = N(0)e^{-kt}[/tex]
In which:
N(0) is the initial amount.k is the decay rate.t is the time in years.In this problem, the parameters are given as follows:
N(t) = 0.51N(0), k = 0.0001.
Hence we solve for t to find the age.
[tex]N(t) = N(0)e^{-kt}[/tex]
[tex]0.51N(0) = N(0)e^{-0.0001t}[/tex]
[tex]e^{-0.0001t} = 0.51[/tex]
[tex]\ln{e^{-0.0001t}} = \ln{0.51}[/tex]
[tex]-0.0001t = \ln{0.51}[/tex]
[tex]t = -\frac{\ln{0.51}}{0.0001}[/tex]
t = 6,733 years old.
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Analyze and sketch the polynomial functions and complete the charts below. State the degree and sign of the leading coefficient of the polynomial functions. Determine the end behavior of the graph of the functions. For 5b, write the polynomial function as a product of linear factors (in factored form).
a. f(x) = –7(x + 2)^3(x – 1)^2(x – 3) Zeros Multiplicity Crosses/Touches
Degree Sign
End behavior
b. m(x) = x^3 – 4x^2
Factored form: m(x) =
Degree Zeros Multiplicity Crosses/Touches
Sign End behavior
Answers
See below for the properties of the functions
How to analyze the functions?The function f(x)
We have:
f(x) = –7(x + 2)^3(x – 1)^2(x – 3)
From the graph, we have the following features:
Leading coefficient: Negative, because -7 is negativeZeros: x = -2 at multiplicity = 3, x = 1 at multiplicity = 2 and x = 3 at multiplicity = 1Crosses = 2Touches = 3End behavior = [tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:-\infty \:[/tex]The function m(x)
We have:
m(x) = x^3 - 4x^2
Factor out x^2
m(x) = x^2(x - 4)
Factor out x
m(x) = x(x)(x - 4)
From the graph, we have the following features:
Leading coefficient: PositiveZeros: x = 0 at multiplicity = 2, x = 4 at multiplicity = 1Crosses = 1Touches = 1End behavior = [tex]\mathrm{as}\:x\to \:+\infty \:,\:m\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:m\left(x\right)\to \:-\infty \:[/tex]Read more about functions at:
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13. Find the perimeter.
Answers
3 + 8 + 5 + 4 + 4 + 4
2+3+8+5+4.
the physical orders 1500 flu injection and use 300 shots in september and 450 shots given in october and 665 given in november what percentage of flu vaccine remains
Answers
Answer:
7%
Step-by-step explanation:
1500 is 100%. We divide 300, 450, and 665 shots by 1500 to get their percentages, 20%, 30%, and 43.333333333333333333333333333%, rounded to 43%. We subtract all the percentages from 100 and we get 7 percent left! (If this is wrong, I am only 10 so don't judge me)
What type of number is √5? Choose all answers that apply:
A:Whole number
B:Integer
C:Rational
D:Irrational
Answers
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What type of number is [tex]\bf{\sqrt 5}?[/tex] Select all that apply
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Let's start by taking a look at all the four sets of numbers.
A: Whole number{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22...∞}The set is shown above. To be honest, this is an infinitely small part of the number set; the whole number set would take FOREVER to type ;)
B: Integers{∞...-2,-1,0,1,2,3,4,5,6,7,8,9...∞}Wow, this set starts at negative infinity and ends at positive infinity!
C: RationalThis set consists of all integers, decimals, and fractions.
D: IrrationalThat's where the desired number [tex]\bf{\sqrt{5}}[/tex] belongs!
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=The\;fourth\;option}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics \not1\theta l}}[/tex]
∞
Drag each label to the correct location on the chart. Not all labels will be used. Given: and are supplementary and are supplementary Prove: The two linear pairs and one supplementary angle with values of 1, 2, and 3 Statements Reasons 1. and are supplementary 1. given 2. and are supplementary 2. given 3. 3. congruent supplements theorem Complete the flow chart to show the proof. vertical angles theorem given congruent complements theorem congruent supplements theorem
Answers
Based on the Congruent Supplements Theorem, <1 = <3 are congruent, given that <1 and <2 and <2 and <3 are supplements.
What does the Congruent Supplements Theorem say?The Congruent Supplements Theorem shows that when two angles are considered to be supplements of a certain angle, then those two angles must be congruent.
Filling in the chart would therefore be:
<1 and <2 are
supplementary <1 = <3
GIVEN Congruent Supplements Theorem
<2 and <3 are
supplementary
GIVEN
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Which statements are true about exponential functions? Check all that apply.
The domain is all real numbers.
The range always includes negative numbers.
The graph has a horizontal asymptote at x = 0.
The input to an exponential function is the exponent:
The base represents the multiplicative rate of change.
Answers
The input to an exponential function is the exponent
The base represents the multiplicative rate of change
Answer:
edge 2023
Step-by-step explanation:
A D E (dudes above me right js making it easier)
If 2x/7 divided by 1=0 then what will be value of x is
Answers
The value of x = -3/2 .
What is an Equation ?An equation is a mathematical statement that relates unknown variable to constants to determine their value.
The equation given is
(2x+3 ) / 7 Divided by 1 = 0
2x +3 = 0
2x = -3
x = -3/2
Therefore the value of x = -3/2 .
The complete equation is
(2x+3)/7
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Jane evaluates x2-3x+5 for x=-2 below.
Step 1: (-2)²-3(-2)+5
Step 2: -4+6+5
=
Step 3: = 7
What, if any, was Jane's mistake?
Jane made no mistakes.
O Jane incorrectly evaluated (-2)² in step 2.
Jane incorrectly added the terms in step 3.
O Jane incorrectly substituted in x=-2 in step 1.
K
Answers
Answer: Jane incorrectly evaluated (-2)² in step 2.
Step-by-step explanation:
[tex](-2)^{2}=4[/tex], not -4.
NO LINKS!!!! What is the transformation of f (x)= x^3:
PART 4:
THIS IS NOT MULTIPLE CHOICE!!!!
10. f(x)= (x+5)^3
11. f(x)= (1/5x)^3
12. f(x)= (-x)^3
Answers
Answer:
10. Left 5
11. Horizontal stretch by a factor of 5
12. Horizontal reflection
Step-by-step explanation:
Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Identify the transformations that take the parent function to the given function.
Question 10
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(x+5)^3[/tex]
Comparing the parent function with the given function, we can see that 5 has been added to the x-value of the parent function.
Therefore, the transformation is:
[tex]f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}[/tex]
Question 11
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=\left(\dfrac{1}{5}x\right)^3[/tex]
Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by ¹/₅.
Therefore, the transformation is:
[tex]y=f\left(\dfrac{1}{5}x\right) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{\frac{1}{5}}[/tex][tex]\textsf{As }\dfrac{1}{\frac{1}{5}}=5 \implies \textsf{horizontal stretch by a factor of 5}[/tex]
Question 12
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(-x)^3[/tex]
Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by -1.
Therefore, the transformation is:
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
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5) Solve the simultaneous equations log(x+y)=0 Solve the simultaneous equations 2logx=log(y+1)
Answers
Answer:
(1,0)
Step-by-step explanation:
Since log (x+y) = 0 you should know x+y = 1
so y = (1-x)
then 2 logx = log (y+1)
log x^2 = log (1-x +1) = log (2-x)
x^2 = 2-x
x^2 + x-2 = 0
(x+2)(x-1) = 0 so x = -2 or +1
then y = 3 or 0
-2,3 and 1,0 since you cannot have a log of a negative number
the only answer is (1,0)
have someone who can can help me with this I need help
Answers
Answer is underlined
BD: 16.8+50.4= 67.2 mm
LM: 4-2.6= 1.4 cm
LM: 4-2.6= 1.4 cm
Kamar Spends of wis salary on School fees and 1/2 of the rematader on rent He spends 3/8 of the remainder on food and saves the rest . He he saves 25,000 shillings, what is his salary.
Answers
Answer:
37.170
Step-by-step explanation:
is hard to explain uwuFind RS.
A. 10
B. 9
C. 12
D. 5
Answers
Answer:
D. 5
Step-by-step explanation:
2x - 6 + 1 + x - 4 = 18
3x - 9 = 18
3x = 27
x = 9
RS = x - 4 = 9 - 4 = 5
Answer: D. 5
Brandon wants to ride his bicycle 21 miles this week. He has already ridden 6 miles. If he rides for 5 more days, write and solve an equation which can be used to determine xx, the average number of miles he would have to ride each day to meet his goal.
Answers
Answer:
Step-by-step explanation:
6 + 5X = 21
5X = 21-6 = 15
X = 15/5 = 3 miles per day on an average
Clasify each polynomial based on the number of terms it contains
Answers
Answer:
Monomial - one term
Binomial - two terms
Trinomial - three terms
Polynomial - any polynomial with more than three terms
Brainliest, please :)
solve equation -4m +5=3m-9
pls workings
Answers
Answer:
2
Step-by-step explanation:
- 4m + 5 = 3m - 9
3m - 9 = 5 - 4m
3m + 4m = 5 + 9
7m = 14
m = 14 / 7
m = 2
Which expression represents the distance Kelli traveled downstream?
0.1(x – 5)
0.1(x + 5)
Answers
The distance that Kelli can swim will be about 6.11 kilometers per hour.
How to calculate the distance?Here is the complete question:
Solve the equation x – 5 = 0.1(x + 5) for x. Round your answer to the nearest hundredth. Kelli can swim about km/hour.
To solve for x, you need to follow SADMEP. SADMEP is subtraction, addition, division, multiplication, exponents, and parentheses.
It follows the same rules as PEMDAS, but SADMEP is only used when solving algebraic equations.
x - 5 = 0.1(x + 5) (use the distributive property)
x - 5 = 0.1x + 0.5 (subtract 0.1x to both sides)
0.9x - 5 = 0.5 (add 5 to both sides)
0.9x = 5.5 (divide both sides by 0.9)
x = 6.11 km/hour.
Therefore, Kelli can swim about 6.11 kilometers per hour.
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Answer:
It's the first one for upstream and the other one for downstream
Step-by-step explanation:
Given that the Earth orbits the Sun with an orbital velocity of about 29.8 km/s and a radius of 1 AU, use the equation above to estimate the total mass in the solar system inside the orbit of the Earth. Is this similar to the mass of the Sun? Remember to convert units to S.I. units of meters, kilograms, and seconds before proceeding so that your answer is in kg.
Answers
Answer:
I would like to use lb if that's ok
If we approximate the function y=sin(x) with a0+a1 x a2 x^2 +a3 x^3, what is a0,a2,a2,a3?
Answers
The coefficients [tex]a_0,a_1,a_2,a_3[/tex] could be chosen to be the coefficients in the Maclaurin series of [tex]\sin(x)[/tex].
We have
[tex]y = \sin(x) \approx a_0 + a_1 x + a_2 x^2 + a_3 x^3 \\\\ \implies y(0) = 0 = a_0[/tex]
[tex]y' = \cos(x) \approx a_1 + 2a_2 x + 3a_3 x^2 \\\\ \implies y'(0) = 1 = a_1[/tex]
[tex]y'' = -\sin(x) \approx 2a_2 + 6a_3 x \\\\ \implies y''(0) = 0 = 2a_2[/tex]
[tex]y''' = -\cos(x) \approx 6a_3 \\\\ \implies y'''(0) = -1 = 6a_3[/tex]
It follows that [tex]a_0=0[/tex], [tex]a_1=1[/tex], [tex]a_2=0[/tex], and [tex]a_3 = -\frac16[/tex].