The ladder reaches 40 feet up the wall.
41 squared (1681) minus 9 squared (81) is 1600. 40 is the square root of 1600.
The required distance between the top of the ladder and the ground is 40 feet.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
We can use the Pythagorean theorem to solve this problem. Let's call the distance from the base of the ladder to the wall "x", and let's call the length of the ladder "y".
According to the problem statement, we know that the ladder is 41 feet long and that the base of the ladder is 9 feet from the base of the apartment building.
y = 41 feet
x = 9 feet
We can use the Pythagorean theorem to solve for the distance between the top of the ladder and the ground. The Pythagorean theorem tells us that:
y² = x² + z²
where "z" is the distance between the top of the ladder and the ground. Plugging in the values we know,
(41 feet)² = (9 feet)² + z²
1681 = 81 + z²
1600 = z²
z = 40 feet
Therefore, the distance between the top of the ladder and the ground is 40 feet.
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Of the 8 planets is our solar system, 4 are considered rocky. If a student randomly selects 1 of those 8 planets as topic for a report, what is the probability that the selected planet will be rocky
Answer:
50%
Step-by-step explanation:
He has a 4/8 that he picks a rocky and a 4/8 that he doesn't. That gives us 1/2 and 1/2. 1/2=0.5 0.5×100%=50%
2.5 lb equals how many cups
You can't really convert that becasue cups is a volume and pounds is a weight. If I have a cup of feathers and a cup of iron filings, then the iron filings will weigh much less than the feathers. A cup different items would not have the same weight - if you know what I mean.
1.) Write f(x) = x2 - 6x + 8 in vertex form
Answer:
f(x) = (x - 3)² - 1
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
Add/subtract ( half the coefficient of the x- term )² to x² - 6x
f(x) = x² + 2(- 3)x + 9 - 9 + 8
= (x - 3)² - 1
A student is asked to find the sum of 197+413 which expression can the student use to find the answer?
addition (+) expression the students used to find the answer.
Solution:
Given data: A student is asked to find the sum of 197 and 413.
Sum means adding two numbers or variables.
For addition, we use + symbol to add two numbers.
First add last digit of the numbers (7+3) = 10.
Put 0 in last and carry 1 to the next left digit top.
Add middle digits with carry over 1 (1 + 9 + 1) = 11
Put 1 and carry another 1 to the next left digit top.
Add first digit of the numbers with carry over 1 (1 + 1 + 4) = 6
Sum of 197 + 413 = 197 + 413
= 610
The addition image attached below.
Hence, addition (+) expression the students used to find the answer.
How many times does 9 go into 143
Answer:
143/9 = 15.89
Step-by-step explanation:
HELP!!! 12 points
1. In the figure, KJ and KL are opposite rays. <1 = <2 and KM bisects
2. Measure the angle and classify it as right, acute, or obtuse.
Answer:
1. m∠MKN = 41°
Step-by-step explanation:
1.
KM bisects so NKM and MKL are equal
2 (3x + 5) + 8x + 2 = 180 (straight angle)
6x + 10 + 8x + 2 = 180
6x + 8x = 180 - 10 - 2
14x = 168
x = 168/14
x = 12
3*12+5 = 41
m MKN = 41
In AABC, mZA=x, mZB = 2x +2, and
m_C= 3x +4. What is the value of x?
1) 29
2) 31
3) 59
4 61
Answer:
x = 29
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180
x + 2x + 2 + 3x + 4 = 180, that is
6x + 6 = 180 ( subtract 6 from both sides )
6x = 174 ( divide both sides by 6 )
x = 29
Rachel ordered early learning software for her daughter from an online retailer. Each item costs
$7.50, and there is a shipping fee of $7.50 for the entire order.
9. What is the cost of Rachel's order if she buys 7 items?
Answer:
60$
Step-by-step explanation:
Shipping is 7.50 and the 7 items are 52.5 total
The country of Sylvania has decided to reduce the number of its illiterate citizens by 3/5 each year. This year there are 9000 illiterate people in the country. Write a function that gives the number of illiterate people in Sylvania, P(t), t years from today. asking for khan
The function to calculate the number of illiterate people in Sylvania t years from today is P(t) = 9000 * (3/5)^t.
Explanation:To write a function that gives the number of illiterate people in Sylvania, P(t), t years from today, we can use the following formula:
P(t) = 9000 * (3/5)^t
This formula represents the reduction in the number of illiterate people by 3/5 each year. To calculate the number of illiterate people t years from today, we multiply the initial number of illiterate people (9000) by the reduction factor (3/5) raised to the power of t.
Answer: 9000( 1 - 3/5 ) ^t
The price of a movie ticket increased from $25 to $30 What does this mean about the new price?
Choose the correct answer below
O A. The new price is 80% of the old price because 25-30 s 8. or 80%
OB. The new price is 80% of the old price because the price decreases by 20%, which is subtracted from 100%
OC. The new price is 125% of the old price because the price increases by $5, which is multiplied by the original price 5x 25 = 125%
O D. The new price is 20% of the old price because the price increases by 55 and 55 is 20% of $25
OE. The new price is 120% of the old price because the price increases by 20%, which is added to 100%
O F. The new price is 750% of the old price because 25 x 30 = 750
The correct option will the new price is 120% of the old one because the price increases by 20%, which is added to 100%.
What is percent of change?Percent of change is determined by the difference between the two values divided by the orginal one, then multiplied by 100.
i.e. percent of change=(change in value/original value)*100
So according to the asked question,
old value of the shoes=$25
new value of the shoes=$30
change in value=30-25=$5
percent of change=((30-25)/25)*100=20%
hence price increases by 20%.
If the old price is 100 and price increases by 20% then new price will be 120.
So the new price is 120% of the old one.
in another way we can calculate that
old value*x%=new value
⇒old value*x/100=new value
⇒x=new value*100/old value=30*100/25=120%
Therefore the new price is 120% of the old one because the price increases by 20%, which is added to 100%.
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The vertical change between 2 points.
Answer:
what does it look like we need that
Step-by-step explanation:
Answer:
Rise
Step-by-step explanation:
The vertical change between two points is called the rise, and the horizontal change is called the run. Just think of the rise as your going up from the bottom to the top. And run as if you were just going from one side to the other.
A large wedding is organised.
one third if the guests choose beef.
five twelfths choose chicken.
69 of the guests choose vegetarian.
How many guests were at the wedding?
I need help please and thank you
4 5 6 7 8 9 10
TIME REMAINING
59:55
A mapping diagram showing a relation, using arrows, between input and output for the following ordered pairs: (negative 3, negative 9), (2, negative 6), (negative 5, 4), (1, 2), (6, 0).
What is the domain of the function shown in the mapping
Answer:
Step-by-step explanation:
(-3,-9) , (2,-6), (-5,4), (1,2), (6,0)
the domain is gonna be ur x values
so the domain of this function is [ -5,-3,1,2,6] <==
** the domain is ur x values and the range is ur y values
Answer: -1
Step-by-step explanation:
i just answered if off of edg.
Solve by elimination. 4x=14-3y 3x-3y=11
Solving by elimination...
4x=14-3y ---> 12x=42-9y
×3
3x-3y=11 ----> 12x-12y=44
×4
12x=42-9y
-(12x-12y=44)
--------------------
12y=-2-9y
21y=-2
y=-2/21
3x-3(-2/21)=11
3x+2/7=11
3x=10 5/7
x=25/7
Answer:
4x=14-3y 3x-3y=11
Step-by-step explanation:
Next in sequence 3, 9, 27, _?
Answer: +81
Explanation: To find the next term in the pattern, begin by studying the pattern. Here, notice that 3 x 3 is equal to 9 and 9 x 3 is equal to 27.
Continuing the same pattern, 27 x 3 is equal to 81.
So the next term in the pattern is +81.
Please help! An angle measuring 3.5 radians is equal to which of the angle measures given below? (Use 3.4 for pi). Check ALL that apply.
A) 630 degrees
B) 200.64 degrees
C) 200 degrees 38'24"
D) 210 degrees
The measure of the angle is;
200.64 degrees ⇒ B
200 degrees 38' 24" ⇒ C
Step-by-step explanation:
To convert the measure of an angle from degrees to radians or from radians to degrees use these rules
If the measure of the angle is x°, then multiply it by [tex]\frac{\pi }{180}[/tex] to find its measure in radiansIf the measure of the angle is x radians, then multiply it by [tex]\frac{180}{\pi }[/tex] to find its measure in degrees∵ The measure of an angle is 3.5 radians
- We need to change its measure to degree, use the 2nd rule
∵ π = 3.14
∴ Its measure in degree = [tex](3.5).(\frac{180}{3.14})[/tex]
∴ Its measure in degree = 200.64°
To find its measure in degree, minutes and seconds, multiply the number before decimal point by 60 to find the number of minutes
∵ 1° = 60'
∵ 0.64 × 60 = 38.4
- That means the number of minutes is 38
∵ 1' = 60"
∵ 0.4 × 60 = 24
- That means the number of seconds is 24
∴ The measure of the angle is 200° 38' 24"
The measure of the angle is;
200.64 degrees
200 degrees 38' 24"
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A cone with a radius of 6 cm and a height of 8 cm has the same volume as a cylinder with a height of 6 cm. What is the radius
of the cylinder?
A)4 cm
B)4 cm
C)6 cm
D) 8 cm
Answer:
The radius of the cylinder is 4 cm.
Step-by-step explanation:
Given:
radius of cone = 6 cm
height of the cone = 8 cm
height of cylinder = 6 cm
We need to find the radius of cylinder.
Solution:
First we will find the volume of cone.
Volume of cone is one third time square of radius times height times π.
framing in equation form we get;
Volume of cone = [tex]\frac{1}{3}\pi r^2h = \frac{1}{3}\pi\times 6^2\times 8 \approx 301.44 \ cm^3[/tex]
Now Volume of cylinder is given by square of radius times height times π.
framing in equation form we get;
Volume of cylinder = [tex]\pi r^2h=18.84r^2[/tex]
Now it has been given that;
Volume of cone is equal to Volume of cylinder.
so we can say that
[tex]18.84r^2=301.44[/tex]
Dividing both side by 18.84 we get;
[tex]\frac{18.84r^2}{18.84}=\frac{301.84}{18.84}\\\\r^2\approx16[/tex]
Taking square root on both side we get;
[tex]\sqrt{r^2}=\sqrt{16} \\\\r=4\ cm[/tex]
Hence the radius of the cylinder is 4 cm.
Ronnie's dog eats 1/2 of a pound of food each day. Ronnie has a bag containing 4 1/2 pounds of dog food. How many days will the bag feed Ronnie's dog?
A middle class family with two working parent receives $100,000 annually. About 40% is withheld (taken out of their paycheck for income tax and retirement plan). What is this family monthly income after the 40% is taken off?
Answer:
$60,000
Step-by-step explanation:
100,000 / 10 = 10,000, 10- 4=6, 10,000 * 6 = 60,000
To determine the monthly income of a family after 40% is withheld from a $100,000 annual income, subtract the amount withheld ($40,000) from the annual income and divide by 12, yielding a monthly income of $5,000.
To calculate the monthly income after taxes for the family, we first need to determine the amount withheld from the annual income for taxes and retirement plans. With an annual income of $100,000 and 40% being withheld, we do the following calculation:
Amount withheld: $100,000 times 0.40 = $40,000After-tax annual income: $100,000 - $40,000 = $60,000Monthly income after tax: $60,000 / 12 months = $5,000Therefore, the family's monthly income after the 40% is taken off would be $5,000.
Are 4(3y-2) and 12y-8 equivalent
Answer:
Yes! 4(3y-2)=12y-8
Answer:
yes 4(3y - 2) = (12y - 8)
Step-by-step explanation:
because if you should expand 4(3y - 2) by multiplying each value within the bracket by 4, you will have 12y - 8
Given ΔFGH ~ ΔLMN, which must be true? Select all that apply.
A. FGLM=FHLN
B. FH ~ LN
C. m∠Fm∠L=m∠Gm∠M
D. GH≅MN
E. m∠H≅m∠N
In similar triangles ΔFGH and ΔLMN, only the corresponding angles are congruent (thus ∠H ≅ ∠N). The sides are proportionate, not necessarily congruent. Other listed options are either incorrect or unclear due to potential misinterpretations or typographical errors.
Explanation:Given that triangles ΔFGH and ΔLMN are similar (ΔFGH ~ ΔLMN), the following must be true based on the concept of similar triangles:
The corresponding angles are congruent, which means that ∠F ≅ ∠L, ∠G ≅ ∠M, and ∠H ≅ ∠N (option E). The corresponding sides are proportionate, meaning that the ratio of corresponding sides (FG/LM, GH/MN, and FH/LN) are equal. However, this doesn't mean that the corresponding sides are congruent. Hence option D is not necessarily true. Option B implies that lines FH and LN are similar, which is not a concept in geometry. Hence it's incorrect. Option A is incorrect because it seems to imply congruence of some unspecified aspect of the triangles, which is not a guaranteed condition under triangle similarity. Option C's meaning is unclear due to potential typographical error or misinterpretation.Learn more about Similar Triangles here:
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25 points. Math question
Answer:
-8
Step-by-step explanation:
I believe it is -8
first you 2(-2) - 4
then you -4 -4= -8
Hope that was helpful.
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]f(x) = 2x - 4 \\ f( - 2) = {?} \\ \\ x = - 2 \\ \\ f( - 2) = 2( - 2) - 4 \\ f( - 2) = - 4 - 4 \\ f( - 2) = - 8[/tex]
=> The answer is -8.
What is this percent of change, i'm confused? 1/4 to 1/8
Answer:
Step-by-step explanation:
Percent change= (1/4-1/8)/1/4 × 100%
= {(2 -1)/8} ÷ 1/4 × 100%
= (1/8 ÷ 1/4) × 100%
= 1/8 × 4/1 × 100%
=1/2 × 100%
= 50%
It is 50% change
Answer:
I believe the answer is 50%.
1/4 x 1/2 = 0.125
125/1000
125/1000 <-- divide numerator and denominator by 125
the above fraction simplifies to 1/8
So, one 1/4 is double the value of one 1/8
Changing all of the values in a data set in the same way is called transmitting
the data.
O A. True
O B. False
Answer:
It’s FALSE
Step-by-step explanation:
Can I get a check to see if these are right please?
The domain is all possible values for x.
Here we can see a parabola the goes sideways.
The vertex of the parabola is at (3,-1).
That means the domain is [tex]x\geq 3[/tex]
Think about it this way, is there any point on the parabola that can have a x coordinate of 4?
The range of a function is all possible y values. Is seems that the parabola stretches infinitely up and down, meaning that all values of y are possible.
Solve y=4x+8x for x
Answer:
x = y/12
Step-by-step explanation:
This figure is made up of a rectangle and parallelogram.
What is the area of this figure?
Enter your answer in the box. Do not round any side lengths.
The area of the figure is 40 units. (rounded off from 39.998 units)
Step-by-step explanation:
1. Area of the figure = Area of Rectangle + Area of Parallelogram.
2. Naming points:
Let the rectangle consist of points A(-6,-1), B(-5,-5), C(3,-3) and D(2,1).
Let the parallelogram consist of points C(3,-3), D(2,1), E(2,7) and F(3,3).
3. Each coordinate has a point on the x-axis and a point on the y-axis. We shall refer to these points as x', x'' ,x''' and so on corresponding to the x-axis values of A, B, C and so on in that order till F. For the y-axis points, we will name them in the series of y', y'', y''' and so on.
In simple words, in A(-6,1), x' = -6; y' = -1
4. Formula for finding area:
Area of a rectangle = length (l) × width (w)
Area of a parallelogram = base (b) x height (h)
5. Finding area of the rectangle:
l = AD = [tex]\sqrt{[x'''' - x']^{2} - [y'''' - y']^{2}}[/tex]
, i.e. AD = [tex]\sqrt{[2 - (-6)]^{2} - [1 - (-1)]^{2}}[/tex]
, i.e. AD = √68 = 8.246 (rounded to 3 decimals) = l
Now, w = AB = [tex]\sqrt{[x'' - x']^{2} - [y'' - y']^{2}}[/tex]
, i.e. AB = [tex]\sqrt{[(-5) - (-6)]^{2} - [(-5) - (-1)]^{2}}[/tex]
, i.e. AB = √17 = 4.123 (rounded to 3 decimals) = w
Area of rectangle = l x w = 8.246 x 4.123 = 33.998 units.
6. Finding area of the parallelogram:
b = DE = 6 units (we can observe this from the graph, i.e. points from 1 to 7 on the y axis)
h = Height is the line drawn perpendicular to the base from point F, which as we can see is 1 unit long.
Hence, Area of parallelogram = b x h = 6 x 1 = 6 units.
7. Now, adding both, we can arrive at the final answer.
Area of the figure = Area of rectangle + Area of parallelogram,
i.e. 33.998 units + 6 units = 39.998 units. (can be rounded off to 40 units)
Odette plants basil from seed and each day measures the height of the plants compared to the soil line. She records her measurements in a scatter plot. Odette calculates the equation of the least squares regression line: Predicted Height = 0.32 • Days in Soil – 1.72 Use the drop-down menus to complete the statements below about what this linear model tells you about the height of a basil plant.
Answer:
The slope of the least squares regression line is:
0.32
The units of the slope of the line are:
centimeters per day.
The slope of the line tells you that for each new day you can predict that a plant's height will increase by about 0.32 centimeters.
The y-intercept of the least square regression line is:
-1.72
The units of the y-intercept of the line are:
centimeters.
The y intercept:
Typical height compared to the soil line.
Step-by-step explanation:
What is y =x-2
Y=4x+1
Answer:
According to my calculations, the answer is (x, y)= ( -1, -3 ). In other words, x= -1 and y= -3
Step-by-step explanation: