In rectangle ABCD shown below, CD = 24 and m angle ABD = 35º. Determine the length of diagonal line BD to the nearest tenth. Show the work that leads to your answer.
Answers
Answer:
BD = 29.3
Step-by-step explanation:
Each half of the rectangle is a right triangle.
The diagonal is the hypotenuse of each right triangle.
Let's focus on right triangle ABD
Reference angle = m<ABD = 35°
AB = CD = 24
Adjacent length = AB = 24
Diagonal = Hypotenuse = BD
To find BD, apply CAH:
Cos 35° = Adj/Hyp
Substitute
Cos 35° = 24/BD
BD × Cos 35° = 24
BD = 24/Cos 35°
BD = 29.3 (nearest tenth)
Related Questions
determin 16x - 4y + 2 = 0
Answers
Answer:
16inches is your answer
17. Omar has a piece of rope. He ties a knot in the rope and measures the new length of the rope.
He then repeats this process several times. Some of the data collected are listed in the table
below.
Number of Knots
Length of Rope
(cm)
4 5 6 7 8
64 58 52 46 40
State, the linear equation that gives the length, y, of the rope after tying x knots.
Answers
Answer:
Step-by-step explanation: If I is intial height (y=I-6x) because Height = intial height + numbrt of knots -6 becuase as shown in the table every knot takes away 6 cm.
The linear equation that represents the length of the rope (y) after tying 'x' knots is: y = f(x) = 88 - 6x
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, 'A' is a coefficient and 'B' is constant".
Here, the number of knots are x = 4, 5, 6, 7, 8.
The length of the rope remains after each knots y = 64, 58, 52, 46, 40.
After tying 5th knot, the length of the rope decreases
= (64 - 58) cm
= 6 cm
After tying 6th knot, the length of the rope decreases
= (58 - 52) cm
= 6 cm
After tying 7th knot, the length of the rope decreases
= (52 - 46) cm
= 6 cm
After tying 5th knot, the length of the rope decreases
= (46 - 40) cm
= 6 cm
Initial length of the rope was = (64 + 4 × 6) cm = 88 cm
With the increase in value of 'x' by 1, the value of 'y' decreases by 6.
Therefore, the required equation: y = f(x) = 88 - 6x
Learn more about a linear equation here: https://brainly.com/question/3269317
#SPJ2
Determine the measure of
CD
from the diagram below.
Answers
Answer:
m(arc CD) = 112°
Step-by-step explanation:
Use the property of intersecting chords and angles between these chords,
m∠CED = [tex]\frac{1}{2}(\text{arc CD}+\text{arc}AB)[/tex]
m∠CED + m∠AED = 180°
80° + m∠CED = 180°
m∠CED = 100°
Now substitute the measure of angle CED and arc AB in the expression,
100° = [tex]\frac{1}{2}(88^{\circ}+\text{arc CD})[/tex]
200° = 88° + m(arc CD)
m(arc CD) = 112°
A family is planning to sell their home. If they want to be left with $116,100 after paying 10% of the selling price to a realtor as a commission, for how much must they sell the house?
Answers
The will need to sell for 116100 / 90 x 100 = $129000
The selling price is $129000
What is selling price?The selling price of an item is the price at which it is sold.
Given that 10% of selling price is the commission.
So the family gets 90% of the selling price, which is given as $116,100.
i.e (90/100) * Selling Price = 116100
Therefore, the selling price is (116100*100)/90 = 129000.
Hence, the family sell the house for the price of $129,000
To learn more about selling price, use the link given below:
https://brainly.com/question/28017453
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Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed. Using weight as the explanatory variable, what is the slope of a line between these two points? Answer choices are rounded to the nearest hundredth.
a. $0.13 / Ib.
b. $4.00 / Ib
c. $6.25 / Ib.
d. $7.75 / Ib.
Answers
Answer:
a. $0.13 / Ib.
Step-by-step explanation:
Slope of a line:
Suppose we have two data-points in a line. The slope is given by the change in the output divided by the change in the output.
In this question:
Input: weight(in pounds)
Output: Weekly cost to feed.
A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed.
Inputs: 0.5, 62.5
Outputs: 2, 10
Change in the outputs: 10 - 2 = 8
Change in the inputs: 62.5 - 0.5 = 62
Slope: [tex]m = \frac{8}{62} = 0.13[/tex]
So the correct answer is given by option A.
Answer:
0.13
Step-by-step explanation:
Trigonometry help please? I need the three answers
Answers
Answer:
Both triangles are triangle rectangles, but the triangles are not similar.
Step-by-step explanation:
By the Pythagorean's theorem, we know that for a triangle rectangle the sum of the squares of the cathetus is equal to the square of the hypotenuse.
Where the cathetus are always the two sides of smaller length.
We also know that two figures are similar if all the correspondent sides are proportional to each other, this means that the figures have the same shape but different size.
First, for triangle A the measures of the sides are:
48, 55, 73
Here the two catheti are 48 and 55, and the hypotenuse is 73.
Then to answer the first question we need to try to apply the Pythagorean's theorem, we should have:
48^2 + 55^2 = 73^2
solving that we get:
5,329 = 5,329
This is true, thus triangle A is a triangle rectangle.
Now for triangle B the measures are: 36, 77 and 85.
So the catheti are 36 and 77, and the hypotenuse is 85
So to check if triangle B is a triangle rectangle the equation:
36^2 + 77^2 = 85^2
must be true, solving both sides we get:
7,225 = 7,225
This is true, so triangle B is a triangle rectangle.
Finally, to check if the figures are similar we need to compare the correspondent sides of both triangles, such that the quotient of correspondent sides must be always the same.
For the hypotenuses, if we compute:
(hypotenuse B)/(Hypotenuse A) we get:
85/73 = 1.16
Now if we do the same for the two smaller catheti we get:
36/48 = 0.75
The quotients are different, thus the triangles are not similar.
G.1.- Una Recta contiene los puntos (-3,7)
y (9,-5) Calcule la ecuación de la recta en la
FORma y=mxtb. Explicar los pasos
Answers
Given:
A line passes through the points (-3,7) and (9,-5).
To find:
The equation of the line in the form of [tex]y=mx+b[/tex].
Solution:
If a line passes through two points, then the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
A line passes through the points (-3,7) and (9,-5). So, the equation of the given line is:
[tex]y-7=\dfrac{-5-7}{9-(-3)}(x-(-3))[/tex]
[tex]y-7=\dfrac{-5-7}{9+3}(x+3)[/tex]
[tex]y-7=\dfrac{-12}{12}(x+3)[/tex]
[tex]y-7=-1(x+3)[/tex]
On further simplification, we get
[tex]y-7=-x-3[/tex]
[tex]y-7+7=-x-3+7[/tex]
[tex]y=-x+4[/tex]
Therefore, the equation of the required line is [tex]y=-x+4[/tex].
Inscribe a circle in a unit square and to r= 1000 random.
a. Suppose that 760 of those darts land in the circle.
b. What would our estimate be if we let n â oo and we applied the same ratio strategy?
Answers
Step-by-step explanation:
area of square = 1
area of a circle in square = [tex]\pi r^2 = \pi *(1/2)^2 = \frac{\pi }{4}[/tex]
bu estimate [tex]p^ = X/n = 760/1000 = 0.76
Therefore,
[tex]\frac{\pi }{4} \approx 0.76[/tex]
[tex]\pi \approx 0.76*4 =3.04[/tex]
b) if n tend to infinity
[tex]\pi will approach 3.14[/tex]
Answer:
uvfhmfa
Step-by-step explanation:
Anyone knows what the answer for this is I am really confused on it
Answers
Suppose a group of 12 students consists of five freshmen and seven sophomores. How many six-student teams can be chosen that consist of three freshmen and three sophomores? Give your answer as an integer.
Answers
Answer:
350
Step-by-step explanation:
help me find answer i need answer please hlep
Answers
Answer:
7
Step-by-step explanation:
This is correct answer bro...
Answer:
7
Step-by-step explanation:
So first off, two numbers that are to the same root can be combined.
In this case we can combine these two values, since they are to the 5th root and are both 7:
[tex]\sqrt[5]{7*7^4}[/tex]
=
[tex]\sqrt[5]{49^4}[/tex]
This can be broken down into 7^2
This gets us [tex]\sqrt[5]{7^5}[/tex]
Remember that we add exponents, together, so in this case it adds up to 5.
You might be wondering...well if its 7^2 and 7^4, wouldnt it be 7^6?
Well, remember this. One of the 7s in 7^2 is from the 7^4, so tecnically it is 7^3 + 7^2, which is 7^5
Anyway, now we have:
[tex]\sqrt[5]{7^5}[/tex]
When you root a exponent, it works like subtraction.
In this case we have a exponent of 5, and a root of 5.
This is 5-5 = 0
So it will just be 7. Because the square and root cancel each other out, leaving us with 7.
Hope this helps!
Also, I just watched you waste someone elses answer so you could ask your own question. Instead of wasting other peopes answers, message me on one of my questions or answers, I will help you for free. :D
If C(-2, 4) and D(-6, -1), then what is the length of CD? Round to the nearest tenth.
Answers
9514 1404 393
Answer:
6.4
Step-by-step explanation:
The length is found from the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((-6 -(-2))² +(-1-4)²) = √((-4)² +(-5)²) = √(16 +25) = √41
d ≈ 6.4
Answer:
6.4Step-by-step explanation:
hope it helps
#GAUTHMATH8a+6ab+5b,-6a-ab-8b and - 4a+2ab+3b
Pls answer this question
Answers
Answer:
4 a+8 ab+8b
Step-by-step explanation:
8 a-4 a+6ab+2ab+5 b+3 b
4 a+8 ab+8b
Can somebody help me? I feel like this is wrong
Answers
Which I got was y=-1/3x+5
I really hope that helps and my deepest apologies if my answer turned out wrong!!
y= -0.3x +5
Consider x1= 9
Y1=2
x2= 0
y2 = 5
Slope is
m = 3 / -9 = 1 / -3 = -0.33333
The entered points belong to a decreasing, linear function.
Equation: y = -0.33333x + 5.
m = 3 / -9 = 1 / -3 = -0.33333
How much is 12,856 ounces in pounds ?
Answers
There are 16 ounces in a pound, so just divide 12,856 by 16, giving you 803.5.
The mean price for a 2,000sq foot home in FL is $240,000 with a Standard Deviation of $16,000. The mean price of the same sized home in OH is $170,000 with a standard deviation of $12,000. Which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?
Find the z score for each state.
Answers
Answer:
The z-score for a home priced at $200,000 in Florida is of -2.5.
The z-score for a home priced at $200,000 in Ohio is of 2.5.
The closeness to the mean is measured by the absolute z-score(disconsidering the signal, the lower the score, the closer to the mean). However, in this case, both z-scores have the same absolute value, so in both Florida and Ohio a home priced at $200,000 is equally close to the mean.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean price for a 2,000sq foot home in FL is $240,000 with a Standard Deviation of $16,000. Home of $200,000.
This means that [tex]\mu = 240, \sigma = 16, X = 200[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200 - 240}{16}[/tex]
[tex]Z = -2.5[/tex]
The z-score for a home priced at $200,000 in Florida is of -2.5.
The mean price of the same sized home in OH is $170,000 with a standard deviation of $12,000. Home of $200,000.
This means that [tex]\mu = 170, \sigma = 12, X = 200[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200 - 170}{12}[/tex]
[tex]Z = 2.5[/tex]
The z-score for a home priced at $200,000 in Ohio is of 2.5.
Which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?
The closeness to the mean is measured by the absolute z-score(disconsidering the signal, the lower the score, the closer to the mean). However, in this case, both z-scores have the same absolute value, so in both Florida and Ohio a home priced at $200,000 is equally close to the mean.
Show number that 0.245 is Rational number
Answers
Answer:
A rational number is one that may be represented in the manner p/q.
245/1000 = 0.245
Step-by-step explanation:
What is the value of x in the equation 1/5x-2/3y = 30, when y = 15
Answers
Answer:
x=200
Step-by-step explanation:
(1/5)x-(2/3)y=30, y=15
(1/5)x-(2/3)*15=30
(1/5)x=40
x=200
A system of equations is shown below:
y = 3x − 7
y = 2x + 1
What is the solution to the system of equations?
(8, 17)
(−8, 17)
(−8, −17)
(8, −17)
Answers
Answer:
(8, 17)
Step-by-step explanation:
y= 3x -7 -----(1)
y= 2x +1 -----(2)
Substitute (1) into (2):
3x -7= 2x +1
Being x terms to one side, constant to the other:
3x -2x= 7 +1
x= 8
Substitute x= 8 into (2):
y= 2(8) +1
y= 16 +1
y= 17
∴ The solution is (8, 17).
Find the equation of the exponential function represented by the table below:
х
y
03
1
1
9
2 27
3
81
Answers
Answer:
$53.07
Step-by-step explanation:
Delta Math
A) work out the value of g.
Give your answer in standard form correct to three significant figures.
B) work out the new value of g. Give your answer in standard form correct to 3 significant figures. (M is increased by 8% and T is increased by 5%).
Answers
Answer:
4547.14
Step-by-step explanation:
m increased by %8 so it'll be
[tex]6.588 \times {10}^{ - 5} [/tex]
and t will be
[tex]1.785 \times {10}^{ - 6} [/tex]
so G =
[tex] \sqrt{ \frac{(6.588 \times {10}^{ - 5}) }{ {(1.785 \times {10}^{ - 6}) }^{2} } } [/tex]
G= 4547
solve 4(8-2x)=2(7-x)
Answers
Answer and Step-by-step explanation:
Solve for x.
First, we divide both sides of the equation by 2.
2(8 - 2x) = 7 - x
Distribute the 2.
16 - 4x = 7 - x
Add 4x to and subtract 7 from both sides of the equation.
9 = 3x
Divide by 3 to both sides of the equation.
x = 3 <-- This is the answer.
#teamtrees #PAW (Plant And Water)
Answer:
x = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
4(8 - 2x) = 2(7 - x)
Step 2: Solve for x
[Division Property of Equality] Divide 2 on both sides: 2(8 - 2x) = 7 - x[Distributive Property] Distribute 2: 16 - 4x = 7 - x[Addition Property of Equality] Add x on both sides: 16 - 3x = 7[Subtraction Property of Equality] Subtract 16 on both sides: -3x = -9[Division Property of Equality] Divide -3 on both sides: x = 3Find the slope and recept of the line Y=7/5x-3
Answers
Answer:
The slope 7/5 and the y intercept is -3
Step-by-step explanation:
Y=7/5x-3
This equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope 7/5 and the y intercept is -3
Which of the following is the graph of f(x)=║x║translated 2 units right, 2 units up, and dilated by a factor of 1/3?
Answers
Answer:
c on edge2021
Step-by-step explanation:
In a circle with a radius of 7.7, an angle intercepts an arc of length 29.6
Find the angle in radians, to the nearest tenth
Answers
9514 1404 393
Answer:
3.8 radians
Step-by-step explanation:
The length of an arc is given by ...
s = rθ . . . . . where r is the radius and θ is in radians
so the angle is ...
θ = s/r
θ = 29.6/7.7 ≈ 3.8
The angle is about 3.8 radians.
Help me please with this math problem
Answers
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
[tex](5x-14)+(8x+12)=180[/tex]
These two angles on the line is 180°
Solve the equation:
[tex]5x-14+8x+12=180[/tex]
[tex]5x+-14+8x+12=180[/tex]
[tex](5x+8x)+(-14+12)=180[/tex] {combine the like terms}
[tex]13x-2=180[/tex]
[tex]13x=180+2[/tex]
[tex]13x=182[/tex]
[tex]x=182/13[/tex]
[tex]x=14[/tex]
PROOF:
{substitute 14 in the place of x}
[tex](5(14)-14)+(8(14)+12)=180[/tex]
[tex]56+124=180[/tex]
[tex]180=180[/tex]
hope this helps....
Use identities to simplify
Answers
(B)
Explanation:
[tex](\sec \beta + 1)(\tan \beta \csc \beta - 1)[/tex]
[tex]=\left(\dfrac{1}{\cos\beta} + 1 \right) \left(\dfrac{\sin \beta}{\cos \beta} \dfrac{1}{\sin \beta} - 1 \right)[/tex]
[tex]=\left(\dfrac{1}{\cos\beta} + 1 \right) \left(\dfrac{1}{\cos \beta} - 1 \right)[/tex]
[tex]= \left(\dfrac{1}{\cos^2 \beta} - 1 \right)[/tex]
[tex]= \left(\dfrac{1 - \cos^2 \beta}{\cos^2 \beta} \right)[/tex]
[tex]= \dfrac{\sin^2 \beta}{\cos^2 \beta}[/tex]
[tex]= \tan^2 \beta[/tex]
25^2 6^3 find prime factorization
Answers
Answer:
With Exponents: 32 × 7 × 401
Without Exponents: 3 × 3 × 7 × 401
Step-by-step explanation:
Hello,
[tex]25^2*6^3\\\\=(5^2)^2*(2*3)^3\\\\=\boxed{2^3*3^3*5^4}\\[/tex]
the distance between Johannesburg and bloemfontein is estimated at 435km. if they travel at an average speed of 120km per hour,how long will it take them to travel from Johannesburg to bloemfontein? give answer in hours ,minutes and seconds
Answers
Answer:
3.625h,217.5min,13050sec
Step-by-step explanation:
S=vt
t=S/v
t=435/120 (km) /(km/h) =3.625h
t= 3.625*60 min = 217.5 min
t=217.5*60sec = 13050 sec
Answer:
t= 3.625 gio 217.5 phút = 13.050 giây
Step-by-step explanation:
s= vt
t=s/v
t= 435/120= 3.625 gio
t= 3.625*60=217.5 phút
t= 217.5*60 = 13.050 giây
When the demand for a good is highly elastic with respect to price, how should a producer want to increase revenue?
Answers
Answer:
When the demand for a good is highly elastic, the producer can increase revenue by reducing the price slightly.
Explanation:
Prices can either be Elastic, Inelastic, or Unitary.
The assumption is that the scenario in the question is in a perfect market. A perfect market is one where there are numerous buyers and sellers and there is little or no gap in information about market conditions such as cost of input, prices of the competition, etc.
When the demand for a product is elastic, it means that it is sensitive to changes in price. Price Elasticity is in degrees. When the demand for a product is highly elastic, it means that small changes in price lead to even greater changes in demand.
So for the producer to increase revenue in the short run (all things being equal) all they need to do is reduce the price slightly. This will increase revenue because it most likely will translate to a more than proportionate increase in quantity demanded.
Recall that markets are dynamic and the most predictable reaction of the other producers to this move will be an equal or even greater reduction in price in order to win back lost customers. Hence to sustainably maintain this position The producer will have to ensure that their product is sufficiently differentiated with unique value additions that are impossible or difficult to replicate.
Cheers