The exponential function will be y= -2(3)^x.
What are exponential functions?
An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Now,
Given points for exponential function are (2, –50), (4, –1250).
and exponential function is y=ab^x
To find a and b put points in the function
-50=ab^2 -->1
-1250=ab^4 --->2
From equation 1
a=-50/b^2
Put value of a into 2
-1250=-50/b^2*b^4
b^2=25
b=5
For b=5, a=-50/5^2=-2
Hence, a=-2
Therefore,
The exponential function will be y= -2*5^x.
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Si 10 obreros construyen un consultorio médico en 12 dias.¿Con cuántos obreros se hará la misma obra en 15 dias?
A total of 8 workers are required for a building time of 15 days.
How many workers are needed to complete a building?
In this problem we find a case of inverse relationship, in which the number of workers (n) is inversely proportional to building time (t), in hours. The situation is represented by following formulas:
n ∝ 1 / t
n = k / t
Where k is the proportionality ratio, which can be eliminated by building the following formula:
n₁ · t₁ = n₂ · t₂
If we know that n₁ = 10, t₁ = 12 and t₂ = 15, then the required number of workers is:
n₂ = n₁ · (t₁ / t₂)
n₂ = 10 · (12 / 15)
n₂ = 10 · (4 / 5)
n₂ = 8
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18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89
The requried, Multiplies(with switching factors.) area given below,
a.
693 x 83 = 57489
83 x 693 = 57489
The answer is 57489.
b.
910 x 45 = 40950
45 x 910 = 40950
The answer is 40950.
c.
38 x 84 = 3192
84 x 38 = 3192
The answer is 3192.
d.
409 x 89 = 36401
89 x 409 = 36401
The answer is 36401.
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Can anyone help me w tvis
The number of weeks that the puppies weigh the same amount will be A. 6 weeks.
The equation that has no solution is A. 13 - 7x = -7x + 13.
The option determined from the graph is B. The ordered pair (25, 6) is a solution to y = x + 40 and y = 3x + 15.
How to calculate the number of weeksPuppy A weighs 4 1/5 pounds at birth and gains 3/4 pound each week. Puppy B weighs 5 2/3pounds at birth and gains 1/2 pound each week.
After how many weeks will the puppies weigh the same amount will be calculated thus:
4 1/5 + 3/4x = 5 2/3 + 1/2x
4.2 + 0 75x = 5.67 + 0.5x
Collect the like terms
5.67 - 4.2 = 0.25x
Divide
x = 1.47 / 0.25
x = 6
Hence ,the number of weeks that the puppies weigh the same amount will be A. 6 weeks.
It should be noted that the equation that has no solution is A. 13 - 7x = -7x + 13. This is because the values gives 0 all through.
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Shirley Garcia is a restaurant supplies salesperson and receives 8% of her total sales as commission. Her sales totalled $15,000 during a given week. Find her commission.
Answer:
8% of $15,000 = .08 × $15,000 = $1,200
can u give an answer
Answer: 0
Step-by-step explanation:
Put 0 in the front box.
this is because you cant divide 11 apples equally into 6 people; 11 isn't a multiple of 6
A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be 99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
The sample size needed to be 99% confident that the sample proportion will not differ from the true proportion by more than 4% is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
[tex]\pi = 0.5[/tex]
Then the sample size for M = 0.04 is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]
n = 1037.
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Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?
possible answers -
By the cross product property, AB2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by AD.
By the cross product property, AB2 = BC multiplied by AD.
The correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:
By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].
To prove that [tex]BC^2 = AB^2 + AC^2[/tex], we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:
Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.
By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).
Using the proportionality of similar triangles, we can write the following ratio:
[tex]$\frac{AB}{BC} = \frac{AD}{AB}$[/tex]
Cross-multiplying, we get:
[tex]$AB^2 = BC \cdot AD$[/tex]
Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:
[tex]$\frac{AC}{BC} = \frac{AD}{AC}$[/tex]
Cross-multiplying, we have:
[tex]$AC^2 = BC \cdot AD$[/tex]
Now, we can substitute the derived expressions into the original equation:
[tex]$BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$[/tex]
It was made possible by cross-product property.
Therefore, the correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:
By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].
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What is the length of Arc LM? Use 3.14 as pi and round your answer to the nearest tenth. please show work, will mark brainliest.
To find the length of arc LM, we need to use the formula for the circumference of a circle:
C = 2πr
In this case, the arc LM is a portion of the circumference of the circle. To find the length of the arc, we need to determine the angle at the center of the circle that corresponds to the arc.
Looking at the image you provided, we can see that angle LOM is a right angle (90 degrees). The angle at the center of the circle, LOCM, is half of the right angle, which is 45 degrees.
To calculate the length of arc LM, we need to find the fraction of the total circumference represented by the central angle LOCM. The fraction is given by:
Fraction of circumference = Angle at center / 360 degrees
Fraction of circumference = 45 degrees / 360 degrees
Fraction of circumference = 1/8
Now, we can calculate the length of arc LM:
Length of arc LM = Fraction of circumference * Circumference
Length of arc LM = (1/8) * (2πr)
Since the radius (r) is not given in the image, we cannot calculate the exact length of arc LM. However, we can provide the formula for the length of arc LM in terms of the radius:
Length of arc LM = (1/8) * (2πr) = πr/4
So, the length of arc LM is πr/4, where r is the radius of the circle.
If you have the value of the radius, you can substitute it into the formula to find the specific length of arc LM.
Reacting with water in an acidic solution at a particular temperature, compound A decomposes into compounds B and C according to the law of uninhibited decay. An initial amount of 0.40 M of compound A decomposes to 0.37 M in 30 minutes. How much of compound A will remain after 2 hours? How long will it take until 0.10 M of compound A remains? After 2 hours, the amount of compound A remaining will be ? M. (Do not round until the final answer. Then round to thenearest hundredth as needed.)
The answers to all parts are shown below.
The law of uninhibited decay is a first-order chemical reaction, which means that the rate of the reaction is proportional to the concentration of compound A.
The rate law can be written as:
rate = k[A]
where k is the rate constant and [A] is the concentration of compound A.
From the given data, we can use the following equation to determine the rate constant:
ln([A]t/[A]0) = -kt
where [A]t is the concentration of compound A at time t, [A]0 is the initial concentration of compound A, k is the rate constant, and t is the time.
Using the given data:
[A]t = 0.37 M
[A]0 = 0.40 M
t = 30 minutes = 0.5 hours
ln(0.37/0.40) = -k(0.5)
k = 0.0486 h⁻¹
(a) How much of compound A will remain after 2 hours?
Using the same equation and substituting the known values:
ln([A]t/[A]0) = -kt
ln([A]t/0.40) = -0.0486 x 2
[A]t/0.40 = e⁻(⁹⁷² /¹⁰⁰⁰⁰)
[A]t = 0.25 M
Therefore, after 2 hours, 0.25 M of compound A will remain.
(b) How long will it take until 0.10 M of compound A remains?
Substituting the known values into the equation again:
ln([A]t/[A]0) = -kt
ln(0.10/0.40) = -0.0486t
t = 4.26 hours
Therefore, it will take approximately 4.26 hours until 0.10 M of compound A remains.
(c) After 2 hours, the amount of compound A remaining will be 0.25 M.
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When Grace opens and lays a shipping box out flat, she sees that the top and the bottom of the box
both measure 10 inches by 14 Inches, the sides of the box both measure 14 inches by 8 inches, and
the front and back of the box both measure 8 inches by 10 inches. What is the surface area of Grace's
strooing box?
The surface area of Grace's shipping box is 664 square inches.
We have,
The box can be divided into six rectangles, each of which represents the face of the box.
To find the surface area of the box, we need to find the area of each face and then add them all up.
The top and bottom of the box are both 10 inches by 14 inches, so the area of each of these faces is:
= 10 x 14
= 140 square inches
The sides of the box are both 14 inches by 8 inches, so the area of each of these faces is:
= 14 x 8
= 112 square inches
The front and back of the box are both 8 inches by 10 inches, so the area of each of these faces is:
8 x 10
= 80 square inches
To find the surface area of the whole box, we add up the areas of all six faces:
= 2(140) + 2(112) + 2(80)
= 280 + 224 + 160
= 664 square inches
Therefore,
The surface area of Grace's shipping box is 664 square inches.
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evaluate xy-y when x = 2 and y = 5
Answer:
5
Step-by-step explanation:
Just do as the problem says:
xy-y = (2)(5)-(5) = 10-5 = 5
Answer: 5
Step-by-step explanation: All you have to do is substitute x & y for their respective numbers. In this case, change x for 2 & y for 5, So xy-y becomes 2(5)-5, which equals 10-5, which is 5.
The EPA fuel economy estimates for automobiles models tested recently found them to be
normally distributed with a mean of 24.8 mpg and a standard deviation of 6.2 mpg. What is
the percentile rank of an automobile that has a fuel economy of 35 mpg?
90th Percentile
O 5th Percentile
O 95th Percentile
10th Percentile
Step-by-step explanation:
(35-24.8) / 6.2 = z-score of + 1.645 corresponding to .9495 =
~ 95th percentile
Please help with that question
The value of function f (α + β) is determined as (3√3 + 1)/3, (2√2 - 3)/3.
What is the value of function f (α + β)?The value of f (α + β) is calculated by applying the following formula as follows;
The given functions;
for α: x² + y² = 4
y is given as -1, the value of x is calculated as;
x² + (-1)² = 4
x² + 1 = 4
x² = 3
x = √3
α = (√3, - 1)
for β: x² + y² = 1
x is given as ¹/₃, the value of y is calculated as;
(¹/₃)² + y² = 1
¹/₉ + y² = 1
y² = 1 - ¹/₉
y² = ⁸/₉
y = √ (8/9)
y = 2√2/3
β = (¹/₃, 2√2/3)
The value of function f (α + β) is calculated as;
f(α + β) = (√3, - 1) + (¹/₃, 2√2/3)
f(α + β) = (3√3 + 1)/3, (2√2 - 3)/3
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100 Points! Algebra question. Photo attached. Sketch the angle. Then find its reference angle. Show your calculations. Thank you!
The reference angle of 13π/8 is 3π/8 and the sketch of the angle is attached
How to sketch the angle and find the reference angleFrom the question, we have the following parameters that can be used in our computation:
Angle = 13π/8
Rewrite as
θ = 13π/8
The above angle is in the fourth quadrant
So, we subtract it from 2π to calculate the reference angle
Using the above as a guide, we have the following:
Reference angle = 2π - 13π/8
Evaluate the difference
Reference angle = 3π/8
Hence, the reference angle is 3π/8 and the sketch of the angle is added as an attachment
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
A
Step-by-step explanation:
i do this all the time math is my thing
Groups 1 and 3 In a class of 42 students, 12 boys and 15 girls know how to read three-letter words in English. 19 boys and 17 girls know how to identify all letters of the alphabet. None of the students in the class can write a sentence of five words if dictated to them. There are 22 boys and 20 girls in the class.
•Using a Venn diagram, show how many boys and girls cannot read a letter or a three-letter word.
•If all students should know how to write a sentence of five words by the end of the academic year, how many groups will you need to form to focus on remedial/tutor support (to teach at the right level)?
• If by the end of the academic year, all students are able to identify all letters, read three-letter words, and write a five-word sentence, what would this Venn diagram look like?
There are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.
How to solveThe Venn diagram is drawn as shown in the attached image, and it shows that the number of boys and girls who cannot read a letter or a three-letter word is marked as (c+d) which represents 13 boys and 8 girls.
Given:
The class has 42 students.
12 boys and 15 girls are said to know how to read three-letter words in English.
19 boys and 17 girls are said to know how to identify all letters of the alphabet.
None of the students in the class is able to write a sentence of five words if dictated to them.
There are in total 22 boys and 20 girls in the class.
Read three-letter words |
|____________|______________|
| | |
| Boys (12) | Girls (15) | Can read three-letter words
|____________|______________|
| | |
| Boys (10) | Girls (13) | Cannot read three-letter words
_______|____________|______________|
| | |
| Boys (9) | Girls (13) | Can identify all letters
|____________|______________|
| | |
| Boys (13) | Girls (7) | Cannot identify all letters
|____________|______________|
To find the number of boys and girls who cannot read a letter or a three-letter word, we need to add up the numbers in the two bottom circles:
Boys who cannot read a letter or a three-letter word: 10 + 13 = 23
Girls who cannot read a letter or a three-letter word: 13 + 7 = 20
Therefore, there are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.
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How many 1/3 inch cubes does it take to fill a box with a width of 2 2/3 inches, length of 3 1/3 inches with a height 2 1/3
The number of 1/3 inch cubes required to fill the box is 62.
Volume of boxVolume = length × width × height
Height = 7/3
Length = 10/3
width = 8/3
Hence ,
Volume = 7/3 × 10/3 × 8/3 = 560/27
Size of cube = 1/3
Number of cubes required = Volume of box / size of cube
Number of cubes = 560/27 × 3/1
Number of cubes = 1680/27 = 62.22
Therefore, it will take 62 1/3 cubes to fill the box
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Help pleaseeeee guys
On performing , the "row-operation" 2R₁ + R₂ → R₂ on the matrix "M", the resulting new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex] .
The matrix "M" is given as : [tex]\left[\begin{array}{ccc}5&1&-5\\0&-2&2\end{array}\right][/tex],
We have to apply the Row-Operation : 2R₁ + R₂ → R₂, on the matrix "M",
Performing the row-operation "2R₁ + R₂ → R₂" on a matrix "M" means multiplying the first-row of "M" by 2, and then adding the resulting values to the second-row of "M" to produce a new value for each element in the second row.
This operation does not affect the first row of "M" and changes the values in the second row of "M".
⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\2\times5+0&2\times 1-2&2\times(-5)+2\end{array}\right][/tex],
⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10+0&2-2&-10+2\end{array}\right][/tex],
⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].
Therefore, the new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].
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What is an equation of the line that passes through the point
(
8
,
7
)
(8,−7) and is parallel to the line
x+2y=18?
100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!
Answer:
[tex]3 {cos}^{2} x - {sin}^{2} x = 0[/tex]
[tex]3 - 3 {sin}^{2} x - {sin}^{2} x = 0[/tex]
[tex]3 - 4 {sin}^{2} x = 0[/tex]
[tex]4 {sin}^{2} x = 3[/tex]
[tex] {sin}^{2} x = \frac{3}{4} [/tex]
sin(x) = +(1/2)√3
x = π/3 + 2kπ or x = 2π/3 + 2kπ
x = -π/3 + 2kπ or x = -2π/3 + 2kπ
(k is an integer)
I NEED YOUR HELP WITH STATISTICS
For a probability distribution to be represented, it is needed that P(X = 0) + P(X = 1) = 0.44. Hence one possible example is:
P(X = 0) = 0.40.
P(X = 1) = 0.04.
Discrete random variable to represent a probability distribution =
The sum of all the probabilities must be of 1, hence:
P(X = 0) + P(X = 1) + P(X = 3) + P(X = 4) + P(X = 5) = 1.
Then, considering the table:
P(X = 0) + P(X = 1) + 0.15 + 0.17 + 0.24 = 1
P(X = 0) + P(X = 1) + 0.56 = 1
P(X = 0) + P(X = 1) = 0.44.
Hence one possible value is:
P(X = 0) = 0.40.
P(X = 1) = 0.04.
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NO LINKS!!! URGENT HELP PLEASE!!!
The distance between Miami, Florida and Bermuda is about 1042 miles. The distance from Bermuda to San Juan. Puerto Rico is about 965 miles, and the distance from San Juan to Miami is about 1038 miles. Find the area of the triangle formed by the three locations.
Answer:
444523.45 square miles
Step-by-step explanation:
By using Heron's formula, we can easily find the area of the triangle formed by Miami, Bermuda, and San Juan, we need to use the lengths of the three sides of the triangle.
Let,
Side a: Distance from Miami to Bermuda = 1042 miles
Side b: Distance from Bermuda to San Juan = 965 miles
Side c: Distance from San Juan to Miami = 1038 miles
Now we can use Heron's formula to find the area of the triangle:
s =[tex]\frac{a+b+c}{2}[/tex]
s = [tex]\frac{1042 + 965 + 1038}{2}=1522.5[/tex] miles
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
A = [tex]\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}=444523.45[/tex]
Therefore, the area of the triangle formed by Miami, Bermuda, and San Juan is approximately 444523.45 square miles.
Answer:
444,523.45 square miles (2 d.p.)
Step-by-step explanation:
To find the area of a triangle formed by the locations of Miami, Bermuda, and San Juan, use Heron's formula.
[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]
Label the three sides of the triangle as 'a', 'b', and 'c', where 'a' is the distance from Miami to Bermuda (1042 miles), 'b' is the distance from Bermuda to San Juan (965 miles), and 'c' is the distance from San Juan to Miami (1038 miles):
a = 1042 milesb = 965 milesc = 1038 milesTo find the half perimeter, s, half the sum of the three side lengths:
[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{1042+965+1038}{2}=1522.5[/tex]
Substitute the values of a, b, c and s into Heron's formula and solve for area, A:
[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}\\&=\sqrt{1522.5(480.5)(557.5)(484.5)}\\&=444523.4468348...\\&=444523.45\; \sf miles^2\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the area of the triangle formed by the three locations is 444,523.45 square miles, to two decimal places.
if you walked 3 blocks north and then 8 blocks west and then 10 blocks south how far are you from your starting point it each block is 2/10 of a mile?
You are approximately 3.4 miles from your starting point.
We have,
To solve this problem, we need to use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.
|\
8 | \
| \
|___\
3
We can see that the three blocks north and 10 blocks south cancel each other out, so we only need to consider the 8 blocks west.
Using the distance formula, we can find that the distance traveled west is:
8 blocks × 2/10 mile per block = 1.6 miles
Now we can use the Pythagorean theorem to find the distance from the starting point:
distance = √(3² + 1.6²)
distance ≈ 3.4 miles
Therefore,
You are approximately 3.4 miles from your starting point.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
4x = 100, so x = 25
The correct answer is C.
please help me with this!
4 glue sticks cost $7.76.
which equation would help determine the cost of 13 glue sticks
choose 1 answer
A x/13 = 4/$7.76
B 13/x = $7.76/4
C 4/$7.76 = 13/x
D 13/4 = $7.76/x
E None of the above
Answer:
13 glue sticks cost $25.22.
Step-by-step explanation:
4 blue sticks cost $7.76, this means that one glue stick costs
$7.76/4 = $1.94.
Let be the cost of the glue sticks, and be the number of glue sticks; then
We can use this equation to find the cost of 13 glue sticks; we just put into our equation and it gives:
So 13 glue sticks cost $25.22.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each sine or cosine value to its equivalent measure
The equivalent sine and cosine values are as follows:
cos(74°) = sin(16°)cos(57°) = sin(33°)sin(32°) = cos(58°)sin(43°) = cos(47°)What is the relationship between sine and cosine angles?The relationship between sine and cosine angles is:
sinθ = cos(90 - θ)
This equation is known as the complementary angle identity for sine and cosine. It states that the sine of an angle is equal to the cosine of its complementary angle (90 degrees minus the original angle).
For example, if we have an angle theta = 30 degrees, its complementary angle would be 90 - 30 = 60 degrees.
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Can someone please answer and provide an explanation for these problems?
62. The slope of the line is 1/8. the equation of line is y = 1/8x - 3/8
63. It has an infinite slope. The equation of line is x = 3
64. The slope of the line is -5. The slope of the new line is 1/5. The equation of line is y = 1/5x - 1
65. The slope of the line is 2/9. The slope of the new line is -9/2. The equation of line is y = -9/2x - 4
How do we identify the slope and equation of line?62) through: (3,0), parallel to y = 1/8x - 3. If a line is parallel to another, they have the same slope. Therefore the slope is 1/8.
For line equation⇒ (y - y1 = m(x - x1))
Substituting (3,0) and slope 1/8 gives us:
(y = mx + b) ⇒ y - 0 = 1/8 × (x - 3)
First, substitute the point and the slope into the equation: 0 = 1/8×3 + b
Then solve for b, the y-intercept: b = -3/8
⇒ y = 1/8x - 3/8
63) through: (3,-1), parallel to x = 0. A line parallel to x = 0 is a vertical line. A vertical line has the equation x = a, where a is the x-coordinate of any point on the line. A line through (3, -1) and parallel to x = 0 would simply be x = 3 or y = -1
64) through: (5, 0), perp. to y= -5x - 4. If a line is perpendicular to another, their slopes are negative reciprocals. The slope of y = -5x - 4 is -5, so the slope of the line we are looking for is -1/(-5) = 1/5
65) through: (-2, 5), perp. to y=2/9x - 1. perpendicular line to y = 2/9x - 1 has the slope that is the negative reciprocal of 2/9, which is -9/2. y = -9/2x - 4.
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What is the surface area of a cone with radius 8 in. and slant height 9 in.?
The total surface area of the cone is 427.04 square inches.
What is the surface area of the cone?For a cone of radius R and slant height L, the total surface area is given by the formula:
S = π*R*L + π*R²
Where π = 3.14
In this case, we know that the radius of the cone is 8 inches, and the slant height of the cone is 9 inches.
Then the total surface area of the cone is:
S = 3.14*8in*9in + 3.14*(8in)²
S = 427.04 in²
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What do they mean and why please
Show that the points (2, 5), (5 , 2) and (6,6) are composites of a triangle
The slopes of the lines connecting all the points are distinct. Hence, they form a triangle.
Proof that 3 points form a triangleTo show that the points (2, 5), (5, 2), and (6, 6) form a triangle, we can calculate the slopes of the lines connecting these points. If the slopes are all distinct, then the points form a triangle.
Let's calculate the slopes:
The slope between (2, 5) and (5, 2):
m₁ = (y₂ - y₁) / (x₂ - x₁)
= (2 - 5) / (5 - 2)
= -3/3
= -1
The slope between (2, 5) and (6, 6):
m₂ = (y₂ - y₁) / (x₂ - x₁)
= (6 - 5) / (6 - 2)
= 1/4
The slope between (5, 2) and (6, 6):
m₃ = (y₂ - y₁) / (x₂ - x₁)
= (6 - 2) / (6 - 5)
= 4/1
= 4
Since the slopes of the lines connecting these points are all distinct (-1, 1/4, and 4), the points (2, 5), (5, 2), and (6, 6) form a triangle.
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