Using the unitary method we calculate that the friend would be 20 miles closer in an hour.
If you are running towards a faraway friend at a speed of 5 miles per hour and she is biking towards you at 15 miles per hour, According to relative motion's concept, the total speed at which you are approaching each other is:
5 miles / hour - (- 15 miles / hour) = 20 miles / hour
Also, we know that
speed= distance/time according to which, after 1 hour, you and your friend would have closed the distance by,
20 miles/hour × 1 hour = 20 miles
Therefore, you would be 20 miles closer to each other after 1 hour.
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What is the value of the expression?
1/2 ÷ 6
Answer:
0.25
Step-by-step explanation:
Answer:
1/12
Step-by-step explanation:
To solve this expression, we need to remember that division should be done before multiplication or addition/subtraction.
So we first simplify the expression by dividing 1/2 by 6:
1/2 ÷ 6 = 1/2 × 1/6
Next, we multiply the two fractions by multiplying their numerators and denominators:
1/2 × 1/6 = (1 × 1)/(2 × 6) = 1/12
Therefore, the value of the expression 1/2 ÷ 6 is equal to 1/12.
What is the sum of the following equation? (2 points)
three tenths plus thirty-nine hundredths equal blank
A. thirty-six hundredths
B. forty-two hundredths
C. sixty-nine hundredths
D. ninety-six hundredths
Answer:
sixty nine hundredths
Step-by-step explanation:
three tenths can be expressed in decimal as 3/10
thirty nine hundredths can be expressed in decimal as 39/100
Therefore the sum of three tenths plus thirty nine hundredths equals
3/10 +39/100
We first find the l.c.m of the two fractions equals 100 so we have 100 as the denominator
then 100 divided by 10 multiplied by 3 +100 divided by 100 multiplied by 39 as illustrated below gives the answer
3/10 +39/100
=30+39/100
=69/100= sixty nine hundredths
Will make you brainlist!
Answer:
x = -2 , y = 2
Step-by-step explanation:
label your equations (1) and (2) the question mention to use elimination method and make x the same for both. To do that multiply equation (1) by 2. than label it (3)so 3x becomes 6x adding the equation (2)+(3) cancels out -6x and 6x so you can find value of yuse value of y to find xhope this helps :)
Elena is testing out a new studying method and wants to know if it works. She decides to compare her spelling test scores from last week and this week. On last week's test, Elena spelled 16 out of the 20 words correctly. On this week's test, she spelled 13 out of the 15 words correctly. On which test did Elena get a higher ratio of correctly spelled words to total words?
Answer:
To determine which test Elena got a higher ratio of correctly spelled words to total words, we need to calculate the ratio of correctly spelled words to total words for each test and compare them.
For last week's test, the ratio of correctly spelled words to total words is:
16/20 = 0.8
For this week's test, the ratio of correctly spelled words to total words is:
13/15 ≈ 0.867
Since 0.867 is greater than 0.8, Elena got a higher ratio of correctly spelled words to total words on this week's test. Therefore, the new studying method appears to be working better for Elena. However, it is important to note that a single comparison is not sufficient to draw a definitive conclusion about the effectiveness of the studying method, and it would be beneficial for Elena to continue tracking her performance over a longer period of time.
Please help me please it would be very appreciated.
the equation of the quadratic function that is moved to the left three, up four, and stretched by a scale factor of two is [tex]y = 2(x + 3)^2 + 4.[/tex]
What is quadratic equation?
A quadratic equation is a type of polynomial equation of degree two, meaning it contains one or more terms that involve x raised to the power of two (i.e., x²
The equation of a quadratic function is generally given by:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola and "a" determines the shape of the parabola.
To move the function to the left by three units, we need to replace "x" with "(x + 3)" inside the parentheses:
[tex]y = a(x + 3 - h)^2 + k[/tex]
To move the function up by four units, we need to add four to the value of "k":
[tex]y = a(x + 3 - h)^2 + (k + 4)[/tex]
To stretch the function by a scale factor of two, we need to multiply "a" by two:
[tex]y = 2a(x + 3 - h)^2 + 2(k + 4)[/tex]
Combining these transformations, we get the final equation:
[tex]y = 2(x + 3 - 0)^2 + (0 + 4)[/tex]
[tex]y = 2(x + 3)^2 + 4[/tex]
Therefore, the equation of the quadratic function that is moved to the left three, up four, and stretched by a scale factor of two is [tex]y = 2(x + 3)^2 + 4.[/tex]
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Draw and label the height of each parallelogram.
Based on the image given, the height of the parallelogram can be expressed as 2 units.
What is the height of a parallelogram?Parallelograms are two-dimensional figures that include four sides as rectangles. However, in parallelograms, the opposite sides are parallel and the vertical or horizontal sides are diagonal. Due to this, the height in a parallelogram can be determined by measuring the distance between the top and bottom lines. Based on this principle, the height of the parallelogram would be 2.
Note: Below I attach the missing image in this question:
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f(x)=3x^2+12+11 in vertex form
Answer:
y = -3(x - 2)^2 + 1. Explanation: x-coordinate of vertex: x = -b/(2a) = -12/-6 = 2 y-coordintae of vertex: y(2) = -12 + 24 - 11 = 1
Step-by-step explanation:
Answer:x-coordinate of vertex:
x = -b/(2a) = -12/-6 = 2
y-coordinate of vertex:
y(2) = -12 + 24 - 11 = 1
Vertex form:
y = -3(x - 2)^2 + 1
Check.
Develop y to get back to standard form:
y = -3(x^2 - 4x + 4) + 1 = -3x^2 + 12x - 11.
Step-by-step explanation:
10340000000 in standard form
Answer:
1034 x 10⁷
Step-by-step explanation:
the seven just means to multiply by 10 seven times
Let me know if this helps.
Amir and Brandon are sharing a cake they bought for 10 dollars. Half of
the cake is chocolate and half of the cake is vanilla. Amir likes chocolate
twice as much as vanilla. Brandon likes chocolate four times as much as
vanilla. They decide to use the divider-chooser method to share the cake. (a) Give a way Amir might split the cake if he’s the splitter. State which
piece Brandon would choose and how much it’s worth to him. (b) Give a way Brandon might split the cake if he’s the splitter. State
which piece Amir would choose and how much it’s worth to him
(a) If Amir is the splitter, he can divide the cake into two equal halves, offer Brandon the first choice, who will likely choose the chocolate half worth 6.67 dollars to him, and Amir will take the vanilla half worth 3.33 dollars to him.
(b) If Brandon is the splitter, he can divide the cake into two equal halves, offer Amir the first choice, who will likely choose the chocolate half worth 5 dollars to him, and Brandon will take the vanilla half worth 5 dollars to him.
(a) If Amir is the splitter, he can divide the cake into two equal halves, one chocolate and one vanilla. He can then offer Brandon the first choice of which half he wants. Since Brandon likes chocolate four times as much as vanilla, he will likely choose the chocolate half, which is worth 6.67 dollars to him (4/5 of the total value of the cake). Amir will then take the vanilla half, which is worth 3.33 dollars to him (1/5 of the total value of the cake).
(b) If Brandon is the splitter, he can divide the cake into two equal halves, one chocolate and one vanilla. He can then offer Amir the first choice of which half he wants. Since Amir likes chocolate twice as much as vanilla, he will likely choose the chocolate half, which is worth 5 dollars to him (1/2 of the total value of the cake). Brandon will then take the vanilla half, which is worth 5 dollars to him (1/2 of the total value of the cake)
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The amount of daily daylight is unrelated to levels of depression in older adults. What type of hypothesis is this?
a) Null hypothesis
b) Alternative hypothesis
b) Research hypothesis
d) Nonsignificant hypothesis
The amount of daily daylight is unrelated to levels of depression in older adults. The hypothesis "The amount of daily daylight is unrelated to levels of depression in older adults" is an example of the null hypothesis.
A null hypothesis is a statement that there is no significant difference between two variables or a relationship between them.The null hypothesis assumes that the observed results or changes in the experiment or data are due to random fluctuations or errors in the measurement process. It is the default hypothesis that is typically tested against an alternative hypothesis.
A researcher tries to disprove or reject the null hypothesis by conducting experiments or collecting data to support the alternative hypothesis. If the null hypothesis is rejected, then the alternative hypothesis is accepted as true. However, if the null hypothesis cannot be rejected, then it remains as the plausible explanation for the observations or outcomes in the experiment.
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Select the interval where
h
(
x
)
>
0
h(x)>0h, left parenthesis, x, right parenthesis, is greater than, 0.
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
−
1
<
x
<
0
−1
The correct statement regarding where the graph of h(x) = x³ has positive signal is given as follows:
x > 0.
How to classify a function as positive or negative?The graph of a function is positive in the regions where the function values are greater than zero, and negative in the regions where the function values are less than zero.
The comparisons to zero are given as follows:
Greater than zero -> above the x-axis.Less than zero -> Below the x-axis.Hence, considering the function defined by the rule y = x³, the graph of the function is classified as positive or negative as follows:
Negative for x < 0.Positive for x > 0.Missing InformationThe function is h(x) = x³, and it's graph is given by the image presented at the end of the answer.
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45/43 as a percentage rounded to the nearest tenth of a percent
Answer:
104.7% to the nearest tenth.
Step-by-step explanation:
Multiply the fraction by 100:
= (45 x 100) / 43
= 104.651.
Transaction ID
Items
1
Bread, Milk
2
Bread, Diaper, Beer, Eggs
3
Milk, Diaper, Beer, Coke
4
Bread, Milk, Diaper, Beer
5
Bread, Milk, Diaper, Coke
6
Bread, Coke, Eggs
7
Beer, Coke
8
Beer, Milk, Bread, Diaper, Eggs
9
Eggs, Diaper
10
Diaper, Beer
Calculate the support, Confidence, and Lift for each of the following rules
Please show work.
3
Rule:
Support
Confidence
Lift
1)
{Bread} -> {Milk}
2)
{Beer} -> {Eggs}
3)
{Beer, Bread} -> {Milk}
4)
{Bread, Eggs} -> {Diapers}
5)
{Milk, Bread} -> {Eggs, Coke}
6)
{Beer, Milk} -> {Bread, Diapers}
7)
{Bread, Milk, Eggs} -> {Diapers}
8)
{Bread, Eggs, Coke} -> {Diapers, Beer}
Confidence in math is the belief in one's ability to understand and solve mathematical problems. Developing confidence in math is important because it can help individuals overcome anxiety and fear of math, which can limit their performance and success in the subject.
1) {Bread} -> {Milk}:
Support: 5/10
Confidence: 5/7
Lift: 5/2.4
2) {Beer} -> {Eggs}:
Support: 4/10
Confidence: 4/9
Lift: 4/3
3) {Beer, Bread} -> {Milk}:
Support: 3/10
Confidence: 3/6
Lift: 3/1.8
4) {Bread, Eggs} -> {Diapers}:
Support: 4/10
Confidence: 4/7
Lift: 4/2.6
5) {Milk, Bread} -> {Eggs, Coke}:
Support: 4/10
Confidence: 4/7
Lift: 4/2.6
6) {Beer, Milk} -> {Bread, Diapers}:
Support: 3/10
Confidence: 3/6
Lift: 3/1.8
7) {Bread, Milk, Eggs} -> {Diapers}:
Support: 2/10
Confidence: 2/5
Lift: 2/2.2
8) {Bread, Eggs, Coke} -> {Diapers, Beer}:
Support: 2/10
Confidence: 2/5
Lift: 2/2.2
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Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
The discount percentage is different, the amount that Lisa pays will also be different.
What exactly is the discounted method?The act of estimating the present value of a future payment or series of cash flows that will be received in the future is referred to as discounting. A discount rate (also known as a discount yield) is the rate at which future cash flows are discounted back to their present value.
We need to know what percentage of the regular ticket price Lisa saves with her railcard. We cannot calculate the exact amount Lisa pays for the ticket without this information.
Assuming Lisa receives a 1/3 discount with her railcard, we can calculate the cost of her ticket as follows:
Discounted price = Regular price minus discount amount
Normal price x Discount percentage = Discount amount
Discount rate = 1/3 = 33.33% (rounded to two decimal places)
Discount amount = £24.90 multiplied by 33.33% = £8.30 (rounded to two decimal places)
Price after discount = £24.90 - £8.30 = £16.60 (rounded to two decimal places)
As a result, if Lisa receives a 1/3 discount with her railcard, she will pay£16.60 for the ticket. However, if the discount percentage is different, Lisa's payment will be different as well.
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Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
Can some one solve this and show their work please
Answer:
m = 2n = 7Step-by-step explanation:
we solve with two equations between the corresponding sides
9m = 7m + 4
9m - 7m = 4
2m = 4
m = 2
----------------------------------
check
9 x 2 = 7 x 2 + 4
18 = 18
this answer is good
n + 6 = 2n - 1
n + 7 = 2n
7 = n
-----------------------------------
7 + 6 = 2 x 7 - 1
13 = 13
this answer is good
The exponential probability distribution is used with: A. A discrete random variable B. A continuous random variable C. Any probability distribution with an exponential term D. An approximation of the binomial probability distribution
The exponential probability distribution is employed with a random variable that is continuous in nature.
What do you mean by exponential probability distribution ?
In the field of probability, a probability distribution refers to a mathematical function that gives the probabilities of various possible outcomes of an experiment. The exponential probability distribution is a probability distribution that models the time between events in a Poisson process, where events occur continuously and independently at a constant average rate. It is a continuous probability distribution, meaning that the random variable takes on values within a continuous range, as opposed to a discrete probability distribution, where the random variable takes on only a finite or countable set of values.
Explanation of the correct answer :
The exponential probability distribution is defined by a single parameter, [tex]\lambda[/tex] which represents the average rate of occurrence of events in the Poisson process.
The probability density function (pdf) of the exponential distribution is given by [tex]f(x) = \lambda e^{(-\lambda x)}[/tex], where x is the time between events. The cumulative distribution function (cdf) is given by [tex]F(x) = 1 - e^{-\lambda x}[/tex].
The exponential probability distribution is used in many applications, such as queuing theory, reliability theory, and finance. For example, it can be used to model the time between customer arrivals in a queue, the time between machine failures in a manufacturing process, or the time until default on a bond.
In summary, the exponential probability distribution is a continuous probability distribution that is used with a continuous random variable, specifically to model the time between events in a Poisson process.
Hence, option B is correct.
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You ride your bicycle 40 meters. How many complete revolutions does the front wheel make?
What’s the area of 5feet 12feet and 13feet, using 4(bxh)
The area of 5feet 12feet and 13feet, 30 square feet
Area calculation.the formula 4(bxh) is used to calculate the area of a rectangle, not a triangle. However, the dimensions 5 feet, 12 feet, and 13 feet are actually the sides of a right triangle (known as a Pythagorean triple), so we can use the formula for the area of a right triangle:
Area = 1/2 x base x height
where the base and height are the two legs of the right triangle.
Using the Pythagorean theorem, we can determine that the legs of the triangle are 5 feet and 12 feet, and the hypotenuse is 13 feet. Therefore, the area of the triangle is:
Area = 1/2 x 5 feet x 12 feet
Area = 30 square feet
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The measure of an angle is 40.6°. What is the measure of its supplementary angle?
Answer: 139.4
Step-by-step explanation:
a supplementary angle is equal to 180 so all we have to do is subtract 40.6 from 180
180 - 40.6 = 139.4
linear equations in one variable
Answer:
x = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
[tex]\frac{x+1}{3}[/tex] - [tex]\frac{x-1}{2}[/tex] = [tex]\frac{1+2x}{3}[/tex]
multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions
2(x + 1) - 3(x - 1) = 2(1 + 2x) ← distribute parenthesis on both sides
2x + 2 - 3x + 3 = 2 + 4x
- x + 5 = 2 + 4x ( subtract 4x from both sides )
- 5x + 5 = 2 ( subtract 5 from both sides )
- 5x = - 3 ( divide both sides by - 5 )
x = [tex]\frac{-3}{-5}[/tex] = [tex]\frac{3}{5}[/tex]
three fair, standard six-faced dice of different colors are rolled. in how many ways can the dice be rolled such that the sum of the numbers rolled is 10? (mathematics teacher calendar problem)
There are a total of 27 combinations that give a sum of 10 when rolling three dice.
We have,
The possible outcomes in the sample space for rolling three dice:
S = {(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 1, 5), (1, 1, 6),
(1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6),
(1, 3, 1), (1, 3, 2), (1, 3, 3), (1, 3, 4), (1, 3, 5), (1, 3, 6),
(1, 4, 1), (1, 4, 2), (1, 4, 3), (1, 4, 4), (1, 4, 5), (1, 4, 6),
(1, 5, 1), (1, 5, 2), (1, 5, 3), (1, 5, 4), (1, 5, 5), (1, 5, 6),
(1, 6, 1), (1, 6, 2), (1, 6, 3), (1, 6, 4), (1, 6, 5), (1, 6, 6),
(2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 1, 4), (2, 1, 5), (2, 1, 6),
(2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 2, 4), (2, 2, 5), (2, 2, 6),
(2, 3, 1), (2, 3, 2), (2, 3, 3), (2, 3, 4), (2, 3, 5), (2, 3, 6),
(2, 4, 1), (2, 4, 2), (2, 4, 3), (2, 4, 4), (2, 4, 5), (2, 4, 6),
(2, 5, 1), (2, 5, 2), (2, 5, 3), (2, 5, 4), (2, 5, 5), (2, 5, 6),
(2, 6, 1), (2, 6, 2), (2, 6, 3), (2, 6, 4), (2, 6, 5), (2, 6, 6),
(3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 1, 4), (3, 1, 5), (3, 1, 6),
(3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 2, 4), (3, 2, 5), (3, 2, 6),
(3, 3, 1), (3, 3, 2), (3, 3, 3), (3, 3, 4), (3, 3, 5), (3, 3, 6),
(3, 4, 1), (3, 4, 2), (3, 4, 3), (3, 4, 4), (3, 4, 5), (3, 4, 6),
(3, 5, 1), (3, 5, 2), (3, 5, 3), (3, 5, 4), (3, 5, 5), (3, 5, 6),
(3, 6, 1), (3, 6, 2), (3, 6, 3), (3, 6, 4), (3, 6, 5), (3, 6, 6),
(4, 1, 1), (4, 1, 2), (4, 1, 3), (4, 1, 4), (4, 1, 5), (4, 1, 6),
(4, 2, 1), (4, 2, 2), (4, 2, 3), (4, 2, 4), (4, 2, 5), (4, 2, 6),
(4, 3, 1), (4, 3, 2), (4, 3, 3), (4, 3, 4), (4, 3, 5), (4, 3, 6),
(4, 4, 1), (4, 4, 2), (4, 4, 3), (4, 4, 4), (4, 4, 5), (4, 4, 6),
(4, 5, 1), (4, 5, 2), (4, 5, 3), (4, 5, 4), (4, 5, 5), (4, 5, 6),
(4, 6, 1), (4, 6, 2), (4, 6, 3), (4, 6, 4), (4, 6, 5), (4, 6, 6),
(5, 1, 1), (5, 1, 2), (5, 1, 3), (5, 1, 4), (5, 1, 5), (5, 1, 6),
(5, 2, 1), (5, 2, 2), (5, 2, 3), (5, 2, 4), (5, 2, 5), (5, 2, 6),
(5, 3, 1), (5, 3, 2), (5, 3, 3), (5, 3, 4), (5, 3, 5), (5, 3, 6),
(5, 4, 1), (5, 4, 2), (5, 4, 3), (5, 4, 4), (5, 4, 5), (5, 4, 6),
(5, 5, 1), (5, 5, 2), (5, 5, 3), (5, 5, 4), (5, 5, 5), (5, 5, 6),
(5, 6, 1), (5, 6, 2), (5, 6, 3), (5, 6, 4), (5, 6, 5), (5, 6, 6),
(6, 1, 1), (6, 1, 2), (6, 1, 3), (6, 1, 4), (6, 1, 5), (6, 1, 6),
(6, 2, 1), (6, 2, 2), (6, 2, 3), (6, 2, 4), (6, 2, 5), (6, 2, 6),
(6, 3, 1), (6, 3, 2), (6, 3, 3), (6, 3, 4), (6, 3, 5), (6, 3, 6),
(6, 4, 1), (6, 4, 2), (6, 4, 3), (6, 4, 4), (6, 4, 5), (6, 4, 6),
(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6),
(6, 6, 1), (6, 6, 2), (6, 6, 3), (6, 6, 4), (6, 6, 5), (6, 6, 6)}
Now,
The combination where the sum is 10 is 27.
ie.
{(1, 3, 6), (1, 4, 5), (1, 5, 4), (1, 6, 3), ........, (6, 1, 3), (6, 2, 2,), (6, 3, 1)}
Thus,
There are 27 ways of combination where the sum is 10.
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In a certain class of 40students, 90% passed ssce mathematics examinations and 75% passed English. If 2 students failed both mathematics and English, what percentage of students passed both examinations
30% percent of the students passed both Mathematics and English.
What is Percentage?A rate, number, or amount in each hundred is known as a percentage
Let's use a Venn diagram to represent the information given in the problem. Let M be the set of students who passed Mathematics, E be the set of students who passed English, and F be the set of students who failed both.
We know that there are 40 students in the class, and 90% passed Mathematics, so the number of students who passed Mathematics is 0.9 × 40 = 36. Similarly, 75% passed English, so the number of students who passed English is 0.75 × 40 = 30.
We also know that 2 students failed both Mathematics and English, so we can label the F section with 2.
where the number in each section represents the number of students who passed the respective exam.
To find the percentage of students who passed both examinations (i.e., the intersection of M and E), we need to add the number of students in the M and E intersection to the F section, then subtract that from the total number of students (40), and finally divide by 40 to get the percentage. That is:
percentage of students who passed both exams = (M ∩ E + F) / 40 × 100%
= (28 + 2) / 40 × 100%
= 30%
Therefore, 30% of the students passed both Mathematics and English.
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Choose the correct answer.
When you get the sum of a data set and divide by the number of values collected, you get the
A)quantitative data
B)qualitative data
C)median
D)mean
Rose graphs this equation as shown x^2-4x+y^2=0 Rose correctly found the what but incorrectly found the what to correct her graph she could what
The equation [tex]x^2-4x+y^2=0[/tex] can be rewritten as [tex]x^2-4x+4+y^2=4[/tex], which is equivalent to [tex](x-2)^2 + y^2 = 2^2[/tex]. This is the equation of a circle centered at (2,0) with a radius of 2.
How to graph this equation?To graph this equation, you could plot the center point (2,0) and then draw a circle with a radius of 2 around that point. Alternatively, you could find a few points on the circle by plugging in values for x and solving for y (or vice versa), and then plot those points to sketch the circle.
If Rose found the correct equation but incorrectly graphed it, she could try using the correct center point and radius to sketch the circle more accurately. Alternatively, she could check her work to see where she made a mistake in graphing the equation.
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The volume of this prism is 4950cm3. The area of the cross-section is 110cm2. Work out x .
Answer:
answer will be my albert enistein calculation is 4500000⁹7765⁵44³=6425786
Write each function in terms of its cofunction. Assume that all angles in which an unknown appears are acute angles. cos(α+20∘)
The given function is cos(α+20°) and its cofunction can be expressed as cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).
Therefore cos(α+20°) in terms of its cofunctions, we need to use the formulas for sin and cos of complementary angles.
The complementary angle of 20° is 70° because 20° + 70° = 90°.
So, we can rewrite cos(20°) as sin(70°) and sin(20°) as cos(70°).
Using the formula for the cosine of the sum of two angles, we can then substitute these values to get:
cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°)
Therefore, expression of cos(α+20°) in terms of its cofunctions is cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).
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A triangle has one side with length 9 and another side with length 6. The angle opposite the side of length 6 measures 40. what is the measure of the angle opposite the side of length 9?
Answer: the angle opposite the side length 9 is 74.62 degrees I think .
Step-by-step explanation:
Suppose the water depth during low tide at a certain bay is about 3.0 m, and at high tide it is about 9.0 m. The natural period of oscillation is about 12 hours, and on a particular day, high tide occurred at 6:45 a.m. Find the amplitude (in meters) of the model. Xm
The amplitude of the model is 3.0 meters.
The amplitude of a harmonic oscillator represents the maximum displacement from the equilibrium position. In the case of tidal oscillations, the equilibrium position is the average water level.
The amplitude of the model can be determined by considering the difference between the high and low tide water depths, which represents the maximum displacement of the water from the average level. Dividing this difference by two gives us the amplitude of the model.
The amplitude of the model can be found using the formula:
Xm = (H - L)/2
where H is the high tide water depth, L is the low tide water depth, and Xm is the amplitude of the model.
Substituting the given values, we get:
Xm = (9.0 - 3.0)/2
Xm = 3.0 meters
Therefore, the amplitude of the model is 3.0 meters.
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On a piece of paper, use a protractor to construct △ABC with m∠A=30° , m∠B=60° , and m∠C=90° .
Which statements about the triangles are true?
Select each correct answer.
AC BC
a c is greater than b c
AC>AB
a c is greater than a b
AC
Answer:
AC<BC = 30+60=90 < 60+90= 150
Step-by-step explanation:
AC>AB 30+90= 120 > 30+60=90
AC<BC 30+60=90 < 60+90= 150
solve the linear system using elimination. -5x+3y=19 and -5x+7y+11
Answer:
x = -5
y = -2
Step-by-step explanation:
-5x + 3y = 19
-5x + 7y = 11
Time the first equation by -1
5x - 3y = -19
-5x + 7y = 11
4y = -8
y = -2
Now put -2 in for y and solve for x
-5x + 3(-2) = 19
-5x - 6 = 19
-5x = 25
x = -5
Let's Check
-5(-5) + 3(-2) = 19
25 - 6 = 19
19 = 19
So, x = -5 and y = -2 is the correct answer.