The first withdrawal from the account is $200 and another is $150
A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression. In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. Yet, both forms provide the same outcome when the values are entered into the formula.
A checking account has a balance of $350
A customer makes two withdrawals
first is $50 more than the other,
let another withdrawal is $x
then first withdrawal is $(50+x)
then,
x+(50+x)=350
2x=300
x=$150
hence first withdrawal is $200
and another is $150
Then he makes a deposit of $75,
So the remaining balance in the account is $75.
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Singular Savings Bank received an initial deposit of $3000. It kept a percentage of this money in reserve based on the reserve rate and loaned out the rest. The amount it loaned out was eventually all deposited back into the bank. If this cycle continued indefinitely and eventually the $3000 turned into $50,000, w
Singular Savings Bank received an initial deposit of $3000. By keeping a percentage of this money in reserve based on the reserve rate, the bank loaned out the rest. Over time, the money loaned out was all deposited back into the bank, and with each additional deposit the bank was able to lend out even more money.
This cycle of lending and depositing continued indefinitely until the initial $3000 had increased to $50,000. This increase in money was possible due to the reserve rate, which allowed the bank to lend out a percentage of the money deposited and to keep a percentage in reserve for themselves.
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gina prepara un postre para 8 personas usa 1/2 de libra de mantequilla 1/4 de libra de azucar ,una lib a de harina y 3/2 libra de queso cuantas libras de ingredientes necesita si para preparar la receta para 16 personas cuantas libras necesita
The amounts needed for the dessert for 16 people is given as follows:
Butter: 1 lb.Sugar: 0.5 lb.Flour: 2 lb.Cheese: 3 lb.How to obtain the amounts?The amounts are obtained applying the proportions in the context of the problem.
For 8 people, the amounts of the ingredients are given as follows:
Butter: 0.5 lb.Sugar: 0.25 lb.Flour: 1 lb.Cheese: 1.5 lb.With 16 people, the number of people doubles, hence the amount of ingredients also doubles, thus the needed amounts are given as follows:
Butter: 1 lb.Sugar: 0.5 lb.Flour: 2 lb.Cheese: 3 lb.TranslationGina is preparing a recipe for 8 people, and the amounts are given as follows:
Butter: 0.5 lb.Sugar: 0.25 lb.Flour: 1 lb.Cheese: 1.5 lb.The problem asks for the necessary amounts for 16 people.
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Raven usually does 5 out of every 7 math problems correctly. Which table accurately shows how many math problems she will do correctly out of 14, 21, or 28 total problems?
Answer:
B.
Step-by-step explanation:
The proportions should be exactly the same for each set of questions and correct questions.
Based on Raven's history, she get 5 of 7.
Choice B. shows exactly that with a scalar of 2, 3, and 4. For Row 2, the set is twice as large, so Raven gets exactly twice as many questions correct and exactly twice as many incorrect.
For Option B., the [tex]\frac{correct}{total}[/tex] always simplifies to [tex]\frac{5}{7}[/tex] for every row.
There are 30 sweets in a bag.
13 of the sweets are yellow.
The rest of the sweets are red.
(a) What fraction of the sweets in the bag are red?
Answer: just do 30 - 13 which = 17
Step-by-step explanation:
subtraction above
What is the area of this shape? (Ignore the erased numbers)
Answer:
a= 528 squared centimeters
Step-by-step explanation:
Area of trapezoid is A=[(a+b)/2]*h
Base 1 is 32 cm
height is 12
since the height is also same as the bottom part as told by the line, do 32+12+12 to get...
56 cm for base 2
Sooo put this to use
a=[(32+56)/2]*12
a=[(88)/2]*12
a=[44]*12
a=528 :)
Answer:
Area 528cm²
That's the answer to your question.
I am really confused, can anyone help?
Answer:
a = 24
b = 10
c = 26
======================================================
Explanation:
We're given a list of possible b values and they are:
4, 5, 8, 10, 12, 24
Let's make a table to show what each value of 'a' would be based on those b values above.
[tex]\begin{array}{|c|c|} \cline{1-2}b & a\\\cline{1-2}4 & 12\\\cline{1-2}5 & 14\\\cline{1-2}8 & 20\\\cline{1-2}10 & 24\\\cline{1-2}12 & 28\\\cline{1-2}24 & 52\\\cline{1-2}\end{array}[/tex]
Example calculation: If b = 4, then a = 2b+4 = 2*4+4 = 12 (first row)
I recommend using spreadsheet software to quickly compute these values. Also, a spreadsheet is useful to organize the data into a table.
Next we'll add a third column c.
This column will be computed using the formula [tex]c = \sqrt{a^2+b^2}[/tex] which is based from the pythagorean theorem [tex]a^2+b^2 = c^2[/tex]
So,
[tex]\begin{array}{|c|c|c|} \cline{1-3} & & \\b & a & c = \sqrt{a^2+b^2}\\\cline{1-3}4 & 12 & 12.6491\\\cline{1-3}5 & 14 & 14.8661\\\cline{1-3}8 & 20 & 21.5407\\\cline{1-3}10 & 24 & 26\\\cline{1-3}12 & 28 & 30.4631\\\cline{1-3}24 & 52 & 57.2713\\\cline{1-3}\end{array}[/tex]
Each decimal value mentioned is approximate. The only time c is an integer is when a = 24 and b = 10.
So that's how I got a = 24, b = 10, c = 26 as the final answer.
Suppose that [infinity] cn x n n = 0 converges when x = −4 and diverges when x = 6. What can be said about the convergence or divergence of the following series?
(a) [infinity] cn n = 0 When compared to the original series, we see that x = here. Since the original series for that particular value of x, we know that this series.
(b) [infinity] cn7n n = 0 When compared to the original series, we see that x = here. Since the original series for that particular value of x, we know that this series.
(c) [infinity] cn(−2)n n = 0 When compared to the original series, we see that x = here. Since the original series for that particular value of x, we know that this series.
(d) [infinity] (−1)ncn7n n = 0 When compared to the original series, we see that x = here. Since the original series for that particular value of x, we know that this series
for (d), the x value has changed, as the (-1) in the series acts as a multiplier and flips the convergence of the original series. This means that when x = -4, the original series converges, but when x = -7, the series in (d) converges. Therefore, the series in (d) converges.
(a) Diverges
(b) Diverges
(c) Converges
(d) Converges: The original series converges when x = -4 and diverges when x = 6. For (a), (b), and (c), the x value remains the same as in the original series, so the convergence or divergence of the series is the same as the original series. However, for (d) the x value has changed. The (-1) in the series acts as a multiplier and flips the convergence of the original series, so the series converges.
The convergence or divergence of a series is determined by the value of x in the series. In this particular case, when x = -4 the original series converges, and when x = 6 it diverges. For (a), (b), and (c), the x value is the same as in the original series, so the convergence or divergence of the series is the same as the original series. However, for (d), the x value has changed, as the (-1) in the series acts as a multiplier and flips the convergence of the original series. This means that when x = -4, the original series converges, but when x = -7, the series in (d) converges. Therefore, the series in (d) converges.
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10+10(x+3)=
\,\,-x-10(-x+1)
−x−10(−x+1)
The sοlutiοn tο the equatiοn is x=7.
What is Equatiοn?An equatiοn is an expressiοn that uses mathematical symbοls tο express the relatiοnship between twο οr mοre variables. Equatiοns are used tο describe physical laws, mοdel real-wοrld prοblems, and sοlve mathematical prοblems. Equatiοns can be written in a variety οf fοrms, frοm simple linear equatiοns tο cοmplex nοnlinear equatiοns. Equatiοns can alsο be used tο determine the prοperties οf certain functiοns and tο evaluate integrals.
Sοlving fοr x,
−10(−x+1)+10+10(x+3)=0
−10x+10−10x+10+100+30=0
−20x+140=0
20x=140
x=7
This equatiοn is an example οf a linear equatiοn. Linear equatiοns are equatiοns that invοlve οnly οne variable and can be represented in the fοrm ax + b = 0, where x is the variable and a and b are cοnstants. Linear equatiοns are useful fοr understanding the relatiοnship between different variables and can be used tο sοlve real-wοrld prοblems. In this equatiοn, the variable x is the unknοwn value that we are trying tο sοlve fοr. By rearranging the equatiοn and applying the apprοpriate algebraic οperatiοns, we were able tο sοlve fοr x. This is an example οf hοw linear equatiοns can be used tο sοlve real-wοrld prοblems.
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Solve for x in given expression.
10 + 10(x + 3) = −x −10(−x + 1)
a physical fitness association is including the mile run in its secondary-school fitness test. the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 40 seconds. find the probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds.
The probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds is 0.0107 or 1.07%.
The probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds is 0.0013.
Given data:
Mean (μ) = 450 seconds
Standard deviation (σ) = 40 seconds
We are required to find the probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds.i.e., we need to find P(x < 358)
Let us first calculate the z-score.
z = (x - μ) / σ
Where,x = 358 seconds
μ = 450 seconds
σ = 40 seconds
z = (358 - 450) / 40 z = -2.3
Using a z-table or calculator, we can find the probability that corresponds to the z-score of -2.3P(z < -2.3) = 0.0107
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Estimate the sum ofand. Write an
equation.
Answer:
I believe this what you're asking:
To estimate the sum of 3.456 and 8.79, we can round each number to one decimal place, and then add them:
3.456 ≈ 3.5
8.79 ≈ 8.8
So, 3.456 + 8.79 ≈ 3.5 + 8.8 = 12.3
Therefore, we can estimate that the sum of 3.456 and 8.79 is approximately 12.3.
In equation form, this can be written as:
3.456 + 8.79 ≈ 3.5 + 8.8 = 12.3
Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]
Give one pair of supplementary angles and one pair of vertical angles shown in the figure below 
Answer:
a. 6 and 2
b. 3 and 8
Step-by-step explanation: Supplementary angles add up to 180 degrees. In this figure angles 6,2 lie on the same line and a straight line has an angle measure of 180 degrees. Vertical angles are opposite to each other and have the same value. 8 and 3 are one example and on that same area, 7 and 4 are too.
a coat cost 95$. alexa has 25$ and plans to save 10$ each month. Describe the numbers of months she needs to save to buy a coat
WILL GIVE BRAINLIST TO BEST ANSWER
A store sells two types of shirts.
Short-sleeved shirts cost $12. Long-sleeved shirt cost $16.
One day, 48 shirts are sold at a total cost of $624. How many MORE short-sleeved shirts did they sell than long-sleeved shirts?
If a store sells two types of shirts. The number of short-sleeved shirts that were sold than long-sleeved shirts is 24 shirts.
How to find the number of shirt?Number of short-sleeved shirts sold =S
Number of long-sleeved shirts sold = L
we know that:
s + l = 48 (equation 1) -- Total number of shirts sold
12s + 16l = 624 (equation 2) -- Total cost of shirts sold
To solve for the number of short-sleeved shirts sold, we can use equation 1 to express "l" in terms of "s":
l = 48 - s
Substituting this into equation 2
12s + 16(48 - s) = 624
Simplifying and solving for "s"
12s + 768 - 16s = 624
-4s = -144
s = 36
Therefore, 36 short-sleeved shirts were sold.
To find the number of long-sleeved shirts sold, we can use equation 1 again:
s + l = 48
36 + l = 48
l = 12
Therefore, 12 long-sleeved shirts were sold.
How many MORE short-sleeved shirts were sold than long-sleeved shirts,:
36 - 12 = 24
So, 24 MORE short-sleeved shirts were sold than long-sleeved shirts.
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a. Solve - 11y -13>42. Graph the solution on a number line.
The solution to the inequality - 11y -13>42 is y < -5.
What is inequality?An inequality is a mathematical statement that compares two quantities using symbols such as <, >, ≤, or ≥ to indicate whether one is less than, greater than, less than or equal to, or greater or equal to the other.
To solve the inequality -11y - 13 > 42, we need to isolate y on one side of the inequality.
-11y - 13 > 42
First, we can add 13 to both sides:
-11y > 55
Next, we can divide both sides by -11, remembering to reverse the direction of the inequality because we are dividing by a negative number:
y < -5
To graph this on a number line,
Here is a rough sketch of the number line:
<=====(●)------------------------
-5
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What is the m∠AHE
m
∠
A
H
E
to the nearest whole number?
Answer:
Below
Step-by-step explanation:
As I posted ....looks to be 147°
The mean SAT score in mathematics, μ, is 53. The standard deviation of these scores is 41. A special preparation course claims that its graduates will score higher, on average, than the mean score 503. A random sample of 70 students completed the course, and their mean SAT score in mathematics was 505. At the 0. 05 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 41.
A. ) Null Hypothesis: B. ) Alternative Hypothesis:C. ) The Value of the test statistic:D. ) The P-Value:
A. [tex]\mu[/tex] ≤ 503
B. [tex]\mu[/tex] > 503
C. t = (505 - 503) / (41 / [tex]\sqrt{70}[/tex]) = 1.38
D. The P-value (0.086) is greater than the level of significance (0.05).
A. Null Hypothesis: The mean SAT score of the students who completed the preparation course is not significantly higher than the mean score of 503.
[tex]\mu[/tex] ≤ 503
B. Alternative Hypothesis: The mean SAT score of the students who completed the preparation course is significantly higher than the mean score of 503.
[tex]\mu[/tex] > 503
C. The Value of the test statistic:
We apply the algorithm below to determine the test statistic:
[tex]t = (\bar x - \mu) / (s / \sqrt{n} )[/tex]
When s is the sample standard deviation, n is the sample size, and x is the sample mean and is the predicted population mean.
In this case,
[tex]\bar x[/tex] = 505,
[tex]\mu[/tex] = 503,
s = 41,
n = 70.
t = (505 - 503) / (41 / [tex]\sqrt{70}[/tex]) = 1.38
D. The P-Value:
We want to test whether the mean SAT score of the students who completed the preparation course is significantly higher than the mean score of 503 at the 0.05 level of significance.
Using a t-distribution table with 69 degrees of freedom (df = n-1), we find that the area to the right of 1.38 is 0.086.
Since this is a one-tailed test (we are testing for[tex]\mu[/tex] > 503), the P-value is 0.086.
Since the P-value (0.086) is greater than the level of significance (0.05), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the preparation course does what it claims, i.e., the mean SAT score of the students who completed the preparation course is not significantly higher than the mean score of 503.
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List the factor pairs for 36x ^ 2 : Identify which pair adds to 15x:
From the listed factor pairs, there are no factor pairs for 36x² that add up to 15x.
How to Determine Factor Pairs?A factor pair is a set of two numbers that can be multiplied together to get a specific product.
The factor pairs for 36x² are:
1 x 36x²
2 x 18x²
3 x 12x²
4 x 9x²
6 x 6x²
To identify which pair adds to 15x, we need to look for the factor pair whose two terms add up to 15x. None of the above factor pairs add up to 15x. Therefore, there is no factor pair for 36x² that adds up to 15x.
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The product of two consecutive square numbers in 900 .
Work out the 2 numbers
Answer:
25&36
Step-by-step explanation:
25 is a square number and so is 36 and there product is 900. They are also consecutive.
Just assemble the square numbers from the least i.e 4 and try solving as asked to see if it gives 900.
Thus you'll land on 25&36
Answer:
5² and 6²
Step-by-step explanation:
Use trial and error
Start from the product of 1² and 2²
1×2²
1×4=4
4<900 (incorrect)
2²×3²
4×9=36
36<900(incorrect)
3²×4²
9×16=144
144<900(incorrect)
4²×5²
16×25=400
400<900(incorrect) *but close
5²×6²
25×36 =900
900=900(correct)
: . 5² and 6² are the two consecutive square numbers.
Please answer the both questions in the photos below ( will mark brainliest if available + 30p )
Answer: Please correct me if I'm wrong and I will remove my answer
1:The system of linear equations can be rewritten as:
4x + y = 4 ...(1)
y = -4a + 4 ...(2)
To determine the classification of the system, we can use the method of substitution:
Substituting equation (2) into equation (1) to eliminate y:
4x + (-4a + 4) = 4
4x - 4a = 0
x - a = 0
x = a
Substituting x = a into equation (2) to find the value of y:
y = -4a + 4
So the solution of the system is (x,y) = (a, -4a+4).
Since the system has a unique solution for any value of 'a', it is a consistent independent system of equations.
2:To find the solution to the equation f(x) = g(x), we need to find the value of x that makes the two functions equal.
f(x) = 2^x + 1
g(x) = -x + 7
Setting them equal to each other:
2^x + 1 = -x + 7
Subtracting 1 from both sides:
2^x = -x + 6
Taking the logarithm of both sides (base 2):
x = log2(-x + 6)
Since log2(-x + 6) is only defined when -x + 6 is positive, we need to check if -x + 6 > 0.
-x + 6 > 0
x < 6
Therefore, the solution to the equation f(x) = g(x) is the intersection point of the two graphs for x < 6.
To graph the two functions, we can use a graphing calculator or plot points. Here are some points for each function:
f(x) = 2^x + 1
(0, 2)
(1, 3)
(2, 5)
(3, 9)
g(x) = -x + 7
(0, 7)
(1, 6)
(2, 5)
(3, 4)
Plotting these points on the same coordinate plane:
We can see that the two functions intersect at approximately (2.6, 4.4) for x < 6. Therefore, the solution to the equation f(x) = g(x) for x < 6 is approximately x = 2.6.
Multiply out and simplify (x-8)²
(x-8)²
(x-8)(x-8)
x(x-8) - 8 (x-8)
x² -8x -8x + 64
x²-16x+64
suppose that there are 32 people in your statistics class and you are divided into 16 teams of 2 students each. you happen to mention that your birthday was last week, upon which you discover that your teammate's mother has the same birthday you have (month and day, not necessarily year). assume that the probability is 1 365 for any given day.
The probability of two people on the same team having the same birthday is: P(A) = 1 / 16
The probability of two people having the same birthday in a group of 32 people is 1/365. This is because there are 365 possible days that a person can have a birthday, and the probability of two people having the same birthday is 1/365.
In this case, there are 16 teams of 2 students each, and the probability of two people on the same team having the same birthday is 1/365.
To calculate the probability of this event occurring, we can use the formula:
P(A) = n(A) / n(S)
Where P(A) is the probability of the event occurring, n(A) is the number of favorable outcomes, and n(S) is the total number of possible outcomes.
In this case, the number of favorable outcomes is 1, since there is only one team that has two people with the same birthday. The total number of possible outcomes is 16, since there are 16 teams.
Therefore, the probability of two people on the same team having the same birthday is:
P(A) = 1 / 16
So, the probability of this event occurring is 1/16.
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Write x² + 12x − 1 in the form (x + a)² + b, where a and b are constants
The given equation x² + 12x − 1 can be written in the form of algebraic identity (x + 6)² -37
Algebraic identities are equations in algebra that hold regardless of the value of each of their variables. The factorization of polynomials makes use of algebraic identities. On both sides of the equation, they have variables and constants.
Write x² + 12x − 1 in the form (x + a)² + b, where a and b are constants.
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added to a variable before being multiplied by it.
[tex]The \ given \ equation\ is\ \\\\x^2+12x-1\\let , \ x^2+12x=1\\\\add \ both\ side \ \frac{12^2}{4}\\\\x^2+12x+\frac{144}{4}=1+\frac{144}{4}\\\\x^2+12x+36=1+36\\x^2+2.6.x+6^2-37\\\\(x-6)^2-37\\\\[/tex]
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P(x)=4x^(5)+3x^(2)+2x+a
The value of a is -9
What is standard form of a polynomial?
When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on.
[tex]P(x)=4x^5+3x^2+2x+a[/tex]
Question might be asking to find the value of 'a' at the point (1, 0) on the graph of [tex]P(x)=4x^5+3x^2+2x+a[/tex]
Substitute the point into the polynomial. i.e., x=1, y=0
=> [tex]0=4(1)^5+3(1)^2+2(1)+a[/tex]
=> 0= 4*1 + 3*1+2 +a
=> 0= 4+3+2+a
=> 0=9 +a
=> a= -9
The value of a is -9
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Complete Question:
Find the value of [tex]P(x)=4x^(5)+3x^(2)+2x+a[/tex]
Cari knows that it is a 45 mile drive from her house to the airport. She also knows that it is a 45 mile drive from her house to her grandparents house in the woods. How many miles is it directly from the airport to her grandparents house in the woods? Show your work.
the direct distance between the airport and Car's grandparents' house in the woods is 63.64 miles
Define Pythagorean theoremThe Pythagorean theorem is a fundamental principle in mathematics that relates to the sides of a right triangle. It is referred that the hypotenuse's square length, which is the side that faces the right angle, is equal to the sum of the squares of the lengths of the other two sides of a right triangle.
Let d be the distance between the airport and Car's grandparents' house in the woods. Therefore, we can use the Pythagorean theorem to solve for d:
d² = 45² + 45²
d² = 2(45²)
d = sqrt(2)× 45
Therefore, the direct distance between the airport and Car's grandparents' house in the woods is approximately 63.64 miles (since sqrt(2) is approximately 1.414).
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A right triangle has a rise of 16 and a run of 4. A similar right triangle with a run of 5 will have a rise of?
Answer:
It will have a rise of 20.
Step-by-step explanation:
We can use ratios:
Rise : Run = 16 : 4 = 4 : 1 = 20 : 5
Hope this helps!
if (5 x - 7) is a factor of the expression: 5 x ^2 - 2 x - 7 then the other factor is
Answer:
(x + 3)
Step-by-step explanation:
Triangle ABC with vertices at A(3, 2), B(2, −1), C(−2, 1) is dilated using a scale factor of 3.5 to create triangle A′B′C′. Determine the vertex of point C′.
C′(−7, 1)
C′(−7, 3.5)
C′(−2, 3.5)
C′(7, −3.5)
I need this now I am doing the exam now there is no time to waste
According to the given information, the coordinates of C′ are (-7, 3.5).
What is the scaling of a triangle?
Scaling is a type of transformation in which the size of an object, in this case, a triangle, is changed while its shape and orientation are maintained. In other words, scaling involves multiplying the coordinates of the vertices of the triangle by a factor called the scale factor.
To dilate a triangle using a scale factor of 3.5, we need to multiply the distance between each vertex and the center of dilation by 3.5. The center of dilation can be any point, but for simplicity, we can choose the origin (0,0).
So, the coordinates of the new vertex C′ can be found by multiplying the distance between the old vertex C(-2,1) and the origin (0,0) by 3.5, and then adding this to the coordinates of the origin.
The distance between C and the origin is [tex]\sqrt{(-2-0)^2+(1-0)^2}[/tex] = [tex]\sqrt{5}[/tex] so the distance between C′ and the origin is [tex]3.5*\sqrt{5}[/tex].
Therefore, the coordinates of C′ are (-23.5, 13.5) = (-7, 3.5).
So, the answer is C′(-7, 3.5).
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solve for c
3 120 10 round your answer to the nearest tenth
The required value of the third side of the triangle is x = 11.78.
How to use law of cosine?We can use the law of cosines to find the value of the third side of the triangle. The law of cosines states that for any triangle with sides a, b, and c and angle C opposite side c,
[tex]$c^2 = a^2 + b^2 - 2ab\cos(C)$[/tex]
In this case, we have sides a = 2 and b = 10 and angle C = 120 degrees. Therefore, we can plug in these values to get:
[tex]$x^2 = 3^2 + 10^2 - 2(3)(10)\cos(120^\circ)$[/tex]
Simplifying the expression inside the parentheses gives:
[tex]$\cos(120^\circ) = -\frac{1}{2}$[/tex]
Plugging this in and simplifying further gives:
[tex]$x^2 = 9 + 100 + 30 = 139$[/tex]
Taking the square root of both sides gives:
[tex]$x = \sqrt{144} = 12$[/tex][tex]$x = \sqrt{139} = 11.78$[/tex]
Therefore, the value of the third side of the triangle is x = 11.78.
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The radius of a circle 4cm and the measure
of the central angle is 45°.
a. What is the area of the sector?
b. What is the area of the segment of a
circle?
Answer:
Step-by-step explanation:
a. To find the area of the sector, we can use the formula:
A = (θ/360)πr^2
where A is the area of the sector, θ is the central angle in degrees, r is the radius of the circle, and π is the constant pi.
In this case, the radius is 4 cm and the central angle is 45 degrees. Substituting these values into the formula, we get:
A = (45/360)π(4^2)
A = (1/8)π(16)
A = 2π
Therefore, the area of the sector is 2π square cm.
b. To find the area of the segment of a circle, we need to subtract the area of the triangle formed by the two radii and the chord from the area of the sector.
The central angle of the sector is 45 degrees, so the angle between the chord and one of the radii is 22.5 degrees. We can use trigonometry to find the length of the chord:
cos(22.5) = adjacent/hypotenuse
cos(22.5) = x/4
x = 4cos(22.5)
So the length of the chord is approximately 3.54 cm (rounded to two decimal places).
The area of the triangle can be found using the formula:
A = (1/2)bh
where b is the length of the base (which is the chord) and h is the height (which is the distance from the midpoint of the chord to the center of the circle). The height is equal to the radius minus half the length of the chord:
h = 4 - (3.54/2)
h = 1.23 (rounded to two decimal places)
Substituting the values of b and h, we get:
A = (1/2)(3.54)(1.23)
A = 2.17 (rounded to two decimal places)
So the area of the triangle is approximately 2.17 square cm.
Finally, we can find the area of the segment by subtracting the area of the triangle from the area of the sector:
Area of segment = Area of sector - Area of triangle
Area of segment = 2π - 2.17
Area of segment = 0.85 (rounded to two decimal places)
Therefore, the area of the segment of the circle is approximately 0.85 square cm.
Help!! Find m
this is geometry btw
The measure of angle ABD as required to be determined from the task content is; 32°.
What is the measure of angle ABD?As evident in the task content;
m<ABD + m<CBD = m<ABC = 90°.
This follows from the fact that the angle ABC is a right angle.
4x - 4 + 2x + 40 = 90
6x = 54
x = 54 / 6 = 9
Ultimately, the measure of angle ABD is; 4(9) - 4 = 36 - 4 = 32.
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