Answer:
u + v = < - 9, - 7 >
Step-by-step explanation:
to sum u and v add the corresponding x and y components of the 2 vectors
u + v
= < - 8, - 5 > + < - 1, - 2 >
= < - 8 - 1, - 5 - 2 >
= < - 9, - 7 >
Which expressions are equivalent to 78 • 7
Question:
Which expressions are equivalent to 78 • 7? Select all that apply. A. 73 • 73 B. 71879 C. (73)3 D. 74 + 75 E. 74 • 75
None of the expressions are equivalent to 78 • 7
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
None because 78 * 7 = 546
None of the options equal to 546.
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A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%. What is the minimum sample size needed?.
The minimum sample size needed is 93.
What is minimum sample size?In order to obtain survey findings that accurately represent a population you are researching while maintaining your chosen sampling error and confidence, you must have a required sample size.
A political scientist polls 300 random selection Atlanta votes cast, asking each one who those who currently support in the city's mayoral race in 2020. While 184 people indicated they would vote for candidate b, 184 people said they would pick for option a, and 15 people stated they felt undecided or would vote for a different candidate.
The community proportion of all Atlanta electors who intend to vote for candidate a was calculated with a 95% confidence level in query 8 by the political researcher. Furthermore, the researcher wants to determine p with a 3% error margin.
n = 101
p = 0.5
e = 5%=0.05
z score at 95% = 1.96
[tex]z score = (observed value - mean of the sample) / standard deviation of the sample[/tex]
On auditing the value to the given equation:
n = 93
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Write an equation dor thi math problemfAt one tore a trophy cot $12. 50. Engraving cot $0. 40 per letter. At another tore, the ame trophy cot $14. 75. Engraving cot $0. 25
The equation we get from the given information that is one award that cost $12.50 was torn. Each letter costs $0.40 to engrave is 2.25x - 0.15y=0.
Given that,
We have to compose an equation for this math issue. One award that cost $12.50 was torn. Each letter costs $0.40 to engrave. The identical trophy cost $14. 75 at another location. Cost of engraving: $0.25
We know that,
Let us take the,
Trophy cot as x and engraving cot as y
We can write as
12.5x+ 0.4y= 14.75x+ 0.25y
12.5x- 14.75x+ 0.4y -0.25y=0
-2.25x + 0.15y=0
2.25x - 0.15y=0
Therefore, The equation we get from the given information that is one award that cost $12.50 was torn. Each letter costs $0.40 to engrave is 2.25x - 0.15y=0.
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Mr. Starnes and his wife have 6 grandchildren: Connor, Declan, Lucas, Piper, Sedona, and Zayne. They have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them. Give a probability model for this chance process.
Probability model for this chance process is:
P(X=2) = [tex]6_C_2*(1/6)^2*(1-1/6)6-2[/tex]
Given:
Mr. Starnes and his wife have 6 grandchildren: Connor, Declan, Lucas, Piper, Sedona, and Zayne. They have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them.
Using binomial distribution:
We are given that there are 6 grand children and 2 of them are needed to picked.
Let number of grandchildren to be choose is X.
Every children has equal chance to get selected, therefore Probability for everyone is 1/6.
P(X) = Bino(6,1/6)
P(X) = [tex]6_C_X*(1/6)^X*(1-1/6)^{6-X}[/tex]
P(X=2) = [tex]6_C_2*(1/6)^2*(1-1/6)^{6-2[/tex]
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Given that
x
= 7.9 m and
θ
= 54°, work out AB rounded to 3 SF.
Answer:
6.39 m
Step-by-step explanation:
( for a right triangle such as this)
Sin (theta) = opp leg / hypotenuse = AB / x
sin (54) = AB / 7.9
7.9 * sin 54 = AB = 6.39 m
Write the following as a number: minus one thousand, eight hundred and five point nine six.
The final number is a decimal number which is equal to -1805.96.
It is given to us that the set of expression is given by -
minus one thousand, eight hundred and five point nine six.
We have to write the given expression as a number.
According to the given information we see that there is a "point" word in the expression. This implies that the final number will be a decimal number.
So, from the given information, we can represent the number as -
-1805.96
Thus, the final number is a decimal number which is equal to -1805.96.
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How do I do this x/12+1=x/3-x/4 and this is for solving linear equations.
Answer:
no solution
Step-by-step explanation:
You want to solve the equation x/12+1=x/3-x/4.
SolutionThere are a couple of ways you can solve this. If you're intimidated by the fractions, you can get rid of them by multiplying the equation by a common denominator. In this case, multiplying by 12 gives ...
x +12 = 4x -3x . . . . . . original equation multiplied by 12
x +12 = x . . . . . . . . . . simplified
12 = 0 . . . . . . . . . . . . subtract x from both sides
This equation is plainly false. No value of x will make it be true.
The given equation has NO SOLUTION.
Alternate solutionYou can do the arithmetic with the coefficients as they are:
x/12 +1 = x(1/3 -1/4)
x/12 +1 = x/12
1 = 0 . . . . . . . . . . subtract x/12; false
The equation has NO SOLUTION.
__
Additional comment
It is a good idea to become comfortable doing arithmetic with numbers however you find them: integers, fractions, mixed numbers, decimals, percents, scientific notation.
A decent calculator can help, if you need it. Modern graphing calculators are fully capable of working with mixed numbers, fractions, percents, and scientific notation. Any spreadsheet can do this, too.
There are very good inexpensive or free apps for phone and tablet that provide all the capability of a good graphing calculator.
Change the Cartesian integral
Integral from nothing to nothing Subscript 0 Superscript 3 Baseline Integral from nothing to nothing Subscript 0 Superscript y Baseline x dx dy∫30∫y0x dx dy
into an equivalent polar integral. Then evaluate the polar integral.Change the Cartesian integral SSX x dx dy into an equivalent polar integral. Then evaluate the polar integral. Choose the correct equivalent polar integral below. O A. sin e 2 cose dr de OB. sin So r2 cose dr de 1/4 Sza So ? So O c. 3/ sin e OD. c/2 3/ sine so So ? ? cos e dr de ? cose dr de The value of the double integral is
The value of the double integral is [tex]I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0[/tex].
Let z* be the common (finite) optimal value of P and D.
Given integral is
[tex]I = \int\limits^3_{y = 0} \int\limits^y_{x=0} {x} \, dxdy[/tex]
The region of integration lies between
y = 0, y = 3, x = 0 & x = y
Let x = rcosθ, y = rsinθ,
[tex]x^{2} +y^{2}= r^{2}[/tex]
At y = 3, rsinθ = 3
Thus r varies from 0 to 3/sinθ
θ varies from π/4 to π/2
Now, dxdy ----> rdrdθ
Therefore,
[tex]I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0[/tex]
Hence the answer is The value of the double integral is [tex]I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0[/tex].
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if the length of one side of a square is increased by 1 inch and that of another side is diminished by 2 inches, a rectangle is formed whose area is 180 inches. find the length of a side of the square
The length of the square is 9 inches when a rectangle with a surface area of 180 inches is created by lengthening one side of a square by 1 inches and shortening another by 2 inches.
Given that,
A rectangle with a surface area of 180 inches is created by lengthening one side of a square by 1 inches and shortening another by 2 inches.
We have to find the square's side length should be determined.
We know that,
Let us take the length of the square as x.
So,
The length of one side of a square is increased by 1 inch means
x+1
The length of other side of the square is diminished by 2 inch to form a rectangle means
2x
The area of the rectangle is length × breath.
180=(x+1)(2x)
2x²+2x-180=0
x²+x-90=0
x²+10x-9x-90=0
x(x+10)-9(x+10)=0
(x+10)(x-9)=0
We get,
x+10=0 ⇒ x=-10
x-9=0 ⇒ x=9
The length can not be negative so x=9
Therefore, The length of the square is 9 inches when a rectangle with a surface area of 180 inches is created by lengthening one side of a square by 1 inches and shortening another by 2 inches.
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Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
Using the definition of divisibility, 2p is the greatest common factor.
In the given question we have to factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
The given polynomial is 2p^3+6p.
Now taking 2p common from both terms
=2(p^2+3)
By the definition of divisibility, we get
2p | 2p^3 and 2p|6p, 2| 2p^3 and 2|6p also p|2p^3 and p|6p.
So, 2,p and 2p are common factors of 2p^3 and 6p.
Hence, 2p is the greatest common factor.
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The right answer is:
Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
2p^3+6p
which of the following sets of correlations correctly shows the highest to lowest degree of relation?
a. -0.91, +0.83, -0.03, -0.10
b. -0.91, +0.83, +0.10, -0.03
c. +0.83, +0.10, -0.91, -0.03
d. +0.83, +0.10, -0.03, -0.93
Option B is the correct answer, The set of correlations which correctly shows the highest to lowest degree of relation is -0.91, +0.83, +0.10, -0.03.
What is correlation?
In statistics, the correlation is a technique used to determine the relationship between the two variables. The correlation's range is from -1 to +1. There are three primary categories of correlation: no correlation, positive correlation, and negative correlation. When the correlation value is zero, there is no association; the correlation value that is closest to zero indicates the weakest degree of relationship.
We must select the set of correlations in the question that accurately displays the highest to the lowest degree of relation.
Option B is the best choice since we must take the absolute value into account in order to determine the relationship's degrees. Here, the absolute values drop from 0.91 to 0.03.
Option A is incorrect since the absolute values decline from 0.91 to 0.03 and then climb to 0.10 in this situation.
Because the absolute values are not listed in decreasing order, Option C is incorrect.
Because the absolute values in this situation are not ordered in decreasing order, Option D is also a incorrect choice.
Therefore, option B, is the correct option.
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Tracy buys 150 shares of upton group and 100 shares of whi health. what is tracy’s total investment? a. $4,940.00 b. $5,040.00 c. $5,914.50 d. $5,988.00
The correct option representing Tracy's total investment is a. $4,940.00.
She bought 150 shared of Upton group that offers each share at the price of $18.96. So, the cost of 150 shares = 150 × 18.96
Performing multiplication on Right and Side of the equation
The cost of 150 shares from Upton group = $2844
The cost of 100 shares of WHI health = 100 × 20.96
Performing multiplication on Right and Side of the equation
The cost of 100 shares of WHI Health = $2096
The total investment will be sum of the cost of these shares.
Total investment = 2844 + 2096
Performing addition on Right Hand Side
Total investment = $4940
Hence, the total investment of Tracy is $4940.
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The complete question is -
Use the information in the table below to answer the following question.
Name of Fund
NAV
Offer Price
Upton Group
$18.47
$18.96
Green Energy
$17.29
$18.01
TJH Small-Cap
$18.43
$19.05
WHI Health
$20.96
NL
Tracy buys 150 shares of Upton Group and 100 shares of WHI Health. What is Tracy's total investment?
a.
$4,940.00
b.
$5,040.00
c.
$5,914.50
d.
$5,988.00
Step 1: Subtract 3 from both sides of the inequality.
Step 2: __________
Step 3: Divide both sides of the inequality by the coefficient of x.
What is the missing step in solving the inequality 5 – 8x < 2x + 3?
Add 2x to both sides of the inequality.
Subtract 8x from both sides of the inequality.
Subtract 2x from both sides of the inequality.
Add 8x to both sides of the inequality.
Answer:
D. Add 8x to both sides of the inequality.
Step-by-step explanation:
Tony is putting money into a checking account. Let represent the total amount of money in the account (in dollars). Let represent the number of Tony has been adding money. Suppose that and are related by the equation . Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What was the starting amount of money in the account? s What is the change per in the amount of money in the account?
Weekly change: 40
Initial investment: 450
Given that,
Tony is transferring funds to his checking account. Let y signify the overall balance of the account's funds (in dollars). Let x be the quantity Bill has been adding money for in weeks. Assume that 40x+450=y represents the equation between x and y.
Given that x is the number of weeks Bill added money, this indicates that he was depositing $40 into the account every week.
Because x denotes the number of weeks he was contributing money and x is by 40, not 450, the initial amount was 450.
Therefore, Weekly change: 40 and Initial investment: 450
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What does 5 less than N mean?.
5 less than N means we subtract 5 to the given variable N. So the expression will be N - 5.
What is Algebra ?Algebra shows the numbers by alphabets in a equation including mathematical operations. In algebra we used alphabet which shows a variable unknown quantity, unknown variables which helps in changing a mathematical statement into an equation.
In the given question a mathematical statement is given and we have to change the mathematical equation into an algebraic expression by using the information.
What does 5 less than N means ?The statement 5 less than N means 5 is being subtracted from N. The mathematical expression for 5 less than N is equal to N - 5.
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is 3 an element of the set {1,2,3}
Answer:
yes
Step-by-step explanation:
3 is inside the brackets
. what is the probability that a number selected at random from the set {2, 3, 7, 12, 15, 22, 72, 108} will be divisible by both 2 and 3 ? individual question
The probability that a number selected at random from the set {2, 3, 7, 12, 15, 22, 72, 108} will be divisible by both 2 and 3 is 3/8.
Given set:
random from the set {2, 3, 7, 12, 15, 22, 72, 108}
From the set:
The number that are divisible by both 2 and 3 is:
12,72,108.
So number of favorable outcomes is = 3
Number of possible outcomes = 8
we know that
probability = favorable outcomes / possible outcomes
= 3/8
= 37.5%
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3. Which statement illustrates the inverse property
of addition?
A. a + 4 = a + (-4)
B. a + (-7 + 7) = a +0
C. a + (a + 2) = a + (-a-2)
D. -a(5+3) = -5a + (-3a)
Answer:
B
Step-by-step explanation:
B. a + (-7 + 7) = a +0
When you remove a from both sides, you're left with -7+7=0 which shows that the opposites of the numbers add up to 0.
a pollster is going to sample a number of voters in a large city and construct a 90% confidence interval for the proportion who support the incumbent candidate for mayor. find a sample size so that the margin of error will be no larger than 0.05. be sure to round up to the next whole number.
Value of n for confidence interval 90% is 66.
What is confidence interval?
A confidence interval, in statistics, refers to the chance that a population parameter can fall between a collection of values for a particular proportion of times.
Main body:
Finding Sample Size for Estimating a Population Proportion:
n = [tex]\frac{z}{M}^{2} }[/tex]p(1-p)
M = is the margin of error
p = is an estimated value of the proportion
We want to construct a 90% confidence interval for with a margin of error equal to 5%.
Because there is no estimate of the proportion given, we use p = 0.50 for a conservative estimate.
For a 90% confidence interval, z = 0.816
n = (0.816/0.05)^2 *0.5(1-0.5)
n = 266.3424*0.5*0.5
n = 66 approximately
Hence value of n = 66 .
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in order to test if the mean from population a is greater than the mean from population b what kind of t-test would you use?
According to the given statement the option B and C are correct:
b) unpaired t-test
c) one-sample t-test
Briefing:We will apply an unpaired test in this situation because both populations are independent and unrelated to one another, making it impossible to pair the data from the two populations.
Consider the statement, "The mean from population A is bigger than the mean from population B," for example. This suggests that we'll utilize a single-tailed, unpaired test. Therefore, option d and b may be the best pairing.
What exactly is a one-sample t-test?To ascertain whether an unknown population mean differs from a given value, the one-sample t-test is a statistical hypothesis test.
What distinguishes a t-test with one sample from one with two samples?The t-value is calculated using your sample data from the two groups and the 2-sample t-test. The procedure is quite comparable to the 1-sample t-test, and the signal-to-noise ratio can still be compared. The 2-sample t-test necessitates independent groups for every sample, unlike the paired t-test.
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The complete question you are looking for is:
In order to test if the mean from Population A is greater than the mean from Population B what kind of t-test would you use? (can be any combination of answers)
a) two-tailed t-test
b) unpaired t-test
c) one-sample t-test
d) one-tailed t-test
e) paired t-test
Nerida Kyle is thinking of buying a car to avoid taking Lyft to work. She is using the cost-benefit principle to evaluate this decision and is calculating the costs and benefits to owning the car over the next year. She's gathered the following information to help her make her decision: The car costs $15,000 to purchase, but she can resell it after a year of use for $13,500. She thinks gas will cost her about $1,200 for the year. The annual insurance premium for her car is $800. Maintenance and repairs will cost about $300 for the year. Using Lyft to get to work would cost her $4,000 for the year. The cost of the car for the year is:
The cost of the car for the year is $3800 for Nerida Kyle and it will cost less than lyft.
The cost of the car for the year will be calculated based on the amount she will spend in total on the car. The formula to be used is -
Total cost = Cost price of the car - Selling price
Cost price of car will be sum of all the expenses, calculated as follows -
Cost price of the car = 15000 + 1200 + 800 + 300
Performing addition on Right and Side of the equation
Cost price of the car = $17,300
Total cost for the year = 17,300 - 13,500
Performing subtraction on Right and Side of the equation
Total cost for the year = $3,800
Hence, Nerida Kyle will spend $3,800 on car which is better than lift.
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a recent article posted to the journal of nutritional science surveyed dog owners to ask about their dog walking habits in order to find out whether the dogs were getting enough exercise. of course, the necessary amount of exercise varies by breed; results were categorized according to breed. read (or glance through) the article below; the study design and results sections are the most relevant.
The correct answer will be, An observational study of dog owners logged into the Channel 4 website
What is Sampling?
If the data are distributed normally, a z test can be used to determine whether the means of two populations are different from one another. This calls for the determination of the value of the z test statistic, along with the setups of the null hypothesis and alternative hypothesis. The decision-making standard is based on the z critical value for Sampling . The z critical value used during hypothesis testing divides the distribution graph into acceptance and rejection zones. The test statistic must fall inside the rejection region in order for the null hypothesis to be rejected; otherwise, it cannot.
a recent article posted to the journal of nutritional science surveyed dog owners to ask about their dog walking habits in order to find out whether the dogs were getting enough exercise.
Using a sample and normally distributed data in this case
Hence, we can say An observational study of dog owners logged into the Channel 4 website
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can someone explain how to do this with the answer pls
Answer:
x = 23
Step-by-step explanation:
The sum of two interior angles is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation based on this information to find the value of x:
2x + 3 + 51 = 100 add like terms
2x + 54 = 100 subtract 54 from both sides
2x = 46 divide both sides by 2
x = 23
What are the 4 ways to solve a system?.
Answer:
I know 3
substitution and elimation method and graphing (sorry i was never taught a fourth method ):
hopes this helps please mark brainliest
a study done on a marriage counseling course showed that the proportion of couples for which the communication program can prevent divorce is . suppose we have strong reason to believe the proportion is less than , and we carry out a hypothesis test. state the null hypothesis and the alternative hypothesis that we would use for this test.
The null hypothesis we get H₀: P≥ 77% and H₁: P< 77% when According to a study on a marriage counselling course, 77% of couples can avoid divorce.
Given that,
According to a study on a marriage counselling course, 77% of couples can avoid divorce with the help of a communication programme. Suppose we do a hypothesis test because we have good reason to assume the proportion is lower than 77%.
We have to describe the alternative hypothesis H₁ and the null hypothesis H₀ that we would employ in this test.
We know that,
According to the task we can say that,
From the definition we can say,
H₀: P≥ 77%
H₁: P< 77%
Therefore, the null hypothesis we get H₀: P≥ 77% and H₁: P< 77% when According to a study on a marriage counselling course, 77% of couples can avoid divorce.
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he length of the hypotenuse of a right triangle is hh , and the radius of the inscribed circle is rr. the ratio of the area of the circle to the area of the triangle is
Solution by e_power_pi_times_i
Since rs = A, where r is the inradius, s is the semiperimeter, and A is the area, we have that the ratio of the area of the circle to the area of the triangle is $\frac{\pi r^2}{rs} = \frac{\pi r}{s}$. Now we try to express s as h and r. Denote the points where the incircle meets the triangle as X,Y,Z, where O is the incenter, and denote AX = AY = z, BX = BZ = y, CY = CZ = x. Since XOZB is a square (tangents are perpendicular to radius), r = BX = BZ = y. The perimeter can be expressed as 2(x+y+z), so the semiperimeter is x+y+z. The hypotenuse is AY+CY = z+x. Thus we have s = x+y+z = (z+x)+y = h+r. The answer is (B) 3,14r/h+r
The ratio of the area of the circle to the area of triangle is πr : h+r.
We know that rs = A
where r is the radius , s is the semi perimeter and A is the area.
We have that the ratio of the area of the circle to the area of the triangle is
πr²/rs = πr/s.
Now we will express s as h and r. Denote the points where the in-circle meets the triangle as X,Y,Z where O is the in-center and denote
AX = AY = z, BX = BZ = y, CY = CZ = x.
Since XOZB is a square
Therefore r = BX = BZ = y.
The perimeter can be expressed as 2(x + y + x), so the semi perimeter is
x + y + z.
The hypotenuse is AY + CY = z + x.
Thus we have s = x + y + z
= (z + x) + y
s = h + r
Therefore the ratio of the area of circle to the area of the triangle will become πr : h+r.
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There are 8 cats at the pet store. 2/3 of the cats are brown. How many cats are not brown
Answer:
3 cats are not brown.
Step-by-step explanation:
First, take the 2/3 and divide 2 by 3 on a calculator to get 0.66. Then, set up this equation on the calculator:
0.66 x 8 = 5.28. We will round this to 5 cats.
Now, we take the 5 cats and subtract it from the total of 8 cats:
8 - 5 = 3 cats.
3 cats are not brown.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 12 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
What is the length of RS in the diagram TQ is 18 units in length?.
The length of RS in the diagram is 25 units.
Given:
TQ = 18 units
From the figure:
TQ = RT
2x + 10 = 18
2x = 18 - 10
2x = 8
divide by 2 on both sides
2x/2 = 8/2
x = 4 units
Both the triangles are congruent by right angled hypotenuse side criteria.
so RS = QS
= 9x - 11
= 9*4 - 11
= 25 units
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Full question:
What is the length of RS in the diagram TQ is 18 units in length?
Diagram is in the image uploaded.
use a quadratic equation to find two real numbers with a sum of 31 and a product of 210. two real numbers with a sum of 31 and a product of 210 are and
Answer:
The numbers are 10 and 21.
Step-by-step explanation:
x + y = 31
xy = 210
x = 31 - y
(31 - y)y = 210
31y - y² = 210
y² - 31y + 210 = 0
(y - 21)(y - 10) = 0
y - 21 = 0 or y - 10 = 0
y = 21 or y = 10
The two real numbers are 10 and 21.
What is a quadratic equation?Quadratic Equations are algebraic expressions of degree 2 in one variable and are of the form ax² + bx + c = 0.
In simpler terms, a quadratic equation is be defined as a polynomial equation of degree 2.
Given that, there are two real numbers with a sum of 31 and a product of 210.
We need to find their values using the concept of quadratic equation,
So, according to the question,
x + y = 31 (eq 1)
xy = 210 (eq 2)
x = 31 - y
(31 - y) y = 210
31y - y² = 210
y² - 31y + 210 = 0
(y - 21) (y - 10) = 0
y - 21 = 0 or y - 10 = 0
y = 21 or y = 10
Hence, the two real numbers are 10 and 21.
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The masts for the Millennium Dome were held up during construction by wire ropes as shown in the diagram. A is 106 m above the ground, C is vertically below A, the gradient of AB is 1 and CD is 53 m. a Find the gradient of AD. b Find the length of BD.
a)The gradient of AD will be 2.
b)The length of BD. will be 159 m.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.
It is given that, A is 106 m above the ground, C is vertically below A, the gradient of AB is 1 and CD is 53 m.
Suppose the length BC is x
Gradient of AB = 1
AB/BC=1
106/x=1
x=106
BC=106 m
CD = 53 m
The gradient of AD is,
m = BC/CD
m=106/53
m=2
b)
The length of BD is found as,
BD=BC+CD
BD=106+53
BD=159 m
Thus, the gradient of AD will be 2 and the length of BD. will be 159 m.
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