in a right triangle with the hypotenuse c and the legs a and b, c^2=2ab. find the measure of each acute angle.

Answer:

$15000 in bonds, $55000 in a CD

Step-by-step explanation:

Let x represent the amount Betsy invests in the B-rated bonds (in thousands). Then she will invest 70-x in a CD. Her interest (in thousands) will be ...

0.15x + .05(70 -x) = 5

0.10x + 3.5 = 5 . . . . . . . eliminate parentheses, collect terms

x + 35 = 50 . . . . . . . . . . multiply by 10

x = 15 . . . . . . . . . . . . . . . subtract 35

Then 70-x = 70-15 = 55

Betsy should invest $15000 in bonds, and $55000 in a CD.

To achieve $5000 in annual interest, Betsy should invest $15000 in B-rated bonds and $55000 in CDs.

Betsy, a recent retiree, requires $5000 per year in extra income. She has $70000 to invest and is considering two options: B-rated bonds paying 15% per year and certificates of deposit (CD) paying 5% per year. To find out how much she should invest in each to realize exactly $5000 in interest per year, we can set up a system of linear equations.

Let x be the amount invested in B-rated bonds and y be the amount invested in CDs. The equations based on the investment and the total interest required would be:

To solve this system, multiply the second equation by 100 to get rid of decimals:

Now, we can multiply the first equation by 5 to get:

Subtracting this from the modified second equation:

Plug the value of x back into the first equation:

Betsy should invest $15000 in B-rated bonds and $55000 in a CD to achieve $5000 in annual interest.

Answer:

Vel_jet_r =  (464.645 mph)  North + (35.35 mph) East

||Vel_jet_r|| =  465.993 mph

Step-by-step explanation:

We need to decompose the velocity of the wind into a component that can be added  (or subtracted from the velocity of the jet)

The velocity of the jet

500 mph North

Velocity of the wind

50 mph SouthEast = 50 cos(45) East + 50 sin (45) South

South = - North

Vel_ wind = 50 cos(45) mph  East  -  50 sin (45) mph North

Vel _wind =  35.35 mph  East  -  35.35 mph North

This means that the resulting  velocity of the jet is equal to

Vel_jet_r =  (500 mph - 35.35 mph) North + 35.35 mph East

Vel_jet_r =  (464.645 mph)  North + (35.35 mph) East

An the jet has a magnitude velocity of

||Vel_jet_r|| =  sqrt ((464.645 mph)^2 + (35.35 mph)^2)

||Vel_jet_r|| =  465.993 mph

Answer:

3.7 < √14 < 3.8

Step-by-step explanation:

First approximation

9 < 14 < 16, so

3 < √14 < 4

Second approximation

14 is closer to 16 than to 9.

Is √14 between 3.7 and 3.8? If so, then

 3.7²  < 14 <   3.8²

13.69 < 14 < 14.44. TRUE

The inequality is 3.7 < √14 < 3.8.

Answer:77

32+27+22+17+12+7+2-3-8-13-15-18=77

Answer:

54

Step-by-step explanation:

The first twelve terms would be, in decreasing order, 32, 27, 22, 17, 12, 7,2, -3, -8,-13,-18,-23.

1. -23+22 = -1

2. -13+12 = -1

3. -18+17 = -1

4. -8+7 = -1

5. -3+2 = -1

Using these five facts, we can simplify this to 32+27 -5(1) = 32+27-5 = 54

Answer:

  80

Step-by-step explanation:

The square of a binomial is ...

  (a +b)^2 = a^2 + 2ab + b^2

You have a=8q, b=5, so the square is ...

  (8q)^2 + 2(8q)(5) + (5)^2

  = 64q^2 +80q +25

The coefficient missing from your given expression is 80.

Answer:

The answer is -3t(t^4 - 6t² - 1) ⇒ third answer

Step-by-step explanation:

∵ -3t^5 + 18t³ + 3t

∵ The common factor is -3t

∴ -3t(t^4 - 6t² - 1)

The observed value when x = 3, estimated to the nearest half unit is y = 4.5.

The observed value is the actual value of the variable. The points on the regression line are called predicted values.

Therefore, the observed value of y when x = 3, estimated to the nearest half unit is y = 4.5. The correct answer is option C.

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Answer: - 2.5n+13.5

Explanation:

[tex]11 - 8.5 = 2.5 \\ - 2.5n \times 1 = - 2.5 \\ it \: is \: negative \: as \: the \: sequence \: \\ decreases\\ 11 - - 2.5 = 13.5 \\ - 2.5n + 13.5[/tex]

The explicit rule for the sequence 11, 8.5, 6, 3.5, 1 is to subtract 2.5 from the previous term.

To find the explicit rule, we look for a pattern in the sequence. We can see that each term is decreasing by a constant amount. Let's calculate the difference between consecutive terms:

- The difference between the second term (8.5) and the first term (11) is 8.5 - 11 = -2.5.

- The difference between the third term (6) and the second term (8.5) is 6 - 8.5 = -2.5.

- The difference between the fourth term (3.5) and the third term (6) is 3.5 - 6 = -2.5.

- The difference between the fifth term (1) and the fourth term (3.5) is 1 - 3.5 = -2.5.

Since the difference is constant and equal to -2.5, we can express the nth term of the sequence, [tex]\( a_n \)[/tex], as:

[tex]\[ a_n = a_{n-1} - 2.5 \][/tex]

where [tex]\( a_{n-1} \)[/tex] is the previous term in the sequence. To express this in terms of n, we need to find the first term of the sequence and then apply the pattern. The first term, [tex]\( a_1 \)[/tex], is 11. Since we are subtracting 2.5 each time, the nth term can be written as:

[tex]\[ a_n = a_1 - (n - 1) \cdot d \][/tex]

where [tex]\( d \)[/tex] is the common difference, which is -2.5. Substituting [tex]\( a_1 = 11 \) and \( d = -2.5 \)[/tex], we get:

[tex]\[ a_n = 11 - (n - 1) \cdot (-2.5) \][/tex]

[tex]\[ a_n = 11 + 2.5n - 2.5 \][/tex]

[tex]\[ a_n = 8.5 + 2.5n \][/tex]

Therefore, the explicit rule for the nth term of the sequence is:

[tex]\[ a_n = 8.5 + 2.5n \][/tex]

This rule gives us the terms of the sequence when we substitute n = 1, 2, 3, 4, 5, etc. For example, for n = 1:

[tex]\[ a_1 = 8.5 + 2.5(1) = 8.5 + 2.5 = 11 \][/tex]

which matches the first term of the sequence.

Answer: (-6) is the answer for your question

Answer:

184

Step-by-step explanation:

1st step

we simplify (5-1) which is just 4 and (3+7) which is 10

and we also simply 6^2 which is 36

now we plug the simplified terms back in

(4)(36+10)

(4)(46)

184

Answer:

184

Step-by-step explanation:

Subtract: 5 - 1 = 4

Power: 6 ^ 2 = 36

Add: 36 + 3 = 39

Add: 39 + 7 = 46

Multiple: 4 * 46 = 184

Please mark as brainiest

Answer:

Step-by-step explanation:

Let n represent the number of laps that Alan completes in 9 minutes. Then n-1 is the number of laps Brian completes, and the difference in their lap times in minutes per lap is ...

  9/(n -1) - 9/n = 3/4 . . . . . minutes

Multiplying by (4/3)n(n -1), we get

  12n -12(n -1) = n(n -1)

  12 = n(n -1)

Solutions to this are n=4 and n=-3. We are only interested in the positive solution, n = 4. Then Alan's speed in m/min is ...

  (4·450 m)/(9 min) = 200 m/min

Brian completes 3 laps in that 9-minute time, so his rate is ...

  (3·450 m)/(9 min) = 150 m/min

Answer:

The correct answer option is B. c = 25 + 2m.

Step-by-step explanation:

We are given that a movie rental club charges a one time fee of $25 to join and $2 for every movie rented.

We are to determine whether which of the given equations in the answer options represent how much you would spend to join the club and rent movies for a year.

The correct answer option is B. c = 25 + 2m.

One time charges = 25 plus $2 multiplied by the number of movies rented.

Answer:

  $5.25

Step-by-step explanation:

If the friend tripled the first purchase and subtracted twice the second purchase, he would have the cost of 3·8-2·5 = 14 notebooks. 7 notebooks would cost half that amount:

  (3·$11 -2·11.25)/2 = $5.25 . . . . . cost of 7 notebooks

Answer:

The marked choice is correct

Step-by-step explanation:

The scale factor is the ratio of the dimensions of the second figure to those of the first:

1.45/5.8 = 0.25

Answer:The scale factor is 0.25. Trust me, its right!

Answer:

They meet in 3 hours

Step-by-step explanation:

Add 4 and 5, this gives you 9 miles an hour. Divide 27 by 9 and it results in 3 hours

Answer:

99.7 °C

Step-by-step explanation:

The units of ciron tell us that in order to have °C in the numerator, we need to divide the heat loss by the product of the mass and ciron:

∆T = (6900 J)/(0.444 j/g°C × 200 g) = 69/0.888 °C ≈ 77.7 °C

This is the change in temperature as the ball cooled, so its initial temperature was ...

22 °C +77.7 °C = 99.7 °C

Answer:

d. 2√34 cm

Step-by-step explanation:

Secant BD is the hypotenuse of right triangle ABD with legs given as AB = 6 cm and AD = 10 cm. Hence the Pythagorean theorem can be used to find BD:

BD = √(AB² +AD²) = √((6 cm)² +(10 cm)² = √136 cm = 2√34 cm

she went a total of 46.75 miles

Answer:

  b² -2ab +a²

Step-by-step explanation:

The first factor can be rearranged to put the minus sign in the middle. Then you have

  (b -a)(b -a) = (b -a)² = b² -2ab +a²

___

If you like, you can also write this as ...

  a² -2ab + b² . . . . . . terms in lexicographical order

_____

The "special product" of interest here is the square of a binomial:

  (p +q)² = p² +2pq +q²

You have p=b, q=-a, so the result is as shown above.

Shouldn’t it be 180 because that half of a circle (360)

I think this should be it!

Answer:

1.2g+0.4

Step-by-step explanation:

The equivalent expression should be 1.2g+0.4.

The equation is (0.7g+0.6h-0.4)+(0.8-0.6h+0.5g)

= (0.7g+0.6h-0.4)+(0.8-0.6h+0.5g)

= 0.7g + 0.6h - 0.4 + 0.8 - 0.6h + 0.5g

= 1.2g + 0.4

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Answer:

1800

Step-by-step explanation:

Given in the question a polygon of 12 sides

Formula to calculate sum of interior angles of 12-gon is

where n is the number of sides

which in this case = 12

plug values in the formula above

(12 - 2)180

12*180 - 180(2)

2160 - 360

1800

Sum of measurements of the interior angles of a 12sided polygon is 1800

Answer:

=1800°

Step-by-step explanation:

A 12 sided figure is called a do-decagon or a 12-gon. The general formula for calculating the sum of all interior angles of a regular polygon is=180(n-2)

n represents the number of sides of the polygon.

Therefore, the sum of all angles= 180(12-2)

=1800°

Answer:

A). Sometimes.

Step-by-step explanation:

Sometimes a translation  because it might be a rotation or a reflection.

Translation in geometry always results in a similar figure. Hence, the correct answer is C.

A similar figure compared to the original figure is **always** a translation.

Translation in geometry involves moving a figure without rotating or flipping it. When a figure is translated, all the points move in the same direction by the same distance. This means that a translation produces a figure that is congruent to the original figure.

Answer:

D. (2, 5)

Step-by-step explanation:

On a graph, (2, 5) is the only point in the solution space.

___

You can evaluate the inequality for each of the points to see which works.

A. 4 > 2·4 -3 . . . . false

B. 12 > 2·9 -3 . . . . false

C. 2 > 2·3 -3 . . . . false

D. 5 > 2·2 -3 . . . . TRUE

Answer:

  2 feet below the ground level at the place where he started.

Step-by-step explanation:

After he adds 12 feet of elevation to the 6 feet above ground level where he launched, Mr Burnam is 6+12 = 18 feet above the ground level where he launched.

If he descends 20 feet, he will be 18 -20 = -2 feet above the ground level where he launched. That is, he is 2 feet below the ground level where he launched. We hope the ground slopes downward somewhat so Mr Burnam is not buried in the ground at that point.

Mr. Burnam ends up at 8 feet above ground.

To determine Mr. Burnam's final position, we need to consider each of his movements:

1. He starts from 6 feet above ground.

2. He ascends 12 feet further, so we add 12 feet to his initial height of 6 feet, which gives us (6 + 12 = 18) feet.

3. Then, he descends 20 feet to meet his wife. We subtract these 20 feet from his current height of 18 feet, which gives us (18 - 20 = -2) feet.

Since he can't be below ground, we adjust the calculation to reflect that he stops at ground level. Therefore, we take the absolute value of the result to find out how far above ground he is after the descent. The absolute value of -2 feet is 2 feet.

Now, we add this to the initial 6 feet from which he launched: (6 + 2 = 8) feet.

So, Mr. Burnam ends up at 8 feet above ground after all the ascending and descending.

Subtract 10k from both sides:

[tex] kx^2+5x-10k = 0 [/tex]

Assuming [tex]k\neq 0[/tex], divide both sides by k:

[tex] x^2+\dfrac{5}{k}x-10 = 0[/tex]

When you write a quadratic equation as [tex]x^2-sx+p [/tex], you know that the two solutions follow the properties

[tex]x_1+x_2=s,\quad x_1x_2=p [/tex]

So, in this case, we have

[tex]x_1+x_2=-\dfrac{5}{k},\quad x_1x_2=-10 [/tex]

Since we know that [tex]x_1=-5[/tex] we have:

[tex]\begin{cases}-5+x_2=-\dfrac{5}{k}\\ -5x_2=-10\end{cases}[/tex]

This system has solution [tex]k=\frac{5}{3},\ x=2[/tex]

Answer:

2

Step-by-step explanation:

One root = -5

We know ,

Other root is 2 .

Answer:

  area of the triangle is about 15,183.766

Step-by-step explanation:

The sum of the two shortest sides is 367, which is greater than the longest side, hence these side lengths can form a triangle.*

The perimeter is ...

  p = 240 +127 +281 = 648

so the semi-perimeter is ...

  s = p/2 = 648/2 = 324

Heron's formula tells you the area is ...

  A = √(s(s -a)(s -b)(s -c)) = √(324·84·197·43) = √230,546,736

  A ≈ 15,183.766

The area of the triangle is about 15,183.766 square units.

_____

* The terms s-a, s-b, and s-c are all positive, which is further evidence the side lengths will form a triangle. If one or more of those factors is negative, the side lengths will not form a triangle.

Answer:

4

Step-by-step explanation:

The distance from B to C is the same as the distance from A to D. Points B and C will both have the same x-value, as do points A and D. Points B and C will have the same difference in y-values (2 -(-2) = 4) that points A and D have.

The distance from B to C is 4 units.

Answer:

  1/6

Step-by-step explanation:

The three numbers, a, b, c, satisfy the equations ...

Subtracting the last equation from the first gives ...

  (a +b +c) -(a +b -5c) = (1) -(0)

  6c = 1

  c = 1/6

Now, we know the sum of the first two numbers is 5/6 (five times the last), and the difference of the first two numbers is 1/6 (equal to the last). Then the least of the first two numbers is ...

  (5/6 -1/6)/2 = 1/3

and the third number, 1/6, is shown to be the smallest.

The smallest of these numbers is 1/6.

____

In order, the numbers are 1/2, 1/3, 1/6.

____

Comment on finding the second-smallest number

For ...

We can find b by subtracting the second equation from the first:

  (a +b) -(a -b) = (5/6) -(1/6)

  2b = 4/6 = 2/3 . . . . . simplify

  b = 1/3 . . . . . . . . . . . . divide by 2

Please note that half the difference of the sum and difference is the generic solution to finding the smallest in a "sum and difference" problem.