x-y-4z=-9
4x-3y-2z=-9
-x-3y-6z=-7

solve

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:

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

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.

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:

  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.

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

Answer:

 =705.79

Step-by-step explanation:

F=P(1+i)n  where F is the Future amount P is the Present amount/Capital i is the interest rate n is the number of periods.

In this case you have the given as follows:

    P = $500 i = 9% n = 4 years

Substituting the values to the formula you'll have:

F=500(1+0.09)^4

 =705.79

Answer:

  B.  4

Step-by-step explanation:

When you perform the multiplication, you get ...

  (x +c)(x +4) = x² + (c+4)x +4c = x² + 8x +4c

Then ...

  c + 4 = 8 . . . . coefficients of x must match

  c = 4 . . . . . matches choice B

Answer:

20

Step-by-step explanation:

The number of combinations of 6 points taken 3 at a time is ...

6!/(3!·(6-3)!) = 6·5·4/(3·2·1) = 5·4 = 20

___

If you number the points 1–6, the points of the 20 triangles will be ...

123 124 125 126 134

135 136 145 146 156

234 235 236 245 246

256 345 346 356 456

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:

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:

The measure of the arc PJ is [tex]75\°[/tex]

Step-by-step explanation:

step 1

Find the measure of angle L

we know that

In a inscribed quadrilateral opposite angles are supplementary

so

[tex]m<L+m<J=180\°[/tex]

we have

[tex]m<J=110\°[/tex]

substitute

[tex]m<L+110\°=180\°[/tex]

[tex]m<L=70\°[/tex]

step 2

Find the measure of arc KJ

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<P=\frac{1}{2}(arc\ LK+arc\ KJ)[/tex]

substitute the values

[tex]95\°=\frac{1}{2}(125\°+arc\ KJ)[/tex]

[tex]190\°=(125\°+arc\ KJ)[/tex]

[tex]arc\ KJ=190\°-125\°=65\°[/tex]

step 3

Find the measure of arc PJ

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<L=\frac{1}{2}(arc\ PJ+arc\ KJ)[/tex]

substitute the values

[tex]70\°=\frac{1}{2}(65\°+arc\ PJ)[/tex]

[tex]140\°=(65\°+arc\ PJ)[/tex]

[tex]arc\ PJ=140\°-65\°=75\°[/tex]

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:

C

Step-by-step explanation:

The equation of a line is given by the formula  [tex]y-y_1=m(x-x_1)[/tex]

Where [tex]x_1[/tex] is the x-coordinate (it is given as 5)

[tex]y_1[/tex] is the y-coordinate (it is given as 1), and

m is the slope (it is given  as -3)

Plugging in all the info into the formula we have:

[tex]y-y_1=m(x-x_1)\\y-1=-3(x-5)[/tex]

From the answer choices, we see that C is the correct answer.

Answer:

c.y-1 = -3(x-5)

Step-by-step explanation:

We have given slope of a line and the point that is passing through the line.

slope  = -3 and (x₁,y₁) = (5,1)

We have to find the equation of line.

y-y₁ = m(x-x₁) is point-slope form of the equation of line where m is slope.

Putting given values in above formula, we have

y-(1) = -3(x-(5))

y-1 = -3(x-5) is the equation of the line through (5,1) with a slope of -3.

Answer:

  84.5%

Step-by-step explanation:

The area of the smaller square is ...

  smaller square = (5.98 cm)^2 = 35.7604 cm^2

The area of the larger square is ...

  larger square = (15.2 cm)^2 = 231.04 cm^2

So, the shaded area is ...

  larger square - smaller square = (231.04 -35.7604) cm^2 = 195.2796 cm^2

Then a randomly chosen point will be in the shaded region this fraction of the time:

  (shaded area)/(larger square area) = 195.2796/231.04 ≈ 0.84522 ≈ 84.5%

Answer:

The graph of the line in the attached figure

Step-by-step explanation:

we have

[tex]y+7=\frac{2}{3}(x+6)[/tex]

This is the equation of a line into point slope form

The slope is [tex]m=\frac{2}{3}[/tex]

The line pass through the point (-6,-7)

To graph the line find the y-intercept

Remember that

The y-intercept of the line is the value of y when the value of x is equal to zero

so

For x=0

[tex]y+7=\frac{2}{3}(0+6)[/tex]

[tex]y+7=\frac{2}{3}(6)[/tex]

[tex]y+7=4[/tex]

[tex]y=4-7=-3[/tex]

The y-intercept is the point (0,-3)

with the point (-6,-7) and (0,-3) plot the line

see the attached figure

Answer:

1234567890

Step-by-step explanation:

1234567890-zxhjk

The right choice is (C) A translation that leaves the origin fixed while changing the shape of the curve

A transformation in which the center of rotation is fixed and everything else on the plane rotates about that point by a given angle is called rotation. A rotation is described by the centre of rotation, the angle of rotation, and the direction of the turn. The centre of rotation is the point that a shape rotates around. Each point in the shape must stay an equal distance from the centre of rotation.

Answer: a translation that leaves the origin fixed while not losing the shapes of the curves

Step-by-step explanation:

Answer:

it is d

Step-by-step explanation:

Answer:

  b.  secants

Step-by-step explanation:

A line that intersects a circle in two places is called a "secant."

___

It is a tangent line if it intersects the circle in one point.

It is a diameter if it is a chord that goes through the center of the circle.

It is a chord if it is a line segment with each endpoint being on the circle. (BE and CD are chords.)

"Cosecant" is the name of the trigonometric function that is the ratio of the hypotenuse of a right triangle to the side opposite the angle of interest.

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

I think this should be it!

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:

1.12 B. sin(s) = cos(u)

1.13 C. showing similar triangles

Step-by-step explanation:

1.12 First of all, it is useful to identify the complementary angles. These are the two acute angles in the same right triangle: (s, u) or (t, v), or the adjacent angles that together make a right ange: (s, t) or (u, v).

Only choices B and D involve complementary angles. Only choice B shows the right relationship between trig functions of those angles.

___

1.13 It helps if you've seen the short, cute proof of the Pythagorean theorem using similar triangles. One of the early steps in the proof is to show the triangles are similar: choice C.

Even if you've never seen that proof, you can still make a good guess as to the correct choice. Choices A and D are just plain incorrect. Choice B might be the end result of the proof of the Pythagorean theorem, but won't be a step in that proof. In any event, the point of the proof is to show AC^2 + BC^2 = AB^2, not the equation of choice B.

That leaves choice C, which is both correct and likely to be a step in the proof.

A. 0

The slope of a horizontal line is always 0.

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:

Step-by-step explanation:

Answer:

The average rate of change of [tex]f(x)=x^2 + 7x + 10[/tex] over the interval [tex]-20\leq x\leq -15[/tex] is -28.

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by this expression:

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

It is a measure of how much the function changed per unit, on average, over that interval.

To find the average rate of change of [tex]f(x)=x^2 + 7x + 10[/tex] over the interval [tex]-20\leq x\leq -15[/tex] you must:

Evaluate x = -15 and x = -20 into the function f(x)

[tex]f(-15)=(-15)^2 + 7(-15) + 10=130\\f(-20)=(-20)^2 + 7(-20) + 10=270[/tex]

Applying the expression for the average rate of change we get

[tex]\frac{f(-15)-f(-20)}{-15+20} \\\\\frac{130-270}{-15+20} \\\\\frac{-140}{5}\\\\-28[/tex]

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)

she went a total of 46.75 miles

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.

Answer:

9%

Step-by-step explanation:

✯Hello✯

↪  We can formulate an equation to help us solve this

↪  800(x%) = 728 in this case x=91

↪  We do 100-91 meaning that this is a 9% decrease on price

↪  To check that this is correct we can work out 9% of 800 which is 72

When subtracting 72 from 800 it is confirmed that 728 is the right amount

❤Gianna❤

Final answer:

To find the percent of decrease in the TV's price, calculate the difference between the original and the new price, divide by the original price, and multiply by 100, which results in a 9% decrease.

Explanation:

To calculate the percent of decrease when the price of a TV is reduced from $800 to $728, you subtract the new price from the original price and then divide by the original price. Next, you multiply the result by 100 to get the percentage.

Step-by-step calculation:

Find the difference in price: $800 - $728 = $72.

Divide the difference by the original price: $72 ÷ $800 = 0.09.

Multiply by 100 to get the percentage: 0.09 x 100 = 9%.

So, the percent of decrease in the price of the TV is 9%.