james invested some money at 13% interest. James also invested $199 more than 3 times that amount at 12%. How much is invested at each rate if James receives $1561.50 in interest after one year? (Round to two decimal places if necessary.)

Answer:

x = 65

Step-by-step explanation:

x = √(25×(25+144))

x = √(25×169)

x = 5×13

x = 65

Answered by GAUTHMATH

[tex]\\ \Large\sf\longmapsto h(t)[/tex]

[tex]\\ \Large\sf\longmapsto 2+8t-3t^2+\dfrac{1}{5}t^3[/tex]

[tex]\\ \Large\sf\longmapsto 2+8(3)-3(3)^2+\dfrac{1}{5}(3)^3[/tex]

[tex]\\ \Large\sf\longmapsto 2+24-3(9)+\dfrac{27}{5}[/tex]

[tex]\\ \Large\sf\longmapsto 26-27+5.4[/tex]

[tex]\\ \Large\sf\longmapsto -2+5.4[/tex]

[tex]\\ \Large\sf\longmapsto h(t)=3.4m[/tex]

Answer:

m= - 2, b = 4

Step-by-step explanation:

structure of a linear equation

y = mx + c

m = gradient / slope

c = intercept

convert the given equation according to this structure of linear equations

4x+2y = 8

2y = -4x + 8

y = -2x +4

according to this intercept is 4 and slope is -2

Answer:

C. (2)

Step-by-step explanation:

an integer is a WHOLE NUMBER

have an amazing day :)

Answer:

2 is an integer

Step-by-step explanation:

An integer is a whole number, it does not have a fractional part

Answer:

(3/2,10)

Step-by-step explanation:

Mid point is ((10-7)/2,(13+7)/2)=(1.5,10)

Answer:

4

Step-by-step explanation:

To start off, we are going to input our x value into our expression.

3|-5| + 2(-5) - 1

Next, we are going to find the absolute value (always positive) of -5 and multiply 2 and -5.

3(5) - 10 -1

Now, we will multiply 3 and 5.

15 - 10 -1

Finally, we are going to combine our like terms (15, -10, and -1)

4

So! Our final answer for this expression is 4!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

54

Step-by-step explanation:

20% of 15 is 3 so Quentin is 18 years old

If Quentin is one thrid his Aunt's age that means his aunt is three times older.

18 * 3 = 54

So his Aunt is 54 years old

The age of Quentin's aunt is 54 years if the Quentin is one third the age of his aunt if we solve by making the Quentin's Aunt age as variable x.

An equation is a formula that expresses the equality of variables.

let the age of the aunt is x years.

According to the question the age of Quentin is x/3 years.

The age of Quentin's  sister is x/3*100/120

=5x/18

We have been given the age of Quentin's sister is 15 years.

So, 5x/18=15

=x=54 years

Hence the age of aunt is 54 years old.

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Answer:

Option B

Step-by-step explanation:

This is the formula :

2(wl+hl+hw)

Step 1 : Take the length, width, and height and substitute the values in.

The required surface area of the rectangular prism is 461.02 square meters (m²).

Surface area is defined as the measure of a region or surface is called as surface area.

The surface area of a rectangular prism can be calculated by adding up the areas of all six faces. The formula for the surface area of a rectangular prism is:

Surface area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

Substituting the given values, we get:

Surface area = 2(12.3m x 4.3m) + 2(12.3m x 10.7m) + 2(4.3m x 10.7m)

Simplifying the expression gives:

Surface area = 461.02m²

Therefore, the surface area of the rectangular prism is 461.02 square meters (m²).

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Answer:

53.68

Step-by-step explanation:

tan54 = bc/39

bc = 39tan54

Step-by-step explanation:

Hey there!

From the given figure;

Angle CAB = 54°

Side AC = 39

To find: side BC

Taking Angle CAB as reference angle;

Perpendicular (p) = BC = ?

Base (b) = AC = 39

Hypotenuse (h) = AB

Taking the ratio of tan;

[tex] \tan( \alpha ) = \frac{p}{b} [/tex]

Keep value;

[tex] \tan(54) = \frac{bc}{39} [/tex]

Simplify it;

1.376381*39 = BC

Therefore, BC = 53.678.

Hope it helps!

Answer:

200 grams

Step-by-step explanation:

80 grams        x grams

-------------- = -------------

6 people        15 people

Using cross products

80 *15 = 6x

1200 = 6x

Divide by 6

1200/6 = 6x/6

200 =x

Step-by-step explanation:

how to find the area

multiply the length times the width

19 × 6 = 114 inches squared

The area of the rectangle is 114 square inches if the length and breadth of the rectangle are 19 inches and 6 inches.

A rectangle is one of the elementary geometric figures. It is a quadrilateral with a pair of equal and parallel sides. All angles of a rectangle are right angles.

The length of the rectangle is given as 19 inches.

The breadth of the rectangle is given as 6 inches.

The area of the given rectangle is given as:

Area = length × breadth

Area = 19 × 6

Area = 114 square inches

Thus, the area of the given rectangle is 114 square inches.

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Answer:

Hello,

polynomial is x²-x+1

Step-by-step explanation:

if a=b*c+r then a=c*b+r

Using a long division, see the picture.

9514 1404 393

Answer:

  400 mL/h

Step-by-step explanation:

The required rate is ...

  (100 mL)/(1/4 h) = 100×(4/1) mL/h = 400 mL/h

Answer:

ACB = JCB

Step-by-step explanation:

ASA means angle - (included) side - angle.

we have one angle confirmed.

we have the connected side BC confirmed (the diagram shows that the side is shared, so it is not only congruent, it is actually identical).

now we need confirmation for the angle at the other end point of that side.

Answer:

a. Relative Growth rate = 10% (6/60 * 100)

b. Number of cells after t hours = 50 * 1.1^t

c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)

d. The number of cells after 6 hours is

= 89 cells

Step-by-step explanation:

A cell divides into two cells every 20 minutes

In one hour, the cell will divide into 60/20 * 2 = 6 cells

Each cell growth 6 cells per hour

Initial population of a culture = 50 cells

t = time in hours

a. Relative Growth rate = 10% (6/60 * 100)

b. Number of cells after t hours = 50 * 1.1^t

c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)

d. The number of cells after 6 hours = initial population * growth factor

= 50 * 1.772

= 88.6

= 89 cells

Answer:

Dependent variable = Total daily cost

Independent variable = number of items manufactured

2500 ;

9750

Step-by-step explanation:

Given the cost function in. A manufacturing company :

C(x) = 7.25x + 2500 ; Where

C(x) = total daily cost

x = number of items manufactured

The Independent variable is the variable whose value causes a change in the measured variable, this is the number of items manufactured, and the variable which charges as the predictor variable charges is the dependent variable (Total daily cost).

2.)

C(0) ;

C(x) = 7.25x + 2500

Put x = 0

C(0) = 7.25(0) + 2500

Cost = 2500

This is the total daily cost even if no items are produced, this is probably the fixed cost of daily production.

3.)

C(1000)

C(x) = 7.25x + 2500

Put x = 1000

C(0) = 7.25(1000) + 2500

Cost = 7250 + 2500

Cost = 9750

This is the total cost including variable cost of producing 1000 items.

Answer: 15

Step-by-step explanation:

Answer:

[tex]c - 2 = 25 + 10 \sqrt c + c[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{c-2} - \sqrt c = 5[/tex]

Required

Isolate radical, then square both sides

We have:

[tex]\sqrt{c-2} - \sqrt c = 5[/tex]

Isolate radical

[tex]\sqrt{c - 2} = 5 + \sqrt c[/tex]

Square both sides

[tex](\sqrt{c - 2})^2 = (5 + \sqrt c)^2[/tex]

[tex]c - 2 = 25 + 2 * 5 * \sqrt c + c[/tex]

[tex]c - 2 = 25 + 10 \sqrt c + c[/tex]

Answer:

D. 11

Step-by-step explanation:

First apply the secant-secant theorem to find the value of x.

Thus,

VU(TU + VU) = VW(BW + VW) (secant-secant theorem)

Substitute

(7)(x + 4 + 7) = (9)(-2 + x + 9)

7(x + 11) = 9(7 + x)

7x + 77 = 63 + 9x

Collect like terms

7x - 9x = 63 - 77

-2x = -14

Divide both sides by -2

x = 7

✔️Find TU

TU = x + 4

Substitute get value of x

TU = 7 + 4 = 11

Answer:

11

Step-by-step explanation:

Answer:

m∠ AEB = m∠ CED ......... By Vertical Angles Theorem.

Step-by-step explanation:

Vertical Angles Theorem: Vertical angle theorem states that vertical angles, angles that are opposite each other and formed by two intersecting lines, are congruent. If two lines intersect each other, we have the two pair of vertical opposite angles. As shown in the figure. Here, ∠ 1 and ∠ 2 are vertical opposite angles, and also they are equal. ∠ 3 and ∠ 4 are also vertical opposite angles, and also they are equal. For, step 3. m∠ AEB = m∠ CED Therefore, the reason for this proof is Vertical Angles Theorem.

Answer:

The answer is "-3.04"

Step-by-step explanation:

[tex]\to \bar{x_1}-\bar{x_2}=9-11=-2[/tex]

Sample distribution:

[tex]z=\frac{\bar{x_1}-\bar{x_2}- \bar{\mu_1}-\bar{\mu_2}}{\sqrt{\frac{\sigma_{1}^2}{n_1}+\frac{\sigma_{2}^2}{n_2}}}\\\\[/tex]

   [tex]=\frac{(-2)-0}{\sqrt{\frac{3^2}{49}+\frac{4^2}{64}}}\\\\=\frac{-2}{\sqrt{\frac{9}{49}+\frac{16}{64}}}\\\\=\frac{-2}{\sqrt{\frac{576+784}{3136}}}\\\\=\frac{-2}{\sqrt{\frac{1360}{3136}}}\\\\=\frac{-2}{\sqrt{0.433}}\\\\=\frac{-2}{0.658}\\\\=-3.039\\\\=-3.04[/tex]

Answer:

d. y+8=2(x-4)

Step-by-step explanation:

There are 2 important parts to this question. First, understanding which slopes are perpendicular. The negative reciprocal of a number will be perpendicular to it. So, since the original slope is -1/2 the new slope should be 2.

Then, remember what the point-slope formula is. The point-slope formula is: [tex]y-y_{2}=m(x-x_{2})[/tex]. So if you plug in the point and slope the new equation looks like, [tex]y--8=2(x-4)[/tex]. Then, simplify for the final answer of [tex]y+8=2(x-4)[/tex].

Answer:

10 or -10,

Read the explanation

Step-by-step explanation:

Rewrite this problem as a numerical expression. As per the wording of this problem, there can be two expressions derived.

1.     [tex]((\frac{1}{6}(10*3)*4)-30[/tex]

2.     [tex]30-((\frac{1}{6}(10*3)*4)[/tex]

Simplify, remember the order of operations. The order of operations is the sequence by which one is supposed to perform operations in a numerical expression. This order is the following:

1. Parenthesis

2. Exponents

3. Multiplication or division

4. Addition or Subtraction

Use this sequence when simplifying and solving the expression:

Expression 1

[tex]((\frac{1}{6}(10*3)*4)-30\\\\=((\frac{1}{6}(30)*4)-30\\\\=(5*4)-30\\\\=20 - 30\\\\= -10[/tex]

Expression 2

[tex]30-((\frac{1}{6}(10*3)*4)\\\\=30-((\frac{1}{6}(30)*4)\\\\=30-(5*4)\\\\= 30-20\\\\= 10[/tex]

Answer:

24 years

Step-by-step explanation:

total ratio =8

older student=40 years

3/8*40 ÷ 5/8=24

can you zoom in on my pic more or no does it say 1/z

Answer:

Option A. Reciprocal

Answered by GAUTHMATH

Answer:

[tex]f(-1) = -10[/tex]

[tex]f(0) =- 8[/tex]

[tex]f(2) = 4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 6x - 4[/tex] --- [tex]x < 0[/tex]

[tex]f(x) = 6x - 8<0[/tex] -- [tex]x \ge 0[/tex]

Solving (a); f(-1)

Here [tex]x= -1[/tex]

[tex]-1 < 0[/tex], so:

[tex]f(x) = 6x - 4[/tex]

[tex]f(-1) = 6 *-1 -4[/tex]

[tex]f(-1) = -10[/tex]

Solving (b); f(0)

Here [tex]x = 0[/tex]

[tex]0 \ge 0[/tex], so:

[tex]f(x) = 6x - 8[/tex]

[tex]f(0) = 6*0 - 8[/tex]

[tex]f(0) =- 8[/tex]

Solving (c) f(2)

Here [tex]x = 2[/tex]

[tex]2 \ge 0[/tex], so:

[tex]f(x) = 6x - 8[/tex]

[tex]f(2) = 6*2 - 8[/tex]

[tex]f(2) = 4[/tex]

Answer:

Step-by-step explanation:

If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:

[tex]11=-5t^2+30t+1[/tex] and

[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get

t = .35 seconds and t = 5.6 seconds

Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.