A woman has a total of $9,000to invest. She invests part of the money in an account that pays7%per year and the rest in an account that pays9%per year. If the interest earned in the first year is$710, how much did she invest in each account? She invested $___ at 7% and $___ at 9%.

Answer:

A = 1160

B = 1160 is already in standard form.

C = 1200

Answer:

Explanation

temperature in a town during day=12.5The temperature in a town is 12.5°F

temperature at night is -23.3°F

difference -23.3°F+12.5°F

=. -10.8

Yes, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

Here,

The differential equation (1-xy)y' = y^2

And,  y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2.

What is Differential equation?

A differential equation is a mathematical equation that relates some function with its derivatives.

Now,

To show y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2, we have to find the solution of differential equation.

The differential equation is;

[tex](1-xy)y'=y^2\\\\\\\\[/tex]

[tex](1-xy) \frac{dy}{dx} = y^2[/tex]

[tex]\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }[/tex]

It is form of  [tex]\frac{dx}{dy} + Px = Qy[/tex],

Where, P is the function of y and Q is the function of x.

Hence, Integrating factor = [tex]e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y[/tex]

The solution is;

[tex]x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c[/tex]

[tex]xy = lny + c[/tex]

Take c = 0, we get;

[tex]xy = lny\\\\y = e^{xy}[/tex]

Hence, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

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Work Shown:

AB+BC = AC

(11) + (2x-1) = 3x+3

2x+10 = 3x+3

2x-3x = 3-10

-x = -7

x = 7

which is then use to find:

As a check,

AB+BC = 11+13 = 24 = AC which confirms the answer.

Answer:

Step-by-step explanation:

What are you trying to find? If you want to find x then:

5x = 134 - 9

5x = 125

x = 25

if you want square root then,

x = √625    or

x = 5^2

Answer:

Step-by-step explanation:

let x = 5, y = 0

so the equation is 4x+y>9

and put the value of x and y in the equation

4 (5) + 0 > 9

20 + 0 > 9

20 > 9, therefore the order pair ( 5,0) satisfies the condition. true

Answer:

-32

Step-by-step explanation:

Pal, it's M A T H

Answer:

-32

Step-by-step explanation:

x-2x-20=12

-x=32

x=-32

.....................

Answer:

12

Step-by-step explanation:

There are 12 1/2's in 6.

To find how many 1/2's there are in 6, you have to divide 6 by 1/2.

6 ÷ 1/2

To divide by a fraction, you have to multiply by the reciprocal (reverse the numerator and denominator of a fraction).

6/1 × 2/1

6 × 2

= 12

Have a lovely rest of your day! :)

Answer:

In equation form it should be: (6-x) -11

Step-by-step explanation:

BOOM!!! Your Welcome

Answer:

x = 4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

I got you bro dont worry

7) No, y has two different values when x = -1.

8) Yes, each value of x maps onto only one value of y.

9) Yes, each value of x maps onto only one value of y.

By cross multiplication, we have found the following results:

a) 20 miles are equal to 32.180 kilometers.

b) 64 kilometers are equal to 39.776 miles.

In this problem we must convert a given value in a unit into its equivalent quantity in another unit of same kind. We must convert miles to kilometers and viceversa by using conversion rates and cross multiplication.

First, we must convert a distance of 20 miles to kilometers by cross multiplication:

x = 20 mi × (1.609 km / 1 mi)

x = 32.180 km

Second, we must convert a distance of 64 kilometers to miles by cross multiplication:

x = 64 km × (1 mi / 1.609 km)

x = 39.776 mi

The graph is missing, but this question can resolved by using conversion rates, that is, a mile equal 1.609 kilometers.

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Answer:

here is the answer⬇️

True, ax=b requires only one solution to be homogeneous. If ax=b is consistent, the ax=b solution set is acquired by translating the ax=0 solution set.

A two-linear equation system can have one solution, an infinite number of solutions, or even no solution. The number of solutions distinguishes equation systems.

Some key features regarding the consistent are-

Therefore, if the equation ax=0 has a trivial solution, the columns of the a matrix A are linearly independent.

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Answer:

43

Step-by-step explanation:

800 × 8% × (8/12)

1. 1.371742E−3

2. 256 .

What is an Exponent?

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 2³) means: 2 x 2 x 2 = 8.

It is written as a small number to the right and above the base number.

Here in the question we find out (9)∧-3 and (4)∧4

1.  (9)∧-3 =x∧n=9−1

x∧n=9-³

=1/9³

=1/9×9×9

=1/729

=0.0013717421124829

=1.371742E−3

2. (4)∧4 =x∧n=4∧4

=4×4×4×4

=256

The meaning of exponent is a symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power.

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The mode of the data is 39 as it's frequency is highest .

Mode is a measure of central tendency . It is the no . which has highest frequency in data .

Data - Frequency

 40   -   6

 35   -   7

 37   -   7

39   -   12      ( max . )

 36   -   5

 38   -   6

 41   -   4

The value of frequency corresponding to 39 is maximum .

Therefore , as 39 occurs most of the time in the data , hence it is the mode of this data .

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Answer: the slope=0

Step-by-step explanation:

[tex]\displaystyle\\(7,-2)\ and\ (7,5)\\[/tex]

                        [tex]\displaystyle\\\boxed {the \ slope=\frac{y_2-y_1}{x_2-x_1} }[/tex]

[tex]x_1=7\ \ \ \ \ x_2=7\ \ \ \ y_1=-2\ \ \ \ \ y_2=5\\Hence,\\\displaystyle\\the slope=\frac{7-7}{5-(-2)} \\\\the\ slope=\frac{0}{5+2} \\\\the\ slope=\frac{0}{7}\\\\ the\ slope=0[/tex]

Answer:

n - 4 = - 15

Step-by-step explanation:

Hope this helps :)

Answer:

-9.5

Step-by-step explanation:

The surface area of a igloo with a 20 ft. diameter is [tex]628ft^{2}[/tex]

According to question statement, we are supposed to find the surface area of an igloo with a 20ft. diameter.

Before solving this question, we should be aware of the fact that an igloo is of a Hemispherical shaped object usually made up of ice.

So for finding out area of igloo we find the surface area of of the hemisphere.

Curved Surface area : [tex]2\pi r^{2}[/tex]

Total Surface area: [tex]3\pi r^{2}[/tex]

where r is the radius of igloo.

Radius is half of the diameter therefore [tex]r=\frac{diameter}{2}[/tex]

[tex]r=\frac{20ft}{2} \\r=10ft[/tex]

Therefore radius is 10 ft.

Curved Surface Area: [tex]2*3.14*10^{2} =628ft^{2}[/tex]

Total Surface Area: [tex]3*3.14*10^{2} =942ft^{2}[/tex]

But as we are supposed to find the surface area therefore the answer is [tex]628ft^{2}[/tex].

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The transformed equation is:

F(x) = G(x + 2) = (x + 2)^2

So we can se that the correct option is D.

We know that the graph of F(x) has the same shape of G(x) = x^2, but shifted to the left 2 units.

Remember that for a random function f(x), a shift of 2 units to the left is written as:

h(x) = f(x + 2).

Then, in this case, we can write:

F(x) = G(x + 2)

Replacing G(x), we can get the transformed equation:

F(x) = G(x + 2) = (x + 2)^2

So we can se that the correct option is D.

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Answer:

A) It can be represented using the formula f(x + 1) = 6/5(f(x)) when f(1) = 10/3.

C) It can be represented using the formula f (x) = 10/3(6/5)/\x-1

What is sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given:

10/3, 4, 24/5, 144/25, ...

From the above sequence we can generate the formula,

f (x) = 10/3

Also, for f(x+1) we can have

x=1,

f(1)= 10/3

f(2)= 4

So, f(x + 1) = 6/5(f(x))

Step-by-step explanation:

Above given the the linear equations. Systems of liner equations in three variables using substitution method, the variables are (-3.2, -0.218, 0.06).

The standard form for the linear equations in two variables is Ax+ By =C. For example, 2x+3y=5 is a linear equation in the standard form. When an equation is given in this form, it's pretty easy to find the both intercepts (x and y). This form is also very useful when solving systems of the two linear equations.

Solve one of the equation for one of it's variables. From the given three variables, there is no incorrect choice so choose to solve for any variable.

x= y+ z -3

Substitute the value from the first variable we solved for into the other equation and solve for the next variable.

(y+z-3) +y +3z = -2

2y+4z= 1

y= [tex]\frac{1+4z}{2}[/tex]

Substitute the value from the two variables that we solved and plug it into the remaining equation and solve for the last remaining variable.

3([tex]\frac{1+4z}{2}[/tex]+z-3) - 2 ([tex]\frac{1+4z}{2}[/tex]) + 3z= -12

3([tex]\frac{1+4z+2z-6}{2}[/tex])- 2([tex]\frac{1+4z}{2}[/tex])+ 3z= -12

3([tex]\frac{6z-5}{2}[/tex])- 2([tex]\frac{1+4z}{2}[/tex])+3z = -12

[tex]\frac{18z-15}{2}[/tex]- 1+ 4z+ 3z= -12

18z-15-2+8z +6z= -24

32z-17=-24

32z=-24+17

z=[tex]\frac{-7}{32}[/tex]= -0.218

therefore, y= 0.06

Now substitute the values:

x= 0.06+(-0.218)-3= -3.2

The three variables are (-3.2, -0.218, 0.06)

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The total costs are the same when a kayak is rented for 5 hours

How do we determine the hours that both have the same costs?

The hours that both shops have the same cost is determined by equating the total cost in shop A to the total  cost in shop B, in short, we need to first of all , model the total cost in each shop based on the straight-line equation formula shown below since the total cost is made of fixed charge and variable charge

y=a+bx

y=total cost

a=fixed charge for each shop

b=hourly fee

x=number of hours

Shop A:

total cost=8+3x

Shop B:

total cost=3+4x

8+3x=3+4x

8-3=4x-3x

5=x

At 5 hours both Shops A and B would have the same cost

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The hours when the cost of renting the kayaks would be the same is 5 hours.

The total cost of renting a kayak is $23.

The equation that can be used to represent the total cost of renting a kayak is a linear function. A linear equation is an equation whose graph is a straight line. A linear equation increases by a predetermined constant. An example of a linear equation is x + 2.

The form that the equation would be is:

Total cost = rental fee + (hourly fee x number of hours)

Total cost at Shop A = $8 + $3h

Total cost Shop B = $3 + $4h

Where h is the number of hours the kayak was rented.

When the total costs are equal, the two above equations would be equal.

$3 + $4h  =  $8 + $3h

Combine similar terms: $4h - $3h=  $8 - $3

Add similar terms together: h = 5 hours

Total cost = $3 + $4(5)

$3 + $20 = $23

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The percentage increase in the student's height is 10.52%.

Here we are given that a student's height increases from 1.52m to 1.68m.

Thus, the absolute increase in the student's height will be-

1.68 - 1.52 = 0.16 meters.

Now, we need to find the percentage increase in the student's height.

The formula for calculating percentage increase is given by-

Percentage increase = change in value/ initial value * 100

Here, the change in value is 0.16 meters and the initial value is 1.52 meters.

Thus, percentage increase in height = 0.16 / 1.52 *100

= 1600/ 152

= 400/ 38

= 200/ 19

= 10.52%

Thus, the increase in the student's height is 10.52%.

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answer:

6/x + 9 = 11

explanation:

6 div. 3= 2

2+9=11