smith put some money in a saving certificate which earns 8% a year. the yearly interest in $600. how much did smith invest?

The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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Answer:

x = –5

Step-by-step explanation:

1) The area of a circle circumscribed about a square is 307.7 cm².

2.a.) The angle ACB is 39 degrees.°.

2b.) The value of x is 5.42.

We shall find the radius to determine the area of a circle.

First,  find the side length of the square:

Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.

Next, find the diagonal of the square, using the Pythagorean theorem:

Diagonal = the diameter of the circumscribed circle.

Diagonal² = side length² + side length²

= 14 cm² + 14 cm²

= 196 cm² + 196 cm²

= 392 cm²

Take the square root of both sides:

Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)

Then, the radius of the circle which is half the diagonal:

Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)

Finally, compute the area of the circle using the formula:

Area = π * Radius²

Area = 3.14 * (9.90 cm)²

Area ≈ 307.7 cm² (rounded to two decimal places)

Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².

2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.

Given that arc AB has a measure of 78°, we can find angle ACB as follows:

Angle ACB = 1/2 * arc AB

= 1/2 * 78°

= 39°

Therefore, the angle ACB is 39 degrees.

2b.) To solve for the value of x, we use the information that the angle ADB =  (3x - 12)⁴.

Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:

(3x - 12)⁴ = 78

Solve the equation for x, by taking the fourth root of both sides:

∛∛((3x - 12)⁴) = ∛∛78

Simplify,

3x - 12 = ∛(78)

Isolate x by adding 12 to both sides:

3x - 12 + 12 = ∛(78) + 12

3x = ∛(78) + 12

Finally, divide both sides by 3:

x = (∛(78) + 12) / 3

x = (4.27 +12) / 3

x = 5.42

So, x is 5.42

Therefore,

1) The area of the circle is 154 cm².

2a.) Angle ACB is equal to 102°.

2b.) The value of x is 5.42

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In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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Answer:

The value of y is 216

(and the value of x is 12)

Step-by-step explanation:

The general formula for a geometric sequence is,

\(a_n = a_1(r)^{n-1}\)

Where n represents the nth term, a_1 is the first term and r is the common ratio,

we see that,

r = 6,

the first term is,

a_1 = (x-6)

the 2nd term is,

a_2 = 3x,

the 3rd term is,

a_3 = y, finding y,

first we find x, using the above given formula we have,

\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)

x = 12,

Now, for y we can use the relation between a_3 and a_2,

\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)

y = 216

Step-by-step explanation:

x^2+5x+7x+35=0

x*x+5x+7x+5*7=0

x(x+5)+7(x+5)=0

(x+7)*(x+5)=0

x=-7 or x=-5

So the function is positive (>0) when

x<-7 and when x>-5

Answer:

The coordinates of the vertex are (-1,-4).

Step-by-step explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

\(y-k=a(x-h)^2\)

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

We are given the function:

\(y=x^2+2x-3\)

We must transform the equation above by completing squares:

The first two terms can be completed to be the square of a binomial. Recall the identity:

\(x^2+2xy+y^2=(x+y)^2\)

Thus if we add and subtract 1:

\(y=(x^2+2x+1)-3-1\)

Operating:

\(y=(x^2+2x+1)-4\)

The trinomial in parentheses is a perfect square:

\(y=(x+1)^2-4\)

Adding 4:

\(y+4=(x+1)^2\)

Comparing with the vertex form of the quadratic function, we have the vertex (-1,-4).

The coordinates of the vertex are (-1,-4).

Answer:

True A. angles one and five are corresponding angles.

True B. angles three and six are alternate interior angles.

False C. angles two and seven are alternate interior angles.

Angles two and seven are alternate exterior angles.

False D. angles five and eight are alternate exterior angles.

Angles five and Eight are verticle angles.

False E. angles two and four are same-sided consecutive angles.

Angles two and four are supplementary angles

True F. angles four and six are same side consecutive angles.

True G. angles one and eight are alternate exterior angles.

The total weight of the bottles the truck carries is 6020 ounces.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

Example:

2 + 1x + 4y = 7 is an expression.

3 + 3x + 3 = 7 is an expression.

We have,

Number of bottles the truck carries = 430

One bottle weight = 14 ounces

Now,

The total weight of the bottles.

= Number of bottles x Weight of one bottle

= 430 x 14

= 6020 ounces

Thus,

The total weight of the bottles the truck carries is 6020 ounces.

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Answer:

2nd answer option : 6^(13/4)

Step-by-step explanation:

what are we doing, when 2 equal base terms with exponents are multiplied ? we add the exponents !

this is like 3⁴×3³ = 3⁷

because

3×3×3×3 × 3×3×3 = 3×3×3×3×3×3×3 = 3⁷

it is that simple.

and that concept is also valid for any kind of number as exponent. even for fractions and so on.

so,

6^3 × 6^(1/4) = 6^(3 + 1/4) = 6^(12/4 + 1/4) = 6^(13/4)

22 cubic inches is the volume of the pyramid.

The volume of the triangular prism is 66 cubic inches.

In order for us to know the volume of the triangular pyramid,

First we need to know the ratio of the volume of triangular prism and the volume of the triangular pyramid.

Volume of the pyramid = 1/3 × volume of the prism.

The volume of the prism is sixty six cubic inches

Now to find the volume of the pyramid plug in the value of volume of the pyramid.

Volume of the pyramid = 1/3 × 66

We get twenty two cubic inches

Volume of the pyramid = 22 cubic inches.

Hence, the volume of the pyramid is 22 cubic inches.

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A triangular pyramid has the same base and height as a triangular prism. The volume of the prism is 66 cubic inches. What is the volume of the triangular pyramid?

Answer:

1

Step-by-step explanation:

The absolute value of -3 is 3, so 4-3=1

Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

First, lets find the general equation for Cost(C) as function of mile driven (m) for each company.

Company A:

Fixed value (initial fee): $40

Variable value (function of mile driven): $0.60

The cost for a truck in company A (Ca) will be:

Ca = 40+0.6m

Company B:

Fixed value (initial fee): $49.50

Variable value (function of mile driven): $0.50

Cb = 49.50+0.5m

The questions asks the value of m in which company A will charge less than company B. Then:

Ca40+0.6m<49.50+0.5m

0.6m-0.5m<49.50-40

0.1m<9.50

m<9.50/0.1

m<95

Answer: m < 95 mile driven.

Answer:

The distance is less than 216 inches.

Step-by-step explanation:

Each feet has 12 inches.

The large shelves in the storage area are 17 feet 8 inches apart

So, in inches, this distance is of:

17*12 + 8 = 212

This distance is less than 216 inches.

Answer:1 just like my answer dawg

Step-by-step explanation:

The equation for the bag with all nuts is 13 / ( 1/4 ) = 52 bags

Given data ,

Bob packs 13 pounds of nuts in bags.

Each bag has 1/4 pound of nuts

Now , the number of bags = pounds of nuts / pounds of nuts in each bag

A = 13 / 1/4

On simplifying the equation , we get

A = 52 bags

Hence , the number of bags is 52 bags

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Answer:

 =6mx^4−7x^4

Step-by-step explanation:

(6m−7)(x^4)

=(6m+−7)(x^4)

=(6m)(x^4)+(−7)(x^4)

\(\huge\text{Hey there!}\)

\(\mathsf{(6m - 7)\times4}\)

\(\mathsf{= (6m - 7)(4)}\)

\(\mathsf{= (6m - 7) 4}\)

\(\mathsf{= 4(6m - 7)}\)

\(\mathsf{= 4(6m) - 4(-7)}\)

\(\mathsf{= 6m(4) + (-7)(4)}\)

\(\mathsf{= 6m(4) - 7(4)}\)

\(\mathsf{= 6m - 28}\)

\(\huge\textbf{Therefore, your answer should be:}\)

\(\huge\boxed{\frak{24m - 28}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

c

Step-by-step explanation:

it's a property of powers, when the base is the same (-5) , you need to

sum the powers when both terms are multiplyng

subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)

Answer

1. x²+2x-24

2. 2x²-1x-15

3. 6x²+19x+10

4. 2x²-11x+5

Answer:

\(x^{2} +2x-24\)

\(2x^{2}-x-15\)

\(6x^{2}+19x+10\)

\(2x^{2}-11x+5\)

Step-by-step explanation:

Answer:

Option 1

Step-by-step explanation:

\(\frac{2x^2 - 7x-4}{x^2 - 5x+4}=\frac{(x-4)(2x+1)}{(x-4)(x-1)}=\frac{2x+1}{x-1}\)

The approximate distance around the outside of the circular field is the circumference = 172.7 feet and the correct option is B.

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π = 3.14).

We shall derive the approximate distance around the outside of the circular field by calculating for the circumference as follows:

Radius of the circular feild = 27.5

circumference of the circular feild = 2 × 27.5 feet × 3.14

circumference of the circular feild = 55 feet × 3.14

circumference of the circular feild = 172.7 feet.

Therefore, the approximate distance around the outside of the circular field is derived as the circumference which is equal to 172.7 feet.

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Answer:

i think the answer is C

Answer:

For this case we must explain how to simplify the following expression:

( -9)(-6)(15)(-7+7)

According to the PEMDAS algebraic resolution order method, operations within parentheses must be performed first.

So, we have:

-7+7

Different signs are subtracted and the major sign is placed.

-7+7=0

Rewriting the original expression we have:

(-9)(-6)(15)(0)=

Every number multiplied by "0" results in "0".

Then, the expression is zero.

(-9)(-6)(15)=0

Answer:

(-9)(-6)(15)(-7+7)=0

Answer:

400

Step-by-step explanation:

(4 × 10^6) / (1 × 10^4) =

= 4/1 × 10^6/10^4

= 4 × 10²

= 400

Answer: 400

Answer:

so the first one is 400,000

the second one is 10,000

try to subtract and if that doesn't help divide the two

Step-by-step explanation:

Step-by-step explanation:

(x,y)-----(-20,-4)-----(-17,-5)

to go from -17 to -20 you subtract 3

to go from -20 to x you subtract 3 again to get -20-3=-23

to go from -5 to -4 you add 1

to go from -4 to y you add 1 again to get -4+1=-3

(-23,-3)  (the midpoint is equidistant from both endpoints)

The first option is the correct one for the line y = x - 2:

" coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2)"

Here we want to identify the graph of the linear equation:

y = x - 2

First, notice that when we evaluate this in x = 0 we get the y-intercept:

y = 0 - 2

y = -2

Then the y-intercept there is (0, -2)

Also, evaluating the linear equation in x = -2, then we will get:

y = -2 - 2

y = -4

So we have the point (-2, -4)

Then the correct option is the first one:

" coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2)"

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The cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

To find the cost of one hosta and one geranium, we can set up a system of equations based on the given information.

Let's assume the cost of one hosta is represented by 'h' and the cost of one geranium is represented by 'g'.

From the information given, we can set up the following equations:

Eugene's spending:

18h + 6g = $150

Jessica's spending:

7h + 16g = $113

We can now solve this system of equations to find the values of 'h' and 'g'.

Multiplying the first equation by 2 and the second equation by 3 to eliminate 'g', we get:

36h + 12g = $300

21h + 48g = $339

Now, we can subtract the second equation from the first to eliminate 'h':

(36h + 12g) - (21h + 48g) = $300 - $339

36h - 21h + 12g - 48g = -$39

15h - 36g = -$39

Simplifying further, we have:

15h - 36g = -$39

Now we can solve this equation for 'h' and substitute the value back into any of the original equations to find 'g'.

Let's solve for 'h':

15h = 36g - $39

h = (36g - $39) / 15

Substituting this value of 'h' into Eugene's equation:

18[(36g - $39) / 15] + 6g = $150

(648g - $702) / 15 + 6g = $150

648g - $702 + 90g = $150 * 15

738g - $702 = $2250

738g = $2250 + $702

738g = $2952

g = $2952 / 738

g ≈ $4

Now, substituting the value of 'g' back into Eugene's equation:

18h + 6($4) = $150

18h + $24 = $150

18h = $150 - $24

18h = $126

h = $126 / 18

h ≈ $7

Therefore, the cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

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