All categories

2 years ago

50 Benson purchased a $1,800 certificate of deposit that earns s

Mathematics

1 answer:

Pavlova-9 [17]2 years ago

5 0

Answer:

3.2%

Step-by-step explanation:

The computation of the annual rate of interest is shown below:

As we know that

Simple interest = Principal × rate of interest × time period

($1,857.60 - $1,800) = $1,800 × rate of interest × 1

$57.60 = $1,800 × rate of interest × 1

So, the rate of interest is

= $57.60 ÷ $1,800 × 100

= 3.2%

Hence, the rate of interest on annual basis is 3.2%

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What is the area of a circular region whose diameter is 10 centimeters?

stepan [7]

Answer:

78cm

Step-by-step explanation:

d = 10

area of a circle = πr^2

22/7 × 5 × 5

78.5cm

6 0

2 years ago

without building the graph, find the coordinates of the point of intersection of the lines given by the equation y=3x-1 and 3x+y

DaniilM [7]

<h2><u>1. Determining the value of x and y:</u></h2>

Given equation(s):

$y = 3x - 1$
$3x + y = -7$

To determine the point of intersection given by the two equations, it is required to know the x-value and the y-value of both equations. We can solve for the x and y variables through two methods.

<h3 /><h3><u>Method-1: Substitution method</u></h3>

Given value of the y-variable: 3x - 1

Substitute the given value of the y-variable into the second equation to determine the value of the x-variable.

$\implies 3x + y = -7$

$\implies3x + (3x - 1) = -7$

$\implies3x + 3x - 1 = -7$

Combine like terms as needed;

$\implies 3x + 3x - 1 = -7$

$\implies 6x - 1 = -7$

Add 1 to both sides of the equation;

$\implies 6x - 1 + 1 = -7 + 1$

$\implies 6x = -6$

Divide 6 to both sides of the equation;

$\implies \dfrac{6x}{6} = \dfrac{-6}{6}$

$\implies x = -1$

Now, substitute the value of the x-variable into the expression that is equivalent to the y-variable.

$\implies y = 3(-1) - 1$

$\implies$ $\ \ = -3 - 1$

$\implies$ $= -4$

Therefore, the value(s) of the x-variable and the y-variable are;

$\boxed{x = -1}$ $\boxed{y = -4}$

<h3 /><h3><u>Method 2: System of equations</u></h3>

Convert the equations into slope intercept form;

$\implies\left \{ {{y = 3x - 1} \atop {3x + y = -7}} \right.$

$\implies \left \{ {{y = 3x - 1} \atop {y = -3x - 7}} \right.$

Clearly, we can see that "y" is isolated in both equations. Therefore, we can subtract the second equation from the first equation.

$\implies \left \{ {{y = 3x - 1 } \atop {- (y = -3x - 7)}} \right.$

$\implies \left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.$

Now, we can cancel the "y-variable" as y - y is 0 and combine the equations into one equation by adding 3x to 3x and 7 to -1.

$\implies\left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.$

$\implies 0 = (6x) + (6)$

$\implies0 = 6x + 6$

This problem is now an algebraic problem. Isolate "x" to determine its value.

$\implies 0 - 6 = 6x + 6 - 6$

$\implies -6 = 6x$

$\implies -1 = x$

Like done in method 1, substitute the value of x into the first equation to determine the value of y.

$\implies y = 3(-1) - 1$

$\implies y = -3 - 1$

$\implies y = -4$

Therefore, the value(s) of the x-variable and the y-variable are;

$\boxed{x = -1}$ $\boxed{y = -4}$

<h2><u>2. Determining the intersection point;</u></h2>

The point on a coordinate plane is expressed as (x, y). Simply substitute the values of x and y to determine the intersection point given by the equations.

⇒ (x, y) ⇒ (-1, -4)

Therefore, the point of intersection is (-1, -4).

<h3>Graph:</h3>

5 0

1 year ago

Questions is <br><br>1)what two bodies of water do the coastal lowlands border

Katena32 [7]

Im pretty sure that the answe would be northern plains

3 0

2 years ago

A ship traveled for a total of 147 miles over the course of 8 hours. Heading south, the ship traveled at an average speed of 15

Cloud [144]

Alright

s=number of hours headd south
e=number of hours headed east

s+e=8

and
total is 147 miles
distance=speed times time
15s+24e=147

we got 2 equations

s+e=8
15s+24e=147
subsitution

s+e=8
minus e both sides
s=8-e
subsitut 8-e for s in other equaton

15s+24e=147
15(8-e)+24e=147
120-15e+24e=147
120+9e=147
minus 120 both sides
9e=27
divide both isdes by 9
e=3

sub back
s=8-e
s=8-3
s=5

it was headed south 5 miles

6 0

2 years ago

Plssss help thankyou

natta225 [31]

Answer:

2nd answer choice No, 6/2 does not equal 2/24 :)

Step-by-step explanation:

6/2=3 while 24/10=2.4

Another way you could think about it:

6*2=12

2+2=4

6*3=18

4+2=6

6*4=24

6+2=8

So 24 ounces of the shake would only be 8 grams of protein.

5 0

2 years ago