MATHEMATICS HIGH SCHOOL

Evaluate the expression, -1 x (-0.1 x -5 + 0.5)

Answers

Answer 1

Answer:

Answer:

-1

Step-by-step explanation:

-1 x (-0.1 x -5 + 0.5)

= -1 x 1

= -1

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Write 6,730,000 in scientific notation

Answers

6.7x10^6 always the the decimal points go between the first 2 numbers, and you count the numbers of decimal places following it to get your scientific exponent

The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?

Answers

The answer is:
a = c ÷ 2
b = P - a - c

The perimeter is the sum of all sides of a polygon. The perimeter of the triangle is:
P = a + b + c
where
P - perimeter of the triangle,
a, b, c - sides of the triangle.

It is given:
P = 14.5 cm
c = 6.2 cm

If, the longest side (c) is twice that of the shortest side (a), then
c = 2a
Therefore, the equation that can be used to find the length of the shortest side is a = c ÷ 2.

⇒ a = c ÷ 2 = 6.2 cm ÷ 2
⇒ a = 3.1 cm

By knowing two sides (c and a) and perimeter (P), we can calculate the length of the third side (b).
If P = a + b + c, then the equation that can be used to find the length of the side b is b = P - a - c.

⇒ b = P - a - c = 14.5 cm - 6.2 cm - 3.1 cm
⇒ b = 5.2 cm

Final answer:

The equation to find the side lengths of the triangle is x + 2x + (14.5 - x - 2x) = 14.5, using x to represent the shortest side.

Explanation:

The subject of this question is a scalene triangle. A scalene triangle is a triangle in which all sides have different lengths. In this specific triangle, we are given the perimeter (which is 14.5 cm), and we know that the longest side is twice the length of the shortest side. The longest side's length is given as 6.2 cm.

Let's denote the shortest side as x. If the longest side is twice that length, we can express it as 2x. Now, the remaining side can be found by subtracting x and 2x from the total perimeter: 14.5 - x - 2x. So our equation becomes x + 2x + (14.5 - x - 2x) = 14.5.

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The perimeter of a rectangle is 90 centimeters. The width of the rectangle can be represented by (x + 2), and its length can be represented by (3x - 5). What are the dimensions of this rectangle in centimeters?A With = 10 and length = 25
B With = 12 and length = 29
C With = 14 and length = 31
D With = 16 and length = 32

Answers

Perimeter of a rectangle=2lenght + 2width
In this case:
Perimeter=90 cm
width=(x+2)
lenght=(3x-5)
Then:

2(x+2)+2(3x-5)=90
2x+4+6x-10=90
2x+6x=90+10-4
8x=96
x=96/8
x=12

with=(x+2)=12+2=14
lenght=(3x-5)=3*12-5=31

Answer: C width=14 and lenght=31.

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation 2x3 + 8x2 = 450 can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.4 inches
5 inches
9 inches
10 inches

Answers

The length of the side of the original cube in the given scenario is 5 inches.

A cube is a three-dimensional figure with equal sides.

Given that

The length of the edge of a cube = x

Also, one of the sides is increased by 4 inches, and another side is doubled,

so, now the new dimensions are x, x+4, 2x, and the shape is a rectangular prism.

The area of the rectangular prism = 450 sq. inches

base × height × length = 450 sq. inches

x × (x + 4) × 2x = 450

2x³ + 8x² = 450

2x³ + 8x² - 450 = 0

x³ + 4x² - 225 = 0

Substitute x=5 to see that it is a root of the equation,

5³ + 4(5)² - 225 = 125 + 100 - 225 = 0

So, x - 5 is a factor of the equation,

Now,

x³ + 4x² - 225 = (x−5)(x² + 9x + 45) = 0

The roots of the quadratic equation are imaginary as

D = 9² - 4 × 1 × 45 = 81 - 180 = -99

The discriminant is negative, therefore, the roots are not real.

So, the length of the side of the original cube is 5 inches.

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the answer i got is 5 inches im glad to help

What is the effective interest rate of an 8% 13-week Treasury bill? Assume it is a $10,000 Treasury bill, and round your answer to the nearest hundredth percent.

Answers

Answer:

The answer is 8.24%.

Step-by-step explanation:

The rate r = 8% is for 1 year or 52 weeks.

As given there are 13 weeks term so total there will be = 4 terms.

So, n = 4

The effective interest rate R is given by:

R = $(1+r/n)^n-1$

= $(1+0.08/4)^4-1$

= $(1.02)^4-1$

= 0.0824

And in percentage, it is 8.24%.

The effective interest rate is $\boxed{8.24\% }$ and the interest is $\boxed{200}.$

Further explanation:

The compound interest rate formula can be expressed as follows,

$\boxed{A = P{{\left( {1 + i}\right)}^n}}$

Here, A represents the amount, P represents the principal amount, i represents the interest rate and n represents the time.

The interest rate in a year is known as the effective interest rate.

The relationship between effective interest rate and nominal interest rate can be expressed as follows,

$\boxed{i = {{\left( {1 + \frac{{{i^n}}}{n}}\right)}^n} - 1}$

Here, i represents the effective interest rate, ${i^n}$ represents the nominal interest rate, n represents the period of interest rate.

Given:

The nominal interest rate is $8\%$ in a 13 week treasury bill.

The amount of Treasury bill is $\$ 10000.$

Explanation:

There are 52 weeks in a year.

The value of n can be calculated as follows,

$\begin{aligned}n&= \frac{{52}}{{13}}\n&= 4\n\end{aligned}$

The effective interest rate can be calculated as follows,

$\begin{aligned}i&= {\left( {1 + \frac{{0.08}}{4}} \right)^4} - 1\n&= {\left( {1.02} \right)^4} - 1\n&= 0.0824\n\end{aligned}$

The interest can be calculated as follows,

$\begin{aligned}{\text{Interest}}&= P* i * t\n&= 10000* 0.08 * \frac{{13}}{{52}}\n&= 200\n\end{aligned}$

The effective interest rate is $\boxed{8.24\% }$ and the interest is $\boxed{200}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Compound interest

Keywords: Principal, invested, interest rate, account, effective interest rate, total interest, 8\% Treasury bill, nearest hundredth percent, amount.

Order the following masses from least to greatest: 500 g, 50 kg, 5,000 mg