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3 years ago

BRAINLIEST ANSWER!!!! #9 1/4 (5x+2)-1/5(x+3)=2 what’s the solution set?

Mathematics

1 answer:

Nina [5.8K]3 years ago

3 0

x=2 from cross multiplying.

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Calculate the value of (6.72 10^5)+ (3.2 x 10^4)<br> Give your answer in standard form.

dangina [55]

Answer:

$7.04\cdot 10^{5}$ <em>or 704,000</em>

Step-by-step explanation:

<u>Standard Form of Numbers</u>

Any number that we can write as a decimal number between 1.0 and 10.0, multiplied by a power of 10, is said to be in Scientific Notation. Some authors consider standard form and scientific form as the same, but others state that standard form is the common form of expressing numbers, i.e., a sequence of digits, separated by thousands by a comma, and separated from the decimal part by a dot.

We'll give here both answers.

We have to calculate:

$6.72\cdot 10^{5}+3.2\cdot 10^{4}$

Since the numbers don't have the same exponent, we must make them equal. Let's make the second number have an exponent of 5, by dividing by 10:

$6.72\cdot 10^{5}+3.2\cdot 10^{4}=6.72\cdot 10^{5}+3.2/10\cdot 10^{5}$

$6.72\cdot 10^{5}+3.2\cdot 10^{4}=6.72\cdot 10^{5}+0.32\cdot 10^{5}$

Now we add:

$6.72\cdot 10^{5}+3.2\cdot 10^{4}=7.04\cdot 10^{5}$

It's correctly expressed in scientific notation. Now to convert to 'standard form', multiply by $10^5=100,000$ :

$6.72\cdot 10^{5}+3.2\cdot 10^{4}=7.04*100,000=704,000$

7 0

3 years ago

The Chewy Candy Company is test marketing a new candy bar in Seoul and Manila.

Anon25 [30]

The first month in which the board will see the cumulative total number of candy bars sold in Manila exceeded the cumulative total in Seoul is of:

3rd month.

<h3>What are linear functions?</h3>

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are defined as follows:

m is the slope, representing the rate of change.

b is the y-intercept, representing the initial value.

For the functions in this problem, the slope and the intercept are given as follows:

Slope: Monthly increase.

Intercept: amount sold by the end of the first month.

Taking the end of the first month as a parameter, the functions are defined as follows:

Seoul: S(m) = 40 + 60(m - 1).

Manila: M(m) = 20 + 80(m - 1).

Then Manila exceeds Seoul when:

M(m) > S(m)

20 + 80m - 80 > 40 + 60m - 60

20m > 40

m > 2.

2.1 for example is in the 3rd month, hence the 3rd month is the correct answer.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

3 0

1 year ago

Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. How many total kilograms of candy did he buy?

nignag [31]

Answer:

1.26 kg.

Step-by-step explanation:

We have been given that Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. We are asked to find the amount of candy bought by Mr. Snow in kilograms.

First of all, we will find the amount of candy in grams by multiplying 90 grams by 14 as:

$\text{Amount of candy bought in grams}=14\times 90$

$\text{Amount of candy bought in grams}=1260$

We know that 1 kilogram is equal to 1000 grams. To convert 1260 grams into kg, we will divide 1260 by 1000 as:

$\text{Amount of candy bought in kilograms}=\frac{1260}{1000}$

$\text{Amount of candy bought in kilograms}=1.26$

Therefore, Mr. Snow bought 1.26 kilograms of candy.

7 0

3 years ago

Find the critical points of the surface f(x, y) = x3 - 6xy + y3 and determine their nature.

Vedmedyk [2.9K]

Compute the gradient of $f$ .

$\nabla f(x,y) = \left\langle 3x^2 - 6y, -6x + 3y^2\right\rangle$

Set this equal to the zero vector and solve for the critical points.

$3x^2-6y = 0 \implies x^2 = 2y$

$-6x+3y^2=0 \implies y^2 = 2x \implies y = \pm\sqrt{2x}$

$\implies x^2 = \pm2\sqrt{2x}$

$\implies x^4 = 8x$

$\implies x^4 - 8x = 0$

$\implies x (x-2) (x^2 + 2x + 4) = 0$

$\implies x = 0 \text{ or } x-2 = 0 \text{ or } x^2 + 2x + 4 = 0$

$\implies x = 0 \text{ or } x = 2 \text{ or } (x+1)^2 + 3 = 0$

The last case has no real solution, so we can ignore it.

Now,

$x=0 \implies 0^2 = 2y \implies y=0$

$x=2 \implies 2^2 = 2y \implies y=2$

so we have two critical points (0, 0) and (2, 2).

Compute the Hessian matrix (i.e. Jacobian of the gradient).

$H(x,y) = \begin{bmatrix} 6x & -6 \\ -6 & 6y \end{bmatrix}$

Check the sign of the determinant of the Hessian at each of the critical points.

$\det H(0,0) = \begin{vmatrix} 0 & -6 \\ -6 & 0 \end{vmatrix} = -36 < 0$

which indicates a saddle point at (0, 0);

$\det H(2,2) = \begin{vmatrix} 12 & -6 \\ -6 & 12 \end{vmatrix} = 108 > 0$

We also have $f_{xx}(2,2) = 12 > 0$ , which together indicate a local minimum at (2, 2).

3 0

2 years ago

Using what you know about right triangle trigonometry, salt the triangle round the side to the nearest 10th and angle measures t

Elden [556K]

Answer:

Angle A = 49° Angle B = 41° Side AB = 30.5

Step-by-step explanation:

Let's work out Angle A and Angle B first. We are given AC and CB, therefore AB must be the hypotenuse as it is the longest side.

AC and CB must be the opposite and adjacent sides, therefore we can use tan(x) = Opposite/Adjacent for working out both Angle A and Angle B.

Angle A:

tan(A) = 23/20 For Angle A, CB (23) is the side opposite the angle and AC (20) is the side in between Angle A and the right angle, also the adjacent side.

A = $tan^{-1}(\frac{23}{20})$ We do the inverse of tan here.

A = 48.9909131

A = 49° Rounding to the nearest degree simply means to the nearest whole number.

Angle B:

tan(B) = 20/23 For Angle B, AC (20) is the side opposite the angle and CB (23) is the side in between Angle B and the right angle, also the adjacent side.

B = $tan^{-1}(\frac{20}{23})$

B = 41.0090869

B = 41°

Side AB:

We can just use Pythagoras' Theorem here to work out AB, but I will also use trigonometry to show you how you can use both formulas. When I use trigonometry, I will only be using Angle A as an example.

Pythagoras' Theorem: $a^{2} + b^{2} = c^{2}$

AC = 20 = a

CB = 23 = b

$20^{2} + 23^{2} = c^{2}$

929 = $c^{2}$

c = $\sqrt{929}$

c = 30.47950131

c = 30.5 Rounding to the nearest 10th simply means rounding to 1 decimal place.

Trigonometry: SOHCAHTOA

Angle A = 49°

AC = 20 I will use AC as our adjacent side instead of CB. They will both give us the same answer anyways.

AB will always be the hypotenuse in the given right-angled triangle.

cos(x) = Adjacent/Hypotenuse

cos(49) = 20/AB

ABcos(49) = 20 Here we multiply by AB, our hypotenuse.

AB = 20/cos(49) Now we divide by cos(49)

AB = 30.48506173 As you can see here, this answer is different from the Pythagoras' Theorem one because we rounded our angle values, meaning out angle values aren't exact! Instead, use Pythagoras' Theorem here for more accurate results instead of Trigonometry.

AB = 30.5 They still give us the same answer in the end!

I hope this helps you!! ^-^

7 0

3 years ago