Solve the equation for x: c a−x/x−a =5x Answer: , a ≠ − 1/5

Answer:

The ratio of x:y is 1/2

Step-by-step explanation:

Let

x----> the number of Kg of brand A

y ---> the number of Kg of brand B

we know that

400x+280y=320(x+y)

400x+280y=320x+320y

400x-320x=320y-280y

80x=40y

x/y=40/80

x/y=1/2

Final answer:

The ratio of Brand A coffee to Brand B coffee (x to y) required to achieve a mixture cost of $320/kg is 1 : 2. This is derived using the weighted average cost formula and simplifying the resulting equation.

Explanation:

To find the ratio of x to y for the mix of Brand A and Brand B coffee beans, we can use a weighted average cost formula since the mixture's cost is given to be $320/kg. Let's assume we have x kilograms of Brand A coffee at $400/kg and y kilograms of Brand B coffee at $280/kg. The total cost for all the coffee is then $400x + $280y.

The combined weight of the coffee is x + y kilograms, and for the mixture to cost $320/kg, the total cost divided by the total weight must equal $320. Therefore, we can set up the following equation:

($400x + $280y) / (x + y) = $320

Multiplying both sides by (x + y) we get:

$400x + $280y = $320x + $320y

Now, we subtract $320y from both sides to isolate terms with x:

$400x - $320x = $320y - $280y

$80x = $40y

Dividing both sides by $40 gives us the simplified ratio:

x : y = 1 : 2

Thus, the ratio of Brand A coffee to Brand B coffee in the mixture to get a $320/kg cost is 1 : 2.

Answer:

an = -1.3n -2.4

Step-by-step explanation:

The formula for an arithmetic sequence is

an = a1 +d (n-1)

where a1 is the first term and d is  the common difference

an = -3.7 - 1.3(n-1)

Distribute

an = -3.7 -1.3n +1.3

an = -2.4 - 1.3n

an = -1.3n -2.4

5 unit to left, 3 units down is the correct answer.

Answer: f(x) has a domain that contains the domain of g(x).

Step-by-step explanation:

The domain of f(x) is: x - 2 > 0

                             -->       x > 2

The domain of the graph g(x) is: x ≥ 3

All of the values of x ≥ 3 are included in x > 2.

ANSWER

36√3 square units.

EXPLANATION

The area of a parallelogram is obtained by multiplying the base by the height.

We use the sine ratio to obtain the height.

[tex] \sin(60 \degree) = \frac{h}{6} [/tex]

[tex]h = 6 \sin(60 \degree) [/tex]

[tex]h = 3 \sqrt{3} [/tex]

The area becomes:

[tex]12 \times 3 \sqrt{3} = 36 \sqrt{3} {units}^{2} [/tex]

Answer:

Vaccinated: 465, 771, 1236

Not Vaccinated: 485, 600, 1085

Total: 950, 1371, 2321

Step-by-step explanation:

Next Question: 465/1236

It is given that:

This means that the total of all the entries i.e. total of each row and each column is equal to 2321

Also, the sum of the second row is equal to: 1085

This means that the sum of second column is: 1371

The table is attached to the answer.

1) domain of the first is ( R ) because of its root(3) and its range is (R) because of its root again

2)and domain of the last , is [0,+infinity)

and for its range , you can draw it such as picture and will be [0,- infinity)

Answer:

1. [tex]Dom(f)=\mathbb{R} [/tex], [tex]Ran(f)=\mathbb{R} [/tex].

2. [tex]Dom(f)=\{x\in \mathbb{R} : x\geq 0 \} [/tex], [tex]Ran(f)=\{x\in \mathbb{R} : x \leq 0 \}  [/tex].

Step-by-step explanation:

1. Since the degree of the radical is an odd number, the radicand can be any real number, then [tex] x [/tex] can take any real value, so the domain of [tex] f [/tex] is the set of all real numbers, [tex] \mathbb{R} [/tex].

Now, if [tex] x\in \mathbb{R} [/tex] , then [tex] x-3 \in \mathbb{R}  [/tex], so  [tex] \sqrt[3]{x-3} \in \mathbb{R}  [/tex], and thus [tex] f(x)\in \mathbb{R} [/tex], which leads us to affirm that the range of  [tex] f [/tex]  is the set of all real numbers, [tex] \mathbb{R} [/tex].

2. Since the degree of the radical is an even number, the radicand can not be a negative number, then [tex] x [/tex] can take only nonnegaive values, so the domain of [tex] f [/tex] is the set of all nonnegative numbers, [tex] \{x\in \mathbb{R} : x\geq 0 \}  [/tex].

Now, if [tex] x\geq 0 [/tex] , then [tex]  \sqrt{x}\geq 0  [/tex] so  [tex]  -3\sqrt{x}\leq 0  [/tex], and thus [tex] f(x)\in \mathbb{R} [/tex], which leads us to affirm that the range of  [tex] f [/tex]  is the set of all nonpositive numbers, [tex] \{x\in \mathbb{R} : x \leq 0 \} [/tex].

Answer:

The answer is A.

Step-by-step explanation:

I got this answer by going through the regular division system.

Answer:

SAS Similarity Theorem

Step-by-step explanation:

we know that

SAS Similarity Theorem: States that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar

In this problem

∠HJZ=∠RJW ----> by vertical angles

and

WJ/HJ=JR/JZ

substitute the values

8/4=6/3

2=2 ----> is true

so

Two sides of triangle HJZ are proportional with the two corresponding sides of triangle WJR and the included angle is congruent

therefore

Triangles are similar by SAS Similarity Theorem

ANSWER

[tex]a_n= \frac{1}{2}( {2}^{n - 1} )[/tex]

EXPLANATION

The corresponding ordered pairs from the graph are:

(2,1) (3,2) (4,4) (5,8)

The y-values are:

1,2,4,8

The first term term is the term before 1,this has to be.

[tex]a_1= \frac{1}{2} [/tex]

The common ratio is

[tex]r = \frac{2}{1} = 2[/tex]

The nth term is given by

[tex]a_n=a_1 {(r}^{n - 1} )[/tex]

Let's substitute the values to get,

[tex]a_n= \frac{1}{2} \times {(2}^{n - 1} )[/tex]

This simplifies to,

[tex]a_n= \frac{1}{2} {(2}^{n - 1} )[/tex]

The graph represents a geometric sequence with a common ratio of 2, best defined by the function an = 2(2)^n – 1.

This graph represents a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the 'common ratio'. In this case, the common ratio is 2, because each y-coordinate is twice the y-coordinate of the point before it (2, 1), (3, 2), (4, 4), (5, 8). Therefore, the sequence is best represented by the option A an = 2(2)^n – 1.

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Check the picture below.

let's notice that 89/36 =>  2 and 17/36, namely 2π or two revolutions and then a bit more, the 17/36 slack, so then -89π/36 = - 2π - 17π/36.

the positive angle will of course be 2π - 17π/36 = 55π/36.

Answer:

The correct answer is last option

x¹⁶y²²

Step-by-step explanation:

Points to remember

Identities

Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾

Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾

(Xᵃ)ᵇ = Xᵃᵇ

To find the correct answer

It is given an expression {X⁶Y⁸}³/X²Y²

By using identities we can write,

{X⁶Y⁸}³/X²Y² = X⁶ˣ³ Y⁸ˣ³/X²Y²

 = X¹⁸Y²⁴/X²Y²

 = X⁽¹⁸ ⁻ ²⁾ * Y⁽²⁴ ⁻ ²⁾

 = X¹⁶Y²²

Therefore the correct answer is last optionX¹⁶Y²²

Answer:

x = 4

Step-by-step explanation:

The volume (V) of the triangular prism is calculated as

V = area of triangular face × length

Area of triangle = [tex]\frac{1}{2}[/tex] bh

b is the base and h the perpendicular height

here b = 9 and h = 12 ← sides at right angles

A = [tex]\frac{1}{2}[/tex] × 9 × 12 = 54 m²

The length of the prism = x and V = 216, hence

54x = 216 ( divide both sides by 54 )

x = 4

Answer:

9 ft

Step-by-step explanation:

The ladder is 15 foot

The height the ladder reaches from the bottom of the wall is 12 ft

The distance (x) from the bottom of the wall to the foot of the ladder is:

Applying the Pythagorean theorem;

x = [tex]\sqrt{15^2 - 12^2}[/tex] = 9 ft

A 15 foot ladder needs to be placed at a distance of 9 foot from the base of the house so that it exactly reaches the top of a 12 foot wall.

In this case;

Therefore;

We are going to find the distance of the ladder from the base of the house on the ground which is the other leg.

Using Pythagoras theorem;

[tex]a^{2} + b^{2} = c^{2}[/tex]

Taking the horizontal distance of the ladder from the wall as b

Then;

[tex]b^{2} = c^{2} -a^{2}[/tex]

therefore,

[tex]b^{2} = 15^{2} -12^{2}[/tex]

[tex]b^{2} = 225 -144[/tex]

[tex]b^{2} = 81[/tex]

[tex]b = \sqrt{81} \\b= 9 ft[/tex]

Hence; the ladder needs to be placed at a distance of 9 foot from the base of the house.

Keywords: Right triangle, Pythagoras rule

Level; High school

Subject: Mathematics

Topic: Pythagoras theorem

Answer:

commutative property: the property stating that changing the order in which two numbers are added or multiplied does not change the value of the sum or product

equivalent: having the same amount, value, area, volume, or force

evaluate: to determine the value of

like terms: terms consisting of the same variables, raised to the same exponent

Step-by-step explanation:

TRUST me this is RIGHT

To analyze whether two algebraic expressions are equivalent, you can use an interactive tool such as an algebra solver or calculator to compare the results of the expressions for various values of x. Simplify the expressions if possible, compare the simplified expressions, and verify the results by substituting different x-values.

To determine if the expressions 7x – 4 and 6x – 4 – x are equivalent, you can use an interactive tool like an online algebra solver or calculator. This process usually involves comparing the results of the expressions for multiple values of x.

Step 1:

Firstly, simplify the expressions if possible. For the second expression, 6x – 4 – x, you can simplify it as 5x – 4.

Step 2:

Now, compare the simplified expressions, you can see that 7x - 4 and 5x - 4 are not equivalent as the coefficients of x (7 and 5) are not equal.

Step 3:

Last, for verification, you can substitute different values of x into both equations and see if the outputs are the same. If the outputs are different then, the equations are not equivalent.

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Answer:

It ends at 7:30.

Final answer:

Tim's swimming practice starts at 7 o'clock and after adding the 30 minutes duration, it ends at 7:30.

Explanation:

The question pertains to adding time, specifically calculating the end time of an activity based on its duration. If Tim's swimming practice starts at 7 o'clock and ends 30 minutes later, the end time can be found by adding 30 minutes to the start time.

Here's how you calculate it:

Start with the initial time of the practice, which is 7:00.

Add the duration of the practice, which is 30 minutes.

Since there are 60 minutes in an hour, adding 30 minutes to 7:00 does not increase the hour value. Therefore, the practice ends at 7:30.

So, Tim's swimming practice ends at 7:30.

Since supplementary angles add up to 180°, you would subtracted the measurement that you have from 180°.

Ex.

180-x= y

X being the measurement that you have, and y being the missing measurement.

For this case we must find three consecutive whole numbers whose sum is equal to 363. These numbers should be close to 120. So, these numbers are:

120,121 and 122. If we add them together we have:

[tex]120 + 121 + 122 = 363[/tex]

Answer:

120,121 and 122

[tex]120 + 121 + 122 = 363[/tex]

Answer:

2294 balls is the approximate number of balls

Step-by-step explanation:

Find the volume occupied a ball of radius 3inches

Volume of a sphere=4/3 [tex]\pi[/tex]×r³

where r is the radius in inches

4/3× [tex]\pi[/tex]×3³ = 36 [tex]\pi[/tex]

=113.11 in³

Find volume of a rectangle prism

v=l×w×h where l is length of prism, w is width of prism and h is height of prism

L=10ft=10×12=120 inches

w=5ft=5×12=60 inches

h=3ft= 3×12= 36 inches

v=120×60×36=259200 in³

Number of balls needed

N=volume occupied by a single ball/volume of the rectangular prism

N=259200/113.11 =2291.57⇒2292 balls

Answer:

3;14;27;48

Step-by-step explanation:

Answer:

3, 12, 27, 48

Step-by-step explanation:

To find the first 4 terms substitute n = 1, 2, 3, 4 into the rule, that is

n = 1 → 3 × 1² = 3 × 1 = 3 ← first term

n = 2 → 3 × 2² = 3 × 4 = 12 ← second term

n = 3 → 3 × 3² = 3 × 9 = 27 ← third term

n = 4 → 3 × 4² = 3 × 16 = 48 ← fourth term

Answer:

d)96π

Step-by-step explanation:

Given:

Cyliner with radius,a= 4

Height b=8

Surface area of cylinder, A=2πrh+2πr^2

=2π(rh+r^2)

=2π(4(8) + 4^2)

= 2π(32+16)

 =2π(48)

 =96π !

Answer: Option D.

[tex]A =96\pi\ cm^2[/tex]

Step-by-step explanation:

The area of the circular bases is:

[tex]A_c = 2\pi(a) ^ 2[/tex]

Where

[tex]a=4\ cm[/tex] is the radius of the circle

Then

[tex]A = 2\pi(4) ^ 2[/tex]

[tex]A = 32\pi\ cm^2[/tex]

The area of the rectangle is:

[tex]A_r=b * 2\pi r[/tex]

Where

[tex]b=8\ cm[/tex]

b is the width of the rectangle and [tex]2\pi r[/tex] is the length

Then the area of the rectangle is:

[tex]A_r=8 * 2\pi (4)[/tex]

[tex]A_r=64\pi\ cm^2[/tex]

Finally the total area is:

[tex]A = A_c + A_r\\\\A = 32\pi\ cm^2 + 64\pi\ cm^2\\\\[/tex]

[tex]A =96\pi\ cm^2[/tex]

Answer:

C.  3x2 − 3x − 60

Step-by-step explanation:

3(x + 4) (x - 5) = (3x+12) (x-5)

(3x+12) (x-5) = 3x2+12x-15x-60

3x2+12x-15x-60 = 3x2 − 3x − 60

C. 3x^2-3x-60 Hope it helps

Answer:

Step-by-step explanation: the answer is 21%

Answer:

21%

Step-by-stStep-by-stepep explanation:

Answer: The answer I got was 39

Step-by-step explanation:

Answer:

Step-by-step explanation:

-1 is included in the inequality. 2 is not included.

-1 ≤ x < 2

So this reads as x is greater than or equal to - 1 and x is less than 2.

Answer: -1 less equals x < 2

Answer:

400000 + 10000 + 300 + 9

Step-by-step explanation:

Just simply take each place value and turn the rest after to zeros, but DO NOT include the zeros that are within the number. Zeros are unnecessary.

I am joyous to assist you anytime.

Answer:

A 36

Step-by-step explanation:

We can determine the scale factor

From triangle ABC BC =9

                     DEF  EF = 90

We multiply by 10

The scale factor is 10

AC ( 10) = DF

We know DF = 360

b  * 10 = 360

Divide each side by 10

10b/10 = 360/10

b = 36

Answer:

x=21

Step-by-step explanation:

Set the two similar sides in a fraction to be compared and set them equal to another set of similar sides whose values are already known. Solve from there. See work for more.

Answer: 401.952380952

Step-by-step explanation: