What is the value of x?

(See attached image for details.)

Enter your answer in the box.

x =

What Is The Value Of X? (See Attached Image For Details.)Enter Your Answer In The Box.x =

Answers

Answer 1

Answer: x = 12

Step-by-step explanation: The given triangle is an equilateral triangle. Equilateral triangles have all angles and all sides equal. Thus, let's solve for x knowing all 3 equations are equal. For this, only 2 equations are necessary.

5x - 22 = 4x - 10

Adding 22 to both sides, we get:

5x = 4x + 12

Subtracting 4x to 5x, we get:

x = 12.

Thus 5*12 - 22 = 38, and 4*12 - 10 = 38, and so is 3*12 + 2 = 38. Thus, we know this is correct.

Answer 2

Answer:

x = 12

Step-by-step explanation:

Hello!

All three angles are congruent, indicating that this is an equilateral triangle.

The rules of this triangle say that all sides are congruent.

We can solve for x by setting any 2 sides equal to each other. I'm picking AB and BC.

Solve for x4x - 10 = 3x + 24x - 3x - 10 = 2x - 10 = 2x = 12

The value of x is 12.


Related Questions

The depreciation method that does not initially use the residual value in depreciation calculations is the.

Answers

An asset loses value over time as a result of use, damage, or obsolescence.

What is depreciation?

An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement for this decline.

The depreciation method that does not initially use the residual value in depreciation calculations is the depreciating balance.

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What is the value of 3 in this number? 728. 36​

Answers

Answer:

The place value of 3 is tens

the 3 is in the value of tens

I need help answering these questions for geometry :)

1. What happens to the measure of the interior angles as the number of sides of the polygon increases? Explain your answer.
2.What happens to the measure of the exterior angles as the number of sides of the polygon increases? Explain your answer.
4. Explain what happens to the total sum of interior angles as the number of sides in the polygon changes.
5. Explain what happens to the total sum of exterior angles as the number of sides in the polygon changes.

Answers

The answers to the question have been written below

The changes to a polygon

1. If the number of sides of the polygon should increase then the measure of the interior angle would increase by 180.

2. A regular polygon has the sum of its external angles as 360. This is solved as 360/n = 0

Hence the value of the exterior would move towards 0 as its sides increases.

4. As the total sum of the of the polygon changes, it would tend towards infinity.

5. The total sum of the exterior angles as the number of sides changes would tends towards 360 degrees.

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Question 10 of 10
Which of the following are necessary when proving that the diagonals of a
rectangle are congruent? Check all that apply.
A. Corresponding parts of similar triangles are similar.
B. Corresponding parts of congruent triangles are congruent.
C. Opposite sides are congruent.
D. Opposite sides are perpendicular.

Answers

I think the option is D, not sure tho
Yes the answers is D ….

Which best describes the data set? it is nonlinear because the ""total houses built"" column does not increase at a constant additive rate. it is nonlinear because the ""months passed"" column does not increase at a constant additive rate. it is nonlinear because the increase in the ""total houses built"" compared to the increase in the ""months passed"" does not show a constant rate of change. it is linear because the increase in the ""total houses built"" compared to the increase in the ""months passed"" shows a constant rate of change.

Answers

Answer :C)It is nonlinear because the increase in the “Total Houses Built” compared to the increase in the “Months Passed” does not show a constant rate of change.

:) hope you have a great day!

A box has 1 red marble, 1 blue marble, and 4 green marbles of the same shape and size. dan draws a marble randomly from the box, replaces it, and then draws another marble randomly. what is the probability of drawing two green marbles in a row? explain your answer.

Answers

[tex]|\Omega|=6^2=36\\|A|=4\cdot3=12\\\\P(A)=\dfrac{12}{36}=\dfrac{1}{3}\approx33.3\%[/tex]

Answer: 1/5

Step-by-step explanation:

There are three kinds of Marbles. (M) marbles

(G) green: 4m

(R) red: 1m

(B) blue: 1m

Dan pulled a green marble out leaving

(G) green: 3m

So, the probability of picking a green marble is 1/5

sorry if I'm wrong/correct me if I'm wrong.

Which formulas could you use to find the volume of a right circular
cone?
OA) V = B-h where B = I-w
OB) V=B-h where B=1r'
OC) V=B-h where B = Tr
OD) V=B-h where B=1-w

Answers

Answer:

The formula for the volume of a cone is V=1/3hπr².

Find the nth term of this number sequence
1, 7, 13, 19, ...

Answers

Answer:

now we have to follow up with the formula n² - n¹

which is 7-1= 6

n³-n²

which is 13-7=6

so therefore the nth term=6

The least common denominator of 5/6, 2/3, and 3/5 is:

Answers

Answer:

30

Step-by-step explanation:

It costs $20 a day to rent a car and $30 for a full tank of gas. If Stacy fills up the tank 3 times and has the car rented for 14 days, how much does she owe?

Answers

Answer:

$20 × 14 days = $280

&30 × 3 = $90

&280 + $90 = $370

Answer:

For car she owes=

$20 x 14 = $280

For tank she owes=

$30 x 3 = $90

Therfore in total she owes,

$280 + $90 = $370

please help I need so much help right now I feel like crying ​

Answers

Answer:

ok the first point there is (-4;-3)

the second point is(0;-6)

write out y=-4x-y……………

Pls help. !!!!!!!!!!!!!!!!!! (Give steps if you can)

Answers

Answer:

[tex]144 cm^{2}[/tex]

Step-by-step explanation:

Step 1: Find the true length of each side

We know that the perimeter is 56cm and the ratio of AD:AB:DC:BC is 5:12:6:5. It is safe to assume that this ratio is the simplified version, which means that if we multiply each of these numbers by a scale factor of [tex]x[/tex], then we get the true length of each side, so we would get [tex]5x, 12x, 6x, 5x[/tex] for the sides. We also know that when we add these numbers, we get the perimeter, which is 56. So, we can create the equation [tex]5x + 12x + 6x + 5x = 56[/tex]. Then, solve the equation for x, which would be 2, and go back and multiply each number with 2 to get the following:

AD = 5*2 = 10cm, AB = 12*2 = 24cm, DC = 6*2 = 12cm, BC = 5*2 = 10cm  

Step 2: Calculate the Height

Now we know the lengths of each side, lets take a look at the formula for the area of a trapezium: [tex]\frac{base_{1} + base_2}{2}*height[/tex]. So, the next step would be to calculate the height. We can draw the height by drawing a line straight down from the vertex D and another straight down from the vertex C. These lines are both the height, and will be the exact same length. We can calculate that the height is 8 because AB is 24 cm, but the length from the height at vertex D to the height at vertex C is 12 cm, so that means that the base of each triangle is 12/2 = 6 cm. Then we can use Pythagorean theorem to figure out that the height is 8cm.

Step 3: Calculate the Area

Lastly, we can calculate the area. The formula is [tex]\frac{base_{1} + base_2}{2}*height[/tex]. In this case, the numbers would be [tex]\frac{12 + 24}{2} * 8 = 144cm^{2}[/tex]

I know this is a lot, so let me know if you have any questions!

On a coordinate plane, a right triangle has points A (negative 5, negative 6), B (negative 5, negative 2), C (negative 2, negative 2). Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line? a rise of 6 and a run of 8 a rise of 8 and a run of 6 a rise of 6 and a run of 5 a rise of 5 and a run of 6

Answers

The rise and run that would give us a similar right triangle on the same given line is: B. a rise of 8 and a run of 6.

What is the Rise and Run of Points on the Same Line?

The rise/run of any two points on the same line are have the same slope value.

Given the coordinates:

A(-5, -6)B(-5, -2)

The rise of triangle ABC = change in y = 4 units

The run of triangle ABC = change in x = 3 units

Rise/run = 4/3

Therefore, a rise of 8 and a run of  6 would give us: 8/6 = 4/3.

This will give us a triangle similar to triangle ABC.

Therefore, the answer is: B. a rise of 8 and a run of 6.

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PLEASE HELP I WILL MARK BRAINLEST

Answers

#1

Error at sign shift due to -

Correct version

[tex]\\ \rm\Rrightarrow (x^3+2x^2-x)-(3x^3-3x^2+2x-4)[/tex]

[tex]\\ \rm\Rrightarrow x^3+2x^2-x-3x^3+3x^2-2x+4[/tex]

[tex]\\ \rm\Rrightarrow x^3+5x^2-3x+4[/tex]

#2

Not multiplied 3x with x

[tex]\\ \rm\Rrightarrow (x^2-3x+2)(x+1)[/tex]

[tex]\\ \rm\Rrightarrow x(x^2-3x+2)+x^2-3x+2[/tex]

[tex]\\ \rm\Rrightarrow x^3-3x^2+2x+x^2-3x+2[/tex]

[tex]\\ \rm\Rrightarrow x^3-2x^2-x+2[/tex]

Think About a Plan Write an indirect proof.
Proof
Given: 41 42
Prove:
p
• What assumption should be the first step of your proof?
. In the figure, what type of angle pair do 21 and 22 form?

Answers

1) Either [tex]\ell \parallel p[/tex] or [tex]\ell[/tex] ∦ [tex]p[/tex] (only two possibilities)

2) Assume [tex]\ell \parallel p[/tex] (one of two possibilities)

3) [tex]\angle 1 \cong \angle 2[/tex] (if two parallel lines are cut by a transversal, the corresponding angles are congruent)

4) But [tex]\angle 1[/tex] is not congruent to [tex]\angle 2[/tex] (given)

5) So [tex]\ell[/tex] ∦ [tex]p[/tex] (only other possibility)

PLEASE HURRY WILL GIVE POINTS AND BRAINLYEST TO FIRST RIGHT!!!

Answers

Answer:

(0, 4) and (-1, 0)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=2x^2+6x+4\\y=-4x^2+4\end{cases}[/tex]

Solve by substitution

Substitute the first equation into the second:

[tex]\implies 2x^2+6x+4=-4x^2+4[/tex]

Add 4x² to both sides:

[tex]\implies 2x^2+6x+4+4x^2=-4x^2+4+4x^2[/tex]

[tex]\implies 6x^2+6x+4=4[/tex]

Subtract 4 from both sides:

[tex]\implies 6x^2+6x+4-4=4-4[/tex]

[tex]\implies 6x^2+6x=0[/tex]

Factor out 6x from the left side:

[tex]\implies 6x(x+1)=0[/tex]

Therefore:

[tex]\implies 6x=0 \implies x=0[/tex]

[tex]\implies x+1=0 \implies x=-1[/tex]

To find the y-coordinates of the found x-values, substitute the found values of x into one of the equations:

[tex]x=0 \implies -4(0)^2+4=4 \implies (0,4)[/tex]

[tex]x=-1\implies -4(-1)^2+4=0\implies (-1,0)[/tex]

Therefore, the solutions to the system of equations are:

(0, 4) and (-1, 0)

Answer:

Solutions:

a) x = 0, y = 4 ⇒ (0, 4)

b) x = -1, y = 0 ⇒ (-1, 0)

Step-by-step explanation:

Given system of equations:

a) y = 2x² + 6x + 4

b) y = -4x² + 4

1. Substitute the value of y in the second equation into the first equation:

⇒ -4x² + 4 = 2x² + 6x + 4

2. Solve for x:

⇒ -4x² + 4 = 2x² + 6x + 4 [subtract 4 from both sides]

⇒ -4x² + 4 - 4 = 2x² + 6x + 4 - 4

⇒ -4x² = 2x² + 6x [subtract 2x² from both sides]

⇒ -4x² - 2x² = 2x² - 2x² + 6x

⇒ -6x² = 6x [subtract 6x from both sides]

⇒ -6x² - 6x = 6x - 6x

⇒ -6x² - 6x = 0 [factor out -6x from the equation]

⇒ -6x(x + 1) = 0

Two cases:

a)

⇒ -6x = 0 [divide both sides by -6]        

⇒ -6x ÷ -6 = 0 ÷ -6

x = 0

b)

⇒ x + 1 = 0 [subtract 1 from both sides]

⇒ x + 1 - 1 = 0 - 1

x = -1

3. Find the value of y by substituting the found x values into one of the given equations:

a) x = 0:

⇒ y = -4x² + 4

⇒ y = -4(0)² + 4

⇒ y = -4(0) + 4

⇒ y = = 0 + 4

⇒ y = 4

coordinate: (0, 4)

b) x = -1:

⇒ y = -4x² + 4

⇒ y = -4(-1)² + 4

⇒ y = -4(1) + 4

⇒ y = -4 + 4

⇒ y = 0

coordinate: (-1, 0)

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Which of the following points is NOT visible if the viewing window of a graphing utility is set at:
Xmin : 6
Xmaz: 6
Ymin : —6
Ymaz : 6

Answers

The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.

What is graphing utility?

A graphing calculator is a portable computer that can plot graphs, solve multiple equations at once, and carry out other variable-related activities.

We have points shown in the coordinate plane.

As the window of a graphing utility is set at:

X(min) : -6

X(max): 6

Y(min) : -6

Y(max) : 6

The points out of 6 will not be visible.

We can draw a square as shown in the attached picture.

The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible.

Thus, the points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.

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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which statements are always true regarding the diagram? Select three options.

m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°

Answers

Answer:

m∠5 + m∠6 =180°m∠2 + m∠3 = m∠6m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

m∠5 + m∠6 = 180° - This is true because the exterior angle and interior angle form a linear pair, and are thus supplementary.

m∠2 + m∠3 = m∠6 - This is true by the exterior angle theorem.

m∠2 + m∠3 + m∠5 = 180° - This is true because the interior angles of a triangle add to 180 degrees.

The three right options are:

m∠5 ₊ m∠6 = 180° which represents a linear pair.

∠2 ₊ ∠3 = ∠6 showing the exterior angle property of triangle.

m∠2  m∠3  m∠5 = 180° as the sum-triangle

sum-triangleproperty.

Given,

the interior angles of the triangle are 2,3,5

the exterior angle at ∠2 is ∠1.

the exterior angle at ∠3 is ∠4.

the exterior angle at ∠5 is ∠6.

Now, take into account a triangle with external angles as ∠1 , ∠4 and ∠6.

Apply the exterior angle property of a triangle.

The sum of the opposing internal angles determines the outer angle of a triangle.

For exterior ∠1 we get

∠1 = ∠5 ₊ ∠3

Similarly, for exterior ∠4 we get

∠4 = ∠5 ₊ ∠2

Then for exterior ∠6 we get

∠6 = ∠2 ₊ ∠3

∴ through the exterior angle property we get the correct option as

m∠6 = m∠2 ₊ m∠3

Now we know the sum-triangle property that sum of the angles in triangle is equal to 180°

m∠2 ₊ m∠3 ₊ m∠5 = 180°

We know the linear pair property i.e, If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.,

m∠5 ₊ m∠6 = 180°

Hence we get the statements which match the diagram are:

m∠5 ₊ m∠6 = 180°

m∠2 ₊ m∠3 ₊ m∠5 = 180°

m∠6 = m∠2 ₊ m∠3

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What is the equivalent exponential expression for the radical expression below? √3+7​

Answers

Answer:

09 l

Step-by-step explanation:

p0-9

The equivalent exponential expression for the given radical expression √(3 + 7) is √10.

To convert the given radical expression √(3 + 7) into its equivalent exponential expression. This process involves using exponentiation to represent the radical form.

The given radical expression is √(3 + 7). To find its equivalent exponential expression, we need to express the radical in terms of an exponent.

Recall that a radical expression of the form √(a) is equivalent to raising 'a' to the power of 1/2. In this case, 'a' is the quantity inside the radical, which is 3 + 7. So, we can write:

√(3 + 7) = (3 + 7)^(1/2).

Next, we simplify the expression inside the parentheses:

3 + 7 = 10.

Now, the expression becomes:

(10)^(1/2).

To further simplify, we raise 10 to the power of 1/2. Recall that raising a number to the power of 1/2 is the same as finding the square root of that number. So:

(10)^(1/2) = √10.

Therefore, the equivalent exponential expression for the given radical expression √(3 + 7) is √10.

To summarize, we transformed the radical expression √(3 + 7) into its equivalent exponential expression √10 by using the rule that √(a) is equal to a^(1/2). By raising the expression inside the radical to the power of 1/2, we simplified it and found the square root of 10 as the final result.

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PLEASE HELPPPP



one gym membership charges $10 a month with a sign-up fee of $45. Another gym does not charge patrons a sign-up fee but costs $25 a month. at what month is the total cost of both memberships the same?

Answers

Answer:

3 Months

Step-by-step explanation:

Please give me Brainliest!

Let’s use m as the month number
The first gym cost will be 10m + 45
The second gym charges 25m
The costs are equal when 10m + 45 = 25m
10m - 10m + 45 = 25m - 10m
45 = 15m
So m = 3. The gyms charges are equal for 3 months. (After that the first gym is cheaper)

You could solve this by graphing the two price schemes and finding where the lines cross
or making a list of the monthly costs for each gym:
Gym A: $55, $65, $75, $85, $95, …
Gym B: $25, $50, $75, $100, $125, …

If an employer reduces the working week from 40 hours to 35 hours, with no
loss of weedy pay, calculate the percentage increase in the hourly rate of pay.

Answers

Answer:

14.285714285714 %

Step-by-step explanation:

suppose the weekly payment is of x dollars

Then

Previous payment : $(x/40) per hour

New payment : $(x/35) per hour

Then

The percentage increase in the hourly rate of pay is :

[tex]=\frac{\frac{x}{35} -\frac{x}{40} }{\frac{x}{40} } \times100[/tex]

[tex]=\frac{\frac{5x}{1400} }{\frac{x}{40} } \times100[/tex]

[tex]=\frac{5x}{1400} \times \frac{40}{x} \times100[/tex]

[tex]=\frac{200}{1400} \times100[/tex]

[tex]=\frac{1}{7} \times100[/tex]

[tex]=14.285714285714[/tex]

Which equation completes the system that is satisfied by the solution (1, 1)?
02x+y = 2
O4x - 2y = 2
02x - 2y = 2
Ox+y = 4

Answers

Answer: B. 4x-2y=2

Step-by-step explanation:

We will work this out one by one. Plug in the x and y values of the solution to the equations and you will see which one is true or false.

A. [tex]2(1)+y(1)=2\\2+1\neq 2[/tex]     B. [tex]4(1)-2(1)=2\\4-2=2[/tex]

C. [tex]2(1)-2(1)=2\\2-2\neq 2[/tex]     D. [tex]x(1)+y(1)=4\\1+1\neq 4[/tex]

With this information, we see that B is the correct answer.

I hope this helped!! Pls mark brainliest!! :))

I believe the answer is B) 4x - 2y = 2

¿Cuáles son las soluciones x1 y x2 de la ecuación x2 − 5x − 6 = 0?

Answers

Answer:

x1 = 4 y x2= 2

Step-by-step explanation:

escuchame

x2 - 5x -6 = 0

(4)^2 - 5(2) - 6 = 0

16 - 10 - 6 = 0

6 - 6 = 0

de nade :)

Which expression is equivalent to (startfraction x superscript negative 4 baseline y over x superscript negative 9 baseline y superscript 5 baseline endfraction) superscript negative 2? assume x not-equals 0, y not-equals 0.

Answers

The equivalent expression of [tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex] is [tex]x^{-10}y^8[/tex]

Complete question

Which expression is equivalent to [tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex]

How to determine the equivalent expression?

The expression is given as:

[tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex]

Apply the exponent law of indices

[tex](\frac{x^{-9}y^5}{x^{-4}y})^{2}[/tex]

Next, we apply the common base law of indices

[tex](x^{4 -9}y^{5-1})^2[/tex]

Evaluate the difference

[tex](x^{-5}y^4)^2[/tex]

Remove bracket

[tex]x^{-10}y^8[/tex]

Hence, the equivalent expression of [tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex] is [tex]x^{-10}y^8[/tex]

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Answer:

y^8/x^10

Step-by-step explanation:

The guy above me is right but just forgot to distribute the negative out of x. :)

A water sample shows 0.033 grams of some trace element for every cubic centimeter of water. Marques uses a container in the shape of a right cylinder with a diameter of 13.2 cm and a height of 19.7 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Marques collected? Round your answer to the nearest tenth.

Answers

Answer:

89.0 grams of trace element

Step-by-step explanation:

Step 1

Find the volume of the sample container.

Given:

Container is a right cylinder with d = 13.2 cm and h = 19.7 cm

Volume formula:

V = πr²h = πd²h/4

Substitute to get:

V = π(13.2)²(19.7)/4 = 2695.9 cm³ (rounded)

Step 2

Find the volume of the trace element, using the given proportion:

2695.9*0.033 = 89.0 grams (rounded)

Sin (5x-28) = cos (3x - 50)

Answers

By using trigonometric identities we can solve the trigonometric equation Sin (5x-28) = cos (3x - 50) for x.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The question is incomplete.

The complete question is:

Solve for X given that sin(5X - 28)° = cos(3X - 50)°.​

We have given:

sin(5X - 28)° = cos(3X - 50)°.

[tex]\rm \sin \left(5x-28\right)=\sin \left(\dfrac{\pi }{2}-\left(3x-50\right)\right)[/tex]

[tex]\rm \left5x-28\right= \left\dfrac{\pi }{2}-\left(3x-50\right)\right[/tex]

[tex]\rm x=\dfrac{4\pi n+156+\pi }{16}[/tex]     (n = 0, 1, 2, ...)

[tex]\rm x=\dfrac{\pi +4\pi n-44}{4}[/tex]

Thus, by using trigonometric identities we can solve the trigonometric equation Sin (5x-28) = cos (3x - 50) for x.

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PLEASE HELP 20 POINTS
Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about point P.
A -105
B -75
C 75
D 105

Answers

Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about point P at; D: 105°

How to Interpret Rotation of objects?

From the given image, If we connect points C of the blue quadrilateral to point C' of the rotated quadrilateral using the center of rotation P, then we will notice that ∠CPC' will be greater than 90°.

Now, the rotation is counterclockwise and it therefore means that the angle of rotation is will be positive and since ∠CPC' is greater than 90°, then we can say that the only correct option is Option D which is 105°

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A packet of low fat vegetable soup has a mass of 70.5 g. find the mass of 50 such packets

Answers

Answer:

300.25

Step-by-step explanation:

The mass of 1 packet of low fat vegetable soup is 70.5g, the mass of 50 packets is 300.25g(70.5x50).

The mass of 50 low-fat vegetable soups has a mass equal to 300.25 g.

Given : The mass of 1 packet of low-fat vegetable soup is 70.5g

To find: The mass of 50 such packets

Concept: In mathematics, a product is the result of multiplication, or an expression that identifies factors to be multiplied. For example, 30 is the product of 6 and 5

The mass of 50 such packets is 70.5x50 i.e., mass of 1 pkt* number of packets given which is given to be 70.5 and 50 respectively

= 300.25 g.

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[tex]\sqrt{6} /\sqrt{27}[/tex]

Answers

[tex]\mathrm{Apply\:the\:laws\:of\:exponents}:\quad \dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b }},\:\quad \:a\ge 0,\:b\ge 0[/tex]

[tex]\dfrac{\sqrt{6}}{\sqrt{27}}=\sqrt{\dfrac{6}{27}}[/tex]

[tex]=\sqrt{\dfrac{6}{27}}[/tex]

[tex]\mathrm{ Cancel \ \ \dfrac{6}{27} \ \ \ ; \ \ \dfrac{2}{9} }[/tex]

[tex]=\sqrt{\dfrac{2}{9}}[/tex]

[tex]\mathrm{Apply\:the\:laws\:of\:exponents}:\quad \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b }},\:\quad \:a\ge 0,\:b\ge 0[/tex]

[tex]=\sqrt{\dfrac{2}{9}}[/tex]

[tex]\sqrt{9}=3[/tex]

[tex]=\dfrac{\sqrt{2}}{3} \ \ === > \ \ \ Answer[/tex]

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer the following

Answers

The set A satisfying the given inequality is A = (-[tex]\infty[/tex], -10].

What are some properties of an inequality relation?

Following are some facts which are true for an inequality relation:

Equal numbers can be added or subtracted from both sides of an inequality without affecting the inequality sign.The Inequality sign is unchanged if both sides are multiplied or divided by a positive number, but when multiplied or divided by a negative number the inequality sign is reversed.

[tex]\frac{5x-2}{8} - \frac{3x-5}{10} &\ge& x+y\\\\\Rightarrow\;\; \frac{13}{40}x + \frac{1}{4}&\ge& x+y\\\\\Rightarrow\;\;\;\;\;\; -\frac{27}{40}x &\ge & y - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\;\; -x &\ge & \frac{40}{27}\left( y-\frac{1}{4} \right).\hspace{1cm}(1)[/tex]

Since y ∈ B, -2 ≤ y ≤ 7. So,

[tex]\;\;\;\;\;\;\;\,-2 - \frac{1}{4}\; \le\; y - \frac{1}{4} \;\le\; 7 - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\; -\frac{9}{4}\; \le\; y - \frac{1}{4} \;\le\; \frac{27}{4}\\\\\Rightarrow\;\;\; -\frac{9}{4}\cdot \frac{40}{27} \;\le\; \frac{40}{27} \left( y-\frac{1}{4} \right) \;\le \;\frac{27}{4}\cdot \frac{40}{27}\\\\\Rightarrow\;\;\;\;\;\;\;\; -\frac{10}{3} \;\le\; \frac{40}{27}\left( y - \frac{1}{4} \right)\; \le\; 10.[/tex]

The set {-x | inequality (1) holds ∀ y ∈ B} is [10, [tex]\infty[/tex]) i.e.

10 ≤ -x ≤ [tex]\infty[/tex].

Multiplying -1 throughout gives

-10 ≥ x ≥ -[tex]\infty[/tex].

x, thus, lies in the range A = (-[tex]\mathbf{\infty}[/tex], -10}.

Learn more about the inequality here.

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Question

Find the set A such that for x ∈ A

[tex]\frac{5x - 2}{8} - \frac{3x - 5}{10} \ge x + y[/tex]

∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.

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