Round the sum of 43.524 +3.004 to the nearest tenth

Answer:  x < [tex]\frac{140}{27}[/tex]

Step-by-step explanation:

[tex]\frac{6}{5}x - 12 < 2 - \frac{3}{2}x[/tex]

[tex]10(\frac{6}{5}x - 12) < 10(2 - \frac{3}{2}x)[/tex]

2(6)x - 10(12) < 10(2) - 5(3)x

 12x  -   120  <   20  -  15x

+15x                        +15x      

 27x   - 120  <   20

         +120    +120

27x              <  140

            [tex]\frac{27x}{27} < \frac{140}{27}[/tex]

              x < [tex]\frac{140}{27}[/tex]

Given equations : Equation A:  4y -3x =16 and

Equation B: -x-8y =3.

We are given a point (-5,0.25) plugging it in first equation

4(0.25) -3(-5) =16

1+15 =16.

16 =16 : Satisfies first equation.

Plugging (-5,0.25) it in second equation.

-(-5)-8(0.25) =3.

5 - 2 = 3.

3=3 : Satisfies first equation.

ANSWER

[tex]x=10[/tex]

and

[tex]y=20[/tex]

EXPLANATION

Since corresponding angles are equal,

[tex]4x+y=60---(1)[/tex]

Alternate angles are also equal, therefore,

[tex]8x+y=100---(2)[/tex]

Equation (2) minus equation (1) gives,

[tex]\Rightarrow 4x=40[/tex]

[tex]\Rightarrow x=10[/tex]

We put [tex]x=10[/tex] in to equation (1)

[tex]4(10)+y=60[/tex]

[tex]y=60-40[/tex]

[tex]y=20[/tex]

To find x and y in the violin string diagram, use the properties of angles formed by transversals and parallel lines. Corresponding angles and interior angles are key relationships. In the example, x = 15° and y = 90°.

The problem involves understanding the relationships between angles formed by transversals and parallel lines. When a violin bow is placed across parallel violin strings, it forms transversals that create various angles.

Given that the violin strings are parallel, the interior angles formed on the same side of the transversal are supplementary. Let's consider the setup of the diagram:

Example: Suppose the violin strings and the bow are positioned in such a way that we can see the angles formed. Assume the given angles are as follows:

Step 1: Since Angle 1 and Angle 2 are corresponding angles and lie between parallel lines:

30° = 2x → 2x = 30° → x = 15°

Step 2: To find y, use the fact that the sum of angles around a point is 360°. Suppose y is opposite to the sum of Angle 1 and another given angle on the same side:

If the other angle on the same side is 60°:

y = 180° - (Angle 1 + 60°) → y = 180° - (30° + 60°) → y = 90°

Thus, the values of x and y are determined to be 15° and 90°, respectively.

Answer:

about 105

Step-by-step explanation:

The answer is 7.21.

Randy should attach the end of the light string approximately 7.21 feet from the base of the mast using the Pythagorean theorem, as the distance from the base to the end of the string forms the leg of a right-angled triangle with the mast and the string itself.

To solve Randy's problem, we need to use the Pythagorean theorem, which is applicable because we are dealing with a right triangle formed by the mast, the ground, and the string of lights. The mast is one leg of the triangle, and the string of lights is the hypotenuse. We are trying to find the length of the other leg, which is the distance from the base of the mast to the point where the end of the light string will be attached.

The formula for the Pythagorean theorem is:

a² + b² = c²

Where:

In this scenario, a is the mast with a known length of 12 feet, c is the string of lights with a known length of 14 feet, and b is the distance from the base of the mast we need to calculate.

By substituting the known values into the theorem, we have:

12² + b² = 14²

Which simplifies to:

144 + b² = 196

Subtracting 144 from both sides:

b² = 196 - 144

b² = 52

Then, take the square root of both sides:

b = √52

After calculating, we find that:

b ≈ 7.21 feet

So Randy should attach the end of the light string approximately 7.21 feet from the base of the mast to reach the top.

Answer: (-3,4) and (9,20)

I think these two points will make the answer you have been looking for.

15.050 < 15.500

notice that 500 is more than 50... so hope this helps a little bit !!!

:)

Answer:

15.050 < 15.500

Step-by-step explanation:

15.050 compare to 15.500

WE need to compare both the decimal numbers

To compare the numbers we compare each digit from left to right

1 is equal to 1

5 is equal to 5

now we compare the number after the decimal point

0 is less than 5 (the numbers in tenths place)

15.050 is less than  15.500

15.050 < 15.500

Answer:

11x - 12

Step-by-step explanation:

Distributive property, also called the distributive law of multiplication and division, lets us distribute a number by multiplying it to each of the numbers in a term separately.

We can expand this expression by clearing the parentheses and combining the like terms here by applying the distributive property:

6 (x-2) + 5x

6x - 12 + 5x ---> (6 is multiplied to both the terms, x and -2, separately)

Now we will combine like terms to get:

6x + 5x - 12

11x - 12

To calculate the average speed, divide the total distance travelled by the total time taken. The speed is approximately 2.31 mph and 3.385 fps.

To calculate the average speed you divide the total distance travelled by the total time taken. In this case, the distance is one mile and the time is 26 minutes.

So, when you divide distance by time, you get approximately 3.385 fps.

https://brainly.com/question/17661499

#SPJ2

The answer is 5.

5^2 = 25        25 - 6 = 19

5 x 2 = 10       10 + 9 = 19

(2x)(x^2)+(2x)(x)+(2x)(-2)+(3)(x^2)+(3)(x)+(3)(-2)

Simplifying

(2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Multiply x * x2

2x3 + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x3 + 2x(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Multiply x * x

2x3 + 2x2 + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)

Remove parenthesis around (2x)

2x3 + 2x2 + 2x(-2) + (3)(x2) + (3)(x) + (3)(-2)

Reorder the terms for easier multiplication:

2x3 + 2x2 + 2 * -2x + (3)(x2) + (3)(x) + (3)(-2)

Multiply 2 * -2

2x3 + 2x2 + -4x + (3)(x2) + (3)(x) + (3)(-2)

Multiply 3 * -2

2x3 + 2x2 + -4x + 3x2 + 3x + -6

Reorder the terms:

-6 + -4x + 3x + 2x2 + 3x2 + 2x3

Combine like terms: -4x + 3x = -1x

-6 + -1x + 2x2 + 3x2 + 2x3

Combine like terms: 2x2 + 3x2 = 5x2

-6 + -1x + 5x2 + 2x3

Answer:

The product is,[tex]-6 + -1x + 5x2 + 2x3[/tex]

explanation:

Simplifying

[tex](2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove the parentheses (2x)

[tex]2x(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]x * x2[/tex]

[tex]2x3 + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove the closing parentheses (2x)

[tex]2x3 + 2x(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]x * x[/tex]

[tex]2x3 + 2x2 + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Remove all parentheses (2x)

[tex]2x3 + 2x2 + 2x(-2) + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Rearrange the terms to make multiplication easier:

[tex]2x3 + 2x2 + 2 * -2x + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]2 * -2[/tex]

[tex]2x3 + 2x2 + -4x + (3)(x2) + (3)(x) + (3)(-2)[/tex]

Multiply [tex]3 * -2[/tex]

[tex]2x3 + 2x2 + -4x + 3x2 + 3x + -6[/tex]

Reorder the terms:

[tex]-6 + -4x + 3x + 2x2 + 3x2 + 2x3[/tex]

Combine like terms: -4x + 3x = -1x

[tex]-6 + -1x + 2x2 + 3x2 + 2x3[/tex]

Combine like terms: 2x2 + 3x2 = 5x2

[tex]-6 + -1x + 5x2 + 2x3[/tex]

Learn more about here Simplified Product here-

https://brainly.com/question/2548064

#SPJ2

Answer:

The answer is 16

Answer:

it is a linear one i think

The classification of angles 1 and 4 as either linear pairs, vertical angles or neither is impossible without more context or a diagram. Linear pairs are adjacent angles that form a straight line and total 180 degrees, while vertical angles are directly opposite each other from an intersection of two lines and are equal.

Without a proper diagram or more context, it's challenging to determine whether angles 1 and 4 are linear pairs, vertical angles, or neither. However, I can explain what these terms mean. Linear pairs are adjacent angles whose non-common sides form a straight line, adding up to 180 degrees. Vertical angles are angles opposite each other when two lines intersect. They are equal in measure. Unfortunately, without a specific diagram indicating the positions of angles 1 and 4, I can't definitively answer your question.

https://brainly.com/question/13954458

#SPJ2

Answer:

24 inches.

Step-by-step explanation:

Two sides of an obtuse triangle measure 10 inches and 15 inches.

The length of the longest side is unknown.

We have to find the smallest possible whole number for length of the unknown side.

Since a triangle is possible only when sum of two sides of the triangle is greater than the third side.

Therefore, length of third side < sum of other two sides

length of third side < 10 + 15

length of third side < 25

Therefore smallest whole number length should be 24 inches.

C. The square root of 3 is an irrational number. I hope that this helps!

7 x [tex]10^{7}[/tex]  times 14.6 x[tex]10^{5}[/tex]

Multiply 7 and 14.6 and add exponents

Final Answer 102.2 and [tex]10^{5}[/tex]

hope that helps :)

7.2 x 10 x 5 x 14.6 x 10 x 5

7.2 x 100000 x 14.6 x 100000

720000 x 1460000 = 1.0512 x 10 x 12

13/25,

any time you see a prime number in the numerator, its in its simplest form.

For this case we have the following fractions:

22/33 42/81 13/25 18/27

Fraction 1: You can divide the numerator and denominator by 11

[tex]\frac{22}{33}= \frac{2}{3}\\[/tex]

Fraction 2: The numerator and denominator can be divided by 3

[tex]\frac{42}{81}= \frac{14}{27}\\[/tex]

Fraction 3: The numerator and denominator can not be divided by the same number.

[tex]\frac{13}{25}\\[/tex]

Fraction 4: The numerator and denominator can be divided by 9

[tex]\frac{18}{27}= \frac{2}{3}\\[/tex]

Answer:  

A fraction that is written in its simplest form is

Fraction 3: [tex]\frac{13}{25}\\[/tex]

Answer: 55 meters

Step-by-step explanation:

Let the height of the building be 'h'.

Since building is standing vertical to the ground making right angle.

Then , the triangle formed is a right triangle .

The given angle of elevation : [tex]32^{\circ}[/tex]

Using trigonometry , we have

[tex]\tan\theta=\dfrac{\text{Perpendicular}}{\text{Base}}\\\\\tan(32^{\circ})=\dfrac{h}{88}\\\\\Rightarrow\ 0.6248693519=\dfrac{h}{88}\\\\\Rightarrow\ h=0.6248693519\times88=54.988502967\approx55\text{ meters}[/tex]

Hence, the approximate height of the building = 55 meters

GameStop's total will be 371.00

Best Buy's total will be 337.90

Best Buy will be the better buy

Your answer is Best Buy

Answer:

The best option for buying the Xbox One is GameStop, as the final price would be of $315.35.

Step-by-step explanation:

GameStop: To obtain the price in GameStop, we must first obtain the 15% discount on the price of 350, and subtract it from the initial price. Then, we must calculate the amount of the tax and add it to the price to obtain the final price.

(350 - (350 x 0.15)) x 1.06 = $315.35

Best Buy: Instead, at Best Buy we simply add the sales price tax.

310 x 1.09 = $337.90

*(The Answer)*= C. Dilation

*(Explanation)*= If you search than you will find that translation, rotation, and refection or the one that are ridged, however, dilation is.

Answer:

The correct option is 2. A dilation is NOT rigid motion transformation.

Step-by-step explanation:

Rigid motion transformation : A transformation is called a rigid motion transformation if a point or object is moved, but the size and shape remain the same.

In rotation, the point of figure is rotated about the center of rotation but the size and shape remain the same.

Therefore rotation is a rigid transformation and option 1 is incorrect.

In dilation, the figure is stretched of compressed by the scale factor k along the center of dilation, so the size of figure is either increase of decrease.

Therefore dilation  is not a rigid transformation and option 2 is correct.

In translated, the point of figure is shifted but the size and shape remain the same.

Therefore translation is a rigid transformation and option 3 is incorrect.

In reflection, the point of figure is reflected about the line of reflection but the size and shape remain the same.

Therefore reflection is a rigid transformation and option 4 is incorrect.

Given

A rectangle is placed inside a circle whose diameter is 13unit all corners of it on the circle.

area of the rectangle = 60 square unit

Find the dimensions of the rectangle.

To proof

As given in the question

rectangle is placed inside a circle whose diameter is 13unit .

now by using the diagram given below

the diagonal of the rectangle is equal to the diameter of the circle.

Thus DB = 13 unit

FORMULA

Area of the rectangle = Length × Breadth

area of the rectangle =  60 square unit

let the value of the length be ( Say AB ) = x

put the value in the above equation

we get

60 = x  × Breadth

[tex]Breadth( say AD)= \frac{60}{x}[/tex]

now in ABD

Using the pythagorus theorem

we get

BD²= AB² + AD²

[tex]13^{2} = x^{2}+ (\frac{60}{x}) ^{2}[/tex]

solving the above equation

we get

[tex]169x^{2}= x^{4} + 3600[/tex]

[tex]x^{4} - 169x^{2}+3600 =0[/tex]  

[tex]x^{4} - 144x^{2} -25x^{2} + 3600 =0[/tex]

[tex]x^{2} (x^{2} - 144) - 25 (x^{2} - 144) =0[/tex]

(x² - 25) (x² -144) =0

The roots are

x = -12 ,-5, 5, 12

-12 and -5 are neglected  because of negative terms .

( Length and breadth of recangle cannot be negative )

thus x = 12 and 5

Two case arise

First case

when

Length of rectangle= 12unit

[tex]Breadth = \frac{60}{12}[/tex]

Breadth of rectangle = 5 unit

Second case

Length of rectangle= 5unit

[tex]Breadth = \frac{60}{5}[/tex]

Breadth of rectangle = 12 unit

Hence proved

Final answer:

To find the dimensions of a rectangle inside a circle with a diameter of 13, we use the Pythagorean Theorem and the area of the rectangle. After substituting values and solving, we find the dimensions are 5 units by 12 units.

Explanation:

To find the dimensions of the rectangle that fits inside a circle with a diameter of 13, one must first recognize that the rectangle forms the sides of a right-angled triangle where the diagonal of the rectangle serves as the hypotenuse of the triangle. This hypotenuse, thus, equals the diameter of the circle, which is 13 units.

Since the area of the rectangle is 60 square units, we let the sides of the rectangle be denoted as length (l) and width (w), with the area equation being l×w = 60.

Using the Pythagorean Theorem, we have: l2 + w2 = 132. We also know that lw = 60, which allows us to solve for one variable in terms of the other. Let's solve for w: w = 60/l. Substituting this into the Pythagorean equation gives l2 + (60/l)2 = 169. Solving this quadratic equation will give us the dimensions of the rectangle that can fit within the circle.

After solving, one finds that the dimensions that satisfy both the area and the Pythagorean Theorem are 5 and 12.

Therefore, the dimensions of the rectangle are 5 units by 12 units.

The product of the expressions 3a + 5 and 6a - 2 is 18a² + 24a - 10. The distributive property is used to multiply each term in the first expression by each term in the second.

The product of the two expressions 3a + 5 and 2a + 4a - 2 can be found using the distributive property. First, combine like terms in the second expression to simplify it to 6a - 2. Now, to find the product, multiply each term in the first expression by each term in the simplified second expression:

Multiply 3a by 6a to get 18a².

Multiply 3a by -2 to get -6a.

Multiply 5 by 6a to get 30a.

Multiply 5 by -2 to get -10.

Combining these products gives you the final answer: 18a² + 24a - 10.

[tex]2\cdot 10^{3x}=26\\10^{3x}=13\\\log 10^{3x}= \log 13\\3x\log 10= \log 13\\3x= \log 13\\\\[/tex]

[tex]x=\frac{\log 13}{3}[/tex]

lmk if you have questions

To find the exact value of x in the exponential equation 2(10)^3x=26, divide both sides by 2, apply the common logarithm, use the power rule of logarithms, and simplify to find that x equals log(13)/3.

To solve the exponential equation 2(10)³ˣ=26 for the exact value of x using logarithms, follow these steps:

Thus, the exact value of x is log(13)/3.

Answer:

12

Step-by-step explanation:

2 times 2 is 4

4 divided by 2 is 2

2 times 2 is 4

2 times 6 is 12

12 divided by 2 is 6

4 plus 2 plus 6 is 12

3[3c^(-9)-1]

hope this helps

Answer:

b

Step-by-step explanation: