The result of a number, when decreased by 66 2/3%, is 432. Find the number

Answer: 7:5

Step-by-step explanation:

The area of a trapezoid with the given parallel sides and height is 4x+8 square units. Therefore, option B is the correct answer.

The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given. The formula for the area of a trapezoid is expressed as, A = ½ (b₁+b₂)×h.

where (A) is the area of a trapezoid, 'b₁' and 'b₂' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between b₁ and b₂).

1) Given that, b₁=x-3, b₂=x+7 and the height=4

Now, area of a trapezoid = 1/2 (x-3+x+7)×4

= 2×(2x+4)

= 4x+8 square units

Hence, option B is the correct answer.

2) The given polynomials are -3x²-7x+9 and -5x²+6x-4.

Here, sum = -3x²-7x+9+(-5x²+6x-4)

= -3x²-7x+9-5x²+6x-4

= -8x²-x+5

Hence, option 1 is the correct answer.

Therefore, the area of a trapezoid is 4x+8 square units.

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Answer:

Sarah must get between a 67 and 85.

Step-by-step explanation:

69 + 75 + 65 + 83 = 292

70 ≥ 1/8(292 + 4x) ≥ 79

70 ≥ 0.5x + 36.5 ≥ 79

67 ≥ x ≥ 85

The correct steps for bisecting line segment AB using a reflective device is given below:

Cutting a line exactly in half is known as bisecting it. Due to the fact that the line you are drawing will be at a right angle to the initial line, it is also sometimes referred to as creating a perpendicular bisector.

A compass, pencil, and ruler are required.

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Answer:

Step-by-step explanation: 32 because 9 x4 lol

Algebraic expression to represent the given situation would be, P = 2N - 7

What is algebraic expression?

When we utilize numbers and words to solve a mathematical problem, we are using algebraic expressions.

Let P represent the number of pennies in Greg's pocket.

We know that the number of pennies is 7 less than twice the number of nickels, which can be written as:

P = 2N - 7

This expression represents the number of pennies in terms of the number of nickels.

Therefore, Algebraic expression to represent the given situation would be, P = 2N - 7

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Rafael will take 75 minutes to run 10 miles at the same rate.

Solution:

We know that Rafael can run 4 miles in 30 minutes.

So, we can find his pace, as follows:

30 minutes/ 4 miles = 7.5 minutes per mile.

So, for 10 miles he will take 7.5* 10 = 75 minutes.

Hence, it will take Rafael 75 minutes to run 10 miles.

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A possible length, in inches, of the third side is equal to 4 inches.

In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.

Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < n < b + c

Where:

n, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem, the possible side lengths of the triangle's third side is given by:

b - c < n < b + c

7 - 4 < n < 7 + 4

3 < n < 11.

Therefore, n could be 4, 5, 6, 7, 8, 9, and 10 inches.

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my brain is playing not smart on me right now

Answer: 9/16

Step-by-step explanation: Also known as (3/4)^2

1. 3x3/4x4

2. 9/4x4

3. 9/16

You can't simplify anymore because it is in the simplest form already.

It will take 15 revolutions per minute.

What is the unit rate?

An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

Here, we have

Given: a wheel for a wheel of winning game makes one revolution in 4 seconds.

Take a time for 1 revolution = 4 seconds

Assume that the unit rate in terms of revolutions per minute is x.

1 rev/4 second = x rev/60 second

4x = 60

x = 15

Hence, it will take 15 revolutions per minute.

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11th term of the given geometric sequence is [tex]a_{n} = 7(5^{n-1})[/tex]

In a Geometric Sequence each term is found by multiplying the previous term by a constant.

Given geometric sequence = 7,35,175

Nth term of the geometric sequence [tex]a_{n}=a_{1} .r^{n-1}[/tex]

[tex]a_{1}=7[/tex]

[tex]r= \frac{35}{7} =5[/tex]

Nth term of the geometric sequence

[tex]a_{n} = 7(5^{n-1})[/tex]

Hence, the Nth term of the given geometric sequence is  [tex]a_{n} = 7(5^{n-1})[/tex]

The value of x is 20 and the property is similar triangle

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Since ∆ ADC and IJH are similar, the ratio of their corresponding sides are equal.

Therefore,1.2/12 = 2/x

1.2x= 12×2

x = 24/1.2

x = 20

Therefore the value of x is 20

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360 guests were at the gala

Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another.

Since the ratio of staff to guests at the gala was 3 to 5.

Let S and G represent the number of staff and guests respectively. From the given information, we can write:

S/G = 3/5

S + G = 576

Thus, S = 576 - G

Put S = 576 - G in S/G = 3/5 and solve for G. That is:

(576 - G)/G = 3/5

3G = 5(576 - G)

3G = 2880 - 5G

3G + 5G = 2880

8G = 2880

G = 2880/8

G = 360

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Answer:51. 2%

Step-by-step explanation:

24+32+(16×4)+7(2+16)=24+32+64+126=246

26g of Epsom salt contains 126g of water of crystallisation.Hence, 100g of Epsom salt contains 100×126/246The % of H2​O in MgSO4​.7H2​O=

Answer:

The number of large bars of chocolate sold is:

1/4 x 208 = 52

The number of small bars of chocolate sold is:

208 - 52 = 156

The total amount of money earned from selling the large bars of chocolate is:

52 x e1 = e52

The total amount of money earned from selling the small bars of chocolate is:

156 x 60p = £93.60

To convert e52 to pounds, we need to multiply by the exchange rate. Let's assume that the exchange rate is £1 = e1.20.

So, e52 = £52 x 1.20 = £62.40

Therefore, the total amount of money earned from selling all 208 bars of chocolate is: £62.40 + £93.60 = £156

The slope of a horizontal line perpendicular to a horizontal line is infinity or undefined.

The slope of a line is the that of the inclination that is makes with a horizontal line.

So, the slope of horizontal line is 1 because the value of tam(0 degrees) is also 1.

A line that is perpendicular to the horizontal line will have a the value of angle to be 90 degrees and we know that,

tan (90 degrees) = undefined/infinity

So, here we are concluding that the slope of any line that is being lying perpendicularly on any horizontally lying line is infinity or undefined.

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Answer:

l is parallel to m and u is parallel to t

Step-by-step explanation:

Parallel line means that never meet each other

Answer:

4 + 0.2 + 0.05

Step-by-step explanation:

Answer:

x = 24°

Step-by-step explanation:

See the attached worksheet.   Let a and b stand for the two unknown angales as shown on the worksheet.  Since the sum of angles across a straight line is 180°, we can express the two angles as:

a = 180°-x, and

b = 180° - 111° or b = 69°

The sum of the interior angles of a quadrilateral is 360°.  Set the four angles equal to 360° and solve for x.

x = 24°

The value of x is 18.

The value of y is 15.6.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

From the figure,

Sin 30 = 9/x

1/2 = 9/x

x = 9 x 2

x = 18

Now,

Using the Pythagorean theorem.

x² = 9² + y²

18² = 81 + y²

y² = 325 - 81

y = √244

y = 15.6

Thus,

x = 18

y = 15.6

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Answer:

a ) one by forty fourth

Step-by-step explanation:

1/11 ÷ 4

= 1/11 x 1/4

= 1/44

therefore, the answer is one by forty fourth

Hope it's helpful..

The required complete table of heights of teachers is shown in the image attached.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
To calculate the height without heels, we need to subtract 4% of the height with heels from the height with heels. This can be done by multiplying the height with heels by 0.96 (which is equivalent to subtracting 4%):

Height without the heels = Height with the heels x 0.96

Using this formula, we can fill in the chart for each teacher.

Thus, the required complete table has been shown in the image attached.

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The closet square inch that is needed to cover the cuboid is 208 inches ( option A)

A cuboid is defined as a three-dimensional shape, that has six rectangular faces, eight vertices and twelve edges.

The surface area of cuboid is given as;

SA = 2(lb+lh+bh)

lb = 33/4 × 4 = 33 in

lh = 23/4 × 4 = 23 in

bh = 23/4 × 33/4 = 759/16

SA = 2( 23+33+759/16)

SA = 46+66+47.44

SA = 207 in

therefore the closet square inches is 208 in²

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Answer:

25

Step-by-step explanation:

The equation of a circle centered at the origin with radius r is given by:

(x^2) + (y^2) = r^2

In this case, the circle is centered at the origin and has a radius of 5, so the equation is:

x^2 + y^2 = 25

Therefore, the equation of the circle is: x^2 + y^2 = 25

The height of the attic in Mr. Lee's house is 6 1/3

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

Mr. Lee's house has two stories and an attic. Therefore:

Height of entire house = height of first floor + height of second floor + height of attic

The first floor is 9½ feet high, the second floor is 8 3/4 feet high, and the entire house is 24 7/12 feet high

9 1/2 = 19/2; 8 3/4 = 27/4; 24 7/12 = 295/12. Let x represent the height of the attic. Substituting:

x + 19/2 + 35/4 = 295/12

x = 19/3

x = 6 1/3

The height of the attic is 6 1/3

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Step 1: Equation for Roller Coaster Height.

The general form for the equation of a circle at the origin is:

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Equation of a Circle (at origin):}}\\\\x^2+y^2=r^2\\\\\bullet \ \text{where 'r' is the radius of the circle}\end{array}\right}[/tex]

It is given that the height of the roller coaster is 30 feet. Thus, r = 30. Plug this into the equation above and solve for 'y.'

[tex]\Longrightarrow x^2+y^2=(30)^2\\\\\\\\\Longrightarrow x^2+y^2=900\\\\\\\\\therefore \boxed{\boxed{y=\sqrt{900-x^2} }}[/tex]

Step 2: Graph of Roller Coaster Model.

Refer to the attached image(s).

Step 3: Equation for Horizontal Distance of Beams.

Going back to the equation we got in step (1), we can solve for the variable ‘x.’

[tex]\Longrightarrow y=\sqrt{900-x^2}\\\\\\\\\therefore \boxed{\boxed{x=\pm\sqrt{900-y^2}}}[/tex]

Step 4: Algebraic Solution for Beam Placement.

Given a height, y = 25 ft. We can plug this into the equation above and solve for 'x.'

[tex]\Longrightarrow x=\pm\sqrt{900-(25)^2}\\\\\\\\\Longrightarrow x=\pm\sqrt{275}\\\\\\\\\Longrightarrow x=\pm5\sqrt{11}\\\\\\\\\therefore \boxed{\boxed{x\approx\pm16.58 \ ft}}[/tex]

Step 5: Placement of Beams.

The beams should be placed 16.58 feet from either side of the origin.

Step 6: Graph of Cable and Strut.

Refer to the attached image(s).

Step 7: Algebraic Intersection of Cable and Strut.

To find the point of intersection, set the two given equations (from model 2) equal to each other and solve for 'x.'

[tex]y=\sqrt{2x+8} \ \text{and} \ y=x-8\\ \\\\\\\Longrightarrow \sqrt{2x+8}=x-8 \\\\\\\\\Longrightarrow 2x+8=(x-8)^2 \\\\\\\\\Longrightarrow 2x+8=x^2-16x+64\\\\\\\\\Longrightarrow x^2-18x+56=0\\\\\\\\\Longrightarrow (x-14)(x-4)=0\\\\\\\\\therefore x=\{14,-4\}[/tex]

In order to determine which value of 'x' is correct we must verify the solution.

When x = 14:

[tex]\Longrightarrow 2(14)+8=(14-8)^2\\\\\\\\\Longrightarrow 36=36 \checkmark[/tex]

When x = -4:

[tex]\Longrightarrow 2(-4)+8=(-4-8)^2\\\\\\\\\Longrightarrow 0\neq 144[/tex]

Thus, the correct x-value is 14. Plug this into either given equations and solve for 'y.'

[tex]\Longrightarrow y =x-8\\\\\\\\\Longrightarrow y =14-8\\\\\\\\\therefore y=6[/tex]

Thus, the point of intersection is (14, 6).

Step 8: Graph of Two Struts.

Refer to the attached image(s).

Step 9: Algebraic Solution for Beam Placement.

To find the x-value of the beam placement, you need to find the point where the two strut equations are 2 feet apart. Set up an equation using the given functions and solve for 'x.'

[tex]\Longrightarrow y=\sqrt{x+8}-\sqrt{x-4}; \ y=2\\\\\\\\\Longrightarrow 2=\sqrt{x+8}-\sqrt{x-4}\\\\\\\\\Longrightarrow 2+\sqrt{x-4}=\sqrt{x+8}\\\\\\\\\Longrightarrow 4\sqrt{x-4}+x=x+8\\\\\\\\\Longrightarrow 4\sqrt{x-4}=8\\\\\\\\\Longrightarrow \sqrt{x-4}=2\\\\\\\\\Longrightarrow x-4=4\\\\\\\\\therefore \boxed{\boxed{x=8}}[/tex]

Step 10: Placement of Beam.

The beams will need to be placed 8 feet from either side of the origin.

From the given data by doing unit conversion, 250 mL is approximately equal to 8.4535 fluid ounces.

Unit conversion is the process of converting a given quantity from one unit of measurement to another.

To convert milliliters (mL) to fluid ounces (fl oz), you can use the following conversion factor:

1 mL = 0.033814 fl oz

To convert, simply multiply the number of milliliters by 0.033814 to get the equivalent volume in fluid ounces.

For example, if you want to convert 250 mL to fluid ounces, you can use the conversion factor as follows:

250 mL × 0.033814 fl oz/mL = 8.4535 fl oz (rounded to four decimal places)

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An explicit formula in slope intercept form for the given expression is aₙ = 5n - 8.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, we can logically deduce that an equation in slope-intercept form that models the situation is given by:

aₙ = -3 + 5(n - 1)

aₙ = -3 + 5n - 5

aₙ = 5n - 8

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