Given: DEF
Prove: DEF is isosceles.

The dimensions of the original piece of rectangular cardboard are 22 in by 40 in

A prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

Given that, Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard, from which she cuts out 9-in squares from each corner. The length of the original piece of cardboard is 18 in more than the width, the volume of the box is 792 in³,

We know that volume of rectangular box = length × width × height

length = x+18-9-9 = x

height = 9

width = x-9-9 = x+18

= (x-18) × x × 9

(x-18)×9x = 792

9x²-162x-792 = 0

x²-18x-88 = 0

Factorizing to find the value of x,

x = 22 and x = -4

Therefore, width of the cardboard = 22 in

Length = 22+18 = 40 in

Hence, the dimensions of the original piece of rectangular cardboard are 22 in by 40 in

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Answer:

$5.86

Step-by-step explanation:

The total was $36.31

We were given the price of 1, which was $1.15

$36.31-$1.15 = $35.16 remaining

Since the other 6 friends ordered the same meal, they would have paid the same price, so we would divide by 6

$35.16/6 = $5.86

The volume of a rectangular prism is, 108 unit³

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A rectangular prism has a width of 2, a height of 9, and a depth of 6.

Now, We know that;

Volume of rectangular prism = Length × Width × Height

Substitute all the values, we get;

⇒ Volume of rectangular prism = Length × Width × Height

⇒ Volume of rectangular prism = 2 × 9 × 6

⇒ Volume of rectangular prism = 108 unit³

Thus, The volume of a rectangular prism = 108 unit³

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Answer:

  3.5%

Step-by-step explanation:

You want the percent error in a measured value of 4.16 g/cm³ in relation to a handbook value of 4.018 g/cm³.

The percentage error is calculated as ...

  % error = ((measured) - (actual))/actual × 100%

  = (4.16 -4.018)/4.018 × 100%

  = 0.142/4.018 × 100% ≈ 3.5%

The given numbers, 4.16 and 4.018 have 3 and 4 significant figures, respectively. Their difference will have 2 significant decimal places, as does 4.16, so should be considered to be 0.14. This value has 2 significant figures, so the final answer will have 2 significant figures.

You will note that we kept all of the digits available throughout the computation, rounding to 2 significant figures only at the end.

You will also note that taking differences of numbers of approximately the same value can result in a loss of significant figures.

Answer: x=15

Step-by-step explanation: try cross multiplying

Answer:

√121 = 11

diffrence of 164 and 11 = 164 - 11 = 153

number = 153

Yes, the triangle can have the angle measures  31[tex]\frac{3}{4}[/tex]°, 53[tex]\frac{1}{2}[/tex]°, 94[tex]\frac{3}{4}[/tex]°.

And the first angle is 31[tex]\frac{3}{4}[/tex]°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

The angle measures of the triangle,

= x,  53[tex]\frac{1}{2}[/tex]°, 94[tex]\frac{3}{4}[/tex]°

The angle measure of x = 180 -  53[tex]\frac{1}{2}[/tex]° - 94[tex]\frac{3}{4}[/tex]°

x = 31[tex]\frac{3}{4}[/tex]°

And, yes, the triangle can have the angle measures  31[tex]\frac{3}{4}[/tex]°, 53[tex]\frac{1}{2}[/tex]°, 94[tex]\frac{3}{4}[/tex]°.

Therefore, the first angle is 31[tex]\frac{3}{4}[/tex]°.

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Answer: 7, equilateral, heptagon

Step-by-step explanation: Hello!

The first thing you can see is that the polygon has 7 sides.  

Secondly, a regular polygon is a polygon that has all equal angles and all equal sides.

An equiangular polygon is a polygon with all equal angles but not all equal sides.

An equilateral polygon is a polygon with all equal sides but not all equal angles.

You can tell by the shape of the polygon that the polygon does not have all equal angles.  The only way you can say that the polygon is equiangular is if it is proven to be true or it is given.  Even if the angles look congruent, you can never say that they are unless you know it for a fact.  This is because diagrams are always misleading.  

This means that the polygon is not a regular polygon and is not an equiangular polygon.  This means that the polygon is equilateral.  Let's check.

All sides clearly show that the measure of each is 8.  Since it is given and it is a fact that all sides are congruent, the polygon is definitely equilateral.  

The last thing you need to do is to find if the shape is a hexagon, heptagon, or octagon.  You can find that by knowing which shapes are which just by counting the sides:

3 sides - Triangle
4 sides - square
5 sides - pentagon
6 sides - hexagon
7 sides - heptagon

8 sides - octagon
9 sides - nonagon
10 sides - decagon
etc.

You know that since the polygon has 7 sides, the shape is a heptagon.

Answer:

The polygon above has 7 sides. It is a heptagon.

The possible rational zeros of the given polynomial are given by: p/q = ±1, ±2, ±3, ±6

What is a polynomial ?

Polynomial can be defined as expression in which combination of variables and coefficients

A rational zero of a polynomial is a rational number that, when plugged into the polynomial, results in zero. To find all possible rational zeros of a polynomial, we can use the Rational Root Theorem.

According to the Rational Root Theorem, if a rational number "p/q" is a zero of a polynomial, where p and q are integers and q ≠ 0, then p must be a factor of the constant term (in this case, 6) and q must be a factor of the leading coefficient (in this case, 2).

So, the possible rational zeros of the given polynomial are given by:

p/q = ±1, ±2, ±3, ±6

We can then test each of these values to see if they are actually zeros of the polynomial. To do this, we simply plug in the value and simplify. If the result is zero, then the number is indeed a zero of the polynomial.

For example, plugging in p/q = -1, we get:

2(-1)^5 + 4(-1)^4 - 3(-1)^2 + (-1) - 6 = 2 - 4 - 3 + 1 - 6 = -14,

which is not equal to zero, so -1 is not a zero of the polynomial.

By testing each of the possible rational zeros in a similar way, we can determine which ones are actually zeros of the polynomial.

Therefore,  The possible rational zeros of the given polynomial are given by: p/q = ±1, ±2, ±3, ±6

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Answer:

[tex]22212[/tex].

Step-by-step explanation:

In base-10, for a number to be divisible by [tex]4[/tex], the last two digits must also be divisible. Among all the two-digit numbers formed with "[tex]\texttt{1}[/tex]" and "[tex]\texttt{2}[/tex]", only [tex]12[/tex] satisfies the requirements as the last two digits of [tex]N[/tex].

For a number to be divisible by [tex]9[/tex], the sum of all the digits must also be divisible. For [tex]N\!\![/tex] to be as small as possible, its digits should add up to the smallest multiple, [tex]1 \times 9 = 9[/tex], instead of larger ones such as [tex]18[/tex].

Since the last two digits of [tex]N[/tex] is [tex]\texttt{1}[/tex] and [tex]\texttt{2}[/tex], the other digits of [tex]N\![/tex] would need to add up to [tex]9 - 1 - 2 = 6[/tex]. To minimize the value of [tex]N\!\![/tex], these digits should consist solely of [tex]\texttt{2}[/tex]: [tex]2 + 2 + 2 = 6[/tex]. Therefore, the answer should be [tex]22212[/tex].

Check the picture below.

the Diagram that would support his plan to use ASA is either option A and Option B.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

The Corresponding portions of Congruent triangles are the complete form of CPCT. Triangles may be shown to be congruent after which the final dimension can be anticipated without actually measuring the triangle's sides and angles. The following are many congruency rules.

Since All triangles given in the options are congruent we need to find which pair of triangles are supposed to be congruent by the property of ASA.

From ASA:

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and the side included between the angles of the second triangle.

Therefore, Either Option A or Option B is the Diagram that would be supportive of his intention to utilize ASA.

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Answer:

[tex]x < - 2[/tex]

That the answer.

The values of the ratios of the perimeters and areas of the red figure to the blue figure, which are similar figures, in the simplest form are:

The ratio of their perimeters:  28/16

The ratio of their areas:  (28)²/(16)²

What is the ratio?

A ratio is a relationship between two things when it is expressed in numbers or amounts.

The ratio of the perimeter of similar figures = a side length of one figure / corresponding side length of the other figure

The ratio of the areas of two similar figures = square of the length of one figure/square of the corresponding length of the other

Thus:

The side length of Red-figure = 28

The side length of the Blue figure = 16

Therefore:

The ratio of their perimeter = Side length of the red figure / Side length of the blue figure

The ratio of the perimeter of the red figure to the blue figure = 28/16

The ratio of their areas = Side length of the red figure / Side length of the blue figure

The ratio of the areas of the red figure to the blue figure = (28)²/(16)²

Hence, The values of the ratios of the perimeters and areas of the red figure to the blue figure, which are similar figures, in the simplest form are:

The ratio of their perimeters:  28/16

The ratio of their areas:  (28)²/(16)²

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The slope-point form of a line can be used to determine the equation for a line that is perpendicular to the line g(x) = 4x + 3 and passes through the point (7,3).

The slope of a line perpendicular to g(x) = 4x + 3 is equal to -1/4, which is the negative reciprocal of g(x slope. )'s Consequently, the perpendicular line's slope is 4.

The equation of the line passing through (7,3) with a slope of 4 can therefore be determined using the point-slope form of a line:

y - 3 = 4(x - 7) (x - 7)

Increasing the right side and reducing it:

y - 3 = 4x - 28

28 more on both sides:

y = 4x + 25

Consequently, y = 4x + 25 is the equation for the line perpendicular to g(x) = 4x + 3 and passing through (7,3).

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The equation for a line that is perpendicular to the line g(x) = 4x + 3 and passes through the point can be found using the slope-point form of a line (7,3).

It forms a 90° angle with one particular spot where the line passes. Finding the perpendicular line requires knowledge of coordinates and line equations. The slope should be a/b if the line's equation is (x1, y1) and its coordinates are (ax + by + c = 0).

The slope of a line perpendicular to g(x) = 4x + 3 is equal to -1/4, which is the negative reciprocal of g(x slope. )'s Consequently, the perpendicular line's slope is 4.

The equation of the line passing through (7,3) with a slope of 4 can therefore be determined using the point-slope form of a line:

Let the equation be

y - 3 = 4(x - 7) (x - 7)

simplifying the above equation we get

y - 3 = 4x - 28

y = 4x + 25

Consequently, the equation for the line parallel to g(x) = 4x + 3 and passing through is y = 4x + 25. (7,3).

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Savings account B offers a higher APY of 5.25%, compared to the 5.13% offered by savings account A.

Interest is a fee charged by a lender to a borrower for the use of money. It represents the cost of borrowing money and is typically expressed as a percentage of the loan amount. Interest is paid over a period of time and is calculated based on the principal amount of the loan, the interest rate, and the length of the loan term.

Simple interest is calculated only on the principal amount of the loan, while compound interest is calculated on both the principal and the accumulated interest over time. Compound interest results in a faster growth of the loan balance compared to simple interest.

APY (Annual Percentage Yield) is the effective annual interest rate, taking into account the frequency of compounding. It can be calculated as follows:

APY = (1 + (APR / n))ⁿ⁻¹

where APR is the annual percentage rate and n is the number of times the interest is compounded in a year.

For savings account A, with a 5% APR and compounding quarterly, n = 4. So,

APY = (1 + (0.05 / 4))⁴⁻¹ = 0.0513 = 5.13%

For savings account B, with a 5% APR and compounding semiannually, n = 2. So,

APY = (1 + (0.05 / 2))²⁻¹ = 0.0525 = 5.25%

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Solving provided question, we can say that  equation of slope intercept will be => y - 30 = mx - 3m

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

from the provided graph,

the coordinates are (3,30)

equation of slope intercept will be

y - 30 = m(x - 3)

y - 30 = mx - 3m

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Answer:

3x+24

Step-by-step explanation:

3*x +3*8

=3x+24

Answer:

3x+24

Step-by-step explanation:

3(x+8)

3×x + 3×8

3x+24

The inverse of functions g(x)=2/x - 1 and f(x)= ⁵√(x-1) + 2 are g⁻¹(x) = 2/(x + 1)  and f⁻¹(x) = (x-2)⁵ + 1 respectively

In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f.

For g(x)=2/x - 1:

Let g(x) = y

y = 2/x - 1

y + 1 = 2/x

x(y + 1) = 2

x = 2/(y + 1)

Since x = g⁻¹(y)

Thus, g⁻¹(x) = 2/(x + 1)          [We just replace y with x]

For f(x)= ⁵√(x-1) + 2:

Let f(x) = y

y =  ⁵√(x-1) + 2

y -2 =  ⁵√(x-1)

(y-2)⁵ = (x-1)

x-1 = (y-2)⁵

x = (y-2)⁵ + 1

Since x = f⁻¹(y)

Thus, f⁻¹(x) = (x-2)⁵ + 1

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The total number of pieces of pie they eat in all is (1 + b) pieces of pie

Number of pieces of pie eaten each = 1 piece

Number of friends= b

Total pieces of pie eaten by all = (Robert + Number of friends) × Number of pieces of pie eaten each

= (1 + b) × 1

= (1 + b) pieces of pie

Therefore, Robert and his friends are a total of (1 + b) pieces of pie.

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Answer:VROOOOOOM

Step-by-step explanation:

E E E EE

Answer:

...............

Step-by-step explanation:

The value of d in terms of w and l is d = √216w / 35l.

The weight of w kg of a metal bar varies jointly as its length L metres and the square of its diameter d mm. If w = 140 when d = 4 and L = 54. The value of d in terms of W and L can be found as follows:

Therefore, using the proportional relationship,

w ∝ ld²

w = kld²

Where,

Therefore,

140 = k × 54 × 4²

140 = 864k

k = 140 / 864 = 70 / 432 = 35 / 216

k = 35 / 54

Therefore, d in terms of w and l is as follows:

w = kld²

d² = w / kl

Hence,

d = √216w / 35l

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Answer:

184

Step-by-step explanation:

1. big rectangle area = 10*(6+5+5) =160

2. top & bottom triangle = (2*1/2 bottom * h)= 6*4 = 24

total 160 +24 =184

Answer:

13728

Step-by-step explanation:

Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.

x + (x + 2) + (x + 4) = 72

3x + 6 = 72

3x = 66

x = 22.

This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.

The answer is 13728.

Answer:12

Step-by-step explanation:

9/12= 3/4   (/3).   3/4=12/16    (x4)

Answer:

y is not a function of x.

Step-by-step explanation:

To know if this is a function, first look in the x column.

If there are no repeated numbers, its a function. Here there is a repeat. 1 is listed twice.

Since there are two different y's that go with the x, when x is 1, this is not a function.

Because (1,8) and (1,12) are the problem. This is not a function because even just one x has more than one y.

Answer:

1.

x = 5√3

y = 10

2.

x = 2√33 in.

3.

y = 11√3

x = 22

4.

x = 7√2

5.

x = 3 m

6.

x = 16

y = 16√3

Step-by-step explanation:

Recall:

30-60-90 triangle ratio of sides:    1 : √3 : 2

45-45-90 triangle ratio of sides:    1 : 1 : √2

Pythagorean theorem: a² + b² = c²

1.

1 : √3 : 2

5 : x : y

1/5 = √3/x

x = 5√3

1/5 = 2/y

y = 10

2.

a² + b² = c²

8² + x² = 14²

64 + x² = 196

x² = 132

x = 2√33 in.

3.

1 : √3 : 2

11 :  y  : x

1/11 = √3/y

y = 11√3

1/11 = 2/x

x = 22

4.

1 : 1 : √2

7 : 7 : x

1/7 = √2/x

x = 7√2

5.

a² + b² = c²

x² + 4² = 5²

x² + 16 = 25

x² = 9

x = 3 m

6.

1 : √3 : 2

x :   y :  32

1/x = 2/32

2x = 32

x = 16

√3/y = 2/32

√3/y = 1/16

y = 16√3

Answer:

First Question. 5942

Second Question. 1363

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(a) The coldest city is city C because it has the lowest temperature.

(b) The warmest city is city B because it has the highest temperature.

The coldest city is the city with the lowest temperature or the city with the least amount of temperature.

The temperature of the cities is given as follows;

City A = -9 ⁰F

City B = 10 ⁰F

City C = - 3.5 ⁰F

Thus, the coldest city is city C because it has the lowest temperature.

The warmest city is city B because it has the highest temperature.

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Answer:17

Step-by-step explanation:

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