Valentina measured a kitchen and made a scale drawing. She used the scale 1 inch : 2 feet. A countertop in the kitchen is 2 inches wide in the drawing. How wide is the actual counter?

Answer:

B

Step-by-step explanation:

According to the Pythagoras theorem, the value of ED is 8.4 cm

Pythagoras theorem:

Pythagoras theorem defines that the right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given,

A, B, C, D, E, F, G and H form a cuboid.

AB = 6.7cm, BC = 2.3cm, and CG = 8.1cm.

Now, we need to find the value of Ed and round off it into 1 decimal place.

Here we have the cuboid with the edges named as A, B, C, D, E, F, G and H.

Now, we have to use the value of BC and CG to find the value of hypotenuse of BG.

Because, BG and ED are opposite to each other.

Which means both have the same hypotenuse value.

So, according to the Pythagoras theorem,

=> BG² = BC² + CG²

=> BG² = (2.3)² + (8.1)²

=> BG² = 5.29 + 65.61

=> BG² = 70.9

So, the value of BG is 8.42.

Therefore, the value of ED is 8.4 When we round off this into one decimal place.

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Answer:

-32

Step-by-step explanation:

-(4)^2 - -2^4 = -16 - 16 = -32

Answer:

Step-by-step explanation:

Well let Krutica’s age = x

K = x,    G = x+5,    D = x-6

K+G+D = 86  

x + x+5 + x-6 = 86

3x = 87

x = 29

Gordon is the eldest of the few:

29 or x+5=

34 years old

Answer: Gordon is 34 years old

Answer:

A = 64 m²

Step-by-step explanation:

Step 1: What is the question asking

Step 2: What is known

Step 3: Conversion

Step 4: Answer the question/solve for the area

Interest rate will cause his money to double in approximately 23 years is 3.13%.

Given:

Arnulfo deposited $55 into a savings account and interest is in semi annually.

For 23 years the interest payments will be = 23*2

= 46

Interest rate = 2*72 / 46

= 144/46

= 72/23

= 3.13%

Therefore Interest rate will cause his money to double in approximately 23 years is 3.13%.

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Answer:

1) 1 A. Yes B. Because the change in x and y is constant

2) 2 A. No B. Although the change in y is

constant, the change in x is not

3) 5. A. No B.Because the change in y is not constant

4) 4,5 A. yes B.Because the change in x and constant

Step-by-step explanation:

Answers:

1st box:  [tex]\boldsymbol{90}[/tex]

2nd box:  [tex]\boldsymbol{90}[/tex]

3rd box:  [tex]\boldsymbol{\text{m}\angle 2 = \text{m}\angle 3}[/tex]

===============================================

Explanation:

Complementary angles form a corner. Note that "complementary" and "corner" both start with "C" to help remember the rule.

By "corner", I refer to a 90 degree angle.

Since [tex]\angle 1\text{ and } \angle 2[/tex] are complementary, we know that [tex]\text{m}\angle 1+\text{m}\angle 2 = 90[/tex] simply by the definition of what it means to be complementary.

---------------

Through similar logic, [tex]\angle 1\text{ and } \angle 3[/tex] are complementary which means [tex]\text{m}\angle 1+\text{m}\angle3 = 90[/tex]

We can then equate the left hand sides (LHS) of both equations since both LHS expressions equal 90. This is an example of the substitution property in action.

That's how we end up with [tex]\text{m}\angle 1+\text{m}\angle 2 = \text{m}\angle 1+\text{m}\angle 3[/tex]

After this point, subtract [tex]\text{m}\angle1[/tex] from both sides to cancel them out. We'll be left with [tex]\text{m}\angle 2 = \text{m}\angle 3[/tex], which concludes with [tex]\angle 2 \cong \angle 3[/tex] to show the two angles are congruent.

Step-by-step explanation:

it is a parallelogram.

that means both pairs of opposite sides are parallel and the sides of each pair are equally long.

the sum of all internal angles is 360°.

the opposing angles are equal.

and therefore neighboring angles are complementary angles (or a linear pair) : together they have 180°.

so,

76 = 4x - 8

84 = 4x

x = 21

-3z + 8 + 76 = 180

-3z + 84 = 180

-3z = 96

z = -32

-3z + 8 = -6y - 10

-3×-32 + 8 = -6y - 10

96 + 8 = -6y - 10

104 = -6y - 10

114 = -6y

y = -19

The given expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex] is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex].

What are Exponents?

What are the Laws of Exponents?

There are major seven Laws of Exponents as follows:

From the given question, we have the expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex]    -----(1)

Here, we can use the power of a power rule to simplify the expression.

The power of a power rule is of the form, [tex](a^{m} )^{n} =a^{m \times n}[/tex]

Solving expression (1) using the power of a power rule, we get

[tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-2 \times 3} }{(x^{6} y^{3} z)^{2 \times 3} }\\\implies [\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]

Therefore, the given expression is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]

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Answer:

$67.50

Step-by-step explanation:

27(2) = 54

27/2 = 13.5

54+13.5 = 67.5

Answer:

67.5

explanation:

27/2= 13.5

5*13.5= 67.5

The GCF: 2x³y

answer: 2x³y2x³y(9y³+1)

The differential equation is 8x-4 when the equation is (2x-3)(2x+1).

Given that,

The equation is (2x-3)(2x+1)

We have to find the differentiative equation.

Calculus differentiates the process of locating a function's derivatives. A derivative is the pace at which one function changes in relation to another. Sir Isaac Newton set the foundations for the laws of differential calculus. Numerous scientific disciplines make use of the limits and derivatives ideas. The essential ideas of calculus are differentiation and integration.

Differentiation is the rate at which one quantity changes in relation to another.

Take the equation

(2x-3)(2x+1)

We can do in two ways

1st way

Multiply

4x²+2x-6x-3

Subtraction

4x²-4x-3

Differentiation

8x-4

The equation is 8x-4.

2nd way

We have a formula in differentiation that is

u.v=uv'+vu'

Take u as 2x-3 and v as 2x+1

(2x-3)(2)+(2x+1)(2)

4x-6+4x+2

8x-4

Therefore, The differential equation is 8x-4 when the equation is (2x-3)(2x+1).

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The missing value of that makes the line that passes the given points have a slope of 0 is determined as: a. 15.

The slope (m) is defined as the rise of a line over its run. The formula for finding the slope (m) of a line is given as:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Given the points (-20, y) and (-11, 15) has a slope (m) of 0. Therefore, let:

(-20, y) = [tex](x_1, y_1)[/tex]

(-11, 15) = [tex](x_2, y_2)[/tex]

m = 0

Substitute the values into the slope formula:

0 = (15 - y) / (-11 -(-20))

0 = (15 - y) / 9

Multiply both sides by 9

0 = 15 - y

0 + y = 15 - y + y

y = 15

The answer is: a. 15.

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The equation to represent the situation is y = 15 + 30x.

The number of hours Sophia used for the guitar training after paying 75 dollars is 2 hours.

Sophia takes guitar lessons at home every Sunday. Her instructor charges $15 to cover home visit costs, and $30 per hour of training. One Sunday, Sophia's mother pays the instructor $75 for the guitar lessons.

The equation that can be used to represent the given situation is as follows:

let

x = number of hours used for the training

y = total cost

Therefore,

y = 15 + 30x

Now, Sophia's mother spent 75 dollars for her daughters training. Let's find the hours Sophia used.

Therefore,

75 = 15 + 30x

75 - 15 = 30x

60 = 30x

divide both sides by 30

x = 60 / 30

x = 2

Therefore, she used 2 hours for the training.

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Answer:

==========================

All angles of a square are 90° regardless of the length of its sides. However, all sides must be the same length.

A square is a term to refer to a geometric figure that is characterized by the following characteristics:

One key to identifying a square and the value of its angles is to add them together. The sum of the angles of any geometric figure must result in 360°.

Additionally, if we mark the diagonals of a square we must take into account that these angles will have a different value. To find this value we must divide the angle in half, because these diagonals divide the figure into two parts.

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The equation which is correct is :

n + q = 104

Since we have given that:

Number of nickels and quarters = 104

Total amount from them = $22

Let the number of nickels be 'n'

Let the quarters be 'q'

So, the equation will be

n + q = 104           -------------------------------------------- (1)

Since we know that

value of nickels = 0.05 dollars

Value of quarters = 0.25 dollars

So, the equation will be

0.05n + 0.25q = $22       ------------------------------------ (2)

So, there are two system of linear equation can be used to find the number of nickels and the number of quarters. i.e.

n + q = 104

0.05n + 0.25q = $22

Using elimination we can find the value of n and q :

0.05( n + q =104 )

⇒0.05n+0.05q=5.2-----------(3)

Now, from equation (2) and (3), we get,

0.05 n + 0.05q = 5.2

0.05 n + 0.25q = 22

(-)       (-)           (-)

------------------------------------

0          + 0.2q = 16.8

q = 16.8 ÷ 0.2

q = 84

Putting the value of q = 84 in equation (1),

   n + q = 104

⇒ n + 84 = 104

⇒ n = 104 - 84

⇒ n = 20

Hence,  n +q =104 equation is correct.

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Answer:

[tex]3a^4b^2-2a^2b+9a[/tex]

Step-by-step explanation:

Because multiplication is the inverse of division, we're able to split this fraction into three separate fractions, which will simplify nicely at the end:

[tex]\frac{21a^5b^3}{7ab}; \frac{-14a^3b^2}{7ab}; \frac{63a^2b}{7ab}[/tex]

We can start by simplifying each fraction since 21, -14, and 63 are all divisible by 7:

[tex]\frac{3a^5b^3}{ab}; \frac{-2a^3b^2}{ab}; \frac{63a^2b}{ab}[/tex]

Finally, when dividing quotients with exponents, we subtract the exponents and we put all of our answers back together since everything was multiplied by each other at the beginning of the problem:

[tex]3a^4b^2-2a^2b+9a[/tex]

The equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.

Isaac made a 30-cup batch of potato salad, and now he is filling 2.5-cup

to-go containers to sell to customers.

Let y represent the number of cups of potato salad remaining,

And x represents the number of to-go containers Isaac has filled,

As per the given situation, we can write the equation as:

y = 30 - x  ....(i)

Substitute the value of x = 2.5 in the above equation,

y = 30 - 2.5

y = 27.5

Thus, the equation y = 30 - x shows the number of cups of potato salad remaining, and its solution is y = 27.5.

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Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.

Given that,

Luke asserts that since the shape is constant, two circles are always isometric.

We have to say is he accurate.

The answer is

No, an isometry keeps the size and shape intact.

Because a shape-preserving transformation (movement) in the plane or in space is called an isometric transformation (or isometry). The isometric transformations include translation, rotation, and combinations thereof, such as the glide, which combines a translation with a reflection.

Therefore, Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.

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a. The smallest number of M & M's possible is 14.

b. The number of green is 24.

c. The ratio of green to yellow to red in 6: 15: 25.

a. When there are only green and yellow M & M's in the bag, the smallest number of M & M's possible will be:

= (2 × 2) + (2 × 5)

= 4 + 10

= 14

b. If there are 84 total green and yellow M & M's in the bag, the number of green will be:

= 2 / (2 + 5) × 84

= 2/7 × 84

= 24 green

c. If red M & M's were added to the bag in part b to get a total of 100, the ratio of green to yellow to red in simplest form will be:

= Green : Yello : Red

= 24 : 60 : 100

= 6 : 15 : 25

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Answer:

============================

Use equation for continuous compound:

Plug in the values and calculate:

Answer:

$5,252.53 (nearest cent)

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=2900 \cdot e^{(0.054 \cdot 11)}[/tex]

[tex]\implies \sf A=2900 \cdot e^{0.594}[/tex]

[tex]\implies \sf A=2900 \cdot 1.81121882[/tex]

[tex]\implies \sf A=5252.53457...[/tex]

Therefore, assuming no deposits or withdrawals are made, the amount of money in the account after 11 years would be $5,252.53 (nearest cent).

Answer: $28.89

Step-by-step explanation: 2% of 1,444.50 is $28.89

Answer:

A. 70.2

Step-by-step explanation:

solve your equation step-by-step.

842.412=x1

Step 1: Cross-multiply.

842.412=x1

(842.4)*(1)=x*(12)

842.4=12x

Step 2: Flip the equation.

12x=842.4

Step 3: Divide both sides by 12.

12x12=842.412

x=70.2

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Answer:

slope and x-intercept is -1/2

y-intercept is 5

The correct option A. 1, is the value of the variable 's' for which the solution of the expression is greatest .

For the given question,

The expression is-

(s + 6) ÷ s

Use the options;

A : s = 1

= (s + 6) ÷ s

= (1 + 6) ÷ 1

= 7

B : s = 2

= (s + 6) ÷ s

= (2 + 6) ÷ 2

= 4

C : s = 3

= (s + 6) ÷ s

= (3 + 6) ÷ 3

= 3

D : s = 4

= (s + 6) ÷ 4

= (4 + 6) ÷ 4

= 2.5

Thus, the value of the variable 's' for which the solution of the expression is greatest is 1.

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Answer:

a = -1
b = -9

Step-by-step explanation:

when x = -2 put -2 for x in the equation:

a(3- (-2)) = -2*(-2) + b and then solve
a(3+2) = 4+b
5a = 4+b

then look at the numbers in the box and try for which number this equation will work. when you put a = -1 and b = -9 you will see it is equal on both sides because each side is -5

The triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.

First, let us understand the SAS congruency theorem:

This one denotes Side - Angle - Side and it means that if 2 sides and one angle of a triangle are equal to the corresponding 2 sides and one angle of another triangle, then they are both congruent.

We are given:

SR and ST are straight lines.

side SX ≅ side SY

side XR ≅ side YT

So,

side SR ≅ side ST

In triangle RSY and triangle TSX;

side SR ≅ side ST (above proved)

∠RSY ≅ ∠TSX (Common)

side SY ≅ side SX (Given)

So, triangle RSY ≅ triangle TSX by SAS congruency theorem.

Thus, the triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.

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