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3 years ago

Four times a number increased by one is between a negative seven and thirteen. Find all numbers.

Mathematics

2 answers:

aleksley [76]3 years ago

5 0

Answer:

Step-by-step explanation:

Let the number be x.

four times the number:

If the exprression is increased by 1, it will become:

4x+1

If the value is between -7 and 13, the value of x will be within the range [-6, 12]

Equating the resulting expression to each end point.

At end point of -6

4x+1 = -6

4x = -6-1

4x = -7

x = -7/4

At the end point of 12:

4x+1 = 12

4x = 12-1

4x = 11

x = 11/4

Hence all the numbers will be within the range [-7/4, 11/4] or -7/4≤x≤11/4

MrRa [10]3 years ago

5 0

Answer:

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Step-by-step explanation:

PLEASE HELP ME!! (I’m struggling in microeconomics) For each scenario see whether you agree. Then determine if the scenario is talking about a price for or price silly then graph the price control to show the results.

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Simplify this expression 9xy4x 3x3y

Alekssandra [29.7K]

Answer:

81 x y^5

Step-by-step explanation:

Simplify the following:

9×3×3 x y^4 y

3×3 = 9:

9×9 x y^4 y

9 x y^4×9 y = 9×9 x y^(4 + 1):

9×9 x y^(4 + 1)

4 + 1 = 5:

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Answer: 81 x y^5

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3 years ago

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Answer:

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Step-by-step explanation:

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4 years ago

Lisa's store collects 5% sales tax on every item sold. If she collected $22.00 in sales tax, what was the cost of the items her

Ede4ka [16]

Since we are looking for the principal amount, then all we have to do is reverse the process of getting the amount of tax. In order to get the principal, you just have to divide 22 with 0.05. The answer is 440 so that is the principal amount you are looking for.

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3 years ago

A quadrilateral has vertices at $(0,1)$, $(3,4)$, $(4,3)$ and $(3,0)$. Its perimeter can be expressed in the form $a\sqrt2+b\sqr

seraphim [82]

Answer:

a + b = 12

Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

$Perimeter = a\sqrt{2} + b\sqrt{10}$

Required

$a + b$

Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$(x_1,y_1) = A(0,1)$

$(x_2,y_2) = B(3,4)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}$

$AB = \sqrt{( - 3)^2 + (-3)^2}$

$AB = \sqrt{9+ 9}$

$AB = \sqrt{18}$

$AB = \sqrt{9*2}$

$AB = \sqrt{9}*\sqrt{2}$

$AB = 3\sqrt{2}$

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

$(x_1,y_1) = B (3,4)$

$(x_2,y_2) = C(4,3)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}$

$BC = \sqrt{(-1)^2 + (1)^2}$

$BC = \sqrt{1 + 1}$

$BC = \sqrt{2}$

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = C(4,3)$

$(x_2,y_2) = D (3,0)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}$

$CD = \sqrt{(1)^2 + (3)^2}$

$CD = \sqrt{1 + 9}$

$CD = \sqrt{10}$

Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = D (3,0)$

$(x_2,y_2) = A (0,1)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}$

$DA = \sqrt{(3)^2 + (- 1)^2}$

$DA = \sqrt{9 + 1}$

$DA = \sqrt{10}$

The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral

$Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}$

$Perimeter = 4\sqrt{2} + 2\sqrt{10}$

Recall that

$Perimeter = a\sqrt{2} + b\sqrt{10}$

This implies that

$a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}$

By comparison

$a\sqrt{2} = 4\sqrt{2}$

Divide both sides by $\sqrt{2}$

$a = 4$

By comparison

$b\sqrt{10} = 2\sqrt{10}$

Divide both sides by $\sqrt{10}$

$b = 2$

Hence,

a + b = 2 + 10

a + b = 12

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3 years ago

During second period, Janet completed a grammar worksheet.

Dmitry_Shevchenko [17]

Answer: 50%

Step-by-step explanation:

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3 years ago

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