4. Mr. Smith makes lemonade. His recipe calls for 1½ cups of water for every cup of concentrate. If Mr. Smith 2 pours all 5 cups of concentrate into a pitcher to serve at a party, how much water should he add?​

Answer: [tex]W'(-3/2, 3), X'(2, -3), Y'(-9/2, -3), Z'(-9, 3)[/tex]

Step-by-step explanation:

When dilating with a scale factor of [tex]k[/tex] centered at the origin,[tex](x,y) \to (kx, ky)[/tex].

The required dilation is given as for Quadrilateral W'X'Y'Z' as W'(-3/2, 2), X'(2, -3), Y'(-9/2, -3) and Z"(-9, 3).

Given that,
Quadrilateral WXYZ has vertices W (-3, 6), X (4, -6), Y (-9, -6), and Z (-18, 6). To determine the coordinates for the point named after it is dilated through the origin by a factor of one-half.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
Quadrilateral WXYZ has vertices W (-3, 6), X (4, -6), Y (-9, -6), and Z (-18, 6).
Scale factor = 1/2
vertices W' (-3/2, 6/2), X' (4/2, -6/2), Y' (-9/2, -6/2), and Z' (-18/2, 6/2).

Thus, the required dilation is given as for Quadrilateral W'X'Y'Z' as W'(-3/2, 2), X'(2, -3), Y'(-9/2, -3) and Z"(-9, 3).

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Formula a = 2b + c in subject to b is b = a-c / 2

Changing the subject of formula is a way of rearranging formula to determine missing variable in terms of other variable

Changing the subject of formula is also known as rearranging formula or changing the subject of an equation.

Given ,

Formula : a = 2b + c

Subtracting by c on both sides,

=> a - c = 2b + c - c

=> a - c = 2b

Dividing by 2 on both sides,

=> [tex]\frac{a-c}{2} = b[/tex]

Formula in subject to b is

b = a-c / 2

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The correct y-intercept, slope, and equation for the line include the following:

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Note: Each interval on this graph represents 1 unit.

By critically observing the graph, we can reasonably and logically deduce the following points through which the line passes through:

Points (x, y) = (0, 4)

Points (x, y) = (10, 0)

Substituting the given parameters into the formula, we have;

Slope, m = (0 - 4)/(10 - 0)

Slope, m = -4/10

Slope, m = -2/5.

At point (0, 4), a linear equation for the line can be calculated by using the slope-intercept form:

y = mx + c

Where:

Substituting the given parameters into the formula, we have;

y = mx + c

y = -2x/5 + 4

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Answer:

[tex]\frac{5}{14}[/tex] c - [tex]\frac{2}{9}[/tex] d

Step-by-step explanation:

Answer:

d = 2 and terms are 6, 8, 10 12 and 14

Step-by-step explanation:

we know

[tex] a_{n} = a_{1} + (n-1)d [/tex]

here a(n) = nth term

a1 = 1st term

n = no. of term

d = common difference

putting the values we get,

178 = 6 + (87-1)d

⇒ 178 = 6 + 86d

⇒86d = 172

⇒ d = 2

So required common difference is 2.

Now the first term is 2

so second term is a2 = 6 + ((2-1)×2) = 8

third term = 6 + ((3-1)×2) = 10

fourth term = 6 + ((4-1)×2) = 12

fifth term = 6 + ((5-1)×2) = 14

The probability that a single doe captured (weighed and released) at random in December is undernourished, using the normal distribution, is given by:

0.1271 = 12.71%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the weights are given as follows:

[tex]\mu = 67, \sigma = 7.9[/tex]

The probability that a doe is undernourished is the p-value of Z when X = 58, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (58 - 67)/7.9

Z = -1.14.

Z = -1.14 has a p-value of 0.1271.

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Step-by-step explanation:

x + 7 = 11

x + 7 - 7 = 11 - 7

x = 4

Hope this helps! :)

Answer:

[tex]\displaystyle 4[/tex]

Explanation:

Use the inverce of Addition [Deduction (or Subtraction)] to arrive at your answer:

[tex]\displaystyle x + 7 = 11 \hookrightarrow -7 + 11 = x \\ \\ 4 = x[/tex]

I am joyous to assist you at any time.

The value of x is 11x+4x=180 and x = 12

The correct option is option c)

What is interior angles?

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles.

We are given that the value of two angle is 11x and 4x

Since both lines are parallel and a line intersects both the lines

Hence the sum of these angles is 180 degrees

Hence we get an equation

11x+4x= 180

15x =180

x=12

Hence the correct option is option c)

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The measurement of Angle ∠5=52°

when two parallel lines are cut by a transversal line, then the resultant alternate interior angles are equal.

In the given figure, lines AB║CD.

And ∠3=52, ∠5=?

By using alternate interior angle property ,

Angle ∠3 and ∠5 are cut by a transversal line, so this both angle will be equal

⇒∠3=∠5=52°

Here, the value of ∠5=52°

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Answer:

35%

Step-by-step explanation:

35 divided by 100 = 0.35 = 35%

In the national park, the probability that a single doe captured (weighed and released) at random in December is undernourished is 25.5%

Data is symmetrically distributed and skew-free in a normal distribution. When the data is shown on a graph, it has the shape of a bell, with the majority of values congregating in the center and diminishing as they move outward.

Due to their structure, normal distributions are sometimes known as bell curves or Gaussian distributions.

Assuming normal distribution we calculate the probability as follows

Definition of variables

mean adult female deer, μ = 67.0 kg

Standard deviation, σ = 7.9 kg

sample, X = 58

Z score, z is given by the formula

= (X - μ) / σ

= (58 - 67) / 7.9

= -1.139 has a p value of 0.2546

P = 25.5%

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Answer:A. x= .100

Step-by-step explanation:because of the distance in miles

Answer: 15.5

Step-by-step explanation: The equation is a. Fill in the letters. 4=a. 15=b. so: Now solve. 4 squared is 16. 15 squared is 225. 225+16= 241.  15.5 is the answer. It's just the Pygotherean Method!

Answer:

- 42 , - 17

Step-by-step explanation:

(a)

substitute x = 5 into f(x) , that is

f(5) = 5² - 10(5) - 17 = 25 - 50 - 17 = 25 - 67 = - - 42

(b)

substitute x = 0 into f(x)

f(0) = 0² - 10(0) - 17 = 0 - 0 - 17 = - 17

The equations that are true include the following:

(8 × 7)/2 - 12 = 22 - (2 × 3)

48 ÷ 8 + 2³ = 5 + 3²

In order to determine the equations that have a true and valid solution, we would simplify and evaluate each of the equations as follows:

(8 × 7)/2 - 12 = 22 - (2 × 3)

Opening the bracket on both sides of the equation, we have:

56/2 - 12 = 22 - 6

28 - 12 = 16

16 = 16 (True).

48 ÷ 8 + 2³ = 5 + 3²

Evaluating the exponents, we have:

48 ÷ 8 + 8 = 5 + 9

6 + 8 = 14

14 = 14 (True).

150/5² = 30 - 4² - 12

Evaluating the exponents, we have:

150/25 = 30 - 16 - 12

6 = 2 (False and incorrect).

9² - 7² = 20 ÷ (7 - 2)

Opening the bracket, we have:

9² - 7² = 20 ÷ 5

Evaluating the exponents, we have:

81 - 49 = 4

32 = 4 (False and incorrect).

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Answer:

62feet

Step-by-step explanation:

10x=620

x=62feet

The perimeter usually gives the length of the figure. In a square, which has al its sides equal, the perimeter of the square will be four times its sides. The maximum width of the rectangle is 62 feet.

The perimeter of a rectangle is defined as the total distance covered by its boundaries or the sides. Since the rectangle is comprised of four sides, the perimeter will be the sum of all four sides. The perimeter is a linear measure and its unit is m, cm, feet, etc.

The equation used to calculate the perimeter of a rectangle is given as:

Perimeter = 2 (l + b)

Here l = length

b = breadth

Here the length is four times the width, l = 4x

Width may be b = x

Then perimeter is:

P = 2 (4x + x) = 620

10x = 620

x = 620 / 10 = 62 feet

Thus the width is 62 feet.

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Answer:

9i

Step-by-step explanation:

         i² = -1

      [tex]\sqrt{-81}=\sqrt{81i^2}\\[/tex]

                [tex]\sf \bf = \sqrt{9*9*i * i}\\\\ = 9i[/tex]

Answer:  The correct answers are:

4^4 (same answer for the equation shown) = 256 (option# B) for the first one

((2^2)^4)*2^-5= 8 (option# B) for the first one

Step-by-step explanation: Confirmed correct

Answer:

First one:

[tex]2^{2} (3+1) *[2(7-5)]^{2}[/tex]

= [tex]2^2(4)* [2(2)]^2[/tex]

= [tex]2^2(4)(4)^2[/tex]

= [tex]2^2(4)(16)[/tex]

= [tex]2^2*2^2*2^4[/tex]

= [tex]4*4*4^2[/tex]

= [tex]4^4[/tex]

The answer is four

and for the second one:

[tex]2^8*\frac{1}{2^5}[/tex]

[tex]2^3 = 8[/tex]

the answer is 8

Reason:

The x value x = 4 repeats itself. We have the input x = 4 lead to multiple outputs (y = 0 and y = 2) at the same time. This is enough evidence to conclude we do not have a function.

A function is only possible if any given input leads to exactly one output.

If you were to plot these points, then you should note (4,0) and (4,2) fail the vertical line test. To pass the vertical line test, it should be impossible to draw a single vertical line through more than one point.

Answer:

a

Step-by-step explanation:

enjoy!

Answer:

b

Step-by-step explanation:

Answer:

  D.  A triangle with angles measuring 75°, 60°, and 45°​

Step-by-step explanation:

Given various triangle descriptions, you want to know which one describes more than one triangle.

The angles and sides of a triangle satisfy a few different relations:

A. Two sides and the included angle can be used with the Law of Cosines to find the length of the third side. That is, a single triangle is created by these measurements.

B. Sides measuring 4, 8, and 15 do not satisfy the triangle inequality, so no triangle is created by these measurements.

C. Sides measuring 6, 8, and 10 satisfy the triangle inequality, so will create a single triangle. (That triangle is a right triangle.)

D. The given angles total 180°, so could be the angle measures of any number of triangles. At least one side length must be specified in order to completely define a single triangle. These measures create more than one triangle.

The possible values for the third side's measurement are3 < x < 17. Any two sides of a triangle's lengths added together must be longer than the third side.

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The value of {f(-1)-f(3)}/(-1-3) is 255/16 when f(x) = [tex]4^{x}[/tex].

According to the question,

We have the following information:

f(x) = [tex]4^{x}[/tex]

Now, we will first find the values of f(-1) and f(3) and then we will put these values into the given operation in order to find its value.

f(-1) = [tex]4^{-1}[/tex]

Now, we will inverse this operation to have positive exponents:

f(-1) = 1/4

f(3) = [tex]4^{3}[/tex]

f(3) = 4*4*4

f(3) = 64

Now, we have f(-1)-f(3) in the numerator. So, we will solve this first:

1/4 - 64

(1-256)/4

-255/4

Now, putting all these values in the indicated operation:

(-255/4)/(-1-3)

(-255/4)-4

255/(4*4)

255/16

Hence, the value of {f(-1)-f(3)}/(-1-3) is 255/16 when f(x) = [tex]4^{x}[/tex].

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The interior angles of triangle add up to give 180 degrees.

The set of all points within a triangle, or all points in the convex hull of the triangle's vertices, is known as the interior of the triangle.

The three angles that make up a triangle's interior are referred to as its interior angles. The total of these three angles is always 180 degrees.

Here given two angles of triangle = 96° and 48°

We know that sum of interior angles = 180°

So x° + 96° + 48° = 180°

x + 144 = 180

x = 180 - 144

x = 36°

To find the value of y,

We know that angle over a straight line is 180°

So ,

96° + y° = 180°

y = 180 - 96

y = 84°

Therefore the value of x = 36° and y = 84° .

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Step-by-step explanation:

A quadratic equation is in the form of

[tex]ax {}^{2} + bx + c[/tex]

C is the y intercept a.k.a the value of c is when x=0,

when x is 0, c is -7 so

c=-7

[tex] {ax}^{2} + bx - 7 [/tex]

Next we know when x is 2, y is 1 so

[tex]a(2) {}^{2} + 2b - 7 = 1[/tex]

[tex]4a + 2b = 8[/tex]

When x is 5, y is -2

[tex]a(5) {}^{2} + b(5) - 7 = - 2[/tex]

[tex]25a + 5b = 5[/tex]

So we have a system of equations, using elimination.

[tex]5a + b = 1[/tex]

[tex] - 6a = 6[/tex]

[tex]a = - 1[/tex]

So

[tex]5( - 1) + b = 1[/tex]

[tex]b = 6[/tex]

Our quadratic is

[tex] - {x}^{2} + 6x - 7[/tex]

Answer:

7

Step-by-step explanation:

[tex]\frac{f(6)-f(4)}{6-4}=\frac{26-12}{6-4}=7[/tex]

Answer: $ 875

Step-by-step explanation:

3,500-0.03(4)

3,499.97/4

= $875

Answer:

x = 1

Step-by-step explanation:

- [tex]\frac{5}{2}[/tex] x + [tex]\frac{3}{4}[/tex] x = - [tex]\frac{7}{4}[/tex]

multiply through by 4 ( the LCM of 2 and 4 ) to clear the fractions

- 10x + 3x = - 7

- 7x = - 7 ( divide both sides by - 7 )

x = 1

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Given equation is:

[tex]-\frac{5}{2}x+\frac{3}{4}x=-\frac{7}{4}[/tex]

Simplifying the left side of the equation.

[tex]\frac{2(-5x)+3x}{4}=-\frac{7}{4}[/tex]

This is equivalent to:

[tex]\frac{-10x+3x}{4}=-\frac{7}{4}[/tex]

This gives:

[tex]\frac{-7x}{4}=-\frac{7}{4}[/tex]

This is equivalent to:

[tex]x=1[/tex]