Graph the equation y = − x² + 8 x − 12 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots of the equation − x² + 8 x − 12 = 0

Using the triangle sum theorem:

There are 5 possible combinations for Jacob's lock combination with increasing digits from left to right, and the product of the digits being 84.

Multiplication is a mathematical operation that involves combining two or more quantities to find their total or product. It is often represented by the "x" symbol or the multiplication sign "⋅". Multiplication is a fundamental operation in arithmetic and is used to calculate the total or result of repeated addition or groups of equal quantities.

The product of the digits being 84 implies that the possible combinations of digits are limited to those whose product is 84. The prime factorization of 84 is 2^2 * 3 * 7. Since the digits must be increasing from left to right and cannot repeat, the possible combinations of digits are:

1, 2, 42

1, 3, 28

1, 4, 21

2, 3, 14

2, 6, 7

So, there are 5 possible combinations for Jacob's lock combination.

Therefore, There are 5 possible combinations for Jacob's lock combination with increasing digits from left to right, and the product of the digits being 84.

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Therefore, the volume of the truncated cuboid is approximately 68 + 4*√(30) cubic meters.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is the amount of three-dimensional space enclosed by the boundaries of an object. Volume is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).

Here,

The truncated cuboid is a solid figure that is obtained by cutting off the top of a rectangular prism (cuboid) with a plane that is parallel to the base. The formula for the volume of a truncated cuboid is:

V = h/3 * (A + √(A*B) + B)

where V is the volume, h is the height of the truncated portion, A is the area of the top face, and B is the area of the base face.

In this case, the height of the truncated portion is 3 m, the top face has an area of 5 m x 8 m = 40 m², and the base face has an area of 8 m x 1.5 m = 12 m². Therefore:

A + B = 40 + 12 = 52 m²

√(AB) = √(4012) = √(480) = 4*√(30)

Substituting these values into the formula, we get:

V = 3/3 * (52 + 4√(30) + 12)

V = 68 + 4√(30)

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Answer:

1 hour and 15 min

Step-by-step explanation:

I think this is right but look it up just to be sure

Step-by-step explanation:48miles in 60 min. 1/4 of 60 is 1so 60 +15 = 1hr 15 min.

The transformation from the graph of f(x) = x to the graph of g(x) = (1/9)·x -2, is a rotation and a translation. The correct option is therefore;

The transformation are a rotation and a translation

A translation transformation is a transformation in which there is a displacement of all points on the preimage figure in a specified direction.

The transformation from f(x) = x to f(x) = (1/9)·x - 2, includes a slope reduction by a factor of (1/9), or rotating the graph of f(x) = x in the clockwise direction, and a translation of 2 units downwards, such that the y-intercept changes from 0 in the parent function, f(x) = x to -2 in the specified function f(x) = (1/9)·x - 2, therefore, the translation includes a rotation clockwise and a translation downwards by two units

The correct option is the second option; The transformation are a rotation and a translation

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The answer is

To solve this problem, we must find the numbers of the linear regression (y = ao + a1*x). They can be found resolving the following equation system:

When you have solved this system, you will get that ao = 3.7488 and a1 = 0.143

Afterward, we must find the error:

Then, we find the value of St:

Finally, the correlation coefficient is equal to:

Therefore, the correlation coefficient is 0.596.

This means that 5% of the 10-1/2-month-old baby boys in the reference population weigh 16.7 pounds or less, and 95% of these baby boys weigh 16.7 pounds or more.

The determination is based on the definition of a percentile. A percentile is a value below which a certain percentage of the data falls. So, in this case, if a weight of 16.7 pounds is at the 5th percentile for 10-1/2-month-old baby boys, then 5% of the baby boys in the reference population have a weight of 16.7 pounds or less. This also means that the remaining 95% of the baby boys in the reference population have a weight of more than 16.7 pounds.

The calculation of percentiles is based on the ranking of the data set. The data is first sorted in ascending order and then divided into 100 equal parts, with each part representing a percentile. The value at each percentile is the value below which a certain percentage of the data falls.

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Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

The answer is NO

Reason

x= 2 y= 1

Now input in the first inequality

y≤ -x + 4

1 ≤ -2 +4

1≤ 2 i.e 1 is less than two

Next inequality

y≤ x +1

1 ≤ 2 + 1

1≤ 3 i.e 1 is less than 3

But 1 is not equal to 3 and also not equal to 2

Hence our answer is NO

Answer:

Coordinates of point C after dilation with a scale factor of 5, centered at the origin will be: C'(10, 5)

Step-by-step explanation:

Given the point C

A dilation with a scale factor of 5 means the size of the coordinates of the image of point P will be 5 times larger than than the original coordinates of point C.

Thus, the rule of dilation by a scale factor 5 is:

(x, y)  →  (5x, 5y)

C(2, 1)  →  (5x, 5y) = (5(2), 5(1)) = C'(10, 5)

Therefore, coordinates of the point C after dilation with a scale factor of 5, centered at the origin will be: C'(10, 5)

Answer:

.

Step-by-step explanation:

Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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Answer:

90

Step-by-step explanation:

for percentage

\(\frac{54}{60}\)×100

= 0.9×100

=90

Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

\(x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}\)

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

\(x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72\)

Answer:

A) 0.25/0.6      B) 40:96    E) 1/3 / 0.8

Step-by-step explanation:

A)

0.25/0.6  = 1/4÷3/5

=5/12

B)

40:96 = 5:12               You can divide 40 and 96 both by 8 to get 5:12

=5/12

E)

1/3 / 0.8 = 1/3 ÷ 4/5

=5/12

Hope this helps :)

The possible value of the third length is an illustration of Triangle inequality theorem

The possible third lengths are 4 units and 6 units

To determine the third length, we make use of the following Triangle inequality theorem.

a + b > c

Let the third side be x.

So, we have:

x + 6 > 3

x + 3 > 6

3 + 6 > x

Solve the inequalities

x > -3

x > 3

x < 9

Remove the negative inequality value.

So, we have:

x > 3 or x < 9

Rewrite as:

3 < x or x < 9

Combine the inequality

3 < x < 9

This means that the possible value of the third length is between 3 and 9 (exclusive)

Hence, the possible third lengths are 4 units and 6 units

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Answer:

Step-by-step explanation:

Three-fourths of the difference of a number and 7 is negative fifteen:

The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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The mortality rate will be 180 per 100000 people.

From the information, 595,700 Americans died of (all forms of) cancer and there is a population of 321 million.

Therefore the mortality rate will be:

= 595700 / 321 million

= 0.0018

Therefore the mortality rate will be 180 per 100000 people.

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Answer:

see below

Step-by-step explanation:

50-3x=8

The first step is subtract 50 from each side

50-50-3x=8-50

-3x = -42

Then divide each side by -3

-3x/-3 = -42/-3

x = 14

Answer:

Because -3x is remain after eliminate 50 on both sides.

Step-by-step explanation:

I. Solve 50 - 3x = 8

            50 - 3x = 8

   -50  +50 - 3x = 8 - 50 => {when 50 is +50}

                  -3x = -42 => {when -50 + 50 = 0 and -3x = -3x}

                      x = (-42)/(-3)

                      x = 14

Hope that help :)

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

ajjvtjeiqwchiedgvgfeggyryftyyyug ytugttbghg

The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.

The expected value for the amount of money made selling all of the candy in one bag can be found by;

Expected value = mean number of candy bars per bag x price per candy bar

Expected value = 12 x $1.25 = $15

Formula for the standard deviation of a product of random variables:

\(SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}\)

where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.

X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:

E(Y²) = $1.25² = $1.5625

E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148

Cov (X,Y) = 0 (because X and Y are independent)

Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:

\(SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))\)

SD = √(592)

SD ≈ $24.33

Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

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The sides of the right triangle are:

a) AC

b) CB

c)  AB

We have the diagram of a right triangle, and we want to identify the side that is opposite to angle B.

That would be the side that does not intercept the vertex B, so it is AC.

Then we want to get the adjacent side to B that is not the hypotenuse.

That would be the side that intercepts vertex B and intercepts the vertex with the small red square, it is CB.

Finally, the vertex is the side opposite to the small red square (90° angle) so it is AB.

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Answer:

x = 50

Step-by-step explanation:

2485 ÷ x = 49 R 35

We know that 2485 ÷ x = 49 R 35, or 2485 ÷ x = 49 + 35

Step 1:

Now, I want to subtract 35 from the left side of the equation:

Step 2:

Now I want to find x. We can start by multiplying both sides by x, then dividing by the coefficient.

x = 50

Check:

-Chetan K

f(x) is discontinuous.

Since LHS ≠ RHS ≠ f(x).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

here, we have,

We have,

f(x) = x + 1, for x ≤ 2

f(x) = 2x - 1, for 1 < x < 2

f(x) = x - 1, for x < 1

Now,

A x = 1

LHS of f(x) = lim f((h - 1)) =  (h - 1 - 1) = 0 -2 = -2

RHS of f(x) = lim  f(h + 1) =  (2(h + 1) - 1) = 2h + 2 - 1 = 0 + 1

f(1) = x + 1 = 1 + 1 = 2

We see that,

LHS ≠ RHS ≠ f(x)

So,

f(x) is not continuous, it is discontinuous.

Thus,

f(x) is discontinuous.

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The complete question.

Show that the following functions are continuous or discontinuous at x = 1.

f(x) = x + 1, for x ≤ 2

f(x) = 2x - 1, for 1 < x < 2

f(x) = x - 1, for x < 1

Answer:

this is my answer but it's on you if you think this answer is correct or wrong

Answer:

oi['po

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lk/

Step-by-step explanation:

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