The Substitution Property of Equality states that if m<2+m<3=m<5 and m<2=25, then _____ ____ m<5​

Answer:

Step-by-step explanation:

The product of roots will be the opposite of the constant in an odd-degree polynomial. The actual zero crossings multiply to give +45, not the -45 that Cade's answer gives.

The numbers Cade lists are the constants in the binomial factors, not the roots of the polynomial. The polynomial's roots are opposite Cade's numbers: 3, -3, -5.

_____

Another way you can tell Cade's answer is wrong is that the sequence of signs of the polynomial coefficients is ++--, so there is one sign change. Descartes' rule of signs tells you that means there is exactly one positive real root. Cade lists two: 3, and 5.

Let's start by using the given roots to write the polynomial in its factored form.
The roots given are x = -3, x = 3, and x = 5. If these are in fact the roots of the polynomial, the polynomial can be written as a product of factors that have these values as solutions. Therefore, the factored form of the polynomial y = x^3 + 5x^2 - 9x - 45 using the roots would be:
y = (x - (-3)) * (x - 3) * (x - 5)
This simplifies to:
y = (x + 3) * (x - 3) * (x - 5)
Now let's expand this factored form to see if we get the original polynomial:
First, let's multiply (x + 3) and (x - 3), which are a difference of squares:
y = (x^2 - 3^2) * (x - 5)
y = (x^2 - 9) * (x - 5)
Now let's distribute (x - 5) into (x^2 - 9):
y = x^3 - 5x^2 - 9x + 45
Comparing this expanded form to the original polynomial y = x^3 + 5x^2 - 9x - 45, we see there's a discrepancy:
The expanded form:    y = x^3 - 5x^2 - 9x + 45
The original form:    y = x^3 + 5x^2 - 9x - 45
As we can observe, the signs of the x^2 term and the constant term are opposite in the expanded form compared to the original polynomial. Therefore, the roots -3, 3, and 5 do not correspond to the polynomial x^3 + 5x^2 - 9x - 45, and the factored form with these roots is incorrect.
To summarize, the factored form of the polynomial y = x^3 + 5x^2 - 9x - 45 given the roots -3, 3, and 5 would be (x + 3) * (x - 3) * (x - 5), but this factored form is incorrect because it does not expand to the original polynomial. Cade's statement about the polynomial crossing the x-axis at -3, 3, and 5 is incorrect.

Answer:

The slope is 3

Step-by-step explanation:

The formula for finding slope is change in y over change in x. Also known as rise over run. Go up 3 and go right 1 to get from one point to the next.

Answer:

=3

Step-by-step explanation:

Lets consider any 2 points on the line such as (0,2)  and  (1,5).

The slope of a line = Δy/Δx

Δy = y₂-y₁

Δx = x₂-x₁

y₁=2

y₂=5

x₁=0

x₂= 1

we can now use these values from the two points on the line.

Gradient= (5-2)/(1-0)

=3

orthogonal = perpendicular.

an altitude in a triangle is the perpendicular distance stemming from a vertex.

where all these orthogonal segments meet is the ORTHOcenter.

The described point M is a Orthocenter.

"The orthocenter is the point where all the three altitudes of the triangle cut or intersect each other. Here, the altitude is the line drawn from the vertex of the triangle and is perpendicular to the opposite side. Since the triangle has three vertices and three sides, therefore there are three altitudes."

"The orthocenter will vary for different types of triangles such as Isosceles, Equilateral, Scalene, right-angled, etc. In the case of an equilateral triangle, the centroid will be the orthocenter. But in the case of other triangles, the position will be different. Orthocenter doesn’t need to lie inside the triangle only, in case of an obtuse triangle, it lies outside of the triangle."

In this figure, the altitudes of triangle JKL is given.

Since, these are altitudes they interest each other at orthocenter.

Hence, A is the correct answer.

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Answer:

The answer is c

Step-by-step explanation:

When the lava cools and hardens it becomes igneous rock.

Answer:

The correct answer is A., "The molten mixture of rock-forming substances, gases, and water from the mantle.."

Answer:

The point is (3 , 6)

Step-by-step explanation:

* Lets explain how to solve this problem

- We want to reflect the point (x , y) across the line y = a, where a

 any constant

- The line y = a is a horizontal line, means parallel to x-axis

- We will change the y-coordinates only because we will move

 up and down

- We will move the point and the line by a units down if a is positive

 or up if a is negative to make the line is the x-axis and also move the

 point by a units as the line

- Then we will reflect the new point across the x-axis means we will

  change the sign of y-coordinate

- After that we will add the value of a again to the y-coordinate to

 the point after reflection

* Lets solve the problem

∵ The point is (3 , 4)

∵ The point will reflect across the line y = 5

- We take the line 5 units down to be the x-axis and also we will take

 the point down 5 units

∴ The point = (3 , 4 - 5) = (3 , -1)

- Now reflect the point across the x-axis by change the sign of the

 y-coordinate

∴ The new point is (3 , 1)

- Now add the y-coordinate of the new point the 5 units which we

 subtracted before

∴ The image of the point P after reflection across the line y = 5 is

  (3 , 1 + 5) = (3 , 6)

* The point is (3 , 6)

Answer:

2030

Step-by-step explanation:

the graph starts to decline 16 years after 2014 so 2014 + 16 = 2030

Answer:

4/5 frames/h

Step-by-step explanation:

Find the ratio frames per hour by dividing frames by hours:

(4 frames)/(5 hours) = (4/5) frames/hour

The question is about calculating a painting rate. Joyce paints 0.8 window frames per hour. This is calculated by dividing the total number of frames by the total number of hours.

The subject of this question is Mathematics as it deals with calculating rates. This can be determined by finding a ratio of the total number of window frames painted, which was four, and the total time taken, which was 5 hours.

We can calculate Joyce's painting rate by dividing the total number of frames she painted by the total number of hours she worked. Which is 4 frames ÷ 5 hours = 0.8 frames/hour. This means that Joyce paints 0.8 window frames per hour.

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Answer:

[tex]110x+29y=333[/tex]

Step-by-step explanation:

Will's meal of grilled chicken strips and carrots contained a total of 333 calories.

The bag of grilled chicken strips contained x servings of 110 calories each, making total 110x.

The bag of carrots contained y servings of 29 calories each making total 29y.

So, the equation that represents the number of servings of chicken strips and carrots that Will may have eaten

[tex]110x+29y=333[/tex]

Answer:

5 = 2x + 1

Step-by-step explanation:

let James be x , then 1 mile more than twice number of mile of James will be 2x + 1 therefore the total number of miles biked by carolina will be 2x + 1 = 5

The equation 5 = 1 + 2x represents the number of miles Jack biked, option fourth is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the number of miles James biked.

Then, according to the problem:

Carolina biked 1 mile, more than twice the number of miles James biked.

5 =  1 + 2x  (as the Carolina biked a total of 5 miles)

Thus, the equation 5 = 1 + 2x represents the number of miles Jack biked option fourth is correct.

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Answer:

is this multiplication?

if so, 4.33

Step-by-step explanation:

just use division:

15.57/3.6=4.325 or rounded to two decimal places 4.33

Answer:

26. [tex]\frac{3}{4} \leq x <7[/tex]

27. [tex]x\leq 5[/tex]

28. [tex]0\leq b<4[/tex]

Step-by-step explanation:

26. [tex]\sqrt{4x-3} <5[/tex]:

Taking square on both the sides to get:

[tex](\sqrt{4x-3} )^2 < (5)^2[/tex]

[tex]4x-3<25[/tex]

[tex]4x<28[/tex]

[tex]x<\frac{28}{4}[/tex]

[tex]x<7[/tex]

For non-negative values for radical:

[tex]4x-3\geq 0[/tex]

[tex]x\geq \frac{3}{4}[/tex]

So solution for this: [tex]\frac{3}{4} \leq x <7[/tex]

27. [tex]2+\sqrt{4x-4}\leq  6[/tex]

Subtracting 2 from both the sides to get:

[tex]2+\sqrt{4x-4}-2\leq  6-2[/tex]

[tex]\sqrt{4x-4}\leq 4[/tex]

Taking square root on both sides:

[tex](\sqrt{4x-4})^2\leq (4)^2[/tex]

[tex]4x-4\leq 16[/tex]

[tex]x\leq \frac{20}{4}[/tex]

[tex]x\leq 5[/tex]

28. [tex]\sqrt{b+12} -\sqrt{b}>2[/tex]

Adding [tex]\sqrt{b}[/tex] to both the sides to get:

[tex]\sqrt{b+12} -\sqrt{b}+\sqrt{b}>2+\sqrt{b}[/tex]

[tex]\sqrt{b+12} >2+\sqrt{b}[/tex]

Taking square on both sides:

[tex](\sqrt{b+12})^2 >(2+\sqrt{b})^2[/tex]

[tex]b+12>(2+\sqrt{b})^2[/tex]

[tex]b+12>4+4\sqrt{b}+b[/tex]

[tex]4+4\sqrt{b} +b<b+12[/tex]

Subtracting [tex]b[/tex] from both sides to get:

[tex]4+4\sqrt{b} +b-b<b+12-b[/tex]

[tex]4+4\sqrt{b} <12[/tex]

Subtracting 4 from both sides:

[tex]4+4\sqrt{b}-4 <12-4[/tex]

[tex]4\sqrt{b} <8[/tex]

Square both sides again:

[tex](4\sqrt{b})^2 <(8)^2[/tex]

[tex]16b<8^2[/tex]

[tex]b<\frac{64}{16}[/tex]

[tex]b<4[/tex]

and for non-negative radical [tex]b\geq 0[/tex]

therefore, solution is [tex]0\leq b<4[/tex].

Answer:

Anita cleans 1/8 of the pool each hour and Chao cleans 1/5 of the pool each hour.

[tex]\frac{x}{8}[/tex] + [tex]\frac{x}{6}[/tex] = [tex]\frac{7}{24}[/tex]

then you take [tex]\frac{1}{(7/4}[/tex] = [tex]\frac{27}{7}[/tex]

your answer will be

Step-by-step explanation:

Answer:

[tex]t =\frac{24}{7}\ hours[/tex]

Step-by-step explanation:

For these types of problems use the following formula.

[tex]\frac{t}{x}+\frac{t}{z} =1[/tex]

Where t is the time it takes them both to clean the entire pool if they work together.

x is the time it takes Anita to clean the pool

z is the time it takes Chao to clean the pool

So:

[tex]\frac{t}{8}+\frac{t}{6} =1[/tex]

Now solve the equation for t

[tex]\frac{7}{24}t =1[/tex]

[tex]t =\frac{24}{7}\ hours[/tex]

Answer:

  3 1/3 ft²/h

Step-by-step explanation:

To find the unit rate, divide square feet by hours:

(5/6 ft²)/(1/4 h) = (5/6)(4/1) ft²/h = 10/3 ft²/h = 3 1/3 ft²/h

Discrete random variables are countable values obtained by counting. Hence the correct options are 2 and 3.

The situations that can be modeled by a discrete random variable from the options provided are:

The number of text messages sent in a month.

The number of students earning a 100 percent on a test.

Sounds like your describing complementary angles (a pair of angles that add up to be 90 degrees) but not super sure based on that description you have there.

Tell me does it look like this:

The adjacent angles' relationship describes angles 1 and 2, angle 1 and angle 2 are adjacent angles option fourth is correct.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have a statement about the angle 1 and angle 2:

A line goes left to right with a ray in the middle creating a right angle and another ray between the right angle, with one labeling the left angle and two labelings the right angle.

We can draw as shown in the picture.

As we can see in the figure, angles 1 and angle 2 are adjacent angles because they have a common vertex.

Angle 2 = 90 degree

Angle 1 = 45 degree

Thus, the adjacent angles' relationship describes angles 1 and 2, angle 1 and angle 2 are adjacent angles option fourth is correct.

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Answer:

  80 in.

Step-by-step explanation:

The dimensions of the dilated picture are ...

  4·4 in = 16 in . . . by . . . 4·6 in = 24 in

Then the perimeter of the painting is the sum of the lengths of its sides ...

  16 in + 24 in + 16 in + 24 in = 80 in

Answer:

80in

Step-by-step explanation:

The scale factor of the dilation is 4, so a 1 inch by 1 inch square on the photograph represents a 4 inch by 4

inch square on the painting.

The height of the image is the product of the height of the preimage and the scale factor.

w=4(6)=24

in

.

The width of the image is the product of the width of the preimage and the scale factor.

h=4(4)=16

in

.

So, the perimeter is

P=2(16)+2(24)=80

in

.

The figure shows two rectangles. The larger rectangle is 16 inches long and 24 inches wide. The smaller rectangle is 4 inches long and 6 inches wide. The sides of the larger rectangle are parallel to the corresponding sides of the smaller one, respectively.

Therefore, the perimeter of the painting is 80

inches.

Explanation:

Use the minimum value of the sine function in place of the sine function in the expression. Evaluate the resulting expression.

  min(g(x)) = 2 min(sin( )) +4 = 2(-1) +4 = 2

The minimum value of g(x) is 2.

Answer:

100°

Step-by-step explanation:

The bottom left and top left angle in a parallelogram are adjacent angles.

From the properties of parallelogram, we know adjacent angles are supplementary, this means they "add up to 180°"

Thus, if one angle is 80, the other angles would be 100 (to make it total 180).

So, top left corner angle measures 100°

Answer:

x=100

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This hyperbola is a horizontal hyperbola of the standard form:

[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]

Since our equation is

[tex]\frac{(x+1)^2}{16}-\frac{(y+5)^2}{9}=1[/tex],

a = 4 and b = 3.

The coordinates for the vertices are (±a, 0) and

the coordinates for the foci are (±c, 0).

We have a, but we need c.  To find c, we use Pythagorean's Theorem:

[tex]c^2=4^2+3^2[/tex] or

[tex]c^2=16+9[/tex] giving us that

c = 5.

But these a and c values have to be figured from the center of the hyperbola which is located at (-1, -5).  

For the vertices, then, we add the a value of 4 and -4 to the x value of the center, which is -1.  The -5 remains, since the vertices and the foci are on the same transcersal axis which is the line y = -5.

For the foci, then, we add the c value of 5 to -1, and again the -5 remains in the y position.

Vertices: (-1+4, -5)-->(3, -5) and (-1-4, -5)-->(-5, -5)

Foci: (-1+5, -5)-->(4, -5) and (-1-5, -5)-->(-6, -5)

Choice C

Answer:

All real numbers

Step-by-step explanation:

The domain of this is all real numbers.  The x values will never keep going down (to negative infinity) and will also never stop growing (to positive infinity).

The domain of a function consists of all possible input values. For a student's major (X), it includes all university majors, for the number of classes taken (Y), it's non-negative integers up to a maximum number, and for the amount spent on books (Z), it's any non-negative real number. X, Y, and Z are random variables as they are determined after an experiment like a survey.

The domain of a function refers to the set of all possible input values that the function can accept. For the cases given:

X, Y, and Z are considered random variables because their values are determined by the outcome of some experiment or random process, like a survey or an academic semester, and are only known once that process is complete. If Z were to equal -7, that would not be a possible value because you cannot spend a negative amount on books; hence, Z must always be non-negative.

Two essential characteristics of a discrete probability distribution include a finite or countably infinite set of values, and the sum of probabilities of all possible values must equal 1.

Considering a geometric experiment, such as drawing cards from a 52-card deck until a specific card is drawn:

Answer:

200 CDs

Step-by-step explanation:

80 is 40% of 200

40% - 80

100% - x

[tex]x=\dfrac{100\%\cdot80}{40\%}=200[/tex]

200 CDs

Answer:

this is your answer below i used a graphing calculator

Step-by-step explanation:

Answer:

It is 27.35 ft up the house

Step-by-step explanation:

The hypotenuse of the right triangle is 28  and the base is 6

We can use the pythagorean theorem to find how high it is

a^2 + b^2 = c^2

6^2 + b^2 = 28^2

36 + b^2 = 784

Subtract 36 from each side

36-36 + b^2 = 784-36

b^2 = 748

Take the square root of each side

b =sqrt(748)

b =27.34958866

It is 27.35 ft up the house

Answer:

Step-by-step explanation:

If you want to compare the 2 slopes, you first have to know what they are.  From the table we can find it by plugging in some numbers to the slope formula and doing the math on it:

[tex]m=\frac{-10-(-15)}{0-(-1)}[/tex]

which gives us a slope of 5.

From the equation, which is in y = mx + b form, m stands for slope.  The number in the m position is 2.  In a sentence:

The slope found in the values from the table, 5, is greater than the slope found in the linear equation, 2.

Part B:  The y-intercept exists where x = 0.  Looking at the values in the table, where x = 0, y = -10.  So the y-intercept of the line in the table is -10.  In y = mx + b, the linear equation, 8 = b, which is also the y-intercept.  So the y-intercept in the table is -10 and the y-intercept in the equation is 8.  The y-intercept is greater in the equation than in the table because 8 is greater than -10

Answer:

i need it too

Step-by-step explanation:

Answer:

It's 3.

Step-by-step explanation:

A line that rises from left to right has a positive slope.

1. confuses me a little because we would say a horizontal line has zero slope - but I guess that's not the same as 'no slope'.

A line that rises from left to right has a positive slope. The correct option is option 3.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

If the right side of the line is higher or has a higher vertical value than the left side of the line, the slope is said to be positive.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

y = mx + c

Here, m is the slope of the line. The slope of the line is the ratio of the rise to the run.

Therefore, a line that rises from left to right has a positive slope. The correct option is 3.

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Answer:

x = 1 and y = -4

Step-by-step explanation:

It is given that,

-2x = 2 + y

-2x - y = 2 ---(1)

-6x - y = -2   ----(2)

To find the solution of equations

Step 1: Subtract eq(2) from eq(1)

-2x - y = 2 ---(1)

-6x - y = -2  ----(2)

4x + 0 = 4

x = 4/4 = 1

Step 2: Substitute the value of x in eq (1)

-2x - y = 2 ---(1)

-2*1 - y = 2

-2 - y = 2

y = -2 - 2 = -4

Therefore x = 1 and y = -4

Answer:

The smaller the sample of people Percy observes, the easier it is to not match the percentage given in the table.

Answer:The smaller the sample of people Percy observes, the easier it is to not match the percentage given in the table.

Step-by-step explanation:

The smaller the sample of people Percy observes, the easier it is to not match the percentage given in the table.

Answer:

  diameter = m - c

Step-by-step explanation:

In ΔABC, let ∠C be the right angle. The length of the tangents from point C to the inscribed circle are "r", the radius. Then the lengths of tangents from point A are (b-r), and those from point B have length (a-r).

The sum of the lengths of the tangents from points A and B on side "c" is ...

  (b-r) +(a-r) = c

  (a+b) -2r = c

Now, the problem statement defines the sum of side lengths as ...

  a+b = m

and, of course, the diameter (d) is 2r, so we can rewrite the above equation as ...

  m -d = c

  m - c = d . . . . add d-c

The diameter of the inscribed circle is the difference between the sum of leg lengths and the hypotenuse.

Answer:

Step-by-step explanation:

I like to use a graphing calculator for finding the zeros of higher order polynomials. The attachment shows them to be at x = -3, -1, +2.

__

The zeros can also be found by trial and error, trying the choices offered by the rational root theorem: ±1, ±2, ±3, ±6. It is easiest to try ±1. Doing so shows that -1 is a root, and the residual quadratic is ...

  x² +x -6

which factors as (x -2)(x +3), so telling you the remaining roots are -3 and +2.

___

For any odd-degree polynomial with a positive leading coefficient, the sign of the function will match the sign of x when the magnitude of x gets large. Thus as x approaches negative infinity, so does f(x).