(2x+3)(4x-7) , you get a new expression of the form ax^2+bx+c what is value of a , b , and c

we have that

Applying the Pythagorean Theorem

c^2=a^2+b^2

substitute given values

c^2=7^2+24^2

c^2=49+576

c^2=625

The zeros of the polynomial function are x = 0, x = 3 and x = ±√2

The equation of the function is given as

f(x) = x⁴ - 3x³ - 2x² + 6x

Factor out x from the equation of the function

So, we have

f(x) = x(x³ - 3x² - 2x + 6)

Factorize the expression in the bracket

So, we have

f(x) = x(x²(x - 3) - 2(x - 3))

Factor out x - 3

So, we have

f(x) = x(x - 3)(x² - 2)

Set the factors to 0

x(x - 3)(x² - 2) = 0

Expand

x = 0, x = 3 and x² = 2

Take the square roots

x = 0, x = 3 and x = ±√2

Hence, the zeros are 0, 3 and ±√2

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In order to calculate the value of 'a', we can use the Pythagorean theorem, where the hypotenuse squared is equal the sum of each leg squared:

In this case, the hypotenuse is 10 and the legs are 'a' and 7, so we have:

So the value of 'a' is √51.

Matilda arrives home at 18.45 after driving 42 kilometers from her workplace at an average speed of 56 km/h.

The time Matilda uses to drive home from her workplace is a function of the distance she travels and the average speed she goes.

Using the above formula gives us the time in hours/minutes that she took for the home drive.

This derived time is then added to the time she leaves her workplace to get the time she arrives home using the 24-hour clocking system.

The time Matilda leaves her workplace = 18:00

The total distance Matilda travels from work to her home = 42 km

The average driving speed that Matilda traveled with = 56 km/h

Time used for driving home (in hours) = Distance/Speed

= 42/56

= 0.75 hours

= 45 minutes (0.75 x 60)

Arrival Time = 18:45 (18:00 + 45)

Thus, using the 24-hour clocking system, the time Matilda is expected to reach her home is 18:45.

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Answer:

Step-by-step explanation:

I haven't done percentages in a while but the answer after I did it would 15 dollars from where I rounded it. You multiply 15 by 270% which is 2.7 and that's the closest to 40. So Kelly would have 15 dollars.

(Fact check me math people)

Answer:

A 90-degree CCW rotation will take the points to the left. of the rotational point.

As you have provided no picture to show Figure M and its image rotations, this is as far as I can provide an answer.

Hope that helps

Answer:

1/119

Step-by-step explanation:

119 is a whole number which you convert into 119/1 then the reciprical would be 1/119

The estimated population is found to be 48 rabbits

The estimated population, P is determined by using the following formula:

[tex]P=T_{F} *T_{L} /M[/tex]

P=estimated population

[tex]T_{F}[/tex]=total animals captured in first trapping

M=recaptured animals that are marked

[tex]T_{L}[/tex]=total animals captured in a later trapping

From the question, [tex]T_{F}[/tex]=20 rabbits, M=5 rabbits, [tex]T_{L}[/tex]=12

P=20*12/5

P=240/5

P=48 rabbits

Hence, the estimated population is 48 rabbits

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Answer:

y = -2/3(x) - 8

Step-by-step explanation:

y = mx + b

y = -2/3(x) + b

given: (-3, -6) x=-3 y=-6

-6 = -2/3(-3) + b

-6 = 2 + b

b= -8

so..

y = -2/3(x) - 8

Answer:

Step-by-step explanation:

[tex]\displaystyle\\p=10^m;q=10^n;p^n*q^m=100\\\\p^n*q^m=(10^m)^n*(10^n)^m=10^{mn}*10^{nm}=10^{2mn}=100^{mn}=100\\\\\Rightarrow\ mn=1[/tex]

The product of y and 5 is greater than or equal to - 20 is 5y ≥ -20

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, the product of y and 5 is greater than or equal to - 20 will be:

(5 × y) ≥ -20

5y ≥ -20

This is the inequality.

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A portion of a square and a portion of a circle were used to create this figure. The perimeter of the figure is 36.28 units.

Given that,

A portion of a square and a portion of a circle were used to create this figure.

We have to find the perimeter of the figure.

Three linear sides are measured in units of 4, 8, 8, 4.

Radius of the circular part = 4 units

Measure of a polygon's circumference equals the polygon's perimeter.

From the figure we can see,

Figure perimeter equals the sum of the lengths of the three straight lines and the circumference of the quarter circle.

Measure of linear sides = 4 + 8 + 8 + 4 = 24 units

Circumference of the quarter circle = 1/4(2πr)

=1/2×π×4

=2×π

=2×3.14

=6.28 units.

Perimeter of the figure is 30+6.28

=36.28 units.

Therefore, the perimeter of the figure is 36.28 units.

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Rational number

Answer:

It is rational, as it is both non-terminating and repeating.

hope it helps :D

Considering the cost of 3 bell peppers are $2.05, 4 tomatoes are $1.09, 2 onions are $0.65 and 5 potatoes are $0.33, and Giorgio used all these vegetables for his dinner, then his meal costed a total amount of $4.45.

As per the question statement, no information about the vegetables Gorgio used for his dinner or their prices are provided in the question statement, and thus we are considering that, Gorgio used 3 bell peppers that costed $2.05, 4 tomatoes at $1.09, 2 onions at $0.65 and 5 potatoes at $0.33 in his dinner recipe.

We are required to calculate how much does Gorgio's dinner meal cost.

To solve this question, we simply have to add up the prices of the ingredients and we will obtain our desired answer.

That is, Gorgio's  meal costed a total amount of $(2.05 + 1.09 + 0.65 + 0.33)

                                                                             = $4.45

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Answer:

1/4

Step-by-step explanation:

2m/8m = 1/4

Answer:

1/4

Step-by-step explanation:

2m ÷8m

Divide

2m

----

8m

Cancel like terms

2

---

8

Divide the top and bottom by 2

2/2

------

8/2

1

-----

4

Answer: Ren first make a mistake in his work at step 1

Step-by-step explanation:

Step 1 :     2x/3   <   36 Step 2  :     x   <   54Step 3  :  

 A number line going from 51 to 57. An open circle is at 54. Everything to the left of the circle is shadedMistake is in 1st step it self which is cascaded in further stepsCorrect would be 2x/3   > 36  as more than 36 employees stated their preference  hence 2x/3 must be greater than 36

Answer: Its a correct me if i'm wrong

Step-by-step explanation:

Grab your notebook or phone and slide it across the desk you're working on. Now turn it so it's facing sideways. Now flip it over on one of its edges so you're looking at the back side of it. All of these motions are rigid motions.

Any way of moving all the points in the plane such that

a) the relative distance between points stays the same and

b) the relative position of the points stays the same.

There are four types of rigid motions that we will consider: translation , rotation, reflection, and glide reflection.

In a translation, everything is moved by the same amount and in the same direction. Every translation has a direction and a distance. See Image-1.

A rotation fixes one point (the roto center) and everything rotates by the same amount around that point. Every rotation has a roto center and an angle. See Image-2.

A reflection fixes a mirror line in the plane and exchanges points from one side of the line with points on the other side of the mirror at the same distance from the mirror. Every reflection has a mirror line. See Image-3.

A glide reflection is a mirror reflection followed by a translation parallel to the mirror. Every glide reflection has a mirror line and translation distance. See Image-4.

Therefore,

Simply put, rigid motions are transformations that preserve the side lengths and angles in a shape. You can see any of these transformations by moving an object you may have around you right now. Grab your notebook or phone and slide it across the desk you're working on. Now turn it so it's facing sideways. Now flip it over on one of its edges so you're looking at the back side of it. All of these motions are rigid motions.

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The number of miles that Mark ran was 50 miles.

We can get the number of miles that Mark runs by first assigning him the figure x.

Since DeSahwn ran 40. 7 miles less than Mark, we can express this thus:

x - 40. 7 miles.

If the number of miles that DeShawn ran was 9.3 miles we can factor that into the equation as follows:

x - 40. 7 miles = 9.3 miles

x = 9.3 + 40.7

x = 50 miles.

Therefore, the total number of miles that Mark ran was 50 miles.

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Answer:

Determine the Parent Function: y=√x

I verified with a graphing calculator: Demsos. y=x^3 will cross intercepts (x) which is not the parent function and y=1/x is a rational function that is not the parent function that is being asked for.

Answer:

Please see photo for explanation and answer.

The equation of a line into slope-intercept form is represented as:

y = mx + c

where m = slope of the line

c = y-intercept of the line

On simplifying 8x - 20y = 40, the equation will be:

⇒ 2 (4x - 10y) = 2 (20)

⇒ 4x - 10y = 20

⇒ 2x - 5y = 10

⇒ 2x - 10 = 5y

⇒ 5y = 2x + (-10)

⇒ y = 2x/5 + (-10/5)

⇒ y = 2x/5 + (-2)

The slope of this line = 2/5

y-intercept of the line = -2

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Answer:

points

Step-by-step explanation:

dunno gl

Answer:

y = (4/5)x + 16

Point-slope form:

y - 12 = (4/5)(x + 5)

Step-by-step explanation:

slope = m; (-5, 12)

m = (4/5)    (x₁, y₁)

y - y₁ = m(x - x₁)

y - 12 = (4/5)(x - (-5))

y - 12 = (4/5)(x + 5)

y - 12 = (4/5)x + 4

  +12                +12

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

y = (4/5)x + 16

I hope this helps!

The given statement "The different between the upper class limit and lower class limit is called width of the class intervals" is True

Frequency distributions should normally contain 5 to 20 equal-width classes, be continuous, exhaustive, and mutually exclusive.

Clarification of the quoted phrase,

The breadth or size of the class interval in a frequency distribution table is the distance between the upper and lower class limits.

A class interval, for instance, is any of the groups 20–25, 25–30, 30-35, etc. There is a five-point spread between the upper and lower limits. the class width is therefore 5.

As a result, the assertion is true.

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Answer:

First and Third

Step-by-step explanation:

The graphs obey the function equations but the intervals are marked incorrect in #s 2 and 4

One thing to keep in mind is that when you have a piecewise function valid on certain intervals, the circle shape denoting the beginning of the interval is very important

If it is a filled circle it denotes a ≤ (or ≥) inequality

If it is an unfilled (hollow) circle it denotes a < (or >) inequality

Looking at the second graph we see that

f(x) = -1 for -∞ < x < -1
Assuming the interval is correctly defined, that solid circle at x = -1, y = -1 should be a hollow circle not a filled circle

Similarly for f(x) = 3x² + 3, the interval is given as -1 ≤ x < ∞ but the starting circle for this interval is an unfilled circle, it should be a filled circle

A similar situation applies to the fourth choice and you should be able to figure that out yourself

Answer: C

Step-by-step explanation:

answer for the first one is 3.55 pets

second one is 1.4790 pets

i hope this helped! :)

Answer: Alternate interior angles and congruent angles.

Step-by-step explanation: The angles are formed when a line cuts two transversals, and they’re inside the two lines, meaning that they are congruent and alternate interior angles.

(I’ve also attached a helpful image from the web!)