Create a trinomial that can be factored and write it in standard form.

Answers

Answer 1

Final answer:

To create a trinomial, use a basic factored form like (x+a)(x+b), and expand this via the distributive property. This yields as an example x²+8x+15, a trinomial in standard form.

Explanation:

To create a trinomial that can be factored and to write it in standard form, we need to consider a basic factored form first. Let's use (x+a)(x+b) as our basic factored form. In this form, 'a' and 'b' are the roots of the trinomial.

To create the trinomial, we then expand this expression by using the distributive property: (x+a)(x+b) = x² + bx + ax + ab, which simplifies to x² + (a+b)x + ab. This is now our trinomial in standard form.

Let's take a concrete example. If we let 'a' be 3 and 'b' be 5, our factored form is (x+3)(x+5). Expanding this, we get x² + 5x + 3x + 15, which simplifies to x² + 8x + 15. Thus, x² + 8x + 15 is a trinomial that can be factored and is written in standard form.

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Related Questions

Find the length of LK

Answers

Since JN = NK, this means that JK has been split into two equal pieces

This points to the fact that the smaller triangle is half of the larger triangle in terms of side lengths

MN = 14 which means LK is twice as long, so LK = 2*MN = 2*14 = 28

In summary,

LK = 28

Brand X soda advertises, "We will give you 20% more soda than Brand Y for a total price that is 10% less than Brand Y's price!" What is the ratio of the unit price of Brand X soda to the unit price of Brand Y soda? Express your answer as a common fraction. ...?

Answers

Let the amount of Brand Y = 1 kg.
Thus the amount of Brand X = (1 kg)(1.20) = 1.20 kg

Let the price of Brand Y = $1.
Thus the price of Brand X = ($1)(0.90) = $0.90.

Hence, the unit price of Brand X is $0.90 / 1.20 kg = $3/4 /kg and the unit
price of Brand Y is $1.00 / 1.00 kg = $1 /kg.

Therefore, the ratio of the unit prices is 3/4.

Answer:

3/4

Step-by-step explanation:

its 3/4 k

Identify the correct slope and y intercept of the equation 2x + 4y = 12.
How would I do this?

slope = 2; y intercept at (0, 12)

slope = 1/2; y intercept at (0, 3)

slope = 1/2; y intercept at (0, 4)

slope = -1/2; y intercept at (0, 3) ...?

Answers

The standard form of a line is an easy way to solve for the properties of a line, such as slope and the intercepts. Take a line with the equation in standard form,

Ax + By = C

The slope here is given by y = -A/B.
The x-intercept here is given by (C/A, 0).
The y-intercept here is given by (0, C/B).

For this problem, the equation is 2x + 4y = 12. Thus,
slope = -2/4 = -1/2
y-intercept = (0, 12/4) = (0, 3)

What is two thousand eight hundred thirty five divided by twenty one?

Answers

In mathematical form, it will be: 2835/21 = 135
So, your answer is 135

Each week, Diana spends 4 hours playing soccer and 6 hours babysitting. Which ratio is equivalent to the ratio of the time Diana spends playing soccer to the time she spends babysitting?

Answers

The ratio is whatever is said first if that makes sense, so what was said first is that Diana spends 4 hours playing soccer to Diana spending 6 hours babysitting. That would be 4/6 (four over six). To find what is equivalent you need to simplify that which would give you 2/3 (two over three)

Let me know if you need more help!

Can you simplify 1/18

Answers

no, 1/18 is the simplest form. :)

is it true or false that many of the same constructions the greeks performed only with a straightedge and compass can be done using only a straightedge and tracing paper?

Answers

True Many of the same constructions the Greeks performed only with straightedge and compass can be done using only a straightedge and tracing paper

Answer: true.

Step-by-step explanation: Here we must see if the use of a compass can be replaced with the use of a tracing paper.

Now, suppose you have a sheet of paper in your table, you can apply pressure in it with your finger at some point, now you can drill a little hole with the point of a pencil at some distance of your finger. Now, with the pencil in place, you can start to rotate it and you will see that an almost perfect circle will appear.

So yes, you can do this, so it's true.

I need help photo attached

Answers

We know that the ratio is 3:5
We need to know:
3 9
--- = ---
5 ?
Multiply means and extremes.
3x = 9*5
3x = 45
Divide and solve:
x = 45/3
x = 15

find the derivative:
y=(4xe^x)/(x^2+1)

Answers

The derivative is:
y= 4(x³−x²+x+1)e×/(x²+1)²

Find the solution set for the open sentence with the given replacement set.
2x + 7 = 19, {4, 5, 6, 7}

Answers

x=6 your welcome:) :)

the answer to the following equation is 6. When 2 is multiplied by 6 the product is 12. 12 added to 7 equals 19.

Which of the following is equivalent to45/46 ?

88/92
135/138
46/45
90/93

Answers

If you'll multiply it by 3, as follows:
45/46 = 135/138 which is equal to Option B.

So, option B is your answer!

Hope this helps!

it would be 135/138

hope this helps you

A wooden fence 6 ft. high and 300 ft. long is to be painted on one side. How many gallons of paint are needed if one gallon covers 400 sq. ft.?

Answers

First, you should calculate the square footage of the fence.6ft∗300ft=1800ft2 Then to find the number of gallons of paint needed, divide the area of the fence by the area covered with each gallon of paint: 1800ft2÷400ft2=4.5 So, 4.5 gallons of paint, or rounding up, 5.

Answer:

4.5 gallons

Step-by-step explanation:

Explane how you can tell 4 is a factor of 30

Answers

That is very difficult, since 4 is not a factor of 30. The prime factorization of 30 is 2*3*5. There is no combination of these numbers that results in 4, so it is not a factor of 30.

Just count. 4 8 12 16 20 24 28 32 oop we past 30 so 4 is not a factor of 30.

Which of the point-slope equations below is correct for the line that passes through points (-4,-4) and (1,3)? Check all that apply.

A. y - 3 = 7/5(x - 1)
B. y - (-4) = 7/5(x - (-4))
C. y - 3 = 7/5(x + 1)
D. y + 4 = 7/5(x - 4)
E. y + 4 = 7/5(x + 4)
F. y + 4 = 5/7(x + 4)

Answers

Correct answer is E.

[tex](-4,-4) \Rightarrow x_1=-4,y_1=-4 \\ (1,3) \Rightarrow x_2=1,y_2=3 \\ \\y-y_1= \frac{y_2-y_1}{x_2-x_1} (x-x_1) \\ \\ y-(-4)= \frac{3-(-4)}{1-(-4)} (x-(-4)) \\ \\ y+4= \frac{3+4}{1+4} (x+4) \\ \\y+4= \frac{7}{5}(x+4) [/tex]

The table shows the amounts of food collected by two homerooms. Homeroom A collects 21 additional items of food. How many more items does Homeroom B need to collect to have more items per student Homeroom A Homeroom B

Students 24 16
Canned Food 30 22
Dry Food 42 24

Answers

The number of food items Homeroom B needs to collect to have more food items per student than Homeroom A is 16

How many more items does Homeroom B need to collect to have more items per student?

Food items collected by homeroom A:

Canned food = 30

Dry food = 42

Additional food items = 21

Number of students = 24

Food items per students = (30 + 42 + 21) / 24

= 93/24

Food items collected by homeroom B:

Canned food = 22

Dry food = 24

Additional food items = x

Number of students = 16

Food items per students = (22 + 24 + x) / 16

= (46 + x) / 16

Number of more food items Homeroom B need to collect to have more items per student than Homeroom A:

(46 + x) / 16 > 93/24

cross product

(46 + x) × 24 > 16 × 93

1,104 + 24x > 1,488

24x > 1,488 - 1,104

24x > 384

Divide both sides by 24

x > 384/24

x > 16

Hence, homeroom B should collect more than 16 food item to have a greater item per student

Answers

jesse ran 42,240 feet

Ethan's club spent $81 for 9 caps for its members each cap cost the same amount how much did each cap cost

Answers

9 DOLLARS MARK ME AS THE BRAINLIEST PLZ

cost/number of caps=81/9=27/3=9/1
$9 per 1 cap

Find the values of x and y that maximize the objective function P=3x+2y for the graph. What is the maximum value? Show all work.

Answers

Since coeficient in front of x is larger than coeficient in front of y that means that value of function P depends more on x than on y. That means that we should look for highest posible x and see highest posible y for that x.

Highest x value is 9 and we can only pick y=0 for it

P = 27

Note that if u decrease x by 1 we can take y=1 but now our value is:
P = 8*3 + 2*1 = 26 which is just confirmation why P depends more on x than on y due to coefficient in front of x.

Answer:

Step-by-step explanation:

Highest x value is 9 and we can only pick y=0 for it

P = 27

Note that if u decrease x by 1 we can take y=1 but now our value is:

P = 8*3 + 2*1 = 26 which is just confirmation why P depends more on x than on y due to coefficient in front of x.

And or

Answer:

Step-by-step explanation:

To find the maximum, input the vertices (0,8), (5,4) and (9,0) into the objective function (P = 3x + 2y) to determine which vertex obtains the maximum value.

NOTE: I don't understand why (5,4) was given on your graph as a vertex.

(0,8): P = 3(0) + 2(8) = 0 + 16 = 16

(5,4): P = 3(5) + 2(4) = 15 + 8 = 23

(9,0): P = 3(9) + 2(0) = 27 + 0 = 27 THIS IS THE LARGEST (MAX) P-VALUE

Suppose that any given year, the value of a certain investment is increased by 15%. If the value is now $15,000, in how many years will the value be $21,000?
...?

Answers

The answer is 2.5 years.

The compound interest formula is:
A = P(1 + r/n)ⁿˣ
A - the final value
P - the initial value
r - the interest rate
n - the number of times interest is compounded by year
t - the numbers of years of investment

We have:
A = $21,000
P = $15,000
r = 15% = 15/100 = 0.15
n = 1 (since this is per year)
t = ?

So:
[tex]21000 = 15000(1 + 0.15/1) ^{1*t} \\ 21000=15000(1+0.15) ^{t} \\ 21000 = 15000 * 1.15 ^{t} \\ 1.15 ^{t}=21000/15000 \\ 1.15 ^{t}=1.4[/tex]

Now, logarithm both sides of the equation:
[tex]log(1.15 ^{t})=log(1.4)[/tex]

Since [tex]log (x^{a}) =a*log(x)[/tex], then [tex]log (1.15^{t}) =t*log(1.15)[/tex]
Therefore:
[tex]t*log(1.15)=log(1.4) \\ t = \frac{log(1.4)}{log(1.15)} \\ t = \frac{0.15}{0.06} \\ t = 2.5[/tex]

Convert 288° to radians.

Answers

1 rad=57.3°
288÷57.3=5.02 rad

A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.
The first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. What is the equation for the situation, written in standard form?

A x2 – 99 = 0
B x2 – 99x = 0
C x2 + 5x + 104 = 0
D x2 + 5x – 104 = 0

Answers

[tex](x+5)x=104[/tex]
[tex]\rightarrow x^{2}+5x=104[/tex]
[tex]\rightarrow x^{2}+5x-104=0[/tex]
which is choice D

The quadratic equation for the word problem, written in standard form is equal to: D. x² + 5x - 104 = 0.

Given the following data:

L = (W + 5) inches.

Area = 104 square inches.

Note: Let the width be x.

How to calculate the area.

Mathematically, the area of a rectangle is calculated by using this formula:

LW = A

(x + 5)x = 104

x² + 5x = 104

x² + 5x - 104 = 0

In Mathematics, the standard form of a quadratic equation is given by ax² + bx + c = 0 ⇔ x² + 5x - 104 = 0.

Read more on quadratic equation here: brainly.com/question/1214333

Which expression represents that an unknown number x is no less than 6?

x ≤ 6
x < 6
x > 6
x ≥ 6

Answers

The answer is x ≥ 6

An unknown number x is no less than 6.
Since it is no less than 6 it can be 6, but it can be more than 6 as well, so the expression is: x ≥ 6

Answer:

D. [tex]x\geq6[/tex]

Step-by-step explanation:

We are asked to find the inequality that represents an unknown number x is no less than 6.

Since we know that no less than 6 means greater than or equal to 6.

So our unknown number x should be greater than or equal to 6.

We can represent this information in an inequality as:

[tex]x\geq6[/tex]

Upon looking at our given choices we can see that option D is the correct choice.

when you shift shift a function, you are ____ it.
A. Moving
B. Stretching
C. Compressing
D. Flipping

Answers

When you shift a function, you are moving it.

e.g
f(x) = x * 3
A shift of that function would be g(x) = x * 3 - 2

In the diagram below, G is the incenter of DEF. m
In the previous question, what is m

Answers

Final answer:

The question involves Physics concepts such as vector addition, moment of inertia, and gravitational force calculations. The incenter mentions seem irrelevant to the Physics calculations related to inertia and force.

Explanation:

The question asked is about calculating the moment of inertia for a specific geometric object (a cylinder) and involves understanding the mass distribution relative to an axis of rotation. This is a common concept in the field of Physics, particularly when dealing with rotational dynamics and inertia.

The mention of the incenter of a triangle appears to be unrelated to the main question, which is more focused on moments of inertia, vector addition, and gravitational force equations as indicated by the provided reference information.

For example, the moment of inertia of a cylinder about a given axis can be calculated using established mathematical formulas. Moreover, vector addition (such as Đ = Ả + 2B - F) includes principles such as scaling, displacement and direction, which are crucial in Physics for predicting the outcomes of combined vector forces.

Lastly, the reference to the mass m of an object cancelling in the equation for g is related to calculating the acceleration due to gravity on Earth, which does not depend on the mass of the falling object.

Final Answer:

In the previous question, m represents the measure of an angle, and without specific information about which angle in Δ DEF is being referred to, a precise value cannot be determined.

Explanation:

The symbol m in geometry typically denotes the measure of an angle. In the context of the given diagram, G being the incenter of Δ DEF suggests that G is the point where the angle bisectors of the triangle intersect. However, to determine the specific measure (m) of an angle, additional details about which angle in Δ DEF is being considered are required.

In geometry, the measure of an angle can vary based on its location within a triangle. The incenter is where the angle bisectors meet, ensuring that the angle formed by connecting G to the vertices of Δ DEF is bisected equally. Without information about the specific angle being referenced, a numerical value for m cannot be provided.

Understanding angle measures and the role of an incenter in bisecting angles is crucial in geometry. Precision in describing angles requires clarity on the specific angle under consideration, allowing for accurate calculations and conclusions.

12 is what percent of 30

Answers

_Brainliest if helped!

12/30 *100% = 40%

What is the magnitude of the size change of the figures formed by these matrices?
[3 -2 1] [6 -4 2]
4 1 -1 8 2-2 ...?

Answers

Based on the given values above, according to my research, the magnitude of the size change of the figures formed by the matrices given would be 2. Hope this is the answer that you are looking for. Thanks for posting your question in brainly.

Answer:

The magnitude of the size change of the figures formed by these matrices is:

Step-by-step explanation:

We are given a first matrix as:

[3 -2 1]

and second matrix is given by:

[6 -4 2]

Since we could clearly observe that when we multiply first matrix by a constant 2 then we obtain a second matrix.

i.e. 2[3 -2 1]=[2×3 2×(-2) 2×1]

= [6 -4 2]

Hence, the change in the magnitude of the size of two matrices is:

Factor the expression.
x squared-25

Answers

x2 - 25 = x2 - 52 = (x - 5)(x + 5)

What is 15 divided by 1,230?

Answers

Simplify things
15(82) = 1230
15 / 1230 = 15/ (15*82)
hence =1/82

Find the product of (3x + 7y)(3x − 7y).

9x2 − 42xy + 49y2

9x2 + 42xy + 49y2

9x2 − 49y2

9x2 + 49y2 ...?

Answers

(3x+7y)(3x-7y)
9x2-21xy+21xy-49y2
9x2-48y2

The correct answer for the product of [tex](3x+7y)(3x-7y)[/tex] is [tex]9x^2+49y^2[/tex].The correct option is [tex]b.[/tex].

Given expression:

[tex](3x+7y)(3x-7y)[/tex]

To simplify multiply first term and second term of first expression with second expression separately:

Simplify:

[tex]3x(3x+7y)+7y(3x-7y)[/tex]

[tex]= 9x^2+21xy +21xy-49y^2[/tex]

Add Like terms:

[tex]= 9x^2+42xy-49y^2[/tex]

The product of [tex](3x+7y)(3x-7y)[/tex] is [tex]= 9x^2+42xy-49y^2[/tex] . The correct option is [tex]b.[/tex]

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A department store has a discount on shoes based on a percentage of the price suppose one pair of shoes is marked down from $70 to $49 what is the price for a $100 pair of shoes after the discount is applied

Answers

We first need to find the difference between $70 and $49.
$70 - $49 = 21

Now we find out what percent $21 is of $70.
21/70 × 100 = 30%.

That means the discount is 30%!

Now we must find 30% of $100, which is $30.

Then we subtract $30 from $100.

$100 - $30 = 70$

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