Identify the 3 terms by name: 5x2 - 7x + 2

Answers

Answer 1

Answer:

5x2-7x-1

Step-by-step explanation:

STEP1:Equation at the end of step 1

((5x2 - 7x) - 3) + 2

STEP2:Trying to factor by splitting the middle term

 2.1     Factoring  5x2-7x-1 

The first term is,  5x2  its coefficient is  5 .

The middle term is,  -7x  its coefficient is  -7 .

The last term, "the constant", is  -1 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -1 = -5 

Step-2 : Find two factors of  -5  whose sum equals the coefficient of the middle term, which is   -7 .

     -5   +   1   =   -4     -1   +   5   =   4


Related Questions

Find an equation for the perpendicular bisector of the line segment whose endpoints are (8,-5)(8,−5) and (4,3)(4,3).

Answers

Answer:

[tex]Correct answer\\y=\frac{1}{2} x-4[/tex]

Step-by-step explanation:

[tex]y-\frac{-5+3}{2} =\frac{-1}{\frac{3-(-5)}{4-8} } (x-\frac{4+8}{2} )\\y+1=\frac{1}{2} (x-6)\\y=\frac{1}{2} x-4[/tex]

Given the interval 0<θ<π/2. Find the angle θ which is formed by the line y = -2x+4 and y = 3x-3
Show your work as well, thank you!​

Answers

Answer:

[tex]\rm\displaystyle \theta = \frac{\pi}{4} [/tex]

Step-by-step explanation:

we want to find the acute angle θ (as θ is between (0,π/2)) formed by the line y=-2x+4 and y=3x-3 to do so we can consider the following formula:

[tex] \displaystyle\tan( \theta) = \bigg| \frac{ m_{2} - m_{1} }{1 + m_{1} m_{2} } \bigg | [/tex]

[tex] \rm \displaystyle \implies\theta = \arctan \left( \bigg | \frac{ m_{2} - m_{1} }{1 + m_{1} m_{2} } \bigg | \right)[/tex]

From the first equation we obtain that [tex]m_1[/tex] is -2 and from the second that [tex]m_2[/tex] is 3 therefore substitute:

[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 - ( - 2) }{1 + ( - 2) (3)} \bigg | \right)[/tex]

simplify multiplication:

[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 - ( - 2) }{1 + ( - 6)} \bigg | \right)[/tex]

simplify Parentheses:

[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 + 2 }{1 + ( - 6)} \bigg | \right)[/tex]

simplify addition:

[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 5 }{ - 5} \bigg | \right)[/tex]

simplify division:

[tex] \rm\displaystyle \theta = \arctan \left( | - 1| \right)[/tex]

calculate the absolute of -1:

[tex]\rm\displaystyle \theta = \arctan \left( 1\right)[/tex]

calculate the inverse function:

[tex]\rm\displaystyle \theta = \frac{\pi}{4} [/tex]

hence,

the angle θ which is formed by the line y = -2x+4 and y = 3x-3 is π/4

(for more info about the formula refer the attachment thank you!)

Consider two vector-valued functions,

[tex]\vec r(t) = \left\langle t, -2t+4\right\rangle \text{ and } \vec s(t) = \left\langle t, 3t-3\right\rangle[/tex]

Differentiate both to get the corresponding tangent/direction vectors:

[tex]\dfrac{\mathrm d\vec r(t)}{\mathrm dt} = \left\langle1,-2\right\rangle \text{ and } \dfrac{\mathrm d\vec s(t)}{\mathrm dt} = \left\langle1,3\right\rangle[/tex]

Recall the dot product identity: for two vectors [tex]\vec a[/tex] and [tex]\vec b[/tex], we have

[tex]\vec a \cdot \vec b = \|\vec a\| \|\vec b\| \cos(\theta)[/tex]

where [tex]\theta[/tex] is the angle between them.

We have

[tex]\langle1,-2\rangle \cdot \langle1,3\rangle = \|\langle1,-2\rangle\| \|\langle1,3\rangle\| \cos(\theta) \\\\ 1\times1 + (-2)\times3 = \sqrt{1^2 + (-2)^2} \times \sqrt{1^2+3^2} \cos(\theta) \\\\ \cos(\theta) = \dfrac{-5}{\sqrt5\times\sqrt{10}} = -\dfrac1{\sqrt2} \\\\ \implies \theta = \cos^{-1}\left(-\dfrac1{\sqrt2}\right) = \dfrac{3\pi}4[/tex]

Then the acute angle between the lines is π/4.

5. What is x in the diagram?

Answers

Answer:

B

Step-by-step explanation:

we rule out all other 3 by the simple fact that the side is 9

the answer is B hope this helps

2 Points

(25x

0
The equation ya

represents Michelle's regular

130(x-38) +950 %> 38

hourly and overtime wage. Based on this equation, what is Michelle's

overtime hourly pay?

A. $30

B. $38

O C. $950

O D. $25

Answers

Answer:

The answer is "35.22".

Step-by-step explanation:

Let the given equation:

[tex]\to 130(x-38) +950 \% \times 38=0\\\\\to 130x- 4940+\frac{950}{100} \times 38=0\\\\\to 130x- 4940+9.5\times 38=0\\\\\to 130x- 4940+361=0\\\\\to 130x- 4579=0\\\\\to 130x= 4579\\\\\to x= \frac{4579}{130}\\\\\to x= 35.22[/tex]

Answer: $25

Step-by-step explanation: took the quiz

the average length of string a and string d is 10x cm. the average length of string b and string c is 8x cm . the average length of strings b , c , d is 6x cm . find the length of string a in terms of x

Answers

Answer:

[tex]a = 18x[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{2}(a + d) = 10x[/tex]

[tex]\frac{1}{2}(b + c) = 8x[/tex]

[tex]\frac{1}{3}(b + c+d) = 6x[/tex]

Required

The value of (a)

We have:

[tex]\frac{1}{2}(a + d) = 10x[/tex] --- multiply by 2

[tex]\frac{1}{2}(b + c) = 8x[/tex] --- multiply by 2

[tex]\frac{1}{3}(b + c+d) = 6x[/tex] --- multiply by 3

So, we have:

[tex]\frac{1}{2}(a + d) = 10x[/tex]

[tex]a + d = 20x[/tex]

[tex]\frac{1}{2}(b + c) = 8x[/tex]

[tex]b + c = 16x[/tex]

[tex]\frac{1}{3}(b + c+d) = 6x[/tex]

[tex]b + c + d= 18x[/tex]

Substitute [tex]b + c = 16x[/tex] in [tex]b + c + d= 18x[/tex]

[tex]16x + d = 18x[/tex]

Solve for d

[tex]d = 18x - 16x[/tex]

[tex]d = 2x[/tex]

Substitute [tex]d = 2x[/tex] in [tex]a + d = 20x[/tex]

[tex]a + 2x = 20x[/tex]

Solve for (a)

[tex]a = 20x - 2x[/tex]

[tex]a = 18x[/tex]

Find the slope of the line that passes through (2 2) and (-1 -2)

Answers

Answer:

4/3

Step-by-step explanation:

The formula is (y1-y2) /(x1-x2)

Answer:

slope = [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (- 1, - 2)

m = [tex]\frac{-2-2}{-1-2}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]

Consider y=h(θ) described in the table. When comparing h(θ) to the parent function f(θ)=cos(θ), which statements are true? Select all that apply.

Answers

2 Answers:

Choice AChoice E

=====================================================

Explanation:

Let's go through the answer choices

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

A)

The lowest point is y = 1, and the highest point is y = 27. Computing the midpoint gets us (yMin+yMax)/2 = (1+27)/2 = 28/2 = 14.

The midline of [tex]h(\theta)[/tex] is y = 14.

Consider that the parent function [tex]\cos(\theta)[/tex] has a midline of y = 0. The jump from y = 0 to y = 14 must mean [tex]h(\theta)[/tex] has a vertical shift of 14.

Choice A is true

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

B)

The period is the length of the cycle. For the function [tex]h(\theta)[/tex], the function starts at [tex]\theta = 0[/tex] and repeats when it gets to [tex]\theta = \frac{\pi}{2}[/tex]. This is a difference of pi/2 units which is the period.

Choice B is false. It contradicts with choice E.

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

C)

Choice C is false. The max for [tex]h(\theta)[/tex] is at y = 27

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

D)

To figure out the amplitude, we can note the vertical distance from the midline y = 14 to the max is 27-14 = 13 units.

Or we can note the distance from the midline to the min is 14-1 = 13 units.

Or we subtract the min and max, and divide by 2:  (yMax-yMin)/2 = (27-1)/2 = 26/2 = 13

Either way, the amplitude is 13 units

Choice D is false.

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

E)

Choice E is true. Refer to choice B to see why this is the case.

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

Side note: one possible function is [tex]h(\theta) = 13\cos(4\theta+\pi) + 14[/tex]. The various pieces of that function (in)directly lead to the amplitude, period, and vertical shift.

The correct two options are h(Ф) has vertical shift of 14 and Choice E

The period of a fuction is x/2

What is a function?

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

Let's go through the answer choices

A)

The lowest point is y = 1, and the highest point is y = 27. Computing the midpoint gets us (yMin+yMax)/2 = (1+27)/2 = 28/2 = 14.

The midline of  is y = 14.

Consider that the parent function  has a midline of y = 0. The jump from y = 0 to y = 14 must mean  has a vertical shift of 14.

Choice A is true

B)

The period is the length of the cycle. For the function , the function starts at  and repeats when it gets to . This is a difference of pi/2 units which is the period.

Choice B is false. It contradicts with choice E.

C)

Choice C is false. The max for  is at y = 27

D)

To figure out the amplitude, we can note the vertical distance from the midline y = 14 to the max is 27-14 = 13 units.

Or we can note the distance from the midline to the min is 14-1 = 13 units.

Or we subtract the min and max, and divide by 2:  (yMax-yMin)/2 = (27-1)/2 = 26/2 = 13

Either way, the amplitude is 13 units

Choice D is false.

E)

Choice E is true. Refer to choice B to see why this is the case.

Side note: one possible function is h(Ф) = 13 Cos(4Ф + π) + 14 . The various pieces of that function (in)directly lead to the amplitude, period, and vertical shift.

To know more about functions follow

https://brainly.com/question/2833285

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Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1.c

Answers

Answer:

[tex]\displaystyle y=\frac{1}{4}x^2[/tex]

Step-by-step explanation:

Let (x, y) be a point on the parabola.

By definition, any point on the parabola is equidistant from the focus and the directrix

The distance from the focus is given by:

[tex]\begin{aligned} d&=\sqrt{(x-0)^2+(y-1)^2\\\\&=\sqrt{x^2+(y-1)^2}\end{aligned}[/tex]

The distance from the directrix is given by:

[tex]d=|y-(-1)|=|y+1|\text{ or } |-1-y|[/tex]

So:

[tex]\sqrt{x^2+(y-1)^2}=|y+1|^[/tex]

Square both sides. Since anything squared is positive, we can remove the absolute value:

[tex]x^2+(y-1)^2=(y+1)^2[/tex]

Square:

[tex]x^2+(y^2-2y+1)=y^2+2y+1[/tex]

Hence:

[tex]x^2=4y[/tex]

So, our equation is:

[tex]\displaystyle y=\frac{1}{4}x^2[/tex]

Put these numbers in order from least to greatest.
9.9, 9.5, and 9 4/5

Answers

9.5, 9 4/5, 9.9

9 4/5 is equal to 9.8

provide explanation too please !


a piano teacher teaches 8 lessons in 6 hours.
the lessons are all the same length.
how long is one lesson, in minutes?

Answers

1 hour is 60 minutes

6 hours x 60 = 360 total minutes

Divide total time by number of lessons:

360/8 = 45

Each lesson was 45 minutes

How many quarters are there in 5 1
? ?
2​

Answers

Answer:

yes

Step-by-step explanation:

51 divided by 25

The point (5,-12) lies on the terminal side of an angel theta in standard position. Find the exact value of cot theta. Express the answer as a fraction reduced to the lowest term

Answers

Answer:

[tex]cot\theta=-\frac{5}{12}[/tex]

Step-by-step explanation:

We are given that the point (5,-12) lies on the terminal side of an angle theta in standard position.

We have to find the exact value of [tex]cot\theta[/tex].

Let

Point (x,y)=(5,-12)

[tex]r=\sqrt{x^2+y^2}[/tex]

Substitute the values

[tex]r=\sqrt{5^2+(-12)^2}[/tex]

[tex]r=\sqrt{169}=13[/tex]

We know that

[tex]cot\theta=\frac{x}{y}[/tex]

Using values

[tex]cot\theta=-\frac{5}{12}[/tex]

write tge following numbers expanded forms.
23900068407​

Answers

Answer:

Step-by-step explanation:

20000000000+3000000000+900000000+60000+8000+400+7

Helppp and explain pleaseeeeee!!!!!!

Answers

7/3 is your answer!

El volumen de un prisma de base rectangular es 24 m3. Si el largo de la base es 2,5 m y su ancho es 4 m, ¿cuál es la altura del prisma?

Answers

Answer:

La altura del prisma es 2,4 m.

Step-by-step explanation:

Para calcular el volumen de un prisma rectangular, es necesario multiplicar sus tres dimensiones, esto es, longitud*ancho*altura. El volumen se expresa en unidades cúbicas.

Entonces:

volumen= longitud*ancho*altura

En este caso, los datos conocidos son:

volumen= 24 m³longitud= largo de la base= 2,5 mancho= 4 maltura= ?

Reemplazando:

24 m³= 2,5 m* 4 m* altura

Resolviendo:

[tex]altura=\frac{24 m^{3} }{2,5 m*4m}[/tex]

[tex]altura=\frac{24 m^{3} }{10 m^{2} }[/tex]

altura= 2,4 m

La altura del prisma es 2,4 m.

Help please guys if you don’t mind

Answers

Answer:

first

2/5m + 8/5

second

22/5

third

11

Matthew grows wheat on his farm. One of his fields produced 66.8 bushels of wheat this year. If wheat is currently selling for $5.40 per bushel, how much will Matthew earn from this field?

Answers

Answer:

Mathew will earn $360.72 from his food

Step-by-step explanation:

We know that:

1 bushel of wheat = $5.40

And Matthew produced 66.8 bushels of heat this year

To find how much Matthew will earn from his field, multiply:

5.40 x 66.8 = 360.72

Therefore he will earn $360.72 from his field.

Hope thjs helps!

$360.73 I’m pretty sure

x ÷ 8.2 = 10. What is the value of x?

Answers

Answer:

82

Step-by-step explanation:

Answer:

82

Step-by-step explanation:

10 times 8.2 would be 82 so you just divide 82 by 10

WILL GIVE BRAINLIEST
Hannah and Han are each trying to solve the equation x² – 8x + 26 = 0. They know that
x = -1 are i& - i, but they are not sure how to use this information to solve for x in their
equation.
Part 1- Here is Hannah's work:
x? - 8x + 26 = 0
X? – 8x = -26
Show Hannah how
to finish her work using completing the square and complex numbers.
Part 2- Han decides to solve the equation using the quadratic
formula. Here is the beginning of his
work
-b+V62-4ac
-(-8)+7-8)2–401|(26)
Finish using the quadratic formula. Simplify the final answer as much as possible.

Answers

Part one:

[tex]x^2-8x=-26[/tex]

Rewrite in the form [tex](x+a)^{2} =b[/tex]

[tex]\left(x-4\right)^2=-10[/tex]

[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]

Solve [tex]x-4=\sqrt{-10} : x=\sqrt{10} i+4[/tex]

Solve [tex]x-4=\sqrt{-10} : x=-\sqrt{10} i+4[/tex]

[tex]x=\sqrt{10}i+4,\:x=-\sqrt{10}i+4[/tex]

Part two:

[tex]x=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:26}}{2\cdot \:1}[/tex]

Simplify [tex]\sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:26}}: 2\sqrt{10} i[/tex]

[tex]=\frac{-\left(-8\right)\pm \:2\sqrt{10}i}{2\cdot \:1}[/tex]

Separate solutions

[tex]x_1=\frac{-\left(-8\right)+2\sqrt{10}i}{2\cdot \:1},\:x_2=\frac{-\left(-8\right)-2\sqrt{10}i}{2\cdot \:1}[/tex]

[tex]\frac{-(-8)+2\sqrt{10}i }{2*1} :4+\sqrt{10}i[/tex]

[tex]\frac{-(-8)+2\sqrt{10}i }{2*1} :4-\sqrt{10}i[/tex]

[tex]x=4+\sqrt{10}i,\:x=4-\sqrt{10}i[/tex]

The solutions are:-

[tex]x=4+\sqrt{10i}\\\\x=4-\sqrt{10i}[/tex]

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given equation is

[tex]x^2- 8x + 26 = 0\\\\x^2-8x=-26\\\\(x-4)^2=-10\\\\[/tex]

[tex](x-4)=[/tex]±[tex]\sqrt{-10}[/tex]

[tex]x=\sqrt{10}i+4\\\\x=-\sqrt{10}i+4[/tex]

So,

[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}\\\\x=\frac{8+-\sqrt{(-8)^2-4(1)(26)}}{2(1)}\\\\x=\frac{8+-\sqrt{(-8)^2-4(1)(26)}}{2(1)}\\\\x=\frac{8+-\sqrt{64-104}}{2}\\\\x=\frac{8+-2\sqrt{10i}}{2}\\\\x=\frac{2(4+-\sqrt{10i})}{2}\\\\x=4+\sqrt{10i}\\\\x=4-\sqrt{10i}[/tex]

Hence, the solutions are:-

[tex]x=4+\sqrt{10i}\\\\x=4-\sqrt{10i}[/tex]

To know more about the equation

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4 1/3 - 2 1/2 divided by 1 2/3

Answers

Answer:

Exact Form: [tex]\frac{17}{6}[/tex]

Decimal Form: 2.83

Mixed Number Form: [tex]2 and 5/6[/tex]

Step-by-step explanation:

Answer:

[tex]1\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]4\frac{1}{3}-2\frac{1}{2}[/tex]

[tex]4\frac{2}{6} -2\frac{3}{6}=1\frac{5}{6}[/tex]

[tex]1\frac{5}{6} =\frac{11}{6}[/tex]

[tex]1\frac{2}{3}=\frac{5}{3}[/tex]

[tex]\frac{11}{6}[/tex] ÷ [tex]\frac{5}{3} =[/tex]

[tex]\frac{11}{6} *\frac{3}{5}=[/tex]

[tex]\frac{11}{2}*\frac{1}{5} =[/tex]

[tex]=\frac{11}{10}[/tex]

[tex]=1\frac{1}{10}[/tex]

Hope this is helpful

How do I do this?? TnT

Answers

Answer:

x = 4

Step-by-step explanation:

Corresponding angles are congruent

4x + 44 = 6x + 36

44 = 2x + 36

8 = 2x

x = 4

Find two integers whose sum is 1 and product is -2
TWO INTERGES

Answers

Answer:

2 and -1

Step-by-step explanation:

sum = 2 + (-1)

= 1

product = 2 × ( -1)

= -2

a box contains 6 dimes, 8 nickels, 12 pennies, and 3 quarters. what is the probability that a coin drawn at random is not a dime

Answers

Add all the coins to get total coins:

6 + 8 + 12 + 3 = 29 total coins

Subtract dimes to find total of the coins that are not dimes:

29 -6 = 23

Probability of not picking a dime is the number of coins that aren’t dimes over total coins:

23/29

Complete the equation for the relationship between the weight and number of months

Answers

Y=5.5x because it just is

Brad bought a piece of industrial real estate for $192,345. The value of the real estate appreciated a constant rate per year. The table shows the value of the real estate after the first and second years:

Year:
1
2

Value (in dollars):
$200,038.80
$208,040.35

Which function best represents the value of the real estate after t years?
A. f(t) = 200,038.80(1.04)^t

B. f(t) = 200,038.80(0.04)^t

C. f(t) = 192,345(0.04)^t

D. f(t) = 192,345(1.04)^t

Answers

Answer:

D. f(t) = 192,345(1.04)^t

Step-by-step explanation:

I took the test and it was right.

Also that is the original price and when you look at exponential functions, the starting point or original price is always first the then rate of increase. The table just shows how it increased in year 1 and 2.

Hope this helps. :)

A function assigns the values. The function that best represents the value of the real estate after t years is f(t) = 192,345(1.04)^t. Thus, the correct option is D.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The initial cost of industrial real estate is $192,345, while the cost after one year is $200,038.80. Therefore, the rate of appreciation is,

[tex]\$200,038.80 = \$192,345(1+R)^t\\\\\$200,038.80 = \$192,345(1+R)^1\\\\\dfrac{\$200,038.80}{\$192,345}=(1+R)^t\\\\1.04 = 1 + R\\\\R = 0.04[/tex]

Hence, the function that best represents the value of the real estate after t years is f(t) = 192,345(1.04)^t. Thus, the correct option is D.

Learn more about Function:

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Please help me on this question

Answers

Answer:

√20

Or

2√5

Step-by-step explanation:

It is very easy just substitute

It will be:

Tell whether the equation Y=Y true or false

Answers

Answer:

its true trust biggie on this one fam

Step-by-step explanation:

its true broski

Triangle HIJ is similar to triangle KLM. Find the measure of side MK. Round your answer to the nearest tenth.

Answers

Answer:

[tex]MK\approx 87.7[/tex]

Step-by-step explanation:

By definition, similar polygons have corresponding sides in a constant proportion. Therefore, we can set up the following proportion (ratio of corresponding sides) to solve for [tex]MK[/tex]:

[tex]\frac{20}{13}=\frac{MK}{57},\\MK=\frac{57\cdot 20}{13}\approx \boxed{87.7}[/tex]

Answer:

87.7

Step-by-step explanation:

Like stated previously similar triangle have side lengths with common ratios

*Create a proportionality to solve for MK*

57/13 = MK / 20

Now solve for MK

Multiply each side by 20

57/13 * 20 = 87.7 ( rounded )

MK/20 * 20 = MK

We're left with MK = 87.7

Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in josiahs account, y, after x years?

a-y=360(1.3)^x
b-y=360(0.3^x
c-y=360(0.03)^x
d-y=360(1.03)^x

Answers

Answer:

y = 360 (1.03)^x

Step-by-step explanation:

Amount in account = principle * (1+ rate) ^ time

When the interest is annual

rate is in decimal form and time is in years

y = 360 ( 1+.03) ^x

y = 360 (1.03)^x

Which numbers are divisible by 2?

A)826

B)270

C)271

Answers

Answer:

A

Step-by-step explanation:

Answer:

A and B, every even number is divisible by two, C is odd

Other Questions
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