Factorise : x²-17x+ 60 Step by Step​

Answers

Answer 1

Answer:

Step-by-step explanation:

x^2 - 17 x + 60

we should find two numbers such that their sum is equal to -17 and product is equal to 60

The two numbers are -12 and -5

now, x^2 - 12 x - 5 x + 60 { splitting the middle term }

x ( x- 12 ) - 5 ( x - 12 )

= ( x - 5 ) ( x - 12 )

hope this helps

plz mark as brainliest !!!!!!                        

Answer 2

Answer:

             x² - 17x + 60 = (x - 12)(x - 5)

Step-by-step explanation:

[tex]x^2-17x+60\quad \implies\quad a=1\,,\quad b=-17\,,\quad c=60\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-17)\pm\sqrt{(-17)^2-4\cdot1\cdot60}}{2\cdot1}=\dfrac{17\pm\sqrt{289-240}}{2}=\dfrac{17\pm\sqrt{49}}{2}\\\\x_1=\dfrac{17-7}{2}=5\quad,\qquad x_2=\dfrac{17+7}{2}=12\\\\\\x^2-17x+60=(x-5)(x-12)[/tex]

or:

    x² - 17x + 60 =

= x² - 12x - 5x +60 =

= x(x - 12) - 5(x - 12) =

= (x - 12)(x - 5)


Related Questions

The average weight of the three lion cubs at the zoo was 288 pounds. Two of the cubs weighed 261 and 252 pounds. What was the weight of the third cub?

Answers

Answer:

351 pounds

Step-by-step explanation:

288 x 3 = 864 pounds

864 - 261 - 252 = 351 pounds

Therefore (261 + 252 + 351)/3 = 288.

So the answer is 351 pounds

Determine which one of the following statements is true. A. Exponential growth will always exceed linear growth. B. Linear growth will always exceed quadratic growth. C. Linear growth will always exceed exponential growth. D. Quadratic growth will always exceed exponential growth.

Answers

Answer:

A. Exponential growth will always exceed linear growth.

Step-by-step explanation:

The rate of growth of a linear function is always constant, that means it remains the same for any value of x or y. For an exponential growth, the rate of change is not constant, it continues to increase as the value of x increases. Therefore since the rate of growth of an exponential growth increases as the x value increases, while that of the linear growth remain constant there would be a point in which the exponential growth will exceed linear growth.

Jak policzyc: [tex](2x^2)^2[/tex] ?

Answers

2^2 • x^ (2•2)
Answer is :
4x^4

The volume of a rectangular prism is the product of its dimensions. If the dimensions of a rectangular prism are
approximately 1.08 feet, 5.25 feet, and 3.3 feet, what is the approximate volume of the cube? Express your answer
using an appropriate level of accuracy.

Answers

Answer:

Hey there!

Volume of a rectangular prism: length (width) (height).

Volume: 1.08 (5.25) (3.3), or 18.71100.

However, because 3.3 is only two significant figures, we round our answer to: 19.

Hope this helps :)

Answer:

18.7 ft^3

Step-by-step explanation:

The volume is the product of the dimensions of the cube:

V = L*W*H, where L and W represent the length and width respectively.

Here,

V = (1.08 ft)(5.25 ft)(3.3 ft) = 18.7 ft^3, which is to 1 decimal place, because the least accurate dimension is also to 1 decimal place.

PLEASE HELP!! what is the equation of a line that is perpendicular to y = 2x + 4 and passes through the point (4, 6)?

Answers

Answer:

The answer is B)

[tex]y = - \frac{1}{2}x + 8[/tex]

Answer:

B.  y = -[tex]\frac{1}{2}[/tex]x + 8

Step-by-step explanation:

The line is perpendicular to line whose equation is:

y = 2x + 4 and;

passes through point (4,6) .

The product slopes of two perpendicular lines is -1.

The slope of the line whose equation is y = 2x + 4 is; 2

Let the slope of the perpendicular line (l2) be [tex]m_{l2}[/tex]

[tex]m_{l2} * 2 = -1[/tex]

[tex]m_{l2}[/tex] = [tex]-\frac{1}{2}[/tex]

Taking another point xy on line l2;

[tex]\frac{y - 6}{x - 4} = -\frac{1}{2}[/tex]

Cross multiplying this gives;

y = -[tex]\frac{1}{2}[/tex]x + 8 which is the equation of the perpendicular line!

2. A cylinder has a height of 4.5 cm and a diameter of 1.5 cm. What is the surface area of the cylinder in square centimeters? Use 3.14 for pi.
21.2
31.8
7.9
24.7

Answers

Answer:

[tex] SA = 24.73~cm^3 [/tex]

Step-by-step explanation:

[tex] SA = 2\pi r^2 + 2\pi r h [/tex]

r = d/2 = (1.5 cm)/2 = 0.75 cm

[tex] SA = 2(3.14)(0.75~cm)^2 + 2(3.14)(0.75~cm)(4.5~cm) [/tex]

[tex] SA = 24.73~cm^3 [/tex]

Answer:

24.7

Step-by-step explanation:

took this exam and got it right

Which expression represents the prime factorization of 243?

Answers

Answer:

[tex]\boxed{3^5}[/tex]

Step-by-step explanation:

Hey there!

Look at the image below↓

By looking at the image we can tell the PR expression is [tex]3^5[/tex].

Hope this helps :)

Answer:

Below in bold.

Step-by-step explanation:

Dividing  by primes:

3 ) 243

3 )  81

3 )  27

3)     9

        3.

So the prime factors of 243 are 3 * 3 * 3 * 3 * 3  or  3^5.

LESSON 2-1 PRACTICE

V 13. Attend to precision. Justify each step in the solution of 5x + 15 -

below by stating a property or providing an explanation for each

5x + 15 = 0

5x + 15 – 15 = 0 – 15

5x = -15

x = -3

Answers

Answer:

Value of x is -3

Step-by-step explanation:

Given:

5x + 15 = 0

Find:

Value of x

Computation:

5x + 15 = 0

From subtracting 15 from both side (LHS and RHS)

5x + 15 – 15 = 0 – 15

5x = -15

From dividing 5 from both side (LHS and RHS)

5x / 5 = -15 / 5

x = -3

So,

Value of x is -3

There are 9 classes of 25 students each, 4 teachers, and two times as many chaperones as teachers.
Each bus holds a total of 45 people.
What is the least number of buses needed for the field trip?

Answers

5 buses is the answer pls mark me brainliest

Least number of bus require for trip = 5 buses

What is Unitary method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

Total number of classes = 9

Number of student in each class = 25

Number of teacher = 4

Number of chaperones = Double of teacher

Bus hold = 45 people

Now,

Total number of student = 9 × 25

                                         = 225

Number of chaperones = 4 × 2

                                         = 8

Total people = 225 + 8 + 4

                     = 237

Least number of bus require for trip = Total people / Bus hold

= 237 / 45

= 5.266

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ2

How many triangles exist with the given side lengths? 2mm,6mm,10mm

Answers

Answer:

Zero

Step-by-step explanation:

2+6=8 which means it can't be. It has to be a length higher than 10

Assume all variables represent non negative numbers . Help please!!

Answers

Answer:

A). [tex]2p^{8}[/tex]

B). [tex]3m^{7}[/tex]

Step-by-step explanation:

A). [tex]\sqrt{4p^{16}}[/tex]

    To get the square root of the given expression we will convert it into the square form.

[tex]4p^{16}=(2)^2(p^{8})^2[/tex] [Since 2×2 = 4 and [tex]p^{8}\times p^{8}=p^{16}[/tex]]

Therefore, [tex]\sqrt{4p^{16}}=\sqrt{2^{2}\times (p^{8})^2 }[/tex]

                             [tex]=2p^{8}[/tex]

B). [tex]\sqrt{9m^{44}}[/tex]

    Since, [tex]9m^{14}=(3)^2\times (m^7)^2[/tex]

    Therefore,  [tex]\sqrt{9m^{44}}=\sqrt{(3)^2\times (m^7)^2}[/tex] [Since 3² = 9 and (m⁷)² = m¹⁴]

                                   [tex]=3m^{7}[/tex]

The graph of
is positive over the interval and negative over the interval . What happens on the graph when ​? Explain.

Answers

Answer:

Positive and negative intervals on a graph

Step-by-step explanation:

The positive regions of a function are those intervals where the function is above the x-axis. It is where the y-values are positive (not zero). The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero). hope this helps you :)

Positive & negative intervals on a graph

7 liters of gasoline between their 4 cars. How many liters of gasoline should each car get?

Answers

Answer:

1.75 liters for each car.

Step-by-step explanation:

Divide:

*7 / 4 = 1.75.

Check:

*1.75 x 4 = 7.

1.75
7 divided by 4

FORM A CUBIC POLYNOMIAL WHOSE ZEROS ARE -3,-1 AND 2

Answers

[tex](x+3)(x+1)(x-2)=\\(x^2+x+3x+3)(x-2)=\\(x^2+4x+3)(x-2)=\\x^3-2x^2+4x^2-8x+3x-6=\\x^3+2x^2-5x-6[/tex]

What is the range of the function graphed below? PLEASE ANSWER ASAP

Answers

Answer: Choice C) [tex]-\infty < y < 2[/tex]

This is a more complicated way to write [tex]y < 2[/tex]

The range is the set of all possible y outputs of a function. So we use the graph to see what y values are possible. The graph shows that y can be anything smaller than y = 2. We can't actually reach y = 2 itself due to a horizontal asymptote here.

In interval notation, the answer would be [tex](-\infty, 2)[/tex] with the curved parenthesis to indicate "do not include y = 2 as part of the range".

Find the he value of n if 4n=6 4

Answers

Answer: 16

Step-by-step explanation:

64/4=16

n=16

Answer:

16

Step-by-step explanation:

4n = 64

n = 16 --------> Divide by 4 on each side

The sum of 6 consecutive integers is 519. What is the third number in this sequence?

Answers

Answer:

86

Step-by-step explanation:

x+x+1+x+2+x+3+x+4+x+5 = 519

6x+15 = 519

6x = 504

x = 84

Third number = x+2 = 86

Answer:

86

Step-by-step explanation:

khan

Bob has taken out a loan of $15,000 for a term of 48 months (4 years) at an interest rate of 6.5%. Using the amortization table provided, what will be his total finance
charge over the course of his loan?
Monthly Payment per $1,000 of Principal
Rate 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $30.65 $23.71 $19.57
7.0% $86.53 $44.77
$30.88
$23.95
$19.80
7.5% $86.76 $45.00
$31.11
$24.18
$20.04
8.0% $86.99 $45.23
$31.34
$24.41
$20.28
8.5% $87.22 $45.46
$24.65
$24.65
$20.52
9.0% $87.45 $45.68
$31.80
$24.89
$20.76
A.
$355.65
O
B.
$975.00
C.
$1,682.40
D.
$2,071.20
E. $17,071.20
Reset
Next
© 2020 Edmentum. All rights reserved.​

Answers

Answer:

  D.  $2071.20

Step-by-step explanation:

The table tells you that Bob's monthly payment on a 4-year loan at 6.5% will be $23.71 per thousand borrowed. The sum of those 48 payments is ...

  48 × $23.71 = $1138.08

That means, Bob pays $138.08 in total finance charge for each $1000 he borrows. He is borrowing 15 times $1000, so his total finance charge will be ...

  finance charge = 15 × $138.08 = $2071.20 . . . matches choice D

Which is the exponential form of log3 x= 11?

Answers

Answer:

[tex]x = 3^{11}[/tex]

Step-by-step explanation:

relation between logarithmic and exponential form is given by

[tex]\log_a x = y \\[/tex] is same as [tex]a^y = x[/tex] where a>0 and a is not equal to 1.

____________________________________________

[tex]\log_3 x = 11 \\\\x = 3^{11}[/tex]

Thus, exponential form is [tex]x = 3^{11}[/tex]

I WANT TO PASS HIGH SCHOOL PLEASE HELP

Given that the quadrilateral EFGH is a trapezoid, m∠H = 62° and m∠HEG = 64° calculate m∠FEG

Answers

Answer:

m∠FEG == 54°

Step-by-step explanation:

you should know that m∠FEG is equal m∠EGH. this is because sides HE and FG are equal this also means opposite angles of this sides (m∠FEG and m∠EGH) are equal.

first find the measure of m∠EGH from triangle EHG.

m∠H + m∠HEG + m∠EGH= 180°

62° + 64° + m∠EGH = 180°

m∠EGH=180° - 126°

m∠EGH=54°

due to the fact that sides HE and FG are equal thus opposite angles of sides HE and FG are also equal.

m∠FEG = m∠EGH = 54°

m∠FEG =54°

A spinner has 3 red spaces, 5 white spaces, and 1 black space. If the spinner is
spun once, what is the theoretical probability of the spinner NOT stopping on
red?
P(Not red) =

Answers

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

If we have 3 red spaces, 5 white spaces, and one blank space, there are a total of 9 spaces.

Since there are 3 red spaces, there is a [tex]\frac{3}{9} = \frac{1}{3}[/tex] chance of getting a red. However, the question asks the probability of not getting a red, so the chances of not getting a red are [tex]1 -\frac{1}{3} = \frac{2}{3}[/tex].

Hope this helped!

(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any
point on the remaining part of the circle.​

Answers

Answer:

The angle subtended by an arc at the center is double the angle subtended by it at any  point on the remaining part of the circle.

Step-by-step explanation:

Let us consider the image attached.

Center of circle be O.

Arc AB subtends the angle [tex]\angle APB[/tex] on the circle and [tex]\angle AOB[/tex] on the center of the circle.

To prove:

[tex]\angle AOB = 2 \times \angle APB[/tex]

Proof:

In [tex]\triangle PAO[/tex]: AO and PO are radius of the circles so AO = PO

And angles opposite to equal sides of a triangle are also equal in a triangle.

So, [tex]\angle PAO = \angle OPA[/tex]

Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.

[tex]\angle AOQ = \angle PAO + \angle OPA=2 \times \angle APO .... (1)[/tex]

Similarly,

In [tex]\triangle PBO[/tex]: BO and PO are radius of the circles so BO = PO

And angles opposite to equal sides of a triangle are also equal in a triangle.

So, [tex]\angle PBO = \angle OPB[/tex]

Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.

[tex]\angle BOQ = \angle PBO + \angle OPB=2 \times \angle BPO .... (2)[/tex]

Now, we can see that:

[tex]\angle AOB = \angle AOQ+\angle BOQ[/tex]

Using equations (1) and (2):

[tex]\angle AOB = 2\angle APO+2\angle BPO\\\angle AOB = 2(\angle APO+\angle BPO)\\\bold{\angle AOB = 2(\angle APB)}[/tex]

Hence, proved.

Hope you could understand.

If you have any query, feel free to ask.

*PLEASE ANSWER* What is the volume of this prism?

Answers

Answer:

23.85

Step-by-step explanation:

→ Work out area of triangle

0.5 × 6 × 3 = 0.5 × 18 = 9

→ Multiply area of triangle by width of prism

9 × 2.65 = 23.85

Write the slope-intercept form of the equation for the line. (-1,-3) (1,1)

Answers

Answer:

y = 2 x − 1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

We can find the slope from the slope equation

m = (y2-y1)/(x2-x1)

   = ( 1- -3)/(1 - -1)

   = (1+3)/(1+1)

   = 4/2

  =2

Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years.

Answers

Answer:

y = 100(3)^t

Step-by-step explanation:

Use the formula y = P(1 + r)^t where y is the new amount, P is the starting amount, r is the rate as a decimal, and t is the time.

Plug in the values given:

y = 100(1 + 2)^t

y = 100(3)^t

Answer:

Step-by-step explanation:

y = 100(3)^t

PLEASE ANSWER ASAP!!!!!!!!!!!!!!!!!!!!! The price of coffee has dropped to $2.30. Yesterday's price was $2.55. Find the percentage decrease. Round your answer to the nearest tenth of a percent

Answers

9.8 percent. All you have to do is subtract 2.30 from 2.55 and then divide that answer by 2.55 and then multiply that by 100

Answer:

9.8%

Step-by-step explanation:

Step 1: Find the change in price

2.55 - 2.30 = $0.25

Step 2: Divide change with original price

0.25 / 2.55 = 0.098....%

Step 3: Multiple by 100 to get percent

0.098 x 100 = 9.8%

A police car drives with a constant speed of 64 mph. How far can it travel in 2 hours?

Answers

Answer:

128 miles.

Step-by-step explanation:

The police car is driving at a constant speed of 64 mph so you simply have to multiply the rate by the time to get the distance.

64 * 2 = 128 miles

Hope this helps!  

The graph shows the equation x2 + y2 = 5. Use the slider for a to move the vertical line on the graph. Based on the vertical
line test, is this equation a function? Why or why not?

Answers

Answer: This equation is not a function.

Step-by-step explanation:

Ok, a function is something like a "machine".

It takes an input value, x, and transforms it into an output value, y.

Such that for every input x, the function can transform it into only one value of y.

for example, if we have a "function" f(x)

such that f(2) = 3 and f(2) = 4

(for the same input, x = 2, we have two different outputs)

Then this is not a function.

Now, the given equation is:

x^2 + y^2 = 5

This is actually the equation for a circle, centered at the point (0, 0) and with a radius equal to √5.

Then, if we want to transform it into y(x), we can see a problem

If x = 0, we have:

0^2 + y^2 = 5

y^2 = 5

then we have two possible values for y:

y = +√5

y = -√5

Then for one value of x, we have two values of y.

This means that this is not a function.

Answer:

No. The vertical line touches the graph at more than one point at once.

Step-by-step explanation:

I just did it

PLEASE HELP!!

Complete the equation.

(13)^2 (13)^-14 (13)^5 = 13 [ ]a0

Answers

Answer:

(13)^2 (13)^-14 (13)^5

=2197

Answer:

13^3

Step-by-step explanation:

-4+2+5=3

is it . that or something else ??

Th sum of a number and two is equal to eight
The equation?

Answers

Answer:

2+n = 8

Step-by-step explanation:

2+ something must equal 8.

8 minus 2 = 6

n=6

Answer:

Let the number be n.

According to question,

2+ n =8

=) n = 8-2

=) n =6

hope you understand.

Other Questions
A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contract- ing when it is cooled from 120.0C to 10.0C? Three crates with various contents are pulled by a force Fpull=3615 N across a horizontal, frictionless rollerconveyor system. The group of boxes accelerates at 1.516 m/s2 to the right. Between each adjacent pair of boxes is a force meter that measures the magnitude of the tension in the connecting rope. Between the box of mass m1 and the box of mass m2, the force meter reads F12=1387 N. Between the box of mass m2 and the box of mass m3, the force meter reads F23=2304 N. Assume that the ropes and force meters are massless. Is it (P)otential or (K)inetic energy In a LRC circuit, a second capacitor is connected in parallel with the capacitor previously in the circuit. What is the effect of this change on the impedance of the circuit Please answer this correctly without making mistakes 100 2/3 as a decimal If the function 5x + y = 1 has the domain {-2, 1, 6}, then what is the corresponding range? If the Fed carries out an open market operation and buys U.S. government securities, the federal funds rate ________ and the quantity of reserves ________. what is the difference between your town's minimum temperatures yesterday? In your answer, list one explanation for why temperature changes during the day. Blood pressure is determined by:________. A. estimating the degree of turbulence in a partly closed vessel. B. listening carefully to the pulse. C. measuring the size of the pulse. D. estimating the pressure needed to close off an artery with an external pressure cuff. E. measuring the force of contraction of the left ventricle. A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Could you use lines and text to draw and label a diagram that represents this situation? Henrietta has owned her house for over 50 years. It has fallen into disrepair, but because she lives on a fixed income, she does not have the money to make the needed repairs. She has a considerable amount of equity in the house. What type of loan would BEST provide Henrietta the funds to make the necessary repairs Winnie is 10 years younger than her boss Greg. In 8 years, Winnie will be half as old as Greg will be then. How old is Greg now? In science class, Jake mixed water with differing amounts of an unknown liquid. After mixing the liquids, he heated 20 milliliters (ml) of each mixture and observed how quickly it boiled. The table shows his results. "A legal owner of property has the right to use that property in any way they want to, and the power to give those rights to another. This is called" Do some online research on one of your favorite personalities. Then list some Spanish words that best describe his or her character and physicaltraits. There are 2 categories of me. There are 13 of me and each one has a specific function in the body. What nutrient am I? what are different risks a business can face? help meplz i want help i bad what are the differences between hyperbole and personification and give one example each