24. Factorise completely the expression: 7x-21+ 2xy - 6y​

Step-by-step explanation:

Step 1: Setting Up the Factors

Our roots are 3, 2, and -4 so

our factors are

[tex](x - 3)(x - 2)(x + 4)[/tex]

Step 2: Initial Test to see if the result equal 30

Let a be a constant, such we have

[tex]a(x - 3)(x - 2)(x + 4) = 30[/tex]

Plug in. 1 for x.

[tex]a(1 - 3)(1 - 2)(1 + 4) = 30[/tex]

[tex]a( - 2)( - 1)(5) = 30[/tex]

[tex]a(10) = 30[/tex]

[tex]a = 3[/tex]

So our equation is

[tex]3(x - 3)(x - 2)(x + 4)[/tex]

Or if you want it simplifed

[tex]3( {x}^{2} - 5x + 6)(x + 4) = 3( {x}^{3} + - {x}^{2} - 14x + 24) = 3 {x}^{3} - 3 {x}^{2} - 42x + 72[/tex]

Answer:

[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]

Step-by-step explanation:

General form of a cubic polynomial function with 3 roots:

[tex]f(x)=a(x-b)(x-c)(x-d)[/tex]

where:

Given roots:

Substitute the given roots into the general form of the function:

[tex]\implies f(x)=a(x-3)(x-2)(x-(-4))[/tex]

[tex]\implies f(x)=a(x-3)(x-2)(x+4)[/tex]

To find the value of a, substitute the given point (1, 30) into the equation:

[tex]\begin{aligned} f(1) & = 30\\\implies a(1-3)(1-2)(1+4) & =30\\a(-2)(-1)(5) & = 30 \\10a & = 30\\\implies a & = 3 \end{aligned}[/tex]

Therefore, the equation of the cubic polynomial function is:

[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]

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Answer:

letter c

Step-by-step explanation:

Using the slope concept, it is found that the thundercloud is 6.43 miles above the ground.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, we have that:

Hence:

tan(65º) = h/3.

h = 3 x tan(65º)

h = 6.43 miles.

The thundercloud is 6.43 miles above the ground.

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Answer:

C

Step-by-step explanation:

given the factors are (x - 7) and (x + 3)

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 3 = 0 ⇒ x = - 3

Answer:

x = 9

Step-by-step explanation:

x-2 = 7

you solve by adding 2 to both sides to maintain equality. and you add by 2 to cancel out the -2 to isolate the x.

x = 9

Answer:

19/40

Step-by-step explanation:

⅛ over 50

⅖ women

5 x 8 = 40

8 x 2 = 16

1 x 5 = 5

16 + 5 = 21

40 - 21 = 19

19/40

Answer:

19/40 are men under 50

Step-by-step explanation:

Given:

[tex]\begin{aligned}\textsf{Men under 50 yrs old} & = \textsf{total proportion of men} - \textsf{proportion of men over 50}\\\\& = \left(1-\dfrac{2}{5}\right)-\dfrac{1}{8}\\\\& = \dfrac{3}{5}-\dfrac{1}{8}\\\\& = \dfrac{3 \cdot 8}{5 \cdot 8}-\dfrac{1 \cdot 5}{8 \cdot 5}\\\\& = \dfrac{24}{40}-\dfrac{5}{40}\\\\& = \dfrac{19}{40}\end{aligned}[/tex]

To check this, let's assign a number to the total number of players and use this to help us calculate the proportion of players who are men under 50 years old.

Let the total number of video game players be 400.

If 2/5 of all video game players are women, then the proportion of all video game players that are men is:  1 - 2/5 = 3/5

⇒ total number of men = 3/5 of 400 = 3/5 × 400 = 240

If 1/8 of all video game players are men over 50 years old then:

⇒ number of men over 50 yrs old = 1/8 × 400 = 50

Therefore:

⇒ number of men under 50 yrs old = 240 - 50 = 190

Finally, the fraction of men under 50 years old from all video game players is the number of men under 50 divided by the total number of men.

⇒ men under 50 years old = 190/400 = 19/40

Answer: 59

Step-by-step explanation:

Order of operations.

52+6x(2)-5

52+12-5

64-5

59

Step-by-step explanation:

52+6×2-10/2

52+6×2-10÷2

52+6×2-5

52+12-5

64-5 =59

my answer is 59.

Answer:

the credit goes to create slavic language isSt. Cyril (or Constantine) and St. Methodius.

St. Cyril ( or Constantine) and St. Methodius are credited with creating an alphabet for several Slavic languages.

Here,

We have to find, Who is credited with creating an alphabet for several Slavic languages.

Who was Slavs?

Slavs are Indo-European people who speak the various Slavic languages of the larger Balto-Slavic linguistic group.

Now,

St. Cyril ( or Constantine) and St. Methodius are credited for creating an alphabet for several Slavic languages.

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The probability that she gets a number greater than 4 is 1/3

A six-sided number cube has the following properties:

Faces = 6

Numbers greater than 4 = 2

The probability that she gets a number greater than 4 is calculated as:

P = 2/6

Simplify

P =1/3

Hence, the probability that she gets a number greater than 4 is 1/3

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Answer:

44 pears and 52 apples

Step-by-step explanation:

pears are 8 more than apple so 52-8 = 44

Number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.

" Number is defined as the count of any given quantity as per given condition."

According to the question,

Given,

Total number of apples [tex]= 52[/tex]

[tex]'x'[/tex] represents the number of pears

[tex]'x+ 8'[/tex] represents the number of apples

As per the given condition required equation we get,

[tex]x + x + 8 = 52\\\\\implies 2x = 52-8\\\\\implies x = \frac{44}{2} \\\\\implies x = 22[/tex]

number of pears [tex]= 22[/tex]

number of apples [tex]= 22+8[/tex]

                              [tex]=30[/tex]

Hence, number of apples and pears in a box is equals to [tex]30[/tex] and [tex]22[/tex] respectively.

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Applying the negative exponent rule, the simplified form of  [tex]x^{-12}[/tex] is: [tex]\frac{1}{x^{12}}[/tex].

The negative exponent rule states that, if [tex]x^{-a}[/tex] then, it can be rewritten as, [tex]\frac{1}{x^a}[/tex].

Given the expression, [tex]x^{-12}[/tex], we can apply the negative exponent rule to rewrite the expression in simplified form as:

[tex]\frac{1}{x^{12}}[/tex].

Therefore, expressing  [tex]x^{-12}[/tex] in a simplified form will give us: [tex]\frac{1}{x^{12}}[/tex].

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The given statement is false.

What is the effect of a row operation on a determinant?

The factor by which a row operation intends to change the determinant is not equal to the determinant of the elementary matrix corresponding to that row operation. Rather, when a row is scaled up by a factor in a matrix, the determinant of that matrix also scales up by that factor.

Similarly, the factor by which a row operation changes the determinant is equal to the factor times the determinant of the elementary matrix corresponding to that row operation.

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Answer:

centre (5,0)

radius:9

I hope it will be helpfulness

Answer:

a)<BAC = EDC,<DEC =ABC,ACB=DFE
b)7

Step-by-step explanation:

According to the definition, two triangles are similar if their corresponding angles are congruent and corresponding sides are proportional. Hence, we can find the dimensions of one triangle with the help of another triangle. If ABC and DEF are two similar triangles, then by the help of below-given formulas, we can find the relevant angles and side lengths.

∠A = ∠D, ∠B = ∠E and ∠C = ∠F

AB/DE = BC/EF= AC/DF

Answer:

fuz what hhde you ha thewebsite and it

Answer:

The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 52 raised to the 3rd power is equal to 56.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

- 0.06 + 7.6p < - 127.74 ( add 0.06 to both sides )

7.6p < - 127.68 ( divide both sides by 7.6 )

p < - 16.8

Answer:

4:1

Step-by-step explanation

this should be the answer from how  u gave the question, also can i get brainliest ;)

The number of hours, h it will take 5 people to build the swing set is; 2.4 hours

From the task content, it follows that it took 6 hours for 2 people to build the swing set, hence, it follows that it'd take 12 hours for 1 person to build the swing.

However, when the work is divided between 5 People, the time taken is therefore; 12/5 = 2.4hours.

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(√3 + √11)² + (√3 - √11)²

Now ,

(√3 + √11)² + (√3 - √11)²

(3 + 11 + 2√3√11)+ (3 +11 - 2√3√11)

14 + 2√33+ 14 - 2√33

14 + 14 = 28

Hence , The value of (√3 + √11)² + (√3 - √11)² is 28 .

Answer:

28

Step-by-step explanation:

(a + b)² + (a - b)² = 2a² + 2b²

(√3 + √11)² + (√3 - √11)²

= 2√3² + 2√11²

= 28

Answer:

fair share

Step-by-step explanation:

all are equal.

In the given image, the length of JI is 6

From the question, we are to solve for JI

From the given image, we can write that

JI + IH = JH

Then,

2x + 28 + 5 = x + 22

Solving for x

2x + 28 + 5 = x + 22

First, collect like terms

2x - x = 22 - 28 - 5

Simplifying

x = -11

But,

JI = 2x + 28

∴ JI = 2(-11) + 28

JI = -22 + 28

JI = 6

Hence, the length of JI is 6

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Answer:

18

Step-by-step explanation:

closest whole numberd are 5, 8 and 5. 5 + 5 = 10 + 8

= 18.

Answer:

[tex]-\frac{1}{2} \vec {c}[/tex]

Step-by-step explanation:

Look at the component form of each vector.

Note that vector c is <4,4> and vector d is <-2,-2>

If one imagined the line that contained each vector, the line for both would have a slope of 1, because [tex]\frac{4}{4}=1=\frac{-2}{-2}[/tex]

Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).

If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector.  This means that there is some number "k", such that [tex]k \vec{c} = \vec {d}[/tex], or equivalently, [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex].

If [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex], we just need to substitute known values and solve for k:

[tex]kc_x=d_x\\k(4)=(-2)\\k=\dfrac{-2}{4}\\k=-\frac{1}{2}[/tex]

Double checking that k works for the y-coordinates as well:

[tex]kc_y=d_y[/tex]

[tex](-\frac{1}{2}) (4)[/tex]    ?    [tex](-2)[/tex]

[tex]-2=-2 \text{ } \checkmark[/tex]

So, [tex]-\frac{1}{2} \vec {c} = \vec {d}[/tex]

Answer:

Step-by-step explanation:

Look at the component form of each vector.

Note that vector c is <4,4> and vector d is <-2,-2>

If one imagined the line that contained each vector, the line for both would have a slope of 1, because

Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).

If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector.  This means that there is some number "k", such that , or equivalently,  and .

If  and , we just need to substitute known values and solve for k:

Double checking that k works for the y-coordinates as well:

   ?    

So,

Answer:

600

Step-by-step explanation:

15*40=600

The number of  ways that he can make the fruit salad if it must contain watermelon is 35.

Selection of the one object from the given samples with replacement or without replacement is called as the permutation. The selection of the items from the sample as they are different with each other.

The salad contains water melon, now we have to select 4 more fruits out of 7.

Using combination

[tex]^{n{C}_r[/tex] = n! / r! (n-r)!

[tex]^{7}C_4[/tex] = 7!/ 4! (7-4)!

      = 7*6*5*4! / 4! * 3*2

      = 35

Hence,  number of ways that he can make the fruit salad if it must contain watermelon is 35.

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Answer: 35 on edge got it right

Step-by-step explanation:

The composite function (boa)(x) is equivalent to √3x-3

Given the following functions

a(x) = 3x +1

b(x) = √x - 4

To determine the composite function (boa)(x)

b(a(x) = b(3x +1)

Substitute 3x + 1 into b(x) to have:

(boa)(x)= √(3x + 1) - 4

(boa)(x) = √3x-3

Hence the composite function (boa)(x) is equivalent to √3x-3

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At x = -1 the value of y will be equal to -2 for the equation y = 3x + 1.

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

Given that:-

The equation will be solved as:-

Y = 3x + 1

Y = 3 ( -1 ) + 1

Y = -3 + 1

Y = -2

I have also plotted the graph of the two equations in the graph the two equations intersect at the point x = 1 and y = -2 so the solution of the equations will be ( -1, -2 ).

Therefore At x = -1 the value of y will be equal to -2 for the equation y = 3x + 1.

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Answer:

????????????????????????????????????????/

Step-by-step explanation: