Factorise completely 8p-12pq​

Answer:

x = 2

Step-by-step explanation:

Collinear means that the points A, B and C all lie in a straight line, hence

AB + BC = AC, substitute values

5x - 1 + 14 = 25 - x

5x + 13 = 25 - x ( add x to both sides )

6x + 13 = 25 ( subtract 13 from both sides )

6x = 12 ( divide both sides by 6 )

x = 2

The value of x is:

                     [tex]x=2[/tex]

Three points are said to be collinear if they lie along a straight line.

Also, it is given that:

Here A, B, and C are collinear points and B is between A and C.

This means that:

           [tex]AB+BC=AC-----------(1)[/tex]

Also we are given:

[tex]AB=5x-1,\ BC=14,\ AC=25-x[/tex]

Using property (1) we have:

[tex]5x-1+14=25-x\\\\i.e.\\\\5x+13=25-x[/tex]

Now on adding x on both the side of the equation we have:

[tex]5x+13+x=25\\\\i.e.\\\\5x+x+13=25\\\\i.e.\\\\6x+13=25[/tex]

Now on subtracting 13 on both the sides of the equation we have:

[tex]6x=25-13\\\\i.e.\\\\6x=12\\\\i.e.\\\\x=\dfrac{12}{6}\\\\i.e.\\\\x=2[/tex]

ANSWER

a) Use the homogeneous property of the binomial expansion to find the missing exponent

b) Use the binomial theorem to find the coefficient

EXPLANATION

The given binomial expansion is:

[tex](x+y)^{12} [/tex]

When we compare this to

[tex](a + b) ^{n} [/tex]

We have

[tex]n = 12[/tex]

Therefore the of each term in the expansion must be 12.

[tex] \implies \: 7 + b = 12[/tex]

[tex]b = 12 - 7[/tex]

[tex]b = 5[/tex]

Since the coefficient of x and y are unity, we use the formula

[tex]^{n} C_r = \frac{n!}{(n - r)!r!} [/tex]

to find the coefficient.

Where n=12 and r=5(the exponent of the y-term).

Therefore the coefficient is

[tex]^{12} C_5= \frac{12!}{(12- 5)!5!} [/tex]

[tex]^{12} C_5= \frac{12!}{7!5!} [/tex]

[tex]^{12} C_5= \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{7! \times 5 \times 4 \times 3 \times 2 \times 1} [/tex]

When we simplify further we get:

[tex]^{12} C_5= 11 \times 9 \times 8 = 792[/tex]

Answer:

The owner needs to mix 11 pounds of chocolate

Step-by-step explanation:

Let

x ----> the number of pounds of chocolate needed

we know that

The linear equation that represent this problem is equal to

[tex]18.90x+3.30(22)=8.50(x+22)[/tex]

solve for x

[tex]18.90x+72.6=8.50x+187[/tex]

[tex]18.90x-8.50x=187-72.6[/tex]

[tex]10.4x=114.4[/tex]

[tex]x=114.4/10.4[/tex]

[tex]x=11\ pounds[/tex]

Answer:

19 is the next number

Step-by-step explanation:

5+2=7

7+3=10

10+4=14

14+5=19

The next number in the pattern is 19.

To complete the number pattern 5, 7, 10, 14, we observe that the differences between the numbers increase by 1. Continuing this pattern, we add 5 to the last number, which results in 19. Thus, the next number in the pattern is 19

To complete the given number pattern: 5, 7, 10, 14, we need to find the rule that governs the pattern. Let's look at the differences between the numbers:

We can see that the differences are increasing by 1 each time. If this pattern continues, the next difference should be 5. So we add 5 to the last number in the pattern:

14 + 5 = 19

Therefore, the next number in the pattern is 19.

Answer:

V=100.63 cubic feet

Step-by-step explanation:

The formula for the volume of the cube is given as

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

Where r=4.3 ft

And h is height = 5.2 ft

Now we put the value of h and r in the formula for volume

[tex]V=\frac{1}{3}\times \pi \times 4.3^{2} \times 5.2[/tex]

[tex]V=\frac{1}{3}\times \pi \times 96.148[/tex]

[tex]V=\frac{1}{3}\times 3.14 \times 96.148[/tex]

[tex]V=\frac{1}{3}\times 301.904[/tex]

V=100.63 cubic feet

To compute the volume of a cone, one needs to use the formula 1/3πr²h, where 'r' represents the radius of the base and 'h' represents the height of the cone. The specific dimensions of the cone are needed to provide a concrete answer. The given options can't be validated without these details.

Without specific parameters such as the radius and height of the cone, we cannot directly calculate the volume of the cone. However, the general formula for finding the volume of a cone is 1/3πr²h, where r represents the radius of the base and h represents the height of the cone. This formula is derived from the geometric principles of a cone's structure. Once the values of r and h are known, they can be substituted into this formula to compute the volume. The answer would then be rounded to the nearest hundredth if necessary. Unfortunately, the choices provided A.32.05 cubic feet, B.38.39 cubic feet, C.56.54 cubic feet, D.100.69 cubic feet aren't helpful without knowledge of the specific cone dimensions.

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the simple fact that 94 is 49 backwards means nothing, anymore than say 001 and 100 are equal quantities or related other than in the digits.

so, 0.49 or 49/100 and 0.94 or 94/100, are two values, both are at the one hundredth level, so to see who is larger, we can nevermind the 100 and look at the numerator, 94 is clearly much larger than 49.

A. the product of the difference of x and 5 and the sum of x and 3.

Not really sure how I should explain this because the answer is just the expression in word form.

The expression (x - 5)(x + 3) correctly corresponds to 'the product of the difference of x and 5 and the sum of x and 3', matching option OA.

The expression (x - 5)(x + 3) is the product of two binomials: the first binomial is the difference of x and 5, and the second binomial is the sum of x and 3. Therefore, the correct description of the expression is 'the product of the difference of x and 5 and the sum of x and 3', which corresponds to option OA. This understanding illuminates how binomials are multiplied and underscores the significance of recognizing the individual terms within the expression to comprehend its meaning and structure effectively.

The answer is:

The fabric will cost $4.58

D.$4.58

Since it's a conversion exercise, we need to pay special attention to the conversion procedure.

From the statement we know that:

[tex]1ft=0.305m[/tex]

So, if she needs 10 feet of fabric, we need to convert it to meters, and then, calculate its cost.

We have that:

[tex]10*1ft=10*0.305m\\\\10ft=3.05m[/tex]

Now, we have that each meter of fabric cost $1.50, so, 3.05m of fabric will cost:

[tex]\frac{1m}{1.50(dollars)}=\frac{3.05m}{cost}\\\\cost=\frac{3.05m*1.50(dollars)}{1m}=4.575(dollars)=4.58(dollars)[/tex]

Hence, we have that the cost of the fabric will be $4.58.

The correct option is: D.$4.58​

Have a nice day!

Answer:

Sarah will need $4.58 for the fabric. therefor, your answer will be...

D: $4.58

Answer:

22

Step-by-step explanation:

With a kite, the top 2 segments are always equal, and the bottom 2 segments are always equal. Also, if you look at the little red lines on the sides, you can see that AD and CD have 2, that means they are the same length

(Also can you please rate this answer as brainliest? I need it to level up.)

Answer:

22 units

Step-by-step explanation:

AD = CD because the two little line marks means they are equal to each other

AD = 22

Answer:

6% ( to nearest percent )

Step-by-step explanation:

The percentage change is calculated as

[tex]\frac{change}{original}[/tex] × 100%

Change = 90 - 85 = 5, hence

percent change = [tex]\frac{5}{85}[/tex] × 100% = [tex]\frac{5(100)}{85}[/tex] = 6%

Answer:

Here, you have to calculate the percentage(%) of change.

To calculate this, you have to use this formula-:

[tex] { \bold{\mathfrak{\frac{change}{new} \times 100}}}[/tex]

Step-by-step explanation:

[tex] = \frac{5}{90} \times 100[/tex]

[tex] = \frac{50}{9 }[/tex]

[tex] = 5.55555[/tex]

Now, you have to round of this percentage to the nearest....

And that will be => 6%.

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Answer:Maybe if you studded you would have the answer young man

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that A tank holds 17 3/5 gallons after losing 36 2/3 gallons, 4 5/6 gallons,and 27 1/12 gallons in 3

Consecutive days. If at the beginning the tank was 20 3/4 gallons short of capacity.

Tank full capacity = loss for 3 days + holding of tank after losing + shortage of capacity

To add these first let us convert these into improper fractions, then take lcd to add

Full capacity = [tex]\frac{88}{5} +\frac{110}{3} +\frac{29}{6} +\frac{325}{12} \\=\frac{88}{5} +\frac{440+58+325}{12} \\=\frac{1056+4115}{60} =[/tex][tex]=86.183[/tex] gallons

Answer:

Step-by-step explanation:

first find one side:

18^2+10^2=c^2, so c=20.59

we need to find the length of one of the sides of the remaining triangle:

20.59^2+2^2=c^2

c=20.68 = the diagonal.

Answer:

2 square root 107

Step-by-step explanation:

Answer:

[tex]\large\boxed{D.\ -x^2+2x+8}[/tex]

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=2x+1,\ g(x)=x^2-7\\\\\text{substitute:}\\\\(f-g)(x)=(2x+1)-(x^2-7)=2x+1-x^2-(-7)=2x+1-x^2+7\\\\=-x^2+2x+(1+7)=-x^2+2x+8[/tex]

Answer:

Option A. [tex]f(x)=86[1.04]^{x}[/tex] ; grows approximately at a rate of 0.4% daily

Step-by-step explanation:

we have

[tex]f(x)=86(1.29)^{x}[/tex]

where

f(x) the number of weeds in the garden

x ----> the number of weeks

Calculate how quickly the weeds grow each day

Remember that a week is equal to seven days

so

[tex]f(x)=86(1.29)^{\frac{x}{7}}[/tex]

Using the law of exponents

b^(x/a) = b^(x*(1/a)) = (b^(1/a))^x

so

[tex]f(x)=86[(1.29)^{\frac{1}{7}}]^{x}[/tex]

[tex]f(x)=86[1.04]^{x}[/tex]

therefore

The rate is approximately

1.04=1+r

r=1.04-1=0.04=4% daily

not sorry, but guy above is w.r.o.n.g

0.4 ain't right

yw for saving you an attempt

Answer:

D. 21.

Step-by-step explanation:

The general form of the equation of a circle is:

(x - a)^2 + (y - b)^2 = r^2  where r is the radius.

Comparing:

(x + 5)^2 + (y + 7)^2 = 21^2

So r^2 = 21^2

making r = √21^2

= 21.

The length of the radius of the circle is 21.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Standard form of a circle is given by the equation,

(x - h)² + (y - k)² = r²

where, (h, k) is the center of the circle and r is the radius of the circle.

Here, given equation is,

(x + 5)² + (y + 7)² = 21²

Comparing this with the standard form,

(-5, -7) is the center and 21 is the radius.

Hence the correct option is D. 21.

Learn more about Circles here :

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Answer:

1.182

Step-by-step explanation:

z is inversely proportional to x:

z = k / x

When x is 4, z is 3.25:

3.25 = k / 4

k = 13

When x = 11:

z = 13 / 11

z ≈ 1.182

1. constant

2. -7 < x < -3

3. (-5,8)

Answer:

r ≤ 29, r-5, The sale price can be compared with the regular price, r-5 ≤ 24

Step-by-step explanation:

The regular price will be at most $5 more than the amount Roopesh has to spend.

The sale price will be $24 or less than that for Roopesh to afford.

Inequality for regular price :

r-5 ≤ 24

r ≤ 29

Therefore, the product Roopesh can afford is $29 or less than that.

!!

Answer:

So we have x+3 if -3<=x<=-1

and                5   if   -1<=x<=1

Step-by-step explanation:

The one piece from -1 to 1 is horizontal so the line is in the form of y=a number.  It goes through 5 on the y-axis so the equation there is y=5.

From -3 to -1, that is a line with positive slope (since that part is increasing).

Slope=rise/run

We see from the filled in dot to the unfilled in dot that the rise is 2 and the run is 2 so the slope is 2/2=1.

So if we did extend this line where we go at on the y-axis?  It would go through 3 because starting from the unfilled dot and rising 1 and running 1 will get us to the 3 on the y-axis.

The equation of a line in slope-intercept form is y=mx+b.

We have m=1 and b=3 so the equation is y=1x+3 or just y=x+3.

So we have x+3 if -3<=x<=-1

and                5   if   -1<=x<=1

Answer:

[tex]\large\boxed{f(x)=\left\{\begin{array}{ccc}x+3&,\ \text{if}\ -3\leq x<-1\\5&,\ \text{if}\ -1\leq x\leq1\end{array}\right}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

Read coordinates of the two points on the first piece:

(-3, 0) and (-2, 1).

Calculate the slope:

[tex]m=\dfrac{1-0}{-2-(-3)}=\dfrac{1}{1}=1[/tex]

Put it and coordinates of the point (-3, 0) to the equation of a line:

[tex]0=1(-3)+b[/tex]

[tex]0=-3+b[/tex]          add 3 to both sides

[tex]3=b\to b=3[/tex]

[tex]\boxed{y=x+3}[/tex]

Read coordinates of the two points on the second piece:

(-1, 5) and (1, 5) - second coordinates are the same.

It's a horizontal segment. Therefore the equation is [tex]y=5[/tex]

ANSWER

Answer:

See below in bold.

Step-by-step explanation:

(x²-2xy+y²)+(x²+2xy+y²)

= x²-2xy+y²+ x²+2xy+y²

= 2x² + 4xy + 2y².

(x²-2xy+y²)-(x²+2xy+y²)

= x²- 2xy + y²- x² - 2xy - y²

= -4xy.

Answer:

2

Step-by-step explanation:

If the constant of proportionality is k then,

y=kx

What number do we multiply by x to get y?

The constant of proportionality is 2.

Answer:

8 x + 38 higher it is not available

central angle/360 = arc length/2pi•r

Let π = pi

Let A = length of intercepted arc

45/360 = A/2(20)π

1/8 = A/40π

8A = 40π

A = 40π/8

A = 5π

Did you follow?

Answer:

The length of the arc is 5π inches

Step-by-step explanation:

* Lets explain the relation between the central angle and its

 intercepted arc

- If the vertex of an angle is the center of the circle and the two sides

 of the angle are radii in the circle, then this angle is called  a

 central angle

- Each central angle subtended by the opposite arc, the name of the

 arc is the starting point and the ending point of the angle

- There is a relation between the central angle and its  subtended arc

 the measure of the central angle equals half the measure of its

 subtended arc

- The length of the subtended arc depends on the measure of its

 central angle and the length of the radius and the measure of the arc

- The measure of the circle is 360°

- The length of the circle is 2πr

- The length of the arc = central angle/360 × 2πr

* Now lets solve the problem

∵ The radius of the circle r = 20 inches

∵ The measure of the central angle is 45°

∵ The length of the arc = central angle/360 × 2πr

∴ The length of the arc = 45°/360° × 2 × π × 20 = 5π

* The length of the arc is 5π inches

Answer:

x = 2/3 , y = -23/12

Step-by-step explanation:

Solve the following system:

{-7.5 x - 1.2 y = -2.7

{1.2 y - 1.5 x = -3.3

In the first equation, look to solve for x:

{-7.5 x - 1.2 y = -2.7

{1.2 y - 1.5 x = -3.3

-7.5 x - 1.2 y = -(15 x)/2 - (6 y)/5 and -2.7 = -27/10:

{-(15 x)/2 - (6 y)/5 = -27/10

Add (6 y)/5 to both sides:

{-(15 x)/2 = 3/10 (4 y - 9)

{1.2 y - 1.5 x = -3.3

Multiply both sides by -2/15:

{x = 1/25 (9 - 4 y)

{1.2 y - 1.5 x = -3.3

Substitute x = 1/25 (9 - 4 y) into the second equation:

{x = 1/25 (9 - 4 y)

{1.2 y - 0.06 (9 - 4 y) = -3.3

1.2 y - 0.06 (9 - 4 y) = 1.2 y + (0.24 y - 0.54) = 1.44 y - 0.54:

{x = 1/25 (9 - 4 y)

{1.44 y - 0.54 = -3.3

In the second equation, look to solve for y:

{x = 1/25 (9 - 4 y)

{1.44 y - 0.54 = -3.3

1.44 y - 0.54 = (36 y)/25 - 27/50 and -3.3 = -33/10:

(36 y)/25 - 27/50 = -33/10

Add 27/50 to both sides:

{x = 1/25 (9 - 4 y)

{(36 y)/25 = -69/25

Multiply both sides by 25/36:

{x = 1/25 (9 - 4 y)

{y = -23/12

Substitute y = -23/12 into the first equation:

Answer: x = 2/3 , y = -23/12

Answer:

x = 2/3  y = -23/12

Step-by-step explanation:

- 7.5x - 1.2y = -2.7

- 1.5x + 1.2y = -3.3​

Add the equations together

- 7.5x - 1.2y = -2.7

- 1.5x + 1.2y = -3.3​

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

-9x                 = -6

Divide each side by -9

-9x/-9 =-6/-9

x =2/3

Now we need to find y

-1.5 (2/3) +1.2y = -3.3

-1 +1.2y = -3.3

Add 1 to each side

-1+1 +1.2y = -3.3+1

1.2y = -2.3

Divide by 1.2

1.2y/1.2 = -2.3/1.2

y =-23/12

Answer:

The 12 ( after 28) should be 14.

This 12 does not belong to the series.

Step-by-step explanation:

After every 2 numbers,  2 is added to the last number, so we have 100-50 + 2 = 52 - 26, and the second of the paired numbers is 1/2 of the first.

So after  28 the numbers should be 14 - 16 - 8 - 10.  The 12 does not belong.

For this case we have that by definition, the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle

How do we have to:

[tex]A = 64 \ ft ^ 2[/tex]

So:

[tex]64 = \pi * r ^ 2[/tex]

We take[tex]\pi = 3.14[/tex]

[tex]r ^ 2 = \frac {64} {3.14}[/tex]

We apply square root:

[tex]r = \pm \sqrt {\frac {64} {3.14}}[/tex]

We choose the positive value:

[tex]r = 4,515[/tex]

If we round we have that the radius is 4.5 feet.

Answer:

4.5 feet

Answer:

The volume of the stairway is

720 cubic inches

Step-by-step explanation:

we know that

The volume of the stairway is equal to the volume of two rectangular prism

The volume of the rectangular prism is equal to

[tex]V=LWH[/tex]

Find the volume of the larger rectangular prism

we have

[tex]L=6\ in[/tex]

[tex]W=10\ in[/tex]

[tex]H=4+4=8\ in[/tex]

substitute

[tex]V=(6)(10)(8)=480\ in^{3}[/tex]

Find the volume of the smaller rectangular prism

we have

[tex]L=6\ in[/tex]

[tex]W=10\ in[/tex]

[tex]H=4\ in[/tex]

substitute

[tex]V=(6)(10)(4)=240\ in^{3}[/tex]

Find the volume of the stairway

Adds the two volumes

[tex]V=480+240=720\ in^{3}[/tex]

Answer:

Option B

Step-by-step explanation:

We have to calculate the volume of concrete used to create the stairway given in the picture.

Volume of the stairway = volume of small stairway + volume of larger stairway

Dimensions of Large stairway = 10 in × 6 in × (4+4)in

                                                 = 10 in × 6 in × 8 in.

Therefore, volume of large stairway = 480 in³

Dimensions of small stairway = 10 in × 6 in × 4 in

                                                = 240 in³

Total volume = 480 + 240

                     = 720 in³

Option B is the answer.

Answer: For part A, Yakob has 9 friends that like Maths best, 6 friends that like History the best, & 15 friends that prefer either English or Science the best.

Part B: There's a graph I made below.

Step-by-step explanation:

You have to use proportions to answer this question. The bar graph is 10 cm total, therefore it is proportional to the 30 friends that Yakob has in total. After that, you can make proportions out of the data in the chart. For example, History is 2 cm out of the 10 cm total. Think proportions! You had to multiply 3 to 10 to get 30, so you have to apply the same thing to the numerator. In this case, multiply 3 to 2 and you'll get 6. 2/10=6/30! I repeated that for the rest and put it into a graph. The prompt wanted you to combine English and Science, so I did that after separately making their proportions. Hope this helps!