Factorise fully the following:

4x² + 28x³

The least possible height of AB is 3.650 m.

What is a word problem?

A word problem is described as a few phrases outlining a "real-life" situation where a problem needs to be solved using mathematics.

For everything from counting pennies to calculating a tip, we can employ the three primary sorts of word problems: part-part whole, separate and join, and multiply and divide.

Given, CD=2.6 m,  BD=12 m

From the figure,

or, tan x = [tex]\frac{AB - 2.6}{12}[/tex]

or, tan 5  [tex]\leq \frac{AB - 2.6}{12}[/tex]

When AB be least, then

[tex]\frac{AB - 2.6}{12}[/tex] = tan 5

or, AB = (12*tan 5) + 2.6

or, AB = 3.650 m

Hence, the least possible height of the  AB is 3.650 m.

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Answer:

x = 1

y = -1

Step-by-step explanation:

6x + 3y = 3 -------------(1)

3x - y = 4 ----------------(2)

Multiply Eq. (2) by 2

2(3x - y) = 4 × 2

6x - 2y = 8 -------------(3)

Subtract Eq. (3) from Eq. (1)

6x + 3y - (6x - 2y) = 3 - 8

6x + 3y - 6x + 2y = -5

3y + 2y = -5

5y = -5

Divide 5 to both sides

y = -5/5

Put y = -1 in Eq. (1)

6x + 3(-1) = 3

6x - 3 = 3

Add 3 to both sides

6x = 3 + 3

6x = 6

Divide 6 to both sides

[tex]\rule[225]{225}{2}[/tex]

The probability is the first and the second case will be 0.625 and 0.3683, respectively.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A pack contains five white balls and three torpedoes. You want to draw two white balls.

Total events = 5 + 3

Total events = 8

You all the while drawing two balls aimlessly. Then the probability that they are both white is given as,

P = 5 / 8

P = 0.625

You all the while drawing two balls aimlessly. Whenever you have drawn two balls, you set back any debases, and redraw with the goal that you again have two drawn balls. Then the probability is given as,

P = [(3/8) x (5/8)] + [(3/8) x (5/8) x (4/7)]

P = (15 / 64) + (60 / 448)

P = 0.3683

The probability is the first and the second case will be 0.625 and 0.3683, respectively.

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Answer:

y = 5/2x + 11.5

Step-by-step explanation:

(-3, 4) (-5, -1)

m = -1-4/ -5+3

m = -5 / -2

m = 5/2

y = 5/2x + b

-1 = 5/2(-5) + b

-1 = -12.5 + b

b = 11.5

y = 5/2x + 11.5

Answer:

y-y1=y2-y1/x2-x1(x-x1)

y-4= (-1-4/-5+3) (x+3)

y-4= -5/-2(x+3)

y=5/2x+15/2+4

y=5/2x+15+8/2

y=5/2x+23/2

1) h=1/5 k

(10/2 = 1/5, 20/4 = 1/5... etc)

2) k=5/4 h

(5/4 = 5/4, 10/8=5/4... etc)

3) h=5/1 k

(25/5 = 5/1, 30/6 = 5/1 ... etc)

Hope this helps!

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The value of x inside the triangle is 24°

How to calculate the value of x(angle)?

The angle of the straight line = 180°

156° + x = 180°

x = 180° - 156°

x = 24°

Hence, the value of x inside the triangle is 24°.

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The minimum number of dogs 24kg is 6 and the maximum number of dogs is 18    

The highest amount or value or number that may be obtained or reached or can be counted is the Maximum value                              

The least amount or value or number that may be admitted or reached or can be counted is the Minimum value            

Here we have a table  

Which represents the masses of various dogs

Mass (x) kg          frequency  

0 ≤ x < 10                    2

10 ≤ x < 20                  7

20 ≤ x < 30                12

30 ≤ x < 40                 6      

Here the mass of dogs is represented in class intervals

a) The minimum number of dogs with a mass of more than 24kg.

From the given table,

24 kg will lie in class intervals 20 ≤ x < 30, and 30 ≤ x < 40                      

In class interval 20 ≤ x < 30, there is a possibility that the mass of dag will be less than 24 kg since it started from 20 kg and is up to 30 kg  

In class interval 30 ≤ x < 40, there is no possibility that the mass will be less than 24 kg since it started from 30 kg and is up to 40 kg

So The minimum number of dogs that have a mass of more than 24kg the frequency of class interval 30 ≤ x < 40

Therefore,

The minimum number of dogs with a mass of more than 24kg is 6

b) The maximum number of dogs that have a mass of more than 24kg.

To get the maximum number of dogs we need to take the class interval of 20 ≤ x < 30 as in this the mass could be more than 24 kg.

And in class 30 ≤ x < 40 the mass will be more than 24 kg.

Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18

Therefore,

The maximum number of dogs with a mass of than 24kg is 18    

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Apply the fraction rule model can be used to find 4/5 divided by 1/10.

What is  fraction rule?

For fractions to be added or subtracted, their denominators must match (the bottom value). the same denominators are used for addition and subtraction. It only requires adding or subtracting the numerators if the denominators are already equal.

[tex]$\frac{\frac{4}{5}}{\frac{1}{10}}$[/tex]

Apply the fraction rule: [tex]$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}$[/tex]

[tex]$=\frac{4 \cdot 10}{5 \cdot 1}$[/tex]

Cancel [tex]$\frac{4 \cdot 10}{5 \cdot 1}: 8$[/tex]

=8

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Answer:

Step-by-step explanation:

If -8 is less than or equal to w, and 3 is greater than or equal to w, then we can combine these two inequalities into a single inequality by combining the left and right sides:

-8 ≤ w ≤ 3

This inequality can be read as "w is greater than or equal to -8 and less than or equal to 3." It represents all values of w that are greater than or equal to -8 and less than or equal to 3, including -8 and 3.

I hope this helps! Let me know if you have any questions.

Answer:

The amount left with her si 62.25

The simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.

What is the domain of the function?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

1.6y+y-4/15y+7/6y=21/3

Move all terms to the left:

1.6y+y-4/15y+7/6y-(21/3)=0

Domain of the equation: 15y!=0

y!=0/15

y!=0

y∈R

Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R

Add all the numbers together, and all the variables

1.6y+y-4/15y+7/6y-7=0

Add all the numbers together, and all the variables

2.6y-4/15y+7/6y-7=0

calculate fractions

2.6y+(-24y)/90y²+105y/90y²-7=0

multiply all the terms by the denominator

(2.6y) * 90y² + (-24y) + 105y - 7 * 90y² = 0

Add all the numbers together, and all the variables

(2.6y) * 90y² + (-24y) + 105y - 7 * 90y² = 0

Add all the numbers together, and all the variables

105y+(+2.6y)*90y² + (-24y) - 7*90y² = 0

multiply elements

-630y+105y+(+2.6y)*90y² + (-24y) = 0

get rid of parentheses

-630y² + 105y + (+2.6y)*90y² - 24y = 0

Add all the numbers together, and all the variables

-630y² + 81y + (+2.6y) * 90y² = 0

Hence, the simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.

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Answer:

  75°

Step-by-step explanation:

You want to know the measure of the image angle B'C'A' after angle A'B'C' is dilated by a factor of 4 about point P. Angle BCA is 75°.

Dilation does not affect angle measures, so angle B'C'A' has the same measure as angle BCA, 75°.

  m∠B'C'A' = 75°

Answer:

Below

Step-by-step explanation:

a + c = 240      re-arrange to   c = 240-a

revenue from child tix = 8.50 ( 240-a)

revenue from adult tix = 12.50 a              summed, the revenues = 2400

8.5(240-a)     +      12.5 a       = 2400

2040   - 8.5 a   + 12.5 a   = 2400

                     4.5 a  = 360

                          a = 80 tix        then c = 240 - a = 160 tix

The probability of choosing red ribbon on both Monday and Tuesday is 1/4.

What is the probability?

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

Given that each morning Tess chooses either red ribbon or blue ribbon at random to wear in her hair.

That means probability of choosing between blue or red is 1/2 in one morning.

Now the probability of choosing red ribbon on both Monday and Tuesday,

1/2 × 1/2

= 1/4

Therefore, the probability of choosing red ribbon on both Monday and Tuesday is 1/4.

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Answer:

See below

Step-by-step explanation:

320 x .1 = 32

320 + 32 = 352

352 x .5 = 176

352 + 176 = 528

320 x .65 = 208

320 + 208 = 528

The proof is shown in the image.

Reasons for statement

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The indefinite integral of given integral ∫√(9+49x^2)dx is ∫√(9+49x^2)dx = [tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex].

In the given question we have to find the indefinite integral.

The given integral is

∫√(9+49x^2)dx

Now finding the indefinite integral using the C for the constant of integration.

An integral is regarded to be indefinite if it has no lower or upper bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C.

We can write it as:

[tex]\int\sqrt{(9+49x^2)}dx = \int\sqrt{[(3)^2+(7x)^2]}dx[/tex]

Taking common 7^2

[tex]\int\sqrt{(9+49x^2)}dx = 7\int\sqrt{[(3/7)^2+(x)^2]}dx[/tex]

Using the formula

[tex]\int\sqrt{(a^2+x^2)}dx = \frac{1}{2}\times\sqrt{a^2+x^2} + \frac{1}{2}\cdot a^2In|x+\sqrt{a^2+x^2}|+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{(3/7)^2+x^2}+\frac{1}{2}\cdot(\frac{3}{7})^2In|x+\sqrt{(3/7)^2+x^2}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{9/49+x^2}+1/2\cdot(9/49)In|x+\sqrt{(9/49)+x^2}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+1/2\cdot(9/49)In|x+\frac{\sqrt{9+49x^2}}{7}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+(9/98)In|\frac{7x+\sqrt{9+49x^2}}{7}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex]

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Answer:

1:4

Step-by-step explanation:

4:16 = 1:?

4/4 = 1

16/4 = 4

= 1:4

Answer:

A Square

B Square

C Circle

D Triangle

Answer:

Below

Step-by-step explanation:

6m + 8+4+3m    <==== 6 and 3 are coefficients    8 and 4 are constants

9m + 12    <===== 9 is a coefficient   12 is a constant

Answer:

The coefficients are 6 and 3

The constants are 8 and 4

Step-by-step explanation:

coefficients are the numbers before the letters.

Constants do not have letters.

Hello,

I hope you and your family are doing well!

To write an expression that is equivalent to 2/3 (4x + 9), you can simply distribute the 2/3 over the parentheses:

2/3 (4x + 9) = (2/3 * 4x) + (2/3 * 9)

This simplifies to:

2/3 (4x + 9) = (8/3)x + (18/3)

Therefore, an expression that is equivalent to 2/3 (4x + 9) is (8/3)x + (18/3).

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Happy Holidays & New Year!

Answer: 2 2/3x + 6

Step-by-step explanation: 1 of 3 ways to find how to make the equivalent is to use the distributive property. So, that means we need to multiply or distribute 2/3 to both 4x and 9. So, 2/3 x 4 is roughly 2 2/3. Also, 2/3 x 9 = 6. So, I combined the like terms to get 2 2/3x + 6 as my equivalent expression. I hope this helps.

The ordered pair of the inequality 6x + 5y < -15 are (2, 0) and (3, 2).

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Considering the provided inequality and the provided ordered pairs, we will check it by replacing one by one in the inequality; if the inequality is fulfilled, they are the solution; otherwise, they are not, so we obtain:

(2, 0):

6x + 5y > 2

6(2)+5(0)>2

12+0>2

12>0

Since the inequality holds, then the ordered pair is a solution.

(7, -8):

6x + 5y > 2

6(7)+5(-8) > 2

42-40>2

2>2

Since the inequality is not satisfied, then the ordered pair is not a solution.

(3, 2):

6x + 5y > 2

6(3)+5(2) >2

18+10>2

28>2

Since the inequality holds, then the ordered pair is a solution.

(-8, 6):

6x + 5y > 2

6(-8)+5(6) >2

-48 + 30 > 2

-18 > 2

Since the inequality is not satisfied, then the ordered pair is not a solution.

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The required value of the production at which the company attained the same profit is 4 thousand skin care items.

Given that,

A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t³ + 8t² + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million.

Here,
Plotting the graph of the polynomial equation,

P(t) = –2t³ + 8t² + 2t,
From the graph at x = 4,
The polynomial gives the same value as it gave at x = 1,

Thus, the required value of the production at which the company attained the same profit is 4 thousand skin care items.

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The correct answer is option B which is  -1.67 is the expected value.

It is a branch of mathematics that deals with the occurrence of a random event.

You have a higher probability of losing money than gaining it due to the distribution of probability.  

There are more chances to lose than win.

As a result, you are expected to lose money.

Only -1.67 is the only negative option, which means that we don't even need to do real math since there's already only one choice.

Hence, the correct answer is option B which is  -1.67 is the answer.

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Answer:

You will Gain 5 points.

Step-by-step explanation:

Got it right on the test!

Answer:

A = 25t + 300

B = 55t + 150

Less than 5 hours, company B would be cheaper.  At 5 hours the cost is equal.  After 5 hours, company A would be cheaper.

Step-by-step explanation:

Company B would be cheaper for lower hours.

The the two equation equal to each other and solve for to find out when the costs will be equal.

25t + 300 = 55t + 150  Subtract 25t from both sides

300 = 30t + 150  Subtract 150 from both sides

150 = 30t  Divide both sides by 30

5 = t

At 5 hours the cost are the same, after 5 hours company A would be cheaper.

Negative 2.5 x greater-than-or-equal-to negative 30 is the equivalent expression of 50 minus 2.5 x greater than or equal to 20

Equivalent expressions can be defined as expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will give you the same value when you simplify

Given: 50 minus 2.5 x greater than or equal to 20

50 - 2.5x ≥ 20

Subtract 50 from both sides:

-2.5x ≥ 20-50

-2.5x ≥  -30

Therefore, the equivalent expression is "negative 2.5 x greater-than-or-equal-to negative 30"

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Answer:

Below

Step-by-step explanation:

For REAL numbers, the discriminant of the Quadratic Formula has to be a positive value (or zero)

b^2 - 4ac   >= 0         where   a = m       b = m-2        c = -m-1  

(m-2)^2 - 4(m)(-m-1) >=0  

5m^2 +4   >= 0      

       5 m^2 +4     <===== will always be >= 0   for any value of 'm'

                                     so all roots will be real