Please need help on this

To factorise fully the expression 5x-15, we must search for the greatest common factor (GCF) that can be taken out of both terms. The expression 5x - 15 can be factorised fully by finding the greatest common factor, which is 5. So the expression factorised fully is 5(x - 3).

To factorise fully the expression 5x-15, we must search for the greatest common factor (GCF) that can be taken out of both terms.

The GCF of 5x and 15 is 5. Thus, we can pull 5 outside of the equation and divide each term by 5.

The equation becomes: 5(x - 3).

So, the expression 5x - 15 factorised fully is 5(x - 3).

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Answer:

(5 + √115)/15 or (5 - √115)/15

Step-by-step explanation:

4/5x+4/3 = 2x

Multiply each term by the least common multiple of the denominators (15x)

12 + 20x = 30x²

Move all the terms to the left-hand side.

-30x² + 20x + 12 = 0

Multiply each term by -1

30x² - 20x - 12 = 0

Remove the common factor (2)

15x² - 10x - 6 = 0

Solve by using the quadratic formula

a = 15, b = -10, c = -6

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\= \frac{-(-10)\pm\sqrt{(-10)^2-4(15)(-6)}}{2(15)}\\\\= \frac{10\pm\sqrt{100 + 360}}{30}\\\\= \frac{10\pm\sqrt{460}}{30}\\\\= \frac{10\pm\sqrt{4\times115}}{30}\\\\= \frac{10\pm2\sqrt{115}}{30}\\\\= \mathbf{\frac{5\pm\sqrt{115}}{15}}[/tex]

x = (5 + √115)/15 or x = (5 - √115)/15

Answer:

See explanation

Step-by-step explanation:

Let x be the number of simple arrangements and y be the number of grand arrangements.

1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so

[tex]x\ge 2y[/tex]

2. A florist can make a grand arrangement in 18 minutes [tex]=\dfrac{3}{10}[/tex] hour, then he can make y arrangements in [tex]\dfrac{3}{10}y[/tex] hours.

A florist can make  a simple arrangement in 10 minutes [tex]=\dfrac{1}{6}[/tex] hour, so he can make x arrangements in [tex]\dfrac{1}{6}x[/tex] hours.

The florist can work only 40 hours per week, then

[tex]\dfrac{3}{10}y+\dfrac{1}{6}x\le 40[/tex]

3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.

The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.

Total profit: $(10x+25y)

Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines [tex]x=2y[/tex] and [tex]\dfrac{3}{10}y+\dfrac{1}{6}x=40[/tex]

But this point has not integer coordinates. The nearest point with two integer coordinates is (126,63), then the maximum profit is

[tex]\$(10\cdot 126+25\cdot 63)=\$2,835[/tex]

To maximize profit, the florist should produce 1 grand arrangement and 2 simple arrangements. The maximum profit is $45.

To maximize profit, the florist should produce a combination of grand and simple arrangements. Let's assume the florist makes x grand arrangements and at least twice as many simple arrangements, which would be 2x or more. Given that the florist can work only a total of 40 hours per week, we can set up the following equation:

18x + 10(2x) ≤ 40

Now, we solve for x to find the number of grand arrangements.

Simplifying the equation, we have 18x + 20x ≤ 40

Combining like terms, we get 38x ≤ 40

Dividing both sides by 38, we find that x ≤ 1.05

Since we can't have a fraction of an arrangement, the florist should produce 1 grand arrangement. From the given information, we know that the florist must produce at least twice as many simple arrangements as grand arrangements. Therefore, the florist should produce at least 2 * 1 = 2 simple arrangements.

The florist's maximum profit can be calculated by multiplying the profit per arrangement by the number of corresponding arrangements.

The profit for the grand arrangement is $25, so the total grand arrangement profit is 1 * $25 = $25. The profit for the simple arrangement is $10, so the total simple arrangement profit is 2 * $10 = $20. Therefore, the maximum profit is $25 + $20 = $45.

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Answer:

there were 2 doctors. first doctor saw 89 patient. Second doctor saw the twice of first doctor. calculate how much patient did second doctor saw

The method to solve the expression is given.

The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.

The given expression,

15- [14 = (15-8) + 13 - 14 - 10

First, we solve the parenthesis.

15-14 = 7 + 13 - 14 -10

Now, adding the terms.

15-14 = 21 - 24

Subtracting the terms.

1 = -3

Which is contradiction.

Therefore, the expression is wrong.

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Answer:

Complementary angles

Step-by-step explanation:

Complementary angles sum to 90°, that is

x + 90 - x = 90°

Thus x and (90 - x) are complementary angles

Step-by-step explanation:

The measure of angle y is 62°.

I solve this by

We know: Measures of interior angles in a triangle add up to 180°.

Therefore we have the equation:

60° + 58° + y = 180°

118° + y = 180°         subtract 118° from both sides

118° - 118° + y = 180° - 118°

y = 62°

The measure of angle x is 122°.

I solve this by

Angles 58° and x are supplementary angles.

Supplementary angles add up to 180°.

Therefore we have the equation:

x + 58° = 180°            subtract 58° from both sides

x + 58° - 58° = 180° - 58°

x = 122°

Answer:

no of students by cost per student?

Answer:The cost of the if 0 students signed up

Step-by-step explanation:I got the answer right :)

Answer:

It depends on how the data are distributed.

Step-by-step explanation:

If the data follow a normal (Gaussian) distribution, which is the most common, then 2 deviations from the mean is considered unusual because less than 4.55% of the data are in this situation.

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h. k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (- 6, - 1), thus

y = a(x + 6)² - 1

To find a substitute one of the roots into the equation

Using (- 3, 0), then

0 = a(- 3 +6)² - 1

0 = 9a - 1 ( add 1 to both sides )

1 = 9a ( divide both sides by 9 )

a = [tex]\frac{1}{9}[/tex], thus

y = [tex]\frac{1}{9}[/tex](x + 6)² - 1 ← in vertex form

Expand factor and simplify

y = [tex]\frac{1}{9}[/tex] (x² + 12x + 36) - 1 ← distribute

y = [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 4 - 1

  = [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 3 ← in standard form

Answer:

The simplest form of the expression is 3² ⇒ 3rd answer

Step-by-step explanation:

- The expression is 3 power 3 multiplied by 3 power 3 over 3 power 4

∵ 3 power 3 = 3³

∵ multiplied by 3 power 3 = × 3³

∵ over 3 power 4 = ÷ [tex]3^{4}[/tex]

- Lets write all of them in one expression

∴ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]

- All the numbers in the expression is 3 to the power

∴ The expression have the same base 3

- Remember: if we have numbers of same base multiplied then we

 add their powers and if divided then we subtract their powers

 [tex]\frac{a^{m}*a^{n}}{a^{q}}=a^{m+n-q}[/tex]

- Lets use this rule to simplify the expression

∵ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]

- Use the rule of the same base above

∴ [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex] = [tex]3^{3+3-4}=3^{6-4}=3^{2}[/tex]

∴ The simplest form of the expression is 3²

Answer:

3 to the 2nd power.

Step-by-step explanation:

Total amount of what?

$8.75 * 7.5

about $65.63

Forgive me if I'm wrong

Hope this helps!

Answer:

Choice C, -1

Step-by-step explanation:

The trick here is to look at this as a pattern.

[tex]\sqrt{-1}[/tex] is i to the 1st power.

[tex]-1[/tex] is i to the 2nd power.

[tex]-\sqrt{-1}[/tex] is i to the 3rd power.

[tex]1[/tex] is i to the 4th power.

So what we do to solve something like this is divide the power by 4, and see how far away the number is from the pattern.

In other words, we divide, and our remainder is how many powers to count up to (a remainder of 0 is the 4th power).

So 34/4 = 8 with a remainder of 2. Therefore, it's i to the 2nd power, which is -1.

This is an exponential growth problem.

The formula is y = a(1+r)^x

Y would be the final answer

a is the starting value

r is the percent of growth

x is the amount of time ( number of weeks)

The equation is:

y(x) = 92(1.06)^x

For 14 weeks replace x with 14:

y(14) = 92(1.06)^14 = 208 pounds.

Answer: W(n) = 92lb*1.06^n

and W(14) = 92lb*1.06^14 = 208lb

Step-by-step explanation:

We know that at the beginning the baby elephant weighs 92Lbs, and for each week it augments by a 6% (or 0.06 in decimals)

Then, at the end of the first week, the weight is:

92lb*1.06 = 97.52lb

at the end of the second week:

(92lb*1.06)*1.06 = 103.37lb

and so on, so you can see that the pattern is:

W(n) = 92lb*1.06^n

where n is the number of weeks after the birth

W(0) = 92lb

W(1) =  97.52lb

...

And we want to know the weight at the end of the 14th week, so we must find:

W(14) = 92lb*1.06^14 = 208lb

Final answer:

To find the radius of the circle, we can use the properties of a right triangle to solve for GH. GH is approximately 10.39cm.

Explanation:

To find the radius of the circle, we can start by observing that the angle GHJ is 15°, and the side GK is 6cm. Since GK is a radius of the circle and it is perpendicular to JH, we can conclude that JH is a diameter of the circle. So, the length of JH is twice the length of GK, which is 12cm.

Now, we can use the properties of a right triangle to find the radius of the circle. We have a right triangle GHJ, where GH is the radius of the circle and JH is the hypotenuse. Using the Pythagorean theorem, we can solve for GH:

GH^2 + GK^2 = JH^2

GH^2 + 6^2 = 12^2

GH^2 + 36 = 144

GH^2 = 108

GH = sqrt(108)

GH ≈ 10.39cm

The radius of the circle is approximately 10.39cm.

Answer:worked 7 hours

Step-by-step explanation:

93 - 65 = 28

28/4 = 7 hours

Michelle worked for 7 hours on the weekend night based on the equation 4h + $65 = $93, where h represents the number of hours worked.

Let's denote the number of hours Michelle worked as "h". She earned $4 per hour for her work, so the total amount she earned from her hourly wage is 4h. Additionally, she earned $65 in tips.

So, the total amount she made can be represented by the equation:

Total earnings = Hourly wage + Tips

$93 = 4h + $65

Now, we can solve for the number of hours Michelle worked:

4h + $65 = $93

Subtract $65 from both sides:

4h = $93 - $65

4h = $28

Now, divide both sides by 4 to solve for "h":

h = $28 / 4

h = 7

Michelle worked for 7 hours on that weekend night.

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Answer:

The inverse property of addition.

Step-by-step explanation:

The number  6 is added to its inverse -6.

The property of real numbers (-6) + 6 = 0 will be Inverse property of addition. Then the correct option is D.

Any of the many numerical laws governing how values are added.

Some Addition properties are as follows:

Associative property of addition – The total is unchanged when the order of the sub-blocks is changed.

For example, (2 + 3) + 4 = 2 + (3 + 4)

Commutative property of addition – No matter how the addends are arranged, the result remains constant.

For example, 4 + 2 = 2 + 4

Identity property of addition – The integer is that summation of 0 and that value.

For example, 0 + 4 = 4

Inverse property of addition – Zero is the result of adding any integer to its inverse.

For example, a + (-a) = 4

The property of real numbers -6+6=0 will be Inverse property of addition.

Then the correct option is D.

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Answer:

-3

Step-by-step explanation:

-(-3) = 3

-(-6) = 6

-3 - (-6) = 3

-c - d

c = -3

-3 - d

d = -6

-3 - (-6)

=-3+6

=3

Answer:

Step-by-step explanation:

-3 - (-6) = x  (u would use Keep Change Flip [KCF] to solve)

-3 + 6 = x

3=x

so the answer is 3

Hope this helps!!

Answer:

6(9x+5)

Step-by-step explanation:

6*9x = 54x

6*5 = 30

The expression should be 6(9x+5)

The equation is 54x + 30

A polynomial represents an expression that comprises of indeterminates and coefficients, which includes only the operations of addition, subtraction, multiplication, and a non-negative integer.

So,

= 54x + 30

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Answer:

$96.51

Step-by-step explanation:

529.57 - 126.08 = 403.49

500 - 403.49 = 96.51

The possible amount you deposit into your account by the ed of the month to avoid paying the service fee would be $96.51

Answer:

$96.51

Step-by-step explanation:

Answer:

The value of the digit 2 in the number 12,600 is 2,000

Step-by-step explanation:

we have the number 12,600

Rewrite the number in expanded form (write the number in its digits value)

[tex]12,600=10,000+2,000+600[/tex]

so

The value of the digit 1 in the number is 10,000

The value of the digit 2 in the number is 2,000

The value of the digit 6 in the number is 600

The dimensions of matrix B must be 3x1 to satisfy the given matrix multiplication where a 2x3 matrix A is multiplied by B to result in a 2x1 matrix C.

The student is asking about the dimensions of a matrix B that when multiplied by a given 2x3 matrix A, results in a 2x1 matrix C. In matrix multiplication, the product of an mxn matrix A and an nxp matrix B yields an mxp matrix C. The resulting matrix, C, has the same number of rows as the first matrix (A) and the same number of columns as the second matrix (B). Additionally, the number of columns in the first matrix must match the number of rows in the second matrix. Therefore, since matrix A has 3 columns, matrix B must have 3 rows for the multiplication to be defined. And since matrix C has 1 column, matrix B must have 1 column as well. So, the dimensions of matrix B are 3x1.

The container with a volume of 2 cubic yards, which is equivalent to 54 cubic feet, would require 3 barrels of sand to fill it up, as the volume of each barrel is 18 cubic feet.

To find out how many barrels of sand will be needed to fill a container with a volume of 2 cubic yards, we first need to convert cubic yards to cubic feet, as the measurement of the barrel volume is given in cubic feet. Since 1 cubic yard is equivalent to 27 cubic feet, 2 cubic yards will be 2 * 27 = 54 cubic feet.

Next, we divide the volume of the container by the volume of one barrel of sand. Hence, the number of barrels needed = 54 cubic feet / 18 cubic feet per barrel = 3 barrels.

So, it will take 3 barrels of sand to fill a container with a volume of 2 cubic yards.

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Answer:

m∠MHJ = 50°

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

Step-by-step explanation:

Best explanation is as shown in the attached figure.

As shown in the figure:

x + 15 = 2x - 20  ⇒ vertex angles are congruent

solve for x ⇒ ∴ x = 35°

So, ∠MHJ =  2x - 20 = 2*35 - 20 = 50°

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

The measure of all angles will be:

∠MHJ = 2X - 20° = 2 * 35 - 20 = 50°

∠JHK = 180° - ∠MHJ = 180 - 50 = 130°

∠KHL = X + 15° = 35° + 15° = 50°

∠LHM = ∠JHK = 130°

Answer:

B 50 degrees

Step-by-step explanation:

Answer:

Im not sure what the answers are on your test but its usually called a domain.

-

-

-

Let me know what the possible answers are if it is a multiple choice question!

Step-by-step explanation:

Answer: many-to-one function

Step-by-step explanation:

Answer:

A. X(–2, 2), Y(–10, 2), Z(–6, 10)

Step-by-step explanation:

This looks a bit tough, but knowing that scale factors less than 1 are ½, ¼, etcetera, I come to this answer, also knowing that in the end, they must have an unproportional relationship.

I hope this is correct, and as always, I am joyous to assist anyone at anytime.

[tex]\bf \cfrac{y}{x}=k\qquad \begin{cases} k=\frac{4}{5}\\ y=\frac{2}{3} \end{cases}\implies \cfrac{~~\frac{2}{3}~~}{x}=\cfrac{4}{5}\implies \cfrac{2}{3}(5)=4x\implies \cfrac{10}{3}=4x \\\\\\ \cfrac{10}{12}=x\implies \cfrac{5}{6}=x[/tex]

In this problem, we solve for 'x' in the equation for constant of proportionality, 'y/x = k', given that 'y' is 2/3 and 'k' is 4/5. Substituting these values in the equation and solving for 'x' gives the result 5/6.

The question refers to the concept of the constant of proportionality which is a key topic in mathematics. We have an equation, y/x = k, where k is the constant of proportionality. Here, we have been given that y = 2/3 and k = 4/5. If we substitute these values into the equation, we will be able to solve for x.

To solve for x, we rearrange the equation by multiplying both sides by x and then dividing by k. This leaves us with an equation in terms of x: x = y/k. Substituting the given values, we get x = (2/3) / (4/5) = 5/6. So, the correct answer according to the provided options is C. X = 5/6.

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Answer:

They bought 0 ticket of closest section and 7 tickets of other section

Step-by-step explanation:

- Callie and Madison went to buy concert tickets for themselves and

  their five friends

- That mean they are 7

- Tickets for the closest section were $45 each

- Tickets for other section were $30 each

- They  ended up spending a total of $210

- Assume that they buy x tickets for closest section and y tickets for

 the other section

∵ They want 7 tickets

∴ x + y = 7 ⇒ (1)

∵ The cost of the closest section ticket was $45

∵ The cost of the other section ticket was $30

∵ They spent $210 on them

∴ 45x + 30y = 210

- All terms have common factor 15, then divide them by 15

∴ 3x + 2y = 14 ⇒ (2)

* Now we have a system of equations to solve

- Multiply equation (1) by -2 to eliminate y

∴ -2x - 2y = -14 ⇒ (3)

- Add equations (2) and (3)

∴ x = 0

- substitute the value of x in equation (1) to find y

∴ 0 + y = 7

∴ y = 7

∵ x represents the number of tickets of the closest section and y

  represents the number of tickets in the other section

∴ They bought 0 ticket of closest section and 7 tickets of other

   section

Answer:

The volume of the sphere is [tex]V=288\pi\ m^3[/tex]

Step-by-step explanation:

The question in English is

Calculate the volume in m^3 of the sphere in which the area of one of its maximum circles is 36pi m^2

we know that

The radius of the maximum circle in the sphere is equal to the radius of the sphere

Step 1

Find the radius of the maximum circle

The area of the circle is

[tex]A=\pi r^{2}[/tex]

we have

[tex]A=36\pi\ m^2[/tex]

substitute and solve for r

[tex]36\pi=\pi r^{2}[/tex]

Simplify

[tex]36=r^{2}[/tex]

take the square root both sides

[tex]r=6\ m[/tex]

Step 2

Find the volume of the sphere

The volume of the sphere is

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

substitute the value of r

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ m^3[/tex]