A top costs £48 in a sale after a 20% reduction. What is the original cost of the top before the sale?

Answer: The width is x-6

Step-by-step explanation:

To find the with factor out the area x^2 - 11x + 30

[tex]x^{2}[/tex] - 11x +30  to factor it find two numbers that multiply to get 30 and add up to get -11 . And that two numbers are -6 and -5 .

[tex]x^{2}[/tex] - 5x - 6x + 30   now group them

([tex]x^{2}[/tex] - 5x) (-6x+ 30)   factor them out.

x(x - 5) - 6(x -5)   Factor x-5 out  

(x-5)(x-6)  since the length is x-5 then the width is x-6.

Answer:

4.4

Step-by-step explanation:

Write the question out as an equation:

7+x/3 = 2x - 5

Rearrange , simplify and solve:

7+x = 3(2x-5) = 6x - 15

7+x = 6x-15

6x - 15 = 7+x

6x = 7+x+15 = 22+x

6x = 22+x

6x-x = 22

5x = 22

x = 4.4

hope this helps.

Good Luck.

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Answer:

Step-by-step explanation:

7+x/3=2x-5

taking 3 on the RHS

7+x=6x-15

22=5x

x=22/5

=4.4

Answer:

It was a gain, specifically 16

Step-by-step explanation:

14 + (-7) = 7

7 + 9 = 16

Please tell me if I'm wrong.

Answer:

The 3rd one is correct.

Step-by-step explanation:

Answer:

[tex]x = p(m-n)[/tex]

Step-by-step explanation:

m = n + [tex]\frac{x}{p}[/tex]

Subtracting n to both sides

=> m-n = [tex]\frac{x}{p}[/tex]

Multiplying p to both sides

=> [tex]x = p(m-n)[/tex]

Answer:

x=p(m-n)

Step-by-step explanation:

m =n + x/p

x/p=m-n

x=p(m-n)

Answer:

Step-by-step explanation:

To find x we use cosine

cos∅ = adjacent / hypotenuse

x is the adjacent

8√3 is the hypotenuse

cos 30 = x / 8√3

x = 8√3 cos 30

To find y we use sine

sin∅ = opposite / hypotenuse

y is the opposite

8√3 is the hypotenuse

sin 30 = y / 8√3

y = 8√3 sin 30

Hope this helps you

Answer:

A

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 3, 5 ] , thus

f(b) = f(5) = - 26 ← value of y for x = 5 from table

f(a) = f(3) = - 10 ← value of y for x = 3 from table

average rate of change = [tex]\frac{-26-(-10)}{5-3}[/tex] = [tex]\frac{-16}{2}[/tex] = - 8 → A

Answer:

7/12 chance

Step-by-step explanation:

(1 2 3 4 5 6)

(1 2 3 4 5 6)

All the possibilities:

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

There are 18 odd sums.

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

There are 3 possibilities whose sums add up to 10.

Since there are 36 total possibilities and 21 numbers that fit the rule of having an odd sum or a sum of 10. There is a 21/36 chance or simplified, 7/12 chance.

Answer:

1/4 or 25% chance

Step-by-step explanation:

the probability of getting each question right is 1/2, so for getting 2 questions right its 1/2 × 1/2, which is 1/4

The probability that a student that guesses gets at least 2 questions correct is 1/4.

The probability of getting a question correct is the same as the probability of getting a question wrong.

The probability of getting the question is correct is;

[tex]= \dfrac{1}{2}[/tex]

The probability of getting the question is wrong is;

[tex]= \dfrac{1}{2}[/tex]

Therefore,

The probability that a student that guesses gets at least 2 questions correct is;

[tex]= \dfrac{1}{2} \times \dfrac{1}{2}\\\\= \dfrac{1}{4}[/tex]

Hence, the probability that a student that guesses gets at least 2 questions correct is 1/4.

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Answer:

Step-by-step explanation:

Hello,

Is this equality true ?

sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x

1. let 's estimate the left part of the equation

[tex]sec(x)csc(x)(tan(x) + cot(x)) =\dfrac{1}{cos(x)sin(x)}*(\dfrac{sin(x)}{cos(x)}+\dfrac{cos(x)}{sin(x)})\\\\=\dfrac{1}{cos(x)sin(x)}*(\dfrac{sin^2(x)+cos^2(x)}{sin(x)cos(x)})\\\\=\dfrac{1}{cos(x)sin(x)}*(\dfrac{1}{sin(x)cos(x)})\\\\\\=\dfrac{1}{cos^2(x)sin^2(x)}[/tex]

1. let 's estimate the right part of the equation

[tex]2+tan^2(x) + cot^2(x)=2+\dfrac{sin^2(x)}{cos^2(x)}+\dfrac{cos^2(x)}{sin^2(x)}\\\\=\dfrac{2cos^2(x)sin^2(x)+cos^4(x)+sin^4(x)}{cos^2(x)sin^2(x)}\\\\=\dfrac{(cos^2(x)+sin^2(x))^2}{cos^2(x)sin^2(x)}\\\\=\dfrac{1^2}{cos^2(x)sin^2(x)}\\\\=\dfrac{1}{cos^2(x)sin^2(x)}[/tex]

This is the same expression

So

sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x

hope this helps

Answer:

1.5mg

Step-by-step explanation:

From the question, we are told that the HCP prescribed 7.5 mg of PO weekly

The therapeutic dosage is given in the question as 5 - 15 mg/m² weekly.

The child's body surface area is given = 0.6m²

The mg of PO that the nurse should administer in each of the three doses given weekly is calculated as

7.5mg/ 5mg/m²

= 1.5 mg of PO

Answer:

there are now 3.5 kilograms of grapes in the basket (the mystery number is 1.5)

Let us suppose that the number of grapes in the box is x and the number of grapes in the basket is y.

It means that the weight of the grapes in the box is x kg and that of basket is y kg.

It has been given that the box had twice as many grapes as a basket. Therefore, we have

Now when we add 2 kg to the basket then the weight of the basket is y+2 and the weight of box will remain same.

Now, we have been given that after 2 kilograms were added to the basket it contained 0.5 kilograms more than the box. Hence, we have

Substituting the value x=2y in the equation, we get

Therefore, the basket contains 1.5 kilograms of grapes.

Answer:

[tex]a^3+3a^2b+3ab^2+b^3[/tex]

Step-by-step explanation:

If have [tex](a+b)^3[/tex], we can solve this as:

[tex](a+b)(a+b)(a+b)[/tex]

So, applying distribution with the first two factors and simplifying, we get:

[tex](a^2+ba+ab+b^2)(a+b)\\(a^2+2ab+b^2)(a+b)[/tex]

Then, multiplying both expressions and simplifying again, we get:

[tex]a^3+a^2b+2a^2b+2ab^2+b^2a+b^3\\a^3+3a^2b+3ab^2+b^3[/tex]

Answer:

Term to add is (3/8)^2 = 9/64

Step-by-step explanation:

Here, we want to know the value that must be added to make the equation a perfect square.

x^2 - 3/4x = 5

x^2 -3/4x -(3/8)^2+ (3/8)^2 = 5

x^2 -3/4x + (3/8)^2 = 5 + (3/8)^2

= (x-3/8)^2 = 5 + (3/8)^2

So the term to add is (3/8)^2 = 9/64

Answer:

[tex]\dfrac{9}{64}[/tex]

Step-by-step explanation:

Given the equation: [tex]x^2-\frac{3}{4}x=5[/tex]

To make the left hand side of the equation a perfect trinomial, we follow these steps.

Step 1: Divide the coefficient of x by 2.

Coefficient of x [tex]=-\frac{3}{4}[/tex]

[tex]-\frac{3}{4} \div 2 =-\frac{3}{8}[/tex]

Step 2: Square your result from step 1

[tex]\implies (-\frac{3}{8})^2 \\=\dfrac{9}{64}[/tex]

Therefore, to make the Left-Hand side a  perfect-square trinomial, we add 9/64.

Answer:

95 degrees

Step-by-step explanation:

All triangles have an interior measure of 180 degrees

180-41-44=95

Answer:

95 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

The attachment will help you with your question:

Answer:

First Option

Step-by-step explanation:

When we graph the expression, we should see that an infinite amount of y-values work. Since the domain comprises of all working x-values, we have (negative infinity, positive infinity) or all real numbers as our range, since we have an infinite amount of y-value outputs.

Answer:

The solution to the question is g = 52

Step-by-step explanation:

Here, we want to find the solution to the equation ;

98 + g = 150

Apparently, we want to find the value of g.

To get the value of g, what we simply need is to bring 98 over the equal sign and this gives

g = 150-98

g = 52

Answer: B or how some people say it the second question. EDGE-MATHMATICS 2022

THE ANSWER IS B

step-by-step explanation: it is the second option  because when you find out what number g is (52) you can take 98-98= 0 + g/52 and get 52.

and then the second part of it says 150-98 which is 52! so  your answer is B hope this helps! have a wonderful day!

Step-by-step explanation:

[tex]a^n={\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]

[tex]\left(b^3\right)^2=\underbrace{b^3\cdot b^3}_{2}=\underbrace{b\cdot b\cdot b}_{3}\cdot\underbrace{b\cdot b\cdot b}_{3}=\underbrace{b\cdot b\cdot b\cdot b\cdot b\cdot b}_{6}=b^6[/tex]

[tex]\left(b^3\right)^2=\underbrace{b^3\cdot b^3}_{2}=b^{3+3}=b^6\qquad\text{used}\ a^n\cdot a^m=a^{n+m}[/tex]

[tex]\left(b^3\right)^2=\left(\underbrace{b\cdot b\cdot b}_{3}\right)^2=b^2\cdot b^2\cdot b^2=b^{2+2+2}=b^6\\\text{used}\ (ab)^n=a^nb^n,\ a^n\cdot a^m=a^{n+m}[/tex]

[tex]\left(b^3\right)^2=b^{3\cdot2}=b^6\qquad\text{used}\ \left(a^n\right)^m=a^{nm}[/tex]

Answer:

  A.  All real numbers

Step-by-step explanation:

We assume that the "linear parent function" is ...

  y = x.

Its range is "all real numbers."

Answer:

all real numbers

Step-by-step explanation:

AP-EX

Answer:

8

Step-by-step explanation:

10-8 x 2 = 4

2 x 2 = 4

4 = 4

The number is 8, which is when subtracted from 10 and the result is multiplied by 2, then the result is 4.

Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.

Let the required number is x.

According to given condition,

When x is subtracted from 10 and the result is multiplied by 2, final result comes as 4.

Implies that,

2 (10 - x) = 4

10 - x = 2

x = 10 - 2

x = 8

The required number is 8.

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Answer: The missing length is 16/3

Step-by-step explanation:

First, you have to find the proportional value between the two lengths on the first figure and the two lengths on the second figure.

The first figure’s lengths are 8 and 9, so the shorter length is 8/9 of the longer length.

Now apply the same proportional value to the second figure.

6 * 8/9 = 48/9

48/9 = 16/3

Answer:

b=69 degrees

Step-by-step explanation

Use the remote interior angle theorem which states that the sum of the two remote interior angles is equal to the exterior angle. Basically, b=(b-36)+(b-33). That will give you b=2b-69. Then b=69. There's ur answer.

Answer:

Step-by-step explanation:

= x^2+6x+9-8=0

=x^2+6x+1=0

D=b^2-4ac

D= 36-4

D=32

x=-b±root D/2a

x=-6+4root2/2     ,    x = -6-4root2/2

simplify you get the least form...

hope it helps

Answer:

The equation of the tangent is [tex]y=-\frac{8}{15}x+\frac{289}{15}[/tex].

Step-by-step explanation:

Center = (0, 0). Point on the circle = (8, 15).

OP is a radius. The slope of the radius = [tex]\frac{15-0}{8-0}=\frac{15}{8}[/tex].

The tangent is perpendicular to the radius.

So, its slope is = [tex]-\frac{8}{15}[/tex].

The tangent passes through (8, 15).

So, the equation is:

[tex]y-15=-\frac{8}{15}\left(x-8\right)\\y-15=-\frac{8}{15}x+\frac{64}{15}\\y=-\frac{8}{15}x+\frac{289}{15}[/tex]

Learn more: https://brainly.com/question/1594198

I hope this helps you

Answer:

42=7(x+5)

42=7x+35

42-35=7x

7=7x

X=7/7=1

Answer:

The correct option is (B).

Step-by-step explanation:

The conditional probability of an event, say A is the probability of that events (A) when it is known that another event, say X has already occurred.

For example, consider the experiment of drawing two marbles from jar consisting of 8 white and 2 red, without replacement. The probability of selecting a red marble after a white marble is known as conditional probability.

In this case it is provided that:

The statement:

"the probability that a student who is a licensed driver is a male"

Is a statement of conditional probability.

This is because it is known from previous information that the student is a licensed driver and we need to determine the probability of this student being a male.

Thus, the correct option is (B).

Answer: 15 sides

Step-by-step explanation: Because the sum of the outer angles is always 360 degrees, if you divide 360 degrees by 24 degrees you get 15 which is the number of equivalent outer angles and therefore 15 vertices and sides to the polygon

Answer: angle is 24 degrees meaning that a regular polygon has more than 6 sides hope this is helpful

Step-by-step explanation:

Answer:

£144

Step-by-step explanation:

DVD to be due on 26 of November

She returned it to the shop on 12 of December

Extra days:

November has a total of 30 days less 26 days=4 extra days

December 12 =12 extra days

Total extra days =4+12=16 days

Fine per day=£9

Total fine paid by Amelia=£9*16

=£144