The sum of two numbers is 66. The difference of the same two number is 38. What are the numbers?

Answer:

4 meters longer.

Step-by-step explanation:

Amit built a sandcastle that measured 600 cm by 600 cm i.e. 6 meters by 6 meters.

Therefore, its perimeter is 2(6 + 6) = 24 meters

Now, afterward, he decided to change the castle size, making it 8 meters by 6 meters.

Therefore, its perimeter is 2(6 + 8) = 28 meters

Therefore, the perimeter of the new castle is increased by (28 - 24) = 4 meters.

If Amit dug a moat around his castle then the new moat will be 4 meters longer than the old one. (Answer)

As the moat is dug around the castle, its length will be the same as the perimeter of the castle.

Answer:

The restaurant Manager can afford 6 employees for the day.

Step-by-step explanation:

Manager can spend at most of $400.

Total Money ≤ $400

Cost to operate bank = $100

Cost for each employee = $50

Let number of employees for the day be[tex]x[/tex]

Hence the equation will become;

[tex]50x + 100 \leq 400[/tex]

Solving this equation we get;

[tex]50x + 100 \leq 400\\50x \leq 400-100\\50x \leq 300\\x\leq \frac{300}{50}\\\\x\leq 6[/tex]

Hence, The restaurant Manager can afford 6 employees for the day.

Answer:

x < = 10

Step-by-step explanation:

i did it on photo math so yah

Answer:

2 × [tex]10^{6}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]

Split the fraction into a product, that is

= [tex]\frac{8.4}{4.2}[/tex] × [tex]\frac{10^{12} }{10^{6} }[/tex]

= 2 × [tex]10^{(12-6)}[/tex]

= 2 × [tex]10^{6}[/tex]

Answer:

18.55, lines m and n are parallel and t is the transversal. If ∠1 = 130o, find the measures of the other angles and give reasons.

Step-by-step explanation:

The measure of angle 8 will be 130° since it corresponds to angle 1, and their measures are equal because lines m and n are parallel.

To find the measure of angle 8 when lines m and n are parallel, and the measure of angle 1 is 130°, it's important to understand the concept of corresponding angles in the context of parallel lines. Corresponding angles are equal when two lines are parallel. Given that angle 1 is 130°, and assuming that angle 1 and angle 8 are corresponding angles (since the question does not specify their positions), the measure of angle 8 is also 130°.

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Answer:

10

Step-by-step explanation:

5 trees * 2 from each = 10 apples

Answer:

10

Step-by-step explanation:

5*2=10

Answer:

=40/33

8/11 divide 3/5 -> 8/11 x 5/3 and multiply 8x5 then 11x3 then u got your answer! :)

Hope this worked :D

Answer:

Your answer is 40/33

Step-by-step explanation:

8/11 * 3/5

flip the fraction

8/11* 5/3

Multiply

Answer:

[tex](150+21m)\ miles[/tex]

Step-by-step explanation:

we know that

[tex]1\ week=7\ days[/tex]

Remember that the speed is equal to divide the distance by the time

Let

s ---> the speed in miles per day

d ---> the distance in miles

t ---> the time in days

[tex]s=\frac{d}{t}[/tex]

[tex]d=st[/tex]

we have

[tex]s=m\ miles/day[/tex]

[tex]t=3\ weeks[/tex]

Convert to days

[tex]t=3(7)=21\ days[/tex]

Find the distance covered in the trip

[tex]d=st[/tex] ----> [tex]d=m(21)=21m\ miles[/tex]

To find out the mileage on Jim’s car after his trip, sum the mileage before his trip (150 miles) plus the mileage of the trip

[tex](150+21m)\ miles[/tex]

Answer:

2. n = 11

4. g = -2

6. t = 21

8. n = 4

10. y = -1

Step-by-step explanation:

2. 63  = -3(1 - 2n)

Dividing both the side by negative 3 we get

[tex]-21=1-2n\\2n=1+21\\2n=22\\n=\frac{22}{2} \\\therefore n=11[/tex]

4. -g + 2(3 + g) = -4(g + 1)

First we will open the bracket by distributive property A( B +C) = AB + AC

[tex]-g+2\times 3 + 2\times g = -4\times g + -4\times 1\\-g+6+ 2g=-4g-4\\\textrm{we will take all the g term the left side and the constant to the right side}\\4g-g+2g=-6-4\\5g=-10\\g=\frac{-10}{5}\\\therefore g=-2[/tex]

6.-3(t +5 ) + (4t + 2) = 8

Using distributive property A( B +C) = AB + AC we get

[tex]-3\times t + -3\times 5 + 4t + 2=8\\-3t-15+ 4t + 2=8\\t=8+15-2\\t=21\\\therefore t=21\\[/tex]

8. -8 - n = -3(2n -4)

Using distributive property A( B +C) = AB + AC we get

[tex]-8 - n = -3\times 2n - -3\times4\\-8-n=-6n+12\\\textrm{all the n terms to the left inside and the constant of the right-hand side}\\6n-n=8+12\\5n=20\\n=\frac{20}{5}\\ \therefore n= 4[/tex]

10. -4( 2 - y) + 3y = 3(y - 4)

Using distributive property A( B +C) = AB + AC we get

[tex]-4\times 2 --4\times y + 3y = 3\times y -3\times 4\\-8+4y+3y =3y-12\\\textrm{all the y terms to the left side and the constant to the right side}\\4y+3y-3y=-12+8\\4y=-4\\y=\frac{-4}{4}\\ \therefore y=-1[/tex]

Answer:

see explanation

Step-by-step explanation:

The second term of sequence P is 2a + b

The third term of sequence Q is 3b + a

Equating gives

2a + b = 3b + a ( subtract a from both sides )

a + b = 3b ( subtract b from both sides )

a = 2b ← as required

Good evening ,

Step-by-step explanation:

4 (b)

The 2nd term of sequence P is 2a+b

The 3rd term of sequence Q is 3b+a

2a+b=3b+a ⇌ (2a-a) = (3b-b) ⇌ a=2b.

:)

Step-by-step explanation:

10. |-41|= 41

12. -|1.5|= -1.5

Answer:

A.) 41

B.) -1.5

Step-by-step explanation:

Absolute value means to make whatever that is inside positive

10.) The absolute value of negative 41 would simply be positive 41

11.) Since the negative sign is on the outside of the absolute value, you do the absolute value of everything inside then apply a negative sign. Absolute value of 1.5 is just 1.5 because it's already positive. Then apply the negative sign, which would make it -1.5

Step-by-step explanation:

[tex]-2(5-4x)<6x-4\qquad\text{use the distributive property}\\\\(-2)(5)+(-2)(-4x)<6x-4\\\\-10+8x<6x-4\qquad\text{subtract}\ 8x\ \text{from both sides}\\\\-10+8x-8x<6x-8x-4\\\\-10<-2x-4\qquad\text{add 4 to both sides}\\\\-10+4<-2x-4+4\\\\-6<-2x\qquad\text{divide both sides by (-2)}\\_{\text{by dividing by a negative number, flip the inequality sign}}\\\\3>x[/tex]

Answer:

the 1st & last paras are fixed.

that leaves 3 to be put in any order

there are 3 choices for the 1st,

2 choices left for the 2nd

and just 1 choice for the last

multiply to get

3*2*1

= 6 ways

We want to find the total number of orders in which we can order the given sentences.

We will see that there are 120 different orders.

There are 5 sentences, let's define them as:

We know that we can order these in any order, so we can think of the situation as 5 empty slots, in each slot, we can put one of the previous statements.

Let's count the number of options for each one of these slots.

On the first one, we have 5 options (5 sentences)

On the second one we have 4, because we already used one on the first slot.

On the third, we have 3 options.

On the fourth, we have 2 options.

On the fifth, we have 1 option.

The total number of combinations is given by the product of these numbers of options.

Combinations = 5*4*3*2*1 = 120

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Answer:

y=3x/2

Step-by-step explanation:

first you want to get the -2y alone so you move the 3x. since it's adding now the opposite of addition is subtraction. now your left with -2y= -3x. since your trying to solve for y now you divide -2 on both sides and your gonna be left with y= -3x/-2. since their both negatives it turns to postive. that's why the answer would be y= 3x/2.

Step-by-step explanation:

this line will cross the origin

to help I'm just going to explain something real quick.

make it into y intercept form (y=mx+b)

-2y=0-3x

y=3/2x +0

the m (3/2) is the slope

and b (0) is the y intercept

if you want to check it then imput a point on the line into the x and y variables

Because the equation contains an absolute value, the shape of the graph would be a V,.

The Y intercept is -1, so this would be the lowest point on the graph.

Replace X with 1 and solve:

y = 2(1) -1 = 2-1 = 1, so another point would be (1,1) and another point would be (-1,1)  ( Absolute value would use both -1 and 1 as the same).

Make 3 points on the graph:

(-1,1) (1,1) ans (0,-1) and draw lines through them.

See attached picture:

The cost of glass is:  £4

The cost of mug =  £2

Step-by-step explanation:

Let g be the number of glasses and

m be the number of mugs

[tex]3g+3m = 18\ \ \ \ \ Eqn\ 1\\6g+4m=32\ \ \ \ \ Eqn\ 2[/tex]

Multiplying equation 1 by 2

[tex]6g+6m=36\ \ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex]6g+6m - (6g+4m) = 36-32\\6g+6m-6g-4m=4\\2m=4[/tex]

Dividing both sides by 2

[tex]\frac{2m}{2} = \frac{4}{2}\\m = 2[/tex]

Putting m=2 in eqn 1

[tex]3g+3(2) = 18\\3g+6 = 18\\3g = 18-6\\3g = 12[/tex]

Dividing both sides by 3

[tex]\frac{3g}{3} = \frac{12}{3}\\g = 4[/tex]

Hence,

The cost of glass is:  £4

The cost of mug =  £2

Keywords: Linear Equation, simultaneous equations

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Final answer:

To find the angle of elevation, we can use the concept of tangent. The angle of elevation is approximately 67.7 degrees.

Explanation:

To find the angle of elevation, we can use the concept of tangent.

Tan(Angel of Elevation) = Opposite/Adjacent

Here, the opposite side is the height of the fair, which is 1800 meters, and the adjacent side is the height of the station, which is 700 meters.

Tan(Angel of Elevation) = 1800/700

Angel of Elevation = tan-1(1800/700)

Using a calculator, the angle of elevation is approximately 67.7 degrees.

Answer:

1.69

Step-by-step explanation:

well to find out the unit rate that would be a pound now we need to find out how much it would cost for 1 lb which would be 3.38 / 2 which would be 1.69 as your answer

Answer:

$1.69 per pound

Step-by-step explanation:

3.38/2=1.69

Answer:

17/8

Step-by-step explanation:

2/1=2

11-2-6-7/8

9-6-7/8

3-7/8

24/8-7/8

17/8

Answer:

C

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x) by c units

• If c > 0 then shift c units up

• If c < 0 then shift c units down

The red graph is a vertical translation f(x) of 3 units down

Thus

y = f(x) - 3 ( add 3 to both sides )

y + 3 = f(x) ← equation of red graph

Answer:

yes

Step-by-step explanation:

Because 6+ 2 equals 8 then plus 3 equals 11 and 11 equals 8+3

Answer:

Step-by-step explanation:

Use PEMDAS:

P Parentheses first

E Exponents

MD Multiplication and Division

AS Addition and Subtraction

[tex]6:(-3)-(-9)[/tex]           first - division

[tex]=-2+9[/tex]          use commutative property a + b = b + a

[tex]=9+(-2)=9-2=7[/tex]

Answer:

The next two terms for the geometric sequence are - 108 and - 324.

Step-by-step explanation:

1. Let's find the next two terms for the geometric sequence which first three terms are as follows:

- 4, 12, - 36.....

Aₓ = Aₓ₋₁ * 3 ; A₁ = - 4

A₁ = - 4

A₂ = A₁ * 3 = - 4 * 3 = - 12

A₃ = A₂ * 3 = - 12 * 3 = - 36

A₄ = A₃ * 3 = - 36 * 3 = - 108

A₅ = A₄ * 3 = - 108  * 3 = - 324

The next two terms for the geometric sequence are - 108 and - 324.

The correct sequence is a. 17, 26, 37.

To determine the next three terms in the sequence, we must first identify the pattern governing the sequence. Let's examine the differences between consecutive terms:

- The difference between the second term (2) and the first term (1) is 1.

- The difference between the third term (5) and the second term (2) is 3.

- The difference between the fourth term (10) and the third term (5) is 5.

- The difference between the fifth term (17) and the fourth term (10) is 7.

We can see that the differences between consecutive terms are increasing by 2 each time. This suggests that the sequence is generated by adding consecutive odd numbers to the previous term. To find the next terms, we continue this pattern:

- The sixth term will be the fifth term (17) plus the next odd number (9), which is 17 + 9 = 26.

- The seventh term will be the sixth term (26) plus the next odd number (11), which is 26 + 11 = 37.

- The eighth term will be the seventh term (37) plus the next odd number (13), which is 37 + 13 = 50.

Therefore, the next three terms of the sequence are 26, 37, and 50, confirming option a as the correct answer.

Answer:

The Slope is 9 and the y-intercept is -2

Step-by-step explanation:

Answer: slope=9

Y-intercept=-2

Step-by-step explanation:

Use y=mx+b where m equals slope and b equals y-intercept

Answer:

Step-by-step explanation:

[tex]-2+4(-x+4)=10\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\-2+(4)(-x)+(4)(4)=10\\\\-2-4x+16=10\qquad\text{combine like terms}\\\\-4x+(-2+16)=10\\\\-4x+14=10\qquad\text{subtract 14 from both sides}\\\\-4x+14-14=10-14\\\\-4x=-4\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{-4}{-4}\\\\x=1[/tex]

Answer:

Option C. [tex]g(x)=(x+5)^{2}[/tex]

Step-by-step explanation:

we know that

The equation of the parent function f(x) (red graph) is

[tex]f(x)=x^{2}[/tex]

This is a vertical parabola open upward

The vertex is the point (0,0) (the origin)

The function g(x) (blue graph) is a vertical parabola open upward

The vertex is the point (-5,0)

The transformation of f(x) to g(x) has the following rule

f(x) -----> g(x)

(0,0) ----> (-5,0)

(x,y) ----> (x-5,y)

That means----> The transformation is a translation of 5 units at left

therefore

The equation of g(x) is

[tex]g(x)=(x+5)^{2}[/tex]

120% = $150

divide both sides by 6

20% = $25

We want the regular price, so 100%.

multiply both sides by 5

100% = $125

Answer:125

Step-by-step explanation:

150/1.20

=125

The recursive formula for given sequence is:

[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]

Step-by-step explanation:

Given sequence is:

-16, 4, -1, ...

First of all, we have to find the common ratio. common ratio is the ratio between two consecutive terms of a geometric sequence

Here

[tex]a_1 = -16\\a_2 = 4\\a_3 = -1\\Now\\r = \frac{a_2}{a_1} = \frac{4}{-16} = -\frac{1}{4}\\r = \frac{a_3}{a_2} = \frac{-1}{4} = -\frac{1}{4}[/tex]

The recursive of geometric sequence is:

[tex]a_n = r * a_{n-1}[/tex]

Putting the value of r

[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]

Hence,

The recursive formula for given sequence is:

[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]

Keywords: Geometric sequence, Recursive formula

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x = - 3

y = -2

Step-by-step explanation:

3x - 8y = 7

x +2y = -7

We standardize the coefficient of one variable such that it addition will result to zero;

3x - 8y = 7

(x +2y = -7)4

Then multiply the one equation with a constant (this case 4) to get;

3x – 8y = 7

4x + 8y = - 28

We add the two equations;

3x – 8y = 7

+

4x + 8y = - 28

=

7x = - 21

x = -21 / 7

x = - 3

Now we evaluate y by replacing the value of x with -4 in one of the equation;

x +2y = -7

-3 +2y = -7

2y = -7 + 3

2y = - 4

y = -2

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V = π·r²·h/3 = π·81·6/3 = 2·81·π = 162π cm³