Help me with this... ​

Answer:

[tex]|3r-15| = -3r+15[/tex] if [tex]r<5[/tex]

Step-by-step explanation:

Given that:

r < 5

To simplify:

|3r−15|

Solution:

First of all, let us learn about Modulus function:

[tex]f(x) =|x| =\left \{ {x, \ if\ {x>0} \atop -x\ if\ {x<0}} \right.[/tex]

In other words, we can say:

Modulus function has a role to make its contents positive.

If the contents are positive, the result will be equal to its contents only.

If the contents are negative, it will add a negative sign to the contents to make it positive.

Now, let us consider the given condition:

[tex]r < 5[/tex]

Multiply both sides with 3. (As 3 is a positive number, the equality sign will not change.)

[tex]3r < 15[/tex]

Subtracting 15 from both sides:

[tex]3r-15<15-15\\\Rightarrow 3r-15<0[/tex]

Now, we know that [tex]3r-15<0[/tex], let us use the definition of Modulus function.

Add a negative sign to the contents because the contents are already negative.

[tex]\\\Rightarrow |3r-15| = -(3r-15)\\\Rightarrow -3r+15[/tex]

So, the answer is:

[tex]|3r-15| = -3r+15[/tex] if [tex]r<5[/tex]

Answer:

5.726

Step-by-step explanation:

First, find the thousandths place value. Note the place values:

5 (one's place value)

.

7 (tenth's place value)

2 (hundredth's place value)

5 (thousandth's place value)

5 (ten thousandth's place value)

Find the thousandths place value. Look at the number located directly next to it (ten thousandth's place value).

Note that:

Since the number is 5, round up.

5.7255 rounded to the nearest thousandths place value is 5.726

~

Answer:

"descends"

Step-by-step explanation:

(just had the same question).

Answer:

Square root of 12 is a interfering because it isn’t a perfect square.

Answer:

It is an integer.

Step-by-step explanation:

Integers are all types of numbers may it be negative or positive but rational numbers are positive and negative fractions or decimals. So √12 is an integer.

Hope this helps.

Answer:

So, 89 Adult tickets were sold.

Step-by-step explanation:

So, we first name our variables, say, a for number of adult tickets, and c for child tickets.

Then we write our system of equations, first the total $ sale:

5.2c + 8.3a = 1087.10

Then we write the 2nd equation, the total number of tickets:

c + a = 156

Now, we can solve the system:

We do have different methods, let's to by subsitution.

make some change to the 2nd equation, to make c the subject: c = 156 - a

Now we plug that into the 1st equation:

5.2(156 - a) + 8.3a = 1087.10

811.2 - 5.2a + 8.3a = 1087.10

811.2 + 3.1a = 1087.10

3.1a = 275.9

a = 89

Answer:

The 1095 represents the amount of transactions already processed.

Step-by-step explanation:

Since this equation is showing us the number of transactions added over time, we know that in A = P(1 + r)^t,

A is the total amount

P is the starting amount

r is the rate

t is the time

So, our 1095 matches with P, and is the starting amount of transactions.

Answer:

The initial number of transactions was 1,095.

Step-by-step explanation:

Answer:

(0, 4)

Step-by-step explanation:

The y-intercept is where the graph crosses the y-axis when x = 0. Since you are given the graph, you can see that when x = 0, the graph crosses y = 4, so our y-int is (0, 4).

Step-by-step explanation:you have to add the two smallest angle and then the big number 11 you'll see if the 2 angles you added are bigger then your 11

Answer:

True

Step-by-step explanation:

you have to use the triangle inequality theorem

9 + 4 > 11

YES

4 + 11 > 9

YES

9 + 11 > 4

YES

therefore, it's true

Answer:

111111 [tex]\times[/tex] 1111110 is the simple expression.

Step-by-step explanation:

The expression to be solved:

[tex]\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1} - \dfrac{777,777\times777,777}{1+2+3+4+5+6+7+6+5+4+3+2+1}[/tex]

First of all, let us solve the first term:

[tex]\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1}\\\Rightarrow \dfrac{6666666\times666666 }{36}\\\Rightarrow \dfrac{6666666\times666666 }{6\times 6}\\\Rightarrow 1111111\times 111111[/tex]

Now, the right term:

[tex]\dfrac{777777\times777777}{1+2+3+4+5+6+7+6+5+4+3+2+1}\\\Rightarrow \dfrac{777777\times777777}{49}\\\Rightarrow \dfrac{777777\times777777}{7 \times 7}\\\Rightarrow 111111 \times 111111[/tex]

So, the expression to be solved becomes:

[tex]1111111\times 111111-111111\times 111111\\\Rightarrow 111111(1111111-1)\\\Rightarrow 111111\times 1111110[/tex]

Answer: 2n+2

Step-by-step explanation:

1. Remove the parentheses

-n-3+3n+5

2. Collect like terms

2n-3+5

3. Calculate the sum

2n+2

Answer:

x = 65°

Step-by-step explanation:

The interior angle of the triangle and 140° are adjacent and supplementary, thus

interior angle = 180° - 140° = 40°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

105° is an exterior angle of the triangle, thus

x + 40° = 105° ( subtract 40° from both sides )

x = 65°

Answer:

65°

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

180 - 105 = 75

180 - 140 = 40

Angles in a triangle add up to 180 degrees.

x + 75 + 40 = 180

x + 115 = 180

x = 180 - 115

x = 65

Answer:

You have to make a frequency table.

Step-by-step explanation:

The classes are

.320- .329

.330-.339

.340 - .349

.350 - .359

.360 - .369

Then, you have to find to find how many values would fall into the class of .340 - .349.

.320 ≤ x ≤.329

All x values that are less than (or equal to) .329 but greater than .320 fall into the class of

.320- .329.

Frequency is just how many numbers are in a class.

Answer:

The solution is the triplet: (a, b, c) = (-3, 0, 0)

Step-by-step explanation:

Let's start with the second equation, and solving for "a":

a - b = -3

a = b - 3

Now replace this expression for a in the third equation:

2 a + b = -6

2 (b - 3) +b = -6

2 b - 6 +b = -6

3 b = -6 +6

3 b = 0

b = 0

So if b = 0 then a = 0 - 3 = -3

now we can replace a= -3, and b = 0  in the first equation and solve for c:

2 a - b + c = -6

2 ( -3) - 0 + c = -6

-6+ c = -6

c = -6 + 6

c = 0

Our solution is a = -3, b= 0 , and c = 0 which can be expressed as (-3, 0, 0)

Answer:

C. 20

Step-by-step explanation:

Constant = Height × Width

Constant = 5 × 4 = 20

Answer:

She will use 5/6 pound for the entire garden

Step-by-step explanation:

Here, we want to know the total number of pounds that will be used for the full garden.

Firstly, she used 1/2 or 0.5 pound for 3/5 of the garden, let the total amount of pound she will use for the full garden be x.

0.5 pound = 3/5 garden

x pound = 1 garden

x * 3/5 = 0.5 * 1

x * 3/5 = 0.5

3x/5 = 0.5

3x = 5 * 0.5

3x = 2.5

x = 2.5/3 or 5/6 pound

Answer:

(-4^9)^2 = -4^18

(4^6)^-3 = 1/4^18

(4^0)^-9 = 4^0

(4^-3)^-3 = 4^9

Step-by-step explanation:

Here, we want to match what we have on the left with the expressions on the right.

(-4^9)^2

= -4^18

(4^6)^-3

= 4^-18 = 1/4^18 according to laws of indices

(4^0)^-9 = 4^0

(4^-3)^-3

= 4^9

Answer:

(-4^9)^2 = -4^18

(4^6)^-3 = 1/4^18

(4^0)^-9 = 4^0

(4^-3)^-3 = 4^9

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

For this question you would follow the BIDMAS rule - (Brackets, Indices, Division, Multiplication, Addition, Subtraction.)

The first thing in this question you need to solve it (9 + 8)

we do this because, when we follow BIDMAS, the first rule is brackets

so, 9 + 8 = 17

The second step is to multiply, as this rule is second,

so, 17 x 2 = 34

Our final step is to solve the last bit, which is 6 x 14

and we know that 6 x 14 = 84

So now that we have 84 and 34, we need to subtract the two numbers as shown,

84 - 34 = 50

And this is how you get the answer 50

i hope this has helped you, please comment if you did not understand it and i will explain it in another way : )

Use pemdas

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Do parenthesis first: (9+8)=17

6x14-17x2

Then do multiplication

6x14=84 17x2=34

Now do subtraction

84-34=50

Therefore your answer is 50

Answer:

9 children tickets

Check:

adult is 5$

child3$

6×5=30

9×3=27

30+27=57

Step by step in photo

Answer:

the answer is 6

Step-by-step explanation:

Answer:

Θ=15

Step-by-step explanation:

AD=DC so triangle BCD is isosceles, so angle DBC = angle BCD = Θ

So angle BDC=180-Θ-Θ=180-2Θ

angle BDE = 180- angle BDC = 180-180+2Θ=2Θ

in triangle BDE all angles must add up to 180

angle BED= 180- angle BEA=180-90=90

so

90+4Θ+2Θ=180

90=6Θ

Θ=15

Answer:

x = 20

Step-by-step explanation:

If AE is a bisector then it divides the angle in half

BAE = EAC

x+30 = 3x-10

Subtract x from each side

30 = 2x-10

Add 10 to each side

40 = 2x

Divide by 2

40/2 =2x/2

20 =x

Answer:

the answer is D which is (4,2)

Step-by-step explanation:

this is how it looks when reflected

Answer:

(2,1) and (5,-5)

Step-by-step explanation:

I just truned it in and it was right.

Answer:

y = 5x-38

Step-by-step explanation:

The slope is m = (y2-y1)/(x2-x1)

                          = (-8 - -3)/(6-7)

                          = ( -8+3)/(-1)

                           =-5/-1

                            =5

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

y = 5x+b

Substitute a point into the equation

-8 = 5(6) +b

-8 = 30+b

-8-30 = 30-30+b

-38 = b

y = 5x-38

Slope formula: y2-y1/x2-x1

-8-(-3)/6-7

-5/-1

5

Find the y-intercept with the formula for slope intercept form.

y = mx + b

-3 = 5(7) + b

-3 = 35 + b

-3 - 35 = 35 - 35 + b

-38 = b

Fill in what we have:

y = 5x - 38

Best of Luck!

Answer:

41m, 30m, 15m

Step-by-step explanation:

A triangle can only be formed if the sum of any 2 side lengths adds up to be greater than the length of the other side.

The combination 41m, 30m, 15m is the only one where any 2 side lengths adds up to be greater than the other side.

We can test this:

41 + 30 > 15

30 + 15 > 41

The solution is Option C.

The sides of the triangles are 15 m , 30 m and 45 m

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Now , the measure of the sides of the triangle are

a)

AB = 8 m

BC = 10 m

AC = 20 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

20 < 10 + 8

20 < 18 which is FALSE

b)

AB = 2.5 m

BC = 2.5 m

AC = 8 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

8 < 2.5 + 2.5

8 < 5 which is FALSE

c)

AB = 15 m

BC = 30 m

AC = 41 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

41 < 30 + 15

41 < 45 which is TRUE

So , triangle ABC with sides 15 m , 30 m and 41 m is a triangle

d)

AB = 25 m

BC = 25m

AC = 75 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

75 < 25 + 25

75 < 50 which is FALSE

Hence , the triangle is with sides 15 m , 30 m and 41 m

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ5

Answer:

4/5

Step-by-step explanation:

t + b = 2.50

t = b+1.50

Substitute

b+1.50+ b = 2.50

Combine like terms

2b + 1.50=2.50

2b =1

b = .5

t = b+ 1.5

t = .5+ 1.5

t = 2

The fraction of the total price

t/2.50

2/2.50

20/25

4/5

Answer:

80% of the total price is torch.

Step-by-step explanation:

Let

t=cost of torch

b=cost of battery

A torch and battery cost £2.50 altogether.

t+b=2.5

The torch costs £1.50 more than the battery.

t-b=1.5

Keep in mind:

When equations of the form

a+b = Sum

a-b = Diff

then the solution is immediately

a=(Sum+Difference)/2

b=(Sum-Difference)/2

and apply the rule,

t=(2.5+1.5)/2 = £2

b=(2.5-1.5)/2 = £1

Torch / total

= 2/2.5

= 80%

Answer:

3a+6+5/(a+2)

Step-by-step explanation:

To do this you replace x with a+2, meaning that 3x+5/x turns into 3(a+2)+5/a+2. Simplified this is 3a+6+5/(a+2)

Answer :

13%

Step-by-step explanation:

Compound interest which is compounded annually calculated using the formula :

A = I( 1 + r/100)^t

Where I = invested amount

r = interest rate ; t = period ; A = final amount

If period = 9years, the rate required to triple the investment equals;

The final amount = 3 * invested amount = 3I

We now have ;

3I = I( 1 + r/100)^9

Divide both sides by I

3 = (1 + r/100)^9

Take the 9th root of both sides

3^(1/9) = (1 + r/100)^(9*1/9)

3^(1/9) = 1 + r/100

r/100 = 3^(1/9) - 1

r/100 = 1.1298309 - 1

r / 100 = 0.1298309

Multiply both sides by 100

r = 12.98309

r = 12.98 = 13%

Answer:

I(3,8)

Step-by-step explanation:

to answer this question we must use this relation :