Solve the compound inequality.
5 < 2x - 1 < 9
Show work

Answer:

There are 9 llamas.

Step-by-step explanation:

For Billy, we have to find a number that is divisible by four, because he has one group of lambs, and 3 times as many llamas, which gives us 4 groups altogether. The number must be below 10 in order to not go above 17 when Milly's number of animals are included, but above 4 itself in order to reach the target of 17 in the first place.

As you can guess, the only number that fits all the criteria is 8. It's divisible by 4 and below 10, but above 4 itself.

If Billy has three times as many llamas as lambs, then he must have 2 lambs, and 6 llamas, as 2 × 3 = 6.

If we know that Billy has 8 animals, then we also know that Milly must have 9 animals, as 17 - 8 = 9.

We also know that Milly has 3 groups of animals; one group of llamas, and two groups of lambs, meaning we divide the number of animals she has by 3.

9 ÷ 3 = 3.

This tells us Milly has just 3 llamas, because 3 is one group of 9, and 3 × 2 = 6,  because she has twice the amount of lambs.

Billy has 2 lambs and 6 llamas.

Milly has 6 lambs and 3 llamas.

The amount of lambs is irrelevant to our final answer, so we can disregard them and do a final sum of 6 + 3 = 9, which gives us our answer.

Answer:

Billy: Has 4 lots of animals

Milly: Has 3 lots of animals

17 animals in total means that Billy must have 4 lots of 2 (8 animals) and Milly must have 3 lots of 3 (9 animals) So Billy has 6 llamas and Milly has 3, giving 9 llamas in total

Answer: 3

Step-by-step explanation:

This problem is looking for the Greatest Common Factor (GCF) of 6 and 15.

Draw a factor tree for each number and see what they have in common.

           Reg         Diet

               6              15

               ∧               ∧

            2   3           3  5

The GCF of 6 and 15 =  3

Each table will contain 2 cans of regular soda and 5 cans of diet soda.

Answer:

segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI  

Step-by-step explanation:

In the picture attached, the triangles are shown.

After the dilation and reflection, there is proportionality between segment FG and segment FI, segment FH and segment FE, and segment HG  and segment EI. More specifically:

Answer:

segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI  

Step-by-step explanation:

In the picture attached, the triangles are shown.

After the dilation and reflection, there is proportionality between segment FG and segment FI, segment FH and segment FE, and segment HG  and segment EI. More specifically:

FG = 1/2*FI

FH = 1/2*FE

HG = 1/2*EI

This answer is right! took the test on FLVS and confirmed it :)

Answer:

I think it's D because the line AC looks like it is splitting the rectangle in half. I think this is right since the angles are congruent. (Angle BAC and Angle ACD)

Answer:

(0, -2)

Step-by-step explanation:

The y-int is where the graph crosses the y-axis when x = 0. The easiest and fastest way to do this problem is to graph the equation using a graphing calc and tracing the graph to find your value.

Answer:

Step-by-step explanation:

for y intercept x=0

thus y= -2

the point is (0,-2)

Answer:

you would multiply length times width witch would be 12in by 30in 360

Answer:

25:16

Step-by-step explanation:

i think its right

Answer: B

Step-by-step explanation:

Makes the most sense out of all the options because it’s the most random or unpredictable

Answer:

0.625

Step-by-step explanation:

divide 5 by 8 to get 0.625

Answer:

0.625

Step-by-step explanation:

Divide the numerator by the denominator

so 5÷8 which equals 0.625.

Answer: C) ΔCAT is congruent to ΔDOG

Step-by-step explanation:

If all the sides of two triangles are congruent, then the triangles are congruent.

Answer:

c. ΔCAT is congruent to ΔDOG

Step-by-step explanation:

Due to each the AAA (angle-angle-angle) and SSS (side-side-side) theorems, if all of the facets and/or angles of triangles are congruent, then the triangles are congruent.

please mark me brainliest!

Answer:

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Answer:

a = 6

Step-by-step explanation:

10a - 41 = 19

10a = 19 + 41

10a = 60

a = 60/10

a = 6

Answer:

a=  6

Step-by-step explanation:

10a - 41=19

+41         +41

10a = 60

÷10    ÷10

a=  6

Answer:

Option A.

Step-by-step explanation:

The given sequence is  

24, 30, 36, 42, 48, ...

It is an AP. Here,  

First term = 24

Common difference = 30-24 = 6

The given explicit formula for nth term is

[tex]a_n=a_1+(n-1)d[/tex]

where, [tex]a_1[/tex] is first term, d is common difference.

Substitute [tex]a_1=24, d=6 \text{ and }n=500[/tex] in the above formula.

[tex]a_{500}=24+(500-1)(6)[/tex]

[tex]a_{500}=24+(499)(6)[/tex]

[tex]a_{500}=24+2994[/tex]

[tex]a_{500}=3018[/tex]

The 500th term of the sequence is 3018.

Therefore, the correct option is A.

Answer:

A is correct

Step-by-step explanation:

Answer:

median: 90

mode: 91

mean: 84.2 or round it to 84

Step-by-step explanation:

Let me know if this helps! have a great day! :)

Answer:

a) Median = 91

b) mode = 91

c)Mean 84.2

Step-by-step explanation:

a) Median is the middle term. So, 6th term

Median = 91

b) Mode is the score which occurs more number of times

91 occurs 3 times

Mode = 91

c) Mean= sum of all data's/Number of data's

            = 85 + 91 + 48 +98 + 99 /5

            = 421/5

  Mean = 84.2

Answer: Rita has $25 saved.

Step-by-step explanation:

You could think about it this way: $69 is $6 less than 3 times the amount of money that she has. So, let's solve this:

1) First you would add $6 to the $69 that the skateboard costs because you     need to know what her savings would be if she multiplied it by 3.

      $69+$6=$75  

2) Now that we know that if we tripled her savings, we would have $75. We can now find out how much she actually has saved up by dividing the total of $75 by 3.

      $75÷3=$25

I hope this helped you with your question!

Answer:

she saved $25

Step-by-step explanation:

Answer:

≈ 68.2°

Step-by-step explanation:

tan X= 20/8

tan X= 2.5

x= tan ⁻¹ 2.5

x ≈ 68.2°

Answer:

Step-by-step explanation:

 To find the size of YXZ we should use some trigonometry but first let's find the length of YZ

(XZ)²+(ZY)²=(YX)²

YX=[tex]\sqrt{20^{2}+8^{2} }[/tex]

    =4[tex]\sqrt{29}[/tex]

Answer:

6 sq units, 4 sq units, 6 sq units

Step-by-step explanation:

Method:

count dots inside ...(a)

the ones on the border of the polygon and divide by two ...(b)

(a)+(b)-1 = area

use this method for the red, green, and yellow polygons.

Red:

(a): 2

(b): 10/2 = 5

2+5-1 = 6 sq units

Green:

(a): 0

(b): 10/2 = 5

0+5-1 = 4 sq units

Yellow:

(a): 3

(b): 8/2 = 4

3+4-1 = 6 sq units

I hope this helps, and plz mark me brainliest!!!!

Answer:

You shoulda showed us the diagram but corresponding angles are the 2 angles on the diagram which are the same, look closely and you could tell which 2 are the same, they also have to be on THE SAME SIDE, right or left

Hope that helps!

Step-by-step explanation:

Answer:

C, Angle 3 and Angle 7

Step-by-step explanation:

heres the full question

In the diagram, which pair of angles are corresponding angles?

Angle 1 and Angle 8

Angle 4 and Angle 6

Angle 3 and Angle 7

Angle 2 and Angle 4

Answer:

(4, 7)     (8, 9)    

(2, 3)     (6, 5)

Step-by-step explanation:

The definition of a parallelogram is a quadrilateral that has two pairs of opposite equal length parallel sides, including equal opposite angle measurements

To simplify the task, we plot the  points on a graph paper for the parallelogram ABCD to get the following points;

B (4, 7)     A (8, 9)    

C (2, 3)     D (6, 5)

The length of the opposite sides AB and CD are;

Length AB = √((9 - 7)² + (8 - 4)²) = √20 = 2·√5

Length CD = √((3 - 5)² + (2 - 6)²) = √20 = 2·√5

The length of the opposite sides AC and BD are;

Length AD = √((9 - 5)² + (8 - 6)²) = √20 = 2·√5

Length BC = √((7 - 3)² + (4 - 2)²) = √20 = 2·√5

The slope of segment AB is (9 - 7)/(8 - 4) = 2/4 =1/2

The slope of segment CD is (5 - 3)/(6 - 2) = 2/4 =1/2

Therefore, since the slopes of segments AB and CD are equal, segments AB and CD are parallel

Similarly, we have;

For segment AD, slope = (9 - 5)/8 - 6) = 4/2 = 2

For segment BC, slope = (7 - 3)/4 - 2) = 4/2 = 2

Therefore, the slopes of segments AD and BC are equal, segments AC and BD are parallel.

Answer:

4² + 5² = x²

Step-by-step explanation:

From the picture, the height of the staircase is:

h = 20 ft -15 ft = 5 ft

And the distance between the staircase and the building is 4 ft.

A right triangle is formed, where the distance between the staircase and the building (4) and the height of the staircase (5) are the legs, and the length of the staircase (x) is the hypotenuse. Using Pythagorean theorem:

4² + 5² = x²

Answer:

The found values are:

A = 1/3

B = -8/3

Step-by-step explanation:

We know that general equation is given by:

y = mx + c

where m is the slope and c is a constant.

x + 3y = -5

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

Slop of the equation is -(1/3). As parallel line have same slope substitute it in the first equation:

Ax + By = 3

By = -Ax - 3

By = (1/3)x - 3

Hence, A = 1/3

Substitute point (-7,2) into the equation:

B(2) = (1/3)(-7) -3

B(2) = -7/3 - 3

B(2) = -16/3

B = -16/6

B = -8/3

Answer:

x ≈ 34.88 square cm

Step-by-step explanation:

Solve by proportional formula:

Area of a sector/area of circle* = sector central arc measure/360

*area of a circle = πr²

x/(53.29π) = 75/360

x/53.29π = 0.2083

x = 11.1020833π

x = 34.8782233

x ≈ 34.88 square cm

Answer:

Other guy is right also i had it on my test x ≈ 34.88 square cm

Step-by-step explanation:

Answer:

C. 1000

Step-by-step explanation:

10 is not a perfect cube.

100 is not a perfect cube, it is a perfect square.

1000 is a perfect cube.

10 × 10 × 10 = 1000

10000 is not a perfect cube.

Answer:

it says 10

Step-by-step explanation:

A decade is 10 years.

apparently

Answer:

a) z = 70.5°

b) s = 83.6°

c) x = 0.7cm

Step-by-step explanation:

We would solve for the above questions using Trigonometric functions of either Sine, Cosine or Tangent.

a) We are given the following values

Hypotenuse = 21 inches

The triangle is divided into two to give us a right angle triangle

The adjacent side = 14inches/2 = 7 inches

We are to find Angle z

The Trigonometric function we are using is Cosine

cos z = Adjacent / Hypotenuse

cos z = 7/21

cos z = 1/3

z = arc cos(1/3)

z = 70.528779366°

To 1 decimal place

z = 70.5°

b) We are given the following values

Hypotenuse = 12 cm

The triangle is divided into two to give us a right angle triangle

The opposite side = 16cm/2 = 8 cm

We are to find Angle s, but it is split into 2

So we represent the half as x

The Trigonometric function we are using is Sine

sin x = Opposite/ Hypotenuse

sin x = 8/12

sin x = 2/3

x = arc sin(2/3)

x = 41.810314896°

Remember in the question, we are to find s.

s = x° × 2

s = 41.810314896 × 2

s = 83.620629792

To 1 decimal place

s = 83.6°

c) From the above diagram, we are to find the Opposite side represented by x

Our triangle is split into two equal halves

Adjacent side = 2cm

Angle θ = 36°/2 = 18°

We are using Trigonometric function tan to solve for question c

tan θ = Opposite/ Adjacent

tan 18° = Opposite/ 2

Cross Multiply = tan 18° × 2

0.3249196962 × 2

= 0.726542528cm

To one decimal place,

x = 0.7cm

Answer:

7/32

Step-by-step explanation:

Combinators. Your best friend in this scenario.

Basically, using combinations helps you to find the different ways that you could get heads three times out of eight. To do that, just get 8!/(3!5!) (this is a formula, not the exact numbers, per say, you should check that out), which ends up as 56. So there's 56 different ways that Peter can flip a coin eight times and land on heads three times.

Then, you divide that by the total number of possibilities, which in this case is 2^8, since every coin you flip gives you two different options, heads or tails.

Simplifying the fraction gets you 7/32.

Answer:

7/32

Step-by-step explanation:

the probability of getting exactly 3 heads when a coin is flipped 8 times in a row is: 7/32.

Answer:

y = x + 16

Step-by-step explanation:

Step 1: Find slope of perpendicular line

Take the negative reciprocal of the 1st line

m = 1

Step 2: Find b

y = x + b

14 = -2 + b

b = 16

Step 3: Write equation

y = x + 16

Answer:

y = x + 16

Step-by-step explanation:

Given the equation y = -x - 1, we see that the slope (the coefficient of the x term) is -1.  A line perpendicular to this one has a slope which is the negative reciprocal of the given equation:   +1.

Using the point-slope formula for the equation of a straight line, we get:

y - 14 = +1(x + 2), or y - 14 = x + 2, or y = x + 16

Answer:

×=19

Step-by-step explanation:

90-22=68

3x+11=68

68-11=57

3x=57

57÷3=19

x=19