Graph the solution set of the inequality and write the solution using interval notation. Please give me a step by step explanation.

Using the angle and segment addition postulates, the measures are:

a. m<TSM = 95°

b. m<SIJ = 93°

c. SR = 12 units

d. PQ = 10 units

The angle addition postulate states that two smaller angles have a sum of measure that is equal to the larger angle they form.

Similarly, the segment addition postulate states that two smaller segments that make up a larger segment have a sum that equals the length of the larger segment.

a. m<TSM + m<MSR = m<TSR [angle addition postulate]

Substitute

32x - 1 + 48 = 48x - 1

Solve for x

32x + 47 = 48x - 1

32x - 48x = -47 - 1

-16x = -48

x = -48/-16

x = 3

m<TSM = 32x - 1 = 32(3) - 1

m<TSM = 95°

b. m<HIS + m<SIJ = m<HIJ [angle addition postulate]

Substitute

x + 40 + 2x + 93 = 133

3x + 133 = 133

3x = 133 - 133

3x = 0

x = 0/3

x = 0

m<SIJ = 2x + 93 = 2(0) + 93

m<SIJ = 93°

c. x + 14 + x + 15 = 23

2x + 29 = 23

2x = 23 - 29

2x = -6

x = -3

SR = x + 15 = -3 + 15

SR = 12 units

d. -6 + 2x + 2x - 4 = 22

-10 + 4x = 22

4x = 22 + 10

4x = 32

x = 32/4

x = 8

PQ = -6 + 2x = -6 + 2(8)

PQ = 10 units

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Answer: QR = 21 Units

P = 2(l) + 2(w)

[tex]88= 2(4z-1) + 2(3z+3)[/tex]

[tex]88 = 8z-2+6z+6[/tex]

[tex]88 +2-6= 8z+6z[/tex]

[tex]84=14z[/tex]

[tex]\frac{84}{14} =\frac{14z}{14}[/tex]

[tex]6 = z[/tex]

[tex]QR = 3z+3[/tex]

[tex]QR = 3(6) +3[/tex]

QR = 21 Units

Answer:

Brand B

Explanation:

The cost for each brand is given below:

• Brand A: 20 ounces for $2.50

• Brand B: 32 ounces for $3.25

To determine the price per ounce for each brand, divide the cost by the number of ounces.

This, we see that Brand B has the lowest price per ounce.

The equation for g(x) =  -(x + 1)² - 4.

Where f(x) = x².

The given parent function is ,

f(x)= x²

f1(x) = -f(x)

So,

f1(x) = -x²

It has also been moved down 4 units.

f2(x) = f1(x) -4

f2(x) = -x² - 4

1 unit has also been shifted to the left.

g(x) = f2( x + 1)

g(x) = -(x + 1)² - 4

As a result, the required equation is.

g(x) = -(x + 1)² - 4.

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Answer:

210 ways

Step-by-step explanation:

This is a combinatorics problem of the general nature of choosing r elements from a sample of n elements

It is indicated by the term
[tex]C(n,r) = $\displaystyle \binom{n}{r} = \dfrac{n!}{( r! (n - r)! )$}\\\\[/tex]

where n! represents the factorial of n = n x (n-1) x (n-2) x .... 3 x 2 x 1

With n = 10, r = 3 there are C(10, 3) ways of choosing the officers

[tex]C(n,r) = C(10,4)\\\\= \dfrac{10!}{4! (10 - 4)! }\\\\\\[/tex]

[tex]= \dfrac{10!}{4! \times 6! }[/tex]

[tex]$\displaystyle = 210[/tex]

The two polygons are calculated to be similar and the correct statement to show the similarity is in option A

To show that the polygons are similar we show that

Comparing the angles

Comparing  the ratio of corresponding sides

10.5 / 7 = 12 / 8 = 6 / 4 = 9 / 6 = 3 / 2

This shows that option A is the correct choice

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Answer:

0.6

Step-by-step explanation:

3/5 as a decimal is 0.6; divide the numerator by the denominator. :)

Data:

Quiz taken: 16

Quiz each week: 1

You can express this as a equation:

Q= Total of quizes taken

W= weeks

As each week the number of quizes Q increase in 1 the change is k=1, and Isabela has already taken 16 quizzes. The number of quizzes can be represented as:

Q0 is the number of quizzes Isabela has already taken.

Then, to have a total of 26 quizzes Isabela have to attend:

Q=26

W=?

You can find the number of weeks by clearing of the equation above the W:

Substract in both sides of the equation 16:

The correct option: B. 5 cm, the image of DE will have the same length as DE, i.e. 5 cm.

For the given question;

DE segment length is 5 cm.

The transformation implemented to DE now is; Rx degrees R₀.-270 degrees.

That is, DE is the segment.

270° counter-clockwise rotation about the origin, then reflected across the x-axis

It is necessary to determine the length of a segment that is the image of DE.

Because, as we all know,

The only transformation that affects the figure's measurements is 'dilation.'

As a result, rotation and reflection have no effect on the shape and size of a segment DE.

Therefore, the image of DE will have the same length as DE, i.e. 5 cm.

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The complete question is-

DE has a length of 5 cm. What is the length of the image of DE after applying the composition Rx degrees R₀.-270 degrees?

A. 2.5 cm

B. 5 cm

C. 10 cm

D. 20 cm

Answer:82

Step-by-step explanation:

Because you need to regroup the numbers, therefore leaving 4-4, which is just a 0, (don't include the 0 in a number).

following a mixed number [tex]\frac{87}{8} + (\frac{75}{6} - \frac{21}{3} )[/tex] , we get  [tex]16 \frac{3}{8}[/tex]

According to the question, given that

Mixed numbers

[tex]\frac{87}{8} + (\frac{75}{6} - \frac{21}{3} )[/tex]

⇒ [tex]\frac{87}{8} + (\frac{25}{2} - 7 )[/tex]

⇒  [tex]\frac{87}{8} + \frac{25}{2} - 7[/tex]

⇒ [tex]\frac{87 + 100 - 56}{8}[/tex]

⇒ [tex]\frac{131}{8}[/tex]

⇒ [tex]16 \frac{3}{8}[/tex]

Therefore, after solving a mixed number [tex]\frac{87}{8} + (\frac{75}{6} - \frac{21}{3} )[/tex] ,  we get  [tex]16 \frac{3}{8}[/tex]

A whole number plus a proper fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for us to comprehend numbers.

A whole number and a legal fraction make up a mixed number. A mixed number like [tex]3\frac{1}{4}[/tex] is one where 1/4 is the correct fraction and 3 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.

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The slope between the scuba diver and fish would be; 0.5 .

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

Given that boat is located a sea level. A scuba diver is given as 80 feet along the surface of the water from the boat and 30 feet below the water surface.

A fish is given as 20 feet along the horizontal plane from the scuba diver and 10 feet.

We are asked to slope between the scuba diver and fish.

The Horizontal distance between diver and fish = 20 feet.

Fish below the scuba diver = 10 feet

Slope between scuba diver and fish is :

Tan Ф =10/20

Tan Ф = 0.5

Therefore, the slope between the scuba diver and fish would be; 0.5 .

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Answer:

8 · (32 · x^5 / 9 x^3 y^4)

Answer:

2.5kg potatoes would approx. cost 4.23$

Step-by-step explanation:

cost of 1kg potato = 1.69$

Therefore, cost of 2kg of potato = 1.69X2

                                                      =3.38

cost of 0.5kg of potato = 1.69\2

                                      = 0.85

Total cost of 2.5kg potato = 2kg + 0.5kg

                                           = 3.38 + 0.85

                                           = 4.23$

Answer:

$4.225

Step-by-step explanation:

2.5kg times per 1.60kg

2.5x1.6=4.225

Answer:

Step-by-step explanation:

What is the Product Rule of Exponents?When multiplying two numbers with the same base, their powers/exponents would be added.For example, .Given:(a²c)³Therefore:(a²c)³ = (a²c)(a²c)(a²c) (a²c)³ = (a²c)³ = Therefore, applying the product rule of exponents, (a²c)³ = .

The required measure of x and y for the concurrent triangle is 4 and 2 respectively.

In congruent geometry, the shapes that are so identical. can be superimposed on themselves.

here,
Since the triangle is are concurrent triangle,
x + 4 = 4y - - - - (1)
x = y + 2 - - - - (2)
Solving the above system of the equation,
y + 2 + 4 = 4y
6 = 3y
y = 6 / 3
y = 2
Now put this y in equation 2
x = 2 + 2
x = 4

Thus, the required measure of x and y for the concurrent triangle is 4 and 2 respectively.

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The height of ∆EBA is 24cm in the given question where two triangles are similar.

Similar triangles are triangles that have the same shape but differ in size. Similar objects include all equilateral triangles and squares with any side length. In other words, if two triangles are similar, their corresponding angles and sides are congruent and in equal proportion. The " symbol here denotes the similarity of triangles.

We know that in two similar triangles, the ratio of corresponding sides are equal to ratio of their heights.

We have given that ∆DBC ≅ ∆EBA

So,

⇒ (36-h)/h = DC/AE

⇒ (36-h)/h = 10/20

Using cross multiplication

⇒ 20(36-h) = 10h

⇒ 720 - 20h = 10h

⇒ - 20h -10h = -720

⇒ -30h = -720

⇒ 30h = 720

⇒ h = 720/30

⇒ h = 24

Thus, the height of ∆EBA is 24cm in the given question where two triangles are similar.

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Full question

Use similar triangles to calculate the height, h cm, of triangle ABE.

10 cm

С

В.

36 cm

E

20 cm

Answer: Infinitely many

The answer is infinitely many

This is because if the sides are parallel, the other measurements must be the same. They can be any measurement

The image point of the point (-1, 9) after the transformation R270° or y-axis as required in the task content is; (1, 9).

It follows from the task content that the image of the point under the rotation transformation; R270° be determined.

Since the pre-image point (-1, 9) exists in the 2nd quadrant, it follows that the transformation; R270° indicates a reflection over the y-axis.

Hence, only the x-coordinate of the pre-image changes sign and therefore, the image is; (1,9).

Ultimately, the image point is; (1, 9).

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The equation of the polynomial function is y = x² + x - 2

The polynomial function is represented on the given graph

From the graph, we can see that:

The curve of the graph crosses the x-axis at the following points

x = -2 and x = 1

This means that the equation of the polynomial function can be calculated as

y = (x - x₁) * (x  - x₂)

Where

x₁ = -2 and x₂ = 1

Substitute x₁ = -2 and x₂ = 1 in the equation y = (x - x₁) * (x  - x₂)

So, we have

y = (x + 2) * (x  - 1)

Open the brackets

y = x² + 2x - x - 2

Evaluate

y = x² + x - 2

Hence, the equation is y = x² + x - 2

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The value of m that makes the expression a monomial is 10/3

From the question, the given parameters are

Monomial: -xy^3m

Degree = 10

The degree of a polynomial is the highest power of the polynomial

This means that

Degree = 10

Degree = 3m

Substitute the known values in the above equation

So, we have

3m = 10

Divide both sides of the equation by 3

m = 10/3

Hence, the value of m is 10/3

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Let

x -----> number of liters of 10% acid solution

y ----> number of liters of 70% acid solution

so

we have that

x+y=90 ------> x=90-y -----> equation 1

Remember that

10%=10/100=0.10

70%=70/100=0.70

20%=20/100=0.20

so

0.10x+0.70y=0.20(90) ------> equation 2

Solve the system of equations

substitute equation 1 in equation 2

0.10(90-y)+0.70y=0.20(90)

solve for y

9-0.10y+0.70y=18

0.60y=18-9

0.60y=9

y=15

Find out the value of x

x=90-y

x=90-15=75

therefore

the answer is

By using the formula for the slope of a line that passes through two points, we will get that the slopes are:

a)  3

b)  -2

c) -1.5

d)  -4

e) 1/4

For a line that passes through two points (x₁, y₁) and (x₂, y₂), the slope is given by the formula:

a = (y₂ - y₁)/(x₂ - x₁)

So we will use that for each of the given pairs.

a) The first pair is (3, 2) and (5, 8), so the slope is:

a = (8 - 2)/(5 - 3) = 6/2 = 3

b) The pair is: (-2, -7) and (-4, -3), so the slope is:

a = (-3 + 7)/(-4 + 2) = 4/-2 = -2

c) The pair is (1, -6) and (-2, -4) so the slope is:

a = (-4 + 6)/(-2 - 1) = 2/-3 = -3/2 = -1.5

d)  The pair is (4, -8) and (-2, 16) so the slope is:

a = (16 + 8)/(-2 - 4) = 24/-6 = -4

e) The pair is (-5, 10) and (7, 13) so the slope is:

a = (13 - 10)/(7 + 5) = 3/12 = 1/4

We found all the slopes for the lines that pass through the given pairs of numbers.

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Answer:

The answer would be 1.9

There really is no way to show the work on this problem since it is decimals

Sarah has taken 4/5 portion of the available water bottles.

How is a ratio determined?
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. A ratio is a comparison or condensed version of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio can be defined as the number that can be used to represent one quantity as a percentage of another.

Given, Total number of water bottles bought = 4
Total number of people sharing the bottles = 5
Since each bottle is divided in equal portion, each portion of bottle = 1/5
Also, Sarah took one portion from each of the four bottles, thus
Sarah has portion of water = 4*(1/5) = 4/5
Sarah has taken 4/5 portion of the available water bottles.

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It is listed below whether area or circumference needs to be calculated.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were expanded out and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter. The term "circumference" can also refer to the circle's actual location, which corresponds to a disk's edge. A sphere's circumference is equal to the length of any one of its great circles. The distance around a circle is its circumference, however this cannot be used as a definition if, as in many introductory presentations, distance is defined in terms of straight lines.

(a) Circumference needs to be calculated.

(b) Area needs to be calculated.

(c) Area needs to be calculated.

(d) Circumference needs to be calculated.

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The perimeter of the rectangle is 29t + 5

Define Perimeter.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.

Given,

width = 7t - 7.5

length = 7.5t + 10

we know, the perimeter of the rectangle (p) = 2 ( l + w)

put the value in given formula,

p = 2 * (7.5t + 10 + 7t - 7.5)

p = 2 * ( 14.5t  + 2.5)

p = 2 * 14.5t + 2.5 * 2

p = 29t + 5

Hence, the perimeter of the rectangle is 29t + 5

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The  values of the given numbers when it is rounded up to the nearest 10 thousands are:

Rounding up can be described as the process that is been used in the mathematics which is been used in the estimation of a particular number in a context.

It should be noted that in rounding the  a number up, it is required to look at the next digit at the right hand of the given figures in a case whereby the digit is less than 5,the digit can be rounded down, but in the case whereby the digit is more that 5 then it can be rounded up .

From the given values, we are given the 990,201 and 159,994  and if this were to rounded up to the nearest 10 thousand then we will start from the right hand sides and round down the values less than 5 and round up the values that is more that 5. and their values will be 990000

and 150000.

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