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State if the three numbers can be the measures of the sides of a triangle. 1) 9, 7, 13 2) 26, 12, 11 3) 11, 2,9 4) 6, 11, 12 Two sides of a triangle have the following measures. Find the range of possible measures for the third side. 5) 12,9 7) 11,6 6) 8, 11 8) 12,8​

Answer:

[tex]-1 \le x\le1.5[/tex]

Step-by-step explanation:

The expression we're given, we want both to be defined because how can you add a defined number to an undefined number?

Square roots only have real solutions for positive numbers and zero

So let's set up an inequality for both square roots

[tex]2x+2\ge0\\\\6-4x\ge0[/tex]

Let's solve the first one

[tex]2x+2\ge 0\\2x\ge-2\\x\ge-1[/tex]

this is the domain of the "first expression"

let's solve the second one

[tex]6-4x\ge 0\\-4x\ge -6\\x\le 1.5[/tex]

We want them to overlap, so we get a compound inequality: [tex]-1 \le x\le1.5[/tex]

since we want both of the expressions to be defined to define the entire thing.

The amount of ingredients needed for 10 apple melon recipe is 25 cups of watermelon, 7.5 cup of cantaloupe and 15 cup of honey, and for 15 is 37.5 cups of watermelon, 11.25 cup of cantaloupe and 22.5 cup of honey.

What do you mean by recipe?

A recipe contains the list of ingredients and set of instructions that tells us how to cook any particular dish.

As given in the question, for one recipe, we need

2 & 1/2 cups of watermelon, 3/4 cup of cantaloupe and 1 &1/2 cup of honey.

We can also say it as:

2.5 cups of watermelon, 0.75 cup of cantaloupe and 1.5 cup of honey.

In order to the amount of ingredients for 10 we need to multiply each ingredient with 10.

so it will become,

25 cups of watermelon, 7.5 cup of cantaloupe and 15 cup of honey.

Similarly, In order to the amount of ingredients for 15 we need to multiply each ingredient with 15.

so it will become, 37.5 cups of watermelon, 11.25 cup of cantaloupe and 22.5 cup of honey.

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Answer:

divide -4 from 20 so t is -5

Step-by-step explanation:

Answer:

t=-5

Step-by-step explanation:

divide both sides by -4 now we have t=-5

Answer: a meter of timber is 5$

Answer:

Rs5

Step-by-step explanation:

40m =Rs 200

Therefore, 1m = 200/40

= Rs 5

Answer:

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

The value of y in the expression (21y-1)=(4x+23)(9x-38) is (103x - 875)/21.

According to the given question

We have a linear equation in two variables

(21y - 1) = (4x + 23)(9x -38)

For finding the value of y solve the above equation by adding and subtracting the like terms.

So, 21y - 1 = 4x(9x -38) + 23 (9x -38)

⇒ 21y - 1 = 48x - 152x + 207x - 874

⇒ 21y - 1 = 103x - 874

⇒ 21y = 103x - 874 + 1

⇒ 21y = 103x - 875

⇒ y =  [tex]\frac{103x - 875 }{21}[/tex]

Hence, the value of y in the expression (21y-1)=(4x+23)(9x-38) is [tex]\frac{103x - 875 }{21}[/tex]

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Answer:

180

Step-by-step explanation:

It's 180 because 75% of 240 is 180.

Answers:

=======================================================

Explanation:

Think of a roller coaster. A sharp drop is where we have a very steep decline. The steeper the line, the more rapid the drop.

The same can be said for when the graph increases as well.

Horizontal portions of the graph are when the elevator isn't moving. The x value (time) is always moving forward of course, but the y value (height of the elevator) is not changing.

Answer:

I don't know

Step-by-step explanation:

There is none

Answer:

its c

Step-by-step explanation:

not sure how to explain it

a) The volume of the cube is 27,271 cubic centimeter

b) The surface area of the cube is 5,400

Well the edge is  30 cm +-  0.1 cm

Volume will be side cubed, so max estimate for volume is (30.1)^3, and minimum  (29.9)^3

So percentage error =   [(30.1)^3  -  30^3/ /  30^3    x  100 = 1,00 %

Surface area is 6 x side squared

So max estimate for area is 6 x 30.1^2,      

minimum  6 x 29.9 ^ 2

So percentage error =   (6 x 30.1^2 - 6 x 30^2) / (6 x 30^2)   x 100 = 0.67 %

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Given:

The function is,

a) The graph of the given function us,

Answer: option B)

b) f(1) and f(5) is,

Answer:

c) the domain of the function is,

Answer:

58.

Step-by-step explanation:

The number of students who travelled by bus = 473 - 9 = 464.

So, the number of students in each bus = 464/8

= 58.

The value of the function at the given value of x = -1 is 5 - 2[f(-1)] = -51

The equation of the function is given as

f(x) = -8x + 20

The function to calculate is given as

5 - 2[f(-1)]

So, we start by calculating the value of the function at x = -1

This is represented as 'f(-1)

So, we have the following equation

f(-1) = -8(-1) + 20

Evaluate the product

So, we have the following equation

f(-1) = 8 + 20

Evaluate the sum

So, we have the following equation

f(-1) = 28

Substitute f(-1) = 28 in the expression 5 - 2[f(-1)]

So, we have

5 - 2[f(-1)] = 5 - 2 x 28

Evaluate the product

5 - 2[f(-1)] = 5 - 56

Evaluate the difference

5 - 2[f(-1)] = -51

Hence, the value is -51

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The value of x comes out to be 9.

Here, we are given that m∠7 = 107 and m∠4 = (8x+1)

From the figure given below, we can see that angle 7 and angle 6 are vertically opposite angles. Thus-

angle 7 = angle 6

measure of angle 6 = 107°

Now, angle 6 and angle 4 are opposite interior angles and the sum of opposite interior angles is equal to 180. Thus-

m∠4 + m∠6 = 180

8x + 1 + 107 = 180

8x + 108 = 180

8x = 180 - 108

8x = 72

x = 72/8

x = 9

Thus, the value of x comes out to be 9.

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Your question was incomplete. Check for the missing figure below.

Total of 10 and $ total of $0.85. The place value denotes a word, whereas the total value denotes a figure. In mathematics, ten numbers are known as symbols or digits.

The sum of the digit and its place value is the total value. Example 1: In the number 58439, what is the place value of digit 4? As a result, digit 4's place value is Hundreds. Market capitalization is the value of a company as determined by the stock market. It is defined as the sum of all outstanding shares' market values. Multiply the number of outstanding shares by the current market value of one share to calculate a company's market cap.

Therefore,

a # total of 10

a $ total of $0.85

·        Since we have 2 unknowns, we need to set up a System of 2 Equations.

·        A System of 2 Equations helps us solve a situation with 2 Unknowns.

Let's set up our 2 equations for # and $.

·        For the # equation:

Let n = # of nickels

Let d = # of dimes

So, n + d = 10

·        For the $ equation, we have to assign a "value" to each of the coins:

A nickel is worth 5 cents or $0.05

A dime is worth 10 cents or $0.10

·        They told us we have 5 cents, a specific # of times + 10 cents, a certain # of times, that = $0.85

So,   $0.05n + $0.10d  

        = $0.85

To solve this, we have to have just 1 unknown, meaning just 1 variable.

· We represent one of the variables in terms of the other. But, which one?

·        Well, since they are asking for # of dimes, let's define a nickel in the duration of a dime.

·        Let's apply this in the simpler # equation:

So, n + d = 10

becomes n = 10 - d

·        So now, in our $ equation, we can just replace "n" with "10 - d", and then solve for d, which is the # of dimes!

$0.05n + $0.10d = $0.85

$0.05(10-d) + $0.10d = $0.85

$0.5 - $0.05d + $0.10d = $0.85

$0.50 + $0.05d = $0.85

$0.05d = $0.35

d = 7

Check this with the # equation:

n + d = 10

n + 7 = 10

n = 3

Does that make sense? Let's see:

3 nickels + 7 dimes = $0.85 ?

3($0.05) + 7($0.10) = $0.85

$0.15 + $0.70 = $0.85

$0.85 = $0.85

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Answer:261

Step-by-step explanation:

4x4x4x4=4x4=16\16x4=64x4=256\256+5=261

symkiiiussksznzznzznzbswwy

The value of the quotient of the polynomials is 2x - 1

The polynomials are given as

2x² + x - 15

x + 3

Where

Dividend = 2x² + x - 15

Divisor = x + 3

The quotient of the polynomials is calculated as

Quotient = Dividend/Divisor

Substitute the known values in the above equation

So, we have

Quotient = (2x² + x - 15)/(x + 3)

Factorize the numerator

Quotient = (x + 3)(2x - 1)/(x + 3)

Cancel out the common factors

Quotient = 2x - 1

Hence, the quotient is 2x - 1

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The length of segment DC is given by the law of sines and trigonometric ratios as approximately 11.3 cm

The law of sines states that in a triangle, the ratio of the sine of an interior angle of a triangle to the length of the side opposite the angle is constant.

The given parameters are;

The figure ABC is a triangle

The figure ADC is a straight line segment

Segment BD is perpendicular to segment AC

The length of segment AB = 8 cm

Length of segment BC = 12 cm

The measure

[tex] \angle ABD = 60^{ \circ} [/tex]

Required;

The length of segment DC

Solution;

[tex] \angle ADB = 90^{ \circ} [/tex]

Definition of segment BD being perpendicular to segment AC

[tex] \angle BAC = 90^{ \circ} - 60^{ \circ} = 30^{ \circ}[/tex]

Using the law of sines, we have;

[tex]AD = AB × sin( \angle ABD) [/tex]

A vertex of the triangle from the question is point B

Which gives;

AD = 8 × sin(60°) = 4•√3

Similarly, from the law of sines, we have;

[tex]\displaystyle{\frac{BC}{sin ( \angle BAC)} = \frac{AB}{sin ( \angle BCA)} } [/tex]

Which gives;

[tex] \displaystyle{\frac{12}{sin ( 30^{ \circ})} = \frac{8}{sin ( \angle BCA)} } [/tex]

[tex] \displaystyle{ sin ( \angle BCA) = \frac{sin ( 30^{ \circ}) \times 8}{12}= \frac{1}{3} }[/tex]

[tex] \displaystyle{ \angle BCA = arcsine \left(\frac{1}{3}\right) }[/tex]

[tex] \displaystyle{DC= 12 \times cos\left(arcsine \left(\frac{1}{3}\right)\right) = 8\cdot \sqrt{2}}[/tex]

Therefore, DC = 8•√2 ≈ 11.3

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Answer: 5.36 gallons

Step-by-step explanation:

0.64 gallons [liquid] are equal to 0.16907 litre

6 - 0.64 = 5.36

We can see that function g(x) is a translation of one unit to the left and 3 units downwards of f(x), thus, the correct options are:

C and E.

Here we have the two functions:

f(x)

g(x) = 4^(x + 1) - 3

And we know that g(x) is a translation of f(x)

Remember that the translations works as follows:

Vertical translation of N units:

g(x) = f(x) + N

If N > 0, the translation is upwards.

If N < 0, the translation is downwards.

Horizontall translation of N units:

g(x) = f(x) + N

If N > 0, the translation is to the left

If N < 0, the translation is to the right.

In this case, we can write g(x) as:

g(x) = f(x + 1) - 3 = 4^(x + 1) - 3

So we will have a translation of one unit to the left and 3 units downwards.

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Given that

Answer:

The answer given by Mia is not reasonable cause, when we sum up the data given by her we will conclude that the expression should be like (12*36) + (24*84) = 1800.

Step-by-step explanation:

Mia has 12 boxes of chocolate chip cookies and 24 boxes of sugar cookies.

Each box of chocolate chip cookies has 36 cookies.

Each box of sugar cookies has 84 cookies.

So, the total number of chocolate chips cookies will be = 12 * 36 ----(i)

And the total number of sugar cookies will be = 24 * 84 -----(ii)

As Mia says she has about 1,800 cookies in all.

So, we can write (i) and (ii) combined as,

(12*36) + (24*84) = 1800

The answer given by Mia is not reasonable cause, when we sum up the data given by her we will conclude that the expression should be like (12*36) + (24*84) = 1800.

Explanation: No, her answer is not reasonable.

Step by Step solution:

According to the given information, Mia has 12 boxes of chocolate chip cookies and 24 boxes of sugar cookies.

Now, each box of chocolate chip cookies has 36 cookies which means she has (36 × 12) = 432 chocolate chip cookies in total, using the unitary method.

Also, each box of sugar cookies has 84 cookies which means she has (84 × 24) = 1008 sugar cookies in total, using the unitary method.

Mia will then have with her in total of [(36 × 12) + (84 × 24)] = 1440 cookies.

It is an incorrect fact that Mia says that she has about 1800 cookies in total.

Hence, Mia has 1440 cookies in total.

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The value of the expression as in the task content is; 1/4.

It follows from the task content that the value of the expression is to be determined.

Hence, since the expression whose value is required to be determined is ; (1 + (1/2))² - 2.

It follows from PEMDAS guidelines that the parentheses be solved first so that we have;

(3/2)² - 2........After solving the parentheses.

Next, the exponent should be solved as follows;

= (9/4) - 2.

And finally, by solving the subtraction; we have;

= 1/4 = 0.25.

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Through the unitary method, we get that 8000 tons of petrochemicals are required to produce 5,000 tons of plastic.

A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value.

Given :

160,000 tons of petrochemicals are required to produce 100,000 tons of plastic.

160,000 tons of petrochemicals produces = 100,000 tons of plastic.

To produce 1 ton of plastic, the required amount of petrochemicals = [tex]\frac{160,000}{100,000} = \frac{8}{5}[/tex] tons...........equation (1)

Let x be the tons of petrochemicals required to produce 5,000 tons of plastic.

Multiplying 5,000 tons on both sides of the equation, we get :

To produce 5,000 tons of plastic =[tex]\frac{8}{5}*5000 = 8000[/tex] tons of petrochemicals

Hence, 8000 tons of petrochemicals are required to produce 5,000 tons of plastic.

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The opposite angles of a parallelogram are equal.

x + y = a+ b

Let's consider a quadrilateral ABCD which is a parallelogram with AC as its diagonal.

We know, in parallelograms opposites' sides are parallel.

So, AB∥DC and AD∥BC

Since AB is parallel to DC and AC is the transversal.

By alternate angles,

∠BAC = ∠DCA

y = a                                                                                           -----------------(1)

Similarly, AD is parallel to BC and AC is the transversal.

The alternate angles,

∠DAC = ∠BCA

x = b                                                                                           -----------------(2)

Adding equations ( 1 ) and ( 2 ),

∠BAC + ∠DAC = ∠DCA + ∠BCA

∠BAD = ∠DCB

x + y = a + b

Similarly, we can prove, ∠ADC=∠ABC

Hence proved, opposite sites of a parallelogram are equal.

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Answer:

[tex]6x^{2} +17x+12[/tex]

Step-by-step explanation:

(3x+4)(2x+3)

use the FOIL method: that is, multiple first pair, outer pair, inner pair, then last pair:

(3x+4)(2x+3)

(3x × 2x) + (3x × 3) +(4 × 2x) + (4 × 3)

[tex]6x^{2} +9x+8x+12[/tex]

= [tex]6x^{2} +17x+12[/tex]

The graph shows the proportional relationship between the amount of time (in minutes). Points (6,3) represent the time required to plant 3 petunias will be 6 minutes.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that there is a proportional relationship between the amount of time (in minutes) Jennifer has been working in her garden, x, and the number of petunias she has planted, y

Points 6 represent the time required to plant 3 petunias i.e. 6 minutes.

Points 3 represent the number of petunias i.e 3.

This indicates that after spending 6 minutes in his garden, he plants 3 petunias.

Thus, the graph shows the proportional relationship between the amount of time (in minutes). Points (6,3) represent the time required to plant 3 petunias will be 6 minutes.

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