writing an equation and drawing its graph to model a real-world situation ​

Answer:

1

Step-by-step explanation:

The line is crossing over the y-axis on the 1.

Answer:

(0,1)

Step-by-step explanation:

The y-intercept is always the point where the line crosses the y-axis.

Answer:

The measure of angle B is 41.5°

The length of side a is 30.6 feet ⇒ to the nearest tenth

The length of side b is 32.9 feet ⇒ to the nearest tenth

Step-by-step explanation:

In the given Δ ABC

∵ m∠A = 38.1°

∵ m∠C = 100.4°

→ By using the fact above

∵ m∠A + m∠B + m∠C = 180°

∴ 38.1 + m∠B + 100.4 = 180

→ Add the like terms in the left side

∴ 138.5 + m∠B = 180

→ Subtract 138.5 from both sides

∴ m∠B = 41.5°

∴ The measure of angle B is 41.5°

∵ a is the opposite side of ∠A

∵ b is the opposite side of ∠B

∵ c is the opposite side of ∠C

→ By using the sine rule

∴ [tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

∵ c = 48.4 ft, m∠A = 38.1°, m∠B = 41.5°, and m∠C = 100.4

→ Substitute them in the sine rule above

∴ [tex]\frac{a}{sin38.1}[/tex] = [tex]\frac{b}{sin41.5}[/tex] = [tex]\frac{48.4}{sin100.4}[/tex]

→ By using cross multiplication between the 1st and the 3rd fractions

∴ a × sin 100.4 = 48.8 × sin 38.1

→ Divide both sides by sin 100.4

∴ a = 30.61429861

∴ The length of side a is 30.6 feet ⇒ to the nearest tenth

→ By using cross multiplication between the 2nd and the 3rd fractions

∴ b × sin 100.4 = 48.8 × sin 41.5

→ Divide both sides by sin 100.4

∴ b = 32.87596206

∴ The length of side b is 32.9 feet ⇒ to the nearest tenth

Answer:

[tex] - \bigg(3a - \frac{5}{2} b) \bigg)^{2} [/tex]

Step-by-step explanation:

[tex]15ab-9a^2-6 \frac{1}{4} b^2 \\ \\ = 15ab-(3a)^2-\frac{6 \times 4 + 1}{4} b^2 \\ \\ = 15ab-(3a)^2-\frac{24+ 1}{4} b^2 \\ \\ = 15ab-(3a)^2-\frac{25}{4} b^2 \\ \\ = 15ab- (3a)^2- \bigg(\frac{5}{2} b \bigg)^2 \\ \\ = - \{ - 15ab + (3a)^2 + \bigg(\frac{5}{2} b \bigg)^2 \} \\ \\ = - \{ (3a)^2 + \bigg(\frac{5}{2} b \bigg)^2 - 15ab \} \\ \\ = - \bigg(3a - \frac{5}{2} b \bigg)^{2} [/tex]

Answer:

Amount of discount =80-70=10$

percentage:-

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac{10}{80}}\times 100 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {10}{4}}5 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {50}{4}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 12.5\% [/tex]

Answer: the answer is 12.5

Step-by-step explanation:

Yes, this is polynomial, and your answer will be:

(2x − 1) (3x − 2) (x^2 + 2x + 2)

Edit:

Factor 6x^4 + 5x^3 − 10x + 4 using the rational roots test.

(2x − 1) (3x^3 + 4x^2 + 2x − 4)

Factor 3x^3 + 4x^2 + 2x − 4 using the rational roots test.

(2x − 1) (3x − 2) (x2 + 2x + 2)

The factorized form of the given polynomial is (2x − 1)(3x − 2)(x² + 2x + 2).

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The polynomial is given in the question, as follows:

6x⁴ + 5x³ − 10x + 4

We have to factor using the rational roots test,

⇒ (2x − 1)(3x³ + 4x² + 2x − 4)

Similarly, factor 3x³ + 4x² + 2x − 4 operates the rational roots test.

⇒ (2x − 1)(3x − 2)(x² + 2x + 2)

Thus, the factorized form is (2x − 1)(3x − 2)(x² + 2x + 2).

Learn more about the polynomial here:

brainly.com/question/11536910

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The probability that the number on the parking space where Jillian parks is greater than or equal to 31 is 45/76 or 0.5921 .

Given, Jillian parks her car randomly in a parking slot of 76 spaces.

Total number of Parking spots : 76

Number of parking spots above number 31 : 76 - 31 = 45

Probability = Successful events/ Total events

Probability = 45/76

The probability that the number on the parking space where Jillian parks is greater than or equal to 31 is 45/76 .

Know more about probability,

https://brainly.com/question/32117953

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Answer:70

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

Answer:

Step-by-step explanation:

370

1 and 2/3 cups of veggies

Answer:

the correct answer is 6.21×10^5

Answer:

6.21 x 10^5

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer: -40

Step-by-step explanation:

1. 30 -20 = 10

2. 10 + 10 = 20

3. 20 - 20 = 0

4. 0 + 60 = 60

5. 60 - 100 = -40

Answer:

x = 6

Step-by-step explanation:

first find the angle

51 + 72 + x = 180

123 + x = 180

x = 180 - 123

x = 57

so the third angle is 57

now find the value of x in the given expression

8x + 9 = 57

8x = 57 - 9

8x = 48

x = 48/8

x = 6

now check whether the value of x is correct or not by evaluating the value of x in expression

8x + 9 = 57

8(6) + 9 = 57

48 + 9 = 57

57 = 57

so its true

Method 2

51 + 72 + (8x + 9) = 180

123 + 8x + 9 = 180

132 + 8x = 180

8x = 180-132

8x = 48

x = 48/8

x = 6

now again you can check by evaluating the value of x in the above expression

Answer:

C |p| = 4

Step-by-step explanation:

If a player wins 4points during each turn, then, the total points will be +4points

If the player looses 4points, total points lost will be -4points

The total number of point p the player can have will be represented as;

|p| = 4 (since is both positive and negative 4 )

Note that the nodulus of a variable will return both positive and negative value of that variable

Answer:

Step-by-step explanation:

-2x -3y = 5

4x + 3y = 17

2x = 22

x = 11

4(2) + 3y = 17

8 + 3y = 17

3y = 9

y = 3

(11,3)

Answer:

x=11, y=-9

Step-by-step explanation:

Answer:

la diagonale più lunga dovrebbe essere 37cm.

Step-by-step explanation:

Se cerchi la diagonale più lunga la formula dovrebbe essere questa:

A=p*(q/2)

234,95 = 12,7*(x/2)

234,95/12,7 = x/2

18,5 = x/2

18,5*2 = x

37 = x

Answer:

Cost = $86.67

Step-by-step explanation:

Given

Yards = 4⅓ (missing part of the question)

Cost per yard = $2.00

Required

Determine cost of chains produced in 10 minutes

If 4⅓ yards is made in a minute, then

4⅓ * 10 yards are made in 10 minutes

Total = 4⅓ * 10

Total = 13/3 * 10

Total = 130/3 yards

Cost of a yard of chain is $2.00.

Cost of 130/3 yards would be:

Cost = $2.00 * 130/3

Cost = $260.00/3

Cost = $86.67 (approximated)

Hence, the required cost is approximately $86.67

Answer:

2 bonus stars

Step-by-step explanation:

0.04 million= 40,000

40000/1701= 23.5

23.5(3)= 70.5

70.5/33= 2 stars

Answer:

3.Yes, because triangle ABC has a 90 degree angle.

4.No, because triangle XYZ doesn’t have a 90 degree angle.

Answer:

144

Step-by-step explanation:

omg, I just said the answer was B.

Answer:

Jessie

Step-by-step explanation:

Jessie answered 4 more times correct that Johnny so she will get a better grade.

Answer:

72 square units

Step-by-step explanation:

area of a paralellogram = bh

Base = 6

Height = 12

6 x 12 = 72 square units

[tex]\huge\mathtt{Hello!}[/tex]

[tex](6x - 23) = (4x + 9)[/tex]

[tex]6x -4x = 9 + 23[/tex]

[tex]2x = 32[/tex]

[tex]x = 16[/tex]

It is because the sides are equal, so the angles opposite to them also are equal.

Have a nice day!

Answer:

The 7th term of given sequence is: 448

Step-by-step explanation:

Given sequence is:

7,-14,28,-56​

Here

a1 = 7

a2 = -14

a3 = 28

First of all we have to find the common ratio. The common ration is the ratio between two consecutive terms of a geometric sequence and is same for all consecutive terms of a geometric sequence.

So,

[tex]r = \frac{a_2}{a_1} = \frac{-14}{7} = -2\\r = \frac{a_3}{a_2} = \frac{28}{-14} = -2\\[/tex]

The common ratio is -2.

The general formula for geometric sequence is given as:

[tex]a_n = a_1r^{(n-1)}[/tex]

Putting values

[tex]a_n = 7.(-2)^{n-1}[/tex]

For 7th term, putting n=7

[tex]a_7 = 7*(-2)^{7-1}\\= 7 * (-2)^6\\= 7 *64\\= 448[/tex]

Hence,

The 7th term of given sequence is: 448

Answer:

A

Step-by-step explanation:

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Step-by-step explanation:

[tex] \bf \underline{Given-} \\ [/tex]

[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ [/tex]

[tex] \bf \underline{What\: to\: do-} \\ [/tex]

To rationalise the denominator

[tex] \bf \underline{Solution-} \\ [/tex]

[tex]\textsf{We have,}[/tex]

[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ [/tex]

[tex]\textsf{The denominator is 5+2√3. Multiplying the numerator and denominator by 7-4√3,}\\[/tex]

[tex]\textsf{we get,}\\[/tex]

[tex] ⟹\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ [/tex]

[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 + 4 \sqrt{3} )(7 - 4 \sqrt{3}) } \\ \\ [/tex]

[tex]\textsf{⬤ Applying Algebraic Identity

(a+b)(a-b) = a² - b² to the denominator}\\[/tex]

[tex]\textsf{We get,}\\[/tex]

[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 {)}^{2} - (4 \sqrt{3} {)}^{2} } \\ \\ [/tex]

[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 8 \sqrt{3 \times 3} }{49 - 48} \\ \\ [/tex]

[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 24 }{1} \\ \\ [/tex]

[tex]⟹(35 - 24) - 6 \sqrt{3} \\ \\ [/tex]

[tex]⟹11 - 6 \sqrt{3} \: \: \: \tt \red{ Ans}. \\ \\ [/tex]

[tex] \bf \underline{Hence \:the \:denominator\: is\: rationalised.}\\[/tex]

Answer:

1.44

Step-by-step explanation:

Answer:

the answer is 1.44

Step-by-step explanation:

Because the exponent of a number says how many times to use the number in a multiplication. In 1.2 exponent 2 the "2" says to use 1.2 twice in a multiplication, so 1.2'2 = 1.2 × 1.2 = 1.44 In words: 1.2'2 could be called "1.2 to the power 2" or "1.2 to the second power.

                      Your welcome