Solve x-4<3 graph the solution

Answer: Option 2

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Step-by-step explanation:

Answer:

[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are called the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The cosine ratio is defined as:

[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]

Note the angle A of the figure has 17 as the adjacent leg and 38 as the hypotenuse, so we can directly apply the formula:

[tex]\displaystyle \cos A=\frac{17}{38}[/tex]

[tex]\cos A=0.4474[/tex]

Using a scientific calculator, we get the inverse cosine:

[tex]A=\arccos(0.4474)[/tex]

[tex]A\approx 63^\circ[/tex]

Since A+B+C=180°, we can solve for C:

C = 180° - A - B

C = 180° - 63° - 90°

C = 26°

Thus:

[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]

In the given right triangle ABC, m∠A ≈ 26.44° and m∠C ≈ 63.56°.

To solve the right triangle ABC, we can use trigonometric ratios. In a right triangle, the three main trigonometric ratios are:

1. Sine (sin): [tex]\(\sin(\theta) = \frac{{\text{opposite side}}}{{\text{hypotenuse}}}\)[/tex]

2. Cosine (cos): [tex]\(\cos(\theta) = \frac{{\text{adjacent side}}}{{\text{hypotenuse}}}\)[/tex]

3. Tangent (tan): [tex]\(\tan(\theta) = \frac{{\text{opposite side}}}{{\text{adjacent side}}}\)[/tex]

Given:

AC = 38

AB = 17

To find the angles m∠A and m∠C, we can use the sine and cosine ratios, respectively.

1. For m∠A:

[tex]\(\sin(m\angle A) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle A= \sin^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]

2. For m∠C:

[tex]\(\cos(m\angle C) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle C = \cos^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]

Let's calculate the angles:

[tex]1. \(m\angle A \approx \sin^{-1}\left(\frac{{17}}{{38}}\right) \approx 26.44^\circ\)\\\\2. \(m\angle C \approx \cos^{-1}\left(\frac{{17}}{{38}}\right) \approx 63.56^\circ\)[/tex]

Therefore, m∠A ≈ 26.44° and m∠C ≈ 63.56° (rounded to the nearest degree).

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Answer:

y = -2/3x

Step-by-step explanation:

A perpendicular line is the negative reverse of the slope of the other line. I'm not sure about the options you have there but hopefully this helps you get your answer.

Answer:

The answer is 5 1/2! So what you are looking for is 1/2.

Step-by-step explanation:

Answer:

11/2

Step-by-step explanation:

Answer:

f

klllllllllk

Step-by-step explanation:

Answer:

30002.5

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

multiply the side by 9

Answer:

5

Step-by-step explanation:

[tex]\sqrt[3]{125} =5*5*5=5[/tex]

The equations that can be used to find out how many pounds of beef, b, she sold each day will be:

d = 6b + 7.

d = 4b + 9

From the information given, the butcher sells a total of b pounds of beef at $6.00 per pound and she also sells some pork for $7.00.

Therefore, the equation will be:

d = (6 × b) + 7.

d = 6b + 7.

d = (4 × b) + 9

d = 4b + 9

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Answer:

z+42+42=180

Step-by-step explanation:

Since it is an isosceles triangle, the two base angles are the same and remember all the angles add to  180. So use this equation:

z+42+42=180

If you need to find z, it is 96.

Check: 96+42+42=180

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Take out lignes

-1/4x-3/7

= -7/12

Answer:

B,D, and the last E

Step-by-step explanation:

Answer:

The temputure is -64

Step-by-step explanation:

Answer:

Subtract 3.1 from 12.9

Hope it helped

Given :

Factory has supplies expenses of $1135.78 a day.

Company earns $60,128.72 in one week.

To Find :

The factory's total profit or loss in one week.

Solution :

Expenses of factory of a week :

E =$( 1135.78 × 7 ) = $7950.46 .

Now, profit is given by :

P = $60,128.72 - $7950.46

P = $52178.26

Therefore, total profit of factory in one week is $52178.26 .

Hence, this is the required solution.

Answer:

Domain: (-∞,∞)

Range:(-∞,∞)

Step-by-step explanation:

The sketch of the given function has been attached and the domain and range both will be (-∞,∞ ).

A straight line on the coordinate plane is represented by a linear function.

A function that fluctuates linearly with respect to the changing variable is referred to as being linear.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

Given the function,

ƒ(x) = -5x + 4

Range of the function ;

Since the value of the function is defined for all real x and the value will be unique so

Range =  (-∞,∞ ).

The domain of the function ;

Since it is defined for all real x so,

Domain =  (-∞,∞ )

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Answer:

x=10 and y= 8.

Step-by-step explanation:

Given that the cost of 1 banana = $0.60

Cost of 1 mango = $1.50.

Total cost= $ 18  

Here, x be the number of bananas and y be the numbers of mangos,

As the number of bananas is 2 more than the number of mangos,

So, x=y+2

[tex]\Rightarrow y=x-2 \cdots(i)[/tex]

Cost of x bananas [tex]=\$ 0.60 \times x[/tex]

Cost of y mangos [tex]=\$ 1.50 \times y[/tex]

Total cost = 0.6x+1.5y

[tex]\Rightarrow 18 = 0.6x+1.5y\\\\\Rightarrow 1.5y=18-0.6x\\\\\Rightarrow y= 12 - 0.4 x \cdots(ii).[/tex]

Solving both the equations (i) as well as (ii), graphically as shown in the figure by plotting both the graphs.

Both the graphs intersect at the point (10,8) as shown in the graph.

So, the solution of both the equations is, (x,y)=(10,8). i.e

The number of bananas = x= 10 and

the number of mangos = y = 8.

Answer:

{x,y}={  11 /69   ,−  11 /10  }

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the total number of miles Rex can travel be x;

If a cab company charges $0.85 per mile, then x miles will cost $0.85x

If the flat rate rate charge is $3.10, the total price for x miles will be;

0.85x + 3.10

Since Rex has no more than $15 to spend on a ride, the inequality to represent the equation will be;

0.85x + 3.10 ≤ 15 (less than or equal to means that the total value cannot exceed $15)

Next is to solve for x

Given

0.85x + 3.10 ≤ 15

subtract 3.10 from both sides

0.85x + 3.10-3.10 ≤ 15-3.10

0.85x ≤ 15-3.10

0.85x ≤ 11.90

x ≤  11.90/0.85

x ≤ 14

This means that Rex can travel 14 miles without exceeding his limit

Answer:

[tex]3.10 + 0.85m \leq 15[/tex]

[tex]m \leq 14.0[/tex]

Step-by-step explanation:

Given

[tex]Flat\ Rate = \$3.10[/tex]

[tex]Addition = \$0.85[/tex] (per mile)

[tex]Maximum\ Amount = \$15[/tex]

Required

Determine the inequality that represents the scenario and solve

Let the number of miles be represented by m.

The company's charges can be calculated using:

[tex]Flat\ Rate + Additional\ Charges * m[/tex]

Substitute values

[tex]\$3.10 + \$0.85 * m[/tex]

Rex can't exceed $15 implies that the company's charges can't exceed Rex's budget.

This is expressed as:

[tex]\$3.10 + \$0.85 * m \leq \$15[/tex]

[tex]\$3.10 + \$0.85m \leq \$15[/tex]

[tex]3.10 + 0.85m \leq 15[/tex] ---- The inequality

Solving for m: Collect Like Terms

[tex]0.85m \leq 15 - 3.10[/tex]

[tex]0.85m \leq 11.9[/tex]

Divide through by 0.85

[tex]m \leq 11.9/0.85[/tex]

[tex]m \leq 14.0[/tex] ---- The solution

Answer:

30 cm

[tex]863.5\ \text{cm}^2[/tex]

Step-by-step explanation:

d = Diameter of cylinder = 4 cm

n = Number of times the strip of paper is turned = [tex]2\dfrac{1}{2}=2.5[/tex]

Diameter of the cylinder will be approximately equal to the diameter of the paper wound. Length of one turn will be circumference of the paper

Circumference of the paper

[tex]c=\pi d\\\Rightarrow c=3\times 4\\\Rightarrow c=12\ \text{cm}[/tex]

Total length of the paper will be the number of turns multiplied by the length of one turn

[tex]l=nc\\\Rightarrow l=2.5\times 12\\\Rightarrow l=30\ \text{cm}[/tex]

Length of the strip of paper is 30 cm.

2.

l = Slant height = 10 cm

d = Base diameter = 10 cm

r = Radius of base = [tex]r=\dfrac{d}{2}=\dfrac{10}{2}=5\ \text{cm}[/tex]

Total surface area of cone is given by

[tex]S=\pi r^2+\pi rl\\\Rightarrow S=\pi r(r+rl)\\\Rightarrow S=3.14\times 5(5+5\times10)\\\Rightarrow S=863.5\ \text{cm}^2[/tex]

The total surface area of cone is [tex]863.5\ \text{cm}^2[/tex].

Answer:

Image point → (6, 1)

Step-by-step explanation:

Given point → (-3, 3)

Transformation to be done → [tex]R_{180}0T_{-3,-4}[/tex]

Transformations to be done,

Step - (1). Translation of the given by 3 units left and 4 units down.

Step - (2). Followed by the rotation counterclockwise 180° about the origin.

Rule for step (1),

(x, y) → (x - 3, y - 4)

By this rule,

(-3, 3) → [(-3 - 3), (3 - 4)]

         → (-6, -1)

Rule for step -2,

(x, y) → (-x, -y)

(-6, -1) → (6, 1)

Therefore, following these two steps coordinates of the image point → (6, 1)  

Answer:

28% .................

Answer:

28%

Step-by-step explanation:

100%/x%=160/44.8

(100/x)*x=(160/44.8)*x       - we multiply both sides of the equation by x

100=3.5714285714286*x       - we divide both sides of the equation by (3.5714285714286) to get x

100/3.5714285714286=x

28=x

x=28

now we have:

44.8 is 28% of 160