Determine whether each triangle should be solved by beginning with the Law of Sines or the Law of Cosines. Then solve each triangle. Round measures of sides and angles to the nearest tenth after calculating. a = 8, b = 7, c = 4 Question 3 options: Law of Cosines; A ≈ 89°, B ≈ 61°, C ≈ 30° Law of Sines; A ≈ 89°, B ≈ 61°, C ≈ 30° Law of Sines; A ≈ 30°, B ≈ 61°, C ≈ 89° Law of Cosines; A ≈ 61°, B ≈ 89°, C ≈ 30°

Answer:

(E) 1

Step-by-step explanation:

2r+ (2r+3 ) < 11

Combine like terms

4r+3 < 11

Subtract 3 from each side

4r +3-3 < 11-3

4r < 8

Divide each side by 4

4r/4 < 8/4

r <2

The only possible choice is 1

Answer:

(E) 1

Step-by-step explanation:

the sum of 2r and 2r+3  less than 11 means :

2r+2r+3<11

we simplify we get :

4r+3<11

we take the 3 to the left :

4r<11-3

means

4r<8

we divide both sides by 4 we get :

r<2

so among all those values only the 1 satisfies the condition 1<2

so the answer is E

Answer:

Step-by-step explanation:

For this case we must graph the following function:

[tex]f (x) = 13x-1[/tex]

We found the cut points:

Cutting point with the y-axis:

We make [tex]x = 0,[/tex]

[tex]y = 13 (0) -1\\y = 0-1\\y = -1[/tex]

Cutting point with the x axis:

[tex]0 = 13x-1\\1 = 13x\\x = \frac {1} {13} = 0.078[/tex]

It is observed that the line has a positive slope, [tex]m = 13[/tex]

The graph is seen in the attached image.

Answer:

See attached image

Quotient is division,

Writing the equation out you get:

3x/4 ≥ -16

Now we can solve by x.

First multiply both sides by 4:

3x ≥ -64

Now divide both sides by 3:

x ≥ -64/3

Answer:

[tex]f(x)=10(5^{2})^{\frac{x}{2}}[/tex]  (first option)

Step-by-step explanation:

we have

[tex]f(x)=10(5)^{x}[/tex]

where

x ----> is the time in years

we know that

Crista wants to manipulate the formula to an equivalent form that calculates every half-year

The exponent will be

x/2 -----> the time every half year

To find an equivalent form

[tex]f(x)=10(5^{a})^{\frac{x}{2}}[/tex]

[tex]10(5)^{x}=10(5^{a})^{\frac{x}{2}}[/tex]

[tex]10(5)^{x}=10(5)^{a\frac{x}{2}}[/tex]

so

[tex]x={a\frac{x}{2}}[/tex]

[tex]a=2[/tex]

The equivalent form is

[tex]f(x)=10(5^{2})^{\frac{x}{2}}[/tex]

C

By the law of sines, [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex] where A, B, C are the angles and a, b, c are the lengths of the sides opposite their respective angles. In this case, [tex]110^{\circ}[/tex] is opposite 4.6 and A is opposite 3.2, so [tex]\frac{sinA}{3.2}=\frac{sin(110^{\circ})}{4.6}[/tex], giving the answer.

Answer:

it’s c

Step-by-step explanation:

Answer:

The graph in the attached figure ( is the third option)

Step-by-step explanation:

we have the compound inequality

[tex]-18> -5x+2\geq -48[/tex]

Divide the compound inequality in two inequalities

[tex]-18> -5x+2[/tex] -----> inequality A

[tex]-5x+2\geq -48[/tex] -----> inequality B

Step 1

Solve inequality A

[tex]-18> -5x+2[/tex]

[tex]-18-2> -5x[/tex]

[tex]-20> -5x[/tex]

Multiply by -1 both sides

[tex]20<5x[/tex]

[tex]4<x[/tex]

Rewrite

[tex]x > 4[/tex]

The solution of the inequality A is the interval ------>(4,∞)

Step 2

Solve the inequality B

[tex]-5x+2\geq -48[/tex]

[tex]-5x\geq -48-2[/tex]

[tex]-5x\geq -50[/tex]

Multiply by -1 both sides

[tex]5x\leq 50[/tex]

[tex]x\leq 10[/tex]

The solution of the inequality B is the interval -----> (-∞,10]

therefore

The solution of the compound inequality is

(4,∞) ∩ (-∞,10]=(4,10]

All real numbers greater than 4 (open circle) an less than or equal to 10 (close circle)

The solution in the attached figure

The zeros of the function are 2 and -1.

The zeros of a function are the values of x when f(x) is equal to 0.

Given function is,  [tex]f(x)=\frac{(x-2)(x+1)}{x(x-3)(x+5)}[/tex]

Equate given function to zero.

          [tex]\frac{(x-2)(x+1)}{x(x-3)(x+5)} =0\\\\(x-2)(x+1)=0\\\\x=2,x=-1[/tex]

Learn more about the Zeros of function here:

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Answer:

B

Step-by-step explanation:

A secant is a line which intersects a circle at 2 points

From the diagram this is XY → B

The correct option is option B: The line segment XY is a secant.

Line segment which intersects the circle at two points is called secant.

We are given circle with center at O.

From the options,

1.  Line UZ :

   UZ intersects the circle at one point. So it can't be secant.

2. Line XY:

    XY intersects the circle at TWO points. So it is a secant.

3. Line XO :

   XO intersects the circle at one point. So it can't be secant.

Therefore the line segment XY is a secant.

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Answer:

x = 142

Step-by-step explanation:

We are given the following expression for which we are to find the solution:

[tex] \sqrt { x + 2 } - 1 5 = - 3 [/tex]

Rearranging the equation to get:

[tex] \ sqrt { x + 2 } = - 3 + 1 5 [/tex]

Taking square root on both sides of the equation to get:

[tex](\sqrt{x+2} )^2=(12)^2[/tex]

[tex]x+2=144[/tex]

x = 142

[tex]\displaystyle\\\sqrt{x+2}-15=-3\\\\\sqrt{x+2}=-3+15\\\\\sqrt{x+2}=12~~\Big|~^2\\\\x+2=144\\\\x=144-2\\\\\boxed{x=142}[/tex]

.

Answer:

[tex]5+\sqrt{x+4}[/tex]

Step-by-step explanation:

The conjugate of the radical expression [tex]a+\sqrt{b}[/tex] is  [tex]a-\sqrt{b}[/tex]

The conjugate of the radical expression [tex]a-\sqrt{b}[/tex] is  [tex]a+\sqrt{b}[/tex]

The sign of the radical becomes its additive inverse in the conjugate,

The given expression is

[tex]5-\sqrt{x+4}[/tex] where [tex]x>-4[/tex] (domain)

The conjugate of this expression is [tex]5+\sqrt{x+4}[/tex]

Answer:

The conjugate is 5+√x+4

Step-by-step explanation:

To find the conjugate of of expression 5-√x+4

when x>-4

First let us understand that in simple terms terms the conjugate of a radical simply involves the change in sign of the radical

in the problem the conjugate of

5-√x+4 is 5+√x+4

it is that simple Just alternate the sign and you are done!!!

Answer:

2, 3, 4, 5, 6, 7 or 8.

Step-by-step explanation:

We know that the sum of two sides on a triangle should ALWAYS be greater than the third side. Then we have:

5-4 < x < 5 + 4

1 < x < 9

Therefore, the lenght of the third side could be any number between 1 and 9. If the lenght of the third side is an integrer, then the lenght could be:

2, 3, 4, 5, 6, 7 or 8.

Answer:

The length of the third side could be all real numbers greater than 1 unit and less than 9 units

Step-by-step explanation:

we know that

The Triangle Inequality Theorem,   states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

Applying the triangle inequality theorem

Let

x ----> the length of the third side

1) 4+5 > x

9 > x

Rewrite

x < 9 units

2) 4+x > 5

x > 5-4

x > 1 units

therefore

The solution for the third side is the interval -----> (1,9)

All real numbers greater than 1 unit and less than 9 units

therefore

The length of the third side could be all real numbers greater than 1 unit and less than 9 units

Answer:

.7995 rounded to the nearest cent is 0.80 cents

Answer:

.7995 rounded to the nearest cent is .80.

Step-by-step explanation:

Rounding with numbers higher than 4 makes them round up, lower than 5 makes them round down.

Answer:

A. glide reflection

Step-by-step explanation:

This is a glide reflection since the figure has been both reflected over a line and transported downwards.

Answer:

a) glide reflection

Step-by-step explanation:

An isometry is a transformation of a figure in the plane that preserves lenght, it could be reflections, rotations, or translations, in the figure you can se what is called a glide reflection, which is a reflection of the figure over a line, and then a translation of the same figure.

Answer:

-19/10,-18/10,-17/10

Step-by-step explanation:

multiply the both numbers up and down by 10.

then find the numbers

Answer:-1, 0, -1.33

Step-by-step explanation: Rational numbers include those with repeating decimals, natural, counting, etc.

Answer:

subtract 2 from each side and o think u decide the last two numbers

Answer:

Step-by-step explanation:2-10x=7

First you have to subtract you 2 on both sides so it would 7-2= 5

You are left with -10x =5

Then you divide your -10x by -10 to get rid of your x

Last you divide 5/-10

Answer:

Events E and F are not independent if the probability of event E occurring is affecting the probability of event F occurring.

Step-by-step explanation:

Two events are independent when the probability of one event occurring has no connection with that of the other event.

Example, when you toss a coin and roll a six sided die, the probability of getting a head or a tail has no connection with the probability of getting any number face.A real life example will be the probability going to the mall and owning a cat at home.These two have no influence on one another.

Mathematically independent events can be calculated as;

P(E∩F)=P(E)-P(F)

The most significant number of homerooms that can be created with an equal number of boys and girls in each is 6.

To answer this question, we need to find the greatest common divisor (GCD) for the number of boys and girls. The GCD is the most significant number that can divide both numbers equally. The GCD of 42 (number of boys) and 48 (number of girls) is 6.

 Therefore, the sixth grade's most significant possible number of homerooms would be 6, with each homeroom having seven boys and eight girls.

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Answer:

The actual distance between the cities is 480 miles.

Step-by-step explanation:

2.5 inches is 20/8 inches, multiply 20 by 24 miles which gives you 480.

Answer:

480 miles.

Step-by-step explanation:

By proportion the actual distance is

(2.5 / 1/8) * 24

= (2.5 / 0.125) * 24

= 20 * 24

= 480 miles.

Answer:

(k ∘ p)(x)=2x^2-12x+13

Step-by-step explanation:

(k ∘ p)(x)=k(p(x))

(k ∘ p)(x)=k(x-3)

(k ∘ p)(x)=2(x-3)^2-5

(k ∘ p)(x)=2(x-3)(x-3)-5

Use foil on (x-3)(x-3) or use this as a formula:

(x+a)^2=x^2+2ax+a^2.

(k ∘ p)(x)=k(p(x))

(k ∘ p)(x)=k(x-3)

(k ∘ p)(x)=2(x-3)^2-5

(k ∘ p)(x)=2(x-3)(x-3)-5

(k ∘ p)(x)=2(x^2-6x+9)-5

Distribute: multiply terms inside ( ) by 2:

(k ∘ p)(x)=2x^2-12x+18-5

(k ∘ p)(x)=2x^2-12x+13

The composite function is [tex]k(p(x))=2x^{2} -12x+13[/tex]

Option b is correct.

Given function are,

               [tex]k(x)=2x^{2} -5,p(x)=(x-3)[/tex]

We have to find composite function [tex]k(p(x))[/tex].

                  [tex]k(p(x))=k(x-3)\\\\k(p(x))=2(x-3)^{2}-5\\ \\k(p(x))=2(x^{2} +9-6x)-5\\\\k(p(x))=2x^{2} +18-12x-5\\\\k(p(x))=2x^{2} -12x+13[/tex]

Thus, the composite function is [tex]k(p(x))=2x^{2} -12x+13[/tex]

Learn more about the composite function here:

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Answer:

8/17

Step-by-step explanation:

Since this is a right triangle, we can use the trigonometric identities

sin Y = opposite side/ hypotenuse

         = 16/34

Dividing the top and bottom by 2

          = 8/17

Answer: Option A

[tex]x=\frac{1+\sqrt{83}i}{6}[/tex] or [tex]x=\frac{1-\sqrt{83}i}{6}[/tex]

Step-by-step explanation:

Use the quadratic formula to find the zeros of the function.

For a function of the form

[tex]ax ^ 2 + bx + c = 0[/tex]

The quadratic formula is:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

In this case the function is:

[tex]3x^2-x+7=0[/tex]

So

[tex]a=3\\b=-1\\c=7[/tex]

Then using the quadratic formula we have that:

[tex]x=\frac{-(-1)\±\sqrt{(-1)^2-4(3)(7)}}{2(3)}[/tex]

[tex]x=\frac{1\±\sqrt{1-84}}{6}[/tex]

[tex]x=\frac{1\±\sqrt{-83}}{6}[/tex]

Remember that [tex]\sqrt{-1}=i[/tex]

[tex]x=\frac{1\±\sqrt{83}*\sqrt{-1}}{6}[/tex]

[tex]x=\frac{1\±\sqrt{83}i}{6}[/tex]

[tex]x=\frac{1+\sqrt{83}i}{6}[/tex] or [tex]x=\frac{1-\sqrt{83}i}{6}[/tex]

Final answer:

The solutions to the equation 3x² - x + 7 = 0 are complex numbers. Using the quadratic formula, we find the solutions to be x = (1 + i√83) / 6 and x = (1 - i√83) / 6.

Explanation:

The solutions of the quadratic equation 3x² - x + 7 = 0 cannot be real numbers because the discriminant (b² - 4ac), in this case, is negative ((-1)² - 4(3)(7) = 1 - 84 = -83). Therefore, we need to use the quadratic formula to find the complex solutions. This formula is given by x = (-b ± √(b² - 4ac)) / (2a). By substituting the values from the equation into the quadratic formula, we obtain the complex solutions.

Quadratic formula application:

x = (-(-1) ± √((-1)² - 4(3)(7))) / (2(3))

x = (1 ± √(-83)) / 6

Therefore, the two complex solutions are x = (1 + i√83) / 6 and x = (1 - i√83) / 6, where i is the imaginary unit.

To confirm these answers, we can substitute each value back into the original equation and verify by simplification that each results in an identity.

Answer:

z=275

Step-by-step explanation:

it has a ratio 1:11

that must be it

Answer:

275

Step-by-step explanation:

z is directly proportional to x:

z = kx

When x is 15, z is 165.

165 = k × 15

k = 11

When x = 25:

z = 11 × 25

z = 275

Answer:

[tex]\large\boxed{y-8=-\dfrac{2}{3}(x+3)}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

We have the equation of a line in the slope-intercept form

[tex]y=-\dfrac{2}{3}x+6\Rightarrow m=-\dfrac{2}{3}[/tex]

and the point (-3, 8).

Substitute:

[tex]y-8=-\dfrac{2}{3}(x-(-3))\\\\y-8=-\dfrac{2}{3}(x+3)[/tex]

Answer:

[tex]y = 18x + 45[/tex]

Step-by-step explanation:

You can use a linear equation of the form

[tex]y = mx + b[/tex] to represent the situation.

where b is the constant amount represented by the intercept with the y-axis, in this case b e is the cost of membership.

m is the slope, and in this case it is the cost per day of renting a team for x days.

y is  the total cost of membership at the club, when renting equipment for X days

So the linear equation is:

[tex]y = 18x + 45[/tex]

Answer:

a=3 b=-2 c=4

Step-by-step explanation:

Answer:

using distance formula or graphing you can find your answer

Step-by-step explanation:

(7,0) from 4 to -3 is -7. Take the absolute vale of -7 and you get 7.

Hope i helped :)

Answer:

Distance from A to B = 7 units

Step-by-step explanation:

We are given the following two points and we are to find the distance between them:

A (4,2)

B (-3,2)

We will be using the distance formula for this:

Distance = [tex] \sqrt { ( x _ 2 - x _1)^ 2 + ( y _ 2 - y _ 1 ) ^ 2 } [/tex]

AB = [tex]\sqrt{(-3-4)^2+(2-2)^2} = \sqrt{49}[/tex] = 7 units

Answer:

1 to 1

Step-by-step explanation:

8 to 8 = 8:8 = 8/8

You can treat a ratio as a fraction. Reduce the fraction 8/8 by dividing the numerator and denominator by 8.

8/8 = 1/1

8 to 8 = 1 to 1

Answer:

1:1

Step-by-step explanation:

A ratio says that "for every _ of this quantity, you have _ of another quantity". This is just saying for every 8 of one thing, you have 8 of another. And then you can simplify, just like a fraction.

Find the area of the rug by multiplying the length by the width:

7 x 5 = 35 square meters.

Now multiply the area of the rug by the cost:

35 square meters x 285 pesos per square meter = 9,975 total pesos.