Which equation is an identity?

8 – (6v + 7) = –6v – 1

5y + 5 = 5y – 6

3w + 8 – w = 4w – 2(w – 4)

6m – 6 = 7m + 9 – m

Answer:

12 2/6

Three times four is 12.

two times one is 2.

two times three is 6.

Answer:

3 1/2 x 4 2/3 = 98/6

*This is without simplest form*

In simplest form:

3 1/2 x 4 2/3 = 16 1/3

Answer:

Here is what i can do i can not exactly tell you the answer but I can help you understand to find the answer because were here to help each other but telling each other the answers is not the key because on an real test you cant use Brainly .com to help you find the answer because they need to see what you know not the internet.

Step-by-step explanation:

The correct option is A) (-1, 1)

See the image

QUESTION 1

The given logarithm is

[tex]8\log_g(x)+5\log_g(y)[/tex]

We apply the power rule of logarithms; [tex]n\log_a(m)=\log_(m^n)[/tex]

[tex]=\log_g(x^8)+\log_g(y^5)[/tex]

We now apply the product rule of logarithm;

[tex]\log_a(m)+\log_a(n)=\log_a(mn)[/tex]

[tex]=\log_g(x^8y^5)[/tex]

QUESTION 2

The given logarithm is

[tex]8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)[/tex]

We apply the power rule of logarithm to get;

[tex]=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)[/tex]

We apply the product to obtain;

[tex]=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)[/tex]

We apply the quotient rule; [tex]\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )[/tex]

[tex]=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})[/tex]

[tex]=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})[/tex]

parts of 10% soln, x

parts of 25% soln, y

total soln, x+y =30

{x(0.1) + y(0.25)}/(x + y) = 0.12...eqn 1

x + y = 30...eqn 2

from eqn 2...=》 x = 30-y

subst for x in eqn 1...

=》 {(30-y)(0.1) + y(0.25)}/ 30-y+y = 0.12

=》 (3-.1y+.25y)/30 =0.12

=》 3+.15y = 3.6

=》 .15y = .6

=》 y =4

using x = 30 - y = 26

ans

26ml of 10% soln

4ml of 25% soln

Using a system of equations to represent the scenario, 26mL of 10% solution and 4mL of 25% solution would be required.

Let ;

From (1)

Substitute (3) into (2)

0.1(30 - b) + 0.25b = 3.6

3 - 0.1b + 0.25b = 3.6

0.15b = 0.6

b = 0.6/0.15

b = 4

From (3) :

a = 30 - 4

a = 26

Hence, 26mL of 10% solution and 4mL of 25% solution would be required.

Learn more : https://brainly.com/question/24423994

Answer:

The distance between the boats is [tex]50\ mi[/tex]

Step-by-step explanation:

we know that

The Pythagoras Theorem states that

In a right triangle

[tex]c^{2}=a^{2}+b^{2}[/tex]

where

c is the hypotenuse

a and b are the legs

In this problem

Let

c  ----> the distance between the boats

a -----> the horizontal distance between the boats

b -----> the vertical distance between the boats

[tex]a=12+18=30\ mi[/tex]

[tex]b=16+24=40\ mi[/tex]

substitute the values

[tex]c^{2}=30^{2}+40^{2}[/tex]

[tex]c^{2}=2,500[/tex]

[tex]c=50\ mi[/tex]

Final Answer:

The distance between the two boats is 50 miles.

Explanation:

To find the distance between the two boats after they have traveled, we need to determine the final position of each boat relative to the island, and then use the Pythagorean theorem to find the distance between these two positions. Let's go through the calculations step-by-step:

Step 1: Determine the final position of each boat relative to the island.
- Boat 1 travels 12 miles east and then 16 miles north. Let’s define east as the positive x-direction and north as the positive y-direction. So, the final coordinates of Boat 1 relative to the island are (12, 16).
- Boat 2 travels 24 miles south and then 18 miles west. Let’s define south as the negative y-direction and west as the negative x-direction. So, the final coordinates of Boat 2 relative to the island are (-18, -24).

Step 2: Determine the differences in the x and y coordinates between Boat 1 and Boat 2.
- The difference in x-coordinates dx is the x-coordinate of Boat 1 minus the x-coordinate of Boat 2:

[tex]\( dx = 12 - (-18) = 12 + 18 = 30 \)[/tex] miles.
- The difference in y-coordinates dy is the y-coordinate of Boat 1 minus the y-coordinate of Boat 2:

[tex]\( dy = 16 - (-24) = 16 + 24 = 40 \)[/tex] miles.

Step 3: Use the Pythagorean theorem to calculate the distance between the two boats.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse c (the side opposite the right angle) is equal to the sum of the squares of the other two sides a and b:
[tex]\[ c^2 = a^2 + b^2 \][/tex]

Here, dx and dy can be considered the lengths of the sides of a right triangle, and the distance between the boats d is the hypotenuse of this triangle. So:
[tex]\[ d = \sqrt{dx^2 + dy^2} \\\\\[ d = \sqrt{30^2 + 40^2} \\\\\[ d = \sqrt{900 + 1600} \\\\\[ d = \sqrt{2500} \\\\\[ d = 50 \][/tex]

Therefore, the distance between the two boats is 50 miles.

Answer:

[tex]\begin{array}{ccccc}\text{January}&\text{February}&\text{March}&\text{April}&\text{May}\\\dfrac{3}{20}&\dfrac{5}{20}&\dfrac{2}{20}&\dfrac{8}{20}&\dfrac{2}{20}\end{array}[/tex]

Step-by-step explanation:

During 5 months Laura wrote

3+5+2+8+2=20 songs.

1. The probability that the song was written in January is [tex]\frac{3}{20}.[/tex]

2. The probability that the song was written in February is [tex]\frac{5}{20}.[/tex]

3. The probability that the song was written in March is [tex]\frac{2}{20}.[/tex]

4. The probability that the song was written in April is [tex]\frac{8}{20}.[/tex]

5. 1. The probability that the song was written in May is [tex]\frac{2}{20}.[/tex]

The probabolity distribution table:

[tex]\begin{array}{ccccc}\text{January}&\text{February}&\text{March}&\text{April}&\text{May}\\\dfrac{3}{20}&\dfrac{5}{20}&\dfrac{2}{20}&\dfrac{8}{20}&\dfrac{2}{20}\end{array}[/tex]

Answer:

Step-by-step explanation:

[tex]B_n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\\B_p = 2, 3, 5, 7\\B_{o_p} = 3, 5, 7\\[/tex]

There are 3 odd primes, namely : 3, 5, 7

The total amount of blocks is 9

The odds of picking and odd prime is [tex]\frac{3}{9} \cdot 100\% = 33,(3)\%[/tex]

Answer:

Cubic yards of dirt needed for project = [tex]1\frac{7}{9}[/tex] cubic yards

Cost of Project = About $44.44

Step-by-step explanation:

To find number of cubic yards of dirt needed, we need to find the volume.

Rectangular Prism Volume = length * width * depth

Note: Length is 9ft, width is 16ft, depth is 4 inches. We need to change depth to ft. So 4 inches = [tex]\frac{1}{3}[/tex] feet.

Now finding the volume (in cubic ft) =  [tex]9*16*\frac{1}{3}=48[/tex]

We know 3 feet is  1 yard. To convert cubic feet to cubic yards, we have to divide it by (3)^3 = 27. Hence:

[tex]\frac{48}{27}=\frac{16}{9}[/tex] cubic yards

* Since dirt is $25 per cubic yard, to find cost, we multiply 25 by 16/9. Hence

Cost of Project = 25 * 16/9 = 400/9 = $44.44

Collin needs to buy 1.76 cubic yards of dirt to fill his 9ft by 16ft garden bed to a depth of 4 inches, and the total cost for the dirt will be $44.

To calculate the cubic yards of dirt Collin needs for his 9ft by 16ft garden bed at a depth of 4 inches, we must first convert the dimensions to consistent units and then find the volume. One yard is equivalent to 3 feet, so the bed has dimensions of 3 yards by 5.33 yards (since 9ft / 3 = 3 yards and 16ft / 3 ≈ 5.33 yards). The depth must also be converted from inches to yards: 4 inches is equal to 4/36 or approximately 0.11 yards (because there are 36 inches in a yard).

Now we'll calculate the volume in cubic yards: 3 yards * 5.33 yards * 0.11 yards = 1.76 cubic yards. Next, to find the total cost, we multiply the volume by the cost per cubic yard: 1.76 * $25 = $44. So, Collin will need to pay $44 to fill his garden bed with dirt.

Here are some of the conversions and calculations used:

https://brainly.com/question/30037972

#SPJ3

Answer:

[tex]\large\boxed{e.\ \{a,\ b,\ c,\ d,\ 0,\ 2\}}[/tex]

Step-by-step explanation:

[tex]\text{The union (denoted by}\ \cup\ \text{) of a collection of sets is the set of all elements of the sets. }\\\\A=\{0,\ 1,\ 2,\ 3\}\\\\B=\{a,\ b,\ c,\ d\}\\\\C=\{0,\ a,\ 2,\ b\}\\\\B\ \cup\ C=\{a,\ b,\ c,\ d,\ 0,\ 2\}[/tex]

Answer:

f(3) = (-∛150)/10

Step-by-step explanation:

Put 3 where x is and evaluate. If you don't want the decimal, you can rationalize the denominator to get an exact form.

  f(3) = ∛(3/(-7·3+1)) = ∛(-3/20)

  = -∛(3·50/(20·50)) = (-∛150)/10 ≈ -0.5313292845913...

_____

Multiplying numerator and denominator by 50 makes the denominator 1000, a perfect cube.

Answer:

Need to see the choices

Step-by-step explanation:

Answer:

Answer is B

Step-by-step explanation:

To find the workers' compensation insurance premium, multiply the payroll for September ($179,805) by the base rate converted to decimal (0.1124), resulting in a premium of $20,210.08 (Option A).

The question involves calculating the premium for workers' compensation insurance based on the total payroll for the month of September. To determine the monthly premium, we need to apply the base rate to the total payroll amount. The base rate is given as $11.24 per $100 in wages paid. We can calculate the premium with the following steps:

Convert the base rate to a decimal by dividing by 100. This will give us 0.1124.

Multiply the total payroll amount ($179,805) by the decimal base rate (0.1124) to get the premium amount.

Let's perform the calculation:

$179,805 * 0.1124 = $20,210.08

Therefore, the correct option is:

A) $20,210.08

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

Explanation:

Triangle PQC is congruent to triangle RQC. We can prove this through use of the hypotenuse leg theorem (HL theorem). Note that PC = RC are congruent radii, and also note that CQ = CQ through the reflexive theorem. We have a pair of hypotenuses and a pair of legs for the right triangles.

Then through CPCTC (corresponding parts of congruent triangles are congruent), we know that the pieces PQ and QR are congruent. For now, let's just call them x. They must add to PR which is 12, so,

PQ + QR = PR ..... segment addition postulate

x + x = 12

2x = 12

x = 6 ..... divide both sides by 2

QR = 6

This shows that if you have a radius perpendicular to a chord of a circle, then the radius will bisect this chord. Bisect means to cut in half.

Step-by-step Answer:

There is a theorem in geometry that states that a perpendicular (CQ) to any chord (PR) bisects the chord.  This means that PQ=RQ=6cm.

Answer:

x = 13

Step-by-step explanation:

The area of a rectangle is found by A = l*w. Since the length here is x and the width is 2x - 8, substitute these values and A = 234 to solve for x.

[tex]A = l*w\\234 = x(2x-8)\\234 = 2x^2 - 8x[/tex]

To solve for x, move 234 to the other side by subtraction. Then remove the common factor between all three terms of 2. Factor and solve.

[tex]2x^2 - 8x  - 234 = 0 \\2(x^2 - 4x - 117) = 0\\2(x - 13)(x+9) = 0\\[/tex]

Set each factor equal to 0 and solve.

x - 13 = 0 so x = 13

x + 9 = 0 so x = -9

Since x is a side length and length/distance cannot be negative, then x = 13 is the length of the rectangle.

a) The given function is

[tex]f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}[/tex]

The domain refers to all values of x for which the function is defined.

The function is defined for

[tex]x^4+x^3-4x^2-4\ne0[/tex]

This implies that;

[tex]x\ne -2.69,x\ne 1.83[/tex]

b) The vertical asymptotes are x-values that makes the function undefined.

To find the vertical asymptote, equate the denominator to zero and solve for x.

[tex]x^4+x^3-4x^2-4=0[/tex]

This implies that;

[tex]x= -2.69,x=1.83[/tex]

c) The roots are the x-intercepts of the graph.

To find the roots, we equate the function to zero and solve for x.

[tex]\frac{x^2-4}{x^4+x^3-4x^2-4}=0[/tex]

[tex]\Rightarrow x^2-4=0[/tex]

[tex]x^2=4[/tex]

[tex]x=\pm \sqrt{4}[/tex]

[tex]x=\pm2[/tex]

The roots are [tex]x=-2,x=2[/tex]

d) The y-intercept is where the graph touches the y-axis.

To find the y-inter, we substitute;

[tex]x=0[/tex] into the function

[tex]f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}[/tex]

[tex]f(0)=\frac{-4}{-4}=1[/tex]

e) to find the horizontal asypmtote, we take limit to infinity

[tex]lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0[/tex]

The horizontal asymtote is [tex]y=0[/tex]

f) The greatest common divisor of both the numerator and the denominator is 1.

There is no common factor of the numerator and the denominator which is  at least a linear factor.

Therefore the function has no holes.

g) The given function is a proper rational function.

There is no oblique asymptote.

See attachment for graph.

Answer:

It is the second one

⇒The given inequality is

x²-y²<9

 [tex]\frac{x^2}{3^2}-\frac{y^2}{3^2}<1[/tex]

⇒The general equation of Hyperbola is

 [tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

→The curve will cut the x axis at (3,0) and (-3,0).

So, the given function matches with the curve of Hyperbola.

⇒When the points are from [-3,3] , the function will satisfy the given Inequality.That is if you take , points prescribed in the given interval the function will satisfy the inequality.

⇒Graph B

Answer:

none of the above

Step-by-step explanation:

A graphing calculator shows the zeros to be x=-2, and a double zero at x=3. Hence the factorization is ...

(x +2)(x -3)^2 = 0

The premise that 4 is a zero is incorrect, and none of the answer choices include (x+2) as a factor. The problem is unworkable as written here.

The sum of all the three interior angles of a triangle are 180 degrees. This does not depend on the positioning of the three sides. The sides can be positioned in any way, but the sum must be 180 degrees.

So, the best possible sets of measurements that could be the interior angle measures of a triangle are : 15°, 75°, 90°  And 60°, 60°, 60°

The sets of measurements that could represent the interior angles of a triangle are those whose angles add up to exactly 180°. The valid options provided are 10°, 10°, 160°; 15°, 75°, 90°; 35°, 35°, 105°; and the equilateral set of 60°, 60°, 60°.

The question pertains to the interior angles of a triangle. According to the Triangle Sum Theorem, the interior angles of a triangle always add up to 180°. Therefore, to determine which sets of measurements could represent the interior angles of a triangle, we must check if the sum of the given angles is equal to 180°.

From the options given, the sets of measurements that represent the interior angles of a triangle are:

Final answer:

The maximum height of the twig is approximately 0.570 meters. The twig will hit the ground approximately 0.683 seconds after being flicked up.

Explanation:

To find the maximum height of the twig, we can use the kinematic equation for vertical motion. The equation is given by:

h = v0y2 / (2g)

Where:

h is the maximum height

v0y is the initial vertical velocity

g is the acceleration due to gravity (approximately 9.8 m/s2)

Plugging in the values, we have:

h = (11 ft/s)2 / (2 * 9.8 m/s2)

Converting the initial velocity from feet per second to meters per second:

11 ft/s * 0.3048 m/ft = 3.35 m/s

Substituting the values into the equation:

h = (3.35) / (2 * 9.8)

Simplifying the equation:

h = 0.570 m

Therefore, the maximum height of the twig is approximately 0.570 meters.

To find when the twig will hit the ground, we can use the equation for time in vertical motion:

t = 2 * v0y / g

Plugging in the values, we have:

t = 2 * 3.35 m/s / 9.8 m/s2

Simplifying the equation:

t = 0.683 s

Therefore, the twig will hit the ground approximately 0.683 seconds after being flicked up.

Answer:

16 minutes

Step-by-step explanation:

3336_____________________________

Answer:

5.25 or 5 1/4 MPH

Step-by-step explanation:

1. convert 15 3/4 into a decimal = 15.75

2. divide the miles canoed (15.75) by the time (3)

    15.75/3 = 5.25 MPH

Answer:

Step-by-step explanation:false

Answer:

The correct answer option is 4/11

Step-by-step explanation:

We know that the word 'probability' has 11 alphabets.

We are to find to find the probability of getting a 'b' or an 'i' from this word.

Probability of getting a b = [tex]\frac{2}{11}[/tex] (since there are 2 b's in probability)

Probability of getting an i = [tex]\frac{2}{11}[/tex] (since there are 2 i's in probability)

Probability of getting 'b' or 'i' = [tex]\frac{2}{11} + \frac{2}{11} = \frac{4}{11}[/tex]

The probability of picking a green jelly bean with the first pick is 4/14 = 2/7, because there are 14 jelly bean in total (6 red + 4 green + 4 blue) and 4 of them are green.

If you pick a green jelly bean at the beginning, you have 13 jelly beans remaining, of which 6 are red. So, the probability of picking a red jelly bean is now 6/13.

You want these two events to happen one after the other, to be more precise you want to pick a green jelly bean with the first pick AND a red jelly bean with the second pick. We know the probabilities of the two events, so we have to multiply them to get the probability of them happening both:

[tex]\dfrac{2}{7}\cdot\dfrac{6}{13}=\dfrac{12}{91}[/tex]

Answer:

The 3 geometric solids with circular cross sections are a sphere, a cone and a cylinder

Step-by-step explanation:

While a cone and a cylinder will not in every direction, if you slice them on a horizontal plane, they will have a circular cross section.

The sphere, cylinder, and cone are three-dimensional geometric solids with circular cross sections, existing in both solid and hollow forms, important in physics for understanding properties like moment of inertia and involvement in superelastic collisions.

Three geometric solids that possess circular cross sections are the sphere, cylinder, and cone. These shapes are known as three-dimensional solid figures. The sphere is a solid figure where all points on the surface are equidistant from the center, resulting in any cross-section through its center being a circle.

A cylinder is a solid with straight parallel sides and a circular or oval cross section. A cone has a flat circular base and tapers to a point called the apex or vertex, creating circular cross-sections when sliced parallel to the base.

In addition to fully solid forms, there are also hollow versions of these shapes, such as the hollow spherical shell, which still have circular cross sections. These solids can be involved in various physics concepts such as rotational dynamics and superelastic collisions. When analyzing the rotational motion or collision attributes of these solids, the shapes' geometrical and mass properties play a crucial role.

For instance, the moment of inertia of a solid sphere differs from that of a hollow spherical shell due to the distribution of mass within the object.

Answer:

A

All real numbers

Step-by-step explanation:

Given in the question a graph

To find the range of graph

The range is the set of possible output values, which are shown on the y-axis.

We can see in the graph that for negative values of x it have positive values, zero and negative values of y.

The graph extends vertically from (-∞,∞), along the y axis. So the range of the function shown in the graph is (-∞,∞).  

Hence, it is concluded that range is All real numbers

Answer:

1999

Step-by-step explanation:

y=-15x^2+64x+360

y=-15(1)^2+64(1)+360

y=409

(y is in millions)

I hope this helps!

Answer:

This is correct PEMDAS

Step-by-step explanation:

Parentheses

Exponents

Multiplication/Division

Addition/Subtraction

Answer:

∠PST = 45°

Step-by-step explanation:

The diagonals of a square bisect the angles

∠SPQ = 90° ⇒ ∠SPT = 45°