Use the properties of logarithms to evaluate each expression. log₁₅ 25+log₁₅9

Answer:

Let r be the number of rides and g be the number of games.

2.50g + 4.00r = 52.50

r = 2g

The equations are 2.5g +4r = 52.5 and g=2r.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Cost of game = $2.50

Cost of ride = $4

let g be the number of games

and, let r be the number of rides taken

total they played = $52.50

So, the equation can be

2.5g +4r = 52.5

and,  number of rides she went on is twice the number of games she played.

So, g = 2r

Hence, The equations are 2.5g +4r = 52.5 and g=2r.

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The solution to given equation 2x / 3 - 1/2 = 2x + 5/6 is x = -1

In this question, we have been given an equation.

2x / 3 - 1/2 = 2x + 5/6

We need to find the solution of given equation.

⇒ 2x / 3 - 1/2 = 2x + 5/6

⇒ (4x - 3)/6 = (12x + 5)/6

⇒ 4x - 3 = 12x + 5

⇒ 4x - 12x = 5 + 3

⇒ -8x = 8

⇒ x = -1

We need to check above solution.

so, substitute x = -1 in LHS of given equation.

LHS

= 2(-1) / 3 - 1/2

= -2/3 - 1/2

= -(2/3 + 1/2)

= -[(4 + 3)/6]

= -7/6

Now, substitute x = -1 in RHS of given equation.

RHS

= 2(-1) + 5/6

= -2 + 5/6

= (-12 + 5)/6

= -7/6

For x = -1, LHS = RHS

Therefore, the solution to given equation 2x / 3 - 1/2 = 2x + 5/6 is x = -1

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Answer:

C. Negative skew

Step-by-step explanation:

I did the test and got it right, plato / edmentum

Tamika's number of visits required to earn a free movie ticket is 14 visits.

According to the question, the given data is;

Tamika has a points card for a movie theatre which are as follow;

Signup rewards = 20 points

Each visit reward = 10.5

Total points needed = 167

Let 'x' be the number of visits.

Total points earned for x number of visits: 10.5x.

Thus, the equation according to statement;

20 + (10.5 × x) = 167

10.5x = 167 - 20

10.5x = 147

x = 147/10.5

x = 14 visits.

Therefore, Tamika's number of visits required to earn a free movie ticket are 14 visits.

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The required distance between the third and first fret would be 64.390 mm.

Arithmetic functions are defined as adding, subtracting, dividing, and multiplying built-in functions.

- Subtraction operation: calculates the difference between the right-hand and left-hand operands.

for example 4 -2 = 2

+ Addition operation: on either side of the operator, additional significances are added.

For example 4 + 2 = 6

We have been given that the distance between the first and second frets is 33.641 mm.

The distance between the second and third frets is 31.749 mm.

So the distance between the third and first fret will be:

⇒ 33.641 + 31.749

Apply the addition operation, and we get

⇒ 64.390 mm

Therefore, the required distance between the third and first fret would be 64.390 mm.

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Answer:

E

Step-by-step explanation:

Substituting x=0 into 1-x², we get:

[tex]\lim_{x \to 0} f(1-x^2)=\lim_{x \to 1} f(x)[/tex]

which does not exist.

The two segments having the same length are line VW and line YZ. Option D

A number line can simply be defined as a straight line with numbers that are  placed at equal intervals or segments along its length.

It is also known as a visual picture or representation of numbers.

From the number line shown, we have the following deductions;

From the above solutions, we can see that line

Line VW is equal in length to line YZ

Thus, the two segments having the same length are line VW and line YZ. Option D

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Using the distance formula the distance between and pair of points Q(-12,2) and T(-9,6) is 5 units

Given,

The points = Q(-12,2) and T(-9,6)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

Substitute the values in the equation

The distance = [tex]\sqrt{(-9--12)^{2}+(6-2)^{2} }[/tex]

[tex]=\sqrt{3^{2}+4^{2} } \\=\sqrt{9+16}\\ =\sqrt{25}[/tex]

=5 units

Hence, Using the distance formula the distance between and pair of points Q(-12,2) and T(-9,6) is 5 units

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The weight of Callie's backpack is 7½ pounds which is calculated by multiplication of the number of times the bag is heavier with the weight of the bag.

Multiplication or product of two constants is defined as the number of times a particular constant is added . If we want to multiply a and b then their product is equal to b times a added.

a+a+a+a....... b times=ab

The multiplication is one of the four basic arithmetic operations that are used in mathematics and everyday lives.

Given the weight of Callie's bag is 2 ½ times the weight of Carl's backpack.

Therefore to calculate the the weight of Callie's backpack we multiply the weight of Carl's backpack with  2 ½.

Weight of Carl's backpack=3 pounds

Therefore weight of Callie's backpack= 2 ½×3 pounds= 7½ pounds

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Given statement 'A vector is in standard position when the initial point is at the origin.' is True.

In given question,

We have been given a statement 'A vector is in ₋standard ₋position when the initial point is at the origin.'

We know that the tail of a vector is the initial point of the vector.

And the head of a vector is the final point of the vector with an arrowhead.

The definition of standard position of vector is: "When a vector is in a standard position the head of the arrow is at a point (x, y) and the tail of the arrow is at the origin."

Therefore, given statement 'A vector is in standard position when the initial point is at the origin.' is True.

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Answer:

Step-by-step explanation:

17.55 x 0.92 = $16.15

Answer:

                           18

7b² + 12b + 19 + -------

                           b - 1

Step-by-step explanation:

(7b³ + 5b² + 7b - 1) ÷ (b - 1)

1 | 7   5   7   -1

  ↓    7  12  19

----------------------

  7    12   19  18

                           18

7b² + 12b + 19 + -------

                           b - 1

I hope this helps!

Answer:

Step-by-step explanation: add the equations

2x² = 30

x² = 15

y² = 12 - 15

    = -3

x4 -y4 = 15² - (-3)²

           = 216

Answer: science

Step-by-step explanation:

The geometric mean between pair of numbers 3√2/7 and 5√2/7 is 0.78.

The geometric mean is the average or mean value that signifies the central tendency of a set of numbers. This is obtained by finding the product of their values.

Geometric mean (GM) is calculated as:

GM = [tex]\sqrt{x y}[/tex]

where x and y are the given two values.

According to the given condition, x = [tex]\frac{3\sqrt{2} }{7}[/tex] and y = [tex]\frac{5\sqrt{2} }{7}[/tex]

Substituting these values in the equation above,

∴GM = [tex]\sqrt{\frac{3\sqrt{2} }{7} \frac{5\sqrt{2} }{7} }[/tex]

= [tex]\sqrt{\frac{30}{49} }[/tex]

= 0.78.

Thus, the geometric mean between the given two numbers is 0.78.

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Step-by-step explanation:

Using the formula c=6p+200 you can plug 350 in for c and solve for p

350=6p+200

-200 -200

150=6p

/6 /6

25=p

So, she can invite 25 people to her birthday party.

Radius = 799.877cm

or = 7.99877m(in meters)

Explanation

Radius of a circle from area: if you know the area A, the radius is r = √(A / π).

➟ r = √(201/3.142)

➟ r = √63.98

➟ r = 7.99877m

According to the question, to calculate the probability of the event which states that tossing a coin to get either head or tail

The total number of a coin is [tex]1[/tex]

And total number of possibilities are {H,T}

Therefore, the total number of favorable outcomes in which either head or tail can come: [tex]1[/tex]

As per question, the probability can be written as:

P(h or t) = P(h) + P(t)

            [tex]= \frac{1}{2} +\frac{1}{2} =1 = 100%[/tex]

Hence, the probability of getting either head or tail is [tex]1[/tex].

The given event is mutually exclusive because it has [tex]100[/tex] percent which is close to tenth of a percent. And these two events cannot happen at the same time also, so they are mutually exclusive.

What are mutually exclusive events?

Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.

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Answer:

False

Step-by-step explanation:

The rate of change/slope of the linear equation is 8.

The y-intercept is the point where x has no value and y does.

And in the linear equation y = 8x+3, the y-intercept is 3.

Therefore, false.

- Thanks.

Answer:

pretty sure it's -5

Step-by-step explanation:

the cubed root if 125 is 5 so you just make it negative

Answer:

y = 5

Step-by-step explanation:

Let's solve your equation step-by-step.

[tex] y{}^{3}=125[/tex]

Step 1: Take cube root.

[tex] \sf \: y= {(125)} ^ {( \frac{1}{3} )}[/tex]

y=5

Answer:

|2x + y - 3z|

Plug in the values

|-4 + 10 - 9|

= |-3|

= 3

Step-by-step explanation:

the answer is (3) because when all the letters are turned into numbers then solved it becomes [-4+10+(-9)] then you have to turn it into a positive because of the lines.

Answer:

[tex] \sf \: x=8 and y=1[/tex]

Step-by-step explanation:

Let's solve your system by elimination.

x+3y=11;4x−y=31

Multiply the first equation by -4,and multiply the second equation by 1.

−4(x+3y=11)

1(4x−y=31)

Becomes:

−4x−12y=−44

4x−y=31

Add these equations to eliminate x:

−13y=−13

Then solve−13y=−13for y:

−13y=−13

−13y/−13=−13/−13

(Divide both sides by -13)

y=1

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

x+3y=11

Substitute1foryinx+3y=11:

x+(3)(1)=11

x+3=11(Simplify both sides of the equation)

x+3+−3=11+−3(Add -3 to both sides)

x=8

Answer:

x = 2, x = -6

Step-by-step explanation:

Given quadratic function in vertex form:

[tex]f(x)=(x+2)^2-16[/tex]

The zeros of a function occur when f(x) = 0:

[tex]\implies (x + 2)^2 - 16 = 0[/tex]

Add 16 to both sides:

[tex]\implies (x + 2)^2 - 16+16 = 0+16[/tex]

[tex]\implies (x + 2)^2 =16[/tex]

Square root both sides:

[tex]\implies \sqrt{ (x + 2)^2} =\sqrt{16}[/tex]

[tex]\implies x+2= \pm 4[/tex]

Subtract 2 from both sides:

[tex]\implies x+2-2= -2 \pm 4[/tex]

[tex]\implies x= -2 \pm 4[/tex]

Therefore:

[tex]\implies x=-2+4=2[/tex]

[tex]\implies x=-2-4=-6[/tex]

The zeros of the given quadratic function are x = 2, x = -6.

Using the definition of slope, the points (3 , -5), (-3 , 3), and (0 , 2) are not collinear.

Three or more points are said to be collinear if they lie on a single straight line.

To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.

m = (y2 - y1)/(x2 - x1)

Getting the slope of each pair of points:

(3 , -5) and (-3 , 3)

m = (y2 - y1)/(x2 - x1)

m = (3 - -5)/(-3 - 3)

m = 8/-6

m = -4/3

(-3 , 3) and (0 , 2)

m = (y2 - y1)/(x2 - x1)

m = (2 - 3)/(0 - -3)

m = -1/3

(3 , -5) and (0 , 2)

m = (y2 - y1)/(x2 - x1)

m = (2 - -5)/(0 - 3)

m = 7/-3

m = -7/3

Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is not equal with each other, then they are not collinear.

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Truth Table is used to perform logical operations in Maths. These operations comprise boolean algebra or boolean functions. It is basically used to check whether the propositional expression is true or false, as per the input values. This is based on boolean algebra.

A truth table is a breakdown of a logic function by listing all possible values the function can attain. Such a table typically contains several rows and columns, with the top row representing the logical variables and combinations, in increasing complexity leading up to the final function.

Here we construct truth table for And operation -

see attachment below -

So because we don't have statements on either side of the "and" symbol that are both true, the statment ~p∧q is false. So ~p∧q=F. Now that we know the truth value of everything in the parintheses (~p∧q), we can join this statement with ∨p to give us the final statement (~p∧q)∨p.

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Answer:

y = 3x

Step-by-step explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (2, 6) ← 2 points on the line

m = [tex]\frac{6-0}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3

y = 3x ← equation of line

Answer:

Step-by-step explanation:

x^2+2x-16-2x = x^2 - 16

= ( x - 4) ( x+ 4)

Answer:

see attached photo for the graph