An electrician charges a $50 house call fee and $65 per hour for the work. Which algebraic expression represents this situation to represent the total cost for h hours of work?

Answer:

Option A is correct.

Yes, by AA similarity criterion

Step-by-step explanation:

AA(Angle-Angle) Similarity Criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

In ΔBAC and ΔCED

[tex]\angle BAC = \angle CED = 17^{\circ}[/tex]   [Angle]        [Given]

[tex]\angle C = \angle C[/tex]     [Angle]          [Common angle]

Therefore, by AA similarity criterion;

[tex]\triangle BAC \sim \triangle CED[/tex]

Therefore,  ΔBAC and ΔCED are similar by AA similarity criterion.

The change in position or displacement of an object in the time interval is known as average velocity of the object. The value of the average velocity is 60 miles per hour.

Given-

A car travels 180 miles north in 3 hours.

Average velocity- The change in position or displacement of an object in the time interval is known as average velocity of the object. It can be positive or negative depending upon the sign of the displacement.

[tex]\overline v=\dfrac{\Delta v}{\Delta t}[/tex]

Here [tex]\Delta v[/tex] is the change in displacement and [tex]\Delta t[/tex] is the change in time.

Use this formula to find the average velocity in the given formula we have to  put the values velocity and time given in the question. Therefore,

[tex]\overline v=\dfrac{180}{3}[/tex]

[tex]\overline v=60[/tex]

Hence, the value of the average velocity is 60 miles per hour.

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Answer:

it is prime

Step-by-step explanation:

Remember:

Prime numbers have 2 factors:

1

Itself

Final answer:

Option c, 15/16, is the correct answer because it cannot be simplified to 7/8, making it not equivalent to 7/8, while the other options are equivalent after simplification.

Explanation:

The question asks us to identify which fraction is not equivalent to 7/8. To determine this, we need to compare each option with 7/8:

Hence, the correct answer is option c, which is not equivalent to 7/8.

Answer:

(C) Square feet

Step-by-step explanation:

In order to take the measurements, he should use the square feet unit of measure.

As, the cubic feet also known as unit of volume can be defined as the volume of the cube with sides of one foot in length. Since, the bathroom is two dimensional therefore, cubic feet can't be used.

Yards are basically a unit of length use to measure length and perimeter and square yards are used in measuring the long space and the bathroom is bit too small for it.

Therefore, square feet should be used to measure.

Answer:

Statement which describes the roots is:

2 real roots

Step-by-step explanation:

If the discriminant D of a quadratic equation follows:

D=0 then there are 2 equal real roots or 1 real root

D>0 then there are 2 unequal real roots

and if D<0 then there are 2 complex roots

Here, we are given  the discriminant of a quadratic equation is 4

i.e. D=4 >0

So, it means quadratic equation has 2 real roots

Hence, statement which describes the roots is:

2 real roots

Hence, statement which describes the roots is:

2 real roots

Answer: The probability that she will guess correctly on the third question [tex]=\frac{1}{4}[/tex]

Step-by-step explanation:

Given: The math test has 10 multiple choice questions, each with 4 answers.

To find  probability that she will guess correctly on the third question, we need to just look at only one question which has 4 options and one of them is the right answer, thus probability of choosing the right answer from 4 option is the fraction of 1 over 4.

The probability that she will guess correctly on the third question

[tex]=\frac{\text{answer of a question}}{\text{total options of a question}}[/tex]

[tex]=\frac{1}{4}[/tex]

Answer:

a.rational number

Step-by-step explanation:

We are given that a real  number 1.68

We have to find that given number belongs to which set

We know that

N={1,2,3...}

Whole numbers set ={0,1,2...}

Integers=Z={...-3,-2,-1,0,1,2,,,}

Rational number :That number which can be written in the form of [tex]\frac{p}{q}[/tex] where q is not equal to zero ,p and q are belongs to integers.

Irrational number: That number which is not rational is called irrational number.

Hence, given number 1.68 belongs to rational numbers set.

Answer : a.rational number

The fourth degree polynomial g(x) with a double zero at x=1, zeros at x=-4 and x=5, and satisfying g(0)=-6 is g(x) = 3/10(x-1)²(x+4)(x-5).

A possible formula for a fourth degree polynomial g(x) with specific characteristics. The polynomial must have a double zero at x=1, zeros at x=-4 and x=5, and must satisfy g(0)=-6.

Since the polynomial has a double zero at x=1, we can represent that part of the polynomial as (x-1)². The other two zeros at x=-4 and x=5 give us factors of (x+4) and (x-5) respectively. Multiplying these factors gives us a polynomial that satisfies the zero requirements: (x-1)²(x+4)(x-5).

Now, we need to find the constant k that will make the polynomial satisfy g(0) = -6. We set up the equation using the known factors:
k(x-1)²(x+4)(x-5) and substitute x with 0 to solve for k. This gives us k(0-1)²(0+4)(0-5) = -6. Solving for k, we find k = 3/10.

Therefore, the formula for the polynomial g(x) is g(x) = 3/10(x-1)²(x+4)(x-5).

Step-by-step explanation:

Answer:

Teddy avoids accidents.

Step-by-step explanation:

The equation sin(-13π/4) = -5π/4 is incorrect.

The correct value for sin(-13π/4) is actually 1/√2 or √2/2, not -5π/4.

Here, we have,

To understand why, let's break down the calculation step by step:

The sine function represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

In this case, we have an angle of -13π/4.

To find the reference angle,

we can add 2π to -13π/4 to bring it into the standard range of angles:

-13π/4 + 2π = -5π/4

Now, we can find the reference angle of -5π/4 in the unit circle or trigonometric table.

The reference angle of -5π/4 is π/4.

Since sine is positive in the second quadrant,

the value of sin(-5π/4) is the same as sin(π/4), which is 1/√2 or √2/2.

Therefore, the correct exact value of sin(-13π/4) is 1/√2 or √2/2, and not -5π/4.

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The cost to rent 1 canoe from the rent made by the group of the girls and boys is $25.

Word problems are a mathematical interpretation by using variables, numbers, and arithmetic operations to solve real-life problems.

From the given information:

Now, we can have a system of equations, and we can solve for the number of canoes and the inner tubes rented.

Using Elimination method:

2c + 3t = 80    --- × (1)

c + 7t = 95       --- × (2)

2c + 3t = 80

-2c + 14t = 190          

 0  +  -11t = -110        

-11t = -110

t = -110/-11

t = 10

From equation (1)

2c + 3t = 80

2c + 3(10) = 80

2c + 30 = 80

2c = 80 - 30

2c = 50

c = 50/2

c = 25

Therefore, we can conclude that the cost of the rent of 1 canoe is $25.

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Answer:

  about 473 mL

Step-by-step explanation:

For liquid measure, there are 16 cups in a US gallon, which is exactly 231 cubic inches. Each cubic inch is exactly 2.54³ = 16.387064 cubic centimeters--the same number of mL.

So, the exact conversion from cups to mL is ...

  1 cup = (231/16)(16.387064) mL = 236.5882365 mL

Multiplying this by 2 gives ...

  2 cups = 473.176473 mL

For many purposes, the nearest mL is sufficiently accurate:

  2 cups ≈ 473 mL

Answer:

36

Step-by-step explanation:

The expression that completes the equation is 3(7+1).

To complete the equation "24 divided by 6 + 20,"

we need to perform the division first, and then add 20 to the result.

    6 | 24 | 4

           24

        _____

            0

Here, Divisor= 6, Remainder= 0 and Quotient= 4

So, 4 + 20 = 24

Then, the equivalent value is

3 (7+1)

= 3 x 8

= 24

Therefore, the expression that completes the equation is 3(7+1).

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The question attached here is incomplete, the complete Question is

Choose the expression that completes the equation.

24 ÷ 6 + 20 =______

2(7 + 10)

4(4 + 3)

3(7 + 1)

3(7 + 7)

option b) 5 km

1 km = 1000 m

Divide the number of meters by 1000:

5000 m / 1000

= 5 km

So, 5000 meters is equal to 5 kilometers.

The correct answer is 5 km.

Answer:

○ [tex]\displaystyle y ≤ -7[/tex]

Step-by-step explanation:

Whenever you divide\multiply by a negative, you reverse the inequality symbol.

I am joyous to assist you anytime.