If m angle 1 = 42 and m angle 2 = 27, then m angle APC =

Answer:

A. 740 - s = 726

Step-by-step explanation:

The equation states: the original number of students, subtracting the number of students that left, represents the number of students now.

Correct option is (A) 740 - s = 726

Given that a high school had 740 students at the start of the year.

However some students left the school. After that, the school had 726 students.

Let 's' be the  the number of students who left the school

Thus as 's' students left the school, there will be deduction of 's' students from the school

Now this deduction 's' would be from the 740 students which were present in the school and the resultant students after deduction is given to be '726'

Thus we can form the mathematical expression as follows,

[tex]740 - s = 726[/tex]

Thus '740 - s = 726' is the requires expression

To obtain a 50% mixture, 2.4 quarts of water must be added to 4 quarts of an 80% mixture.

To solve this problem, we'll use the concept of mixtures.

Let's denote:

x = the number of quarts of water to be added.

We have 4 quarts of an 80% mixture. This means that in these 4 quarts, 80% is the actual substance (let's call it A) and 20% is water.

So, the amount of substance A in the 4 quarts is [tex]\(0.80 \times 4 = 3.2\)[/tex]quarts, and the amount of water is [tex]\(0.20 \times 4 = 0.8\)[/tex] quarts.

When we add \(x\) quarts of water, the total amount of water becomes 0.8 + x, and the total volume of the mixture becomes 4 + x quarts.

For the mixture to be 50%, the amount of substance A in the mixture should be equal to the amount of water. So, we set up the equation:

[tex]\[3.2 = 0.5 \times (4 + x)\][/tex]

Solving for x:

[tex]\[3.2 = 2 + 0.5x\]\[0.5x = 3.2 - 2\]\[0.5x = 1.2\]\[x = \frac{1.2}{0.5}\]\[x = 2.4\][/tex]

So, 2.4 quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture.

To find the unit rate of $32.05 for 15 gallons, divide the total cost by the number of gallons, resulting in $2.14 per gallon. This unit rate helps to compare the cost per gallon with other price points.

The unit rate is a way to compare a quantity to one unit of another quantity. For the case of $32.05 per 15 gallons, we can calculate the unit rate by dividing the total cost by the number of gallons to find the cost per one gallon.

Step-by-step Calculation

This means the unit rate, or the cost for one gallon of gasoline, is $2.14 per gallon.

Comparing this with other unit prices provided: $2.20 per gallon, $2.00 per gallon, $1.80 per gallon, $1.60 per gallon, $1.40 per gallon, $1.20 per gallon, and $1.00 per gallon, we can observe how this unit rate fits within the broader range of prices and quantities.

Let

L--------> the length of the rectangle

W-------> the width of the rectangle

we know that

the perimeter of the rectangle is equal to

[tex]P=2L+2W[/tex]

[tex]P\leq 96\ cm[/tex]

so

[tex](2L+2W)\leq 96[/tex] ---------> equation [tex]1[/tex]

[tex]L=5W[/tex] ---------> equation [tex]2[/tex]

Substitute equation [tex]2[/tex] in equation [tex]1[/tex]

[tex]2*(5W)+2W\leq 96[/tex]

therefore

the answer is the option

2w+2⋅(5w)≤96

Answer:

2w+2⋅(5w)≤96

Step-by-step explanation:

Volume is a measurement that quantifies the amount of three-dimensional space occupied by an object, substance, or region.

Volume is a fundamental physical quantity that describes the extent or size of an object in the context of its three dimensions: length, width, and height.

Volume is commonly expressed in cubic units, such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or cubic feet (ft³), depending on the system of measurement used. It can apply to various entities, including solid objects, liquids, gases, or even abstract concepts like the volume of data.

For solid objects, the volume represents the total amount of space enclosed within its boundaries. It is typically determined by measuring or calculating the product of the object's length, width, and height or through more complex mathematical formulas for irregular shapes.

In the case of liquids or gases, the volume refers to the amount of space occupied by the substance within a container. It can be measured directly using tools such as graduated cylinders or indirectly through displacement methods.

Understanding volume is essential in fields like physics, engineering, architecture, chemistry, and many others where knowledge of spatial quantities is required for designing, analyzing, or describing various objects or systems.

learn more about Volume: https://brainly.com/question/76841

#SPJ6

its b sis.

:') your welcome

The value of s from the equation 0.7(3s+4)−1.1s = 7.9 is 5.1.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

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.

We have,

Equation:0.7(3s+4)−1.1s=7.9

Now, solving equation for s we get

2.1 s + 2.8 - 1.1 s = 7.9

1 s = 7.9- 2.8

s = 5.1

Thus, the value of s is 5.1

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ3

The required expression is equivalent to −10+(−40)+(−90) is  −10+(−90)+(−40). Option D is correct.

Given that,
An equivalent expression to −10+(−40)+(−90)  is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,

= −10+(−40)+(−90)
= -10 -40 - 90
= -140

a
= −(10−40)+(−90)
= +30 - 90
= -60

b
= −10−(40−90)
=-10+50
= 40

c
= 10+40+90
= + 140

d
=−10+(−90)+(−40)
= -10 - 90 -40
=-140

Thus, the required expression is equivalent to −10+(−40)+(−90) is  −10+(−90)+(−40). Option D is correct.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:  the correct option is

(D) [tex]c=\dfrac{d+ab}{a}.[/tex]

Step-by-step explanation:  We are given to solve the following equation for the value of c :

[tex]a(c-b)=d~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the given equation for c, we need to take c on one side and all other values on the other side of the equation.

The solution for c of equation (i) is as follows :

[tex]a(c-b)=d\\\\\Rightarrow ac-ab=d\\\\\Rightarrow ac=d+ab\\\\\Rightarrow c=\dfrac{d+ab}{a}.[/tex]

Thus, the required value of c is [tex]c=\dfrac{d+ab}{a}.[/tex]

Option (D) is CORRECT.

To find out if 95 is closer to 64 or 125, we compare the absolute differences. 95 is 31 units away from 64 and 30 units away from 125. Therefore, 95 is closer to 125.

To determine whether 95 is closer to 64 or 125, we need to calculate the absolute differences between 95 and each of the two numbers:

Since 30 is smaller than 31, 95 is closer to 125 by 1 unit.