What is the value of 21 + 62 – (35 – 8) • 3?

Yes, this is a valid argument. This argument uses the Law of Detachment.

The Law of Detachment states that if the hypothesis of a true conditional statement is true, then the conclusion must be true as well. The Law of Detachment is the most often employed deductive reasoning theory.

Given:

Points X and Y both lie on plane R.

Conclusion: Points X and Y are coplanar.

The argument is true because,

The term "coplanar" refers to "being on the same plane." Coplanar points are points that are on the same plane. A group of points in space is said to be coplanar if there is a geometric plane that contains all of them.

Hence, the Conclusion is Points X and Y are coplanar.

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Answer:

[tex]\textsf{C:}[/tex]

[tex]\begin{cases}s + h = 40\\18s + 14h = 700 \end{cases}[/tex]

Step-by-step explanation:

Given information:

Define the variables:

Create an equation for the total number of scarves and hats sold:

⇒ s + h = 40

Create an equation that represents the total amount made from sales considering the cost per item:

⇒ 18s + 14h = 700

Therefore, the system of equations that represents the given constraints is:

[tex]\begin{cases}s + h = 40\\18s + 14h = 700 \end{cases}[/tex]

Answer: length 20

width 10

Step-by-step explanation:

L = 2W

W+W+L+L=60

2W+2W+2W=60

6W=60

•1/6 to both sides

W=10

L=20

Answer:

Length = 20 in

Width = 10 in

Step-by-step explanation:

Given information:

Define the variables:

Perimeter of a rectangle

[tex]P = 2(w + l)[/tex]

where:

Substitute the given values into the formula and solve for x:

[tex]\begin{aligned}\textsf{Perimeter of rectangle}&=\sf 2(width + length)\\\implies 60&=2(x+2x)\\60&=2(3x)\\60&=6x\\x&=10\end{aligned}[/tex]

Substitute the found value of x into the expressions for width and length.

Solution

Answer:

$75

Step-by-step explanation:

basically 7.50 x 10

Answer: 1/4 is more

Step-by-step explanation:

1/4=25%

25%>15%

1/4>15%

1/4 is more than 15%

Answer:The width of the room is .

Step-by-step explanation:

Consider the provided information.

It is given that the whole room has an area 46 14/15 sq yd.

This can be written as:

yd.

Now consider the figure shown below:

From the figure we know that the length of the rectangular meeting room is  yd.

The area of rectangle is

Let width of the rectangle is w yard.

Hence, the width of the room is .

active attachment

Step-by-step explanation:

The width of the room is .

Step-by-step explanation:

Consider the provided information.

It is given that the whole room has an area 46 14/15 sq yd.

This can be written as:

yd.

Now consider the figure shown below:

From the figure we know that the length of the rectangular meeting room is  yd.

The area of rectangle is

Let width of the rectangle is w yard.

Hence, the width of the room is .

active attachment

The equation of the line with slope -3/4 and y intercept 9 is y=-3/4x+9.

Based on the conditions formulate:

m=-3/4

and b = 9

Write the equation of the linear function:

y=mx+b

substitute m=-3/4 and b=9 into y=mx+b:

y = -3/4x+9

A line's equation must be in the Slope-Intercept Form, y = mx + b, in order to be graphed using its slope and y-intercept.

This format makes it simple to read off the slope and y-intercept values. The y-intercept is the constant term b, whereas the slope is just the m coefficient of the variable x.

plot the y intercept (0,9) in the xy axis.

Use the slope to locate a different point beginning at the y-intercept. The direction you travel from one point to another is contained in the slope.

Hence the required graph is plotted.

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Answer:

y=-3x+13

Step-by-step explanation:

step one you will need to find the slope by the Y2 minus y1 all over x2 minus X1 formula. so you would have -2 - 4 all over 5 - 3 . you will get -6 over 2 which is equal to -3 . that means that -3 is the slope .

Step 2 you can find the equation with the point slope form formula . the point slope form formula is y-y1=m(x-x1). by substituting your values into these equation you can find the equation of this line . you can substitute any point into it as long as it is on the line . let's use (3,4) where 3=x1 and 4=y1.

step 3. simplify. you will get y-4=-3(x-3). keep in mind I substituted -3 into the equation because -3 is the slope.

you can simplify this if you want to . you will get y=-3(x-3)+4. it becomes through foiling, y=-3x+9+4. it simplifies to y=-3x+13.

The unknown variable, h of the equation is 18

A variable is a number represented by a letter in an equation.

The unknown variable in the equation is variable h.

Therefore, let's find the value of h.

A = 1 / 2 h(B + b)

where

Therefore, let's substitute the known values in the equation.

153 = 1 / 2h(10 + 7)

153 = 1 / 2 h(17)

153 = 17 / 2 h

cross multiply

153 × 2 = 17h

306 = 17h

divide both sides by 17

h = 306 / 17

Therefore,

h = 18

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Answer:

2

Step-by-step explanation:

The true statement is Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a sequence of rigid motions.

The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Given:

MATH is congruent to quadrilateral WXYZ.

Then congruent sides are

MA= WX

AT = XY

TH = YZ

and, congruent angles are

<M = <W

<A = <X

<T= <Y

<H = <Z

So, if the quadrilateral is congruent then they equal in measure.

Hence, the true statement is  Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a sequence of rigid motions.

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Answer:

∠ 2 = 140°

Step-by-step explanation:

the left base angle in the triangle and 110° are a linear pair and sum to 180°

base angle + 110° = 180° ( subtract 110° from both sides )

base angle = 70°

the 2 sides of the triangle are congruent so Δ is isosceles with base angles congruent.

the vertex of the Δ is then

(180 - 70 - 70)° = 180° - 140° = 40°

the vertex and ∠ 2 are a linear pair and sum to 180° , that is

∠ 2 + 40° = 180° ( subtract 40° from both sides )

∠ 2 = 140°

The rate at which the car is traveling is given as  1.5 miles/minute.

Given that,

This double-number line depicts the overall distance traveled by a car. It is necessary to determine the car's speed in miles per hour (mph).

Distance is referred to as an object moving between two points in time at a specific speed.

here,

The distance traveled = 150 miles

Time taken = 100 minutes

Rate = distance/time

Rate = 150 / 100

Rate = 1.5 miles per minute

Thus, The rate at which the car is traveling is given as  1.5 miles/minute.

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The image of the function after the translation is g(x) = 6x - 4

Translation involves shifting a function across the coordinate plane

The given parameters are:

f(x) = 6x + 2

The transformation is given as

Translation 6 units down

Mathematically, this transformation can be represented as

(x, y) = (x, y - 6)

When represented as a function, we have

g(x) = f(x) - 6

Substitute the equation f(x) = 6x + 2 in the equation g(x) = f(x) - 6

So, we have the following equation

g(x) = 6x + 2 - 6

Evaluate the like terms

g(x) = 6x - 4

Hence, the equation of g(x) is g(x) = 6x - 4

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Answer:

B

Step-by-step explanation:

V = 27(0.8)^1

V = 21.6

V = 27(0.8)^2

V = 17.28

And more

Answer:

500

Step-by-step explanation:

she can build 5 in 6 minutes. 6 × 10 is 1 hour

so you would do 5 × 10 = 50

then multiply 50 × 10 hours = 500 toys

Answer:

Patricia will build 500 toys in 10 hours

Step-by-step explanation:

5 toys                   ? toys

---------         =        ----------

6 minutes            10 hours

so we would turn the hours into minutes which would be

600 minutes.

5 toys                   ? toys

---------         =        ----------

6 minutes            600 mins

Then we would cross multiply and that will give us how many toys she can build in 10 hours, which is 500 toys.

To be a function, each input can only go to one output

A. The input 1 goes to two different output values

(1,6) (1,7) causes it not to be a function

B. This is a function. Each input has only one output value

C. The input 0 goes to two different output values

(0,-5) snf (0,4) causes it not to be a function

The relation is the relationship between two or more sets of values. Suppose, x and y are two sets of ordered pairs. If set x has a relation with set y, then the values of set x are called domain whereas the values of set y are called range. A relation from a set A to a set B is a subset of A×B. Hence, a relation R consists of ordered pairs (a,b), where a∈A and b∈B. If (a,b)∈R, we say that is related to, and we also write aRb. A connection between the elements of two or more sets is a relation. The sets must be non-empty. A subset of the Cartesian product also forms a relation R. A relation may be represented either by the Roster method or by the Set-builder method.

Answer:

X= 15 is Undefined

Y= -3 is Zero

Y= 1/2x - 4 is a positive slope

The amount of time it takes to reach the beam of sum from sun to earth is 200 seconds approximately

What is division?

Division is one of the basic arithmetic operation in which we find a number such the product of the number with the denominator is equal to the numerator.

We are given that the distant of earth from sun is 9.3 ×10^7

And the speed of light is 1.86×10^5

We divide the distance by the speed to get the value of time

[tex]\frac{9.3}{1.86}[/tex]×[tex]\frac{10^7}{10^5}[/tex]

On simplifying we get

200 seconds

Hence, The approximate time require to reach the beam of sun from sun to earth is 200 seconds

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The size of the tank would be suggested to hold 60 small fish is 75 gallon-tank option (C) is 75 gallon-tank.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

A pet store clerk suggested 4 small fish for a 5-gallon fish tank.

4 small fish = 5-gallon

60 small fish = x gallon

x = (5)(60)/4

x = 75 gallon-tank

Thus, the size of the tank would be suggested to hold 60 small fish is 75 gallon-tank option (C) is 75 gallon-tank.

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Required Lagrange multipliers are 14,14.

What are Lagrange multipliers?

We have to minimize f(x,y)=x+y'

subject to xy=196 ............(1)

x>0,y>0

Let L(x,y,d)= f(x,y)+d(XY-196)

∀L= [tex](\frac{Lx}{Ly} )=(\frac{1+dy}{1+dx} )[/tex]

For critical points,

∀L=0

⇒[tex](\frac{1+dy}{1+dx} )=\frac{0}{0}[/tex]

⇒ x,y= -1/d

Substituting in equation 1, we get,

d=±1/14

d=+1/14 ⇒ x=y=-14 (neglect)

d=-1/14 ⇒ x=y=+14

∵ x>0, y>0.

Hence, x=y=14

Function's maximum or minimum

f(x,y)=f(14,14)=28

Required Lagrange multipliers are 14,14.

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The farmer has 28 cows from a total of 80 animals in the farm.

Each chicken has two legs and each cow has four legs. The farmer has a total of 216 legs among all the animals, which are 80. Then, we can represent the situation with the following system of linear equations:

x + y = 80

4 · x + 2 · y = 216

Where:

The system can be solved easily by some algebraic handling:

x = 80 - y

4 · (80 - y) + 2 · y = 216

320 - 4 · y + 2 · y = 216

320 - 2 · y = 216

2 · y = 320 - 216

2 · y = 104

y = 52

x = 80 - 52

x = 28

The farmer has 28 cows.

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The area of the triangle is 13 square units.

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hello

the question presented here related to compound interest and we can solve that using the formula

let's proceed to substitute the values into the equation

the compounded interest compounded monthly at 6% for 5 years is 3375

The amount is  3250

The accumulated amount is calculated using the initial investment and  interest earned in the given duration

The formula for simple interest is  P×R×T and further, it is divided  by 100

SI= 2500 ×  6 × 5 =75000 ÷100 = 750

Now, for calculating the accumulated amount we will add the initial investment and the interest gained

ie, 2500+750 =3250

Here we are using the simple interest method to calculate the interest as it is assumed to be taken as simple interest when nothing is specified.

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The z-score corresponding to a score that is 12 points above the mean is 2.

The z-score is a numerical measurement used in statistics to determine the sample data value's relationship to the mean of a group of values, measured in terms of standard deviation from the mean. It is measured as the difference of the sample data value and the sample mean over the standard deviation, such that

z-score = (x – μ) / σ

where x = sample data value

μ = mean

σ = standard deviation

If the sample score is 12 points above the mean, then (x – μ) = 12.

(x – μ) = 12

σ = 6

Substitute the values to the z-score formula.

z-score = (x – μ) / σ

z-score = 12/6

z-score = 2

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Answer: b + 24 = 68

Step-by-step explanation:

we are told the zoo has 68 different species of birds so the equation will be = 28. The answers showing = 24 are already wrong.

transported means they are taken away, so we have to subtract 24 (animals that stayed in the zoo) to find b which are the remaining species moved to the barn.

b + 24 = 68
  -  24    -24

b = 44 (transported to the barn)
     24 ( stayed in the zoo)
    68 ( total number of species of birds)

The correct expression to show the species of transported birds will be;

⇒ b + 24 = 68

Where, b is the number of transported birds.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Total number of birds in Roaring Zoo = 68

Number of stayed birds in Zoo = 24

Let number of transported birds = b

Then, We can formulate;

Total number of birds = Stayed birds + Transported birds

Substitute all the values, we get;

⇒ 68 = 24 + b

Therefore,

The correct expression to show the species of transported birds will be;

⇒ b + 24 = 68

Where, b is the number of transported birds.

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Answer:

(2, 1) and (4, 2): [tex]\frac{1}{2}[/tex]

(-4, 5) and (-3, -7): [tex]-12[/tex]

Step-by-step explanation:

Hello! Let's help you with that problem there!

So we know that in a slope intercept form, it is depicted as [tex]y=mx+b[/tex]. There are two ways to essentially find m, which is slope in this case. The first method is the [tex]\frac{rise}{run}[/tex] method. This is typically used when you have a graph to look off from and it's just a matter of counting the displacement from one point to another.

However, there is another way to find the slope given 2 points and that is what we are going to do here, since we have no graph to reference and have all the relevant information to find the slope using this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

With this formula, we can plug in the coordinate values and solve for the slope!

(2, 1) and (4, 2):

[tex]m=\frac{2-1}{4-2}[/tex]

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

Therefore, the slope of these points is [tex]m=\frac{1}{2}[/tex]

(-4, 5) and (-3, -7):

[tex]m=\frac{-7-5}{-3-(-4)}[/tex]

[tex]m=\frac{-12}{1}[/tex]

[tex]m=-12[/tex]

Therefore, the slope of these points is [tex]m=\frac{-12}{1}[/tex] or [tex]m=-12[/tex]

The correct answer is B