MATHEMATICS HIGH SCHOOL

What is the intersection of plane STXW and SVUT?A. SV
B. ST
C. YZ
D. TX

Answers

Answer 1
Answer: B. ST is the intersection of plane STXW and SVUT.
Answer 2
Answer:

Answer: B. ST.


Step-by-step explanation: The intersection of two planes, if exists, is a straight line. Since the planes STXW and SVUT have S and T as common points and we can always draw a straight line given any two points in a plane, so ST is the line joining the points S and T, and hence, it is the intersection of the two given planes.

Thus, the correct option is B. ST.


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The sum of two numbers is 100, their difference is 56, what are the two numbers?

Answers

\large\bf{\underline{\underline{\mathfrak{Question}:}}}

The sum of two numbers is 100, their difference is 56, what are the two numbers?

\large\bf{\underline{\underline{\mathfrak{Solution}:}}}

Let'sassume that,

:{\Longrightarrow{\small{\rm{The\:one\:number\:=a}}}}

:{\Longrightarrow{\small{\rm{The\:other\:number\:=b}}}}

Now,accordingto thequestion,

:{\Longrightarrow{\small{\rm{a+b=100\:\:....(i)}}}}

:{\Longrightarrow{\small{\rm{a-b=56\:\:....(ii)}}}}

Here, substitution method must be applied.

Now,use the first equation

:{\Longrightarrow{\small{\rm{a+b=100}}}}

:{\Longrightarrow{\small{\rm{a=100-b}\:\:....(iii)}}}

Putthevalueofequation(iii)inequation(ii)

:{\Longrightarrow{\small{\rm{a-b=56}}}}

:{\Longrightarrow{\small{\rm{100-b-b=56}}}}

:{\Longrightarrow{\small{\rm{100-2b=56}}}}

:{\Longrightarrow{\small{\rm{2b=56-100}}}}

:{\Longrightarrow{\small{\rm{2b=-44}}}}

:{\Longrightarrow{\small{\rm{b=(-44)/(-2)}}}}

:{\Longrightarrow{\small{\rm{b=\frac{\cancel{-44}}{\cancel{-2}}}}}}

:{\Longrightarrow{\small{\rm{b=(22)/(1)}}}}

{\therefore{\small{\rm{b=22}}}}

Now,putthisvalueinequation(iii)forgettingtheanswer.

:{\Longrightarrow{\small{\rm{a=100-22}}}}

{\therefore{\small{\rm{a=78}}}}

For verification:

Put the value of a and b in the equation (i)and(ii)

Wehave,

:{\Longrightarrow{\small{\rm{a=78}}}}

:{\Longrightarrow{\small{\rm{b=22}}}}

Incase1:

:{\Longrightarrow{\small{\rm{78+22=100}}}}

:{\Longrightarrow{\small{\rm{100=100}}}}

:{\Longrightarrow{\small{\rm{L.H.S=R.H.S}}}}

Incase2:

:{\Longrightarrow{\small{\rm{78-22=56}}}}

:{\Longrightarrow{\small{\rm{56=56}}}}

:{\Longrightarrow{\small{\rm{L.H.S=R.H.S}}}}

Hence,verified!

Answer: X = 78 and Y = 22.

Step-by-step explanation:

Let's call the two numbers X and Y. We are given two pieces of information:

1. The sum of the two numbers is 100, so we can write this as an equation: X + Y = 100.

2. The difference between the two numbers is 56, which can also be written as an equation: X - Y = 56.

Now, you have a system of two equations with two variables:

1. X + Y = 100

2. X - Y = 56

You can solve this system of equations by adding the two equations together to eliminate the Y variable:

(X + Y) + (X - Y) = 100 + 56

This simplifies to:

2X = 156

Now, divide both sides by 2 to solve for X:

2X / 2 = 156 / 2

X = 78

Now that you know the value of X, you can substitute it into one of the original equations to find the value of Y. Let's use the first equation:

X + Y = 100

78 + Y = 100

Subtract 78 from both sides:

Y = 100 - 78

Y = 22

So, the two numbers are X = 78 and Y = 22.

Sunshine Honda sold 112 cars this month. If that is 40% greater than last month, how many cars were sold last month?

Answers

100 \% + 40 \% =140 \% \n \n 140 \% - 112 \ cars \n \n 100\% - x \n \n x=(112\cdot 100\%)/(140\%) =(11200)/(140) = 80 \ cars \n \nAnswer : \ were \ sold \ last \ month \ 80 \ cars
Let the last month sold car be x 112=40% of x+x so by solving it easily u get ur answer n x=80

Multiply 3⁄4 × 16⁄9 .
A. 64⁄27
B. 3⁄4
C. 27⁄64
D. 4⁄3

Answers

Answer:

Option D (4)/(3)

Step-by-step explanation:

we know that

The product of two fractions is equal to the product of the numerators divided by the product of the denominators

so

(3)/(4)*(16)/(9)=(3*16)/(4*9)\n \n=(48)/(36)\n \n=(24)/(18)\n \n=(4)/(3)
I believe that the answer to this question is D. 4⁄3

When applied to a triangle, a dilation with a positive scale factor does not preserve __________. A. angle measure B. orientation C. shape D. length

Answers

d. length because it's a dilation 

Answer:

The correct answer is d) length

The line passes through the points (x1, y1) and (x2, y2). The slope of the line is: a) x2−x1y2−y1​ b) y2−y1x2−x1​ c) x1−x2y1−y2​ d) y1−y2x1−x2​

Answers

Answer:

b

Step-by-step explanation:

the slope m of a line passing through (x₁, y₁ ) and (x₂, y₂ ) is

m = \frac{y_{2-y_(1) } }{x_(2)-x_(1) } ← slope formula

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. Find the rate at which the area within the circle is increasing after each of the following.after 1 s = after 3 s = after 7 s =

Answers

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