When is it best to solve a system of equations using substitution?​

Answer: A right triangular prism is a 3-dimensional geometric shape that has a triangular base and three rectangular faces that connect the base to the top. A rectangular prism has three pairs of rectangular faces that are congruent, these faces are perpendicular to each other and connected by edges.

So, in a right triangular prism there are 3 rectangular faces which are the lateral faces (the one that connects the base and the top)

A triangular prism also has 3 triangular faces which are the base faces

So in total, a right triangular prism has 3 rectangular faces and 3 triangular faces.

Step-by-step explanation:

Answer:

m∠5+m∠6=180°

m∠2+m∠3=m∠6

m∠2+m∠3+m∠5=180°

Step-by-step explanation:

Verify each option

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

Therefore Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

Therefore this option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

Therefore this option is always true

case E) we have

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

This option is always true

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From the engineers formula given, making d the subject of the formula gives us; d = 300F/(11(F - 13))

We are given the engineers formula as;

F = (¹¹/₃₀₀)d(F - 13)

Where;

F is the strength of the steel in kilopound per square inch.

d is the diameter of the rocker in millimeters.

From the given formula, we can start by;

Multiply both sides by 300 to get;

300F = 11d(F - 13)

Divide both sides by 11(F - 13) to get;

d = 300F/(11(F - 13))

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Using the formula of midpoint of a line, the coordinate of the endpoint k is (-6, 31)

The midpoint of a line is the point that is halfway between the two end points of the line. It can be found by taking the average (mean) of the x-values and the average (mean) of the y-values of the two endpoints.

The formula of midpoint of a line is given as;

M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2

Since we have the midpoint and one endpoint, we can use the coordinate to find the missing coordinate.

The x - coordinate is calculated as;

-1 = (4 + x₁) / 2

-2  = 4 + x₁

x₁ = -2 - 4

x₁ = -6

The y - coordinates is calculated as;

8 = (-15 + y₁) / 2

16 = -15 + y₁

y₁ = 16 + 15

y₁ = 31

The coordinates of k is (-6, 31)

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Answer: 109 it says 109 in the corner of b and d

Answer: h=14

Step-by-step explanation:

If x=-18, then

h=17+(-18)/6

h=17+(-3)

h=17-3

h=14

Answer:

Step-by-step explanation:

so, the calculation was :  h = 17 + [tex]\frac{-18}{6\\}[/tex]

To subtract "[tex]\frac{-18}{6}[/tex] " we need to make it the same denominator  as "17"

(it's not written but technically 17 = [tex]\frac{17}{1}[/tex] )

Yet, we see that [tex]\frac{-18}{6} =\frac{-3* 6}{1*6}[/tex]

We just need to remove both the 6 that are not useful here and :

[tex]\frac{-3*6}{1*6} =\frac{-3}{1}= -3[/tex]

We obtain h = 17 - 3 = 14

hope it helped :)

Answer:

pretty sure it's B. Let me know if im wrong

Step-by-step explanation:

Answer:

Mean - 6.2  Median - 7  Mode - 9

Step-by-step explanation:

You can find the mean by adding all the given numbers and dividing them by how many numbers you added.

The median is the middle value of the set of numbers, order them from least to greatest and find the middle value.

Mode is the number that occurs the most.

The total number of units of energy produced in the two days is 71,402.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Monday:

Energy = 37,124

Tuesday:

Energy = 37,124 - 2846 = 34278

The total energy produced.

= 37124 + 34278

= 71402

Thus,

The total number of energy in two days is 71,402.

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Prime numbers of the form p and p+2, where p is a prime number, are known as twin prime numbers.

A twin prime is a prime number that is either 2 less or 2 more than another prime number. For example, the number 3 and 5 are twin primes, because they are both prime and the number 5 is 2 more than 3. Similarly, the number 5 and 7 are also twin primes, because they are both prime and the number 7 is 2 more than 5.

Therefore, Twin primes are considered as interesting numbers in number theory because of their relative rarity, rare in nature and because they are the building blocks for certain types of primes such as Sophie Germain primes and safe primes.

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Answer:

I can’t tell if both number are positive, ones negative ect but here’s the answer if both are negativ, let me know if the numbers are negative or positive and I can come back and give ya the right answer! Xoxo

Step-by-step explanation:

The number of seconds it takes ball to before hit the ground is 6 seconds.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Given that, a ball is thrown from the top row of seats in a stadium the function h(t)=-16t²+80t+96 gives the height, in feet, of the ball t seconds after it is thrown.

When ball hits the ground h=0

So, -16t²+80t+96=0

-16(t²-5t-6)=0

t²-5t-6=0

By using splitting middle term method, we get

t²-6t+1t-6=0

t(t-6)+1(t-6)=0

t-6=0 or t+1=0

t=6 or t=-1

Time can not be negative integer.

Therefore, the number of seconds it takes ball to before hit the ground is 6 seconds.

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The simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]

The given expression is [tex](a^0 b^-4 cde^3)^2[/tex]

We know that any number raised to the power of 0 is 1.

Therefore,[tex]a^0 = 1[/tex].

Also, any number raised to the power of -1 is its reciprocal.

Therefore, [tex]b^-4 = 1/b^4[/tex]

Simplifying the above expression we get

[tex](1*1/b^4 * cde^3)^2 = (cde^3/b^4)^2[/tex]

Now, we apply the rule that [tex](a^m * a^n) = a^(m+n)[/tex]

So, [tex](cde^3/b^4)^2 = c^2 d^2 e^6 / b^8)[/tex]

Hence the simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]

Please note, when an exponent is raised to another exponent, we can multiply the exponents, so [tex](a^m)^n = a^(m*n)[/tex]

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On solving the question, we can say that y using the given information we can prove that similar angle m ∠ABC = m ∠EDC.

Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.

Given:

m ∠1 = m ∠2

m ∠2 = m ∠4

We have to prove that m ∠ABC = m ∠EDC

∠EDC = ∠3 + ∠4

m ∠ABC = m ∠1 + m ∠2

m ∠EDC = m ∠3 + m ∠4

m ∠1 + m ∠2 = m ∠3 + m ∠4      

m ∠ABC = m ∠EDC

Hence, by using the given information we can prove that  

m ∠ABC = m ∠EDC.

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Answer:

$100 + $375 + $41(4) = $516

$516 - $425 = $91

$91 / $5 = 18.2 cars

Therefore, the four student government officers must wash 18 cars in order to have enough money to pay for the trip.

Answer:

Step-by-step explanation:

1. ( -2, 2), (-1, 5)

   (5 - 2)/(-1 + 2)= 3/1= 3

2. (-4, 2), (2, 0)

   (0 - 2)/(2 + 4) = -2/6 = -1/3

3. (0, 3), (5, 1)

(1 - 3)/(5 - 0)= -2/5

4. (0, 0), (1, 1)

  (1 - 0)/(1 - 0)= 1/1= 1

5. (3, 0), (3, 1)

(1 - 0)/(3 - 3) = 1/0 = undefined

6. (0, -1)  (1, -1)

   (-1 + 1)/(1 - 0)= 0/1 = 0

Answer: 24

Step-by-step explanation:

Given that m=5 and n=3, we can plug our values into the given expression to evaluate.

(5)(3)+9                  [multiply]

15+9                        [add]

24

The reason we multiplied before we added was due to the order of operations. Order of operations tells us to always multiply or divide first before we add or subtract. In this case, the multiplication happens to come first so we multiply, then add.

On solving the provided question, we can say that - by formula of simple interest we have SI = [tex]2200 X 2 X 4/100 = > 17600/100 = > 176[/tex]

Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. For instance, he will only pay his portion of the 100% interest if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you lend money, you must charge interest. Most of the time, interest is expressed as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

here

principal, p = 2200

rate, r = 2%

time, t = 4 rs,

so SI = P X R X T/100

SI -

[tex]2200 X 2 X 4/100\\17600/100\\176[/tex]

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The line y = - x has a coordinate value of (4, - 4) passing through the origin.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A line passes through the origin, (−1, 1) and (4, n).

So, The slope of the line is,

m = (1 - 0)/(- 1 - 0).

m = - 1.

Now,

1 = -1(-1) + b.

b = 0.

y = - x.

At x = 4,

y = - 4.

So, The point (4, n) is (4, - 4).

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Answer:

(2,4)

Step-by-step explanation:

The vertex of a parabola in the form of [tex]y=a(x-h)^2+k[/tex] is [tex](h,k)[/tex]. In this function, we have [tex](2,4)[/tex] as our vertex.

When we divide 26 by 3 we get 8 as a quotient and 2 as a remainder, the Mixed Fraction is [tex]8\frac{2}{3}[/tex]

A full number plus a legal fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for humans to comprehend numbers.

A full number and a legal fraction make up a mixed number. A mixed number like [tex]2\frac{x}{y}[/tex] is one where 1/4 is the correct fraction and 2 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.

Steps to convert Improper fraction to Mixed Fraction :

So when we divide 26 by 3 we get 8 as a quotient and 2 as a remainder so the Mixed Fraction is : [tex]8\frac{2}{3}[/tex]

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The data represented by the steam-leaf plot is 115, 138, 145, 145, 156, 166, 168, 168, 175, and 187.

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf.

9 I 0 ⇒ 9 on the stem and 0 on the leaf read as 90.

Given, A stem leaf plot and the leaf represents the tens digit.

As the leaf represents tens digits the data set can be represented by,

115, 145, 145, 175, 156, 166, 187, 138, 168, 168.

Representing the data set in ascending order we have,

115, 138, 145, 145, 156, 166, 168, 168, 175, 187.

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Considering the definition of a line, the linear function that represents the total cost when x tickets are ordered is c= 20.5x + 5.50.

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know:

Being Total cost= set price per ticket× amount of tickets + 5.50, then:

108=set price per ticket× 5 + 5.50

108 - 5.50= set price per ticket× 5

102.5= set price per ticket× 5

102.5÷5= set price per ticket

20.5= set price per ticket

Finally, the total cost is Total cost= 20.5× amount of tickets + 5.50.

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Answer:

Its letter A

Step-by-step explanation:

The equation of the linear function represented by the table in slope intercept form is y = -4x - 5.

What is slope-intercept form?

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

Given two points (x,y), the slope is the change in y divided by the change in x.

The points are (1,-9) and (3,-17) -

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

m = [-17-(-9)]/(3-1)

m = -8/2

m = -4

Then the slope equation will be -

y = -4x + b

Taking points (1,-9) and substituting in the equation to get the value of b -

-9 = -4(1) + b

-9 = -4 + b

-9 + 4 = b

b = -5

Therefore, the slope intercept form of equation is y = -4x - 5.

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A function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

A relation is a function if it has only One y-value for each x-value.

Given a a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45

and that g(0) = -2 and g(-9) = 6,

x=-20 then g(-20)=-5

x=-19 then g(-19)=-4

x=-18 then g(-18)=-3

x=-17 then g(-17)=-2

x=-16 then g(-16)=-1

x=-15 then g(-15)=0

x=0 then g(0)=-2

x=-9 then g(-9)=6

By observing this we can say that as x values are decreasing the function values are increasing and vice versa

So option D is correct

Hence, a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20

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Answer:

d7-dx=(20x|x-3|+40)x  x-3 (|x-3+2)x| x-3|

Step-by-step explanation:

Hope this helps :D

An equation of the line in slope-intercept form that is perpendicular to line g and passes through the point (1, −2) is y = 3x - 5.

Mathematically, the standard form of the equation of a straight line (slope-intercept form) is given by this mathematical expression;

y = mx + c

Where:

From the information provided, we have the following points on line g:

Point = (-3, 6)

Point = (0, 5)

Next, we would determine the slope of line g as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (5 - 6)/(0 - (-3))

Slope, m = -1/3

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-1/3 × m₂ = -1

m₂ = 3

At point (1, -2), an equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - (-2) = 3(x - 1)

y + 2 = 3x - 3

y = 3x - 3 - 2

y = 3x - 5

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The sum of the interior angle measures of the polygon is 900 degrees

From the image shown, we can see that the polygon has 7 sides.

A polygon with seven sides is called a heptagon

It is important to note that the number of triangles in a heptagon is 5.

Also, the sum of angles in a triangle is 180 degrees.

Now, the formula for calculating the sum of interior angles of a polygon is expressed as;

= (n - 2) 180

Where; n is the number of sides of the polygon

Substitute the value

= (7-2)180

Subtract the value

= 5(180)

= 900 degrees

Hence, the sum is 900 degrees

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