List five vectors in Span (V₁ V₂). Do not make a sketch.
V₁ = (8 2 7 )
V₂ = (-6 4 0 )
List five vectors in Span (V₁ V₂).
(Use the matrix template in the math palette. Use a comma to separate vectors as needed. Type an integer or a simplified fraction for each vector element.)

The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line.

Write in slope intercept form

2y = 8x - 6

y = 8x/2 - 6/2

y = 4x - 3

Using the slope intercept, slope m is 3.

The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.

Slope of perpendicular line = -1 / ( 4 )

Slope of perpendicular line = -1/4

Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - 3 ) = (-1/4)( x - (-3) )

( y - 3 ) = (-1/4)( x + 3 )

y - 3 = (-1/4)x - 3/4

y = (-1/4)x - 3/4 + 3

y = (-1/4)x + 9/4

Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.

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Therefore ,option 3 is hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.

Any three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.

Here,

From the provided figure, it is clear that there are two triangles.

ABC and EFG are the triangles.

AB = EF

AC = FG

BC = EG

As a result, the triangles ABC and EFG are congruent according to the triangle's SSS theorem, and angle A is equal to angle D.

Therefore ,D and E are hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.

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The volume of the parallelopiped is 14 cubic units

The volume of a parallelopiped with vector sides a, b and c is given by

V = (a × b).c

Given that the parallelopiped has sides

So, we have that

(a × b) = (2, 1, 0) × (3, -1, 2) = (2 × 3)i × i + (2 × -1)i × j + (2 × 2)i × k + (1 × 3)j × i + (1 × -1)j × j + (1 × 2)j × k + (0 × 3)k × i + (0 × -1)k × j + (0 × 2)k × k

Since

So,

(a × b) = (2, 1, 0) × (3, -1, 2) = (6) × 0 + (-2)k + -(4)j + 3i + (-1) × 0 + (2)i + -(3)j + -(0)i + (0) × 0

= 0 -2k - 4j + 3i + 2i - 3j - 0 + 0

= 5i  -7j - 2k

= (5, -7, -2).

Since (a × b) = (5, -7, -2)

So, the volume of the parallelopiped is

V = (a × b).c

= (5, -7, -2).(4, 0, 3)

= 5 × 4 + (-7 × 0) + (-2 × 3)

= 20 - 0 - 6

= 14.

So, the volume is 14 cubic units.

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a. The exact volume, in cubic inches, of water flowing out of the pipe every second is 32π cubic inches.

b. The height, in inches, of the water in the tank after 5 minutes is 600 feet.

c. It will take 0.132 minutes to fill 75% of the tank

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, Water flows at 2 feet per second through a pipe with a diameter of 8 inches so it is a cylindrical shape.

Therefore, The exact volume, in cubic inches, of water flowing out of the pipe every second is,

= π(4)²×2.

= 32π cubic inches.

The volume of the cylindrical tank is,

= π(7.5)²×6.

= 337.5π cubic inches.

The height, in inches, of the water in the tank after 5 minutes would be

= (32π×300)/π×16).

= 600 feet.

Now, 75% of 337.5π cubic inches is (0.75×337.5π) = 253.125π cubic inches.

Therefore the time required to fill 75% of the tank is,

= [(253.125π/32π)]/60 minutes.

= 7.91/60 minutes.

= 0.132 minutes.

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The equation that represents the linear function is y = 11 + 7x.

What is the solution to the linear equation?

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

We have given the rules:

x: a number

y: 11 more than 7 times x.

Linear equations are the equations of degree 1. It is the equation for the straight line.

The standard form of the linear equation is ax+by+c =0,

where a ≠ 0 and b ≠ 0.

From the given conditions we can form the linear equation:

That is,

y = 11 + 7x,

Hence, the equation that represents the linear function is y = 11 + 7x.

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Answer:

is greater than

Step-by-step explanation:

7/8 is bigger than 2/4

The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .

Given equations ,

[tex]x^{2}[/tex] + 81 = 0  ,[tex]x^{2}[/tex]-22 = -26 , 3[tex]x^{2}[/tex]-18=21 ,2[tex]x^{2}[/tex] +15 = -13

What is Quadratic equation ?

quadratic equation can be defined as the equation which is in the form of a[tex]x^{2}[/tex]+bx + c = 0 .

where a,b,c are constants .

By solving we get ,

[tex]x^{2}[/tex] +81 = 0

[tex]x^{2}[/tex] = -81

x = 9i , -9i

[tex]x^{2}[/tex] - 22 = -26

[tex]x^{2}[/tex] = -26 + 22

[tex]x^{2}[/tex] = -4

x = 2i,-2i

3[tex]x^{2}[/tex] - 18 = 21

3[tex]x^{2}[/tex] = 18+21

3[tex]x^{2}[/tex] = 39

[tex]x^{2}[/tex] = 13

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex]

2[tex]x^{2}[/tex] +15 = -13

2[tex]x^{2}[/tex]  = -13-15

2[tex]x^{2}[/tex]  = -28

[tex]x^{2}[/tex]  = -14

x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i

Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .

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Answer: I say 13

Step-by-step explanation:

Answer:

The World Health Organization (WHO) defines health as 'a state of complete physical, mental and social wellbeing and not merely the absence of disease or infirmity'

On solving the provided question, we can say that - the range [tex]|x + 1| = 0[/tex] [tex]x + 1 = 0 = > x = -1[/tex] and [tex]y = 3[/tex]

Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

The regions where the absolute values are zero are known as the vertex points of an absolute value function.

[tex]|x + 1| = 0\\x + 1 = 0\\x = -1[/tex]

[tex]y = |-1 + 1| + 3\\y= 0 + 3\\y = 3[/tex]

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The perimeter of the rectangle is 19n + 7.

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

The perimeter of a rectangle is the sum of the whole sides of the rectangle.

Therefore, let's find the perimeter of the rectangle with width of 6n - 3.5 ft and length of 3.5n + 7 ft. Hence,

perimeter of a rectangle = 2(l + w)

where

Therefore,

w = 6n - 3.5

l = 3.5n + 7

Hence,

perimeter of a rectangle = 2(6n - 3.5 +  3.5n + 7)

perimeter of a rectangle = 2(6n + 3.5n - 3.5 + 7)

perimeter of a rectangle = 2(9.5n + 3.5)

perimeter of a rectangle = 19n + 7

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Answer:

To factor the first expression, "0.7 times square root of 300", we can rewrite it as:

0.7 * sqrt(300)

The prime factorization of 300 is 2 * 2 * 3 * 5 * 5, so we can rewrite the expression as:

0.7 * sqrt(2 * 2 * 3 * 5 * 5)

Since the square root of a number is the same as the square root of that number's prime factorization, we can rewrite the expression as:

0.7 * sqrt(2) * sqrt(2) * sqrt(3) * sqrt(5) * sqrt(5)

Combining like terms, we get:

0.7 * 2 * sqrt(2) * sqrt(3) * sqrt(5)

= 1.4 * sqrt(2) * sqrt(3) * sqrt(5)

This is the fully factored form of the expression "0.7 times square root of 300".

To factor the second expression, "-0.125 times square root of 192", we can rewrite it as:

-0.125 * sqrt(192)

The prime factorization of 192 is 2 * 2 * 2 * 2 * 2 * 2, so we can rewrite the expression as:

-0.125 * sqrt(2 * 2 * 2 * 2 * 2 * 2)

Since the square root of a number is the same as the square root of that number's prime factorization, we can rewrite the expression as:

-0.125 * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2)

Combining like terms, we get:

-0.125 * 6 * sqrt(2)

= -0.75 * sqrt(2)

This is the fully factored form of the expression "-0.125 times square root of 192".

Answer:

for the second one the answer is - square root of 3

Step-by-step explanation:

i could only solve the second one sorry

Step-by-step explanation:

minimum.

since the term with x² has a positive factor, this will grow exponentially in the positive direction compared to the other terms, so y (the functional value) will grow and grow with growing distance of x to the vertex.

and that makes the vertex the minimum of the parabola (which opens upwards).

if the factor would be negative (like -x² - 2x + 10), the vertex would be a maximum, and the parabola would open downwards.

The number of acorns that Frank have in the other hand will be 14.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.

Since Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand.

When Frank has 5 on one hand, the number of acorns that Frank have in the other hand will be:

= 10 + 9 - 5

= 14

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Complete question

Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand. Frank has 5 on one hand. How many acorns does frank have in the other hand

Answer:

it is not factorable

Step-by-step explanation:

There are no factors of 24 that will make -4, so it is not factorable

Step-by-step explanation:

first we need to identify the lines themselves.

the line from bottom left to top right is simply

y = x

the line is solid, so the points on the line are included.

the dotted line (the points on the line itself are not included) goes through

(0, 2) and (3, 0)

the y-intercept is therefore 2 (the y value when x = 0).

and for the slope

x changes by +3 (from 0 to 3).

y changes by -2 (from 2 to 0).

the slope is -2/+3 = -2/3

and the line is

y = (-2/3)x + 2

we see that the desired gray area is above both lines (">"), and we need to consider, whether the points in the lines are included or not.

so, the system of inequalities is

y >= x

y > (-2/3)x + 2

Answer: We know that the order from the doctor is 450mg

The stock available has a value of 150mg

Order/Available stock=450mg/150mg=3 tablets

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

1. Since you are told x=35. Plug it into x.

35-25

2. Simplify

35-25=5

Answer: 10

Step-by-step explanation:

x-25

substitute 35 for x

35-25 = 10

The length of x is 6 in simplest radical form.

'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'

According to the given ,

Perpendicular = 3

Hypotenuse = x

We know,

sin∅ = 3/x

∅ = 30°

⇒ sin30 = 3/x

⇒ 1/2 = 3/x  [ sin30 = /2  ]

⇒ x = 3 * 2

⇒ x= 6

Hypotenuse = 6

Applying Pythagoras theorem:

Hypotenuse² = Perpendicular² + Base²

6² = 3² + Base²

6² - 3² = Base²

Base² = 25

Base = √25

Base = 5

We can conclude the value of x to be 6.

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According to the given cosecant function the value of csc 0 is equal to 6/5.

The sine function has a reciprocal called the cosecant function. The cosecant function is the hypotenuse divided by the opposite side, just like the sine function is the opposite side divided by the hypotenuse. The hypotenuse and legs are terms for the two sides that are not at the right angle.

It is given that:

[tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]

According to trigonometric identity,

[tex]csc^2\ alpha - cot^2\alpha = 1\\csc^2\ 0 -\frac{11}{25} =1\\csc^2\ 0 = \frac{36}{25} \\csc\ 0= \frac{6}{5}[/tex]

Therefore the value of csc 0 is equal to 6/5.

Complete question;

Given that [tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]

find csc 0.

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The measurement of the hypotenuse is obtained as 9 units using the Pythagoras theorem.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

According to the graph -

The perpendicular measures 4 units.

The base measures 3 units.

To find the hypotenuse g apply the Pythagoras theorem -

(hypotenuse)^2=(base)^2+(perpendicular)^2

(g)^2=(3)^2+(4)^2

(g)^2=9+16

(g)^2=25

g=[tex]\sqrt{25}[/tex]

g=5

Therefore, line segment g measures 5 units.

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Answer:

( 7,-1 )

Step-by-step explanation:

The weight of the jar after solving equation simultaneously is w=0.

A set of two or more first-degree equations with two or more connected unknowns is known as a system of linear equations.

A system of equations is solved by determining the value of each unknown until the system's equations are all satisfied. That is, it is necessary to find the values of the unknowns so that, when substituted, they will produce the suggested solution in both equations.

j+w=1.5

2j+w=3

Simultaneously solving gives

w=0

the weight of jar is 0.

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The possible radius and height for Cone B are 3 units and 16 units respectively

The formula for calculating the volume of a cone is expressed mathematically;

Volume = 1/3 πr²h

Given that;

From the information given, we have that;

Now, let the height of cone B be 16 units

Substitute the value into the formula, we have;

48π = 1/ 3 × π × r² × 16

multiply the values, we have

48 = 16r²/3

cross multiply

16r² = 144

Divide both sides by 16

r² = 144/16

r² =9

Find the square root of both sides

r = 3units

Hence, the values are 3 units and 16 units

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The correct comparison between two function is

Both functions are increasing, but function g increases at a faster average rate.

The Correct option is (B).

If the slope of a function is continuously increasing or constant in an interval, the function is known as an increasing function.

Let us assume

f(x) = [tex]ab^x[/tex]+ c

so, at x=0, f(0)=-10

a +c = -10

Similarly, by satisfying the above table in the f(x)

f(x) = -33/5 [tex](1/11)^x[/tex] - 17/5

and, f'(x) > 0

Thus, f(x) is an increasing function.

Now, g(x) = -18 [tex](1/3)^x[/tex] +2

g'(x) = -18 [tex](1/3)^x[/tex] log(1/3)

as log 1/3 <0

So, g'(x) > 0

Thus, g(x) is an increasing function.

For any x ∈ f(x) and x ∈ g(x), g'(x) > f'(x).

Hence, Both functions are increasing, but function g increases at a faster average rate.

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The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation and is equal to 1/504.

Permutations refer to the arrangements of objects in certain order or way.

The number of alternative arrangements in a set can be calculated mathematically using a permutation where the order of the configurations is important.

The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation.

The probability is obtained as 1 / ₉P₃

where;

₉P₃ = 9! / (9 - 3)!

₉P₃ = 9! / 6!

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

6! = 6 * 5 * 4 * 3 * 2 * 1

₉P₃ = 504

Hence, the probability = 1/504

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Exact Circumference = 4pi feet

Approximate Circumference = 12.56 feet (when using pi = 3.14)

======================================================

Explanation:

The larger circle has a 3 foot radius.

The inner circle has a 3-1 = 2 foot radius.

Let's find the circumference of the smaller inner circle, which represents the glass window and ignores the metal frame surrounding it.

C = 2pi*r

C = 2pi*2

C = 4pi

The exact circumference is 4pi feet. This is the perimeter around the circle.

If you wanted, you can use an approximation like pi = 3.14 to find that 4pi = 4*3.14 = 12.56 feet is the approximate circumference.

Answer:

y = [tex]\frac{3}{4}[/tex]x + 3

Step-by-step explanation:

find the slope m

m = [tex]\frac{y2 - y1}{x2 - 21}[/tex]

m = [tex]\frac{3 - 0}{0 - - 4}[/tex]

m = [tex]\frac{3}{4}[/tex]

y = mx + b

find b

insert y1 and x1 into the equation

0 = [tex]\frac{3}{4}[/tex](-4) + b

0 = -3 + b

b = 3

y = [tex]\frac{3}{4}[/tex]x + 3

Answer:

y-4=-7/4(x+4)

Step-by-step explanation:

Point Slope Form: y-y*sub*1=m(x-x*sub*1)

Parallel lines have the same slope as the line to which they are parallel.

y-4=-7/4(x+4)

Hope this helps :)

The candy bar will each person get will be 4 / 15.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that three friends went to the movies. They shared 4/5 of a candy bar. If they share the bar equally.

The amount of candy shared by each person will be,

Amount = ( 4 / 5 ) ÷ 3

Amount = 4 / 15

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