Solve the formula for t.


V=6πrt+7πr^2


t=

The length of the rectangular garage will be 13 while the width will be 10.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

The perimeter of the rectangle = 2( length + width).

It is known that,

Area of rectangle = length × width.

130 = L× W

L = 130/W

The perimeter of the rectangle = 2( length + width).

46= 2( L+ W)

L + W = 23

130/W + W = 23

130 + W² = 23W

W² - 23W + 130 = 0

W² -13W - 10W + 130 = 0

W(W - 13) -10(W - 13) = 0

(W - 13)(W - 10) = 0

W = 13,10

For W = 13

L = 23 - 13 = 10

For W = 10

L = 23 - 10 = 13

Let's say the bigger dimension is the length and the smaller is the width.

Length = 13 and Width = 10

Hence "The length of the rectangular garage will be 13 while the width will be 10".

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Using the substitution the system of equations y + 4 = x and 10x + 2y + 16 is solved to be

Substitution involves replacing a value with it's equal

The given equation include

y + 4 = x

10x + 2y + 16

substituting x = y + 4 into 10x + 2y + 16

10x + 2y + 16

= 10(y + 4) + 2y + 16

= 10y + 40 + 2y + 16

collecting like terms

= 12y + 16

12y = -16

y = -16/12

y = -4/3

substituting y = -4/3 into x = y + 4

x = -4/3 + 4

x = 8/3

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Answer:

c, d, f

Step-by-step explanation:

acute angles are small and less then 90 degrees so we know if it’s wide it’s not acute it’s an obtuse angle

Angle a is a right angle because of the box it has which is 90 degrees

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Answer:

f, e, c, d

Step-by-step explanation:

Angles that are acute are less than 90 degrees only. Not over, not exactly 90, but only below.

F is an acute angle.

A is a right angle.

B is an obtuse angle.

C is an acute angle.

D is an acute angle.

E is an acute angle.

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Answer:

m = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the roots can be found using the discriminant

Δ = b² - 4ac

• if b² - 4ac > 0 then roots are real and irrational

• if b² - 4ac = 0 then the roots are real and equal

• if b² - 4ac < 0 then roots are not real

For

(m + 1)t² + 5 = - 6t ( add 6t to both sides )

(m + 1)t² + 6t + 5 = 0 ← in standard form

with a = m + 1 , b = 6 , c = 5

for the equation to have only one solution then

b² - 4ac = 0

6² - 4 × (m + 1) × 5 = 0

36 - 20(m + 1) = 0 ( subtract 36 from both sides )

- 20(m + 1) = - 36 ( divide both sides by - 20 )

m + 1 = [tex]\frac{-36}{-20}[/tex] = [tex]\frac{9}{5}[/tex] ( subtract 1 from both sides )

m = [tex]\frac{4}{5}[/tex]

To know if the equation of this line k(x) = 3x - 6 is true, you should determine its slope and then write the equation in slope-intercept form.

In Mathematics, the y-intercept of any graph generally occur at the point where the value of "x" is equal to zero (x = 0), which is -6 in this scenario.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Making slope (m) the subject of formula, we have the following:

Slope, m = (y - c)/x

Slope, m = (0 - (-6))/2

Slope, m = (0 + 6)/2

Slope, m = 6/2

Slope, m = 3.

For the equation of this line, we have the following:

y = mx + c

y = k(x) = 3x - 6 (True)

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Using the ratio of 2:5 to make the shade, we need 5.7L of red paint and 28.6L of yellow paint.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

We use the ratio formula while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.

This is basically a fraction that represents the number of times a quantity is greater or less than another.

To make the orange shade, we simply need to add them in ratio of 2:5. This has to be solved using the fraction and ratio.

2 + 5 = 7

(2/7) * 20 = 5.7 L

(5 / 7) * 40 = 28.6L

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Answer:

answer is 3.2

Step-by-step explanation:

Simplifying

8[4 + -1a] = 2a

[4 * 8 + -1a * 8] = 2a

[32 + -8a] = 2a

Solving

32 + -8a = 2a

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-2a' to each side of the equation.

32 + -8a + -2a = 2a + -2a

Combine like terms: -8a + -2a = -10a

32 + -10a = 2a + -2a

Combine like terms: 2a + -2a = 0

32 + -10a = 0

Add '-32' to each side of the equation.

32 + -32 + -10a = 0 + -32

Combine like terms: 32 + -32 = 0

0 + -10a = 0 + -32

-10a = 0 + -32

Combine like terms: 0 + -32 = -32

-10a = -32

Divide each side by '-10'.

a = 3.2

Simplifying

a = 3.2

Answer:

a = 3.2

Step-by-step explanation:

if the linear equation is: 8 (4-a)=2a the value of a would be 3.2 because

a = 16/5 which equals to 3 1/5 which is the same as 3.2

The measure of angle VUT is ∠VUT = 70°.

What are angles in a linear pair?

When two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to each other after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is always 180°. These angles are also referred to as supplementary angles.

In the given figure, ∠RVU and ∠UVT are in linear pair, so by using the property of angles in a linear pair, we can write

                ∠RVU + ∠UVT = 180°

                  120° + ∠UVT = 180°

                         ∠UVT = 60°

Now as we know the sum of all angles of a triangle is equal to 180°,

               ∠UVT + ∠VTU + ∠VUT = 180°.

                   60° + 50° + ∠VUT =180°

                       110° + ∠VUT = 180°

                        ∠VUT = 180° - 110°

                        ∠VUT = 70°

Hence, the measure of angle VUT is ∠VUT = 70°.

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Answer:

A.  56

Step-by-step explanation:

Let the three consecutive integers be:

Given:

Create an equation with the given information and solve for x:

[tex]\implies x+(x+1)+(x+2)=2x+30[/tex]

[tex]\implies 3x+3=2x+30[/tex]

[tex]\implies 3x+3-2x=2x+30-2x[/tex]

[tex]\implies x+3=30[/tex]

[tex]\implies x+3-3=30-3[/tex]

[tex]\implies x=27[/tex]

Therefore, the three consecutive integers are:

So the sum of the first and last integer is:

[tex]\implies 27+29=56[/tex]

Answer:

a) 56 --- (27, 28, 29)

Step-by-step explanation:

Forming the equation,

→ x + (x + 1) + (x + 2) = 2x + 30

Now the value of x will be,

→ x + (x + 1) + (x + 2) = 2x + 30

→ x + x + 1 + x + 2 = 2x + 30

→ 3x - 2x = 30 - 3

→ [ x = 27 ]

The last integer will be,

→ x + 2

→ 27 + 2 = 29

Sum of first and last integer is,

→ x + (x + 2)

→ 27 + (27 + 2)

→ 27 + 29 = 56

Hence, required answer is 56.

Answer:

Approximately 51.21 cm

Step-by-step explanation:

to find circumference we multiply the diameter by pi

16.3pi

51.21 cm

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Answer:

C = 51.182 cm

Step-by-step explanation:

The circumference is given by

C = pi * d  where d is the diameter

C = pi * 16.3

C = 16.3 pi

We can approximate pi by 3.14

C = 16.3 * 3.14

C = 51.182 cm

The given graph of the function f (x) = 4x² will be facing up , has a minimum and it's horizontally compressed.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The graph of the function f(x) = 4x² compares to its parent function

f(x) = x².

Now,

By graph we have;

Function f (x) = 4x² is facing up because it is positive function.

And, It has a minimum because any quadratic function that faces up will have a minimum.

Since, In the figure below, f(x)=4x² (red) has more slope, So it's condensed toward the y-axis.

Hence, if the coefficient is bigger than 1, then the function will be horizontally compressed.

Thus, It's horizontally compressed.

Therefore, The given graph of the function f (x) = 4x² will be facing up , has a minimum and it's horizontally compressed.

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Answer:

142 degrees

Step-by-step explanation:

we just add the 2 angles we know

74+68

142

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A. The signal of each coefficient is given by:

B. The coefficient closest to zero is of B.

C. The coefficient with the least value is of C.

The transformations are vertical stretch/compression of the absolute function.

Then the signal is defined as follows:

The coefficient closest to zero is for the biggest vertical compression, which is of B, for which the graph stretches horizontally and compresses vertically.

The least value is for the biggest reflected stretching, which is in item c, in which the curve has a larger vertical stretch than in item d.

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Answer:

simplify 8/6, and you get 4/3.

This is a coincidence, because this is a Pythagorean triple,

which means: opp = 4, adj = 3, hyp = 5

now, we can solve the rest easily

sin(0) = 4/5

cos(0) = 3/5

sec = 5/3 (opposite of cos)

The area of trapezium is 114.9 units.

What is trapezium?

trapezium could be a convex quadrilateral with specifically one combine of opposite sides parallel to every alternative. multiple star could be a two-dimensional form that seems as a table once drawn on a sheet of paper. In geometry, a quadrilateral is outlined as a polygonal shape with four sides and 4 vertices

Main body:

area of trapezium = (a+b) h/2

where a, b are parallel sides and h is height of trapezium.

according to question :

a= 6.8

h = 9.3

As we know tan a = x/y

tan 40° = 9.3 / y

y = 11.1 units

b = 6.8 +y

b = 6.8+ 11.1

b = 17.9

Put value of a , b , h in formula

area = (17.9 + 6.8) 9.3/2

hence ,area of trapezium is approx = 114.9 units

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Answer (with explanation):

1. Given

2. UY ≅ WY

3. Definition of Midpoint

4(statement). ∠UYX ≅ ∠VYW

4(reason). Side-Angle-Side SAS

5. Vertical Angle Theorem

in most proofs, (almost ALL the proofs) the first reason is always given.

you need given before you do anything.

on 2., the reason is Definition of Midpoint so you can tell it's UY is congruent to WY (uses the theorem)

on 3., it's the other way around and similar to 2. so the answer is definitely Definition of a Midpoint

on 4. statement and reason, you're side UY, angle Y, and side YX to prove that side VY, angle Y, and side YW are congruent. so, use the ∠UYX ≅ ∠VYW with the SAS

and on 5., you use vertical angles to say that ∠UYX reflects to ∠VYW so they are the same (aka congruent)

Answer:

[tex]\large\begin{array}{|l|l|}\cline{1-2}\sf Statement&\sf Reason\\\cline{1-2}1.\;\textsf{$Y$ is the midpoint of $UW$ and $VX$}&1.\;\sf Given\\\cline{1-2}2.\;UY \cong WY & 2.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}3.\;VY \cong XY&3.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}4.\;\angle UYX \cong \angle VYW&4.\; \sf Vertical\;Angle\;Theorem\\\cline{1-2}5.\; \triangle UYX \cong \triangle VYW &5.\;\sf Side-Angle-Side\;(SAS)\\\cline{1-2}\end{array}[/tex]

Step-by-step explanation:

Midpoint

The point that is halfway between the endpoints of the line segment.

Side-Angle-Side (SAS) Congruence Theorem

If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, the triangles are congruent.

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

[tex]\large\begin{array}{|l|l|}\cline{1-2}\sf Statement&\sf Reason\\\cline{1-2}1.\;\textsf{$Y$ is the midpoint of $UW$ and $VX$}&1.\;\sf Given\\\cline{1-2}2.\;UY \cong WY & 2.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}3.\;VY \cong XY&3.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}4.\;\angle UYX \cong \angle VYW&4.\; \sf Vertical\;Angle\;Theorem\\\cline{1-2}5.\; \triangle UYX \cong \triangle VYW &5.\;\sf Side-Angle-Side\;(SAS)\\\cline{1-2}\end{array}[/tex]

Answer:

-33

Step-by-step explanation:

just fill in the values

3-6^2

3-36

-33

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Answer:

-33

Step-by-step explanation:

a = 3; b = -6

a - b² = 3 - (-6)² = 3 - 36 = -33

Answer:

567

Step-by-step explanation:

when you multiply negative with negative the result is always positive.

when you multiply negative with positive the result is always negative.

thus, you have (-3)*21= -63

then

-63*9= 567

y = 6x  + 1 is the line of the equation which has a gradient of 6 and passes through the point (3, 19)

What is a gradient?

A straight line's steepness can be determined by looking at its gradient. A line's gradient does not have to be a whole integer and might be positive or negative. A line's gradient can either be uphill (positive value) or downward (negative value).

Here, we have

Equation of line

y = mx  + c

m = Slope of line = Gradient  = 6

= y = 6x + c

a line passes through (3, 19)

so, we find the value of c

= 19 = 6(3)  + c

= c = 1

Now, we put the value of c in the equation and we get

= y = 6x  + 1

Hence,y = 6x  + 1 is the line of the equation which has a gradient of 6 and passes through the point (3  19)

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Answer:

7650 rupees

Step-by-step explanation:

Use I = Pnr

Here P = Principal = 20000 rupees

n = time = 4.5 years

r = rate of interest = 8.5% = 8.5/100

The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

In a geometric sequence,

The third term is 100 and the eighth term is 3.125.

Now,

We know that;

The nth term of geometric sequence is,

⇒ [tex]T_{n} = a r^{n - 1}[/tex]

Hence, The third term is;

⇒ [tex]T_{3} = a r^{3 - 1} = 100[/tex]

⇒ [tex]a r^{2} = 100[/tex]   ..(i)

And, The eighth term is,

⇒ [tex]T_{8} = a r^{8 - 1} = 3.125[/tex]

⇒ [tex]a r^{7} = 3.125[/tex]   ..(ii)

Divide equation (ii) by (i), we get;

⇒ ar⁷ / ar² = 3.125/100

⇒ r⁷ / r² = 3125 / 100000

⇒ r⁷⁻² = 3125 / 100000

⇒ r⁵ = 3125 / 100000

⇒ r = 5/10

Thus, The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

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Answer:

focusing is your key to get this

Step-by-step explanation:

Answer:

y= -x+1

Step-by-step explanation:

The slope of a line that is perpendicular to a graph is equal to the negative reciprocal of the graph's slope.

slope = 1  negative reciprocal = - (1/1) = -1

Now, you have to find the y-intercept by using the given points (3,-2) and the slope that was found (-x)

y= -x+b

-2=-3+b

1=b

y= -x+1

The cosine and sine functions are presented as follows;

(a) cosine function is; f(x) = 5·cos((4/3)·x - (13·π/27)) + 2.5

(b) f(x) = -5·sin((4/3)·x - 530/3) + 2.5

A sine function is a periodic function used bases on the sine of an angle.

(a) The cosine function is f(x) = a·cos(b·x - c) + k

Where;

a = The amplitude

The amplitude = (Max - Min)/2

Therefore;

a = (7.5 - (-2.5))/2 = 5

f = b/(2·π)

c = The phase shift

k = The vertical shift

The minimum is at x = 200° = (200/360)·(2·π) = 10·π/9

The period = 270° = 3·π/2

Frequency, f = 2/(3·π)

b = 2·π·f = 2·π×2/(3·π) = 4/3

When the function is at the minimum point, θ = π

Therefore;

(4/3)×(10·π)/9 - c = π

c = 13·π/27

k = The minimum value + a

Therefore, k = -2.5 + 5 = 2.5

The cosine function is therefore;

f(x) = 5·cos((4/3)·x - (13·π/27)) + 2.5

(b) The negative sine function is found as follows;

f(x) = a·sin(b·x - c) + k

b = 4/3

k = 2.5

Minimum point sin((4/3)200 - c) = 180

((4/3)200 - c) = 180

c = 260/3

Using a negative sign function, we get;

((4/3)200 - c) = 90

c = 530/3

The equation is therefore;

f(x) = -5·sin((4/3)·x -530/3) + 2.5

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The Vertical opposite angles are ∠1 = 141° ; ∠2 = 39° ; ∠3 = 141° ; ∠4 =39°

The given angle cover the whole circle which will have 360°

∠1 + ∠2 +∠3 + ∠4 = 360°

∠1 + 39° +∠3 + ∠4 = 360°

Vertically Opposite angle:

Hence, ∠1  = ∠3 and ∠2 = ∠4. So  ∠4 = 39°

∠1 + 39° +∠3 + 39° = 360°

Let x be the ∠1 and ∠3;

x + 39° +x + 39° = 360°

2x = 360° - 78°

2x = 282°

x = 141°

Now, we know all the angles with respect to Vertical opposite Angles  .

∠1 = 141°

∠2 = 39°

∠3 = 141°

∠4 =39°

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Answer: x = 9/2

Step-by-step explanation:

Given

5(2x + 1) = 50 (divide both sides by 5)

2x + 1 = 10 (subtract 1 from both sides)

2x = 9 (divide both sides by 2)

x = 9/2

Step-by-step explanation:

Solve the inequality for x.

10x > 9(2x - 5) - 11

10x > 18x - 45 - 11

10x > 18x - 56

subtract 18x from both sides:

10x - 18x > 18x - 56 - 18x

-8x > - 56

divide both sides by -8 and remember to flip the sign:

-8x/-8 < - 56/-8

x < 7

This means that x can be any number below 7.

In set builder notation: (-∞ , 7).

Answer:

A) [tex]\frac{484}{7}[/tex]cm

B)[tex]44[/tex]in

C)[tex]\frac{880}{7}[/tex]mi

D)[tex]\frac{660}{7}[/tex]yd

Step-by-step explanation:

The formula for the circumference of a circle is:

[tex]C=2\pi r[/tex]

Within the problem it is stated to use [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex] so our equation will be:

[tex]C=2\frac{22}{7}r[/tex] which simplifies to  [tex]C=\frac{44r}{7}[/tex]

The variable [tex]r[/tex] in the equation for the circumference represents 'radius' which is half the diameter, for circle's A and C we are given a diameter. We can divide these numbers in half to get a radius. From there we plug in each radius to get circumference of each circle!

A)

[tex]\text{Diameter}=22\\\text{Radius {\it (r)}}=\frac{\textit{diameter}}{2}=\frac{22}{2}=11\\\text{Circumference}=\frac{44(11)}{7}=\frac{484}{7}[/tex]

B)

[tex]\text{Radius {\it (r)}}=7\\\text{Circumference}=\frac{44(7)}{7}=\frac{308}{7}=44[/tex]

C)

[tex]\text{Diameter}=40\\\text{Radius {\it (r)}}=\frac{\textit{diameter}}{2}=\frac{40}{2}=20\\\text{Circumference}=\frac{44(20)}{7}=\frac{880}{7}[/tex]

D)

[tex]\text{Radius {\it (r)}}=15\\\text{Circumference}=\frac{44(15)}{7}=\frac{660}{7}[/tex]

Remember to include units of measurement in your answers.

The student who can write more words per minute is Marcus because he writes at a speed of 1.3 words per second, that is, in one minute he writes 79.8 words while Rhys writes at a speed of 1.1 words per second and in one minute he writes 66.66 words.

To identify the speed at which students write we must divide the number of words the student writes in time (seconds) as shown below.

Marcus

Rhys

Using the information above, we need to multiply the number of words each student types per second by the number of seconds that equals one minute.

Rhys

Marcus

According to the information above, Marcus has a faster typing speed than Rhys because he types 79.8 words in one minute, while Rhys types 66.6 words in the same time.

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