Which of the following systems has equations that are dependent?

1. 2x + 2y = 6
4x + 4y = 4

2. 2x + 2y = 6
2x - 2y = 6

3. y = -x+3
y = -x-3

4. 2x+2y = 6
y = -x + 3

Answer:

a) x = 128 degrees

b) Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Step-by-step explanation:

Given:

attached diagram

ABC is a straight line

Solution:

a) Find x

ABC is a straight line

angle ABD = supplement of CBD = 180-CBD = 180-116 = 64 degrees.

x is the central angle of the arc APD

so angle ABD is the inscribed angle which equals half of the arc angle =>

angle ABD = x/2 = 64 degrees

Solve for x

x/2 = 64

x = 2*64

x = 128 degrees

b.

Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Quadrilaterals.

Basically we know that, the sum of opposite angles of a quadrilateral inscribed in a circle is always 180°.

so applying this law here, we get as,

2X + (3X-10) = 180°

=> 5X - 10° = 180°

=> 5X = 190°

=> X = 190°/5

=> X = 38°

thus the angle X= 38°.

Answer:

(5a^2-4)*(25a^4+20a^2+16)

Step-by-step explanation:

Answer:

Its B, (5a^2-4)(25a^4+20a^2+16)

Step-by-step explanation:

Edge 2020

Answer:

a= 4[tex]\sqrt{6}[/tex]

b= 8[tex]\sqrt{2}[/tex]

c= 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

45-45-90 triangle

x - x - [tex]\sqrt{2}[/tex]

30-60-90 triangle

x - 2x - x[tex]\sqrt{3}[/tex]

Answer:

25/18

Step-by-step explanation:

Additive inverse of a number X is the number which when is added to X =0

ex: additive inverse of 2 is -2 since 2 +(-2)=0

Multiplicative inverse of a number N is the number which when multiplied by N gives 1

ex: multiplicative inverse of 6/7 is 7/6

6/7*7/6=1

Ex of reciprocal is

5/9 & 9/5

7/6 & 6/7

Additive inverse of -5/6=5/6

Multiplicative inverse of 4/12 is 12/4

Reciprocal of 9/5 is 5/9

(5/6)*(12/4)*(5/9)=25/18

Answer:

(5/6)*(12/4)*(5/9)=25/18

Step-by-step explanation:

Answer:

1 & 3 only

Step-by-step explanation:

Answer:

A. 41

Step-by-step explanation:

5a - b² + 2c(a-b)

Put a = 2, b = -3, and c = 4.

5(2) - (-3)² + 2(4)(2-(-3))

Evaluate.

10 - 9 + 2(4)(2+3)

10 - 9 + 8(5)

10 - 9 + 40

1 + 40

= 41

Answer:

[tex]41[/tex]

Step-by-step explanation:

Given that,

[tex]a = 2 \\ b = - 3 \\ c = 4[/tex]

Let's solve now,

[tex]5a - {b}^{2} + 2c(a - b) \\ 5 \times 2 - ( { - 3}^{2} ) + 2 \times 4(2 - ( - 3)) \\ 10 - ( - 3 \times - 3) + 8(2 + 3) \\ 10 - 9 + 8 \times 5 \\ 10 - 9 + 40 \\ 1 + 40 \\ = 41[/tex]

Answer:

$0.56/lb

Step-by-step explanation:

Given

Cost of a chicken = $2.15 per pound

26 pound of a chicken = $41.34

Required

Calculate how much saved.

The first step is to calculate the unit price of a chicken when 26 pound of chicken was bought.

Unit Price = Price ÷ Weight

Unit Price = $41.34 ÷ 26lb

Unit Price = $1.59/lb

The next step is to calculate the difference between these two prices

Difference = |$1.59/lb - $2.15/lb|

Difference = |-$0.56/lb|

Difference = $0.56/lb

The calculated difference is the amount saved per pound of chicken when I bought 26 pound of chicken.

Answer:

Greater than the original = 2, 4

Less than the original = 5

Same as the original = 1, 3

Step-by-step explanation:

Let the original value be x.

1. A $30 increase followed by a $30 decrease.

New value [tex]=x+30-30=x[/tex], it is same as original value.

2. A 20% decrease followed by a 40% increase.

Afer 20% decrease.

New value [tex]=x-\dfrac{20}{100}x=x-0.2x=0.8x[/tex]

Afer 40% increase.

New value [tex]=0.8x+\dfrac{40}{100}(0.8x)=0.8x+0.32x=1.12x[/tex], it is greater than original value.

Similarly check the other values.

3. A 100% increase followed by a 50% decrease.

New value [tex]=x+\dfrac{100}{100}x-\dfrac{50}{100}(x+x)=x[/tex], it is same as original value.

4. A 75% increase followed by a 33% decrease

New value [tex]=x+\dfrac{75}{100}x-\dfrac{33}{100}(x+0.75x)=1.1725x[/tex], it is greater than the original value.

5. 55% decrease followed by a 25% increase

New value [tex]=x-\dfrac{55}{100}x+\dfrac{25}{100}(x-0.55x)=0.5625x[/tex], it is less than the original value.

Therefore, Greater than the original = 2, 4, Less than the original = 5, Same as the original = 1, 3 .

A 100% increase followed by a 50% decrease

A $30 increase followed by a $30 decrease

55% decrease followed by a 25% increase

A 20% decrease followed by a 40% increase

A 75% increase followed by a 33 1/3% decrease

Answer:

a) 8

b) 2 1/4 hours

c) 4 7/8 hours

d) 4 1/8 hours

Step-by-step explanation:

a) LCD to be used to solve this problem is calculated as the Lowest common denominator of the above mixed fractions.

We have 1 1/2 hours and 1 1/8 hours

The lowest common denominator is the denominator calculated by

Multiplying the two denominators together and dividing by the common factor of the two denominators

Hence , we have

2 × 8 = 16

The common factor of 2 and 8 = 2

LCD = 16/2 = 8

b) How long did Matt drive?

We are told that Matt drove twice as long as John

John drove for 1 1/8 hours

Hence, the number of hours that Matt drove for =2 × 1 1/8

= 2 × 9/8 = 9/4 hours = 2 1/4 hours

c) How long the Sam, John and Matt drive ?

We are told in the question that

Sam drove for 1 1/2 hours

John drove for 1 1/8 hours

Matt drove for 2 1/4 hours

We would sum up the number of hours that each of them drove.

1 1/2 + 1 1/8 + 2 1/4

The Lowest common multiple of denominators is 8

= (1 + 1 + 2)( 4 + 1 +2/8)

= 4(7/8)

= 4 7/8 hours

d) How many hours is left for Bob to drive

We are told that the entire journey = 9 hours

The number of hours Sam, John and Matt drove for has been calculated in question c as 4 7/8 hours

The number of hours Bob will drive for is calculated as

9 hours - 4 7/8 hours

= 4 1/8 hours

Answer:

Step-by-step explanation:

7 + 3i / 2 - 5i would be clearer if written as (7 + 3i) / (2 - 5i).  We must remove the symbol i from the denominator, and that can be accomplished by multiplying both 7 + 3i and 2 - 5i by the conjugate 2 + 5i:

(2 + 5i)(7 + 3i)

--------------------

     4 + 29

which simplifies to     14 + 6i + 35i - 15 over 33, or

-1 + 41i

------------

    33

The number of possible outcomes there could be at the end of their game is 6 outcomes

This is a permutation problem since it required arrangement

If Alex, Toby, and Samuel are playing a game together and at the end, they will make a classification with one of them in first  place, one of them in Second place and one of them in Third place, this can be done in 3! ways

Since n! = n(n-1)(n-2)!

Hence 3! = 3(3-1)(3-2)

3! = 3 * 2 * 1

3! = 6 ways

Hence the number of possible outcomes there could be at the end of their game is 6 outcomes

Learn more here: https://brainly.com/question/24115376

Answer:

B) 128.3 square yards

Step-by-step explanation:

A = (n/360 deg)(pi)r^2

where n = central angle of sector.

A = (75/360)(3.14159)(14 yd)^2

A = 128.3 yd^2

Answer:

B. 128.3 yards

Step-by-step explanation:

Area of a Sector Formula: A = ∅/360πr²

Simply plug in our variables:

A = 75/360(π)(14)²

A = 5π/24(196

A = 128.3

Answer:

The correct statements are:

1: mEFD = mEGD

3: mED = mFD

5: mFD = 120°

Step-by-step explanation:

Let's analyse each statement:

1: mEFD = mEGD

Let's find the value of the angle ECD, using the sum of the internal angles of a quadrilateral:

[tex]60 + 90 + 90 + mECD = 360[/tex]

[tex]mECD = 120\°[/tex]

The angle ECD is a central angle, related to the arc ED, so the arc ED also has 120°.

The angle EFD inscribes the arc ED, so we have:

[tex]mEFD = mED/2[/tex]

[tex]mEFD = 120/2 = 60\°[/tex]

So the angles mEFD and mEGD are equal. The statement is TRUE.

2. mEGD = mECD

This statement is FALSE, because mEGD = 60° and mECD = 120°

3. mED = mFD

If mED is 120° and mEF = mFD, we have:

[tex]mED + mEF + mFD = 360[/tex]

[tex]2*mFD = 360 - 120[/tex]

[tex]mFD = 120\°[/tex]

So the statement is TRUE, both arcs have 120°.

4. mEF = 60°

This statement is FALSE, because we calculated before that mEF = mFD = 120°

5. mFD = 120°

This statemente is TRUE, because we calculated before that mFD = 120°.

So the correct statements are 1, 3 and 5

The true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]

Start by calculating the measure of angle ECD.

We have:

[tex]\angle ECD = 2 * \angle EGD[/tex]

So, we have:

[tex]\angle ECD = 2 * 60[/tex]

[tex]\angle ECD = 120[/tex]

The above means that:

[tex]\overset{\huge\frown}{ED} = 120[/tex]

So, the measure of angle EFD is:

[tex]\angle EFD = 0.5 * \overset{\huge\frown}{ED}[/tex]

[tex]\angle EFD = 0.5 * 120[/tex]

[tex]\angle EFD = 60[/tex]

From the question, we have:

[tex]\angle EGD = 60[/tex]

So, it is true that:

[tex]\angle EFD =\angle EGD[/tex]

To calculate the measure of arc FD, we have:

[tex]\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} + \overset{\huge\frown}{EF} =360[/tex]

Lengths EF and DE are congruent.

So, we have:

[tex]2\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} =360[/tex]

[tex]\overset{\huge\frown}{DE} = \overset{\huge\frown}{ED} = 120[/tex]

So, we have:

[tex]2\overset{\huge\frown}{FD} + 120 =360[/tex]

Divide through by 2

[tex]\overset{\huge\frown}{FD} + 60 =180[/tex]

Subtract 60 from both sides

[tex]\overset{\huge\frown}{FD} =120[/tex]

This means that:

[tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex] are true

Hence, the true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]

Read more about cyclic theorems at:

https://brainly.com/question/26168678

Answer:

Step-by-step explanation:

x=✓64*36=✓8^2*6^2

x=8*6

x=48

Answer:

x = 3

Inverse matrix:

[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\ \frac{1}{3} & -\frac{1}{3} \end{pmatrix} \quad[/tex]

Step-by-step explanation:

Determinant: ad - bc

a = 3, b = 2, c = 3, d = -1

3 * (-1) - (2 * x) = -9

-3 - 2x = -9

-2x = -6

x = 3

For matrix

[tex]A = \begin{pmatrix}a & b\\c & d\end{pmatrix} \quad[/tex]

the inverse is

[tex]A^{-1} = \dfrac{1}{ad - bc}\begin{pmatrix}d & -b \\-c & a\end{pmatrix}\quad[/tex]

Here we have: det = -9

a = 3, b = 2, c = 3, d = -1

Inverse matrix:

[tex]A^{-1} = \dfrac{1}{-9}\begin{pmatrix} -1 & -2 \\ -3 & 3 \end{pmatrix}\quad[/tex]

[tex]A^{-1} = \begin{pmatrix} \frac{-1}{-9} & \frac{-2}{-9} \\\frac{-3}{-9} & \frac{3}{-9}\end{pmatrix} \quad[/tex]

[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\\frac{1}{3} & -\frac{1}{3}\end{pmatrix}\quad[/tex]

Answer:

125.6 cubed inches

Step-by-step explanation:

1. 3.14(2)^2(10) - Multiply 3.14 with 2 squared and 10.

2. First find out what is 2 squared, which is 4. Then, multiply 4 with 3.14, which is 12.56.

3. Now, multiply 12.56 with 10 or just move the decimal point one place to the right, which gives you 125.6 cubed inches.

Answer:

A

Step-by-step explanation:

The zeroes of the function are the x values when f(x) = 0 so we can write:

0 = x² + x - 30

0 = (x + 6)(x - 5) (To factor this we need to find 2 numbers that have a sum of 1 and a product of -30; these numbers are 6 and -5)

x + 6 = 0 or x - 5 = 0 (Use Zero Product Property)

x = -6, 5

Hey there! :)

Answer:

A. x = -6 and x = 5.

Step-by-step explanation:

Given:

f(x) = x² + x - 30

Factor the equation by finding two numbers that sum up to 1 and multiply into -30. We get:

-5, 6

Use these to express this quadratic function in factored form:

f(x) = (x - 5) (x + 6)

Set each factor equal to 0 to solve for the zeros of the equation:

0 = x - 5

x = 5

-------------

0 = x + 6

x = -6

Therefore, the correct answer is A. x = -6 and x = 5.

Answer:

the equation of the line in slope-intercept form is;

[tex]y=8x-26[/tex]

Step-by-step explanation:

First use the formula for the slope of the segment that joins the two given points:

[tex]slope=\frac{y_2-y_1}{x_2-x_1} =\frac{6-(-2)}{4-3}=\frac{8}{1} =8[/tex]

now that we have the slope, we can use the point-slope form of a line to find the line with slope 8 that passes through any of the given points, for example through (3, -2):

[tex]y-y_0=m\,(x-x_0)\\y-(-2)=8\,(x-3)\\y+2=8\,(x-3)\\y=8x-24-2\\y=8x-26[/tex]

Answer:

True.

Step-by-step explanation:

The function is indeed a polynomial. We have the single variable [tex]x[/tex] plus a constant [tex]\pi[/tex] (it's irrational, but it's still simply just a constant number). This fits the definition of polynomials.

Answer:

41°

Step-by-step explanation:

First note that m arc BC = m∠BZC

The reason is because a central angle of a circle is always congruent to its

intercepted arc.

Also m∠BAC is one-half m arc BC, as the measure of an inscribed angle is half the measure of its intercepted arc.

Hence, the calculation is given below:

m∠BZC = 82°

m arc BC = m∠BZC

m arc BC = 82°

m∠BAC = 1/2 × 82°

m∠BAC = 41°

It is important to note that

∠DCA ≅ ∠BAC because alternate interior angles are congruent.

So m∠DCA = m∠BAC.

Therefore, m∠DCA = 41°.

Answer:

Option A) Speed = 1/20 of an inch per minute

Step-by-step explanation:

Given:

Distance = 6 inches

Time = 120 mins

Required:

Average Speed = ?

Formula:

Average Speed = Total Distance Covered / Total Time Taken

Solution:

Speed = 6/120

Speed = 1/20 of an inch per minute

Answer:

[tex]\frac{1}{20}[/tex] of an Inch per minute

Step-by-step explanation:

Speed = Distance ÷ Time

So....

6 ÷ 120 = 0.05 or [tex]\frac{1}{20}[/tex]

Also by process of elimination

[tex]\frac{1}{2}[/tex] of an inch per min would complete 6 inches in 12 min.

2 inches per min would complete 6 inches in 3 min

20 inches per minute would complete 6 inches in a few seconds.

Answer:

As x increases, the rate of change of f(x) exceeds the rate of change of g(x).

Step-by-step explanation:

Hope this helps :)

Answer:

radius

Step-by-step explanation:

That "fixed distance" is the 'radius' of the circle.

Answer:

C

Step-by-step explanation:

It is an iscoceles triangle because there are 180 degrees in a triangle and the right angle plus the 45 degree equals 135 and 180 minus 135 is 45.

Since it is an iscoceles triangle that means that n = 3 and the pythagorean theorom says that a^2 + b^2 = c^2 which means that m = 3^2 plus 3^2 with a root.

3^2 is 9 so you get 18

the root of 18 is infinite, however can be simplified to 3 root to 2 because 3 times 3 equals 9 times 2 equals a root of 18

Hope this helps!

Answer:

the amount of fuel consumed every 100 kilometers is 62.5 litres.

Step-by-step explanation:

To determine the amount of fuel consumed every 100 kilometers.

Note: since the graph is a straight line graph (linear graph) the amount of fuel consumed every 100 kilometers is constant (i.e the same for every 100 kilometers). So, we only need to derive the amount of fuel consumed any 100 kilometers on the graph.

From the graph, the amount of fuel consumed for the first 100 kilometers is;

[tex]F = F_0 - F_{100} .........................1[/tex]

[tex]F_0 = 500\\F_{100} \simeq 437.5\\[/tex]

substituting into equation 1.

[tex]F = F_0 - F_{100} \\F = 500 - 437.5\\ F = 62.5 litres\\[/tex]

Therefore, the amount of fuel consumed every 100 kilometers is 62.5 litres.

Answer:500

Step-by-step explanation:got it on Kahn

Answer:

20 units

Step-by-step explanation:

The perimeter of a rectangle is

P = 2(l+w)

P = 2( 3x+2 + 4x)

Adding like terms

P = 2( 7x+2)

We know the perimeter is 74 units

74 = 2 ( 7x+2)

Divide by 2

74/2 = 2/2 (7x+2)

37 = 7x+2

Subtract 2 from each side

37-2 = 7x+2-2

35 = 7x

Divide by 7

35/7 = 7x/7

5 =x

We want to find the length RS = PQ = 4x

RS = 4x = 4*5 = 20

Answer:

[tex]m = 5 \sqrt{3}[/tex]

[tex]n = 5[/tex]

Step-by-step explanation:

Given

The triangle above

Required

Find the missing lengths

The missing lengths can be calculated by applying trigonometry ratios

From the triangle above,

the Hypotenuse is 10

Angle = 60

Calculating m

The relationship between m, the Hypotenuse and angle 60 is defined as follows;

[tex]sin \theta = \frac{Opp}{Hyp}[/tex]

Where [tex]\theta = 60[/tex]

[tex]Opp = m[/tex]

[tex]Hyp = 10[/tex]

The above formula becomes

[tex]sin60= \frac{m}{10}[/tex]

Multiply both sides by 10

[tex]10 * sin60= \frac{m}{10} * 10[/tex]

[tex]10 * sin60= m[/tex]

In radical from, [tex]sin60 = \frac{\sqrt{3}}{2}[/tex]

[tex]10 * sin60= m[/tex] becomes

[tex]10 * \frac{\sqrt{3}}{2}= m[/tex]

[tex]\frac{10* \sqrt{3}}{2}= m[/tex]

[tex]5 \sqrt{3}= m[/tex]

[tex]m = 5 \sqrt{3}[/tex]

Calculating n

The relationship between n, the Hypotenuse and angle 60 is defined as follows;

[tex]cos\theta = \frac{Adj}{Hyp}[/tex]

Where [tex]\theta = 60[/tex]

[tex]Adj = n[/tex]

[tex]Hyp = 10[/tex]

The above formula becomes

[tex]cos60= \frac{n}{10}[/tex]

Multiply both sides by 10

[tex]10 * cos60= \frac{n}{10} * 10[/tex]

[tex]10 * cos60= n[/tex]

In radical from, [tex]cos60= \frac{1}{2}[/tex]

[tex]10 * cos60= n[/tex] becomes

[tex]10 * \frac{1}{2}= n[/tex]

[tex]\frac{10*1}{2}= n[/tex]

[tex]5 = n[/tex]

[tex]n = 5[/tex]

Answer:

Step-by-step explanation:

5. cut the five fruits into 3 equal parts....

5x3=15 pieces

15/3(bowls)=5 pieces in each bowl

cut the fruits in multiples of 5 divisible by 3....that many ways possible

(similarly 4th qstion can be done)!!

Answer:

6 Units squared.

Look at file for explanation.