For the following systems of equations, match each diagram on the left with its solution on the right.

Answer:

x=5,y=-1

Step-by-step explanation:

5x– 2y = 27

-3x +2y=-17

Add the two equations together to eliminate y

5x– 2y = 27

-3x +2y=-17

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

2x  = 10

Divide by 2

2x/2 = 10/2

x = 5

Now find y

-3x +2y = -17

-3(5)+2y = -17

-15+2y =-17

Add 15 to each side

-15+15 +2y = -17+15

2y = -2

Divide by 2

2y/2 = -2/2

y =-1

Answer:

x = 8; y = 12.

Step-by-step explanation:

x + y = 20

x = -y + 20

3x + 4y = 72

3(-y + 20) + 4y = 72

-3y + 60 + 4y = 72

y = 12

x + 12 = 20

x = 8

Check your work!

3(8) + 4(12) = 72

24 + 48 = 72

72 = 72

Hope this helps!

Answer:

X=-12 and Y= 32

Step-by-step explanation:

x+y=20 -> 1

3x+4y=72 -> 2

Form 1,

[x+y=20]×4

4x+4y=60 ->3

Form 2,

3x+4y=72

4y= 72 -3x ->4

Sub (4) into (3)

4x+72-3x= 60

x = -12

Sub X=-12 into (1)

-12+y=20

y= 32

Hope this helps.

Answer:

288π

Step-by-step explanation:

V=4 /3πr^3 is the formula. We have the diameter, so the radius is half (6). We now have V=4 /3π(6)^3 = 4/3π216 = 288π.

Answer:   [tex]t_9=\dfrac{1}{2^8}[/tex]

Step-by-step explanation:

[tex]t_n=t_1\times r^{n-1}\\\\Given: t_1=1,\quad r=\dfrac{1}{2}\\\\\\t_9=1\times\bigg(\dfrac{1}{2}\bigg)^{9-1}\\\\\\.\quad =\large\boxed{\dfrac{1}{2^8}}[/tex]

Answer:

Step-by-step explanation:

Given the coordinates P(-2, -3). Q(2, - 6). R(6. - 3). S(2, 1), to determine the type of shape the quadrilateral is, we need to find the measure of the sides. To get the measure of each sides, we will take the distance between the adjacent coordinates using the formula to formula for calculating the distance between two points as shown;

D = √(x₂-x₁)²-(y₂-y₁)²

For the side PQ with the coordinate P(-2, -3). Q(2, - 6)

PQ = √(2-(-2))²-(-6-(-3))²

PQ = √(2+2)²-(-6+3)²

PQ = √4²-(-3)²

PQ = √16-9

PQ = √7

For the side QR with the coordinate Q(2, - 6) and R(6, -3)

QR = √(6-2))²-(-3-(-6))²

QR = √(4)²-(3)²

QR = √16-9

QR = √7

For the side RS with the coordinate R(6. - 3) and S(2, 1)

RS = √(2-6)²-(1-(-3))²

RS = √(-4)²-(1+3)²

RS = √16-(4)²

RS = √16-16

RS = 0

For the side PS with the coordinate P(-2, -3) and S(2, 1)

PS = √(2-(-2))²-(1-(-3))²

PS = √(4)²-(1+3)²

PS = √16-(4)²

PS = √16-16

PS = 0

For the quadrilateral to be a rectangle, then two of its sides must be equal and parallel to each other. A rectangle is a plane shape that has two of its adjacent sides equal and parallel to each other. Since two of he sides are equal i.e RS = PS and PQ = QR then the quadrilateral PQRS is a rectangle. Both rhombus and square has all of its sides equal thereby making them wrong.

from the above picture

2,3 = 1 quadrant

5,-6 = 4 quadrant

2,0 = on x axis

-5,2 = 2 quadrant

-2,-4 =3 quadrant

0,-2 = on y axis

Answer:

B. Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C.

Step-by-step explanation:

Translation and reflection are examples of methods of rigid transformation. Translation ensure that each point on a given figure is moved the same distance with respect to the reference plane. Reflection involves the flipping of a given figure across a given line.

From the question, both reflection and transformation would map the triangles into one another. Since the reference line contains AB, then the two triangles are congruent and would share a common side.

Thus, the triangle pairs that can be mapped into each other is that of option B.

Based on the information given, the triangle pairs that can be mapped to each other using both a translation and a reflection across the line containing AB will be A. Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A.

The triangle pair that can be mapped to each other using both translation and reflection across line containing AB is the first triangle pair.

The first figure consists of ΔXYZ and ΔABC that are a reflection of each other across the line AB and a translation.

Learn more about triangles on:

https://brainly.com/question/12261308

Answer:

b

Step-by-step explanation:

The answer is b because we are looking for opposites

The opposite of +x is -x

While the opposite of -3 is +3

with this, we can switch them around.

this gives us the inverse of 3-x

Answer:

1/4

Step-by-step explanation:

The slope of a graph is always the rate of change for every value of x, in this case, days. Since she is adding 1/4 of a mile to her run each day, this means that the slope of this linear relationship is 1/4.

She increases a full mile in 4 days, just a little note.

Step-by-step explanation:

Hi, there!!!!

The main purpose of developing si unit is to have standard unit of measurements and to bring uniformity in whole world in terms of measurements.

I hope it helps you...

Answer:

(-1, -2) last answer

Step-by-step explanation:

x = 1 is a vertical line

Answer:

(-1, -2)

Step-by-step explanation:

This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.

Answer:

1.26 * 10 ^6

Step-by-step explanation:

1260000

Scientific notation is of the form a* 10 ^b

where a is a number between 1 and less than 10

Move the decimal 6 places to the left

1.26 ( dropping the extra zeros)

b = +6 since we moved the decimal 6 places)

1.26 * 10 ^6

The number 1260000 in scientific notation is 1.26 x [tex]10^6[/tex].

We have,

1260000

Write the zeroes in powers of 10.

Write a number between 1 to 10 along with the power of 10.

Now,

126 x 10000

This can be written as,

126 x [tex]10^4[/tex]

Now,

126 can be written as 126/100 x 100.

i.e

1.26 x 100 or 1.26 x 10²

Now,

1.26 x 10² x [tex]10^4[/tex]

1.26 x [tex]10^{2 + 4}[/tex]

1.26 x [tex]10^6[/tex]

Thus,

The number 1260000 in scientific notation is 1.26 x [tex]10^6[/tex].

Learn more about scientific notation here:

https://brainly.com/question/18073768P

#SPJ6

Answer:

Option D. 6√5.

Step-by-step explanation:

Please see attached photo for details.

The value of x can be obtained by using pythagoras theory as illustrated below:

In triangle ΔABC:

x² = z² + 12².... (1)

In triangle ΔABD:

15² = x² + y²...... (2)

In triangle ΔACD:

y² = z² + 3²....(3)

Substitute the value of y² in equation 3 into equation 2. We have:

15² = x² + y²

15² = x² + z² + 3²... (4)

From equation:

x² = z² + 12²

Make z² the subject

z² = x² – 12²

Substitute the value of z² into equation 4. We have:

15² = x² + z² + 3²

15² = x² + x² – 12² + 3²

15² = 2x² – 12² + 3²

225 = 2x² – 144 + 9

Collect like terms

225 + 144 – 9 = 2x²

360 = 2x²

Divide both side by 2

360/2 = x²

180 = x²

Take the square root of both side

x = √180

Expressing in surd form, we have:

x = √(36 x 5)

x = √36 x √5

x = 6√5

Answer:  Exponential function

Step-by-step explanation:

A linear function is the form[tex]f(x)=mx+c[/tex] , where m is the constant rate of change of y with respect to x and c is the y-intercept.

An exponential growth function is in the form [tex]f(x)=A(1+r)^x[/tex], where r is the rate of growth (generally in percent) and A is initial value.

If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .

Hence it is an exponential equation.

Answer:

Sister is 70

Step-by-step explanation:

John is 39.

8 less than twice his age is

39*2-8 = 70

Answer:

70 years old.

Step-by-step explanation:

Since John's sister is 8 years younger than TWICE his age, we just need to multiply 39*2 which equals 78. Now we just need to subtract 8 which equals 70.

Hope this helps!! <3

Answer:

[tex]\boxed{d = 54 yards}[/tex]

Step-by-step explanation:

Formula for diagonal is as follows:

[tex]d = \sqrt{l^2+w^2}[/tex]

Where d is diagonal, l is length (50 yards) and w is width (20 yards)

[tex]d = \sqrt{(50)^2+(20)^2}[/tex]

[tex]d = \sqrt{2500+400}[/tex]

[tex]d = \sqrt{2900}[/tex]

d = 53.85 yards

d ≈ 54 yards

Answer:

[tex]\boxed{\mathrm{54 \: yards}}[/tex]

Step-by-step explanation:

The shape of the pool is a rectangle.

The diagonal of a rectangle can be found through a formula by using Pythagorean theorem.

[tex]d^2=l^2 +w^2[/tex]

[tex]d=diagonal\\l=length\\w=width[/tex]

The length is given 50 yards, and width is given 20 yards. Find the diagonal.

[tex]d^2 =50^2 +20^2[/tex]

[tex]d^2 =2500+400[/tex]

[tex]d^2 =2900[/tex]

[tex]d=\sqrt{2900}[/tex]

[tex]d \approx 53.851648[/tex]

[tex]d \approx 54[/tex]

Step-by-step explanation:

Let the other endpoint be (x,y)

Since, (1,6) is the midpoint between (9,1) and (x,y)

Therefore,

1=(9+x)/2

=> 2=9+x

=> x= -7

and,

6=(1+y)/2

=>12= 1+y

=> y=11

So, the other endpoint is ( -7, 11)

Answer:

Step-by-step explanation:

Let the coordinates of Endpoint 2 be

(x ,y)

The midpoint of the endpoints is given by

[tex](1,6) = ( \frac{9 + x}{2} , \frac{1 + y}{2} )[/tex]

Where x and y are coordinates of Endpoint 2

Comparing with the midpoint we have

[tex]1 = \frac{9 + x}{2} \\ 2 = 9 + x \\ \\ x = 2 - 9 \\ \\ x = - 7[/tex]

[tex]6 = \frac{1 + y}{2} \\ 12 = 1 + y \\ \\ y = 12 - 1 \\ \\ y = 11[/tex]

Therefore x = - 7 and y = 11

The coordinates of Endpoint 2 are

Hope this helps you

From top to bottom, the answers are

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

Explanation:

The first system of equations has each equation with the same slope 2, but different y intercepts. This indicates we have parallel lines. Parallel lines never cross, so there are no solutions. A solution is where the two lines cross.

The second system of equation has one solution where the two lines cross. This is because the slopes are different

The third system has infinitely many solutions. We have the same line graphed out twice. One line is directly on top of the other to yield infinitely many intersection points.

The fourth system is similar to the second system. Different slopes lead to exactly one solution. The y intercept doesn't affect the number of solutions (whether its 0, 1 or infinitely many)

For each equation shown, they are in the form y = mx+b with m as the slope and b as the y intercept.

Answer:

20

Step-by-step explanation:

Given that:

The study group n = 4

number of participants = 10

the sum of squares for the between-groups source of variation is  60

The objective is to determine the mean square  between groups in this study

The mean square  between groups in this study compares the means of the group with the  sum of squares for the between-groups source (i.e the grand mean)

For this analysis;

the degree of freedom = n-1

the degree of freedom = 4 - 1

the degree of freedom =  3

Thus; the mean square between groups = [tex]\dfrac{60}{3}[/tex]

the mean square between groups = 20

Answer:

59.0

Step-by-step explanation:

Given a right angled triangle, ∆XYZ, to know which trigonometric ratio formula to apply in finding the measure of angle X, note the following:

Opposite side to angle X = 6

Hypotenuse = 7

Therefore, we would apply the following trigonometric ratio formula to solve for m<X:

[tex] sin X = \frac{6}{7} [/tex]

[tex] sin X = 0.8571 [/tex]

[tex] X = sin^{-1}(0.8571) [/tex]

[tex] X = 58.99 [/tex]

[tex] m < X = 59.0 [/tex] (rounded to nearest tenth)

Answer:

Step-by-step explanation:

First we must know that the sum of all the exterior angle of all polygons is 360°.

Measure of each angle of a polygon = 360°/total sides of the polygon

Since a regular nonagon has 9 sides, the measure of each angle of a polygon is expressed as thus;

Measure of each angle of a polygon  = 360°/9

Measure of each angle of a polygon  = 40°

Hence the measure of an exterior angle x of a nonagon is 40°

Answer:

B in Edg

Step-by-step explanation:

Answer:  10 hours

Step-by-step explanation:

The 10hp pump takes x hours to empty the pool which means it gets [tex]\dfrac{1}{x}[/tex] of the job done in one hour.

The 6hp pump takes x+5 hours to empty the pool which means it gets [tex]\dfrac{1}{x+5}[/tex] of the job done in one hour.  

Together, they can get [tex]\dfrac{1}{x}+\dfrac{1}{x+5}[/tex] of the job done in one hour.

It is given that together they get the job done in 6 hours which means they get [tex]\dfrac{1}{6}[/tex] of the job done in one hour.

10 hp pump + 6 hp pump = Together

[tex]\dfrac{1}{x}\quad +\quad \dfrac{1}{x+5}\quad =\quad \dfrac{1}{6}[/tex]

Multiply by 6x(x+5) to eliminate the denominator:

[tex]\dfrac{1}{x}(6x)(x+5) +\dfrac{1}{x+5}(6x)(x+5) = \dfrac{1}{6}(6x)(x+5)[/tex]

Simplify and solve for x:

6(x + 5) + 6x = x(x + 5)

6x +  30 + 6x = x² + 5x

       12x + 30 = x² + 5x

                  0 = x² - 7x - 30

                  0 = (x - 10)(x + 3)

                  0 = x - 10         0 = x + 3

                  10 = x             -3 = x

Since the number of hours cannot be negative, disregard x = -3.

So, the only valid answer is x = 10.

Answer:

Step-by-step explanation:

First we have to find out area of the base

[tex]s = \frac{a + b + c}{2} [/tex]

[tex] = \frac{5 + 12 + 13}{2} [/tex]

[tex] = \frac{30}{2} [/tex]

[tex] = 15[/tex]

Area of base = [tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]

[tex] = \sqrt{15(15 - 5)(15 - 12)(15 - 13)} [/tex]

[tex] = \sqrt{15 \times 10 \times 3 \times 2} [/tex]

[tex] = \sqrt{5 \times 3 \times 5 \times 2 \times 3 \times 2} [/tex]

[tex] = 2 \times 3 \times 5[/tex]

[tex] = 30 \: {cm}^{2} [/tex]

Now, let's find the volume of triangular pyramid

[tex] = \frac{1}{3} \times a \times h[/tex]

[tex] = \frac{1}{3} \times 30 \times 12[/tex]

[tex] = 120 \: [/tex] cm³

Hope this helps..

best regards!!

Answer: is your  first option

Step-by-step explanation:

after going over all the available equations, your first option is the only one that had results that were much more reasonable than the others. hope it helps.

Answer: M^10

Step-by-step explanation:

since the base number is the same, just add up the exponents: 2+5+3=10

Answer:

Step-by-step explanation:

If its like M^2 x M^5 x M^3 (exponents)

then just add 2+5+3=10

so M^10

Its a rule when the bottom (M) is the same you add the exponents.

If its 2M x 5M x 3M then you multiply

2x5x3=30

so 30M

Hope this helps!

Answer:

b=-a

Step-by-step explanation:

Answer:

m∠D = 94°

Step-by-step explanation:

Quadrilateral ABCD is also called a cyclic quadrilateral or a quadrilateral that is inscribed in a circle.

Opposite angles in a cyclic Quadrilateral are supplementary, i.e the sum of two opposite angles in a Quadrilateral = 180°

m∠A + m∠C = 180°

m∠A = 74°

74° + m∠C = 180°

m∠C = 180° - 74°

m∠C = 106°

In a cyclic quadrilateral, the total sum of the angles outside the circle = 360°

i.e =

m∠AB + m∠BC + mDC + mAD = 360°

m∠DAB= ( m∠C) × 2

= 106° × 2 = 212°

m∠DAB = m∠AD + m∠AB

m∠AD = 79°

212° = 79° + m∠AB

m∠AB = 212° - 79°

= 133°

m∠ABC = m∠AB + m∠BC

m∠AB = 133°

m∠BC= 55°

m∠ABC = 133° + 55°

= 188°

We are asked to find m∠D

m∠D = 1/2m∠ABC

m∠ABC = 188°

m∠D = 1/2 × 188°

m∠D = 94°

Therefore, m∠D = 94°

Answer:  $26.70 per hour

Step-by-step explanation:

Regular hours consists of 8 hrs

Overtime hours is 12 - 8 = 4 hours

Regular pay at "x" per hour = 5(8)(x) = 40x

Overtime pay at "2x" per hour = 5(4)(2x) = 40x

                                                  Total pay = 80x

Total Pay = $2136 = 80x

                     [tex]\dfrac{\$2136}{80}=x[/tex]

                   $26.70 = x

Answer:

It is C

Step-by-step explanation:

42.60=43.00

587.70=588.00

27.99=28.00