1) Eliminate one of the variable terms on one side of each multi-step equation: Multi-Step Equation 7a-6=7+ 2a 11 - 3b = 3b + 4 -2b-5=6 - 5b Equivalent Two-Step Equation​

The equation has 2 irrational roots and two real distinct solutions.

It is a solution to an equation that occurs only once and differs in value from other solutions.  If the discriminant is zero, there are no real solutions. The discriminant equation is Δ = b² - 4ac. If the discriminant is greater than zero it has two irrational roots. Another alternative for a distinct solution is the coincident solution. The values of the discriminant show how many roots and solutions the equation may contain.

Given, 2x² - 6x - 15 = - 7

The discriminant of the equation is D = b² - 4ac

Here, a = 2, b = - 6, c = - 15

D= 36 - 4(2)(-15)

36 + 120 = 156

Here, D > 0 and it is not a perfect square.

So, the equation has 2 irrational roots.

And the equation has two real distinct solutions.

To know more about distinct real solutions, visit:

https://brainly.com/question/20651207

#SPJ1

Equation of a line in slope-intercept form:

m is the slope

b is the y-intercept

As you have the slope (m= -4) and a point (6,1) you use it in the equation above to find the y-intercept, as follow:

(6,1) x=6 y=1

m= -4

Solve b:

A tile pattern is represented by the equation "y = 6x + 4".



A) what does the six represent in the pattern

B) what does the four represent in the pattern

C) how many times will there be in the 75th figure.​

_______________________

if x represents the figure number and y represents the number of tiles.

A) what does the six represent in the pattern

The six represent

B) what does the four represent in the pattern

C) how many times will there be in the 75th figure.​

Answer:

85

Step-by-step explanation:

There is a property of angle of triangles.

Exterior angle = Sum of opposite interior angles

7x + 8 = 3x - 9 + 61

7x + 8 = 3x + 52

7x - 3x = 52 - 8

4x = 44

x = 44/4

x = 11

m∠WHG = 7x + 8

               = 7 ( 11 ) + 8

               = 77 + 8

m∠WHG = 85

Answer:

Angle WHG is 85 degrees.

Step-by-step explanation:

X = 11.

7(11) + 8 = 85.

180 - 85 = 95 (Angle FHG.)
3(11) - 9 = 24 (Angle GFH.)
A triangle's angles always add up to 180 degrees.

24 + 95 + 61 = 180.
To double check, 180 - 95 = 85 degrees.

I hope this helped! And as for finding X, I kind of forgot how to get X, so I tried X being number 5-10 first, then tried 11, and it worked. Sorry for the late response.

Given: The weights of Water melon displayed using a histogram as shown in the figure

To Determine: The weight of the fourth bin

From the histogram, it can be seen that the x-axis represents the weight of the watermelons, while the y-axis represents the quantity

It can observed that the fourth been has 4 watermelons as shown below:

From the above, 4 watermelons marked with red circle on the y-axis, and their weights marked red on the x-axis

Hence, the weight of 4 watermelons is at least 12pounds but no more than 16pounds, the second option

A biscetor is a line that curs another one exactrly at its midpoint. If the diagonals of the paallelogram bisect each other, this means that both cut the other in exact halves.

For example

For the square ABCD, its diagonals BD and AC cut each other in point M.

M is their midpoint, which means that the haves of each diagonal are the same:

For diagonal AC you get that AM=MC

For diagonal BD you get that BM=MD

This means that the diagonals bisect each other and have the same midpoint M

the total cost is:

$50.72

Answer:

∠ A = 34°

Step-by-step explanation:

complementary angles sum to 90° , then

5x - 11 + 6x + 2 = 90

11x - 9 = 90 ( add 9 to both sides )

11x = 99 ( divide both sides by 11 )

x = 9

Then

∠ A = 5x - 11 = 5(9) - 11 = 45 - 11 = 34°

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{2}}} \implies \cfrac{ -5 }{ 5 } \implies - 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- 1}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-x+2\implies {\Large \begin{array}{llll} y=-x+6 \end{array}}[/tex]

Answer:

$64.00

Step-by-step explanation:

The speed of the plane in still air is 87 kilometers, and the speed of the wind is 87 kilometers.

A plane traveled 1160 kilometers to Havana and back.

The trip there was with the wind. It took 10 hours.

The trip back was into the wind. The trip back took 20 hours.

What is speed, distance, and time?

The formula speed distance time is used to explain the relationship between speed, distance, and time. That is speed = time/distance. To put it another way, distance divided by speed equals time. You can figure out the third input if you know the first two.

Consider,

s = plane speed in still air

w = speed of the wind

then

(s+w) = ground speed with the wind

and

(s-w) = ground speed against the wind:

A dist equation for each way (dist = speed * time)

10(s+w) = 1160

20(s-w) = 1160

Simplify divide the 1st equation by 13, and the 2nd equation by 26, and you have:

s + w = 116

s - w = 58

Using adding s & eliminates w,

2s = 174

s = 174/2

s = 87 km plane speed in still air

The wind speed

87 + w = 96

w = 9 km is the wind speed

Hence, the speed of the plane in still air is 87 kilometers, and the speed of the wind is 87 kilometers.

To learn more about speed, distance, and time visit:

https://brainly.com/question/26046491

#SPJ1

The equation of the line passes through the x intercept of 2x - 3y = 6 and parallel to x + 4y = -3 is  y = (-1/4)x + 3/4   .

In the question ,

it is given that ,

the required line is parallel to x + 4y = -3 ,

x + 4y = -3

4y = -x -3

dividing both sides by 4 , we get

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

the slope is -1/4 .

the required line passes through the x intercept of 2x - 3y = 6  .

for x intercept , put y=0 ,

we get

2x -3(0) = 6

2x = 6

x = 6/2

x = 3

the point is (3,0) .

The equation of the line passing through the point (3,0) and the slope -1/4 is

(y-0) = (-1/4)(x-3)

y = -1/4(x - 3)

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

Therefore , the equation of the line passes through the x intercept of 2x - 3y = 6 and parallel to x + 4y = -3 is  y = (-1/4)x + 3/4   .

The given question is incomplete , the complete question is

What is the equation of the line passes through the x intercept of 2x - 3y = 6 and parallel to x + 4y = -3 ?

Learn more about Equations here

https://brainly.com/question/28822230

#SPJ1

1. The table of values showing the amount Kevin owes his friend after t weeks is as follows:

Week    Amount Owed

0               $90

 1               $85

2               $80

3               $75

4               $70

...

18              $0 ($5 - $5)

2. The equation representing the amount (L) Kelvin owes his friend after t weeks is L = 90 - 5t.

An equation is a mathematical statement showing that two mathematical expressions using the equation symbol (=) are equal or equivalent.

Equations establish the numerical relationship existing between two or more mathematical expressions, numbers, values, or variables.

Week    Amount Owed

0               $90

 1               $85 ($90 - $5)

2               $80 ($85 - $5)

3               $75 ($80 - $5)

4               $70 ($75 - $5)

The total amount borrowed = $90

The amount of repayment = $5

The repayment period = weekly

Let the balance after t weeks of payment = L

L = 90 - 5t

In eighteen weeks, Kevin will complete the repayment of the loan.

Check:

If t = 18

L = 90 - 5t

L = 90 - 5(18)

L = 90 - 90

L = 0

Learn more about equations at https://brainly.com/question/2972832

#SPJ1

Answer:

1/4

Step-by-step explanation:

Answer:

1/4 barrel of root beer

Step-by-step explanation:

4 pounds of sassafras = 1 barrel of root beer

algebraically, this is 4s = 1r

divide both sides by 4

1s = 1/4r

so 1 pound of sassafra can make 1/4 barrel of root beer

The equation for a straight line is given by

where m is the slope and b is the intercept.

The formula to calculate m is,

Now the value of b can be calculated as, y intercept which here is, 10

Therefore, the required equation is, y=3x+10

so if you want money and I give you 6dollers and remaining 4$it is 1. 1/4

Given:

To solve for j :

Explanation:

Multiplying by 2 on both sides,

Adding 38 on both sides, we get

Final answer:

The value of j is 6.

Answer:

Step-by-step explanation:

(3.00 - 2.40)/2.40  = p/100;

Then. 0.60/2.40 = p/100;

1/40 = p/100;

p = 100/40;

p = 2.5;

The percentage increase was 2.5%;

The solution for the equation would be (-4,-16) as the definition of solution of equation says "A number that can be entered for the variable to produce a true number statement is the solution to an equation".

A number that can be entered for the variable to produce a true number statement is the solution to an equation. One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side. Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the given equations on a graph and locate the point(s) where they all intersect to solve a system by graphing. You can find the values of the variables you are solving for by finding the coordinate of this point.

The equation is,

y=4x

x+y=-20

x+4x=-20

5x=-20

x=-4

y=-4*4

y=-16

(x,y)=(-4,-16)

According to the definition of solution of equation, "A number that can be entered for the variable to produce a true number statement is the solution to an equation," the answer to the equation would be (-4,-16).

To know more about equation,

https://brainly.com/question/10413253?referrer=searchResults

#SPJ1

Answer:

[tex]98533 \frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{2956}{0.03}=\frac{295600}{3}=98533 \frac{1}{3}[/tex]

Answer:

the equation of life is 9/3 plus 875 div by 34 when the sun is blue.

Step-by-step explanation:

your welcome

Question:

Solution:

The diagram of a triangle ABC, where C is the right angle is:

Now, by definition and according to the data of the problem, we get that:

that is:

now, to find the cos(B), first, we must find the missing side of the triangle. To do that, we can apply the Pythagorean theorem:

now, with respect to angle B, we obtain that:

So that, we can conclude that the correct answer is:

Five times as large= multply by 5

As large as five times

Then

X =5x 3x6 =

X = 90

The area of a rectangle is the product of its length and breadth. The maximum area enclosed by the fence is 36800 square meter  and the dimensions of the enclosed area are 115 meter and 320 meter. The width is given as 115 meter.

A rectangle is a type of parallelogram that has equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

The dimensions of the given rectangle are (650 - 2x) and x.

Then, the area of the given rectangle can be written in terms of x as

A(x)  = x(650 - 2x)

In order to find the maximum area enclosed take the derivative of A(x) and equate it to zero as follows,

(660 - 2x) - 2x = 0

=> 4x = 660

=> x = 660 / 4

=> x = 115

Now, the maximum area is the value of A(x) at x = 115 as below,

= 115 × (650 - 2×115)

= 115 × 320

= 36800

The dimensions for the maximum area are 115 and (650 - 2 × 115) = 320.

Hence, the largest area enclosed is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter. The width is given as 115 meter.

To know more about rectangle click on,

https://brainly.com/question/25501702

#SPJ1

Step-by-step explanation:

What is the slope of the line passing through the points (0, - 5) and (4, 2)?

slope = change in rise/change in run

OR:

slope = change in y/change in x

your point format is: (x , y)

SO:

slope = (-5 - 2) / (0 - 4)

slope = -7/-4

slope = 7/4

Answer:

[tex]\sf \dfrac{7}{4}[/tex]

Step-by-step explanation:

       (0 , -5)  ⇒ x₁ = 0 & y₁ = -5

       ( 4 ,2)   ⇒ x₂ = 4  & y₂ = 2

[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}\\\\[/tex]

           [tex]\sf = \dfrac{2-[-5]}{4-0}\\\\\\\=\dfrac{2+5}{4}\\\\\\=\dfrac{7}{4}[/tex]

The perimeter of JKF is 28 cm.

What is perimeter?

The perimeter of a triangle is the distance around it, which is the sum of the lengths of its sides. The formula for the perimeter of a triangle is: Perimeter = a + b + c where a, b, and c are the lengths of the three sides of the triangle.

Given, triangle JKL and DEF is similar.

If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b.

Given,

perimeter of triangle DEF =28 cm

10 + 6+ third side = 28

third side = 12

Hence,

using the property of similar triangle,

perimeter of DEF/perimeter of JKL = DF/JL

28/ x = 12/4.5

28/x = 2.6

x/28 = 1/2.6

x = 28/2.6

x = 10.7 cm

The perimeter of triangle JKL = 10.7 cm

To know more about perimeter, visit:

https://brainly.com/question/17394545

#SPJ1

SOLUTION:

For parallelograms; opposite sides are congruent;

Thus;

The shorter opposite sides must be equal too, thus;

Thus, for the figure to be a parallelogram, x = 6 and y = 10

We will have that Absolute Value is the magnitude of a value and is denotated as follows:

| x | : The absolute value of x.

When we speak about magnitude we refer just to possitive values. For example:

*The absolute value of 3:

| 3 | = 3

*The absolute value of -45:

| -45 | = 45

From this, we can clearly see that we "keep the number" but not the sign.

Answer:

N550

N4960

Step-by-step explanation:

10 days

First day: N10

Second day: N20

Third day: N30

...

Tenth day: N100

Sum of sequence: 10 + 20 + 30 + 40 + ... + 80 + 90 + 100

sum = (n/2)[2a+(n−1)d]

a = 10; n = 10; d = 10

sum = (10/2) × [2(10) + (10 - 1)(10)]

sum = 5[20 + 9(10)]

sum = 5[110]

sum = 550

Answer: N550

31 days

First day: N10

Second day: N20

Third day: N30

...

Thirty-first day: N100

Sum of sequence: 10 + 20 + 30 + 40 + ... + 290 + 300 + 310

sum = (n/2)[2a+(n−1)d]

a = 10; n = 31; d = 10

sum = (31/2) × [2(10) + (31 - 1)(10)]

sum = 15.5[20 + 30(10)]

sum = 15.5[320]

sum = 4960

Answer: N4960