What should be done to these equations in order to solve a system of equations by elimination?

If Lin is solving the inequality [tex]15-x < 14[/tex] and she know the solution is x = 1 , then the solution of  inequality is [tex]x > 1[/tex] .

The inequality that Line is solving is [tex]15-x < 14[/tex] ,

the solution of the equation [tex]15-x = 14[/tex] is given as x = 1 ;

we have to find the value of x for which the given inequality expression is true ,

Case(i) , let us take [tex]x > 1[/tex] ,

So , putting x = 2 , in the inequality ,

we get ; [tex]15-2 < 14[/tex]

= 13 < 14 , that is TRUE .

Case(ii) , let us take [tex]x < 1[/tex] ,

So , putting x  = 0 in the inequality ,

we get ; [tex]15-0 < 14[/tex]

= 15 < 14 , that is FALSE .

Therefore , the solution of the inequality is x > 1 .

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Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.

Triangle congruence: Two triangles are deemed to be congruent if all three of their corresponding sides and angles have the same magnitude. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "≅".

When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general. Finding all six dimensions is necessary, though.

Given that,

GH ≅ JH

FH ≅ HI

And,

∠GHF = ∠JHI

Therefore,

ΔGHF ≅ ΔJHI (SAS Congruency)

∴ FG = IJ (CPCT theorem)

Hence proved that FG = IJ with CPCT theorem for ΔGHF ≅ ΔJHI by SAS Congruency rule.

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Answer:

The common divisor that leaves a reminder of 6 is 324

Step-by-step explanation:

Given

1626, 1950 and 2274

Required

Common divisor that leaves a remainder of 6

First, we subtract 6 from each number

[tex]1626 - 6 = 1620[/tex]

[tex]1950 - 6 =1944[/tex]

[tex]2274 - 6 = 2268[/tex]

Next, we find the common divisor of 1620, 1944, 2268

[tex]1620 \to 2 * 2 *3 * 3*3*3*5[/tex]

[tex]1944 \to 2 * 2 * 2 * 3 * 3 * 3 * 3 * 3[/tex]

[tex]2268 \to 2 * 2 * 3 * 3 * 3 * 3 * 7[/tex]

The common factors are:

[tex]Common = 2 * 2 * 3 * 3 * 3 * 3[/tex]

[tex]Common = 324[/tex]

Answer:B

Step-by-step explanation: Because it right

Answer:

156km

Step-by-step explanation:

Given data

The red Maserati traveled at a speed of 120km/h for 5 hours one day.

Distance = speed*time

Distance= 120*5

Distance= 600km

The green Ford Pickup traveled at a speed of 74km/h for 6 hours

Distance = speed*time

Distance= 74*6

Distance= 444km

Hence the difference is

=600-444

=156km

Answer: 8.075: gotta get somebody else to do this one...sorry. and 0.08 = 8

Step-by-step explanation:

Did this with a classmate couple months ago. Hope this helps. :)

Answer:

17.3 if I am right mark me brainless pls

If Hermione paid 98 coins and Luna paid 28 coins, Hermione paid for 672 Chocolate Frogs.

We can start the problem by using algebra. Let x be the number of Chocolate Frogs that Hermione paid for. Then we know that:

x + (2016 - x) = 2016 (the total number of Chocolate Frogs)

Also, we know that the cost of the Chocolate Frogs Hermione paid is 98 coins, and the cost of the Chocolate Frogs Luna paid is 28 coins. Let's assume the cost of each Chocolate Frog is y. Then we can write:

x * y = 98 and (2016 - x) * y = 28

Now we have a system of two equations with two variables (x and y). To find the value of x, we can use any method to solve the system of equations, such as substitution or elimination.

Using substitution, we can solve for y in the second equation and substitute it into the first equation:

(2016 - x) * y = 28

y = 28 / (2016 - x)

x * (28 / (2016 - x)) = 98

x * (28 / (2016 - x)) = 98

x = 98 * (2016 - x) / 28

Solving for x, we get:

x = 2016/3

So Hermione paid for 2016/3 = 672 Chocolate Frogs.

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Answer:

Hermione paid for 1,568 frogs.

Step-by-step explanation:

First, do 98 + 28. That will give you 126. Then do 2,016 / 126. That gives you 16. 16 x 98 = 1568 frogs.

Let's do Luna's to check our work.

28 x 16 = 448 frogs. 448 + 1568 = 2,016. So, Hermione paid for 1,568 frogs.

Answer:

−(b+20)

Step-by-step explanation:

The only thing we could possibly do is factor out the negative since there are no factors no squared numbers.

PLS MARK BRAINLIEST

Answer: 24 bunches of cilantro

Step-by-step explanation:

1. Set a proportion with the given information, which should be 1/1.60 = x/38.40.

2. Cross multiply. Now the equation should 1.60x = 38.40.

3. Divide by 1.60 to get x alone to find out how many bunches of cilantro you can buy with $38.40. This should give you x = 24 bunches of cilantro.

Answer:

24 bunches

Step-by-step explanation:

The person below is correct

Answer:

a) 3[tex]x^{4}[/tex]

b) 1024[tex]x^{10}[/tex]

Step-by-step explanation:

[tex]\frac{12x^{7} }{4x^{3} }[/tex]

[tex]\frac{3(4)xxxxxxx}{4xxx}[/tex]  We can cancel out a 4 and 3 x's.  That leaves

3xxxx

or 3[tex]x^{4}[/tex]

[tex](2x)^{2}[/tex] x [tex](2x)^{3}[/tex] x [tex](2x)^{5}[/tex]  can be written in expanded form

[(2)(2)xx] x [(2)(2)(2)xxx] x [(2)(2)(2)(2)(2)xxxxx]

(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)xxxxxxxxxx

1024[tex]x^{10}[/tex]

The volume of a right square pyramid PABCD is 50.91 cubic units

Let l be the side length of right squared pyramid and h be the height.

We know that the formula for the volume of the right squared pyramid.

V = a²h / 3

And the formula for the height of right squared pyramid.

h = (1/√2)a

Here, the side length (a) = 6 units

So, using above formula of height,

h = (1/√2) × 6

h = 6/√2

h = 3√2 units

Now using the formula for the volume of the right squared pyramid, the volume of pyramid PABCD would be,

V = (6² × 3√2) / 3

V = 6² × √2

V = 36√2

V = 50.91 cubic units

Therefore, the volume of PABCD is 50.91 cubic units

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Straight line has the equation is, y = 5x - 4.

An endless number of points that are connected on both sides of the point make up a straight line.

The slope of a straight line, "m," is determined by:

m = y2 - y1 / x2 - x1

A linear equation has the expression y = mx + b in slope-intercept form. X and Y are the variables in the equation. The numbers m and b stand for the line's slope (m) and the value of y at x = 0.

The graph's acquired points are (0,-4) and (1,1)

The slope is ,

m = 1-(-4) / 1-0

  = 5/1

  = 5

The line's equation will be as follows since it crosses the y-axis at its intersection point, where C = -4.

⇒ y = mx + c

⇒ y = 5x + (-4)

⇒ y = 5x - 4

As a result, y = 5x - 4 is the equation for the straight line depicted below.

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The solution of the equation is x = -1 and y = -3.

And the intersection point is (-1, -3).

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation.

And simultaneous equation is the system of equation.

Given system of equations:

y = x-2      ...... equation 1

y = −3x−6  ...... equation 2

To solve the system of equations:

Substitute the value of y from the equation 1 to equation 2,

we get,

x - 2 = -3x - 6

x + 3x = -6 + 2

4x = -4

x = -1

Then y = -1 -2 = -3.

By graphically:

1). Draw the linear equation on the graph.

2). And the intersection point of the lines is a solution of the equation.

3). The solution is x = -1 and y = -3.

The complete graph is given in the attached image.

Therefore, the solution is x = -1 and y = -3.

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Answer:

1/12

Step-by-step explanation:

Assuming his choices are equally likely (important: he's choosing randomly)...

Probability of selecting chocolate: 1/4  (1 of 4 equally likely choices)

Probability of selecting waffle cone:  1/3

Probability of selecting both:  1/4 x 1/3 = 1/12

Now, if you'll excuse me, I'm off to get ice cream!  :-)

Step-by-step explanation:

ok so first use this formula. V= 4/3 * 3.14 * 9 to the power of 3. so multiply 4/3 and 3.14 and then multiply 9 and 9 and 9 and then multiply that all together

Answer:

$302

Step-by-step explanation:

p(x) 3x^4 = x^4-3x^2+5

We put 3 in for x and solve

3(3)^4 = 3^4 -3(3)^2 + 5

3(81) = 81 -3(9) + 5

243 = 81 - 27 + 5

243 = 59

Then we add 243 with 59 and get

$243 + $59 = $302

So, they spend together $302

If you can, please give me a Brainliest; thank you!

Answer:

i think it's C

Step-by-step explanation:

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

Explanation:

Let x be the number of gallons used up. It's some positive real number.

We'll use the formula

miles = (mpg)*(number of gallons)

to help figure out how much fuel is used. The trip is 432 miles, and the mpg rating is 31

So,

miles = (mpg)*(number of gallons)

432 = 31*x

31x = 432

x = 432/31

x = 13.9354838709678  which is approximate.

Multiply that with the 2.79 to get the final answer.

2.79*x = 2.79*13.9354838709678 = 38.8800000000001

The 1 at the very end is probably due to some rounding error, but then again it may be accurate. Either way, that value rounds to 38.88

Side note: The 31 mpg rating is very likely an average value and not the same throughout the trip. This is due to the car changing speeds at different points of the journey. In reality, the true answer will vary slightly from the 38.88 figure we just calculated (but it should be fairly close).

The total amount of money that Tom and his friend would spend on gas during the trip is $38.88.

The first step is to determine the total amount of gas that would be needed during the trip.

Gas that would be needed = 432 / 31 = 13.94

The second step is to multiply the gas that would be needed by the cost of gasoline: $2.79 x 13.94= $38.88

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Answer:

Incomplete Question. Send Full question pls.

Answer:

[tex] \approx \: 7.33 \: {cm}^{2} [/tex]

Step-by-step explanation:

Area of the blue shaded region

[tex] = \frac{ \theta}{360 \degree} \times \pi r_1^2 - \frac{ \theta}{360 \degree} \times \pi r_2^2 \\ \\ = \frac{ \pi\theta}{360 \degree} ( r_1^2 - r_2^2) \\ \\ ( r_1 = 4 \: cm, \: \: r_2 = 3\: cm, \: \: \theta = 120 \degree) \\ \\ = \frac{ 3.14 \times 120 \degree}{360 \degree} ( 4^2 - 3^2) \\ \\ = \frac{ 3.14 }{3} \times 7 \\ \\ = \frac{21.98}{3} \\ \\ = 7.32666667 \\ \\ \approx \: 7.33 \: {cm}^{2} [/tex]

Answer:

7

Step-by-step explanation:

An example of x-intercept is (3,0).

Here x=3 is the x-intercept in this line.

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

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Answer:

21

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

The angle formed by the intersection of a tangent to a circle and an intersecting secant is 1/2 (Arc PS - arc PR)

PS = 208

PR = 74

Solution

x = 1/2 (208 - 74)

x = 1/2 (134)

x = 67

The volume of the building block in terms of x is V = x⁶/1728

Volume is the amount of space a substance occupies.

Since building blocks are in the shape of a cube. The dimensions of the building blocks are based on the length of the packaging box, which is defined as x²/12 centimeters, where x is the length of the packaging box.

Since the building blocks are in the shape of a cube, its volume is the volume of a cube.

The volume of a cube is given by V = L³ where L = length of side of cube.

To find the volume of the building block, since the length of the building block is L = x²/12, then we find the volume of the building block by substituting L into V.

So, V = L³

V = (x²/12)³

= x⁶/12³

= x⁶/1728

So, the volume of the building block is V = x⁶/1728

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Answer:

Step-by-step explanation:

There are 100 cm in 1 meter. the dimensions are 400cm by 250cm. depending on which way you turn them, they will fit better. if you take 400 divided by 16, you will have a row of 25 wide and if you divide 250 by 10, you will have a length of 25. you now have 25 rows of 25. 25x25 is 625 tiles.

Hope this helps

Answer:

3 and 3/20

Step-by-step explanation:

For the given equations , the solutions are as follows :

(a) the equation [tex]6x + 8 = 7x + 13[/tex] has exactly one solution , and the solution is  .

(b) the equation [tex]6x + 8 = 2(3x + 4)[/tex] has Infinitely Many Solutions .

(c) the equation [tex]6x + 8 = 6x + 13[/tex] has No Solution .

Equation (a) ;

the equation is given as [tex]6x + 8 = 7x + 13[/tex] , we solve the equation further ,

we get ;

[tex]7x - 6x = 13 - 8[/tex] ;

[tex]x = 5[/tex] ;

So , the equation has exactly one solution and the solution is [tex]x = 5[/tex] .

Equation (b) ;

the equation is given as [tex]6x + 8 = 2(3x + 4)[/tex] , we solve equation further ,

we get ;

[tex]6x + 8 = 6x + 8[/tex] ;

On solving further ,

we have ;

[tex]8 = 8[/tex] ;

So , the equation has infinitely many solutions .

Equation (c) ;

the equation is given as [tex]6x + 8 = 6x + 13[/tex] , we solve equation further ,

we get ;

[tex]8 = 13[/tex] ;

and we know that [tex]8\neq 3[/tex] ,

So , the equation have No Solution .

The given question is incomplete , the complete question is

For each equation determine whether it has no solutions, exactly one solution, or is true . for all values of x (and has infinitely many solutions). If an equation has one solution, solve to find the value of x that makes the statement true.

(a) 6x + 8 = 7x + 13

(b) 6x + 8 = 2(3x + 4)

(c) 6x + 8 = 6x + 13

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