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2 years ago

(-3, 11) a solution to the systems of equations: x – 3y = -36 and 3x + 4y = 48 true or false

Mathematics

2 answers:

Cloud [144]2 years ago

3 0

Answer:

TRUE and FALSE (please look at step-by-step)

Step-by-step explanation:

How to know if it's true or false, you just simply plug in the given numbers to the x and y values.

x = -3

y = 11

for the x - 3y = -36 equation:

-3 -3(11) = -36

-3 - 33 = -36

This equation is true.

for the 3x + 4y = 48 equation:

3(-3) + 4(11) = 48

-9 + 44 = 35

This equation is false.

Nutka1998 [239]2 years ago

3 0

This equation is false

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Georgia [21]

Answer:

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Step-by-step explanation:

If they both added the same amount of yellow dye, than blue will determine how dark their icing is. Since Mariana added less blue, her dye will be lighter!

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2 years ago

2, 9, 16, 23, Number pattern expression equations

algol [13]

Answer:

see below

Step-by-step explanation:

2+7 = 9

9+7 = 16

16+7 = 23

We are adding 7 each time

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3 years ago

Read 2 more answers

Find the vertex, the axis of symmetry, and the y-intercept of the graph.

UNO [17]

Given:

Given that the graph of the parabola.

We need to determine the vertex, the axis of symmetry and the y - intercept of the graph.

Vertex:

The vertex of the parabola is the point at which the parabola changes its direction.

From the graph, it is obvious that the parabola changes its direction at the point (-2,0)

Hence, the vertex of the graph is (-2,0)

Axis of symmetry:

The axis of symmetry is the line that divides the parabola exactly into two equal halves.

Hence, from the graph, it is obvious the line x = -2 divides the graph exactly into two equal halves.

Hence, the axis of symmetry is x = -2.

y - intercept:

The y - intercept of the parabola is the value of y when x = 0.

In other words, the y - intercept of the graph is the value of y when the line passes through the y - axis.

Thus, from the graph it is obvious that when x = 0, the value of y is -3.

Hence, the y - intercept of the graph is -3.

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3 years ago

8 1/2 - 6 1/4 please subtract

Alexandra [31]

Answer:

2.25

Step-by-step explanation:

8.5-6.25

(8-6)+(0.5-0.25)

2+0.25

2.25

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2 years ago

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PLZ HELP!!! Use limits to evaluate the integral.

Marrrta [24]

Split up the interval [0, 2] into n equally spaced subintervals:

$\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]$

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

$r_i=\dfrac{2i}n$

where $1\le i\le n$ . Each interval has length $\Delta x_i=\frac{2-0}n=\frac2n$ .

At these sampling points, the function takes on values of

$f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}$

We approximate the integral with the Riemann sum:

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3$

Recall that

$\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4$

so that the sum reduces to

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}$

Take the limit as n approaches infinity, and the Riemann sum converges to the value of the integral:

$\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}$

Just to check:

$\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28$

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2 years ago