What is the solution to the system of equations?
y = 1/3x - 10
2x + y = 4
A) (-8,6)
B) (-6, 16)
C) (6,-8)
D) (16, -6)​

Answer:

8x2-4x+72. good luck.

Step-by-step explanation:

Answer is B but what kind of question is this? You don't even have to find the equation just find which one is different from the others.

A) y+2 = 4x-4

y = 4x-6

B)y-2 = 4x+4

y= 4x+6

C)y = 4x-6 (same with A )

D)y-6 = 4x-12

y= 4x-6 (Same with A and C)

So b is the different one.

Answer:

Is an scalene obtuse triangle

Step-by-step explanation:

step 1

Find the type of triangle by the measure of the interior angles

we know that

If applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex] ----> we have a right triangle

[tex]c^{2} > a^{2}+b^{2}[/tex] ----> we have an obtuse triangle

[tex]c^{2}< a^{2}+b^{2}[/tex] ----> we have an acute triangle

where

c is the greater side

we have

[tex]c=\sqrt{19}\ units[/tex]

[tex]a=2\ units[/tex]

[tex]b=\sqrt{12}\ units[/tex]

substitute

[tex]c^{2}=(\sqrt{19})^{2}=19[/tex]

[tex]a^{2}+b^{2}=(2)^{2}+(\sqrt{12})^{2}=16[/tex]

so

[tex]19 > 16[/tex] -----> [tex]c^{2} > a^{2}+b^{2}[/tex]

we have an obtuse triangle

step 2

Find the type of triangle by the measure of the sides

we have that

The measure of its three sides is different

therefore

Is an scalene triangle

Answer:

[tex]\large\boxed{36x^3a+45xa=9xa(4x^2+5)}[/tex]

Step-by-step explanation:

[tex]36x^3a=(9xa)(4x^2)\\\\45xa=(9xa)(5)\\\\36x^3a+45xa=(9xa)(4x^2)+(9xa)(5)=9xa(4x^2+5)[/tex]

Answer:

A

Step-by-step explanation:

it would equal 34 nd on the bottom would be 32 so AAAA

(3,7) ordered pair is the solution to the system.

A finite collection of equations for which we searched for common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized.

Given

2x+4y = 34

6x +2y = 32

x = 3

[tex]2*3[/tex] + 4y = 34

[tex]6*3[/tex] + 2y = 32

18 + 2y = 32

y = 7

(3,7) ordered pair is the solution to the system.

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Answer:

Step-by-step explanation:

X=2

Answer:

120

Step-by-step explanation:

Slope = rise / run

1/20 = 6 / run

run = 120

Answer:

(c-3) (4n)

Step-by-step explanation:

5n(c - 3) - n(C - 3) =

Factor out (c-3) from each term

(c-3) (5n-n)

Simplify the 2nd term

(c-3) (4n)

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

In this case:

m = -5

b = -8

so...

y = -5x - 8

Hope this helped!

Answer:

B

Step-by-step explanation:

Slope-intercept form of a line:

y = mx + b

m = slope

b = y-intercept

The question asks for a line w/ a slope of -5 and y-int of -8.

B would be the correct choice as in y = -5x - 8,

m (slope) = -5 and

b (y-int) = -8.

U ARE  GOING TO MULTIPLY THEM ALL TOGETHER

The required solutions to the equation (x - 2)(x + 10) = 13 are x = -11 and x = 3.

Simplification involves using rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.

We can solve the equation (x - 2)(x + 10) = 13 using the following steps:

Therefore, the solutions to the equation (x - 2)(x + 10) = 13 are x = -11 and x = 3.

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[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-4-4}{6-(-4)}\implies \cfrac{-8}{6+4}\implies \cfrac{-8}{10}\implies -\cfrac{4}{5}[/tex]

[tex]\bf \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-4=-\cfrac{4}{5}[x-(-4)]\implies y-4=-\cfrac{4}{5}(x+4) \\\\\\ y-4=-\cfrac{4}{5}x-\cfrac{16}{5}\implies y=-\cfrac{4}{5}x-\cfrac{16}{5}+4\implies y=-\cfrac{4}{5}x+\cfrac{4}{5}[/tex]

Answer:

equilateral

Step-by-step explanation:

If all 3 sides of a triangle are the same length, then it is an equilateral triangle.

scalene: no sides the same length

isosceles: 2 sides the same length

equilateral: 3 sides the same length

Answer:

C. [tex](x-3)^2+(y-1)^2=2^2[/tex]

Step-by-step explanation:

The standard equation of a circle, given the radius r units and center (h,k) is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

From the question, we have the center of the circle to be (3,1) and the radius is 2 units.

We substitute the center and radius of the circle into the equation to get:

[tex](x-3)^2+(y-1)^2=2^2[/tex]

The correct answer is C

Not enough information (attach the statements).

The formula for finding the midpoint of a line segment is[tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex].  Plug in and solve:

[tex](\frac{2-3}{2} , \frac{3-2}{2})[/tex]

(-1/2, 1/2)

(-0.5, 0.5)

Hope this helps!!

The midpoint of the segment is (-0.5, 0.5)

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

Given points: (2, 3) and (-3.-2).

The formula for midpoint is

(x1+x2/2, y1+y2/2)

= (2-3/2, 3-2/2)

=(-1/2, 1/2)

= (-0.5, 0.5)

Hence, the midpoints of the segment is  (-0.5, 0.5).

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Answer:

25

Step-by-step explanation:

Is means equals and of means multiply

16 = 64% * W

Change to decimal form

16 = .64 * W

Divide each side by .64

16/.64 = .64W/.64

25 = W

Answer:

25

Step-by-step explanation:

We can model this question with:

16 = 0.64x

x represents "what number."

0.64x = 16

Divide 0.64 from both sides

0.64x ÷ 0.64 = 16 ÷ 0.64

16 ÷ 0.64 = 25.

Therefore, 16 is 64% of 25.

Answer:

fog(x)=[tex]x^2+8[/tex]

Step-by-step explanation:

Here we are given two functions

f(x) = x+2

g(x)=[tex]x^2+6[/tex]

We are required to find fog(x)

fog(x) is a composite function.

fog(x) = f(g(x))

g(x) = [tex]x^2+6[/tex]

f(g(x)) = f( [tex]x^2+6[/tex] )

f(x)= x+2

Hence we replace x in f(x) with [tex]x^2+6[/tex]

f(g(x))=([tex]x^2+6[/tex])+2

f(g(x))=[tex]x^2+8[/tex]

Hence

fog(x) = [tex]x^2+8[/tex])

Answer:

[tex]f(x)=(x-3)^{2}(x-2)(x-1)[/tex]

Step-by-step explanation:

we know that

The roots (or x-intercepts) of the equation are

x=1 -----> with multiplicity 1

x=2 -----> with multiplicity 1

x=3 -----> with multiplicity 2 (because is a turning point)

so

The factors are

[tex](x-1), (x-2), (x-3),(x-3)[/tex]

The equation is equal to

[tex]f(x)=(x-3)(x-3)(x-2)(x-1)\\ \\f(x)=(x-3)^{2}(x-2)(x-1)[/tex]

To write a quadratic equation in factored form, find two binomials that when multiplied together yield the original quadratic. Factoring is essential in understanding the roots and the shape of a parabolic graph. For more complex quadratics, techniques like completing the square might be required.

When we are looking to write the equation of a graph in factored form, we are typically dealing with a polynomial function, and specifically when the graph is of a parabola, we are working with a quadratic equation. Factoring a quadratic equation involves finding two binomials that when multiplied together give us the original quadratic. For example, if we have a graph of a quadratic with its roots at x = p and x = q, the factored form would be y = a(x - p)(x - q), where a represents the leading coefficient.

If given an equation like 6x² + xy - y² - 17x - y + 12 = 0, it can be factored into two linear terms, which represents the intersection of two lines. In cases where completing the square is needed, such as x² - ( ) x = -() y, we add to each side (half the coefficient of x)² to form a perfect square on the left-hand side, leading us to an equation of the form (x − A)² = -4a(y − B).

Learning about graphing polynomials provides insights into how the constants in an equation affect the shape of the curve. By adjusting coefficients and analyzing the individual terms, we can understand how these terms combine to produce the overall graph of the polynomial.

Answer:

The volume is 113.04 cubic inches

Step-by-step explanation:

We are given:

Radius = r = 3 inches

As we know the formula for finding the volume of sphere is:

[tex]V=\frac{4}{3} \pi r^{3} \\Putting\ values\ of\ \pi \ and\ r\\V = \frac{4}{3} * 3.14 * (3)^3\\= \frac{12.56}{3} * 27\\= \frac{339.12}{3}\\ =113.04\ cubic\ inches[/tex]

The volume is 113.04 cubic inches ..

Answer: D. 61.2 cm

Step-by-step explanation:

The formula to calculate the circumference of a circle is given by :-

[tex]\text{Circumference}=\pi d[/tex], where d is the diameter of the circle.

In the given picture.,  we have the diameter of circle = 19.5 cm

Then , the circumference of the circle is given by :-

[tex]C=(3.14) (19.5)=61.23\approx61.2\ cm[/tex]

Hence, the circumference of the circle = 61.2 cm

Answer:

61.2

Step-by-step explanation:

Answer:

3/20

Step-by-step explanation:

First simplify the fractions

2/10   Divide top and bottom by 2

  = 1/5

9/12  Divide top and bottom by 3

= 3/4

2/10 * 9/12

1/5*3/4

Multiply the top

1*3 = 3

Multiply the bottom

5*4=20

3/20

Answer:

5 6 7 is the correct answer

Step-by-step explanation:

The possible lengths of the shortest straw are 5 inches, 6 inches, 7 inches and 8 inches

The lengths of the two straws are given as: 9 inches and 12 inches

Represent the length of the shortest straw with x.

So, we have the following inequality

[tex]x + 9 > 12[/tex]

Subtract 9 from both sides

[tex]x > 3[/tex]

This means the length of the shortest straw is greater than 3 inches

Hence, the possible lengths are 5 inches, 6 inches, 7 inches and 8 inches

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Answer:

LR is 12

Step-by-step explanation:

LP is hypotenuse and PR is base so LR is perpendicular

formula to calculate perpendicular is

p^2=H^2 -b^2

p^2=15^2-9^2

p^2=225-81

p^2=144

p=12(root of 144 is 12)

Answer:

it would be 24 cuz 15 + 9 = 24

ANSWER

-2 shift the graph of the basic function down by 2 units.

EXPLANATION

The given cosine function is:

[tex]y = - 2 - 3 \cos(x + \pi) [/tex]

This equation can be rewritten as:

[tex]y = - 3 \cos(x + \pi) + - 2[/tex]

We compare this to

[tex]y = a \cos(bx + c) + d[/tex]

The effect d has on the graph is that, it shifts the graph up by d units.

If d is negative the graph shifts down by d units.

Since d=-2, the graph will shift down by 2 units.

Answer:

Vertical Shift Down 2 Units

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Because none of the X coordinates are the same.

a. Practically speaking, you compute the differential in much the same way you compute a derivative via implicit differentiation, but you omit the variable with respect to which you are differentiating.

[tex]y=\cos x\implies\boxed{\mathrm dy=-\sin x\,\mathrm dx}[/tex]

Aside: Compare this to what happens when you differentiate both sides with respect to some other independent parameter, say [tex]t[/tex]:

[tex]\dfrac{\mathrm dy}{\mathrm dt}=-\sin x\dfrac{\mathrm dx}{\mathrm dt}[/tex]

b. This is just a matter of plugging in [tex]x=\dfrac\pi3[/tex] and [tex]\mathrm dx=0.1[/tex].

[tex]\boxed{\mathrm dy\approx-0.087}[/tex]

The differential dy for y = cos(x) is evaluated by finding the derivative of y which is -sin(x), then multiplying by dx. For x = π/3 and dx = 0.1, the calculated differential dy is approximately -0.0866 when rounded to three decimal places.

The differential dy of a function y with respect to x is given by the derivative of y with respect to x, multiplied by dx. For the function, y = cos(x), the derivative of y is -sin(x), hence dy = -sin(x)dx.

To evaluate dy for x = π/3 and dx = 0.1, we substitute x into -sin(x) and multiply by dx. This results in dy = -sin(π/3) × 0.1, which simplifies to dy = -0.1 √3/2. Rounding to three decimal places, dy ≈ -0.0866.

Answer:

[tex](-\frac{7}{6} )[/tex]

Step-by-step explanation:

From the question the emerald was located at a depth which is between -1/2 and -1 2/3 meters

This statement can be written as

[tex](-1\frac{2}{3}) -(-\frac{1}{2} )[/tex]

To get the depth, you find the depth of the emerald location, you find difference between the two mentioned depths

[tex]-(1\frac{2}{3} )-(-\frac{1}{2} )\\\\[/tex]

Change first term to improper fraction

[tex]=-(\frac{5}{3} )-(-\frac{1}{2} )\\\\[/tex]

Find the LCM to solve the operation the involves the fractions.The Least common multiple here is 6 i.e 3*2

[tex]=(-\frac{5}{3} )-(-\frac{1}{2})\\[/tex]

[tex]=\frac{-5}{3} +\frac{1}{2} =\frac{-10+3}{6} =\frac{-7}{6}[/tex]

The number that could represent the depth at which the emerald was located is

[tex]=\frac{-7}{6}[/tex]

Answer:

∠3 = 60°

Step-by-step explanation:

Since g and h are parallel lines then

∠1 and ∠2 are same side interior angles and are supplementary, hence

4x + 36 +3x - 3 = 180

7x + 33 = 180 ( subtract 33 from both sides )

7x = 147 ( divide both sides by 7 )

x = 21

Thus ∠2 = (3 × 21) - 3 = 63 - 3 = 60°

∠ 2 and ∠3 are alternate angles and congruent, hence

∠3 = 60°

The measure of angle 3 is 60 degrees, the correct option is B.

Given

In the diagram, g is parallel to h.

The measurement of angle 1 is (4x +36).

The measurement of angle 2 is (3x-3).

Interior angles;

The angles that lie in the area enclosed between two parallel lines that are intersected by a transversal are also called interior angles.

∠1 and ∠2 are the same side interior angles and are supplementary then the sum of both angles is equal to 180 degrees.

[tex]\rm 4x+36+3x-3=180\\\\7x+33=180\\\\7x=180-33\\\\7x=147\\\\x=\dfrac{147}{7}\\\\x=21[/tex]

The measure of the angle 2 is = 3(21)- 3= 63 - 6 = 60 degrees.

Hence, Angle 2 and ∠3 are alternate angles and congruent then the measure of angle  3 is 60 degrees.

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