What is the solution to this system of equations?

4x + 5y = 7

3x – 2y = –12

Answer:

(x²/4) + (y²/16) ≤ 1

Step-by-step explanation:

The general form of the ellipse in the graph is

x²/4 + y²/16 = 1

we want to find the inequality which represents the shaded area this will determine whether which of the following 2 choices are correct

Choice 1: x²/4 + y²/16 ≥ 1

Choice 2: x²/4 + y²/16 ≤ 1

we note that point (0,0) lies inside the shaded area. Which means if we substitute (0,0), it should create an equality that is valid.

try choice 1: 0²/4 + 0²/16  = 0 ≥ 1 (not valid because obviously zero is smaller than 1)  

try choice 1: 0²/4 + 0²/16  = 0 ≤ 1 (this is valid, hence choice 2  is the answer)

Answer:

80 dollars.

Step-by-step explanation:

Let the amount that A get be [tex]x[/tex] dollars.

B will get the rest of the 336 dollars. That will be [tex]336 - x[/tex] dollars.

[tex]\displaystyle \frac{5}{16}[/tex] of what B get will be the same as what A gets. In other words,

[tex]\displaystyle \frac{5}{16}(336-x) = x[/tex].

Add [tex]\displaystyle \frac{5}{16}x[/tex] to both sides of the equation:

[tex]\displaystyle \frac{5}{16}\times 336 = (1 + \frac{5}{16})x[/tex].

[tex]\displaystyle x = \frac{\displaystyle \frac{5}{16}\times 336}{\displaystyle 1 + \frac{5}{16}} = 80[/tex].

In other words, A gets 80 dollars.

Answer:

80

Step-by-step explanation:

The ladder resting against the house forms a triangle similar to the one in the image below

To answer this question you must use Pythagorean theorem

[tex]a^{2} +b^{2}=c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = x

b = 4

c = 20

^^^Plug these numbers into the theorem

[tex]x^{2} +4^{2} =20^{2}[/tex]

solve for x

[tex]x^{2}[/tex] + 16 = 400

[tex]x^{2}[/tex] = 384

x = 8√6

or

x ≈ 19.5959....

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The exact values of sin2Ф and cos2Ф are as follows:

sin2Ф = 0.8983

cos2Ф = 0.4394

Step-by-step explanation:

sin Ф = 9/17 = perp/hyp = y/r

we know that:

r² = x²+y²

17² = x² + 9²

x² = 208

x = 4√13

cos Ф = base/hyp = x/r = (4√13)/17

Solving sin2Ф

we know that:

sin2Ф = 2 sinФ cosФ

= 2*(9/17)*((4√13)/17)

= (72√13)/289

= 0.8983

Solving cos2Ф:

we know that:

cos2Ф = 1 - 2sin²Ф

= 1 - 2(9/17)²

= 1 - 0.5606

= 0.4394

Answer:

no real solution is the answer

If you have to list your extraneous solutions somewhere, that would be x=0.

Step-by-step explanation:

Cool thing here is the radical, the thing with the square root, is already isolate.

So we need to square both sides as a first step.  (Whenever you raise both sides to even power, you must definitely check your solutions as some might not actually be solutions to the original equation)

So upon squaring both sides I get:

x^4+16=(x^2-4)^2

Now I will write (x^2-4)^2 as (x^2-4)(x^2-4) and foil it!  This gives me:

x^4+16=x^4-8x^2+16

Subtract x^4 and 16 on both sides:

       0=-8x^2

Divide both sides by -8

      0=x^2

Therefore x=0.

0 isn't actually a solution though because when you plug it in you get 4=-4 which is not true.

Answer:

I think is A

Hope it helpsv

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Its has been dilated using O as the center.

Answer:

log_2((x^4+4x^3)/3)

Step-by-step explanation:

First step would be distribute that - into the ( )

3log_2(x)-log_2(3)+log_2(x+4)

Now take care of coefficients of the logs... bring them up as powers of the inside

log_2(x^3)-log_2(3)+log_2(x+4)

or

+log_2(x^3)-log_2(3)+log_2(x+4)

Now for the product and quotient rule! If it has a + in front of it, it will go on top. If it has a - in front of it, it will go on bottom.

Like this:

log_2 (x^3(x+4)/3)

or

log_2((x^4+4x^3)/3)

So inside that log base 2 thing the top is x^4+4x^3

and that bottom is 3

Answer:

[tex]log_{2}(\frac{x^{3}(x+4)}{3})[/tex].

Step-by-step explanation:

[tex]3log_{2}x-(log_{2}3-log_{2}(x+4))[/tex]

[tex]log_{2}x^{3}-log_{2}(\frac{3}{x+4})[/tex]

[tex]log_{2}(\frac{x^{3}}{\frac{3}{x+4}})[/tex]

[tex]log_{2}(\frac{x^{3}(x+4)}{3})[/tex].

y = ∛ (x + 6 - 3) = ∛ (x +3) -----------> graph this

(see attached)

Check: from formula above, when x = -3, y = 0

Check that this point exists on the graph... it does (check OK!)

edit reason: typo

The area of a parallelogram is base times height.    Each side can be a base, and has a particular height associated with it.

Here the height associated with the 1.5 base is 2.7, and the height associated with the 3.6 base is h.  So

[tex]1.5(2.7)=3.6 h[/tex]

[tex]h=15(27)/360= 1.125[/tex]

Answer: 1.125 units

Without the necessary details related to the parallelogram's area or base and side lengths, it is impossible to calculate the precise height of the parallelogram. The snippets provided relate to different mathematical problems and do not apply to the calculation of a parallelogram's height.

To find the height h of the parallelogram, we have several different pieces of information provided in the snippets, and each one appears to address a distinct mathematical problem. However, none of the given pieces align directly with calculating the height of a parallelogram.

To calculate the height of a parallelogram, usually the area and the base length are given, or you would use trigonometric relationships if angles and side lengths are known. Since none of these crucial pieces of information are provided, we will focus on demonstrating a general approach to solve such a problem through a proportion method that was mentioned:

Set up a proportion to find the height of the actual model.

For example, if a scale model uses a 1 cm height to represent 0.5 m in reality, and the actual height in the model is 75 cm, then using the proportion:

This approach would yield the height x in the actual model. However, we cannot precisely find the height h of the provided parallelogram without specific details related to its area or base and side lengths.

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[tex]\bf \begin{array}{ccll} miles&feet\\ \cline{1-2} 1&5280\\ x&8900 \end{array}\implies \cfrac{1}{x}=\cfrac{5280}{8900}\implies 8900=5280x \\\\\\ \cfrac{8900}{5280}=x\implies 1.6856\approx x\implies \stackrel{\textit{rounded up}}{1.7=x}[/tex]

Answer:

I would try 1.7

Final answer:

The equation of the quadratic graph with a focus of (3, 6) and a directrix of y=4 is (x-3)² = 4(y-5).

Explanation:

To find the equation of a quadratic graph with a focus of (3, 6) and a directrix of y=4, you'll need to use the definition of a parabola. A parabola is the set of all points that are equidistant from a single point, called the focus, and a line, known as the directrix. In this case, since the directrix is horizontal (parallel to the x-axis) and the focus has a y-coordinate greater than the directrix, the parabola opens upwards.

The vertex of the parabola is equidistant from the focus and directrix, so its y-coordinate is halfway between the focus's y-coordinate and the directrix's y-value, which is 5. Because the x-coordinate of the focus is 3, the vertex is at (3, 5). The equation of a parabola in vertex form is (x-h)² = 4p(y-k), where (h,k) is the vertex and 4p is the distance between the vertex and the focus or the vertex and the directrix.

In this problem, the distance p is 1 (since the y-coordinates of the vertex and focus differ by 1). Thus, the equation of the parabola is (x-3)² = 4(y-5). This is the standard quadratic form for a parabola opening upwards with vertex at (3, 5) and focus at (3, 6).

Answer:

B

Step-by-step explanation:

The sum of the 3 interior angles of a triangle = 180°

Check the sums of the given sets of angles

90° + 42° +58° = 190° ≠ 180° ← not valid

60° + 60° + 60° = 180° ← Valid

100° + 48° + 42° = 190° ← not valid

31° + 75° + 70° = 176° ← not valid

Answer:

The answer is

60°, 60°, and 60°

Answer:

12

Step-by-step explanation:

For the sake of showing work I will replace the empty space with an x like so...

[tex]\frac{1}{6} =\frac{2}{x}[/tex]

To find out what x is you must cross multiply (aka butterfly)

1*x = 2*6

1x = 12

x = 12

***If you don't understand the "cross multiply" technique  let me know in the comments and I'll be happy to explain.

To make these fractions equivalent the empty spot must be 12

[tex]\frac{1}{6} = \frac{2}{12}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

8x+ 6 is the translated mathematical expression.

Step-by-step explanation:

We are given the following English expression which are to translate into a mathematical expression:

'The sum of 6 and the product of 8 and x” into a mathematical expression'

Translating it in small chunks:

1. the sum of 6 ---> +6

2. product of 8 and x ---> 8x

Therefore, combining these we get the mathematical expression 8x + 6

For this case we must rewrite the given expression mathematically.

The sum of 6 and something else is written as:

[tex]6+[/tex]

The product of 8 and x is written as:

[tex]8x[/tex]

Finally, the expression is given by:

[tex]6 + 8x[/tex]

Answer:

The expression is given by:

[tex]6 + 8x[/tex]

For this case we must find the product of the following expression:[tex]-3x ^ 3 (-2x ^ 2 + 4x + 7)[/tex]

We apply distributive property to the terms within parentheses:

[tex](-3x ^ 3 * -2x ^ 2) + (- 3x ^ 3 * 4x) + (- 3x ^ 3 * 7) =[/tex]

We take into account that:

[tex]- * - = +\\- * + = -[/tex]

To multiply powers of the same base, put the same base and add the exponents.

[tex]6x ^ {3 + 2} -12x ^ {3 + 1} -21x ^ 3 =\\6x ^ 5-12x ^ 4-21x ^ 3[/tex]

Answer:

Option B

Answer:

26

Step-by-step explanation:

x is a degree so it can't be no more then 60 so the angle should be 26

The value of x is 60 degrees, as determined through a series of geometric deductions based on the properties of triangles and semicircles. Here option B is correct.

The sum of the angles in a triangle is 180 degrees.

The sum of the angles in a semicircle is 180 degrees.

The angle opposite to the diameter of the circle is 90 degrees.

Therefore, the angle x in the first triangle is 180 - 90 - 52 = 38 degrees.

The angle x in the second triangle is 180 - 38 - x = 142 - x degrees.

The angle x in the second triangle is also equal to the angle x in the semicircle, which is 180 - 52 - x = 128 - x degrees.

Equating the two expressions for the angle x in the second triangle, we get 142 - x = 128 - x.

Solving for x, we get x = 60 degrees. Here option B is correct.

To learn more about value

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Step-by-step explanation:

2x² + 8y = 121.5

x² - 8y = 121.5

Add the equations together to eliminate the y terms.

3x² = 243

x² = 81

x = 9

Answer:

Step-by-step explanation:

Answer: 3,-4,5

Step-by-step explanation:

Answer:

[tex]\sqrt{53i}[/tex]

Step-by-step explanation:

We need to find [tex]\sqrt{-49-4}[/tex]

We know that √-1 = i

Adding -49 and -4 and solving

[tex]\sqrt{-49-4}\\\sqrt{-53}\\\sqrt{53i}[/tex]

Since 53 is not a perfect square so our answer is:

[tex]\sqrt{53i}[/tex]

Answer:

4 1/4 gallons

Step-by-step explanation:

5 gallons are needed.

Convert one gallon into quarts and one quart into pints.

3 quarts and 2 pints, minus 3 quarts and 1 pint.

The result is 4 gallons and 1 pint.

He needs 4 galloons and 1 pint .

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

A painter needs 5 gallons of paint to finish a house.

He has 3 quarts and 1 pint.

Now, Convert one gallon into quarts and one quart into pints.

3 quarts and 2 pints

= 0.75 + 0.125

= 0.875 gallons

So, amount of paint needs = 5- 0.875    

                                            = 4.125

Hence, 4 gallons and 1 pint paint does he need.

Learn more about Unit Conversion here:

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Answer:

Roberto wins:1/4

roberto loses:3/4

Step-by-step explanation:

Answer:

Roberto wins:1/4

roberto loses:3/4

Step-by-step explanation:

6 < k

k is greater then 6. That means that you will go to the right of 6. This will show that k can be any number larger then 6

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex](x)^{2}+(y)^{2}=90,000[/tex]

Step-by-step explanation:

we know that

The equation of the circle (the roof of the Colosseum) in standard form is equal to

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

where

(h,k) is the center and r is the radius

we have

(h,k)=(0,0) ----> is the origin

[tex]r=600/2=300\ ft[/tex] ----> the radius is half the diameter

substitute

[tex](x-0)^{2}+(y-0)^{2}=300^{2}[/tex]

[tex](x)^{2}+(y)^{2}=90,000[/tex]

Answer:

3/16

Step-by-step explanation:

The nth term of a geometric series is:

an = a₁ (r)^(n - 1)

Given a₁ = 6, r = 1/2, and n = 6:

a₆ = 6 (1/2)^(6 - 1)

a₆ = 3/16

bearing in mind that parallel lines have the same exact slope, hmmm what is the slope of y = -10x + 3 anyway?

[tex]\bf y=\stackrel{\downarrow }{-10}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/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 (\stackrel{x}{5},\stackrel{y}{-6})~\hfill \begin{array}{llll} y-(-6)=-10(x-5) \\\\\\ y+6=-10(x-5) \end{array}[/tex]

To find the inverse of the given function, we need to switch the roles of x and y and solve for y.

To find the inverse of a function, we need to switch the roles of x and y, and then solve for y. So, let's start:

Given f(x) = 4x

Switching the roles, we have x = 4y

Now, solve for y:

x = 4y

Divide both sides by 4:

y = x/4

The inverse function is h(x) = x/4. Therefore, the correct option is h(x) = x/4.

A full circle is 360 degrees.

XY is 45 degrees.

Multiply the circumference by the fraction of the angle:

104 x (45/360) = 13

The answer is A. 13 cm.

Answer:

Arc length = 13 cm.

Step-by-step explanation:

Given  : A circle with circumferences = 104 cm , central angle = 45°.

To find :  what is the length of arc AB.

Solution : We have given  circle with circumference = 104 cm , central angle = 45°.

Arc length = [tex]\frac{theta }{360} * circumference[/tex].

 Plug the values circumference = 104 cm , central angle = 45°.

Arc length = [tex]\frac{45 }{360} * 104[/tex].

Arc length = 0.125 * 104

 Arc length  = 13 cm .

Therefore,  Arc length = 13 cm.