Solve the system of equations. 2x + 3y = 1 5x + 2y = 8 What is the solution?

Answer:

1. x = 49.10 - 5 divided by 2.10

2. 21 miles

Answer:

X=49.10

21 miles

Step-by-step explanation:

First, you need to divide 2.10 and the $5 . which will give you 4.2.

this has nothing to do with the problem lol.

I would keep on mulitiplying if i were you.

And, once you hit 21 miles, you will get $44.10 and the $5 which will equal 49.10 :).

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ K(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\qquad L(\stackrel{x_2}{-4}~,~\stackrel{y_2}{6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-4-2}{2}~~,~~\cfrac{6-4}{2} \right)\implies \left( \cfrac{-6}{2}~~,~~\cfrac{2}{2} \right)\implies (-3~,~1)[/tex]

the answer is...... (-3,1)

[tex]4x^{2} -4x - 1 = 0[/tex]

To solve for the zeros you can use the quadratic formula:

[tex]\frac{-b plus/minus\sqrt{b^{2}-4ac } }{2a}[/tex]

a = 4

b = -4

c = -1

[tex]\frac{-(-4) plus/minus\sqrt{(-4)^{2}-4(4)(-1) } }{2(4)}[/tex]

[tex]\frac{4 plus/minus\sqrt{16+16 } }{8}[/tex]

[tex]\frac{4plus/minus\sqrt{32} }{8}[/tex]

[tex]\frac{4plus/minus4\sqrt{2 } }{8}[/tex]

[tex]\frac{1 plus/minus\sqrt{2} }{2}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

The quadratic equation 4x^2 - 4x - 1 = 0 can be solved by using the quadratic formula -b ± √b² - 4ac / 2a. After substituting the coefficients into the formula, we get 4 ± √((-4)^2 - 4 * 4 * -1) / 2 * 4. These roots are the solution to the equation.

The subject of the question is the solution of a quadratic equation which can be found using the quadratic formula. For the given equation 4x^2 - 4x - 1 = 0, the values of a, b, and c as per the general quadratic equation (ax^2 + bx + c = 0) are a = 4, b = -4 and c = -1. The quadratic formula to solve for x is -b ± √b² - 4ac / 2a.

Substituting the given values in to the formula we get the solution for x: 4 ± √((-4)^2 - 4 * 4 * -1) / 2 * 4, which can further be solved to get the two roots of the quadratic equation.

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Answer:

3x^2−13x+4

Step-by-step explanation:

(x−4)(3x−1)

=(x+−4)(3x+−1)

=(x)(3x)+(x)(−1)+(−4)(3x)+(−4)(−1)

=3x^2−x−12x+4

=3x^2−13x+4

Answer:

Option A. 3x² - 13x + 4 is the answer.

Step-by-step explanation:

A conference room is in the shape of a rectangle. Its floor has a length of (x - 4) and width of (3x - 1) meters.

The expression that represents the area of the room is (x - 4)(3x -1) meter²

We further simplify this expression representing the area of the conference room.

(x - 4)(3x -1) = x(3x -1) - 4(3x -1) [Distributive law]

= 3x² - x - 12x + 4

= 3x² - 13x + 4

Option A. 3x² - 13x + 4 is the simplified form of the given expression.

Final answer:

The quadratic function equivalent to the polynomial 2 + 7c – 4c2 – 3c + 4 when simplified and written in standard form is – 4c2 + 4c + 6.

Explanation:

When you simplify and write the polynomial 2 + 7c – 4c2 – 3c + 4 in standard form, the quadratic function equivalent is – 4c2 + 4c + 6. First, combine like terms by adding the constants and the terms with c. This gives you – 4c2 + (7c – 3c) + (2 + 4), which simplifies to – 4c2 + 4c + 6.

The standard form of a quadratic equation is ax2 + bx + c = 0. In the case of the simplified polynomial, a = -4, b = 4, and c = 6. If needed, you can use the quadratic formula to find the roots of this quadratic equation by substituting these values into the formula.

The maximum height that the dolphin jumps is 8 ft.

A parabola is a planar curve which symmetrical across its vertex.

The standard equation of a parabola is given by:

y = (x-h)² + k

Where (h, k) is the vertex of the parabola.

The maximum height that the dolphin reaches is the y-coordinate of the vertex of the parabola. We can change the given quadratic equation to standard form as follows:

h = -8t² + 16t

Subtract and add 8:

h = -8t² + 16t - 8 + 8

h = -8 (t² - 2t + 1) + 8

h = -8 (t - 1)² + 8

The negative coefficient outside the square term means that the parabola opens downward. From this standard form, we can see that the vertex of the parabola is (1, 8). This means that the maximum height that the dolphin can reach is 8 ft.

Therefore, we have found that the maximum height the dolphin jumps is 8 ft.

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Final answer:

The dolphin reaches its maximum height after 2 seconds and jumps 32 feet.

Explanation:

To find the maximum height the dolphin jumps, we need to determine the time it takes for the dolphin to reach its highest point. The equation given is h = -8t^2 + 16t, where h represents the dolphin's height at any given time t. Since the dolphin jumps straight up, its final velocity at the highest point is 0. Setting h = 0 and solving the resulting quadratic equation, we can find the time it takes for the dolphin to reach its maximum height.

Using the equation -8t^2 + 16t = 0, we can factor out -8t to get t(-8t + 16) = 0. This yields two solutions: t = 0 and t = 2. As time cannot be negative, we discard t = 0. Therefore, the dolphin reaches its maximum height after 2 seconds.

To find the maximum height, we substitute t = 2 in the equation h = -8t^2 + 16t. Plugging in the value, we get h = -8(2)^2 + 16(2) = -8(4) + 32 = 0 + 32 = 32 feet. Thus, the maximum height the dolphin jumps is 32 feet.

[tex]\text{Hey there!}[/tex]

[tex]\frac{5}{4}+\frac{3}{4}\div-\frac{2}{3}\ -\ \frac{5}{6}[/tex]

[tex]\frac{5}{8} +\frac{3}{4}=\frac{11}{8}[/tex]

[tex]\frac{-2}{3}-\frac{5}{6}=\frac{-3}{2}[/tex]

[tex]\text{Problem becomes:}\frac{11}{8}\div\frac{-3}{2}[/tex]

[tex]\frac{11}{8}\div\frac{-3}{2}=\frac{-11}{12}[/tex]

[tex]\boxed{\boxed{\bf{Answer:\frac{-11}{12}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

9

Step-by-step explanation:

6 ÷ 2(1+2)

= 6 ÷ 2 x 3

= 3 x 3

= 9

The correct answer is 9

First you have to divide 6/2 is 3

Then you distribute 3 into the parentheses

3(1+2) = (3*1)+(3*2)

Then you solve

(3*1)=3

(3*2)=6

So,

6+3=9

Answer:

To plot a decimal on a coordinate plane you plot it between the two whole numbers its close to.

Step-by-step explanation:

Answer:

Pretend that H is the midpoint of AB, connect O and H

=> OH is the median of ΔOAB

Since we know that OA = OB => ΔOAB is an isosceles triangle

=> OH is also the height of ΔOAB

=> ∠OBA = ∠OAB = (180° - ∠AOB)/2 = (180° - 120°)/2 = 60°/2 = 30°

Now look at ΔOHB (that you create by connecting O and H)

We have:

cos30° = BH/OB

=> BH = cos30° · OB = √3/2 · x = (√3 x)/2

Because we have H as the midpoint of AB, we know that:

AB = 2 · BH = 2 · (√3 x)/2 = √3 x

So the answer is B

The equation

[tex]w=112+8t[/tex]

means that you choose a value for the input variable t, and you compute the correspondent value for the output variable w.

So, if the input is t = 176, the output will be

[tex]w=112+8\cdot 176 = 112+1408 = 1520[/tex]

Similarly, the ordered pair (4, 144) means that if you choose 4 as input, you get 144 as output, in fact you have

[tex]w=112+8\cdot 4= 112+32= 144[/tex]

Answer:

The first one is 8

The second one is 144

Step-by-step explanation:

I just did it on brainly

Answer:

[tex]k=26/3[/tex]

Step-by-step explanation:

we have

[tex]g(x)=3k-5x[/tex]

we know that

If the graph of g(x) passes through the point (3,11)

then

the ordered pair (3,11) must satisfy the equation g(x)

Substitute

[tex]x=3,g(3)=11[/tex]

[tex]11=3k-5(3)[/tex]

[tex]11=3k-15[/tex]

[tex]3k=11+15[/tex]

[tex]3k=26[/tex]

[tex]3k=26[/tex]

[tex]k=26/3[/tex]

Answer:

He should have written the square root of [tex]y^8[/tex] in the answer as [tex]y^4[/tex], not [tex]y^2[/tex]

Step-by-step explanation:

We need to remember that:

[tex]\sqrt[n]{x^n}=x[/tex]

The Product of powers property states that:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

The Power of a power a property states that:

[tex](a^m)^n=a^{(mn)}[/tex]

Let's check the procedure made by Jamal to simplify the expression [tex]\sqrt{75x^5y^8 }[/tex] where [tex]x\geq0[/tex] and [tex]y\geq0[/tex]:

[tex]=\sqrt{25*3*x^4*x*y^8}[/tex] (This is correct)

[tex]5x^2y^2\sqrt{3x}[/tex] (Jamal made a mistake)

The correct procedure is:

[tex]=\sqrt{25*3*x^4*x*y^8}[/tex]

[tex]=5x^2y^4\sqrt{3x}[/tex]

Because:

[tex]\sqrt{y^8}=\sqrt{(y^4)^2}=y^4[/tex]

Therefore: He should have written the square root of [tex]y^8[/tex] in the answer as [tex]y^4[/tex], not [tex]y^2[/tex],

Answer:

He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.

Step-by-step explanation:

its A on Ed

Answer:

About 609,000 Cowboy stadiums could fit inside of Mount Everest

Step-by-step explanation:

we have

The estimate volume of Mount Everest is at around [tex]2,413\ km^{3}[/tex]

The Dallas Cowboys Stadium has a volume of [tex]140,000,000\ ft^{3}[/tex]

step 1

Convert ft³ to km³

we know that

1 km=3,280.84 ft

so

[tex]140,000,000\ ft^{3}=140,000,000*(1/3,280.84)^{3}=0.003964\ km^{3}[/tex]

step 2

To find how many Cowboy stadiums could fit inside of Mount Everest, divide the volume of Mount Everest by the volume of the Dallas Cowboys Stadium

[tex]2,413/0.003964=608,729[/tex]

Round to the nearest Thousands

[tex]608,729=609,000[/tex]

The volume of Mount Everest is about 609,000 times greater than the volume of the Dallas Cowboys Stadium

Approximately 608,570 Dallas Cowboys Stadiums could fit inside the volume of Mount Everest.

To answer this question, we first need to convert the volume of Mount Everest and Dallas Cowboys Stadium to the same units. Given that 1 cubic kilometer (km³) is equal to approximately 35.31 billion cubic feet (ft³), so the volume of Mount Everest is approximately 2,413 km³ * 35.31 billion ft³/km³ = 85.199 trillion ft³.

The volume of the Dallas Cowboys Stadium is 140 million ft³. Now, we can find out how many Cowboy stadiums could fit inside of Mount Everest by dividing the volume of Mount Everest by the volume of the stadium.

Mount Everest volume / Dallas Cowboys Stadium volume = 85.199 trillion ft³ / 140 million ft³ = approximately 608,570 Dallas Cowboys Stadiums.

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Answer:

37, 39

Step-by-step explanation:

n + 1/3 (n + 2) = 50

Multiply both sides by 3 to cancel out the 1/3:

3n + (n + 2) = 150

Simplify:

4n + 2 = 150

4n = 148

n = 37

n + 2 = 39

Answer:

37 and 39.

Step-by-step explanation:

Let the two odd numbers are x and ( x + 2 ) Then by statement " Sum of the first number and one third of second number is equal to 50."

So equation will be

x + [tex]\frac{1}{3}[/tex] (x+2) = 50

We multiply the equation by 3

3x + ( x+2 ) = 150

3x + x + 2 = 150

4x + 2 = 150

4x = 150 - 2 = 148

x = 37

So numbers are 37 and 39.

Answer:

Answer:

The fourth graph

Step-by-step explanation:

Let x = width

The length is one less than 3 times the width, so length = 3x - 1

So we have a rectangle with length, 3x - 1, and width, x

So the area = y = (3x-1)(x)

So our equation:

y = (3x - 1)*(x)

If we check the x-intercepts, we see that y = 0 when x = 0 and 1/3.  The only graph that has (0,0) and (1/3, 0) is the fourth graph, making that one our graph.

Step-by-step explanation:

Answer:5 cups

Step-by-step explanation:

21 cups divided by 4.2 is

5L are needed in 21 cups.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

1 L= 4.2 Cups

and, for 21 cups =  21/4.2

                          = 210/42

                          = 5 L

Hence, 5L are needed in 21 cups.

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[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{5}}x\stackrel{\stackrel{b}{\downarrow }}{-3}\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}\qquad \qquad \cfrac{7}{5};-3[/tex]

The formula y=mx+b which this equation is in shows the slope as m and y-intercept as b. In this situation where m is the fraction 7 over 5 and b is -3. So the slope is 7/5 and the y-intercept is -3

Answer:

1017.36 square inches

Step-by-step explanation:

The globe is in the shape of a sphere. As we given the diameter of the globe

d = 18 inches

We have to find the radius of globe first

[tex]Radius=r=\frac{d}{2}\\r=\frac{18}{2}\\r=9\ inches[/tex]

The formula for finding the surface area is:

[tex]Surface\ Area=4\pi r^{2}\\Putting\ the\ values\ of \pi \ and\ r\\Area=4*3.14*(9)^{2} \\=4*3.14*81\\=1017.36\ square\ inches[/tex]

Hence, the surface area is 1017.36 square inches ..

Answer:

I think the second option is correct.

because the unknown angle is 90.

and if replace anyone of the x with 90 the equation isn't correct except with the second option.

Step-by-step explanation:

if you want me to show you how I got 90 degree for x just tell me and I'll show you

Hope this helps

Answer:

The value of x is 2.5 to the nearest tenth

Step-by-step explanation:

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Now lets solve the problem

∵ x is opposite to the angle of measure 23°

∵ 6 is adjacent to the angle of measure 23°

∴ tan(23°) = x/6 ⇒ × 6 to both sides

∴ x = 6 × tan(23°) = 2.5

* The value of x is 2.5 to the nearest tenth

Answer: [tex]x=2.5[/tex]

Step-by-step explanation:

You need to remember the identity:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

You can identify in the figure that for the angle 67°:

[tex]\alpha=67\°\\opposite=6\\adjacent=x[/tex]

Then you need to substitute these values into  [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for "x":

[tex]tan(67\°)=\frac{6}{x}\\\\xtan(67\°)=6\\\\x=\frac{6}{tan(67\°)}\\\\x=2.5[/tex]

Answer:

25 girls

Step-by-step explanation:

Let

x denote number of boys

and

y denote number of girls

According to the statement that total 45 people came,

x+y = 45      => Eqn 1

And total paid amount was 175

So,

5x + 3y = 175    => Eqn 2

For solving, We will use the substitution method

So, from eqn 1

x = 45-y

Putting value of x in eqn 2

5(45-y) +3y = 175

225 - 5y + 3y = 175

-2y+225 = 175

-2y = 175-225

-2y = -50

2y = 50

y = 25

Putting y =25 in eqn 1

x+25 = 45

x = 45 - 25

x = 20

As y= 25

So, 25 girls came to the dance ..

Answer:

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

Step-by-step explanation:

The given quadratic equation is:

[tex]\frac{4}{5}x^2=2x-\frac{4}{5}[/tex]

We multiply through by 5 to get:

[tex]4x^2=10x-4[/tex]

Rewrite in standard quadratic form;

[tex]4x^2-10x+4=0[/tex]

Or

[tex]2x^2-5x+2=0[/tex]

Split the middle term to get:

[tex]2x^2-4x-x+2=0[/tex]

Factor to get:

[tex]2x(x-2)-1(x-2)=0[/tex]

Factor further to get:

[tex](2x-1)(x-2)=0[/tex]

Either [tex](2x-1)=0[/tex] or [tex](x-2)=0[/tex]

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

Answer: b on edge 2020

Step-by-step explanation:

Answer:

2. The reasonable domain is restricted to positive real numbers.

Step-by-step explanation:

The variable "x" is time in years from when the experiment began. It makes no sense to have negative values of x, as the experiment had not yet begun in negative time.

___

I would include x=0 in the domain, too, though you already know the amount of remaining element at x=0 and don't have to use the function to calculate it.

__

x might be restricted to integers if you're only measuring the remaining amount once a year.

The maximum value of 1500 applies to the *range* of the function, not its domain.

The minimum value of 1500 has nothing to do with anything.

Answer:

B) the reasonable domain is restricted to positive real numbers

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

f=8

Step-by-step explanation:

Given,

6f=48

f=48/6

f=8

Verification:

6*8=48 ✓

Answer:

divide by six

f=8

8

Step-by-step explanation:

i just did the assiment

Answer:

Reflect over the y-axis

Step-by-step explanation:

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed).

Notice that B is 5 horizontal units to the right of the y-axis, and B' is 5 horizontal units to the left of the y-axis.

The reflection of the point (x,y) across

the y-axis is the point (-x,y).

Answer:

Step-by-step explanation:

-5x + 10 = 15y

(-5(x-2))/15

(-x+2)/3 = y

5x - 10((-x+2)/3)

5x - ((-10x + 20)/3)=-40

5x + (10x-20)/3

15x + 10x - 20 = -120

25x = -100

x = -4

5x + 15y = 10

-20 + 15y = 10

30 = 15y

y = 2

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}5x+15y=10\\5x-10y=-40&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}5x+15y=10\\-5x+10y=40\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad25y=50\qquad\text{divide both sides by 25}\\.\qquad\qquad\boxed{y=2}\\\\\text{Put the value of y to the first equation:}\\\\5x+15(2)=10\\5x+30=10\qquad\text{subtract 30 from both sides}\\5x=-20\qquad\text{divide both sides by 5}\\\boxed{x=-4}[/tex]