If the following ordered pairs are equal find x and y
a) (3x+4y, 10) and (20, 40-3y)​

Answer:

If you mean 2 and 3 it would be (x-2)(x-3)=0

Step-by-step explanation:

(x-2)=0

x-2=0 move the two on the other side to get positive

x=2

(x-3)=0

x-3=0 move the three on the other side to get positive

x=3

Final answer:

To find the greatest possible width of the rectangle, set up an equation based on the given information and solve for the width.

Explanation:

The greatest possible value for the width of the rectangle can be calculated by setting up an equation based on the given information.

Let the width be 'w'.

Since the length is three times the width, the length is '3w'.

The perimeter of a rectangle is twice the sum of its length and width. So, 2(3w + w) ≤ 112.

Solving this inequality gives the maximum width as 14 cm.

Answer:

Step-by-step explanation:

b

Answer:

Step-by-step explanation:

Remember that the solution of a linear system of equations is shown by the interception point between those lines.

In this case, the interception point is at (2,3).

Also, the horizontal line is [tex]y=3[/tex]. Notice that the solution are is below this line, that means the inequality that represents that part is [tex]y\leq 3[/tex].

Now, the other line has y-intercept at -1, that means [tex]b=-1[/tex].

Then, we use two points (0,-1) and (2,3) to find its slope.

[tex]m=\frac{3-(-1)}{2-0}=\frac{4}{2}=2[/tex]

So, the equation that represents that line is [tex]y=2x-1[/tex].

Notice that the area of solution is above this line, that means the inequality is

[tex]y>2x-1[/tex]

Therefore, the sytem that represents the graph is

[tex]y>2x-1\\y\leq 3[/tex]

Notice that we used [tex]\leq[/tex] for the solid line and [tex]>[/tex] for the not solid line.

Final answer:

The most helpful form to determine the time for the ball to hit the ground is Option A, h(t) = -16(t - 3)(t + 1), as it is already in factored form, making it easy to find the positive root, which represents the time when the ball would hit the ground.

Explanation:

When attempting to determine the time required for the ball to hit the ground in a quadratic model, we are essentially looking for the time when the height of the ball, h(t), is zero. To find this, we need to find the roots of the quadratic equation. Function A, h(t) = -16(t - 3)(t + 1), is already factored, which makes finding the roots straightforward. When dealing with quadratic equations, remember that negative time values do not make sense in this context, so we are only interested in the positive root.

The most helpful form for this task would therefore be Option A, h(t) = -16(t - 3)(t + 1), as the roots can be easily read from the factored form, which directly gives the times when the ball reaches the ground level without further calculation. In this case, the positive root t = 3 seconds represents the time when the ball would hit the ground. Ignoring the root t = -1 because time cannot be negative.

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

4x - 3y = 34 → (1)

3x + 2y = 17 → (2)

Multiply (1) by 2 and (2) by 3 to eliminate the term in y

8x - 6y = 68 → (3)

9x + 6y = 51 → (4)

Adding (3) and (4) term by term allows x to be found

17x = 119 ⇒ x = 7

Answer:

the answer is C

Step-by-step explanation:

Answer:

3rd choice

Step-by-step explanation:

In division for variables with same base, you do subtract top exponent minus bottom exponent. She did that correctly since -3-(-1)=-3+1=-2 and -2-1=-3.  

The problem said m=-2 and n=4 and she replace m with (-2) and n with (4). She did this correctly.

You can multiply base numbers unless the exponents are the same 4 doesn't have the exponent -2 on it so you can't do (4(-2))^(-2)

The error is the 3rd option.

We start with

[tex]\dfrac{4m^{-3}n^{-2}}{m^{-1}n}[/tex]

Simplifying the exponents, we have

[tex]\dfrac{4m^{-3}n^{-2}}{m^{-1}n} = 4m^{-3}n^{-2} (mn^{-1}) = 4m^{-3+1}n^{-2-1}=4m^{-2}n^{-3}[/tex]

So, the exponents are ok.

If we plug the values, we have

[tex]4m^{-2}n^{-3} \mapsto 4(-2)^{-2}(4)^{-3} = 4\cdot \dfrac{1}{(-2)^2}\cdot\dfrac{1}{4^3} = 4\cdot \dfrac{1}{4}\cdot \dfrac{1}{64} = \dfrac{1}{64}[/tex]

So, she didn't apply the exponent -2 correctly.

Check the picture below.

so we can simply use the pythagorean theorem for each triangle and get "w" and "z".

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{15^2-13^2}=w\implies \sqrt{225-169}=w\implies \sqrt{56}=w\implies 7.48\approx w \\\\\\ \sqrt{10^2-4^2}=z\implies \sqrt{100-16}=z\implies \sqrt{84}=z\implies 9.17\approx z \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{w+z}{16.65}~\hfill[/tex]

Applying the Pythagorean Theorem, the approximate distance in feet, between the two poles is: b. 16.65 feet

Recall:

For a right triangle where c is the hypotenuse and a and b are the other legs of the right triangle, the Pythagorean Theorem states that: c² = a² + b².

The distance between the two poles = BC + DC

Given:

Apply the Pythagorean Theorem to find BC and DC respectively.

Length of BC:

BC = √(AC² - AB²)

BC = √(15² - 13²)

BC = 7.48 feet

Length of DC:

DC = √(EC² - ED²)

DC = √(10² - 4²)

DC = 9.17 feet

The distance between the two poles = 7.48 + 9.17 = 16.65 feet

Learn more about Pythagorean Theorem on:

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Answer:

[tex]future \: value \: minus \: interest[/tex]

Present value is not equal to any of the given options. It is the current value of a future sum of money, considering the time value of money and interest rate.

The correct definition of present value is None of the above. Present value refers to the current value of a future sum of money, taking into account the time value of money and the interest rate. It is calculated using the formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

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The answers are:

[tex]Hypothenuse=28ft+7ft=35ft\\LongerLeg=28ft\\ShorterLeg=28ft-7ft=21ft[/tex]

Since we are working with a right triangle, we can use the Pythagorean Theorem, which states that:

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

Then, we are given the following information:

Let be "a" the shorter leg and "b" the the longer leg of the right triangle, so:

[tex](7ft+b)^{2}=(b-7)^{2}+b^{2}[/tex]

We can see that we need to perform the notable product, so:

[tex](7ft+b)^{2}=(b-7ft)^{2}+b^{2}\\\\7ft*7ft+2*7ft*b+b^{2}=b^{2}-2*7ft*b+7ft*7ft+b^{2}\\\\49ft^{2} +14ft*b+b^{2}=b^{2}-14ft*b+49ft^{2}+b^{2}\\\\49ft^{2} +14ft*b+b^{2}=-14ft*b+49ft^{2}+2b^{2}\\\\-14ft*b+49ft^{2}+2b^{2}-(49ft^{2} +14ft*b+b^{2})=0\\\\-28ft*b+b^{2}=0\\\\b(-28ft+b)=0[/tex]

We have that the obtained equation will be equal to 0 if: b is equal to 0 or b is equal to 28:

[tex]0(-28+0)=0[/tex]

[tex]28(-28+28)=28(0)=0[/tex]

So, since we are looking for the side of a leg, the result that we need its 28 feet.

Hence, we have that the answers are:

[tex]Hypothenuse=28ft+7ft=35ft\\LongerLeg=28ft\\ShorterLeg=28ft-7ft=21ft[/tex]

Have a nice day!

Answer:

Base = 21 ft

Height = 28 ft

Hypotenuse =  35 ft

Step-by-step explanation:

It is given that,the shorter leg of a right triangle is 7ft shorter than the longer leg. The hypotenuse is 7ft longer than the longer leg

Let longer leg = x then shorter leg  = x - 7 and hypotenuse = x+ 7

To find the side lengths of triangle

Here Base = x-7

Height = x

Hypotenuse = x + 7

By using Pythagorean theorem we can write,

Base² + height² = Hypotenuse²

(x - 7)² + x² = (x + 7)²

x² -14x + 49 + x² = x² +14x + 49

x² - 14x = 14x

x² - 28x = 0

x(x - 28) = 0

x = 0 or x = 28

Therefore the value of x = 28

Base = x - 7 = 21

Height = 28

Hypotenuse = 28 + 7 = 35

Answer:

The vertex is (1,-3)

Step-by-step explanation:

Just look for the numbers that make the inner parts 0. Here, x - 1 is 0 when x = 1 and y + 3 is 0 when y = -3.

Answer:

Step-by-step explanation:

Compare:

(y+3)^2=12(x-1)

(y - k)^2 = 12(x - h)

Here we see that k = -3 and h = 1.  Thus, the vertex of this horiz. parabola is (1, -3).  We know that this parabola is horiz. because it's y or y+3 that is squared, not x or x-1.

Answer:

The correct answer option is D. 168 units³.

Step-by-step explanation:

We are given a prism with known side lengths and we are to find its volume.

We know that the volume of a prism is given by:

Volume of prism = area of base × height

Here the base is a triangle so the base area will be:

Base area = 1/2 × base × height = 1/2 × 6 × 8 = 24  units²

Volume of prism = 24 × 7 = 168 units³

For this case we have that by definition, the volume of a prism is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

The base of the prism is a triangle, then:

[tex]A_ {b} = \frac {6 * 8} {2} = 24 \ units ^ 2[/tex]

Thus, the volume is:

[tex]V = 24 * 7\\V = 168 \ units ^ 3[/tex]

Now, the prism volume is [tex]168 \ units ^ 3[/tex]

Answer:

Option D

Answer: Second Option

5 to the power of 1 over 6

Step-by-step explanation:

The square root of the cubic root of 5 is written as follows

[tex]\sqrt[2]{\sqrt[3]{5}}[/tex]

Now use the following property of the roots

[tex]\sqrt[m]{\sqrt[n]{x}}=\sqrt[m*n]{x}[/tex]

In this case [tex]m = 2[/tex] and [tex]n=3[/tex] and [tex]x=5[/tex]

So we have that

[tex]\sqrt[2]{\sqrt[3]{5}}=\sqrt[2*3]{5}[/tex]

[tex]\sqrt[2*3]{5}=\sqrt[6]{5}[/tex]

Now use the following property

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

So we have that:

[tex]\sqrt[6]{5}=5^{\frac{1}{6}}[/tex]

The answer is the second option

5 to the power of 1 over 6

Answer:

5 to the power of 1 over 6

Step-by-step explanation:

Answer:

Its B. y^2 + 3y + 13x - 1

Step-by-step explanation:

It's easy add or subtract the like terms.

Hope my answer has helped you if not i'm sorry in advance.

Answer:

[tex]\boxed{6\sqrt{2 i}}[/tex]

Explanation:

[tex]\sqrt{-72}=\sqrt{-1}=\sqrt{72}[/tex]

[tex]\sqrt{-1} \sqrt{72}[/tex]

Then you apply imaginary number rule.

[tex]\sqrt{72 i }[/tex]

[tex]\sqrt{72}=6\sqrt{2}[/tex]

[tex]\boxed{6\sqrt{2 i}}\checkmark[/tex], which is our final answer.

Hope this helps!

Thanks!

Have a nice day! :)

-Charlie

Explanation on how to simplify the square root of a negative number.

Simplify the square root of -72: To simplify the square root of a negative number like -72, first rewrite it as the square root of 72 times the square root of -1. The square root of 72 can be simplified as 6√2, making the final answer 6i√2.

Answer:

The values of y are 1 , 2 , 5 , 10 ⇒ answer B

Step-by-step explanation:

* We will use the substitution method to solve the problem

- The quadratic equation is y = x² + 4x + 5

- The values of x are -2 , -1 , 0 , 1

- We will substitute the values of x in the equation to find the

  values of y

# At x = -2

∵ y = x² + 4x + 5

∵ x = -2

∴ y = (-2)² + 4(-2) + 5  = 4 - 8 + 5 = 1

∴ y = 1

# At x = -2

∵ y = x² + 4x + 5

∵ x = -1

∴ y = (-1)² + 4(-1) + 5  = 1 - 4 + 5 = 2

∴ y = 2

# At x = 0

∵ y = x² + 4x + 5

∵ x = 0

∴ y = (0)² + 4(0) + 5  = 0 + 0 + 5 = 5

∴ y = 5

# At x = 1

∵ y = x² + 4x + 5

∵ x = 1

∴ y = (1)² + 4(1) + 5  = 1 + 4 + 5 = 10

∴ y = 10

* The values of y are 1 , 2 , 5 , 10 ⇒ from left to right

dlqndpQAI:?s

Step-by-step explanation:

Konichiwa~! My name is Zalgo and I am here to help you out on this great day. Hmm, how do you define slope... Well, the slope or "gradient" of a line is a number that describes both the steepness and direction of the line itself. Now, slope is "a surface of which one end or side is at a higher level than another; a rising or falling surface".

I hope that this helps you! :P

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me Brainliest? I'd greatly appreciate it! Arigato~! X3)

Answer:

h(9) = 62

Step-by-step explanation:

Equate 8x - 10 = 62 and solve for x

8x - 10 = 62 ( add 10 to both sides )

8x = 72 ( divide both sides by 9 )

x = 9

That is h(9) = 62

Answer:

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{We have the equation:}\ f(x)=-\dfrac{2}{3}x+\dfrac{1}{3}\to y=-\dfrac{2}{3}x+\dfrac{1}{3}\\\\the\ slope:\ m=-\dfrac{2}{3}\\\\the\ y-intercept:\ b=\dfrac{1}{3}[/tex]

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})~\hspace{10em} slope = m\implies 6 \\\\\\ \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-(-3)=6[x-(-1)]\implies y+3=6(x+1) \\\\\\ y+3=6x+6\implies y=6x+3\implies -6x+y=3\implies 6x-y=-3[/tex]

Answer:

Cube

Step-by-step explanation:

Im not sure what the option choices are but a cube has 6 faces. :)

Answer:

hexahedron

Step-by-step explanation:

Answer:

c) rad 3/2

Step-by-step explanation:

If Cos 30° equals rad 3/2 then the sin 60° equals rad 3/2.

0.625 cannot be rounded to the nearest whole number.

However it may be round to the hundredth which in this case would be 0.62

If you want to round it to the tenth then you could round it to 0.6

The reason to why you cannot round 0.625 to the nearest whole number is because it is still a decimal and does not have a whole number to round up too.

Hope this helps! :3

The solution after round it to the nearest whole number is, 1

We have to given that,

A number is,

⇒ 0.625

Since, Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value.

Now, We can round it to the nearest whole number as,

⇒ 0.625

⇒ 1

Thus, The solution after round it to the nearest whole number is, 1

Learn more about the rounding number visit:

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Answer:

No

Step-by-step explanation:

We are given the following equation of a function and a table for the corresponding values of this function:

[tex]y=390+11(x)[/tex]

We are to determine if the equation and the table represent the same function.

To check that, we will substitute the value of x in the equation to see if it gives the same values of y as in the table.

[tex]y=390+11(-30)[/tex] ---> (-30, 60)

[tex]y=390+11(-28)[/tex] ---> (-28, 82)

[tex]y=390+11(-26)[/tex] ---> )-26, 104)

Since these paired values differ from the ones given in the table. Therefore, table and equation do not represent the same function.

NOOOO the answer is no now just trust me and get your free answer boom..

Answer:

- 120

Step-by-step explanation:

-2 x² + 8 x = 0

x = - 6

Substitute x = - 6 into -2 x² + 8 x = 0

- 2 x² + 8 x = 0

- 2 × ( - 6² ) + 8 × ( - 6 ) = 0

( - 2 × 36 )  + ( 8 × -6) = 0

- 72 + ( - 48 ) = - 120

Answer:

-7

Step-by-step explanation:

The coordinates of the point wich divide the segment AB, where [tex]A(x_A,y_A),\ B(x_B,y_B)[/tex] in ratio [tex]m:n[/tex] can be calculated using formula

[tex]C\left(\dfrac{nx_A+mx_B}{m+n},\dfrac{ny_A+my_B}{m+n}\right)[/tex]

In your case,

[tex]A(-4,-10)\\ \\B(-11,-7)\\ \\m:n=3:4\Rightarrow m=3,\ n=4[/tex]

Hence,

[tex]C\left(\dfrac{4\cdot (-4)+3\cdot (-11)}{3+4},\dfrac{4\cdot (-10)+3\cdot (-7)}{3+4}\right)\\ \\C\left(-\dfrac{49}{7},-\dfrac{61}{7}\right)\\ \\C\left(-7,-\dfrac{61}{7}\right)[/tex]

Therefore, x-coordinate of the point that divides AB into a 3:4 ratio is -7.

Answer:

x < 3

Step-by-step explanation:

Given

x - 5 < - 2 ( add 5 to both sides )

x < 3

Answer:

x < 3

Step-by-step explanation:

The points in inequalities like these is to get x by itself. This being said, since 5 is being subtracted from x, we need to add 5. Whenever you do this, you need to add to both sides. The 5 being added to the -5 will cancel out. -2+5 is 3. Now the equation remains as x < 3

Hope this helps!!!

Answer:

The function has a domain of all real numbers.

The function is a reflection of y =³√x.

Step-by-step explanation:

1. The function is always increasing. - False

(Taking a cube root makes the number smaller so the domain of the function should be decreasing)

2. The function has a domain of all real numbers. - True

The cube root of real number is also real so the minus sign would not result in an imaginary number as it is outside the radical.

3. The function has a range of {y |– ∞ < y < ∞ }. - False

4. The function is a reflection of y =³√x. - True

5. The function passes through the point (3, –27). - False

(these coordinates do not satisfy the function)

Answer:

The best estimate for the solution of the system of equations is the ordered pair (7, 0.5)

Step-by-step explanation:

The way to solve this problem is to take a deep look into the picture, where we can see that the interception between the lines occurs right in x=7. thus, eliminating the first choice.

Next, we can see that the interception is somewhere far from the 'x' axis, hence 'y' variable can not be zero in this point.

Thus, we have our possible solution, without knowing anything else, the ordered pair (7, 0.5).

Remember, a system of equation has a solution when an interception occurs between its equations

ANSWER

[tex] \frac{5a}{3} [/tex]

EXPLANATION

The given fractions are:

[tex] \frac{{a}^{3} + {a}^{2} b}{5a} \times \frac{25}{3b + 3a} [/tex]

We factor to obtain:

[tex]\frac{{a}^{2}(a + b)}{5a} \times \frac{25}{3(a + b)} [/tex]

We cancel the common factors to get:

[tex]\frac{{a}(1)}{1} \times \frac{5}{3(1)} [/tex]

We multiply the numerators and also multiply the denominators to get:

[tex] \frac{5a}{3} [/tex]

Therefore the two fractions simplifies to [tex] \frac{5a}{3} [/tex]