Which expression gives the distance between the points (4,6) and (7,-3)

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]

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

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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!!!

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

4^(x- 3) = 18

ln[4^(x- 3)] = ln(18)

ln4(x - 3) = ln(18)

ln4x - ln4(3) = ln18

ln4x = ln18 + 3ln4

x = [ln18 + 3ln4]/ln4

x = 5.0849625007

x is approximately 5.085.

To solve the equation 4^x - 3 = 18, isolate the exponential term, take the logarithm of both sides, apply the power rule, and then divide to solve for x. The solution to the nearest thousandth is x ≈ 2.416.

To solve the equation 4^x - 3 = 18, first add 3 to both sides of the equation to isolate the exponential term:

4^x = 18 + 3

4^x = 21

Now, take the logarithm of both sides. You can use any logarithm base, but it's most common to use either the natural logarithm (ln) or the common logarithm (log base 10). For this example, we'll use the common logarithm.

log(4^x) = log(21)

Using the power rule for logarithms, which states that log(a^b) = b * log(a), you can write:

x * log(4) = log(21)

Now, divide both sides by log(4) to solve for x:

x = log(21) / log(4)

Use a calculator to find the value of x. Be sure to round your answer to the nearest thousandth, as the problem instructs. The answer comes out to:

x ≈ 2.416

This value of x solves the original equation when rounded to the nearest thousandth.

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]

Answer:

you would first have a straight, increasing line with a small slope. (walking slowly and consistently)

then you have a flat, straight line (not moving as you pet the kitten)

then you have a big, increasing slope (running fast)

then it's straight line again(distance doesnt change at friend's house)

and then a decreasing line with pretty big slope all the way to the x axis(running home)

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:

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:

monomial

Step-by-step explanation:

because it has one variable which in this case is b and one number in this case is 10

Answer:

MONOMIAL

Step-by-step explanation:

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:

-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:

Step-by-step explanation:

The graph of g(x) is the same as that of f(x), EXCEPT that the graph of f(x) has been translated upward by 2 units.

The function is added and with a positive number so the function will shift towards the left , Option D is the correct answer.

A function can be defined as an algebraic expression which states relation between an independent and a dependent variable.

A function always comes with a defined range and domain.

It is given in the question that

There are two functions

g(x), f(x)

and they are related as

g(x)=f(x)+2.

and it has been asked that which statement given in the option describes it the best.

A. The graph of g(x) is the graph of f(x) shifted 2 units to the right.

B.The graph of g(x) is the graph of f(x) shifted 2 units down.

C.The graph of g(x) is the graph of f(x) shifted 2 units up.

D. The graph of g(x) is the graph of f(x) shifted 2 units to the left.

When a function is added , subtracted or multiplied it shifts or translates, and the new function is called the translated function

As the function is added and with a positive number so the function will shift towards the left.

Therefore , D is the answer the graph of G (x) is the graph of f(x) shifted 2 units to the left.

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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]

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.

Answer:

C

Step-by-step explanation:

Nice work using latex. I admire anyone who has skills with it.

It looks like this question can be grouped using to sets of brackets.

(4r^3 + 10r^2) : Pull out the common factor. 2r^2* (2r + 5)

The second set of brackets is a little bit tricker. Minus signs are not to be ignored.

(-10r - 25) : -5(2r + 5)

Now put both together,

2r^2(2r + 5) - 5(2r + 5)            

Notice that there is a common factor on either side of that isolated minus sign. The common factor is 2r + 5. Use the distributive property to pull it out.

(2r + 5)(2r^2 - 5)

It looks like C will be the answer.

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:

c) rad 3/2

Step-by-step explanation:

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

Answer: [tex]y=-\frac{5}{2}x-1[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Write the equation of the given line in Slope-Intercept form by solving for "y":

[tex]5x + 2y = 12\\\\2y=-5x+12\\\\y=-\frac{5}{2}x+6[/tex]

You can observe that the slope of this line is:

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

Since the slopes of parallel lines are equal, then the slope of the other line is:

 [tex]m=-\frac{5}{2}[/tex]

Now, substitute the slope and the point (-2, 4) into  [tex]y=mx+b[/tex] and solve for "b":

[tex]4=-\frac{5}{2}(-2)+b\\\\4=\frac{10}{2}+b\\\\4-5=b\\\\b=-1[/tex]

Then the equation of the line parallel to the given line is:

[tex]y=-\frac{5}{2}x-1[/tex]

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

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Answer:

Domain: All the real numbers

Range: All the real numbers

Step-by-step explanation:

The domain of a function is the complete set of possible values of the independent variable 'x'. That is to say, all the values that 'x' can take:

In this case, f(x)= 2x+1, the independent variable has no restrictions. Meaning that 'x' can take all the Real Values. In set notation: x∈ℝ.

The range of a function is the complete set of all possible resulting values of the dependent variable 'y'. In this case, given that the independent variable has no restrictions, the dependent variable 'y' can take any value. So, the range is: y ∈ ( −∞, ∞ ) - All the real numbers.

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

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)

let's notice the y-coordinate is the same for both points, thus is a horizontal line.

Check the picture below.

Answer:

Choice C)

[tex]\displaystyle \frac{g(7) - g(4)}{7 - 4} = \frac{5}{6}[/tex].

Step-by-step explanation:

The average rate of change of a function is:

[tex]\displaystyle \frac{\text{Change in Function Value}}{\text{Change in Independent Variable}}[/tex].

Note that [tex]\text{Change} = \text{Final Value} - \text{Initial Value}[/tex].

For this question,

As a result,

As a result,

The average rate of change in the value of [tex]g(x)[/tex] between [tex]x = 4[/tex] and [tex]x = 7[/tex] will be:

[tex]\displaystyle \frac{g(7)-g(4)}{7 - 4}[/tex].

Answer: the graph decreases from left to right

Step-by-step explanation:

because the price over time is getting cheaper the graph will decrease from 0 onward

(pls mark me the brainliest)

Answer:

The graph decreases from left to right.

Step-by-step explanation:

Given,

The original cost of the straw, P = $ 150.00,

The rate of decreasing per year, r = 1.5% = 0.015

Thus, the price after x years,

[tex]C(x)=P(1-r)^x[/tex]

[tex]\implies C(x) = 150(1-0.015)^x=150(0.985)^x[/tex]

Which is an exponential function,

∵ An exponential function [tex]f(x) = ab^x[/tex] has,

Decay : if 0 < b < 1,  ( decreasing from left to right )

Growth : if b > 1,  ( increasing from left to right )

Since, 0.985 < 1

Thus, the graph is decreasing from left to right,

if x = 2,

C(2) = [tex]150(0.985)^2[/tex] = 145.53375 ≠ 147.75,

I.e. (2, 147.75) does not lie on the graph,

If x = 3,

C(3) = [tex]150(0.985)^3[/tex] = 143.35 ≠ 141.20

i.e. (3, 141.20) does not lie on the graph.

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:

[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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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: