Which expression could be used to calculate the length, in feet, of the rectangle?

Answer:

X * (X +1) = 420

X^2 + X = 420

X^2 + X -420 = 0

X = 20

Step-by-step explanation:

For this case we have [tex]20 * 21 = 420.[/tex] We must find an equation that allows us to find the smallest value. So:

Let "x" be the variable that represents the smallest number. Thus, "x + 1" represents the consecutive integer. The equation would be given by:

[tex]x * (x + 1) = 420\\x ^ 2 + x = 420\\x ^ 2 + x-420 = 0[/tex]

To factor, we must find two numbers that multiply as a result -420 and sum as a result 1.

These numbers are:

[tex]21, -20\\21-20 = 1\\21 * (-20) = -420[/tex]

Thus, the factorization is:

[tex](x-20) (x + 21) = 0[/tex]

The roots are:

[tex]x = 20\\x = -21[/tex]

Effectively, the smallest integer was found,[tex]x = 20[/tex].

Answeer:

[tex]x ^ 2 + x-420 = 0\\(x-20) (x + 21) = 0[/tex]

125x=10y.

That is my best shot, I'm sorry lol.

x = total number of candies

[tex]\bf \stackrel{\textit{my brother}}{\cfrac{1}{5}x}+\stackrel{\textit{my friend}}{\cfrac{1}{4}x}+11~~=~~\stackrel{\textit{total}}{x} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{x}{5}+\cfrac{x}{4}+11 \right)=20(x)}\implies 4x+5x+220=20x\implies 9x+220=20x \\\\\\ 220=11x\implies \cfrac{220}{11}=x\implies 20=x~\hspace{10em}\stackrel{\textit{to my brother}}{\cfrac{20}{5}\implies 4}[/tex]

Answer:

y = - 4x - 13

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 4, thus

y = - 4x + c ← is the partial equation of the line

To find c substitute (- 2, - 5) into the partial equation

- 5 = 8 + c ⇒ c = - 5 - 8 = - 13

y = - 4x - 13 ← equation of line

The equation of the line with slope -4 passing through the point (-2, -5) is y = -4x - 13.

To find the equation of a line with a given slope that passes through a specific point, you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. In this case, the slope is -4 and the line passes through the point (-2, -5). Plugging these values into the point-slope form, the equation becomes y - (-5) = -4(x - (-2)), which simplifies to y + 5 = -4(x + 2). Expanding the right side gives y + 5 = -4x - 8. To solve for y, subtract 5 from both sides to get y = -4x - 13.

Answer:

For the graph, 111 is the: y-intercept

In the situation, it represents the hiker's: starting distance

11 is the: slope

It represents the hiker's: speed

Hope this helped C:

The question pertains to the physics of a hiker ascending and descending a mountain, considering potential energy changes and work done by the hiker. The scenario's analysis includes calculations of potential energy at various altitudes relative to sea level, given the hiker's mass.

The scenario involves a hiker ascending and descending a mountain, which can be analyzed from a physics perspective, particularly focusing on potential energy, work, and energy conservation. The hiker's journey begins at 200 m above sea level, progresses to an overnight hut at 800 m, descends to another hut at 500 m, and finally returns to the starting point. The mass of the hiker is given as 70 kg.

When the hiker ascends to a height of 800 m, she gains potential energy, which can be calculated using the formula Potential Energy (PE) = mass (m) × gravity (g) × height (h). Therefore, the increase in potential energy when reaching the first hut is:

PE = 70 kg × 9.8 m/s2 × (800 m - 200 m)

Similarly, when descending to the second hut, the hiker loses some potential energy. Finally, upon returning to the starting point, the hiker's potential energy returns to its initial value, assuming the starting point is the reference level of potential energy.

The exercise involved in hiking up and down the mountain also involves work done against the force of gravity and could be discussed in terms of energy expended by the hiker.

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Answer:

option A

The base is e^-1

Step-by-step explanation:

Given in the question a function, f(x) = (1/e)[tex]^{x}[/tex]

This function can also be write as.

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

by using Negative Exponent Rule

[tex]x^{-n}=\frac{1}{x^{n}}[/tex]

This says that negative exponents in the numerator get moved to the denominator and become positive exponents.

Answer:

8.46

Step-by-step explanation:

59+6=65 65 divided by 508= 7.815 (7.82) 6 divided by 508=84.666 (8.67) then subtract 8.67 from 508 = 499.33 divided by 59 = 8.46 thats your answer.

Answer:

$8

Step-by-step explanation:

x=chaperone tickets

59(x+2)+6x=508

59x+118+6x=508

65x+118=508

65x=508

x=6

therefore 6+2=8

Answer:

A

Step-by-step explanation:

That the answer Plss follow me thanks

The equivalent expressions for the perimeter of a square whose side length is represented by the expression n -1.5 are A and F, specifically: n + n + n + n - 1.5 - 1.5 - 1.5 - 1.5 and 4(n - 1.5)

The length of a side of a square is given by the expression n - 1.5. The perimeter of a square is calculated by adding up all its four sides. Hence, in this case, the perimeter would be (n - 1.5) + (n - 1.5) + (n - 1.5) + (n - 1.5). Perform the addition to get 4n - 6, simplifying to 4(n - 1.5). From the provided options, the equivalent expressions for the perimeter of the square are A and F, that is, n + n + n + n - 1.5 - 1.5 - 1.5 - 1.5 and 4(n - 1.5).

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Answer:

focus point of  satellite is (-125,-3)

Step-by-step explanation:

The question is on finding the focus point of a parabola

Given y²+6y-3x+3=0

Rewrite the equation

y²+6y=3x-3

Complete square on both sides

y²+6y+9=3x-3+9

Factorize

(y+3)²= 3x+6---------------------------------------(a)

(y+3)²= 3(x+2)

Compare  equation (a) to standard equations for parabola

(y+3)²= 3(x+2)

(y-b) ²= 2p(x-a),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(b)

2p=3------------divide both sides by 2

p=3/2

Vertex (a,b)=( -2,-3)........from equation (b)

Focus point is given by  (a+p/2 , b)...........................(c)

Substitute values in equation c above;

(-2+3/4 , -3) = (-5/4 ,-3) =(-1.25, -3)

Answer:

Step-by-step explanation:

We have four congruent triangles with base b = 16cm and height h = 12cm.

The formula of an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A=\dfrac{(16)(12)}{2}=(8)(12)=96\ cm^2[/tex]

The latearal area:

[tex]L.A.=4A\to L.A.=4(96)=384\ cm^2[/tex]

For the surface area we need the area of a base.

The base is a square with side a = 16cm.

The area of the base:

[tex]B=16^2=256\ cm^2[/tex]

The surface area:

[tex]S.A.=L.A.+B\to S.A.=384+256=640\ cm^2[/tex]

Notice that 242 = 4*60.5. This means after 242 minutes, the sample decays to [tex]\dfrac1{2^4}=\dfrac1{16}[/tex] of its original amount. So you end up with

[tex]\dfrac{100\,\mathrm g}{16}=\boxed{6.25\,\mathrm g}[/tex]

After 242 minutes, 6.25 grams of Bismuth-212 remain from an original 100-gram sample, calculated based on its half-life of 60.5 minutes through the concept of radioactive decay.

The question involves calculating the amount of Bismuth-212 left from a 100-gram sample after 242 minutes, given its half-life of 60.5 minutes. To find the amount of Bismuth-212 remaining, we use the formula for radioactive decay which involves dividing the total time by the half-life to determine the number of half-lives that have passed.

First, calculate the number of half-lives passed:
Number of half-lives = Total time / Half-life = 242 minutes / 60.5 minutes = 4

Next, calculate the remaining amount after each half-life. After 1 half-life, 50 grams remain; after 2 half-lives, 25 grams; after 3 half-lives, 12.5 grams; and after 4 half-lives, 6.25 grams remain.

Therefore, 6.25 grams of Bismuth-212 remains after 242 minutes.

Answer:

(n+4)(n+5)

Step-by-step explanation:

Answer:

(n + 4)(n + 5)

Step-by-step explanation:

to factor n² + 9n + 20, we need to find 2 numbers that when multiplied together equal 20 and when added together equal 9

these two numbers are 4 and 5 so the factorization looks like this:

(n + 4)(n + 5) < you can FOIL this out to check if the solution is correct, and you would get: n² + 9n + 20

Answer:

It is the secon option ∆TRS ≈ ∆TPQ ; SAS

Step-by-step explanation: angle t is equal to angle t because it is the same angle

line TR divided by line TP is equal to line TS divided by TQ

Answer:  The correct option is

[tex](B)~\triangle TRS\sim \triangle TPQ,~SAS\sim.[/tex]

Step-by-step explanation:  We are given to check whether the triangles in the figure are similar or not. If so, we are to state the similarity statement.

From the figure, we note that

in the triangles TPQ and TRS, we have

[tex]TP=42,~TQ=28,TR=42+6=48,~~TS=28+4=32.[/tex]

Therefore, the ratios of the corresponding sides of two triangles are

[tex]\dfrac{TP}{TR}=\dfrac{42}{48}=\dfrac{7}{8},\\\\\\\dfrac{TQ}{TS}=\dfrac{28}{32}=\dfrac{7}{8}.[/tex]

Now, in ΔTPQ and ΔTRS, we have

[tex]\dfrac{TP}{TR}=\dfrac{TQ}{TS},\\\\\\m\angle TPQ=m\angle TRS~~~\textup{[common angle]}[/tex]

So, triangles TPQ and TRS are similar by SAS proportionality postulate.

Thus, the correct option is

[tex](B)~\triangle TRS\sim \triangle TPQ,~SAS\sim.[/tex]

Answer:

76 mL

Step-by-step explanation:

40*19/10

40*19= 760 / 10 = 76mL

the correct answer is A. 316.7 mL.

The question involves calculating the fluid volume that a 19 kg dog would receive if fluids were administered at a rate of 40 mL/kg/day. Here is the step-by-step calculation:

Therefore, the correct answer is A. 316.7 mL.

Answer:

Inequality: 50-1.99x=30

She has 10 days.

Step-by-step explanation:

So, she starts off with with $50. From there, she is buying songs that are $1.99 (everyday). You could do this multiple ways:

Guess and Check, or use Algebra.

But for Algebra:

If we graph this out, the y intercept would be (0, 50), because she is starting out with $50. From there, she is spending 1.99 each day, so the slope would be 1.99/1. So basically, we would write this as 50-1.99x (that is the expression).

We would also set this equal to 30, because we are trying to see how many days it would take to still keep her balance above $30, but make it as close to 30 as possible. (x represents the # of days.

So the inequality would be 50-1.99x=30

And, when we isolate the variable and solve, we would see that she can buy a total of 10 songs over 10 days. (So basically, she has 10 days to stay over $30).

Sarah can use her $50 gift card to download a $1.99 song for 10 full days before her balance falls below $30. This is found by solving the inequality 50 - 1.99d > 30, which indicates the maximum days she can download with the card's balance staying above the threshold.

Sarah's problem can be represented by an inequality that describes the number of $1.99 song downloads she can make before her $50 music gift card drops below $30. To find out how many days she can continue to download a song without going below a $30 balance, we'll represent the number of days as d, and the cost per day as $1.99.

The inequality will be: 50 - 1.99d > 30.

Step 1: Subtract 50 from both sides to isolate the term with d.

-1.99d > -20

Step 2: Since we're dealing with a negative coefficient for d, divide both sides by -1.99, and flip the inequality sign (a rule when dividing by a negative).

d < 20/1.99

d < 10.05

Since Sarah can't download a fraction of a song, she can download a song for full days without the balance going below $30 for 10 days.

Therefore, Sarah can download a song for 10 full days with the balance of her gift card staying above $30. After that, her balance would drop below $30 if she continues.

The whole circle is 360 degrees. So cut the circle in half and BDC=180

To find the measure of arc BDC, use the triangulation measurements and the angular displacements ZBOC and ZDOC. Apply geometric principles and the law of sines, then relate the arc's angle to the circle's circumference to approximate the arc measure.

To find the measure of arc BDC, we must consider the geometrical properties of circles and triangles mentioned in the provided information. Since the arc length for a small part of the circle can be approximated as equal to the straight-line segment, we can use this approximation along with the given relationships to solve for the arc BDC measurement.

First, establish a second control point (B) in a triangulation network and measure the interior angles at points A, B, and C. The 'law of sines' can be used to determine lengths of the sides of the triangles formed. Once you have the lengths AC and BC, you can measure CD and BD to fix point D in a coordinate system.

This geometric consideration allows us to construct right triangles and use the Pythagorean theorem to find missing lengths. To calculate the measure of arc BDC, we can add the displacement angles (ZBOC and ZDOC) which can be found by using the angular displacement values between 2 and 2.5 seconds, and between 2.5 and 3 seconds. Using these angles and the lengths of segments BC, CD, and BD, we can apply the principle that in a circle, the ratio of the arc's length to the circumference is equal to the ratio of the angle to 360 degrees.

Answer:

14 in

Step-by-step explanation:

Does it want me to explain what the in.cm,mm,m are or what id it in its

The net of cube has 6 identical squares with side 14 units.

Net diagram is a 2-dimensional plane figure which can be folded to form a 3-dimensional figure. Or we can say net diagrams are the figures which obtained by unfolding some 3D figures.

Given that, the cube with edges 14 units.

A solid shape with six square faces is called a cube. Because every square face has the same side length, each face is the same size. A cube has 8 vertices and 12 edges. An intersection of three cube edges is referred to as a vertex.

The net of cube has 6 squares

Therefore, the net of cube has 6 identical squares with side 14 units.

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The equation that can be used to solve for b is Tan (30)= 5/b.

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The equations that can be solved for 'b' are 'Tan (30)= 5/b' and 'Tan (30) = 10/b', resulting in solutions 'b = 5/Tan(30)' and 'b = 10/Tan(30)' respectively.

The equations that can be used to solve for 'b' are Tan (30)= 5/b and Tan (30)=10/b. To solve for 'b' in these scenarios, you would rearrange the equations to isolate 'b'. For example, in the first equation, multiplying both sides by 'b' and then dividing by Tan(30) would give you 'b = 5/Tan(30)'. In the second scenario, 'b = 10/Tan(30)'. These are the solutions for 'b' and indicate the values 'b' would need to be for the equations to hold true.

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Answer:

(4, 7)

Step-by-step explanation:

The midpoint formula is (((x1 + x2)/2), ((y1+y2)/2)))

x1 +x2 = 1 +7 = 8

8/2 = 4

y1 + y2 = 10 + 4 = 14

14/2 = 7

(4, 7) is the midpoint

Answer:

M = (4, 7)

Step-by-step explanation:

Using the midpoint formula

M = [[tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

with (x₁, y₁ ) = P(1, 10) and (x₂, y₂ ) = Q(7, 4)

M = [ [tex]\frac{1}{2}[/tex](1 + 7), [tex]\frac{1}{2}[/tex](10 + 4) ] = (4, 7)

Answer:

10.4 cents

Step-by-step explanation:

40 pecans/$3.84 gives you pecans per dollar

Answer:

$4.60

Step-by-step explanation:

To find the amount of tax, multiply the number of gallons by the tax per gallon.

20*.23 = $4.60

Answer:

Less than 100. Z=83

Step-by-step explanation:

The mean is the average found by adding the sum of the data points and dividing by the number of them. Here there are 3 cars whose speeds are 101, 116, and Z or unknown. The mean of them is 100. Solve for Z.

100 =(101+116+Z)/3

300=217+Z

83=Z

Answer:

8 cm

Step-by-step explanation:

The circumference (C) of a circle is

C = π d  ← d is the diameter

Here C = 8π, hence

πd = 8π ( divide both sides by π )

d = [tex]\frac{8\pi }{\pi }[/tex] = 8 cm

A circle is a curve sketched out by a point moving in a plane. The diameter of the circle whose circumference is 8π cm is 8cm.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The circumference of a circle is given by πD, where D is the diameter. Now, the circumference can be written as,

Circumference of the circle = πD

8π cm = πD cm

D = 8 cm

Hence, the diameter of the circle whose circumference is 8π cm is 8cm.

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Answer:

Slope = 1/5

Step-by-step explanation:

passing through points A(5,4) and B(0,3)

Slope = (4 - 3)/(5 - 0) = 1/5

Answer:

I think it’s C

Step-by-step explanation:

The answer would be B, Supplementary Angle, Since half the circle would be 180 degrees also if this isn’t enough information,

C= equilateral triangle

To find this answer we need to know what a cube is. A cube is a prism whose sides all have the same length. It's something like the three dimensional version of a square. In the figure below, we have labeled each length of the cube as [tex]x[/tex]. Also, the vertex we taken is in blue color, so we need to find each side length of the triangle. Since the cross section passes through the midpoints of three edges that intersect at the same vertices of the cube, then:

[tex]L_{1}=\sqrt{(\frac{x}{2})^2+(\frac{x}{2})^2} \\ \\ L_{1}=\sqrt{\frac{x^2}{4}+\frac{x^2}{4}} \\ \\ L_{1}=\sqrt{\frac{2x^2}{4}} \\ \\ L_{1}=\sqrt{\frac{x^2}{2}} \\ \\ L_{1}=\frac{x}{\sqrt{2}} \\ \\ L_{1}=\frac{x}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \\ \\ L_{1}=\frac{\sqrt{2}x}{2}[/tex]

Since this is a cube, then it is true that:

[tex]L_{1}=L_{2}=L_{3}=\frac{\sqrt{2}x}{2}[/tex]

Since the side lengths have the same value, this is an equilateral triangle.

Answer:

y = 11.2 in

Step-by-step explanation:

Given a tangent and a secant from an external point to a circle, then

The square of the measure of the tangent is equal to the product of the external part and the entire secant, that is

5(5 + y) = 9²

25 + 5y = 81 ( subtract 25 from both sides )

5y = 56 ( divide both sides by 5 )

y = 11.2

Answer: y = 11.2

Step-by-step explanation:

Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (8, 1) and (x₂, y₂ ) = (24, 9)

m = [tex]\frac{9-1}{24-8}[/tex] = [tex]\frac{8}{16}[/tex] = [tex]\frac{1}{2}[/tex]

Divide the number of wooden cabinets by the number of days.

24 / 8 = 3

Carlos installed an average of 3 cabinets each day.

To find the average number of cabinets installed each day, we divide the total number of cabinets installed by the number of days. In this case, Carlos installed 24 cabinets in 8 days, so we divide 24 by 8 to get an average of 3 cabinets installed each day.

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Answer:

-5 and 2

Step-by-step explanation:

Apexvs

Answer:

-5 and 2

Step-by-step explanation:

Apex