A landscaping business is purchasing plants from a nursery to finish a project. It will
cost $14 each to buy each tree and $7 each to buy each bush. The landscaper wishes to
keep the spending to no more than $870. Let t be the number of trees and b be the
number of bushes.
Select the inequality that describes the situation.
14t+7b> 870
O 14t+ 76 2 870
O 14t+7b < 870
O 14t+7b ≤ 870

The triangles are similar as follows:

ABC ~ DEF

The criteria is AA(angle angle)

Similar triangles are the triangles that have corresponding sides as a ratio of each other and corresponding angles congruent to each other.

Therefore, the corresponding angles of the triangles are suppose to be congruent and the corresponding sides in proportion for it to be similar.

Hence, If two triangles have two of their angles equal, the triangles are similar by AA(angle angle).

Therefore, the triangles are similar by AA.

Triangle ABC is similar to triangle DEF.

The criteria for the similarity is AA.

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However, the recent 2022 Social Security Trustees report finds that in 2034, retirees will start receiving a reduced benefit if Congress doesn't fix funding issues for the social program. In other words, Social Security will exist after 2034, but retirees will only receive 77% of their full benefit starting then.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{4 }{ 5 }\implies \cfrac{\$ 4}{5~apples}\implies \cfrac{0.8}{1}~\cfrac{\$}{apples}~\hfill \textit{80 cents per apple}[/tex]

The people that have posted the meme after 8 days using the exponential equation y=t^3 will be 512.

What are Exponential Equations?

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 62^y - 7 = 121, etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc.

Now,

To find number of people who have re-posted

we need to make a exponential equation

Here, As cindy tags meme to 3 people in starting and they also tag 3 people in subsequent days, then equation will be y=t^3 where t=no of days.

No of people after 8 days,

y=8^3

y=512 (no of people after 8 days)

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This is an example of geometric growth, So after 8 days 6561 people will have re-posted the meme.

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Answer:

$5520×6÷100×7=2318.40

a) The increasing line y = 2x is plotted on the graph given at the end of the answer.

b) The horizontal line y = 3 is plotted on the graph given at the end of the answer.

c) The point of intersection of the two graphs is given as follows: (1.5, 3).

The increasing line is given as follows:

y = 2x.

Hence we plot a few points of coordinate (x,y), from the numeric values of the function, and connect them through a line.

The numeric values of the function are given as follows:

The horizontal line is given as follows:

y = 3.

Meaning that a single horizontal line through y = 3 is traced, for which we are going to use the same domain as the increasing line.

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Answer:

To calculate the interest earned on an investment, we can use the formula:

A = P(1 + r)^t

Where A is the amount in the account after time t, P is the initial principal or deposit, r is the interest rate, and t is the time in years.

In this case, the initial deposit is $8,241.78, the interest rate is 5.5% (or 0.055 as a decimal), and the time is 31 days.

Since the interest is compounded daily, we need to calculate the number of compounding periods for 31 days, which is 31 days.

Therefore, the formula becomes:

A = 8241.78(1+0.055)^31

To calculate the interest earned, we will subtract the initial deposit from the final amount in the account

Interest = A - P

So the interest earned in 31 days will be:

$8241.78 * (1+ 0.055)^31 - $8241.78 = $35094.06

The missing angle x of the interior angles of the quadrilateral is; x = 40°

The sum of interior angles of a quadrilateral is 360°. Now, we are given the interior angles of this quadrilateral as;

(2x + 20)°

2x°

2x°

(2x + 20)°

Thus;

(2x + 20)° + (2x + 20)° + 2x° + 2x° = 360°

8x + 40 = 360

8x = 360 - 40

8x = 320

x = 320/8

x = 40°

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Answer:

Step-by-step explanation:

The general form of the equation for the line described by the point-slope form y + 3 = −2/7 (x − 5) is y = -2/7x + 19/7.

Answer:

4 x [tex]10^{8}[/tex]

Step-by-step explanation:

Round the number to

400,000,000

4 x [tex]10^{8}[/tex]

We moved the decimal 8 places.

Answer:

4 x 10^8 (four times ten to the power of eight) is the best approximation of the number 399,867,231 written in scientific notation.

Step-by-step explanation:

15ft

Step-by-step explanation:

bc I said so..............

6. The measure of angle BEC is 48°

7. The measure of angle 1 is 41°

8. The value of x is 12

   The measure of angle UST is 36°

6. The angles AEB and BEC form a straight line whose angle measure is 180°.

So that,

∠AEB + ∠BEC = 180°

132° + ∠BEC = 180°

∠BEC = 180° - 132°

∠BEC = 48°

7. The angles 1 and 5 form a right angle whose measure is 90°.

So that,

∠5 + ∠1 = 90°

49° + ∠1 = 90°

∠1 = 90° - 49°

∠1 = 41°

8. The angles RSU and UST form a right angle whose measure is 90°.

∠RSU + ∠UST = 90°

(5x - 6)° + (2x + 12)° = 90°

(7x + 6)° = 90°

7x° = (90 - 6)°

7x° = 84°

x = 12

∠UST =  (2x + 12)°

∠UST =  (2(12) + 12)°

∠UST =  (24 + 12)°

∠UST = 36°

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Answer: The appropriate dosage of medicine for a 180 Ib person is 12 ounces.

Step-by-step explanation:

From the word problem, we know that:

Since we are given w (the amount the person weighs is 180 Ib), we can plug the value into the equation to solve for t.

t= 3 + 0.05 (180)

t = 3 + 9

t = 12

So the appropriate dosage of medicine for a 180 Ib person is 12 ounces.

The border should be 6 inches wide.

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

Given that, A picture is to be put on a poster board that is 18 in. by 22 in. there is to be an even amount of poster board around the picture, the area of the picture is 192 in.²

Let the marginal space left is x in

Therefore,

(18-x)(22-x) = 192

396 -18x - 22x + x² = 192

x² - 40x + 204 = 0

Factorizing the expression, we get,

x = 34 or x = 6

(Note :- Neglecting 34 because 34 is grater than the dimensions given)

Therefore, the marginal space is 6 inches.

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Answer:

14

Step-by-step explanation:

Para simplificar esta expresión, debemos seguir el orden de las operaciones, también conocido como PEMDAS: paréntesis, exponentes, multiplicación y división (de izquierda a derecha), y suma y resta (de izquierda a derecha).

1. Comience por simplificar la expresión dentro de los paréntesis.

4-2[6-3+4(5-7)]

4-2[6-3+4(-2)]

4-2[6-3-8]

4-2[-5]

4+10 = 14

2. Ahora sustituya el valor simplificado dentro de los paréntesis en la expresión original:

-3+{14}+3

3. Ahora podemos sumar y restar de izquierda a derecha.

-3+14+3 = 14

Entonces, la expresión simplificada es 14.

Answer: There is no solution for these equations.

Explanation: This equation system is not solvable. Because we cannot eliminate x or y while holding one of them in the equation.

Answer:

We can use the formula for the area of a circle and the information provided to find the approximate area of the circle.

The formula for the area of a circle is A = πr², where r is the radius of the circle.

We know that the distance from the center of the circle to the chord AB is 6 and the length of the chord AB is 10.

We can use the Pythagorean theorem to find the radius of the circle.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So, we can use this theorem to find the radius of the circle as follows:

r² = (length of the chord /2)² + (distance of the chord to the center)²

r² = (10/2)² + 6²

r² = 25 + 36

r² = 61

r ≈ 7.8

Now that we know the radius of the circle, we can use the formula for the area of a circle to find the area of the circle:

A = πr²

A ≈ π (7.8)²

A ≈ 191.8

The approximate area of the circle is 192 square units.

The domain of the composite function f(g(x)) is equal to (x - 2)/(4 + 4x).

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domain of the function f(g(x)) as follows:

f(g(x)) = 1 ÷ 12/[(x - 2) + 4]

f(g(x)) = 1 ÷ [12 + 4(x - 2)]/(x - 2) {simplify the denominator to a single fraction}

f(g(x)) = 1 ÷ (12 + 4x - 8)/(x - 2) {open bracket for 4(x - 2)}

f(g(x)) = 1 ÷ (4 + 4x)/(x - 2) {simply like terms}

f(g(x)) = 1 × (x - 2)/(4 + 4x) {changing division to multiplication}

f(g(x)) = (x - 2)/(4 + 4x)

Therefore, the result (x - 2)/(4 + 4x) is the domain of the composite function f(g(x)).

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ES = 10.63 units

The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places. Therefore, by measuring the length of the line segment that connects the two sites, the distance between them may be determined.

When given a straight line on a graph, you can find the length of this line by using the Distance Between Two Points Formula. This formula uses the vertices of the beginning and ending points of a straight line to find the length of the line, which is the distance between the two points.

The Distance Between Two Points Formula is:

= √(( x₂  – x₁ )² + ( y₂ – y₁) ²)

The vertices of the line ES are E ( -3, -4 ) and S ( 4, 4 ).

The distance is:

= √(( 4  – (-3) )² + ( 4 ( - 4 )) ²)

= 10. 63 units

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The point that satisfies this inequalities y > -(1/3)x - 2 and y > 2x + 6 is (2, 15)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Given the linear inequalities:

y > -(1/3)x - 2    (1)

y > 2x + 6       (2)

Plotting both inequalities:

The point that satisfies this graph is (2, 15)

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The approximate area of the shaded region of the circle is 191 metres squared.

The radius of the circle below is given as 9 metres. The approximate area of the shaded region of the circle can be found as follows:

area of the shaded region = area of the circle - area of the sector uncoloured

Therefore,

area of the circle = πr²

where

Therefore,

area of the circle = π × 9²

area of the circle = 81π m²

Hence,

area of the sector uncoloured = ∅ / 360 × πr²

where

Therefore,

area of the sector uncoloured = 90 / 360 × π × 9²

area of the sector uncoloured = 1 / 4 × π × 81

area of the sector uncoloured = 81 / 4 π

Hence,

area of the shaded region = 81π  - 20.25π

area of the shaded region = 60.75π

area of the shaded region = 190.755

area of the shaded region = 191 m²

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Answer:

15%

Step-by-step explanation:

markup = 16100 - 14000 = 2100

percent markup = 2100/14000 × 199% = 15%

Answer: The percent markup is 15%.

Using the provided conditions and values, This is solved with the concept of word problem, The answer is first, second and third aircrafts have 576,512 and 864 seats.

A word problem in mathematics is a problem that is written in natural language (i.e., words) rather than in mathematical notation. It presents a real-world scenario that requires the use of mathematical concepts and skills to solve. Word problems often involve finding unknown quantities based on given information, and they can be challenging because they require students to understand the problem and translate it into mathematical equations or formulas. They are often used in primary and secondary education to help students apply their math skills to real-world situations and develop critical thinking skills.

A mathematical expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that represents a mathematical statement or equation. Mathematical expressions can be evaluated to find a numerical value. They can also be simplified by applying the order of operations (PEMDAS) to combine like terms or to remove unnecessary parentheses. Additionally, mathematical expressions can also be used to represent the relationship between different variables.

Let x be the number of seats on the second aircraft. Then, the first aircraft has x+64 seats and the third aircraft has 2x-152 seats.

We know that the total number of seats for all three aircraft is 1900, so we can set up the following equation:

x + (x+64) + (2x-152) = 1900

Solving this equation gives us x = 512, which means the second aircraft has 512 seats. We can then use this information to find the number of seats for the other two aircraft:

First aircraft: 512 + 64 = 576 seats

Third aircraft: 2(512) - 152 = 864 seats.

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The required difference is equal to 25x/42

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: Alton shoveled snow on 5/6 of his driveway before lunch. Then he shoveled 2/7 of it after lunch.

Let the total snow quantity be x then we have

Before lunch as = 5/6×x

                           =5x/6

After lunch = 5x/6 × 2/7

                   =5x/21

∴ Difference = 5x/6 - 5x/21

                     =35x-10x / 42

                     = 25x/42

Hence, The required difference is equal to 25x/42

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Answer:

To find out how many years it would take to double an initial investment with a 1% annual interest rate, you can use the rule of 72. The rule of 72 states that you can divide 72 by the annual interest rate to find out how many years it would take to double an investment.

In this case, you would divide 72 by 1 to get 72 years. Therefore, it would take 72 years for an investment of $1,000 at a 1% annual interest rate to have a future value of $2,000.

The area of carpet that will be needed for the hole is 6 square feet

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

The hole has a rectangular shape.

Therefore the area of the hole =l×w

length = 3ft

width = 2ft

area of the hole = 3×2 = 6 squared feet

therefore the area of the carpet that will be needed for the hole is 6 square feet

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let's take it from the basic one dolla!!  So how long for one dolla to turn into 3?

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 3\\ P=\textit{original amount deposited}\dotfill &\$1\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &4\\ t=years \end{cases}[/tex]

[tex]3 = 1\left(1+\frac{0.08}{4}\right)^{4\cdot t} \implies 3=1.02^{4t}\implies \log(3)=\log(1.02^{4t}) \\\\\\ \log(3)=t\log(1.02^{4})\implies \cfrac{\log(3)}{\log(1.02^{4})}=t\implies \stackrel{years}{13.870\approx t} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 3\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 3 = 1e^{0.08\cdot t} \implies \log_e(3)=\log_e(e^{0.08t})\implies \log_e(3)=0.08t \\\\\\ \ln(3)=0.08t\implies \cfrac{\ln(3)}{0.08}=t\implies \stackrel{years}{13.733\approx t}[/tex]

Answer:

Step-by-step explanation:

To prove that OHAP is a square, we need to show that all four sides are congruent and all four angles are right angles.

Since AOB is a right isosceles triangle, we know that angle OAB and angle OBA are both congruent to 90 degrees, which means that they are both right angles. Since [OH] is the altitude relative to [AB], it bisects angle OAB, which means that angle AOH and angle HOA are both congruent to 45 degrees. Since P is the symmetric of H with respect to OA, we know that OA is congruent to OP, and we also know that OH is congruent to OP. Therefore, all four sides of OHAP are congruent, which means that OHAP is a square.