Sue and Pam are sisters, but they live far from each other. They both
want a garden at their respective homes, and they decide they want to
build identical flower gardens that are in the shape of a triangle.
They spend a lot of time emailing and talking on the phone, trying to
figure out how to make these triangular gardens exactly the same.
• Sue suggests that they each make their gardens with brick walls
outlining the gardens, and they should make sure all three angles
of the two triangles are the same: 30, 60, and 90. Sue asserts
that this will make their gardens congruent.
Pam likes the idea of the wall, but instead she thinks that they
should make their triangles equal by making one wall 7 feet long
with a 30 angle attached to it. Sue says the other two walls
will match up to make a triangle, and that their triangles will
be equal.
The two women can't agree on the best method. They hire you to help
them with the design.
Determine if either of their methods will create congruent
triangular gardens. Use your congruent triangle theorems, like
SSS, ASA, SAS, to decide.
If you don't think that a method will work, you must explain why
the method will not work.
How do you think Sue and Pam should create congruent triangular
gardens?

On solving the provided question we cans ay that equation will be => x *(x+1) = 12 => x = 6, -2

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

a pack of pencils, a pack of pens, and a notebook for = $12.

the pack of pens cost = $1 more than the pack of pencils,

let,

x = cost of pen

y = cost of note book

equation will be

x *(x+1) = 12

x^2 + x = 12

(x+2)(x-6) = 0

x = 6, -2

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Answer:

16052.47m²

Step-by-step explanation:

area of a circle=πr²

π=314

3.14×71.5×71.5=16052.465m²

=16052.47m²

Answer:

16,060.61 m² (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a circle}\\\\$A=\pi r^2 $\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]

Given:

Substitute the given radius into the area of a circle formula and solve for A:

[tex]\implies A= \pi \cdot 71.5^2[/tex]

[tex]\implies A= 5112.25 \pi[/tex]

[tex]\implies A= 16060.6070...[/tex]

[tex]\implies A= 16060.61\; \sf m^2\;(2 \; d.p.)[/tex]

Therefore, the area of the circle is 16,060.61 m² (2 d.p.).

Answer:

2.88 markup per rose

Step-by-step explanation:

12.24/12 = 1.02 per rose

46.8/12 = 3.9 per rose

3.9 - 1.02 = 2.88 markup per rose

The PCR in terms of t is 6,912in3t, rounded to the nearest hundredth.

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Answer:

The sum of the exterior angles of a quadrilateral is 360 degrees. This is because the exterior angle of a polygon is supplementary to the interior angle (the angle formed by two adjacent sides). The sum of the interior angles in a quadrilateral is 360 degrees (180 x 2) and since the exterior angles are supplementary to the interior angles, the sum of the exterior angles is also 360 degrees.

Uday Tahlan

Answer:

Increases by 71% to the nearest whole number

Step-by-step explanation:

=((12-7) /7 )x100

=57×100

=0.714286×100

=71.4286%change

=71.4286%increase

Answer:

$15 per hour

Step-by-step explanation:

270/18= 15, if you take the total which is 270 and divide that by the number of hours she works each week it equals 15

The value of the discount that will be give for the doll is $54.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

From the information, it should be noted that there's a 15% discount. The value of the discount will be:

= 15% × $360

= $54

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A Barbie doll costs $360 and has a 15% discount. How much is the discount?

The expression (5/3x+4)^2 in simplest trinomial form is (25x^2+36x+96)/6.

An algebraic expression with three terms is called a trinomial. One or more terms in an algebraic expression each have variables and constants. These expressions utilise separators like +, -, ×, and ÷ that are symbols or operations. This algebraic statement encompasses polynomials, monomials, binomials, and trinomials.

The given expression is -

(5/3x+4)^2

Solve it to get the trinomial -

= (5/3x+4)^2

= 25/(3x+4)^2

= 25/(6x^2+6x+16)

= (25x^2/6) + 6x + 16

= (25x^2+36x+96)/6

Therefore, the trinomial obtained is (25x^2+36x+96)/6.

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Answer:

7

Step-by-step explanation:

f(30)=-11

f(30)=-3/5(30)+k

-11=-18+k

+18 +18

7=k

Therefore , the solution of the given problem of range comes out to be option b is y ≤ -5 .

The variable range is calculated by determining its maximum observed value and deducting its minimum observed value (minimum). Possible range or variational bounds: different pricing for steel; different designs; The breadth or scope of a process or action: insight a weapon's projectile's maximum or anticipated range. A list or set's range is the integer between its lowest and maximum. Aligning all the numbers will help you find the region. The lowest number should then be subtracted from the greatest number.

Here,

Given :

=> y = -3x² - 12x -17 or

=> f(x) =  -3x² - 12x -17

To find the range :

=> If a < 0 the range of f(x) ≤ y

=> If a > 0 the range of f(x) ≥ y

As a =-3

So ,  vertex(xv ,yv ) = (-2 , -5)

=> y ≤ -5

Therefore , the solution of the given problem of range comes out to be option b is y ≤ -5 .

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[tex]\it P(A)=\dfrac{n^o\ de\ casos\ favorables\ de\ A}{n^o\ total\ de\ casos\ posibles}\\ \\ \\ n^o\ total\ de\ casos\ posibles=100\\ \\ n^o\ de\ casos\ favorables=50+30=80\\ \\ P(A)=\dfrac{\ 80^{(20}}{100}=\dfrac{4}{5}[/tex]

A graph which shows the relationship given in the table is: B. graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 56 through the point 1 comma 54.

In this scenario, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot while the total amount of sunglasses would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

From the scatter plot (see attachment) which models the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 56

Therefore, the y-intercept is equal to (0, 56).

In conclusion, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days (x) and total amount of sunglasses (y).

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Answer:

D

Step-by-step explanation:

rise over run

from the points you go up 3, then 2 to the right

3/2

Answer:

Step-by-step explanation:

hcg

Answer:

2 miles / half-hour

Step-by-step explanation:

You will notice that the y intercepts the x at every half-hour interval

Ex: 2 at 30 min, 4 at one hour, 6 at one hour 30 minutes...

The cost of 650 bricks which are right rectangular prisms is $1774.5.

What is a rectangular prism?

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.

The dimensions of the right rectangular prism brick is -

width, w = 7 in

length, l = 3 in

height, h = 3(1/4) in = 3.25 in

Find the volume of the brick -

Volume = w × l × h

Volume = 7 × 3 × 3.25

Volume = 68.25 in³

The volume occupied by 650 bricks is -

V650 = 68.25 × 650

V650 = 44362.5 in³

The cost of cubic inch of brick is $0.04.

The cost of 650 bricks is -

Total cost = 44362.5 in³ × $0.04

Total cost = $1774.5

Therefore, the total cost is obtained as $1774.5.

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Answer:

7/8

12.5%

Step-by-step explanation:

As a result, it is discovered that the answer to the given function problem is slant sample points of y = x -4.

Mathematical studies cover the areas and prospective applications of geometry as well as numbers and their variants, equations, and related structures. A group of inputs that collectively produce a similar result is referred to as a "function." Each input contributes to a single, distinguishable consequence in an output-input connection known as a function. Each activity has a scope, which is also known as a region or city or municipality. Commonly, functions are denoted by the letter f. (x). The origin is X. Across operations, one-to-one action, many-to-one activity, on activity, and on

Here,

Every one of the three asymptotes can be used to construct a rational function because rational functions can take any form.

This is depicted in both the linked graph and the graph of the function f(x that serves as a representation. The function's asymptotes are as follows.

The asymptotes for the vertical slope are x = -4,

The horizontal asymptotes are Y = 0 and.

Slant has an asymptote of Y = x -4.

An exponential function is used in our example function. That isn't generally perceived of as a polynomial, but it may be expressed as an endless degree polynomial. A rational function is typically described in publications as the percentage of polynomials.

As a consequence, the solution to the given function problem is slant sampling points, which are y.

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Answer:

D

Step-by-step explanation:

add -2 to the other side of the equation to isolate y

Answer:

Number of republicans = 207 Number of democrats = 245

Step-by-step explanation:

Here you go

(x + 38) + x = 452 x + 38 + x = 452 2x = 452 - 382x = 414x = 414 / 2 x = 207

Answer: 6

Step-by-step explanation:

Since M is the midpoint of LN, M divides LN by exactly half.

This means that LM and MN have the same length.

Using this, we can set up the equation:

3x=2x+2

x=2

Since we now know the value of x, let's use it to find LM.

LM = 3x = 6

So the answer is 6.

In 37 years and 6 months, Jacob will be 1.5 years older than his uncle Todd.

In 37 years and 6 months, Jacob will be 1.5 years older than his uncle Todd.

Hello, using the information provided, write an equation to get the answer to this question:

33 years old Todd

12 years old Jacob

So, Jacob's age plus the amount of years asked equals 1.5 Todd's age (1.5 x 33).

(12+x)

12 +x = 1.5 (33) (33)

working out x

12 +x = 49.5

x= 49.5 -12

: x = 37.5 years

Given that 12 months make up a year, 0.5 years is equal to half a year.

12 times 0.5 years equals 6 months.

In 37 years and 6 months, Jacob will be Todd's age by a factor of 1.5.

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Answer:

about 100 feet

Step-by-step explanation:

Answer:

            4  to  1

Step-by-step explanation:

                                                Tablespoon of cocoa   to Tablespoon of sugar

                                                                          8             :                2

                                                                          [tex]\frac{8}{2}[/tex]              :                [tex]\frac{2}{2}[/tex]

                                                                          4             to                1

When recipe is doubled:                             ( 8 x 2)         to        (2 x 2)

                                                                         16             :              4

                                                                         [tex]\frac{16}{4}[/tex]             :               [tex]\frac{4}{4}[/tex]

                                                                          4           to              1

It can be observed that the ratio remains the same

The rate of change of function A is greater than the rate of change of function B. This is the statement which best compares the rate of change of the two functions.

What is rate of change?

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.

The formula for rate of change is:

[tex]m=\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]

The points for first function A are

(7,21) and (8,24).

So, the rate of change is:

[tex]m=\frac{24-21}{8-7}[/tex]

m= 3/1 = 3

The points for second function B are

(2,4) and (3,6).

So, the rate of change is:

[tex]m=\frac{6-4}{3-2}[/tex]

m= 2/1 = 2

The rate of change of function A is 3, while the rate of change of function B is 2.

Hence, the rate of change of function A is greater than the rate of change of function B.

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Answer:

Step-by-step explanation:

8. ( - 3, 6 )

10. ( - 7, 9 )

The average rate of change of filling the water heater is solved to be

The results indicate that 1 1/3 is the ratio of the rate of change of water height to time.

The average rate of change for the points t = 3 and t = 6  is solved using the formula

m = (y₀ - y₁) / (x₀ - x₁)

m = (3 - 7) / (3 - 6)

m = (-4) / (-3)

m = 4/3

m = 1 1/3

The values means that the rate of change of of height of water to time it takes is equal to 1 1/3

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The correct answers are X=76.5 and Perimeter= 210.9.

Perimeter is the distance around the outside of a shape. It is a measurement of length and is calculated by adding up the lengths of all the sides of a shape. Perimeter is often used to measure the size of outdoor areas such as a garden, park, or pool, or to find the length of fencing needed for a yard.

To solve for x, use the formula x = (P + Q - R)/2 where P, Q, and R are the lengths of the sides of the triangle. Thus, x = (AST + APQ - APR)/2 = (176 + 140 - 126)/2 = 76.5. To find the perimeter of the triangle STU, use the formula Perimeter = ST + SU + TU = 176 + 28 + 6 = 210.9.

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Answer: 6x+28

Step-by-step explanation:

The perimeter of the triangle is the distance around the triangle.

We need to apply our ability to convert word problems in to mathematical expressions.

we were told that the bottom of the triangle is [tex]x[/tex] units.

From the diagram perimeter

The length of the bottom of the triangle is [tex]x[/tex]

14 more than 4 times the bottom will be [tex]4x+14[/tex]

14 more than the bottom of the triangle will be [tex]x+14[/tex]

So, [tex]x+4x+14+x+14[/tex][tex]=6x+28[/tex]

Answer:

6x+28

Step-by-step explanation: