Rachael’s patio has an area of 290 square feet. If the patio is shaped like a square, what is the approximate side length?
A. about 72.5 feet
B. about 145 feet
C. about 17 feet
D. about 24 feet

Answer:

1.38p=C

Step-by-step explanation:

each pound is $1.38 and pounds is p they have to equal to C, the total.

To prove two triangles congruent, postulates like SSS, SAS, ASA, or the HL Theorem are typically used. The Pythagorean theorem finds the lengths of sides of a right triangle, but does not alone prove congruency without additional information.

Without seeing the specific details of the triangles in question, we cannot definitively say which theorem or postulate would be used to prove them congruent. However, common tools used in proving the congruence of triangles are Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA) postulates, as well as the Hypotenuse-Leg (HL) Theorem which specifically applies to right triangles. From the details given in the question, the Pythagorean theorem is mentioned. The Pythagorean theorem is used to find the sizes of the sides of a right triangle but it does not prove congruence between two triangles. To use it as a part of congruence proof, one usually needs additional information like other sides' measurements or angles' measurements.

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[tex]\left\{\begin{array}{ccc}6x+2y+1=13+10y-x\\5x=y+26-2x\end{array}\right\\\\\left\{\begin{array}{ccc}6x+x+2y-10y=13-1\\5x+2x-26=y\end{array}\right\\\left\{\begin{array}{ccc}7x-8y=12&(**)\\y=7x-26&(*)\end{array}\right\\\\\text{substitute}\ (*)\ \text{to}\ (**)\\\\7x-8(7x-26)=12\\7x-(8)(7x)-(8)(-26)=12\\7x-56x+208=12\\-49x=12-208\\-49x=-196\qquad\text{divide both sides by (-49)}\\\boxed{x=4}\\\\\text{put the value of x to}\ (*)\\\\y=7(4)-26\\y=28-26\\\boxed{y=2}\\\\\boxed{x=4\ and\ y=2}[/tex]

[tex]\text{Put the values of x and y to the expression}\ 2x(-3+y):\\\\2(4)(-3+2)=8(-1)=-8\\\\Answer:\ \boxed{\text{The valuie of the expression is -8}}[/tex]

Answer:

A. a. 9x^4 b. 3x^5y

Step-by-step explanation:

a. 5x^4 + 4x^4

Since these are to the same power, they are like terms and we can add them

9x^4

b. 12x^5y − 9x^5y

Since these are to the same power, they are like terms and we can subtract them.

3x^5y

Approximately 95% of data falls within 2 standard deviations (±2) of the mean is true of normally distributed data. Thus option C is correct.

Data are presented in the following figure and skew-free in a standard deviation. As one moves away from the center, the values start to taper off and the majority of values are concentrated in this area. In a standard deviation, the measurements of central tendency  are identical.

Just around 95% of the information in a normal distribution should be within three standard deviations from the mean. This is in accordance with The rule that states that One standards standard of the norm contains about 68% of the observations is presented.

Therefore, option C is the correct option.

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The  table which represents a linear function is:

Last table.

        x         y

        1         -5

        2         0

        3         5

        4         10

We know that a function is linear if the rate of change is constant.

i.e. the ratio of difference in y value to the corresponding difference in x value is constant.

i.e. for two values (x,y) and (x',y') the rate of change is given by:

[tex]\text{Rate\ of\ change}=\dfrac{y-y'}{x-x'}[/tex]

In each of the tables we observe that the difference in x-value is constant i.e. 1.

since, 2-1=1

3-2=1

and 4-3=1

Now, the function will be linear for which the difference in the y-value is constant.

a)

        x       y

        1       5

        2       9

        3       5

        4       9      

The difference in the y-value is as follows:

9-5=4

5-9= -4

9-5= 4

Since, the difference is not constant.

Hence, the function is not linear.

b)

        x       y

        1       -5

        2       10

        3       -15

        4        20

 The difference in the y-value is as follows:

10-(-5)=15

-15-10= -25  

20-(-15)=35

Hence, the function is not linear ; since the difference in the y-value is not constant.

c)

        x         y

        1         5

        2        10

        3        20

        4        40

 The difference in the y-value is as follows:

10-5=5

20-10=10

40-20=20

Since, the difference in the y-value is not constant.

Hence, the function is not linear.

d)

        x         y

        1         -5

        2         0

        3         5

        4         10

 The difference in the y-value is as follows:

0-(-5)=5

5-0=5

10-5=5

Since, the difference in the y-value is constant.

Hence, the function is linear.

The absolute value of 8/9 is 8/9 or |8/9| = 8/9 after using the concept of the absolute value function.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The number is 8/9.

As we know, if x is any real number then the absolute value of the x can be written as:

|x| = x; x > 0

|x| = -x; x < 0

We have; x = 8/9

|8/9|

and 8/9 > 0

|8/9| = 8/9

Thus, the absolute value of 8/9 is 8/9 or |8/9| = 8/9 after using the concept of the absolute value function.

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Answer:23.4% Is the percentage that resulted in tails.

Answer:

23.4%

Step-by-step explanation:

[tex]\frac{\frac{x}{4}+\frac{1}{8}}{\frac{x^2}{4}}=\frac{\frac{2x}{8}+\frac{1}{8}}{\frac{x^2}{4}}=\frac{\frac{2x+1}{8}}{\frac{x^2}{4}}=\frac{2x+1}{8}:\frac{x^2}{4}=\frac{2x+1}{8}\cdot\frac{4}{x^2}=\frac{2x+1}{2x^2}[/tex]

Answer:

21 h^10

Step-by-step explanation:

(7h^3)(3h^7)

Lets multiply

7*3  h^3 h^7

When the bases are the same , we add the exponents (x^a * x^b) = x ^ (a+b)

21 h^(3+7)

21 h^10

[tex]Use\ a^n\cdot a^m=a^{n+m}\\\\(7h^3)(3h^7)=(7)(h^3)(3)(h^7)=(7)(3)(h^3)(h^7)=21h^{3+7}=\boxed{21h^{10}}[/tex]

The more painstaking way would be to divide the spinner up into 100 pieces, and shade in 5 of those pieces. Since 5/100 = 0.05 = 5% this means that landing on any of the 5 pieces has a 5% chance of happening.

A better way to do this is to use 20 slices instead. This works because 5/100 reduces to 1/20 (divide top and bottom by 5). Instead of shading in 5 slices, Mark should shade in 1. If you use a calculator, you should see that 1/20 = 0.05 = 5% as well.

The second option is more practical but even then a spinner with 20 sections is still a lot. I think it might be better for Mark to pull random numbers out of a hat, or let the computer generate random numbers.

Mark should divide the spinner in 20 equal sized sections.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.

The more painstaking way would be to divide the spinner up into 100 pieces, and shade in 5 of those pieces.

Since 5/100 = 0.05 = 5% this means that landing on any of the 5 pieces has a 5% chance of happening.

A better way to do this is to use 20 slices instead.

This works because 5/100 reduces to 1/20 (divide top and bottom by 5). Instead of shading in 5 slices, Mark should shade in 1.

If you use a calculator, you should see that 1/20 = 0.05 = 5% as well.

The second option is more practical but even then, a spinner with 20 sections is still a lot.

It is better for Mark to pull random numbers out of a hat, or let the computer generate random numbers.

Hence he should divide the spinner in 20 equal sized sections.

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Answer:

Design B bulbs will likely last longer than design A bulbs

Step-by-step explanation:

The B box  part spans higher numbers than the A box  and  the median of B bulbs is higher than median of the A bulbs.

Answer:

Design B bulb will likely last longer than design A bulbs

Step-by-step explanation:

Got it right on IM

so first off, let's simplify both equations, starting off by multiplying both sides by the LCD of all fractions, to do away with the denominators.

[tex]\bf \cfrac{10(x-y)-4(1-x)}{3}=y\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{10(x-y)-4(1-x)=3y} \\\\\\ 10x-10y-4+4x=3y\implies \boxed{14x-13y=4} \\\\[-0.35em] ~\dotfill\\\\ 7+x-\cfrac{x-3y}{4}=2x-\cfrac{y+5}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( 7+x-\cfrac{x-3y}{4} \right)=12\left( 2x-\cfrac{y+5}{3} \right)} \\\\\\ 84+12x-3(x-3y)=24x-4(y+5) \\\\\\ 84+12x-3x+9y=24x-4y-20\implies \boxed{-15x+13y=-124}[/tex]

now, let's do some elimination on those two simplified equations.

[tex]\bf \begin{array}{cllcl} 14x&-13y&=&4\\ -15x&+13y&=&-124\\\cline{1-4} -x&&=&-120 \end{array}~\hfill x=\cfrac{-120}{-1}\implies \blacktriangleright x=120 \blacktriangleleft \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{14(120)-13y=4}\implies 1680-13y=4\implies 1680-4=13y \\\\\\ 1676=13y\implies \blacktriangleright \cfrac{1676}{13}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 120~,~\frac{1676}{13} \right)~\hfill[/tex]

Answer:

A.The signs change from negative to positive.

Step-by-step explanation:

We are given that trapezoid in quadrant III rotates 180 degrees clockwise about the origin.

We have to find the effect of rotation on the sign of  coordinates .

We know that the transformation rule of rotation 180 degrees about the origin is given by

[tex](x,y)\righatarrow (-x,-y)[/tex]

When a trapezoid lie in III quadrant then the coordinates of all four points are negative because in III quadrant x and y are both negative.

When the trapezoid rotates 180 degrees clockwise about the origin then by using the given rule the sign of coordinates from negative to positive.

Hence, option  A is true.

The signs of both x and y coordinates of a trapezoid in Quadrant III change from negative to positive after a 180° clockwise rotation about the origin, resulting in a new position in Quadrant I.

When a trapezoid positioned in Quadrant III, where both x and y coordinates are negative, undergoes a 180° rotation clockwise about the origin, the signs of both coordinates change. This type of rotation is a half-circle and results in the figure being mirrored over the origin into the quadrant directly opposite Quadrant III, which is Quadrant I. Here, both the x and y coordinates become positive, as any point that was (-x, -y) in Quadrant III will become (x, y) in Quadrant I after a 180° rotation.

This transformation aligns with the properties outlined for rotational symmetry operations, reversing the direction of both the x and y vectors without altering their magnitudes. The correct answer to the student's question is therefore option A: The signs change from negative to positive.

Answer:

8,3, and 10 or 6,4, 10, or 12, 2, and 10

Step-by-step explanation:

You just multiply each of the 3 numbers to equal 240

There are plenty of triples of numbers (x,y,x) that satisfy x*y*z = 240. Some integer candidates include (1,1,240), (1,2,120), (2,5,24), (3,5,16), (4,6,10) and many more. If you don’t restrict your attention to integers, there are even more candidates.

Hope This Helps!!!

-Austint1414

Answer:

-13 -i

Step-by-step explanation:

The first step is to find the sum

5-9i and -4+7i

Add the real parts and then the imaginary parts

5+-4 = 1

-9i + 7i = -2i

5-9i + -4+7i = 1 -2i

Now we subtract 14 -3i

1 -2i - (14 -3i)

Subtract the real parts and then the imaginary parts

1-14 = -13

-2i - -3i = -2i+3i = i

1 -2i - (14 -3i) = -13 -i

Sample space--

A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.

i.e. the sample space while flipping a coin is: {H,T}

The sample space while tossing a six-sided die is: {1,2,3,4,5,6}

Here it is given that:

A bag has six balls labeled:  A,B,C,D,E,F

        This means that the sample space is given by:

                      Sample space={ A,B,C,D,E,F}

             Then the sample space is:

                      Sample space= {D,E,F}

The sample space of a bag with balls labeled A to F is {A, B, C, D, E, F}. For the event of choosing a letter from A to E, the outcomes are {A, B, C, D, E}.

To answer the student's question about the sample space and the event of choosing a letter from A to E, we must first understand the concept of sample space in probability. The sample space is the set of all possible outcomes of a probability experiment. In this case, since the bag contains six balls labeled A, B, C, D, E, and F, the sample space describing all possible outcomes is {A, B, C, D, E, F}.

Now, the event of choosing a letter from A to E simply means finding all the outcomes within the sample space that meet the criteria of being letter A, B, C, D, or E. Therefore, the outcomes for this event are {A, B, C, D, E}.

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Answer: that would be 76% hope that helps

Step-by-step explanation:

The price of the 60-inch television decreased by 24%. This was determined by subtracting the sale price from the original price, dividing by the original price, and multiplying by 100.

To calculate the percent decrease in the price of the television, we need to find the difference in the original price and the sale price, then divide that by the original price, and multiply by 100 to get the percentage.

Original Price: $1050

Sale Price: $798

So, the difference is $1050 - $798 = $252

The percent decrease is ($252 / $1050) * 100 = 24%. So, the price of the 60-inch television decreased by 24%.

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Answer:

51.5 gallons.

Step-by-step explanation:

Given that amount of gallons of paint used by Alisa [tex]=\frac{3}{4}[/tex]

Given that amount of gallons of paint used by Better [tex]=50+\frac{3}{4}[/tex]

Now we need to find about how many gallons of paint do they use together. To find that we just need to amount of gallons used by both.

[tex]\frac{3}{4}+50+\frac{3}{4}[/tex]

[tex]=\frac{3}{4}+\frac{3}{4}+50[/tex]

[tex]=\frac{6}{4}+50[/tex]

[tex]=1.5+50[/tex]

[tex]=51.5[/tex]

Hence final answer is 51.5 gallons.

Answer:

C

Step-by-step explanation:

plug in y = 2x into the first equation

3x+2x = 10

5x = 10

x = 2

put it into the second equation because its easier

y = 2(2)

y = 4

(2, 4)

Everything looks good, but I would write LJ = LJ (or JL = JL) for line e just so it's clear you're talking about the same line segment.

Though to be fair, JL is the same as LJ so it really doesn't matter. I guess it will depend on how picky your teacher is.

Also, I almost forgot, but line c should have angle markers so that your teacher knows you are talking about two angles.

Answer:

3

Step-by-step explanation:

48 - 24 = 24

24 - 12 = 12

12 - 6 = 6

6 - 3 = 3

Thats the pattern

Plzzz mark brainlest and thank me

Answer:

13 units

Step-by-step explanation:

Given points (10,–7)  and (5,5)

To find distance between points we apply distance formula

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

(x1,y1) is (10,–7)   and (x2,y2) is (5,5)

Plug in the values in the formula

[tex]D = \sqrt{(5-(-7))^2+(5-10)^2}[/tex]

[tex]D = \sqrt{(12)^2+(-5)^2}[/tex]

[tex]D = \sqrt{(144+25)}[/tex]

[tex]D = \sqrt{169}[/tex]

D= 13

[tex]\left\{\begin{array}{ccc}2y+x=-17\\5x-4y=-15\end{array}\right\\\\\left\{\begin{array}{ccc}x+2y=-17&\text{multiply both sides by 2}\\5x-4y=-15\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+4y=-34\\5x-4y=-15\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad7x=-49\qquad\text{divide both sides by 7}\\.\qquad\boxed{x=-7}\\\\\text{Put the value of x to the first equation:}\\\\2y+(-7)=-17\\2y-7=-17\qquad\text{add 7 to both sides}\\2y=-10\qquad\text{divide both sides by 2}\\\boxed{y=-5}\\\\Answer:\ \boxed{x=-7\ and\ y=-5\to(-7,\ -5)}[/tex]

Answer: -125

Step-by-step explanation:

(5*5*5)*-1

(25*5) *-1

125 * -1

-125

Answer:

-125

Step-by-step explanation:

5*5*5 = 125

125*-1 = -125

Answer:

13 Boxes with $41 left over

Step-by-step explanation:

600/43 = 13.6

43 x 13 = 559

600 - 559 = 41