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The value of x is 8  

If all of the corresponding sides and angles of two triangles are identical, then those triangles are said to be similar triangles. In similar triangles, the ratio of the corresponding sides will be equal.

If two triangles ΔABC and ΔXYZ are similar triangles the ratio of the corresponding sides will be equal

=> AB/XY = BC/YZ = AC/ZX

Here we have

ΔDEF and ΔABC  

From both triangles,

The ratio of corresponding sides = DE/AB and FD/AC

As we calculate,  \(\frac{19.2}{3.2} = \frac{39}{6.5} = 6\)    

Thus the ratio of corresponding sides is same and equal to 6

=> \(\frac{FE}{BC} = 6\)  

=> \(\frac{48}{x} = 6\)

=> \(6x = 48\)

=> x = 8  

Therefore,

The value of x is 8    

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You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

y= 10x² + 7x + 2.8

Step-by-step explanation:

because the 10x was used twice then the it went to the line of 7x and went down to 2.8 then for the second time it went to 10x

Answer:

-10x^2+7x+4 Would be the correct option

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Answer:

\(\blue{\rule{100pt}{999999pt}}\) \(\blue{\rule{100pt}{999999pt}}\)

Answer:

Mean of Connors 3 card is 9

Step-by-step explanation:

Solution

Minimum of 3cards is 6

range is 7

max -min=7

max=min+7

max=7+6

max=13

Mean=6+13+8/3=27/3=9

Answer:

Mean of Connors 3 card is 9

Step-by-step explanation:

Solution

Minimum of 3cards is 6

range is 7

max -min=7

max=min+7

max=7+6

max=13

Mean=6+13+8/3=27/3=9

Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

Answer:

A becomes (0, -1)

B becomes (4, -1)

C becomes (1, -5)

Step-by-step explanation:

When any coordinate is reflected over x-axis, it y-coordinates are transformed into its opposite.

So,

A becomes (0, -1)

B becomes (4, -1)

C becomes (1, -5)

Answer:

Let x be the number of gallons of the 20% solution and let y be the number of gallons of the 5% solution.

Your system would be:

x+y=15

0.2x+0.05y=(0.13)(15)

Solve the system using either elimination or substitution method, or a combination of the two.

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Answer:

x=6; y=5

Step-by-step explanation:

5x+10y=.8

x+y=11

Wyatt has 6 nickels and 5 dimes.

Given that Wyatt has X nickels and Y dimes, and he has no more than 11 coins worth no less than $ 0.80 combined, to determine one possible solution the following calculation must be performed:

Therefore, Wyatt has 6 nickels and 5 dimes.

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Answer:

157.95 ÷58.5

=2.7

Step-by-step explanation:

.. . ... .

The graph is shown below.

We use an open dot at zero because x is only less than 0,

it's not less than or equal to 0.

So we have an open dot at 0 going to the left.

Answer:

Negative times a negative equals a positive

25x + 30x

55x

The equation of a line that passes through points (2,5) and (4,3) is

y = -x+7.

Finding the equation of a line:

First, we need to find out the slope for the given points.

(X1,Y1) = (2,5)

(X2,Y2) = (4,3)

formula for slope(m) = \(\frac{Y2 - Y1}{X2 - X1}\)

substitute the points in the above formula

\(\frac{3 - 5}{4 - 2}\) = \(\frac{-2}{2}\)

\(\frac{-2}{2}\) = -1

slope for the given points(m) = -1.

m = -1

The equation of a line is y-y1 = m(x-x1), where x and y are variables.

substituting the values in the above equation then :

y-5 = -1(x-2)

y-5 = -x+2

y+x = 2+5

x+y = 7

y = -x+7

Therefore, the equation of the line passing through the points (2,5) and (4,3) is y = -x+7

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Answer:

Recursive formula of an arithmetic sequence is given by the expression,

                          Tn=a+(n−1)d

                 Where, Tn= nth term

                              a= First term of the sequence

                              n= Number of term

                              d= Common difference

Therefore, number of sticks in the 6th pattern are 32.

                   And number of sticks in the nth pattern are Tn=5n+2

From the picture attached,

Number of sticks in 1st pattern = 7

Number of sticks in 2nd pattern = 12

Number of sticks in 3rd pattern = 17

Sequence formed is 7, 12, 17..... nth term

This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.

Therefore, nth term of the sequence will be,

       Tn=a+(n−1)d

       Tn=7+(n−1)5

       Tn=5n+2

If n=6,

       Tn=7+(6−1)5

       Tn=7+25

Tn=32

Hope it helps !

Have a great day!

Answer:

Step-by-step explanation:

Let the amount Emily started with be 100x

Amount spent at grocery 1/2 of the money:

                                                                 \(\frac{1}{2} \ of \ 100x = 50x\)

Remaining amount  

                         \(=100 x - 50x = 50x\)

Amount spent at the Bakery 1/2 of what is left :

                                                                      \(\frac{1}{2} \ of \ 50x = 25x\)

Remaining amount

                      \(= 50x - 25x = 25x\)

Amount spent on CD , 1/2 of what is left :

                                                               \(=\frac{1}{2} \ of \ 25x = \frac{1}{2} \times 25x = 12.5x\)

Remaining amount

                     \(= 25x - 12.5x = 12.5x\)

But given the amount left is $6

That is  ,

                \(12.5x = 6\\\\x = \frac{6}{12.5} = 0.48\)

Therefore amount Emily had in beginning = 100 x  = 100( 0.48) = $48

Answer:

x- coordinate = 5

Step-by-step explanation:

Given a parabola in standard form , f(x) = ax² + bx + c ( a ≠ 0 ) , then

The x- coordinate of the vertex is

x = - \(\frac{b}{2a}\)

f(x) = x² - 10x + 3 ← is in standard form

with a = 1 , b = - 10 , then x- coordinate of vertex is

x = - \(\frac{-10}{2}\) = 5

Answer:

675 km/hr and 75 km/hr

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*(40/60)=500 and (x-y)*(50/60)=500. Solving it, we get x=675 and y=75

Answer:

The surface area is 23

Step-by-step explanation:

Good Luck!

Answer:

A=2(wl+hl+hw)=2·(8·10+5·10+5·8)=340

Step-by-step explanation:

Answer:

Approximately \(0.157\).

Step-by-step explanation:

Let \(X\) denote the speed of a car. The question is asking for \(P(60 \le X \le 70)\).

That probability is equal to \(P(X \le 70)- P(X \le 60)\).

Find each of \(P(X \le 60)\) and \(P(X \le 70)\) using a \(Z\)-table.

Calculate the \(Z\) value for \(x = 70\) and \(x = 60\):

At \(x = 70\), \(\displaystyle z = \frac{x - \mu}{\sigma} = \frac{60 - 55}{5} = 3\).

At \(x = 60\), \(\displaystyle z = \frac{x - \mu}{\sigma} = \frac{70 - 55}{5} = 1\).

In other words: \(P(X \le 70) = P(Z \le 3)\) whereas \(P(X \le 60) = P(Z \le 1)\).

Look up \(P(Z \le 3)\) and \(P(Z \le 1)\) on a \(Z\)-table. The question is asking that the answer be rounded to the nearest thousandth. Therefore, keep at least more decimal places than that in intermediate values.

\(P(Z \le 3) \approx 0.9987\) and \(P(Z \le 1) \approx 0.8413\).

Therefore:

\(\begin{aligned}P(60 \le X \le 70) &= P(X \le 70)- P(X \le 60) \\ &= P(Z \le 3) - P(Z \le 1) \approx 0.157\end{aligned}\).

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

no

yes

no

yes

Step-by-step explanation:

thats the answer

Answer:

=82

Step-by-step explanation:

the value of

x + y²

putting x=1,y=9

we get,

1+(9)^²

=1+81

=82

Answer:

34. (c) 12

35. (a) -12

36. (a) 51

37. (a) 13

Step-by-step explanation:

34.)

\( \implies \: \sf\dfrac{4}{xx + 2} = \dfrac{6}{2xx - 3} \\ \\ \implies \: \sf4(2xx - 3) = 6(xx + 2) \\ \\ \implies \: \sf 8xx - 12 = 6xx + 12 \\ \\ \implies \: \sf 8xx - 6xx = 12 + 12 \sf \\ \\ \implies \: \sf 2xx = 24 \\ \\ \implies \: \sf xx = \dfrac{24}{2} \\ \\ \implies \: \sf xx = 12 \\ \)

Hence, Required answer is option (c) 12.

35.)

\( \implies \: \sf \dfrac{xx - 2}{2} = \dfrac{3xx + 8}{4} \\ \\ \implies \: \sf2(3xx + 8) = 4(xx - 2) \\ \\ \sf 6xx + 16 = 4xx - 8 \\ \\ \implies \: \sf 6xx - 4xx = - 8 - 16 \\ \\ \implies \: \sf 2xx = - 24 \\ \\ \implies \: \sf xx = \dfrac{ - 24}{2} \\ \\ \implies \: \sf xx = - 12 \\ \)

Hence, Required answer is option (a) -12.

36.)

\( \implies \: \sf\sqrt{xx - 2} = 7 \\ \\ \implies \: \sf xx - 2 = {(7)}^{2} \\ \\ \implies \: \sf xx - 2 = 49 \\ \\ \implies \: \sf xx = 49 + 2 \\ \\ \implies \: \sf xx = 51\)

Hence, Required answer is option (a) 51.

37.)

\( \implies \: \sf \sqrt{2xx - 10} = 4 \\ \\ \implies \: \sf 2xx - 10 = {(4)}^{2} \\ \\ \implies \: \sf 2xx - 10 = 16 \\ \\ \implies \: \sf 2xx = 16 + 10 \\ \\ \implies \: \sf 2xx = 26 \\ \\ \implies \: \sf xx = \dfrac{26}{2} \\ \\ \implies \: \sf xx = 13 \\ \)

Hence, Required answer is option (a) 13.

There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.

First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:

The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.

The mean is calculated as follows:

Mean = (all data values added together) / (number of data values)

However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.

The standard deviation equation is as follows:

Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":

No of the size of the data collection, the mean rises by precisely K.

No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.

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Answer:

\(\huge{\boxed{ \sf{x = 23}}}\)

Step-by-step explanation:

\(\sf{x - 15 = 8}\)

Since, we are asked to find the value of x . move 15 to right hand side and change its sign.

⇒ \(\sf{x = 8 + 15}\)

Add the numbers : 8 and 15

⇒ \(\sf{x = 23}\)

The value of x is 23.

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Answer

23

Step-by-step explanation:

x-15=8

x-15(+15)=8(+15)

x=23