The longer base of an isosceles trapezoid measures 23 ft. The nonparallel sides measure 9 ft, and the base angles measure 80°. Find the length of a diagonal.

Answer:

2(x^2)-1

Step-by-step explanation:

The square of a number is just the number squared. We don't know what the number is so I will just say it is x. So we have 2 times x^2. Then we have to minus 1 from that. So 2(x^2)-1.

Hope this helps! :D

The expression "1 less than twice the square of a number" can be represented mathematically as [tex]\(2x^2 - 1\)[/tex], where x is the variable representing the number.

Expression: [tex]\(2x^2 - 1\)[/tex]

Step 1: Square the number x:

[tex]\((x)^2 = x^2\)[/tex]

Step 2: Multiply the squared number by 2:

[tex]\(2 \cdot x^2 = 2x^2\)[/tex]

Step 3: Subtract 1 from the result of step 2:

[tex]\(2x^2 - 1\)[/tex]

This is the final expression that represents "1 less than twice the square of a number."

For example, if we substitute a specific value for x, let's say x = 3:

Step 1: Square the number: [tex]\(3^2 = 9\)[/tex]

Step 2: Twice the squared number: [tex]\(2 \cdot 9 = 18\)[/tex]

Step 3: Subtract 1: 18 - 1 = 17

So, when x = 3, the expression [tex]\(2x^2 - 1\)[/tex] evaluates to 17.

To know more about square, refer here:

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Answer:

After 13 days (Rounded) If you dont round it's [tex]\frac{90}{7}[/tex] or 12[tex]\frac{6}{7}[/tex]

Step-by-step explanation:

Perry: 180 - 6x = 8x

180 - 6x + 6x = 8x + 6x

180 = 14x

180/14 = 14x/14

90/7 = x

Answer:

-9 3/4

Step-by-step explanation:

FG = GH

9x+15 = 5x+4

Subtract 5x from each side

9x+15-5x = 5x+4-5x

4x+15 = 4

Subtract 15 from each side

4x+15-15 = 4-15

4x = -11

Divide by 4

4x/4 = -11/4

x = -11/4

FG = 9x+15

FG = 9*(-11/4) +15

  = -99/4+15

    -99/4 + 60/4

   = -39/4

  = -9 3/4

Answer:

3  7777/10000

Step-by-step explanation:

Answer:

[tex]3\frac{7}{9}[/tex]

Step-by-step explanation:

[tex]3.777...=3+0.777...[/tex]

[tex]0.777...=x\\7.777...=10x[/tex]

[tex]10x-x=7.777...-0.777...\\9x=7\\x=\frac{7}{9}[/tex]

The answer is [tex]3\frac{7}{9}[/tex]

Answer:

[tex]2x - 10 = 3x - 40 \\ x \: terms \: togather \\ 3x - 2x = - 1 0 + 40 \\ x = 30 \\ thank \: you[/tex]

Answer:

D. y = 1 • 3^x

Step-by-step explanation:

Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is  

y

=

0

.

Horizontal Asymptote:  

y

=

0

Answer:

13/15

Step-by-step explanation:

Answer:13/15

Step-by-step explanation:

Answer:

g(f(x)) = x^2 + 1

? = 2

grey box = 1

Step-by-step explanation:

Answer:

g(f(x)) = [tex]x^{2}[/tex] + 1

Answer:

The answer is B. p= 46

Step-by-step explanation:

23+23=46-23=23

Answer:

your answer is B

Step-by-step explanation:

Answer:

lost 120

Step-by-step explanation:

10% of 1200 is 120 so you subtract 120 from 1200

Answer:

120

Step-by-step explanation:

Loss = (Loss%)(C.P)

Loss = (10%)(1200)

Loss = (10/100)(1200)

Loss = 120

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

what link because I am unable to find one here please ensure to include the link

Answer:

How can Mass and Speed Influence KE?

The goal of this experiment was to determine how mass and speed influence KE. This is significant because you would know whether to add more or less mass/speed if you were in a position where you required something to move higher. We filled the bean bag with a set amount of water, then dropped it to see how much mass it had. After that, you kept track of how high the bean bag went. The same thing happened with the speed, but the amount of liquid in the bottle was the same; it was just dropped from different heights. My theory is that the KE will increase as mass increases. This is also true of speed; if the bean bag is dropped from a higher altitude, it will launch farther than before.

The data I gathered in the lab confirmed my hypothesis. When the bottle's height was increased, the bean bag rose higher than before. I also tested four different masses: 0.125 kilograms, 0.250 kilograms, 0.375 kilograms, and 0.500 kilograms. The bean bag rose higher each time it was placed on a greater bulk.

On the speed test, the bean bag would frequently go higher than the bottle drop point, but not always. Furthermore, when it was dropped from the same height each time, the results differed significantly, for example, when it was dropped from 1.28, the results were 1.14, 1.30, and 1.30. Mass, on the other hand, was all in the same number range, with the exception that the numbers were somewhat different.

I used the calculations KE= 12 mv2 and Ht v2/2g. The initial step was to compute an object's kinetic energy, using the formula m=mass v=speed. The second was to determine the height at which I needed to drop something in order to reach a specific speed, where Ht=Height and g=Gravitational Acceleration of 9.8 m/s2.

I utilized these to create tables that depicted relationships between various variables, such as mass and KE or speed and height. My data kept increasing the entire time I was conducting the lab; when there was more mass/speed, the table had greater numbers.

This proves that my first theory was correct: as m/s increases, KE increases accordingly because they are all linear. When the bean bag height exceeded the water bottle drop mark, I was taken aback.

To summarize, my theory was supported by my data. When more mass or speed was introduced, the data values increased. This means that if I wanted more kinetic energy for something, I'd know to increase the mass or the speed of the object that was supplying the energy.

This hypothesis is valid because when you have greater mass, you also have more energy. So, if you drop a baseball, it isn't very heavy, so it will only propel the bean bag a short distance. However, because a bowling ball is quite heavy and has a lot of energy when it falls, it would force the bean bag to fly very high.

To improve this experiment, I would create the lever from a smoother material so that energy is not lost due to friction from the wood rubbing together. Perhaps a scanner or video camera to better document how far the bean bag traveled. All of these would aid the lab in obtaining more precise results, and they might perhaps be used in the future.

Step-by-step explanation:

Don't copy this word for word or you'll get in trouble.

Answer:

265x{2} + 40x

Step-by-step explanation:

Squared mean to multiply the number times itself. So 15x times 15x.

[tex]15x^{2} = 225x[/tex]{2}

Then the problem says to add, but because one is squared and th other is not, they cannot be combined. So the answer is:

[tex]225x{2} + 40x

Answer:

see below

Step-by-step explanation:

15x^2 + 40x

These are not like terms so they cannot be combined.

If you mean

(15x) ^2 + 40x

(15x * 15x) + 40x

225x^2 + 40x

They are still not like terms so they cannot be combined.

Answer:

0.36

Step-by-step explanation:

Answer:

[tex] \sqrt{5} \times \sqrt{15} \times \sqrt{3} \\ \\ \sqrt{5 \times 15 \times 3} \\ \\ = 5 \times 3 \\ \\ = 15[/tex]

[tex]\\ \rm\longmapsto \sqrt{5}\times \sqrt{15}\times \sqrt{3}[/tex]

[tex]\\ \rm\longmapsto \sqrt{5\times 15\times 3}[/tex]

[tex]\\ \rm\longmapsto \sqrt{5\times 5\times 3\times 3}[/tex]

[tex]\\ \rm\longmapsto 5(3)[/tex]

[tex]\\ \rm\longmapsto 15[/tex]

Answer:

The perimeter of the triangle is about 17.1 units.

Step-by-step explanation:

The perimeter of a triangle is the sum of its three side lengths.

We can see that the two legs of the triangle both measure five units.

To find the third segment, we can use the Pythagorean Theorem since the x-axis is perpendicular to the y-axis. Recall that:

[tex]a^2 + b^2 = c^2[/tex]

Where a and b are the two legs and c is the hypotenuse.

Our two legs are 5 and 5. Hence:

[tex](5)^2 + (5)^2 = c^2[/tex]

Solve for the hypotenuse:

[tex]\displaystyle \begin{aligned} c &= \sqrt{(5)^2 + (5)^2} \\ &= \sqrt{2(5)^2} \\ &= 5\sqrt{2}\end{aligned}[/tex]

Hence, our perimeter will be:

[tex]\displaystyle P = 10 + 5\sqrt{2} \approx 17.1 \text{ units}[/tex]

In conclusion, the perimeter of the triangle is about 17.1 units.

Answer:

x^2-8x+12

Step-by-step explanation:

(x-2)(x-6) roots= 2,6

x^2-6x-2x+12

=x^2-8x+12

[tex]\\ \rm\Rrightarrow 2.98\times 1.5[/tex]

[tex]\\ \rm\Rrightarrow 2.98\times \dfrac{3}{2}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{8.94}{2}[/tex]

[tex]\\ \rm\Rrightarrow 4.47[/tex]

Answer:

A. linear

Step-by-step explanation:

Answer:

The slope is -2

Step-by-step explanation:

(-2, 8) and (1, 2)

Slope formula:

m= (y2-y1)/(x2-x1)

Work:

m= (2 - 8)/(1 + 2)

m= (-6)/3

m = -2

Step-by-step explanation:

the radius cuts the segment into two equal parts because it is perpendicular to the chord

Answer:

Step-by-step explanation:

As O is the mid point of the circle

Similarly, B also becomes the mid point of the line AC.

So, line OB divides AB and BC equally.

Hence, lines AB = AC, but they are asking to prove congruency of triangles.

So, u have to join OA and OC.

Same way,   line OB divides ∠OBA and ∠OBC.

So it is proved that AB = AC

Step-by-step explanation:

For every clockwise 90-degree rotation on a point (x, y), the resulted transformation will be (y, -x).

Now, counterclockwise 270 degree rotation is equivalent to clockwise 90 degree rotation. Then, for instance, point H=(2 ,-1) will be transformed into the image H'=( -1,2)

this is loki ez

but just go in order

Answer:

7 dimes and 12 nickels.

Step-by-step explanation:

12 nickels = $0.60 and 7 dimes = $0.70. $0.70 + $0.60 = $1.30.

Weighted average is the average of a set using different weight for each element in the set. The final grade when homework and test scores are 59 and 64 is 62.35

Given that:

[tex]Homework = 59[/tex]

[tex]Test = 64[/tex]

The test score is greater than the homework score. So, the test will be weighted using 67%, while the homework will be weighted using 33%.

The final grade is calculated as follows:

[tex]Grade = 67\% \times Test + 33\% \times Homework[/tex]

So, we have:

[tex]Grade = 67\% \times 64 + 33\% \times 59[/tex]

[tex]Grade = 42.88 + 19.47[/tex]

[tex]Grade = 62.35[/tex]

Hence, the final grade is 62.35

Read more about weighted average at:

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Answer:

0.71, 78%, 0.8, [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

78% = 0.78

7/8 = 0.875

Answer:

4/5

Step-by-step explanation:

y=k/x

2/5=k/2

cross multiply

5k=4

k=4/5

substitute 4/5 for k

y=4/5/x

y=4/5/1

y=4/5

9514 1404 393

Answer:

Step-by-step explanation:

The relationship description tells you that profits depend on purchases. Therefore, profits are the dependent variable; purchases are the independent variable.