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Cerrena [4.2K]
3 years ago
12

FACTOR the following quadratic expression: x^2-3x-18. Clearly show your steps OR explain your reasoning and CHECK your answer by

multiplying to get back to the starting expression. A correct answer without a CHECK and work/ explanation will NOT receive full credit! NOTE: Press and hold the SHIFT button and press 6 to make the "^" exponent symbol. Someone plz help its doe in 10 min
Mathematics
1 answer:
kakasveta [241]3 years ago
6 0

Answer:

The factors of x² - 3·x - 18, are;

(x - 6), (x + 3)

Step-by-step explanation:

The given quadratic expression is presented as follows;

x² - 3·x - 18

To factorize the given expression, we look for two numbers, which are the constant terms in the factors, such that the sum of the numbers is -3, while the product of the numbers is -18

By examination, we have the numbers -6, and 3, which gives;

-6 + 3 = -3

-6 × 3 = -18

Therefore, we can write;

x² - 3·x - 18 = (x - 6) × (x + 3)

Which gives;

(x - 6) × (x + 3) = x² + 3·x - 6·x - 18 = x² - 3·x - 18

Therefore, the factors of the expression, x² - 3·x - 18, are (x - 6) and (x + 3)

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What is the perimeter of the figure
anastassius [24]

Answer:

Option A.

P=73.4\ units

Step-by-step explanation:

see the attached figure with letters to better understand the problem

In this problem we have a triangle with a circle inscribed in it

so

A.F=A.B\\C.B=C.D\\E.F=E.D

step 1

Find the length side B.C

C.B=A.C-A.B

substitute the given values

C.B=23-14=9\ units

step 2

Find the length side C.D

Remember that

C.D=C.B

therefore

C.D=9\ units

step 3

Find the length side E.D

we know that

E.D=E.C-C.D

substitute the given values

E.D=22.7-9=13.7\ units

step 4

Find the length side E.F

Remember that

E.F=E.D

therefore

E.F=13.7\ units

step 5

Find the length side A.F

Remember that

A.F=A.B

therefore

A.F=14\ units

step 6

Find the perimeter

P=23+22.7+13.7+14

P=73.4\ units

6 0
3 years ago
At an opening of a new art gallery the owner hired a caterer to serve light snacks. The owner created a budget for 150 people to
Vsevolod [243]

Answer: $357 is more amount budgeted for food increase.

Explanation:

Since we have given that

Number of people according to the budget = 150

Cost of food per person= $4.25

Total cost of food is given by

150\times 4.25=\$637.5

If the number of guests attending the opening was 56% more than expected,

So, number of guests now is given by

150\times 0.56=84\\\\150+84=234

Total cost of food is given by

234\times 4.25=\$994.5

Difference between them is given by

994.5-637.5=\$357

Hence, $357 is more amount budgeted for food increase.

8 0
3 years ago
Pls help and show workings <br> Due ASAP
Tanya [424]

Answer:

ASA angle side angle

Step-by-step explanation:

DE=JH(given)

angle E= angle H (given)

angle D=angle J (given)

4 0
2 years ago
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Gennadij [26K]

Answer: Rotations, reflections, translations (A, C, and E)

Imagine you had a camera aimed at a triangular figure on a piece of paper. If you rotate the camera, then the image of the triangle appears to rotate. In reality it's the other way around. What this means is that the triangle is not changing at all. It keeps the same size, shape, area, perimeter, etc. This applies to when the camera pans left or right, ie shifts from side to side. The triangle will translate but again the triangle isn't changing at all. It's merely an illusion. Reflections are the same way. Imagine having a piece of glass or a mirror that reflects the image which is an identical copy; although everything is flipped.

Dilations are not isometries because the image is a different size then the pre-image. The same shape is maintained though. Note: the scale factor must be some number other than 1.

another note: "isometry" breaks down into "iso+metry" with "iso" meaning "same" or "equal", and "metry" meaning "measure". So if you had 2 identical yard sticks, then they are isometrical or equal in length.

4 0
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Arisa [49]
Slope=6 because the slope travels upwards by 6
4 0
2 years ago
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