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We should multiply the expression by (9+√14) fraction.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

To rationalize the terms, we multiply both the denominator and denominator by the conjugate of the denominator.

The denominator is 9-√14 and its conjugate is; (9+√14).

(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)

                       =  (5-√7)(9+√14)/(9²-14)

                      = (45 + 5√14 - 9√7 - √98)/(81-14)

                       =  (45 + 5√14 - 9√7 - √98)/67

                       = (45 + 5√14 - 9√7 - 7√2)67

This is the rationalized expression.  

The denominator is (9-√14) and its conjugate is (9+√14).

Learn more about multiplications;

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Answer:

45 [tex]ft^2[/tex]

Step-by-step explanation:

Multiply 9 · 10 = 90 then divided by 2 = 45

Answer:

45

Step-by-step explanation:

Did the test

Answer:

b. 7

[tex] \frac{56}{x} = 8 \\ 8x = 56 \\ x = 7[/tex]

Answer:

I say A or B but in favor A

Step-by-step explanation:

Answer:

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Answer:

m<F = 44°

length of FH = 15

length of GF = 21

Perimeter of ∆FGH = 50

Step-by-step explanation:

✔️Find m<F using the sum of triangle theorem:

The small box indicates angle 90°. Sum of a triangle is 180°. Therefore,

m<F = 180° - (90° + 46°)

m<F = 180° - 136°

m<F = 44°

✔️Find FH using trigonometric function:

Reference angle = 46°

Length of Opposite side = FH = ?

Length of Adjacent side = GH = 14

Apply TOA because we are concerned with the OPP and ADJ sides:

Tan 46° = Opp/Adj

Tan 46° = FH/14

14*Tan 46° = FH

14.4974243 = FH

FH = 15 (approximated to nearest whole number)

✔️Find GH by applying either a trigonometric function or just simply apply pythagorean theorem:

Pythagorean theorem is given as,

c² = a² + b²

c is the longest side (hypotenuse) = GF = ?

a = GH = 14

b = FH = 15

Thus:

GF² = 14² + 15²

GF² = 421

GF = √421

GF ≈ 21 (nearest while number)

✔️Perimeter of ∆FGH = GH + GF + FH

= 14 + 21 + 15

= 50

Step-by-step explanation:

seriously another one its ok i can do it

Answer:

Did you mean to attach something?

Step-by-step explanation:

I don't see the illustration... without it I cannot answer the question.

Answer:

0, 0, 4, -3

Step-by-step explanation:

Answer:

The answered 5 math questions, and 5 science questions.

5 * 3 = 15

5 * 10 = 50

15 + 50 = 65

Step-by-step explanation:

Answer:

[tex]\left[\begin{array}{ccc}1&0\\0&4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\3\end{array}\right][/tex]

Step-by-step explanation:

A matrix is an algorithm that has many applications. It is composed of a series of numbers (typically coefficients of variables) organized in a pattern. When dealing with a matrix, one must always remember the rule (rows by columns). One such application is that a matrix can facilitate the process by which one solves a system of equations.

When given the following system:

y = 5

4x = 3

One can see that not all of the equations have all variables in them. Yet, bear in mind that any number times zero is zero, therefore, one can rewrite the equation such that it has all of the variables if one ensures that the coefficient of the missing variable is (0).

y + 0x = 5

0y + 4x = 3

Now organize this in the form of a matrix, the coefficients of the variable go in a (4 x 4) since there are now (4) elements. The variables are vertically arranged in a (2 x 1), and the equation results are also vertically arranged in a (2 x 1).

[tex]\left[\begin{array}{ccc}1&0\\0&4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\3\end{array}\right][/tex]

Answer:

New width = 12 in.

Step-by-step explanation:

Original height = 2 in.

Original width = 3 in.

New height = 8 in.

New width = x = ?

The shape of the original painting and the shape of the new painting are similar, therefore, the ratio of their corresponding linear measurement will be equal.

Thus:

New height/original height = new width/original width

8/2 = x/3

Cross multiply

2x = 3*8

2x = 24

2x/2 = 24/2

x = 12

New width = 12 in.

Answer: x=-3

Step-by-step explanation:

i don't really know if this is what I was supposed to do, but i did 6 divided by x=-2 and got x=-3

Answer:

40197 these many 5s make up 200985 so 4 are left to make 200989

Step-by-step explanation:

Answer:

40197.8

Step-by-step explanation:

200989 ÷ 5

40197.8

Answer:

m<A = 84

AC = 9

Step-by-step explanation:

We can find the measure of Angle A by using the sum of interior angles of a triangle theorem.

48+48+A=180

96+A=180

A=84

We can then use the isosceles triangle similarity theorem and reason that since this is an isosceles triangle and one of the side lengths (AB) is 9, the other (AC) would also be 9.

Answer:

4/15

Step-by-step explanation:

4/10*6/9

2/5*2/3

4/15

Answer: 2 circle to the right

Step-by-step explanation:

You would need to add 2 circles to keep it balanced.

Answer:

1.95

Step-by-step explanation:

area = (1/2 ×1 ×1 )×3 = 1.5 ( for sides)

area = ( 1/2 ×1 ×0.9) = 0.45 for base

area =1.5+0.45 = 1.95

Answer:

x = 48 degrees

Step-by-step explanation:

(2x + 2) + (x + 34) = 180

3x + 36 = 180

3x = 180 - 36

3x = 144

x = 144 / 3

x = 48 degrees

I hope this helps :)

Answer:

B. x = 48

Step-by-step explanation:

(x + 34)+(2x + 2) = 180°. Angles on a straight line

x+2x = 180 - (34+2)

3x = 180 - 36

3x ÷3 = 144 ÷3

x = 48°

Answer:5

Step-by-step explanation:

Answer:

Step-by-step explanation:

take x degree as reference angle

using sin rule

sin x=opposite/hypotenuse

sin x=10/15

sin x=0.66

x=sin 42

therefore x=42 degree

Answer:

2,000,000 - 2 million

20,00,000 - 20 lakhs

Answer:

10 lakh = 1,000,000

So 20 lakh is = 2 million

Hope it helps!

9514 1404 393

Answer:

  3x -5y = -38

Step-by-step explanation:

The equation of the perpendicular line can be formed by swapping the coefficients of x and y in the given equation, negating one of them. The new constant will be the one that lets the given point satisfy the equation.

  given: 5x +3y = 5

  perpendicular: 3x -5y = constant

At the given point, the constant is ...

  3(-6) -5(4) = -18 -20 = -38

So, the desired equation is ...

  3x -5y = -38

Answer:

To factor means to express as a product. To expand means to multiply something out.

Step-by-step explanation:

please answer my question for me pleaseeee

Answer:

B

Step-by-step explanation:

A story about someone's life, written by that person.

Good luck with the rest!

Answer:

Option B, A story about a person's life, written by that person

Step-by-step explanation:

We can take Autobiography, the term auto refers to by one's self, therefore autobiography would mean a story written by a person about them selves.

Hope this helps!

Answer:

The volume of the composite figure is approximately 3567.198 cubic feet.

Step-by-step explanation:

The composite figure consists in the combination of a right cone and a cuboid. The volume of the composite ([tex]V[/tex]), in cubic feet, figure can be determined by this expression:

[tex]V = \frac{1}{3}\cdot \pi \cdot r^{2}\cdot h + w\cdot H \cdot l[/tex] (1)

Where:

[tex]r[/tex] - Radius of the circle of the right cone, in feet.

[tex]h[/tex] - Height of the cone, in feet.

[tex]w[/tex] - Width of the cuboid, in feet.

[tex]H[/tex] - Height of the cuboid, in feet.

[tex]l[/tex] - Length of the cuboid, in feet.

If we know that [tex]r = 10\,ft[/tex], [tex]h = 10\,ft[/tex], [tex]w = 20\,ft[/tex], [tex]H = 7\,ft[/tex] and [tex]l = 18\,ft[/tex], then the volume of the composite figure is:

[tex]V = \frac{1}{3}\cdot \pi \cdot (10\,ft)^{2}\cdot (10\,ft) + (20\,ft)\cdot (7\,ft)\cdot (18\,ft)[/tex]

[tex]V = \left(\frac{1000\pi}{3} + 2520\right)\,ft^{3}[/tex]

[tex]V \approx 3567.198\,ft^{3}[/tex]

The volume of the composite figure is approximately 3567.198 cubic feet.

Answer:

C, -7+12

Step-by-step explanation:

-7--12= 5

-7--12 can also be -7+12

Answer:

The answer is c

Step-by-step explanation:

-7-(-12) = 5