[tex]4x+2=2(x+6)[/tex]

Solve for x.

Answer:

5

Step-by-step explanation:

We know that we can use the Pythagorean theorem

a^2 + b^2 =c^2

where a and b are the legs and c is the hypotenuse

one of the legs is 12 and the hypotenuse (diagonal) is 15

a^2 + 12^2 = 15^2

a^2 +144 = 169

a^2 +144-144 =169-144

a^2 = 25

Taking the square root of each side

sqrt(a^2) = sqrt(25)

a = 5

Answer:

l = 9 cm

Step-by-step explanation:

Using Pythagoras' identity in one of the right triangles with legs width w, length l and hypotenuse h , then

l² + w² = h²

l² + 12² = 15²

l² + 144 = 225 ( subtract 144 from both sides )

l² = 81 ( take the square root of both sides )

l = [tex]\sqrt{81}[/tex] = 9

Answer:

4

Step-by-step explanation:

A=ch

then,

2ft×2ft

4ft

Answer:

7/6

Step-by-step explanation:

p=3/4*q

q=14/9*r

so p=3/4*14/9r=7/6r

Answer:

SP is Rs 800.

Step-by-step explanation:

MP = Rs 875

Discount = Rs 75

so

SP = MP - discount

= Rs 875 - Rs 75

= Rs 800

Answer:

Option B

Step-by-step explanation:

From the picture attached,

In ΔABC,

m∠B = m∠C = 75° [Isosceles triangles]

By applying triangle sum theorem,

m∠A + m∠B + mC = 180°

m∠A + 75° + 75° = 180°

m∠A = 180° - 150°

m∠A = 30°

In triangle PQR,

m∠P = m∠Q [Isosceles triangle]

By applying triangle sum theorem,

m∠P + m∠Q + m∠R = 180°

2(m∠P) + 30° = 180°

m∠P = 75°

m∠P = m∠Q = 75°

In ΔABC and ΔRPQ,

m∠B ≅ m∠Q [Given]

m∠C ≅ m∠R [Given]

Therefore, by AA property of similarity of two triangles, both the triangles will be similar.

ΔABC ~ ΔRPQ

Option B will be the answer.

Answer:

Step-by-step explanation:

44.4--0.4=-44

Answer:

0.167

Step-by-step explanation:

1 dice has 6 faces, 2 dice will have a total of 12 faces

1 dice has 1 face with a 3 on it, so 2 dices will have 2 total 3s on them.

2 /12 = 1/6 = 0.16666666666

Rounded to 3 d.p = 0.16666

= 0.167

Answered by Gauthmath

Answer:

hlo buddy

are u free now.. nhjm....

We know

[tex]\boxed{\Large{\sf Circumference=\pi d}}[/tex]

[tex]\\ \Large\sf\longmapsto Circumference=\dfrac{22}{7}\times 23.4[/tex]

[tex]\\ \Large\sf\longmapsto Circumference=\dfrac{514.8}{7}[/tex]

[tex]\\ \Large\sf\longmapsto Circumference=73.5in[/tex]

Answer:

Equation is y = mx + 2

Step-by-step explanation:

General equation of line:

[tex]{ \boxed{ \bf{y = mx + b}}}[/tex]

Substitute in considerance of the question:

[tex]{ \sf{ y = mx + 2}}[/tex]

If m is given, substitute for m to the answer.

Answer:

6.8=6 8/5

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hope it help

Answer:

181 ÷ 2

= 90.5 feet

...........

Answer:

hence the profit percent is 58%.

Answer:

43.49

Step-by-step explanation:

let his normal hourly rate be x

16x+7x/2=848

39x/2=848

x=848 ÷ 39/2

=43.48717

Given:

The data set is:

0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9

To find:

The correct statement that represents the box plot of the data correctly.

Solution:

We have,

0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9

Divide the data in 2 equal parts.

(0, 1, 1, 1, 2), 3, (4, 4, 6, 6, 9)

Divide each parenthesis in 2 equal parts.

(0, 1), 1, (1, 2), 3, (4, 4), 6, (6, 9)

Here,

Minimum value = 0

First quartile = 1

Median = 3

Third quartile = 6

Maximum value = 9

A number line goes from 0 to 10. The whiskers range from 0 to 9, and the box ranges from 1 to 6. A line divides the box at 3.

Therefore, the correct option is D.

Answer:

its d

Step-by-step explanation: my yt Tray Clayps

Answer:

Step-by-step explanation:

Let largest value of data be L

and smallest value of data be S.

We are given that the range and coefficient of range of the data are 17 and 0.2 respectively.

Range formula is given by = Largest value - Smallest value

                   17  =   L - S

                  L = 17 + S ---------- [Equation 1]

Coefficient of range formula = (Largest - Smallest) ÷ (Largest + Smallest)

                                       0.2   =    l-s/l+s

                                      0.2 = 17/l+s

                 L + S = 17/0.2 = 85

So,    L + S = 85

       17 + S + S = 85   {using equation 1}

           2*S = 80

             S = 80/2 = 40

Putting value of S in equation 1, we get L = 20 + 40 = 60

Therefore,  Largest value, L = 60

               smallest value, S = 40

vhhg

Step-by-step explanation:

rrgggggggjjhjjhgghghhh

Answer:

Part 1)

[tex]\displaystyle \left((2-x)^2 + 1)\right) + (2\sqrt{3} - 1 ) \left(x^2 + 1\right)[/tex]

Or simplified:

[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]

Part 2)

The value of x for which the given expression will be the lowest is:

[tex]\displaystyle x = \frac{\sqrt{3}}{3}\approx 0.5774[/tex]

And the magnitude of ∠BAC is 60°.

Step-by-step explanation:

We are given a ΔABC with an area of one. We are also given that AB = 2, BC = a, and CA = b. CD is a perpendicular line from C to AB.

Please refer to the diagram below.

Part 1)

Since we know that the area of the triangle is one:

[tex]\displaystyle \frac{1}{2} (2)(CD) = 1[/tex]

Simplify:

[tex]\displaystyle CD = 1[/tex]

From the Pythagorean Theorem:

[tex]\displaystyle x^2 + CD^2 = b^2[/tex]

Substitute:

[tex]x^2 + 1 = b^2[/tex]

BD will simply be (2 - x). From the Pythagorean Theorem:

[tex]\displaystyle (2-x)^2 + CD^2 = a^2[/tex]

Substitute:  

[tex]\displaystyle (2-x)^2+ 1 = a^2[/tex]

We have the expression:

[tex]\displaystyle a^2 + (2\sqrt{3} - 1) b^2[/tex]

Substitute:

[tex]\displaystyle = \boxed{\left((2-x)^2 + 1)\right) + (2\sqrt{3} - 1 ) \left(x^2 + 1\right)}[/tex]

Part 2)

We can simplify the expression. Expand and distribute:

[tex]\displaystyle (4 - 4x + x^2 + 1)+ (2\sqrt{3} -1)x^2 + 2\sqrt{3} - 1[/tex]

Simplify:

[tex]\displaystyle = ((2\sqrt{3} -1 )x^2 + x^2) + (-4x) + (4+1-1+2\sqrt{3})[/tex]

Simplify:

[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]

Since this is a quadratic with a positive leading coefficient, it will have a minimum value. Recall that the minimum value of a quadratic always occur at its vertex. The vertex is given by the formulas:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = 2√3, b = -4, and c = (4 + 2√3).

Therefore, the x-coordinate of the vertex is:

[tex]\displaystyle x = -\frac{(-4)}{2(2\sqrt{3})} = \frac{1}{\sqrt{3}} =\boxed{ \frac{\sqrt{3}}{3}}[/tex]

Hence, the value of x at which our expression will be the lowest is at √3/3.

To find ∠BAC, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

Substitute:

[tex]\displaystyle \tan \angle BAC = \frac{CD}{x}[/tex]

Substitute:

[tex]\displaystyle \tan \angle BAC = \frac{1}{\dfrac{\sqrt{3}}{3}} = \sqrt{3}[/tex]

Therefore:

[tex]\displaystyle\boxed{ m\angle BAC = \arctan\sqrt{3} = 60^\circ}[/tex]

Answer:

x=4

x=-5

Step-by-step explanation:

in order for this to be equal to 0, 1 or both of the factors has to be 0, because anything multiplied by 0 is 0.

123 * 29382 * 8139* 0 = 0

x-4 = 0

x = 4

x+5 = 0

x=-5

Answer:

its the 3rd choice.

Step-by-step explanation:

Firstly, we find angle BDC (180-90-30=60)

Now that we found it we can use the sine rule to find DB (which i put as an x), which is sin60/14=sin30/x, by cross multiplication, we find that its equal to a decimal number, i will use its root version to this easier, its equal to 14sqrt3/3 inches.

And now we use the pythagorean theorem to find DC, we find that it is equal to 28sqrt3/3

Now, we find angle BAC (180-90-(30+15)=45)

Again, we use the sine rule to find AB (whom i will refer to as x and from whom we will subtract DB to find the length of AD), so we cross multiply in sin45/14=sin(30+15)/x, it is equal to 14.

So since AB-DC=AD

14-(14sqrt3/3)= 5.917096231 (and we ound that to a 5.9)

Answer:

the answer is -10

Step-by-step explanation:

x=x

y=5

then

3x+5y=-5

3x+5*5=-5

3x=-5-25

3x=-30

x=-30/3

•°•x=-10

Answer:

A

Step-by-step explanation:

3x+5*5=-5

x=-10

Answer:

where is the rest of the question??

Step-by-step explanation:

If the perimeter is 16' the sum of the length and width must be 8'. Assuming that area is non 0 possible dimensions are:

1x7 2x6 3x5 4x4 5x3 6x2 7x1

Answer:

96 ounces each day

Step-by-step explanation:

Divide the 24 bottles by 3

24/3 = 8

8bottles per day

8 bottles *12 ounces per bottle

96 ounces each day

Answer:

x

Step-by-step explanation:

Answer:

4.

Step-by-step explanation:

The highest exponent is 4 so the degree is 4.

Answer:

PR = 39 cm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

PR² + PQ² = QR² , that is

PR² + 80² = 89²

PR² + 6400 = 7921 ( subtract 6400 from both sides )

PR² = 1521 ( take the square root of both sides )

PR = [tex]\sqrt{1521}[/tex] = 39

Answer:

[tex]PR=39[/tex]

Step-by-step explanation:

The triangle (PQR) is a right triangle. This means the triangle has a (90) degree angle, such is indicated by the box around one of the angles in the triangle. One of the properties of the sides of a right triangle is the Pythagorean theorem. The Pythagorean theorem states the following:

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

Where (a) and (b) are the legs of the right triangle, or the sides adjacent to the right angle. (c) is the side opposite the right angle of the triangle triangle, in other words, the hypotenuse. Substitute the respective legs into the formula for the Pythagorean theorem and solve for the unknown,

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

Substitute,

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

[tex]PQ^2+PR^2=QR^2[/tex]

[tex]80^2+PR^2=89^2\\[/tex]

Simplify,

[tex]80^2+PR^2=89^2\\[/tex]

[tex]6400+PR^2=7921[/tex]

Inverse operations,

[tex]6400+PR^2=7921[/tex]

[tex]PR^2=1521\\\\PR=39[/tex]