Solve this question please

Answer:

Son's Age: 11

Mary's Age: 33

Step-by-step explanation:

Let set Mary and her son as variables,

M = Mary's age

S  = Mary's son age

Breakdown:

"Mary is three times as old as her son"

M = 3S

"In 12 years, Mary's age will be one less than twice her son's age"

M + 12 = 2(S + 12) - 1

we add 12 to both sides as it will be in 12 years for both

We know that M = 3S, so we plug this in

3S + 12 = 2(S + 12) - 1

Now solve for S (son's age),

3S + 12 - 12 = 2(S + 12) - 1 - 12

3S = 2(S + 12) - 13

3S = 2S + 24 - 13

3S - 2S = 2S - 2S + 24 - 13

S = 24 - 13

S = 11

To find Mary age, plug in her son age ,

M = 3S

M = 3(11)

M = 33

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Answer:

7:24pm

Step-by-step explanation:

At 50 mph, it will take 195/50 = 3.9 hours to reach London

3.9 hours = 3 .9 * 60 = 3 hours and 54 minutes(54 = 0.9 * 60 )

3:30 + 3:34 ==> 7:24

(one way to do this is to add up the hours and minutes separately so we get 6:84) Since 84 minutes = 1 hour and 24 minutes, just add 1:24 to 6 to get 7:24

Another way to do this is to see that if the distance was 200 miles, then it would take exactly 4 hours (200/50) to reach at 7:30pm But it is short by 5 miles. At the speed of 50mph, the time taken to travel 5 miles = 60/50 * 5 = 6 minutes so deduct 6 minutes from 7:30pm to get 7:24pm

If the train is slower average speed, then the arrival time is delayed beyond 7:24pm

Answer:

10

Step-by-step explanation:

The arc length of the semicircle is

As x = 42, this means a+4 is 42/180 of the arc length of the circle, 5a+10.

So,

Answer:

11.2 km/hr

Step-by-step explanation:

Shea's speed: 48km/1.25hr=38.4 km/hr

Chris's speed: 62km/1.25hr= 49.6 km/hr

Vav= 49.6-38.4= 11.2 km/hr

The sum of the interior angle is 1080 and each angle measure is 135 degrees.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have an octagon

In an octagon the number of sides = 8

The sum of the angles in the octagon is given by:

= (n - 2)×180

n = 8

= (8 - 2)180

= 6×180

The sum of the interior angle = 1080

Each angle = 1080/8 = 135 degree

Thus, the sum of the interior angle is 1080 and each angle measure is 135 degrees.

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Answer:

The rectangular table

Step-by-step explanation:

Square table: 36*36=1296

Rectangular table: 20*42=1460 [tex]in^{2}[/tex]

Circular table: [tex]\pi * 21^{2}[/tex]≅1384

6.0000000001

Ans right

Answer:

parameter

Step-by-step explanation:

As per the question, the answer is ∠CAB is congruent to ∠BAD.

An isosceles triangle named BDC is positioned within a circle. The segments of the circle they pass through are congruent because the faces of the triangles BC and BD are congruent, or identical.

Due to the triangle's faces BC and BD being identical and congruent

BC=BD

Additionally, the segments of the circle it goes across are congruent.

In the case of ΔBAC & ΔBAD

AC=AD= the radius of the circle

AB=BA

Thus, BAC is consistent with BAD according to SSS guidelines.

As a result, the central angles of the sections are also congruent; hence, BAD and CAB are congruent.

As a result, ∠BAD is equivalent to ∠BAC OR ∠CAB.

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Answer:

B on edge

Step-by-step explanation:

CAD

The proof will be given as:- [tex]\dfrac{tanx+Cotx}{Coscx Cosx} = Sec^2x[/tex].

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The proof will be given as:-

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = \dfrac{tanx}{coscxCosx}+\dfrac{Cosx}{CoscxCosx}\\\\[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} =\dfrac{\dfrac{Sinx}{Cosx}}{\dfrac{Cosx}{Sinx}}+\dfrac{\dfrac{Cosx}{Sinx}}{\dfrac{Cosx}{Sinx}}[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = \dfrac{Sin^2x}{Cos^2x}+1[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = tan^2x+1}[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} =Sec^2x[/tex]

Therefore the proof will be given as:- [tex]\dfrac{tanx+Cotx}{Coscx Cosx} = Sec^2x[/tex].

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Volume is a three-dimensional scalar quantity. The volume of the triangular prism is 66cm².

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the length of the triangle is 4cm, while the width of the triangle is 11cm, therefore, the area of the base of the triangle will be,

Area of triangle = 0.5 × 4cm × 11cm

Area of triangle = 22 cm²

Now, the volume of the prism with a base area of 22cm² and a height of 3 cm is,

Volume of the triangular prism = 22cm² × 3cm = 66cm³

Hence, the volume of the triangular prism is 66cm².

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Pythagoras' theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The correct option is D.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

A triangle has points to monkeys, giraffes, and lions. The distance between lions and monkeys is 11 feet and between monkeys and giraffes is 16 feet. The distance between lions and giraffes is the hypotenuse of x feet. The equation that will find the distance between the lions and giraffes is,

c² = 11² + 16²

c² = 121 + 256

c² = 377

Hence, the correct option is D.

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Answer:

D on edge) 121+ 256...

Answer:

minimum value is 3, maximum value is 4.459

Step-by-step explanation:

[tex] log_{2}(8) = \frac{ log(8) }{ log(2) } = 3[/tex]

[tex] log_{2}(22) = \frac{ log(22) }{ log(2) } = 4.459[/tex]

Answer:

Step-by-step explanation:

Step-by-step explanation:

Given:

[tex]y = {x}^{2} - x - 6[/tex]

To find the x-intercepts set y to 0 and solve for x which is done below:

Therefore x-intercepts:(3,0),(-2,0)

To figure out the y-intercept , substitute 0 for x and simplify

Hence, The y-intercept is (0,-6)

(skipped the steps as you've already figured it out)

Likewise A:

X-intercepts:

Therefore,x-intercepts:(3,0),(-2,0)

Y-intercept:

⇒y=-0²+0+6

⇒y=6

Therefore, y-intercept (0,6)

The vertex:(0.5,6.25)

The difference between the two parabolas is that The blue parabola is the result of reflection over x-axis of the red one.

Answer:

a.

The x-intercepts are 3 and -2

The y-intercept is -6

The vertex is (1/2 , -25/4)

b.

The two parabola are symmetric across the x-axis

Step-by-step explanation:

x² - x - 6

[tex]=x^{2}-2\times \frac{x}{2} +\frac{1}{4} -\frac{1}{4}-6[/tex]

[tex]=(x-\frac{1}{2} )^{2} -(\frac{1}{4}+6)[/tex]

[tex]=(x-\frac{1}{2} )^{2} -\frac{25}{4}[/tex]

The x-intercepts :

(x-1/2)² = 25/4

Then

x - 1/2 = 5/2 or x - 1/2 = -5/2

Then

x = 3 or x = -2

The y-intercepts :

We get the y-intercept by replacing x by 0 in the trinomial :

0² - 0 - 6 = -6

b.

we notice that :

-x² + x + 6 = -(x² - x - 6)

Then

-x² + x + 6

[tex]=-(x-\frac{1}{2} )^{2} +\frac{25}{4}[/tex]

The x-intercepts :

[tex]-(x-\frac{1}{2} )^{2} +\frac{25}{4}=0[/tex]

⇔ (x-1/2)² = 25/4

Then

x - 1/2 = 5/2 or x - 1/2 = -5/2

Then

x = 3 or x = -2

The y-intercepts :

We get the y-intercept by replacing x by 0 in the trinomial :

0² + 0 + 6 = 6

Answer:

Step-by-step explanation:

Remark

An altitude is a very special line. It must start from one of the angles and connect with the side opposite that angle. The connection must form a right angle.

It cannot start anywhere else -- certainly not in the middle of a line which would make the altitude of random importance. It could not be accurately reproduced.

Answer:

(−∞,1)

Step-by-step explanation:

Answer:

x divided by 4

Step-by-step explanation:

4 bags

O O

O O

strawberries would go in each

so lets say like 24 strawberries

24 (x) / 4 = 6

so six strawberries a bag

hope this helps like put a picture in your head

Answer:

m = 3

Step-by-step explanation:

Gradient of a line is given by the formula

m= (y2-y1) /(x2-x1) which is change y divided by change in x

m = (-4-2)/(-2-0)

m = -6/-2

m = 3

Answer: the gradient is 3

Step-by-step explanation:

for a full explanation refer to the document and the ones written colorfully are the explanation. So, if you want just the workings they are the ones written in black.

and I drew an eye! Have a nice day!

Answer: [tex]-1, \frac{4}{3}[/tex]

Step-by-step explanation:

[tex]3x^{2}-5x+6=10-4x\\\\3x^{2}-x-4=0\\ \\ (x+1)(3x-4)=0 \\ \\ x=\boxed{-1, \frac{4}{3}}[/tex]

Answer:

x = -1
x = 4/3

Step-by-step explanation:

Hello!

First, let's convert the equation into Standard Form: [tex]ax^2 + bx + c = 0[/tex]

We can solve this by factoring the quadratic. We have to find two numbers that multiply to [tex]ac[/tex] but add up to [tex]b[/tex].

The two numbers would be -4 and 3. We can expand -x to -4x + 3x, and then factor by grouping.

Use the Zero Product Property. Set each factor to zero and solve for x.

The solutions to the quadratic are -1 and 4/3.

Answer:

0 represents the ground level

Answer:

No solution

Step-by-step explanation:

 7x + 2y = 16 ----------------(I)

-21x - 6y = 24 -----------------(II)

[tex]\sf \dfrac{a_1}{a_2}=\dfrac{7}{-21}=\dfrac{-1}{3}\\[/tex]

[tex]\sf \dfrac{b_1}{b_2}=\dfrac{2}{-6}=\dfrac{-1}{3}[/tex]

[tex]\sf \dfrac{c_1}{c_2} =\dfrac{16}{24}=\dfrac{2}{3}\\\\ \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}[/tex]

So, the lines are parallel and has no solution

Answer:

3 different ways

Step-by-step explanation:

2, 3, and 5 are all prime numbers under 6

Answer:

19-73 19-73 is fine thanks 70-65-46 024 465 8554 48-57

Answer:

x = -3 when f(x) = -5

f(0) = 3

Step-by-step explanation:

When f(x) = -5, that means they have told you the y value. When y = -5, x = -3.

If the number is in the parentheses of the function, they are giving you the x value. When x  = 0, y = 3

Step-by-step explanation:

first you should do is that find the common difference which is 9

Answer:

160

Step-Step Explaining:

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