Write 150 as a product of primes. Use index notation where appropriate.

Answer:

[tex]a = -9[/tex]

[tex]b = 4[/tex]

Step-by-step explanation:

Given

Sequence: a+3b, a+7b, a+11b

2nd term = 19

5th term = 67

Required

Find a and b

First, the 5th term needs to be calculated;

Using formula for Arithmetic Progression (AP), the formula goes thus

[tex]T_n = T_1 + (n - 1)d[/tex]

Where n = 5

T_1 = a + 3b ------------ FIrst term

[tex]d = T_2 - T_1 or T_3 - T_2[/tex] --- Difference between two successive terms

[tex]d = a + 7b - (a + 3b)[/tex]

[tex]d = a + 7b -a - 3b[/tex]

[tex]d = a - a + 7b - 3b[/tex]

[tex]d = 4b[/tex]

So, [tex]T_n = T_1 + (n - 1)d[/tex] becomes

[tex]T_5 = a + 3b + (5 - 1)4b[/tex]

[tex]T_5 = a + 3b + (4)4b[/tex]

[tex]T_5 = a + 3b + 16b[/tex]

[tex]T_5 = a + 19b[/tex]

Now that we have values for 2nd and 5th term;

From the second, T2 = 19 and T5 = 67

This gives

[tex]a + 7b = 19[/tex] --- Equation 1

[tex]a + 19b = 67[/tex] ---- Equation 2

Make a the subject of formula in (1)

[tex]a = 19 - 7b[/tex]

Substitute these values in equation 1

[tex]a + 19b = 67[/tex] becomes

[tex]19 - 7b + 19b = 67[/tex]

[tex]19 + 12b = 67[/tex]

Collect like terms

[tex]12b= 67 - 19[/tex]

[tex]12b = 48[/tex]

Divide both sides by 12

[tex]\frac{12b}{12} = \frac{48}{12}[/tex]

[tex]b = 4[/tex]

Recall that b = 4

Substitute a = 19 - 7b and nothing will hire

[tex]a = 19 - 7(4)[/tex]

[tex]a = 19 - 28[/tex]

[tex]a = -9[/tex]

Hence, the values of a and b are -9 and 4 respectively.

Answer:

9 cm

Step-by-step explanation:

Since PQ and RS are opposite each other, then in a parallelogram, the lengths will be congruent.

Therefore 2x+5=4x+1

2x=4

x=2

If you plug x=2 into the the original equation, you get 9 cm.

The measure of PQ is 9 centimeters.

Important information:

The oppositie sides of a parallelogram are equal.

[tex]PQ=RS[/tex]

[tex]2x+5=4x+1[/tex]

[tex]5-1=4x-2x[/tex]

[tex]4=2x[/tex]

Divide both sides by 2.

[tex]2=x[/tex]

Now, find the measure of PQ.

[tex]PQ=2x+5[/tex]

[tex]PQ=2(2)+5[/tex]

[tex]PQ=4+5[/tex]

[tex]PQ=9[/tex]

Therefore, the measure of PQ is 9 centimeters.

Find out more about 'Parallelogram' here:

https://brainly.com/question/7099686

Answer:

1/2

Step-by-step explanation:

The results of the roll can be

1,2,3,4,5,6

The rolls that are less than 4 are 1,2,3

P( less than 4) = number of rolls less than 4 / total

                        = 3/6

                         =1/2

Answer:

2

Step-by-step explanation:

f(x) = 2x

Let x =1

f(1) = 2*1

f(1) = 2

Answer:

f(1)=2

Step-by-step explanation:

We are given the equation:

f(x)=2x

We also know that x=1. Therefore, we can substitute 1 in for every x.

f(1)= 2(1)

Multiply 2 and 1

f(1)=2

f(x) when x=1 is 2.

Answer:

$5 per hour.

Step-by-step explanation:

$15 per 3 hours.

[tex]15/3=5[/tex]

[tex]3/3=1[/tex]

$5 per 1 hour.

Answer:

the sale price is 52.50

Step-by-step explanation:

30% discount means that the person pays 70% of the original price

multiply 75 by 70% written as a decimal 0.70

75*0.70 = 52.50

Answer:

im assuming its b because the quality for the pic is bad and i cant really see it

Step-by-step explanation:

Answer:

the answer is c i believe

Answer:

14 ° and 76 °

Step-by-step explanation:

We have that two angles are complementary, if the sum of their amplitudes is 90 °.

The complementary angles need not be consecutive or have any point in common.

Alpha and Beta are complementary if:

Alpha + Beta = 90 °

In this case it would be:

X - 76 ° = 90 °

X = 90 ° - 76 °

X = 14 °

Which means that each angle measures 14 ° and 76 °

Answer:

95

Step-by-step explanation:

Let x be the number of children

10x+35 = money

15x+5 = money

Set  the equations equal

10x+35 = 15x+5

Subtract 10x from each side

35 = 5x+5

Subtract 5 from each side

30 =5x

Divide by 5

30/5 =5x/5

6 =x

There are 6 children

10x+35 = money

10(6) +35

60+35

95

The amount of money is 95

Answer:

C and D are correct: -1 and 0.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

x^3 - 5x2 - 8x + 48 = 0

You haven't supplied a list . To confirm which value is the correct one substitute the values for x and see if the result is 0.

Since the last term is  48 you could try some of the factors of 48 :  1, -1, 2, -2, 3 -3  and so on.

Answer: [tex]\frac{(x+4)(x-1)}{(x+4)(x+2)}[/tex] which is the same as [tex]\frac{x^2+3x-4}{x^2+6x+8}[/tex]

If the math notation does not load properly, or the font size is too small, then it says ( (x+4)(x-1) )/( (x+4)(x+2) ) which is the same as (x^2+3x-4)/(x^2+6x+8)

==========================================================

Explanation:

We see that x cannot equal -2, as this prevents the denominator (x+2) from becoming zero. If x = -4, then x+4 = 0. So x not allowed to be -4 means (x+4) is prevented in being zero, and this is the missing factor in the denominator. We can never divide by zero.

Multiply top and bottom of this given fraction by (x+4) to get [tex]\frac{(x+4)(x-1)}{(x+4)(x+2)}[/tex]

Note how the (x+4) terms divide and cancel to get back to the original fraction given. The portion [tex]x \ne -4[/tex] sticks around to make sure the domains line up properly.

----------

Optionally you can expand out each product in the numerator and denominator to get

(x+4)(x-1) = x^2-x+4x-4 = x^2+3x-4

(x+4)(x+2) = x^2+2x+4x+8 = x^2+6x+8

I used the FOIL rule

So, [tex]\frac{(x+4)(x-1)}{(x+4)(x+2)} = \frac{x^2+3x-4}{x^2+6x+8}[/tex]

Answer: 12i + 21

Step-by-step explanation:

You want to apply foil to the first two terms.

You get 3 + 11i - 20i^2. i is equal to the square root of -1, so when you square it, you will get -1. Then do -1 x -20 to get +20

So far you have (11i + 23) - (-i + 2).

Im 99% sure the answer is 12i + 21

Answer: 17

Step-by-step explanation:

Use the Pythagorean theorem.

C^2 = A^2 + B^2

So, C is always the hypotenuse which is the longest side length and the side length diagonal of the right angle. Side "s" is the hypotenuse.

Square sides AB and BD

It looks like this:

C^2 = 8^2 + 15^2

8^2 = 64

15^2 = 225

225 + 64 = 289

the square root of 289 is 17

17 = s

Answer:

pentegon

Step-by-step explanation:

The certain polygon has its vertices at the following points: (1, 1), (1, 8), (4, 7), and (4, 3) is a trapezoid option (C) is correct.

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 coordinates of a polygon, the coordinate plane:

points: (1, 1), (1, 8), (4, 7), and (4, 3)

After, connecting the points to each other.

We will see, after joining the points, the polygon will be a trapezoid.

Thus, the certain polygon has its vertices at the following points: (1, 1), (1, 8), (4, 7), and (4, 3) is a trapezoid option (C) is correct.

Learn more about the regular polygon here:

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Answer:  b) FALSE

Step-by-step explanation:

In order to show triangle congruency, you must be able to prove one of the following theorems:

SAS: Side-Angle-Side

SSS: Side-Side-Side

AAS: Angle -Angle-Side

ASA: Angle-Side-Angle

HL: Hypotenuse-Leg   (can only be used for right triangles)

We are only given information about two of the sides being congruent but no information on the third side or any of the angles so we canNOT prove the triangles are congruent.

Answer:

b.

Step-by-step explanation:

everything under x= 2 is x+1 meaning x<2 and at 2 it starts x+2

Answer:

The correct option is b.

Step-by-step explanation:

x + 1 ...........................x ≤ 5

x+2 .............................x ≥ 2

Answer:

first Horizontal translation right '2' units  and  vertical translation up '-4' units    

E ( -3 +2 , 4+(-4)) → E¹(-1 ,0)

F(-5 +2 , -1 +(-4)   → F¹(-3 ,-5)

G( 1+2 , 1+(-4)   → G¹(3 ,-3))

Step-by-step explanation:

Explanation:-

Now we will applying below rules

Type of transformations                 change to co-ordinate point

vertical translation up 'd' units                 (x,y)→(x, y+d)

vertical translation down 'd' units            (x,y)→(x, y-d)

Horizontal translation left 'C' units            (x,y)→(x-c, y)

Horizontal translation right 'C' units           (x,y)→(x+c, y)

Now we will apply rule is

first Horizontal translation right 'C' units  and  vertical translation up 'd' units    

Given E( -3 ,4 ), F(-5 ,1) and G(1,1)

first Horizontal translation right '2' units  and  vertical translation up '-4' units    

and it translated  E ( -3 +2 , 4+(-4)) → E¹(-1 ,0)

                           F(-5 +2 , -1 +(-4)   → F¹(-3 ,-5)

                           G( 1+2 , 1+(-4)   → G¹(3 ,-3))

Answer:C, The answer is the third option

Answer:

C

Step-by-step explanation:

AC & BC are adjacent sides.

If two sides share a vertex, then they are adjacent sides

Answer:

C: 12/45

Step-by-step explanation:

You have to divide the numerator and the denominator by the same number, and if once you divide it you get the fraction then it's the right answer. So lets take 12/45 and try it.

12/3 =4

45/3 =15

4/15

Answer:

0.705

Step-by-step explanation:

Data:

walks=0.65 and is late=0.4;is not late=0.6

cycles=0.35 and is late=0.1;is not late=0.9

The probability of sheila walking and not being late:  

0.65 x 0.6=0.39  

AND probability of being not late and cycling:

0.35 x 0.9=0.315

therefore,the probability of sheila walking or cycling and still not being late:

0.39+0.315=0.705

Answer:14:28:98

Step-by-step explanation:

To divide a value by a ratio, we first find the total number of parts:

1+2+7 = 10

Then, we divide the value by the number of parts and multiply it by the number of parts in each section of the ratio:

140 divided by 10 = 14.

Part 1: 14 x 1 = 14

Part 2: 14 x 2 = 28

Part 3: 14 x 7 = 98

Answer:

60 m³

Step-by-step explanation:

A rectangular prism also called a cuboid is a shape that have six faces that are rectangles. The volume of a rectangular prism is the product of its length, width and height, i.e volume = length (l) × breadth (b) × height (h).

Given a prism with a base of length (l) = 5 m  by width (w) = 3 m and a height (h) = 4 m.

Volume= l × b × h

Volume = 5 m × 4 m × 3 m = 60 m³

Answer:

60m3

Step-by-step explanation:

Answer:

[tex] \boxed{112} [/tex]

Step-by-step explanation:

[tex]Evaluate - 4v {c}^{2} \: where \: v= - 7 \: and \: c= - 2 : \\ = > - 4v {c}^{2} \\ = > - 4( - 7) {( - 2)}^{2} \\ \\ {( - 2)}^{2} = 4: \\ = > - 4( - 7)4 \\ \\ - 4( - 7) = 28: \\ = > 28 \times 4 = 112[/tex]

Answer:

2520

Step-by-step explanation:

Answer:

£12

Step-by-step explanation:

Mathematically, we know that the mean is calculated by dividing the sum of the numbers by the count of the numbers.

Now, when they were 6 and the mean is £5, this means that the total is simply

6 * 5 = £30

Now, when a new student join, there is an increase in the value of the mean.

A new student joining means they are now 7 with the total now 7 * £6 = £42

Now the difference between the total of 6 and 7 will be £42 - £30 = £12

This value represents what the new pupil receive each week

Answer:

false

Step-by-step explanation:

Answer:

x= -1, y= 3

Step-by-step explanation:

First, label the 2 equations.

x +2y= 5 -----(1)

x +3y= 8 -----(2)

(2) -(1):

x +3y -(x+2y)= 8 -5

x +3y -x -2y= 3

y= 3 (simplify)

subst. y=3 into (1):

x +2(3)= 5

x +6= 5

x= 5 -6 (bring constant to 1 side)

x= -1

Answer:

[tex]40 \:mm[/tex]

Step-by-step explanation:

An equilateral triangle has 3 equal sides.

[tex]\frac{120}{3} =40[/tex]

Answer:

40mm

Step-by-step explanation:

Perimeter of an equilateral=3a

120=3a

a=120/3

a=40mm