How to factorise completely please help this is algebra
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If a photo below is being enlarged you a 24 negative by 30 inches current. The scale factor being used to enlarge it is: 6.

Given:

Enlarged size=24 negative by 30 inches

Original size=4 in, 5 in

Using this formula

Let k represent the (ratio) scale factor being used to enlarge it

Scale factor/Enlarged size/Original size

Let plug in the formula

K=24/4

K=6

K=30/5

K=6

Therefore if a photo below is being enlarged you a 24 negative by 30 inches current. The scale factor being used to enlarge it is: 6.

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The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.

An equation is an expression that shows the relationship between two numbers and variables.

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Let f(t) represents the number of subscribers and t represents the time in months. Hence:

[tex]f(t) = 250(1.4)^t[/tex]

a = 250, b = 1.4

The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.

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Answer: 250,      1 month,      and    1.4

Answer:

8 one-dollar bills

3 five-dollar bills

2 ten-dollar bills

Step-by-step explanation:

Let x = # of one-dollar bills, y = # of five-dollar bills, and z = # of ten-dollar bills. Total amount in the wallet is $43, so the first equation would be 1x + 5y + 10z = 43. Next, there are 4 times as many one-dollar bills as ten-dollar bills, so x = 4z. There are 13 bills in total, so x + y + z = 13

x + 5y + 10z = 43

x = 4z

x + y + z = 13

x + 5y + 10z = 43

x + 0y - 4z = 0

x + y + z = 13

5y + 14z = 43

-y - 5z = -13

5y + 14z = 43

-5y - 25z = -65

-11z = -22

z = 2

x = 4z

x = 4*2 = 8

x + y + z = 13

8 + y + 2 = 13

10 + y = 13

y = 3

Answer:

23

Step-by-step explanation:

The values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].

To find the values of x:

Given equation: [tex](x+7)(x-9)=25[/tex]

Then: [tex]x(x-9)+7(x-9)=25[/tex]

Using the distributive property: [tex]a.(b+c)=a.b+a.c[/tex]

[tex]x^{2} -9x+7x-63=25[/tex]

Combine like terms:

[tex]x^{2} -2x-63=25[/tex]

Subtract 25 from both sides and obtain:

[tex]x^{2} -2x-88=0[/tex]

Using completing square form:

Add and subtract [tex](\frac{2}{2} )^{2} =1[/tex] we have:

[tex]x^{2} -2x-88+1-1=0\\(x-1)^{2} -89=0[/tex]

Add 89 to both sides we have:

[tex](x-1)^{2} =89[/tex]

Taking square roots on both sides, obtain:

[tex]x-1=[/tex] ± [tex]\sqrt{89}[/tex]

Add 1 to both sides we have:

[tex]x=1[/tex]±[tex]\sqrt{89}[/tex]

Therefore, the values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].

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The complete question is given below:

Use completing the square to solve (x + 7)(x – 9) = 25 for x.

The time it will take for the car to skid for 150 feet is 8.23 seconds.

The function D(t) = 18t² − 130t gives the distance a car going a certain speed will skid in t seconds.

The time the it would take for the car to skid for 150 feet can be calculated as follows:

Therefore,

D(t) = 18t² - 130t

150 =  18t² - 130t

18t² - 130t - 150 = 0

divide by 3

9t² - 65t - 75 = 0

Hence,

t = 65 ± 5√277 / 18

t = 8.23425471586 or -1.01166666667

Hence,

t = 8.23 seconds.

Therefore, the time it will take for the car to skid for 150 feet is 8.23 seconds.

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The ratio of white to black horses is 2:5.

Ratio expresses the relationship between two or more numbers. Ratio is used to compare two or more numbers with each other. It shows the frequency that one value is contained within other value(s).

The ratio of white to black horses = number of white horses : number of black horses

The ratio of white to black horses = 6 : 15

6 : 15 is not expressed in its simplest form yet. To convert the ratio to its simplest form, divide the numbers by a common factor of 6 and 15. A common factor is a number that divides two or more numbers perfectly with leaving any remainder. A common factor of both numbers is 3

(6/3) : (15/3) =  2 : 5

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The number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.

If the two work together;

Time taken for both to complete the task = Surveyors rate of work + Apprentice rate of work

= 1/8 + 1/7

= (7+8) / 56

= 15/56 hours

Therefore, the number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.

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Answer: D

Step-by-step explanation: The line of best fit is a straight line that passes through as many points as possible and has around the same number of points above and below it. D meets those requirements the best.

Answer:

Line D

Step-by-step explanation:

Line D is most fit because it intercepts more of the dots on the graph, if not, comes close to touching the majority of them.

Using the algebraic equation, (2x + 6)/5 = 4x - 3, it has been proved that x = 7/6

Algebraic Proof for the Given Algebraic Equation

The given algebraic equation is,

(2x + 6)/5 = 4x - 3

2x + 6 = 5(4x - 3)

2x + 6 = 20x - 15

20x - 15 = 2x + 6

This algebraic equation can be written as,

20x - 2x - 15 = 6

18x = 15 + 6

18x = 21

x = 21/18

x = 7/6

Hence, using the given algebraic equation, it has been proved that the value of x is 7/6.

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If they work together, they need 15/8 hours to assemble one shelving unit.

What does work mean in math?

According to tittle, we know worker A can  assemble a shelving unit in 5 hours , which means worker A can finish 1/5 of work in 1 hour . And worker B can finish 1/3 of work in 1 hour.

If A & B work together , they will spend the same time t to assemble only one shelving .

That means,                  1/5t + 1/3 t = 1                         (equation)

1/5 t is worker A's workload during time t , 1/3 t is worker B workload.

So,   1/5 t + 1/3t = 1  is the answer

     ⇒ 5t + 3t = 15

     ⇒ t = 15/8 hours

If they work together, they need 15/8 hours to assemble one shelving unit.

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Answer:

Letter C is the correct answer or  1/5 t + 1/3t = 1

Answer:

  i) 441π cm² ≈ 1385.4 cm²

  ii) 196π cm² ≈ 615.8 cm²

Step-by-step explanation:

The areas of circles with radius 21 cm or diameter 28 cm can be found using the appropriate area formula.

The formula for the area of a circle based on its radius is ...

  A = πr²

When the radius is 21 cm, the area is ...

  A = π(21 cm)² = 441π cm² ≈ 1385.4 cm²

The formula for the area of a circle based on its diameter is ...

  A = (π/4)d²

When the diameter is 28 cm, the area is ...

  A = (π/4)(28 cm)² = 196π cm² ≈ 615.8 cm²

Answer:

Before multiplying by pi. 441π cm²

After multiplying by pi. 1384.74 cm²

Step-by-step explanation:

The formula for area of a circle is πr².

r=radius

Square the radius.

21²=441

If they want the answer in this form: 441π cm². If not, then use 3.14 for π.

441*3.14=1384.74

The answer is 1384.74 cm².

Hope this helps!

[tex]\bf{ (x^2-5x)(2x^2+x-3)}[/tex]

[tex]\bf{Distribute \ the \ sum \ group. }[/tex]

[tex]\bf{Expand \ the \ distribution \ of \ terms. }[/tex]

[tex]\bf{Remove \ parentheses. }[/tex]

[tex]\bf{Collect \ like \ terms. }[/tex]

[tex]\bf{Simplify}[/tex]

Answer:

4

Step-by-step explanation:

1. Convert from mixed number to fraction

[tex]5\frac{1}{2} =\frac{5(2)+1}{2} =\frac{11}{2}[/tex]

[tex]1\frac{3}{8}=\frac{(1)(8)+3}{8} =\frac{11}{8}[/tex]

2. Divide fractions

[tex]\frac{\frac{11}{2} }{\frac{11}{8} } =\frac{(11)(8)}{(11)(2)} =\frac{8}{2} =4[/tex]

Hope this helps

Answer:r=14°

Step-by-step explanation:

(5r-5)°+ (8r+3)°=180

(Sum of angles on a straight line =180°)

Collect like terms

5r+8r-5+3=180

13r-2=180

13r=180+2

13r=182

r=182/13

r=14°

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Given:

f(x) = ln(x)

n = 4

c = 3

nth Taylor polynomial for the function, centered at c

The Taylor series for f(x) = ln x centered at 5 is:

[tex]P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+ \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]

Since, c = 5 so,

[tex]P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+ \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}[/tex]

Now

f(5) = ln 5

f'(x) = 1/x ⇒ f'(5) = 1/5

f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25

f'''(x) = 2/x³  ⇒ f'''(5) = 2/5³ = 2/125

f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625

So Taylor polynomial for n = 4 is:

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Hence,

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

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Answer:

5/3

Step-by-step explanation:

z = (Distributed score - Mean)/Standard deviation= (80-70)/6 = 5/3

Step-by-step explanation:

z = (specific score - mean) / standard deviation

in our case

z = (80 - 70)/6 = 10/6 = 5/3 = 1.666666... ≈ 1.67

as most z-tables round the z-scores to hundredths.

not to forget : the sign matters. so, don't worry, if you have e.g. a specific score of 60 :

(60 - 70)/6 = -10/6 = -5/3 = -1.666666... ≈ -1.67

you did not do anything wrong. that is all ok and valid.

Answer:

it's side length equals to 8.

Step-by-step explanation:

An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle.

Perimeter: 3 x side of equilateral triangle

[tex]24 = 3 \times each \: sides[/tex]

divide both sides by 3

[tex]one \: of \: its \: side = 8[/tex]

Thus, as all the three sides equals to 8.

Hope it helps!

Answer:

68

Step By Step Explanation:

Evaluate for a=3,b=2

(5)(3)(2)+(4)(2)+(10)(3)

(5)(3)(2)+(4)(2)+(10)(3)

=68

Answer:

The solution is 68

Step-by-step explanation:

a = 3 and b = 2

5ab+4b+10a

= 5(3)(2)+4(2)+10(3)

= 5(6)+8+30

= 30+8+30

= 38+30

= 68

The base side of the isosceles triangle in discuss as described in the task content is; 10cm.

According to the task content, the area of the isosceles triangle is 60 square cm.

Since, the length of its longest sides is 13 cm and since it follows from convention that the bisection of an isosceles triangle results in the formation of two right-triangles.

Consequently, it follows from Pythagoras triples that the height of each right triangle is 12 and its base is; 5.

Consequently, the base of the whole isosceles triangle is; 2 × 5 = 10cm.

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Answer:

-65

Step-by-step explanation:

23-2(17+3^3)

23-2(17+27)

23-2(44)

23-88

=-65

The graph of the four linear equations is the one we can see below, such that:

Here we have the set of linear equations:

We want to graph these 4 lines on the same coordinate axis.

The line:

y = -3

Is an horizontal line at y = -3

The line:

x = -3

Is a vertical line at x = -3.

And the other two are common linear equations that are graphed in the usual way, then the graph of all the linear equations is the one you can see below.

Where:

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Given

[tex]f(x) = \begin{cases} -x^2 - 1 & \text{if }x \neq 5 \\ -3 & \text{if }x=5 \end{cases}[/tex]

we have

[tex]\displaystyle \lim_{x\to5} f(x) = \lim_{x\to5} (-x^2-1) = -5^2-1 = \boxed{-26}[/tex]

since we are approaching [tex]x=5[/tex], so effectively [tex]x\neq 5[/tex] and we use the definition of [tex]f(x)[/tex] under that condition.

The y-coordinate that completes the point exists 5.

An ordered pair (x, y) denotes the x-and-y coordinates of a general point, where x exists the input value of a function and y exists the output value of a function.

The output value exists y = f(x) and must be found using the rule (function) to the given input value.

In this case the rule exists f(x) = - 3x + 2, and the input value, x, exists - 1 (the first value of the ordered pair).

This exists the mathematical procedure:

x = - 1

f(x) = f (-1)

Then substitute the value x = -1 then

f(-1) = -3 (-1) + 2 = 3 + 2 = 5.

Therefore, the correct answer is option b) 5.

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The volume of the triangular prism as described is; 20 cubic foot.

A triangular pyramid refers to pyramid which has a triangular base

It follows from the formula for calculating the volume of a triangular prism that;

Volume = (1/3) × base area × height.

Consequently,

volume of the prism = (1/3) ×5 × 12

Volume = 20 cubic foot

Therefore, volume of the triangular prism as described is; 20 cubic foot.

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Answer:

Value of a is 16.

Step-by-step explanation:

Solution Given:

we know that

Geometric mean=[tex]\sqrt{a*b}[/tex]

By using this formula

20=[tex]\sqrt{a*25}[/tex]

20=5[tex]\sqrt{a}[/tex]

dividing both side by 5, we get

20/5=5/5*  [tex]\sqrt{a}[/tex]

4=[tex]\sqrt{a}[/tex]

squaring both side

4²=a

:. a=16

Answer:

(8,14)

Step-by-step explanation:

3x+2y=52

3x+1y=38 Subtract these equations using elimination method to get y=14

Then substitute y=14 to either equation

the bottom one is easier so

3x+1(14)=38 distribute 1 to 14 and any number times one is 1

3x+14=38 Subtract 14 from both sides

3x=24 Divide by 3

x=8 so check now

3(8)+1(14)=38

24+14=38?

38=38? yes