factorise the following expressions:
a) 14w + 21
b) 27x+18​

Answer:

34 and ⅔

Step-by-step explanation:

added in the picture

The water travels in 3 seconds.

The correct option is (C).

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given information-

x          0       1       2       3      4      5

f(x)     1.5      2     1. 5     0    -2.5   -6

The image of table attached below.

Here, x represents the time (sec) and f(x) represent the height in feet above the pool’s water line.

From the table,

Hence, the water travel through the air for the 3 seconds.

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Answer:

12 km

Step-by-step explanation:

Let the total distance to be traveled = x

[tex]\sf \dfrac{4}{5} \ of \ the \ journey = 48\\\\[/tex]

        [tex]\sf \dfrac{4}{5}*x = 48\\\\[/tex]

             [tex]x = 48*\dfrac{5}{4}[/tex]

                = 12 * 5

            x = 60 Km

Distance still to traveled = 60 - 48 = 12Km

The parent function y=1/x²

If a function f(x) is shifted horizontally by k units the parent function f(x) becomes f(x+ k) where k>0

Here, the parent function y=1/x²

Add 3 to x in the denominator as the graph is shifted to left 3.

and, Add 1 to the fraction, because the graph is shifted up 1 unit.

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Answer

12

Step-by-step explanation:

The statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).

Linear inequality is defined as the comparison of two values using greater than, less than, greater than or equal to, and less than or equal to.

Using the general formula for linear inequality,

y >mx+ b

y > 3/4x - 2

Where m = slope of the graph

b = interception at y axis

Therefore, the statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).

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The speed that Jo walked for the first 15 minutes is; 6 km/hr

The distance - time graph is missing and so i have attached it.

Now, the formula for speed is;

Speed = Distance/time

The distance after 15 minutes from the graph is 1.5km.

Now, 15 minutes when converted to hours is 15/60 = ¹/₄ hr

Thus, the speed that Jo walked for the first 15 minutes is;

Speed = 1.5/(¹/₄)

Speed = 6 km/hr

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10. The missing conversion is 20.32 inches

11. Total number of red cars is 34

12. Total number of blue cars is 36

13. Total number of silver cars is 70

Ratio is the number of times a quantity is contained more  or less than another in a whole.

Analysis:

10. If 1 inch = 2.54cm

     Then 8 inches = 8 x 2.54cm = 20.32 cm

     First car park: Total number of cars = 60

     ratio of red:blue:silver = 1:2:3

     Total ratio = 1+2+3 = 6

     number of red cars = 1/6 x 60 = 10

     number of blue cars = 2/6 x 60 = 20 cars

     number of silver cars = 3/6 x 60 = 30

   second car park: Total number of cars = 80

    ratio of blue: red: silver = 2:3:5

    total ratio = 2+3+5 = 10

    number of red cars = 3/10 x 80 = 24

    number of blue cars = 2/10 x 80 = 16

    number of silver cars = 5/10 x 80 = 40

11.  Total number of red cars = 10+24 = 34

12.  Total number of blue cars = 20+16 = 36

13.  Total number of silver cars = 30+40 = 70

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:f < 0 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 33 + 6f < 33[/tex]

[ subtract 33 on both sides ]

[tex]\qquad \tt \rightarrow \: 33 - 33+ 6f < 33 - 33[/tex]

[tex]\qquad \tt \rightarrow \: 6f < 0[/tex]

[tex]\qquad \tt \rightarrow \: f < 0[/tex]

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The correct answer is option B which is mixture B will have the highest ratio of blue paint.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

The given ratios are:-

Mixture A = [tex]\dfrac{5}{12} = 0.41[/tex]

Mixture B = [tex]\dfrac{6}{6}= 1[/tex]

Mixture C = [tex]\dfrac{4}{12}= 0.33[/tex]

Mixture B = [tex]\dfrac{5}{6}=0.83[/tex]

Here the ratio of mixture B is the highest among all the options available.

Therefore the correct answer is option B which is mixture B will have the highest ratio of blue paint.

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Answer:

6.75 servings

Step-by-step explanation:

[tex] \frac{3}{4} \times 9 = \frac{27}{4} = 6 \frac{3}{4} = 6.75[/tex]

Answer:

9 servings

Step-by-step explanation:

feel free to ask where you don't understand.

Answer:

B. Exactly One Solution

Step-by-step explanation:

Given:

[tex]7(y+3)=5y+8[/tex]

Expand the brackets:

[tex]\implies 7y + 21 = 5y + 8[/tex]

Subtract 21 from both sides:

[tex]\implies 7y + 21-21 = 5y + 8-21[/tex]

[tex]\implies 7y=5y-13[/tex]

Subtract 5y from both sides:

[tex]\implies 7y-5y=5y-13-5y[/tex]

[tex]\implies 2y=-13[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{2y}{2}=\dfrac{-13}{2}[/tex]

[tex]\implies y=-\dfrac{13}{2}[/tex]

Therefore, the equation has exactly one solution.

The value of a2+b2 = 0.05

The value of a3+b3 = 41.73

Concept: (a+b)2 = a2+b2+2ab

(a-b)2 = a2+b2-2ab

(a+b)3 = a3+b3+3a2b+3ab2

(a-b)3 = a3-b3-3a2b+3ab2

(I) a²+b²=(1/7-4✓3)²+(1/7+4✓3)²

⇒ ( 1/49 - 48) +(1/49 + 48)=(1-2352/49) + (1+2353/49)

⇒ -47.97 +48.02= 0.05

(ii) a³+b³=(1/7-4✓3)³+(1/7+4✓3)³

⇒(-6.78)³ +(7.07)³

⇒-311.66 +353.39= 41.73

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The x-intercept is (16, 0) and y- intercept is (0, 6).

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Given: 24x+64y=384

For y- intercept, put x=0

Then,

24*0+64y=384

64y= 384

y= 6

Now, for x- intercept put y=0

Then,

24x+64*0=384

24x= 384

x= 15

Hence, the x-intercept is (16, 0) and y- intercept is (0, 6).

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Answer:

Sample Answer: Substitute 0 for the x-value in the equation and solve for y. The result is y = 6, so the y-intercept is at (0, 6). Next, substitute 0 for the y-value in the equation and solve for x. The result is x = 16, so the x-intercept is at (16, 0).

Step-by-step explanation:

The constant of proportionality will be 3.

The complete question ks given below:-

Explain how to find the constant of proportionality for the ratio of robins to cardinals. A 2-column table with 4 rows. Column1 is labelled Cardinals with entries 5, 6, 9, and 10. Column 2 is labelled Robins with entries 15, 18, 27, and 30.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

Given data will be arranged as follows:-

robins              15, 18, 27,  30.

cardinals         5, 6, 9, 10.

The constant of proportionality will be calculated by taking a ratio of the data:-

[tex]\dfrac{Cardinals}{Robins} =\dfrac{15}{5}=\dfrac{18}{6}=\dfrac{27}{9}=\dfrac{30}{10}=3[/tex]

Therefore the constant of proportionality will be 3.

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Both the Red and Yellow lines are lines of symmetry, Option D is correct.

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Lines of symmetry in a figure are lines that divide the figure into equal parts.

The given figure is a square as we observe the four sides are equal in the given shape.

In a square, there are four lines of symmetry, each of which divides it into two identical parts.

The symmetry lines of a square are both its diagonals and the lines joining the midpoints of its opposite sides (bisectors).

In the given Figure, the Red lines cuts the shape into 2 equal halves vertically and the Yellow line cuts the shape into 2 equal halves diagonally.

Hence, both the Red and Yellow lines are lines of symmetry, Option D is correct.

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Answer:

quadratic with a common second difference of 4

Step-by-step explanation:

quadratic equations: Quadratic equations are the polynomial equations of degree 2 example - a[tex]x^2\\[/tex]+ b[tex]x[/tex] + c = 0.

                               [tex]\begin{array}{cc}x&y\\-2&8\\-1&2\\0&0\\1&2\\2&8\end{array}\right][/tex]

from the table it is clear that,

function is y = 2[tex]x^2\\[/tex]

so the function is not linear as the equation specifies.

formula to find second difference of a quadratic equation:

f(x + 2) - 2f(x + 1) + f(x)

therefore;

[tex]2(x+2)^2[/tex] - [tex]4(x+1)^2[/tex] + [tex]2x^2[/tex]

[tex]2(x^2 + 4x + 4) - 4(x^2 + 2x+ 1 ) + 2x^2[/tex]

[tex]2x^2 + 8x + 8 - 4x^2 - 8x - 4 + 2x^2[/tex]

[tex]4x^2 - 4x^2 + 8x - 8x +8 - 4[/tex]

4

therefore, the answer is quadratic with a common second difference of 4

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Answer:

Shape is rectangle

Area of rectangle = length * width

= 5 * 3

= 15 units²

The closest benchmark for 99% is 100%.

We know that benchmarks in mathematics are the norm or point of comparison that something can be measured, compared, or evaluated against. Benchmark values are values that can be used to estimate and contrast other values or quantities. Typically, benchmark figures are multiples of 10 or 100. 0 percent, 10 percent, 25 percent, 50 percent, 75 percent, and 100 percent are the most popular benchmark percentages.

Here we have to find the closest benchmark for 99%. Clearly, from the definition 100% is the required answer.

We can conclude that the closest benchmark for 99% is 100%.

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Answer:

At the end of the multi step problem

Answer: 128

Step-by-step explanation:

[tex]4^3 = 4*4*4 = 16*4 = 64[/tex]

[tex]8^2 = 8*8 = 64[/tex]

[tex]64+64 = 128[/tex]

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: a_{33} = 1\degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

In a matrix, [tex] \sf a_{ij} [/tex] represents an element in " i " th row and " j " th column.

Henceforth, element [tex] \sf a_{33} [/tex] represents element in 3rd row and 3rd column.

[tex]\qquad \tt \rightarrow \:a_{33} = 1[/tex]

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Answer:

Rational.

Step-by-step explanation:

[tex]\textbf{A rational number is a real number that can be expressed as}~ \dfrac{p}{q},\\\\\textbf{where}~ p~ \textbf{and}~ q~ \textbf{are integers.}\\\\ \boxed{50.2 = \dfrac{502}{10}}\\\\ \textbf{50.2 can be expressed as a ratio of two integers,}~ \textbf{so it is a rational number.}[/tex]

Answer:

Step-by-step explanation:

Solve for x in the equation

x/5 - 2 = 11

x/5 = 11 + 2

x/5 = 13

x = 5 * 13

x = 65

-----------------

check

65/5 - 2 = 11

13 - 2 = 11

11 = 11

the answer is good

Answer:

4

Step-by-step explanation:

The median is the middle number when the list is sorted from least to greatest or greatest to least.

We make this list to get 2,3,4,5,8 or 8,5,4,3,2 and the middle number in both lists is 4.

Answer: 3

Reason:

Going from x^2 to (x+5)^2 means we shift the graph 5 units to the left.

The +3 at the end shifts the parabola up 3 units. This is because we add 3 to each y value. For instance a point like (0,25) moves to (0,28)