Three years ago, dedrick's age was a third of francisca's age. in 13 years, francisca's age will be twice dedrick's age. how old are they now?

The correct values of a and b to rewrite the expression as (x + a)(x + b) are:

a = 9

b = -8

So, (x + 9)(x - 8) is the correct form of the given expression.

Here, we have to rewrite the expression x² + x - 72 in the form (x + a)(x + b), we need to find two numbers a and b such that when multiplied,

it give us the constant term -72 and when added, it give us the coefficient of the x term, which is 1.

The expression x² + x - 72 can be factored as follows:

x² + x - 72

= x² + 9x - 8x - 72

=x(x+9) -8(x+9)

= (x + 9)(x - 8)

Therefore, the correct values of a and b to rewrite the expression as (x + a)(x + b) are:

a = 9

b = -8

So, (x + 9)(x - 8) is the correct form of the given expression.

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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:

y=ax+b

a=-0.6020457867

b=-2.256697516   <------- There is your value for b, which is the answer to the problem.

You can use these values for a and b to generate an equation in slope-intercept form, which you can then enter under Y= and view the graph.

Step-by-step explanation:

The value of y is multiplied by 2 each time when the value of x increases by 1 and this can be determined by using the arithmetic operations.

Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.

Given that,

Table --    x            y

                1            20

                2            40

                3            80

                4            160

                5            320

The following steps can be used in order to describe how the y values are changed over each interval:

Step 1 - When value of (x = 1) and the value of (y = 20).

Step 2 - When value of (x = 2) and the value of (y = 40).

Step 3 - When value of (x = 3) and the value of (y = 80).

Step 4 - When value of (x = 4) and the value of (y = 160).

Step 5 - From the above steps, it can be concluded that the value of y is multiplied by 2 each time when the value of x increases by 1.

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Answer:

hey diddle the medians the middle

you add and then divide for the mean

the mode is the one you see the most and the range is the difference between.

Hope this helps you with your question

Step-by-step explanation:

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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Answer: 2

Step-by-step explanation:

The opposite of a negative number is the corresponding positive number.

The function would become an exponential decay function.

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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Step-by-step explanation:

please mark me as brainlest

Answer:

Graph B

Step-by-step explanation:

When graphing inequalities:

Given inequality:

[tex]y-5 > 2x-10[/tex]

Rearrange the given inequality to make y the subject:

[tex]\implies y-5+5 > 2x-10+5[/tex]

[tex]\implies y > 2x-5[/tex]

Therefore, we need to draw a dashed line and shade above it.

To draw the line:

Replace the > with = to find two points on the line:

[tex]\implies y=2x-5[/tex]

[tex]x=0 \implies y=2(0)-5=-5 \implies (0,-5)[/tex]

[tex]x=3 \implies y=2(3)-5=1 \implies (3,1)[/tex]

Plot the two found points: (0, -5) and (3, 1)

As the inequality is  y > 2x - 5

The inequality equation is solved and the solution is plotted on the graph

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y - 5 > 2x - 10

On simplifying , we get

Adding 5 on both sides , we get

y > 2x - 5

where 2 is the slope and 5 is the the intercept

Now , let the first point be P ( 0 , -5 )

when x = 0 and y = -5

-5 > -5

And , the graph of the inequality is plotted

Hence , the inequality is solved

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Answer:

Standard Deviation is s = 2.9

Step-by-step explanation:

Count = [tex]N[/tex] = 5

Mean = [tex]x^-[/tex] = 9

Variance = [tex]s^2[/tex] = 8.5

SD Formula = [tex]s = \sqrt \frac{1}{N - 1} (x_{i} - x^-)^2[/tex]

Variance Formula[tex]s^2 = \frac{(x_{i} - x^-)^2}{N- 1}[/tex]

Step 1: Calculate the variance

[tex]= \frac{(7-9)^2 + (5-9)^2 + (10-9)^2 + (11-9)^2 + (12 -9)^2 }{5-1}[/tex]

[tex]=\frac{34}{4} = 8.5[/tex]

Step 2: Apply square root/SD formula

[tex]=\sqrt{8.5} = 2.9[/tex]

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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The correct option is B. The Wolverines' distribution is negatively skewed, but the Panthers' distribution is symmetric.

Data is symmetric if the median is in the mid of the box plot and the box is mid to the line connecting both whiskers.

The box plot showing scores for the Panthers basketball team has the median shown by a vertical line dividing the box into 2 equal halves.

Also, both whiskers on either side are relatively equal which shows that the data set for bulldogs is symmetric.

On the other side, the box plot for wolverine shows the median closer to the upper quartile.

That shows that the data set for team Wolverines' distribution is negatively skewed.

The correct option is B. The Wolverines' distribution is negatively skewed, but the Panthers' distribution is symmetric.

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Answer:

10.5 is the correct answer.

Step-by-step explanation:

Due to the fact Triangle CAB has "6" as its length, and Triangle FDE has "2" as its length, you multiply 3.5 and 3.

3.5 x 3=10.5

2 x 3=6

3.5/2=10.5/6, so the answer is 10.5.

Answer:

Step-by-step explanation:

Find the value of x, given that the two triangles are similar.

​

Given that the two triangles are similar we can solve with a proportion

6 : 2 = x : 3.5

x = 6 * 3.5 : 2

x = 21 : 2

x = 10.5

The quadratic equation is  3x² - 27.

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

Given:

The roots are 3 and -3

We have

α= 3   and β=-3

So,

α+β = -b/a  and αβ = c/a

α+β = 0 =-b/a and  αβ= -9 = c/a

Comparing from above

a=1, b= 0 and c=-9

Also, the leading coefficient is 3.

Then the quadratic equation is,

= 3(ax² + bx + c)

= 3( x² +0x- 9)

Hence, the quadratic equation is 3x² - 27.

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The side length of the original cube is 1.95 inch.

Let each side length of each cube be 'x' inch.

Given : New side = (x+4 ) inch

Another new side = 2x inch

Since the sides are not equal, so it forms a cuboid in the case of new sides as given.

Also, according to question,

The volume of new rectangular prism is 450 cubic inches

= (x+4)*2x*x = 450

⇒ 2x cubed 8x squared =450

=16x5=450= 1.95 inch ( by taking out the cubic root of x3=7.5)

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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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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:

choosing 1 red marble

choosing 1 white marble, replacing it, and choosing another white marble

choosing 1 white marble

Step-by-step explanation:

red marble has a 30 percent chance

1 white marble and then replacing and another white marble is 25% chance

1 white marble is 50% chance

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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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

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 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:

Answer: 2

Step-by-step explanation:

By the geometric mean theorem,

[tex]\sqrt{8k}=4\\\\8k=16\\\\k=\boxed{2}[/tex]

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:

57 square units

Step-by-step explanation:

Area is = Length x Width

Given:

f(x)= 4x + 3    Length

g(x)=2x-5      Width

x = 4

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

Width

g(x)=2x-5

g(4)=2(4)-5

g(4)= 3

Length

f(x)= 4x + 3

f(4) = (4)(4) + 3

f(4) = 19

Area = (length)*(width)

Area = f(x)*g(x) for x = 4

Area = (f(4))*(g(4))

Area = (19)*(3)

Area = 57 square units

Answer:

34 and ⅔

Step-by-step explanation:

added in the picture

[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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