Three years ago the sum of the ages of father and his son was
48 years and three years hence father's age will be three times
that of his son. Find the present ages of the father and his son.​

Answer:

f(x)=|x+6|

Step-by-step explanation:

because it is moving the function without changing the slope

Answer:

The signs will be + and -

Step-by-step explanation:

Required

The signs in the parenthesis of difference of two squares

Let the expression be:

[tex](x^2 - a^2)[/tex]

Expand

[tex]x^2 - a^2 = x^2 -ax + ax - a^2[/tex]

Factorize

[tex]x^2 - a^2 = x(x -a) + a(x - a)[/tex]

Factor out x - a

[tex]x^2 - a^2 = (x +a)(x - a)[/tex]

See that the sign in front of a is + and - in the parentheses

Answer:

d.

Step-by-step explanation:

The gradient is -5 meaning that it's going downwards as x increases

The y-intercept is 3

Feel free to mark as brainliest :D

Answer:

follow me and I will answer it

Answer:

The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.

Step-by-step explanation:

Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. Test if more people are using now.

At the null hypothesis, we test if the same number of people is still using, that is, the mean is 350. So

[tex]H_0: \mu = 350[/tex]

At the alternate hypothesis, we test if this mean increased, that is:

[tex]H_1: \mu > 350[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

350 is tested at the null hypothesis:

This means that [tex]\mu = 350[/tex]

After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25.

This means that [tex]n = 35, X = 405, s = 25[/tex].

Test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{405 - 350}{\frac{25}{\sqrt{35}}}[/tex]

[tex]t = 13.02[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean above 405, which is a right-tailed test with t = 13.02 and 35 - 1 = 34 degrees of freedom.

Using a t-distribution calculator, this probability is of 0.

The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.

Answer:

A

Step-by-step explanation:

The pattern is blue red blue red

+

The pattern is vertical horizontal vertical horizontal

Answer:

A.

The second figure adds another red horizontal line to the first. The third adds a vertical blue line to the second. The fourth must add a red horizontal line to the third.

Answer: 125.6

Step-by-step explanation:

The surface area of the given composite figure will be 384 square cm.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

In the given image we have a composite figure one is a rectangular cuboid and the other is a triangular prism. The surface area will be equal to the sum of all the outer sides of the figure.

The surface area of the triangular shape will be calculated as:-

SA = 2( Area of triangle ) + Area of rectangular surfaces

SA = 2 ( (1/2) B x H )  + (5 x 6 ) + ( 6 x 3  )

SA = ( 3 x 4 ) + (  30 ) + ( 18 )

SA = 12 + 30 + 18

SA = 60 square cm

The surface area of the rectangular cuboid will be calculated as:-

SA = ( 4 x 6 ) + 2 ( 158 x 4 ) + 2 ( 15 X 6 )

SA = 24 + 120 + 180

SA  = 324 square cm

Total surface area will be = 324 + 60 = 384 square cm.

Therefore the surface area of the given composite figure will be 384 square cm.

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For the given condition the age of the son will be 69 years.

A mathematical equation asserts the equality of two expressions, which may or may not contain variables or integers. Equations are fundamental concerns, and efforts to rationally address them have served as the primary driving forces behind the creation of mathematics.

Suppose the two-digit number is x,

The father's and son's ages are 10x+y and 10y+x respectively.According to the given condition,

(10x+y) -(10y+x)=27

9x-9y=27

x-y=27/9

x-y=3

The value of x and y will be 4 and 1.

At x=9 and y=6, the age of the son is obtained as,

=10×6+9

=69 years

Thus, the age of the son will be 69 years.

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Answer:

I'm pretty sure it's either 3.1 or 4.1

Step-by-step explanation:

Answer:

x = (571 ± √186217) / 18

x ≈ 7.74840677368558702303.. or 55.69603767075885742140..

x ≈ 7.75 or 55.70

Step-by-step explanation:

y = -9x² + 571x – 3884.

x = (-b ± √b² – 4ac) / 2a

x =

(-(571) ± √((571)² – 4((-9) × (-3884))) / 2(-9)) →

(-571 ± √(326041 – 4(34956))) / -18) →

(-571 ± √(326041 – 139824)) / -18) →

(-571 ± √(186217)) / -18 →

(571 ± √186217) / 18 →

Answer:

E. j<5.5

Step-by-step explanation:

Step by step explanation

Answer:

Add I think

If there is a plus sign shouldnt it be adding

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Please find the complete question in the attached file.

[tex]\bar{x}=650\\\\\sigma =24\\\\n=36\\\\[/tex]

Calculating the sampling distribution of the sample mean:

[tex]\to \mu=\mu_\bar{x}=650[/tex]

Calculating the sampling distribution of the standard deviation:

[tex]\to \sigma_\bar{x}=\frac{\sigma}{\sqrt{n}}=\frac{24}{\sqrt{36}}=\frac{24}{6}=4[/tex]

the standard form of a quadratic formula is

y = ax^2 + bx + c

in this case you will solve using foil method

(× - 4)(x + 3)

(x × x) +( x × 3 )(- 4 × x) ( -4)× 3))

x^2 + 3x - 4x -12

x^2 - x - 12

therefore

y = x^2- x - 12

Answer:

f(-1) = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 1 - x² + x³

f(-1) is x = -1 for the function f(x)

Step 2: Evaluate

Step-by-step explanation:

Total amount of cookies= 268

One bag can hold 8 cookies

268 / 8 = 33 (remainder 4)

He can make as many as 33 bags, and there are 4 cookies left over.

Answer:

1/3

Step-by-step explanation:

there are 4 numbers total that are less than 3 and there are 12 sides total

so 4/12 would be the total and 1/3 would be simplified

Answer:

–x² + 12x + 5

Step-by-step explanation:

x² + 3x

–2x² + 9x + 5

The sum of the above expression can be obtained as follow:

.... x² + 3x

+ –2x² + 9x + 5

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

–x² + 12x + 5

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Thus, the sum of x² + 3x and –2x² + 9x + 5 is –x² + 12x + 5

9514 1404 393

Answer:

  5 and 8

Step-by-step explanation:

Factor pairs that make 40 are ...

  40 = 1×40 = 2×20 = 4×10 = 5×8

The pair that has a sum of 13 is 5 and 8.

Answer:

A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Step-by-step explanation:

Answer:

BR is about 7.3084 cm

Step-by-step explanation:

the sum of the exterior angles of any polygon is 360. The measure ox x would be 360/15= 24

since I want BR, I will use cos (adj/hyp)

cos24=s/8

.9135=s/8

7.3084=s

9514 1404 393

Answer:

  10, (x+4), (x -1)

Step-by-step explanation:

The given volume expression can be factored as ...

  V = 10x² +30x -40

  = 10(x² +3x -4)

  = 10(x +4)(x -1)

The expressions representing length, width, and height might be ...

  10, (x+4), (x -1)

Answer:

Aisha would pay 21 dollars for 8 slices.

Equation 2x(x=number of slices)+5

Step-by-step explanation:

Answer:

The total cost was $182.91.

Step-by-step explanation:

Tax formula:

tax=tax percentage×amount

Tip formula:

tip=tip percentage×amount

solve

First find the tax. Write 14% as the decimal 0.14 before using it in the equation.

tax

= tax percentage×amount

= 0.14×136.50

= 19.11

The tax was $19.11.

Now find the tip. Write 20% as the decimal 0.20 before using it in the equation.

tip

= tip percentage×amount

= 0.20×136.50

= 27.3

The tip was $27.30.

Finally, find the total cost.

total cost

= cost + tax+tip

= 136.50+19.11+27.30

= 182.91

Answer:

182.91

Step-by-step explanation:

Answer:

[tex]C.[/tex] 5/7 × 2/3

Step-by-step explanation:

Answer:

Given

A

Find the inverse of f(x):

B

C

Answer:

It is 20%

Step-by-step explanation:

$60 - $40 = $20

Answer:

The null hypothesis will be rejected

Step-by-step explanation:

The null hypothesis is that people who favour ban on stem cell research is less than or equal to 0.61

The alternate hypothesis is that people who favour ban on stem cell research is greater than 0.61

Proportion of population = 0.61

Total events = 360

Sample size = 554

Sample proportion = 360/554 = 0.649

As per test statistics –  

Z = (p-p0)/sqrt {(p0 (1-p0))/n} = (0.649 -0.61)/ {(0.61 (1-0.61))/554}

= 0.039/0.021

= 1.857

P (Z<1.857) = 1- P (Z<1.857) = 1-0.9664 = 0.0336

So alpha value is 0.064.  

Thus, we will reject the null hypothesis