MATHEMATICS HIGH SCHOOL

A quadrilateral with 90 degree angles is shown. The lengths of the left and right sides are 10 and 2 y + 4. The lengths of the top and bottom sides are 18 and 10 + 2 x.What is the value of x?

Answers

Answer 1

Answer:

Answer:

x=3

Step-by-step explanation:

2 times 3 plus 4 equals 10

Answer 2

Answer:

Answer:

x=3

Step-by-step explanation:

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A store is selling lemons at 2 for $3. Each lemon yields 2 tablespoons of lemon juice. How much will it cost to buy enough lemons to make a 9-inch lemon pie requiring 1/2 cup of lemon juice?

Answers

Answer:

It will cost $6 to buy enough lemons.

Step-by-step explanation:

Consider the provided information.

To make a 9-inch lemon pie requiring 1/2 cup of lemon juice.

1 cup = 16 tablespoons

1/2 cup = 8 tablespoons

That means we only need 8 tablespoons.

Each lemon yields 2 tablespoons of lemon juice.

Number of lemon required =8 ÷ 2 = 4

That means we need only 4 lemon.

Store is selling lemons at 2 for $3 that means 4 lemons for $6.

Hence, it will cost $6 to buy enough lemons.

Answer:

6 dollars to buy enough lemons

Step-by-step explanation:

Choose a method the find the product 16x60

Answers

the product is 960 because 0x6=0,6×6=36 so 60 times 6 is 360 thenn you go to the bottom & bring down one zero under your first zero ,multiply 1 times the zero which equals 0 ofc & 6×1=6 so it'll be 360 + 600= 960

The answer is 960 because 16 times 60 is =960

Suface areas- cones
wdh

Answers

Answer:

Step-by-step explanation:

The slant height of a cone is the length of a segment from the base to the vertext along the surface of the cone.

You can use the given dimenstions as the legs of a right triangle, and the slant heifght is rthe hyopotenuse.

L^2 = r^2 + h^2

L^2 = 5^2 + 12^2

L^2 = 169

L = 13

The slant heiht is 13 cm.

LA = (pi)rL

LA = (pi)(5 cm)(13 cm)

LA = 65(pi) cm^2

In the diagram below, the top of each stair is parallel to the floor. What is the value of y?(Picture below.)

Answers

25°
as the stair is // to floor
we can use alternate angle

Which of the following represents the zeros of f(x) = x3 − 12x2 + 41x − 42?7, −3, 2
7, −3, −2
7, 3, 2
7, 3, −2

Answers

Given the polynomial function $f(x)=x^3-12x^2+41x-42.$

The integer zeros should be divisors of free term -42.

The divisors of -42 are:

$\pm 1, \pm 2, \pm 3, \pm 6, \pm 7, \pm 14, \pm 21, \pm 42.$

If some of these number is zero of f(x), then f takes 0 value at this point.

Check them:

$f(1)=1^3-12\cdot 1^2 + 41\cdot 1-42=1-12+41-42=-12\neq 0;$

$f(-1)=(-1)^3-12\cdot (-1)^2 + 41\cdot (-1)-42=-1-12-41-42=-96\neq 0;$

$f(2)=2^3-12\cdot 2^2 + 41\cdot 2-42=8-48+82-42=0;$

$f(-2)=(-2)^3-12\cdot (-2)^2 + 41\cdot (-2)-42=-8-48-82-42=-180\neq 0;$

$f(3)=3^3-12\cdot 3^2 + 41\cdot 3-42=27-108+123-42=0;$

$f(-3)=(-3)^3-12\cdot (-3)^2 + 41\cdot (-3)-42=-27-108-123-42=-300\neq 0;$

$f(6)=6^3-12\cdot 6^2 + 41\cdot 6-42=216-432+246-42=-12\neq 0;$

$f(-6)=(-6)^3-12\cdot (-6)^2 + 41\cdot (-6)-42=-216-432-246-42=-936\neq 0;$

$f(7)=7^3-12\cdot 7^2 + 41\cdot 7-42=343-588+287-42=0.$

Since the third degree polynomial function may have only 3 zeros, then you can end this process and state that zeros are 2, 3 and 7, because f(2)=0, f(3)=0 and f(7)=0.

Answer: correct choice is C

Answer: Zeroes are,

7, 3, 2

Step-by-step explanation:

Here, the given cubic equation,

$f(x) = x^3 - 12x^2 + 41x - 42$

Since, at x = 7,

$f(7)=(7)^3-12* 7^2+41* 7 - 42 = 343 - 12* 49 +287 - 42 = 343 - 588 + 245=0$

Thus, 7 is one of the zeroes of f(x),

⇒ x - 7 is a factor of f(x),

By the long division method ( shown below ),

We found that,

$x^3 - 12x^2 + 41x - 42=(x-7)(x^2-5x+6)$

$=(x-7)(x^2-3x-2x+6)$ ( By middle term splitting )

$=(x-7)(x(x-3)-2(x-3))$

$=(x-7)(x-3)(x-2)$

For finding the zeroes, f(x) = 0,

$(x-7)(x-3)(x-2)=0$

⇒ x -7 =0 or x-3 =0 or x-2 =0

⇒ x = 7 or 3 or 2

What is the mean of the data set? {21, 23, 25, 25, 26, 28, 28, 28, 31, 33}

Answers

Answer:

Mean = 26.8

Step-by-step explanation:

In order to calculate the mean of a data set, we add up all the values in the data set and divide the sum by the number of values.

The formula for the mean is:

$\sf Mean = \frac{\textsf{Sum of all values}}{\textsf{Number of values}}$