Factorise the following:
9x²+3x²

The expression with a value of 12 and containing four numbers and two different operations are 2 × 2 + 4 + 4 = 12.

To write an expression with a value = 12 it should contain four numbers and two different operations, we can use the following method:

Firstly, multiplying :

2 × 2 = 4                   -----1

secondly, adding:

4 + 4 = 8                   -----2

finally, adding 1 and 2 we get,

4 + 8 = 12

Therefore, the expression with a value of 12 containing four numbers and two different operations is 2 × 2 + 4 + 4 = 12.

Another example is 35 ÷ 5 + 10 ÷ 2 = 12.#

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Answer:

AB = 6, BC = 6

AB = 4, AC = 4√2

BC = 2√2, AC = 4

(if im not wrong)

To write an absolute value equation with two solutions, we need to separate the equation into two cases: one for the positive value and one for the negative value.

The general form of an absolute value equation is |x - h| = k, where h is the value that the variable is being compared to and k is the value that the absolute value is equal to.

For example, to write an absolute value equation with two solutions that equal 3, we can separate the equation into two cases:

Case 1: x - h = k

x - 3 = 3

x = 6

Case 2: x - h = -k

x - 3 = -3

x = 0

So the equation is |x - 3| = 3 with solutions x = 6 and x = 0.

Another example is |x+2| = 4. The solutions to this equation can be found by setting x+2 = 4 and x+2 = -4.

x+2 = 4 => x = 2

x+2 = -4 => x = -6

So the equation |x+2| = 4 has solutions x = 2 and x = -6

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Answer:

= 1/5

Step-by-step explanation:

The reciprocal number results from dividing the number 1 by the origial number, by example:

Original number:   a

reciprocal number: 1/a

In this case:

original number: 5

reciprocal number: 1/5

The horizontal distance of the ball when it hits the ground is equal to 119.671 feet.

According to statement, we find the equation of the path covered by the ball, that is, a quadratic equation of the height of the ball (h), in feet, in terms of horizontal distance (x), in feet. In this case we need to determine a value of x greater than zero such that h = 0, that is to say:

- 0.01 · x² + 1.18 · x + 2 = 0

The roots of the quadratic equation can be found easily by quadratic formula:

x = - 1.18 / [2 · (- 0.01)] ± [1 / [2 · (- 0.01)]] · √(1.18² - 4 · (- 0.01) · 2)

x = 59 ± 60.671

The only realistic solution for the horizontal distance of the ball is x = 59 + 60.671 = 119.671 feet.

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Answer:

42 students

Step-by-step explanation:

5 out of 7 students are car riders. This means 2 out of 7 students are bus riders. 12 students are bus riders.

12 = 2x/7, where x is the total number of students.

So, 84 = 2x

This means that x = 42. 2/7 of 42 is 12 so this is correct.

Answer: 15 degrees.

Step-by-step explanation:

A bisector divides an angle in half. So, we know the total angle of ABC is 20 degrees, as show in blue. We draw the bisector BD in the middle, meaning each side is 10 degrees, show in green. This means angle ABD is 10 degrees and angle CBD is is 10 degrees. We bisect angle CBD with BE, shown in red. This means that we have two 5 degree angles on either side,  angle CBE and angle EBD. Lastly, we need to find angle ABE, highlighted in orange. We add the components, which are angle DBA, measuring 10 degrees, and angle EBD, measuring 5 degrees. When added together, this equals 15 degrees, which is our final answer for angle ABE.

Answer:

[tex]log_{3}11[/tex]

Step-by-step explanation:

[tex]3^x=11[/tex]

[tex]x=log_{3}11[/tex]

Hope this helps :)

Please let me know if this is correct or not

Have a great day!

Answer:

x=2.18265833 x=ln(11)/ln(3)

Step-by-step explanation:

Move all terms not containing x to the right side of the equation. Subtract 7 from both sides.

3x= 11

Take the natural logarithm of both sides of the equation to remove the variable from the exponent. ln(3x)=ln(11)

Expand ln (3x) by moving x outside the logarithm.x ln(3)=ln(11)

Divide each term in xln(3)=ln(11) by ln(3) and simplify.

Simplify the left side.

Cancel the common factor of ln(3).

Answer: 2.5

Step-by-step explanation:

An inequality that represents the value of height h of rectangular prism  is h ≤ 3

We know that the formula for the volume of a rectangular prism,

V = l × w × h

where l is the length of the rectangular prism,

w is the width of the rectangular prism

and h is the height of the rectangular prism

Here, we ahve been given a rectangular prism with sides 3 ft, 4 ft, and h ft

l = 4 ft, w = 3 ft

The volume of a rectangular prism with sides 3 ft, 4 ft, and h ft must be at least 36 cubic ft.

V ≥ 36

Using the formula of the volume of a rectangular prism we get an inequality,

l × w × h ≥ 36

4 × 3 × h ≥ 36

We solve an inequality that represents the value of h.

12 × h ≥ 36

Divide both sides by 36

(12h/12) ≥ (36/12)

h ≥ 3

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It is difficult to estimate the exact number of smartphones in the group and the standard deviation, as this depends on what type of smartphones each person has. It could take between 1 and 8 people to find a smartphone, depending on the number of smartphones already in the group.

The number of smartphones in the group of 8 people is difficult to estimate, as it depends on the type of smartphone each person has. For example, if there are 2 people with iPhones, 3 people with Android phones, and 3 people with Windows phones, then there would be 8 smartphones in the group. However, if there is only one person with an iPhone and the other 7 have different types of phones, then there would be only 4 smartphones in the group. The standard deviation of the number of smartphones in the group would depend on how many different types of smartphones are present and the total number of smartphones in the group. The amount of time it would take to find a smartphone would depend on the number of smartphones already in the group. If there are already 4 or more smartphones, then it would take only 1 person to find a smartphone. If there are only 3 smartphones, then it could take up to 8 people before one of them has a smartphone.

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Answer:

Step-by-step explanation:

80

Answer:

80

Step-by-step explanation:

To find 125% of 64, you can multiply 64 by 1.25.

125% of 64 = 64 x 1.25 = 80

So, 125% of 64 is 80.

Check the picture below.

[tex]\tan(37^o )=\cfrac{\stackrel{opposite}{49}}{\underset{adjacent}{DB}}\implies DB=\cfrac{49}{\tan(37^o )} \\\\\\ \sin(56^o )=\cfrac{\stackrel{opposite}{DB}}{\underset{hypotenuse}{AD}}\implies AD=\cfrac{DB}{\sin(56^o )} \\\\\\ AD=\cfrac{ ~~ \frac{49}{\tan(37^o )} ~~ }{\sin(56^o )}\implies AD=\cfrac{49}{\tan(37^o ) \sin(56^o )}\implies AD\approx 78.43[/tex]

Make sure your calculator is in Degree mode.

Answer:

(-90)

Step-by-step explanation:

45*-2 = (-90)

Answer: ▾ 1. Henry has 8 dozen cookies and bakes 48

cookies an hour.

a. (4,2.9)

Step-by-step explanation:

The statement is describing a linear relationship between the number of hours and the number of cookies produced. This can be represented by a linear equation of the form y = mx + b, where x is the number of hours and y is the number of cookies.

The point (4, 2.9) represents the number of cookies produced after 4 hours, which is 2.9 dozen (8 dozen * 0.36) which is 48 cookies.

▼ 2. Julian drives home from work and averages

2

mile per minute. He has to travel 4.5

miles.

b. (1,144)

Explanation:

The statement is describing a linear relationship between the time in minutes and the distance traveled.

The point (1,144) represents the distance traveled after 1 minute, which is 144 miles, which is 4.5260 miles.

▾ 3. Using a laptop on battery power causes the

battery to decrease 10% an hour.

c. (5,50)

Explanation:

The statement is describing a linear relationship between the number of hours and the percentage of battery power remaining.

The point (5,50) represents the percentage of battery power remaining after 5 hours, which is 50% of the original battery power.

So based on the given information, I matched the linear functions with the points that makes the statement true as

▾ 1. Henry has 8 dozen cookies and bakes 48

cookies an hour.

a. (4,2.9)

▼ 2. Julian drives home from work and averages

2

mile per minute. He has to travel 4.5

miles.

b. (1,144)

▾ 3. Using a laptop on battery power causes the

battery to decrease 10% an hour.

c. (5,50)

Please note that these answers are based on the information provided in the problem statement and may not be the only possible answers.

The pair of equations y = 0 and y = -5 has no solutions.

The pair of equations y = 0 and y = -5 can be written as:

y = 0

y = -5

Since both equations have the same value of y, 0 and -5, the equations are not equal and therefore there is no solution.

The pair of equations y = 0 and y = -5 have no solutions. This is because the equations have the same value of y, 0 and -5, which means that the equations are not equal. Therefore, there is no solution to this pair of equations. To determine if the pair of equations has a solution, you must check to see if the equations are equal. If the equations are not equal, then there is no solution. In this case, the equations are not equal, and thus there is no solution.

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No, it is not unusual to have 0 boys. Each of the four possibilities (0 boys, 1 boy, 2 boys, 0 girls) has a probability of 1/4, so it is equally likely to have 0 boys as any other outcome.

The probability distribution for the number of boys if a couple has 2 kids is as follows:

P(0 boys) = 1/4,

P(1 boy) = 2/4,

P(2 boys) = 1/4.

The expected number of boys is the weighted sum of the number of boys (0, 1, and 2) multiplied by the respective probability of each:

[tex]E(# boys) = 0*1/4 + 1*2/4 + 2*1/4 = 1 boy.[/tex]

The standard deviation is calculated using the formula:

[tex]SD = sqrt(P(0 boys)*(0-1)^2 + P(1 boy)*(1-1)^2 + P(2 boys)*(2-1)^2) = sqrt(1/4*1 + 2/4*0 + 1/4*1) = sqrt(1/4) = 0.5.[/tex]

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The output a needed to satisfy the consumer and interindustry demands is 12 units, and the output b needed to satisfy the consumer and interindustry demands is 6 number of units.

a) Output a = 12 (units)

b) Output b = 6 (units)

1. Calculate the total consumer demand (CD):

CD = 12 + 20 + 8 = 40 (units)

2. Calculate the total interindustry demand (ID):

ID = 4 + 5 + 9 = 18 (units)

3. Calculate the total production (TP):

TP = CD + ID = 40 + 18 = 58 (units)

4. Calculate the output a and b needed to satisfy the consumer and interindustry demands:

a) Output a = TP - ID = 58 - 18 = 40 (units)

b) Output b = CD - Output a = 40 - 12 = 28 (units)

The output a needed to satisfy the consumer and interindustry demands is 12 units, and the output b needed to satisfy the consumer and interindustry demands is 6 number of units.

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The five kinds of variables are nominal, ordinal, interval, ratio, and binary. Nominal variables are categorical variables with no numerical value.

The five kinds of variables are nominal, ordinal, interval, ratio, and binary. Nominal variables are categorical variables that don't have numerical values.  An example would be a survey asking respondents to select their gender as male or female.

Ordinal variables have an inherent order and can be ranked. An example would be a survey asking respondents to rate a product on a scale from 1 to 10. These variables are usually used when the items being measured are at different levels or degrees.

Interval variables have an absolute zero point and can be measured in equal intervals. An example would be measuring temperature in Celsius.

Ratio variables have a zero point and can be measured in ratios. An example would be measuring time in seconds.

Binary variables are either one or zero, and are commonly used in computer science. An example would be a survey asking respondents to select yes or no to a particular question.

Overall, each of these five kinds of variables are used to measure different types of data in different ways. Depending on the type of data being collected, one or more of these variables may be used.

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Assuming the pressure and temperature remain the same, it would take 8.576 min for the same volume of UF6 to effuse through a porous membrane.

The effusion rate of a gas is determined by its molecular weight and the temperature and pressure of the system.

1. Calculate the molecular weight of Kr:

Molecular weight of Kr = 39.0983 g/mol

2. Calculate the molecular weight of UF6:

Molecular weight of UF6 = 352.03 g/mol

3. Calculate the ratio of the molecular weights:

Ratio of molecular weights = 352.03/39.0983 = 9.00

4. Calculate the effusion rate of UF6:

Effusion rate of UF6 = 8.576 min x 9.00 = 77.184 min

The effusion rate of a gas is determined by its molecular weight and the temperature and pressure of the system. To calculate the effusion rate of UF6, we first need to calculate the ratio of the molecular weights of Kr and UF6. Then, we can use this ratio to calculate the effusion rate of UF6, which is 77.184 min.

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Answer:

Step-by-step explanation:

The first step to determine the implied domain of the function is to identify any restrictions on the variables x and y. In this case, the function 2y + x^(1/3) = 3x + x^2 does not have any restrictions on x and y, therefore the domain is all real numbers.

We can express this as an interval notation:

(-∞, ∞)

This means that the function is defined for any real value of x and y, which means the domain of the function is all real numbers.

The e coordinates of the point on the directed line segment are  (-5, -3).

The cartesian plane is a two-dimensional coordinate plane that is formed when two parallel lines meet. The X-axis is the horizontal line, and the Y-axis is the vertical line. On the Cartesian plane, the coordinate point (x, y) indicates that the point is on the right of the origin if the sign of x is positive; otherwise, the point is on the left of the origin.

Given coordinates (-8, -6) and (4, 6) make a line segment,

and point in the line divide in ratio 1:3

the equation point is,

(x, y) = [tex][(\frac{mx_2 + nx_1}{m + n} ), (\frac{my_2 + ny_1}{m + n} )][/tex]

m = 1, n= 3

x₁ = -8, x₂ = 4, y₁ = -6, y₂ = 6

solving for x,

x = [tex](\frac{mx_2 + nx_1}{m + n} )[/tex]

x = [1(4) + 3(-8)]/4

x = -20/4

x = -5

solving for y,

y = [tex](\frac{my_2 + ny_1}{m + n} )[/tex]

y = [1(6) + 3(-6)]/4

y = -12/4

y = -3

(x, y) = (-5, -3)

Hence the coordinates are  (-5, -3).

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Answer:

Height = 100 cm.

Surface Area = 625 cm^2.

Step-by-step explanation:

The volume of the cube is identical to the volume of the cuboid.

Volume of the cube = 5^3 and volume of cuboid is base area * height.

5^3 = 2.5 * 0.5 * h     (where h is the height of the cuboid).

h = 5^3/1.25

  = 100 cm.

The surface area is:

A = 2 * area of base + 2 * area of 1 side + 2 area of other side

   = 2 * 1.25 + 2* 100 * 0.5 + 2 * 100 * 2.5

   = 2.5 + 100 + 500

   = 602.5 m^2.

You are designing a 5 kilometer course for charity run. The design now has been covers 4,908.5 meters, hence, you need to add more 91.5 meters on the course.

The conversion from yard to meter is:

1 yard = 0.9144 meters

The course streets and the distances after converted into meters are:

main street to 6th ave.  781 yards = 714.15 meters

6th ave. to pleasant road 1,250 yards = 1143 meters.

pleasant road to city park 275 yards = 251.46 meters

route through city park 2,337 yards = 2,136.95 meters

city park to main street 725 yards = 662.94 meters

Total course = 714.15 + 1143 + 251.46 +  2,136.95 +  662.94

Total course = 4,908.5 meters

The design is 5 km = 5000 meters. Therefore, you still need to add:

5000 - 4,908.5 = 91.5 meters more course.

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The perimeter of the figure is 58 feet if the missing side length is 10 feet.

Perimeter is defined as the length of the circumference or outline of the geometry. This means that is the sum of the all the external side lengths of an image or figure.

From the two-dimensional geometry in the attached image, we see the dimensions as;

The missing side length = 15 - 5 = 10 ft

Therefore, we will add all the external lengths to get the perimeter as;

Perimeter of the figure = 5 + 7 + 10 + 10 + 15 + 11

= 58 feet

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The value of the SW is 12 units.

What is a chord in a circle?

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle that passes through the center of the circle.

Since we want to find SW to get SV, we can change SW to x.

We already know the other lengths:

ST = 3

SU = 18

SW=x

SV=x-3

So, 3(18)=x(x-3).

From here, we see that when expanded, this becomes 54 = x² - 3x.

Solving the quadratic, we see that SW is 12, therefore SV is 9.

Hence, the value of the SW is 12 units.

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complete question: Let TU and VW be chords of a circle, which intersect at S, as shown. If ST = 3, TU = 15, and VW = 3, then find SW.

Answer:

cost of 1 crate of lettuce = x

cost of 1 crate of cabbage = y

[tex]4x + 3y = 34.2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(1)[/tex]

[tex]2x + 5y = 31.8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(2)[/tex]

Multiplying eq. (2) by 2

[tex]4x + 10y = 63.6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(3)[/tex]

(3)-(1)

[tex]7y = 29.4 \\ y = \frac{29.4}{7} \\ y = 4.2 \\ [/tex]

Putting this in (2)

[tex]2x + 5(4.2) = 31.8 \\ 2x = 10.8 \\ x = 5.4[/tex]

.'. Cost of 1 crate of lettuce= $5.40

Cost of 1 crate of cabbage= $4.20

Answer:

Let 1 crate of lettuce be X and 1 crate of cabbage be y.

Now from question,

4 crates of lettuce and 3 crates of cabbage costs 34.20$

i.e.4x+3y=34.20----(1)

Also,

2 crates of lettuce and 5 crates of cabbage costs 31.80$

i.e. 2x+5y=31.80----(2)

Multiplying eqn (2) by 2 then subtracting from (1), we get,

4x+3y - {2(2x+5y)}=34.20-(2×31.80)

or,4x-4x+3y-10y=34.20-63.60

or,-7y= -29.40

:.y=4.20

Putting value of y in eqn 1 we get,

4x=34.20-12.60

or,4x=21.60

or,X=21.60/4

:.X=5.40

Hence,Cost of each crate lettuce i.e.X=5.40$

and,each crate cabbage i.e y=4.20$

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Answer:

Un industriel souhaite fabriquer une boîte sans couvercle à partir d'une plaque de métal de

24

Step-by-step explanation:

The squares represent a visual representation of equivalent fractions. Each square is divided into a certain number of equal parts, and the number of parts that are shaded in represents the numerator of the fraction. The total number of parts the square is divided into represents the denominator of the fraction.

In the first square, it is divided into 23 equal parts and 8 of them are shaded in. Therefore, the fraction represented by that square is 8/23.

In the second square, it is divided into 812 equal parts and 23 of them are shaded in. Therefore, the fraction represented by that square is 23/812. Since both squares are divided into the same number of equal parts, the fractions 8/23 and 23/812 represent the same quantity, just in different forms. Therefore, they are equivalent fractions.

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