Write as an equation: The product of a number and 12 is 78.
A. 12n=78
12
n
=
78
B. n+12=78
n
+
12
=
78
C. 12−n=78
12
−
n
=
78
D. 12=78n

Answer:

10u²

Step-by-step explanation:

The formula for area of a triangle is b*h/2. When you plug in the numbers, you get 10. Hope this helps!

Answer:

H (3x,3y)

Step-by-step explanation:

Dilation is a transformation when figure is enlarged or reduced by scale factor. During dilation, every point of preimage is dilated by scale factor, so it means each coordinate of that point must be multiplied by scale factor.

Hence, H(3x,3y) can be the result of dilation with scale factor of 3.

Answer:

The answer is B

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

y > 5x-4

This inequality is greater than, so it would be a dotted line

You would have a solid line when it is greater than or equal to ≥  or less than or equal to ≤

Answer:

30 or 120 /4

Step-by-step explanation:

a^p/q here p denotes power raised and q denotes inverse power or root. So, 60^1/2 denotes square root of 60 raised to power 1.

Answer:

option b is the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]=(1 +tan\theta)^2 + (1 - tan\theta)^2\\=(1+2tan\theta+tan^2\theta)+(1-2tan\theta+tan^2\theta)\\=2(1+tan^2\theta)\\=2sec^2\theta.\\[/tex]

Answer:

16/50 or 32% chance of getting a multiple of 3

Step-by-step explanation:

Starting at 0 and going to 50, there are 16 numbers in the range that are multiples of 3.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, and 48

Attached is a chart for reference!

So, 16 of the 50 numbers are multiples of 3, making your odds 16/50 (divide that to get .32 which = 32%!)

step by step explanation:

(multiples of 3)= 3 , 6 ,9, 12 ,15, 18 ,21 ,24, 27, 30, 33, 36 ,39 ,42, 45 and 48

probability (multiples of 3)= nó of required outcome/ nó of possible outcome

16 /50 = 8/25 ( you get this after dividing 16/50)

in percentage 8/ 25 would give you 32%

The irrational number that can be multiplied to produce 1 is - √41/41

Let the following expression

-√41 x = 1

We are to find the value of x that will make the expression true

√41 x = -1

Divide both sides by √41

√41 x/ √41 = -1/ √41

x = - √41/41

Hence the irrational number that can be multiplied to produce 1 is - √41/41

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[tex]f(x) =4 x {}^{3} - 4x {}^{2} - 16x + 16[/tex]

[tex]divide \: by \: x - 2[/tex]

[tex]4x {}^{2} \: into \: (x - 2) = 4x {}^{3} - 8x {}^{2} [/tex]

[tex]g(x) = 4x {}^{2} - 16x + 16[/tex]

[tex]4x \: into \: (x - 2) = 4x {}^{2} - 8x[/tex]

[tex]z(x) = - 8x + 16[/tex]

[tex] - 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder[/tex]

[tex]f(x) = (x - 2)(4x {}^{2} + 4x - 8)[/tex]

[tex]f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^{2} + 4x - 8 = 0 \\ [/tex]

[tex]x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(4)( - 8) } }{2(4)} = \frac{ - 4 + \sqrt{144} }{8} = \frac{ - 4 + 12}{8} = 1[/tex]

[tex]x = 2[/tex]

[tex]x = \frac{ - 4 - 12}{8} = \frac{ - 16}{8} = - 2[/tex]

Answer: B

Step-by-step explanation:

Edge 2023

Hello!  

To find the mass of the liquid by itself, subtract the mass of the container from the mass of the liquid and container.

⇒ 1,300 - 250

⇒ 1,050 grams

∴ The mass of the liquid by itself is 1,050 grams.

Answer:

Birds = 8

Mice = 6

Step-by-step explanation:

Conditions

Let the birds = x

Let the mice = y

Equations

x + y = 14

2x + 4y = 40

Solution

Using the top equation solve for x

x = 14 - y

Use this result to substitue for x

2(14 - y) + 4y = 40                      

Remove the brackets

28 - 2y + 4y = 40

Combine

28 + 2y = 40

Subtract 28 from both sides

28 - 28 + 2y = 40 - 28

2y = 12

Divide by 2 on both sides

2y/2 = 12/2

y = 6

Solve for x

x + y = 14

x + 6 = 14

Subtract 6 from both sides

x + 6 - 6 = 14 - 6

x = 8

Answer:

7 mice and 7 birds

Step-by-step explanation:

14 heads would mean there are 14 animals in total, as each animal has one head.

Birds have two legs, and mice have four.

2+4=6

40/6=6.67 (recurring)

6.67*2=13.3 (recurring)

6.67*4=26.67 (recurring)

Animal legs can't be in decimal numbers, so we can round the numbers.

13.3 becomes 13, 26.67 becomes 27.

13+27=40

Now we can see that there are 13 bird legs and 27 mice legs.

Divide the bird legs by 2 to get 6.5

Divide the mice legs by 4 to get 6.75

Again, we can't have a decimal of an animal, so we can round.

6.5 becomes 7, and 6.75 also becomes 7.

Therefore, there is 7 of each type of animal.

Answer:

Step-by-step explanation:

Answer:

obtuse because 6^2+10^2<10^2

Step-by-step explanation:

The given triangle whoe sides are 6cm, 10cm, and 12cm is an obtuse triangle and it can be determine by using pythagorian theorem, i.e. 6^2 + 10^2 < 12^2.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.

here, we have,

Given :

The side lengths of a triangle are: 6cm, 10cm, and 12cm.

Pythagorian theorem can be used to find out that the triangles are acute or obtuse. According to pythagorian theorem, the sum of square of shorter side is equal to the square of the third side of the right angle triangle.

According to pythagorian theorem:.

That is, H^2 = P^2 + B^2.

There are some rules to find the triangle is obtuse or acute:

If  H^2 > P^2 + B^2, than the triangle is obtuse.

If H^2 < P^2 + B^2, than the triangle is acute.

Now, applying pythagorian theorem:

we get,

6^2 + 10^2 = 12^2

136 = 144

Here, it is clearly observe that 136 <  144, i.e. 6^2 + 10^2 < 12^2 therefore, the triangle is obtuse.

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The amount of the temperature decrease will be 332 °C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The oven temperature was at 325 degrees because my mom just finished baking a pie.

I increased the temperature, 75 degrees, so I could bake a pizza.

Then the temperature will be

⇒ 325 °C + 75 °C

⇒ 400 °C

After the pizza was cooked, I turned off the oven.

The oven cooled to the room temperature of 68 degrees.

Then the amount of the temperature decrease will be

⇒ 400 °C – 68 °C

⇒ 332 °C

The remaining question is given below.

How much did the temperature decrease?

More about the Algebra link is given below.

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The formula to convert degrees Fahrenheit to Celsius is:

[tex]\bf{^{\circ}C=\dfrac{5}{9}(^{\circ}F-32) \ \ \to \ \ \ Formula }[/tex]

Convert 59°F to degrees Celsius.

Add the number 59 in the formula, and solve.

        [tex]\bf{=\dfrac{5}{9}(59-32) }[/tex]

Subtract 32 from 59.

         [tex]\bf{=\dfrac{5}{9}(27) }[/tex]

Multiply 5 x 9 = 135, then divide 135/9 = 15.

         [tex]\bf{=15 \ ^{\circ}C}[/tex]

Therefore 59 °F = 15 °C. The correct option is "D".

The value of ? and X are 24 and 32 respectively

A triangles is 2D shape with three sides and angles.

From the given diagram, the ratio of similar sides is equal to a constant as shown;

15/20 = 9+15/20+x

Cross multiply

15/9+15 = 20/20+x

15/24 = 20/20+x

Comparing with the given ratio

? = 24

X = 20+x

Find x

15(20+x) = 480

300 + 15x = 480

15x = 180

x =12

X = 20 +x

X= 32

Hence the value of ? and X are 24 and 32 respectively

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The probability that he got at least 2 questions correct is 0.756.

Probability is simply how probably something is to appear. every time we're uncertain approximately the final results of an occasion, we can communicate approximately the possibilities of positive outcomes and how in all likelihood they may be. The analysis of occasions ruled through chance is called data.

Basic Probability Rules

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The family consumes 3 whole pizzas in total. They should order 3 whole pizzas to have enough for everyone.

To find out how many whole pizzas the Hayden family should order, we can calculate the total number of pizzas they need.

Since each person always eats 3/4 of a pizza, the total amount they eat can be calculated as follows:

3/4 + 3/4 + 3/4 + 3/4 = 4 × (3/4) = 3

So, the family consumes 3 whole pizzas in total. Therefore, they should order 3 whole pizzas to have enough for everyone.

As for the picture, imagine a circle representing a whole pizza. Divide it into four equal parts to represent each person's portion (3/4). Repeat this division three times to represent the three pizzas needed.

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Answer:

18

Step-by-step explanation:

Polygon A : Polygon B = x : 3x

4A = 24

A = 6

B = 18

B is the larger polygon so the perimeter is 18.

Answer:

Its a right isosceles triangle

Answer:

right isosceles

Step-by-step explanation:

it has the right at the top

(3(1) + 9)² - 64

(3 + 9)² - 64

(12)² - 64

= 144 - 64

= 80

Using an exponential function, the inequality is given as follows:

[tex]9400(0.857)^t < 6000[/tex]

The solution is t > 2.9, hence the tax status will change within the next 3 years.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

For this problem, the parameters are given as follows:

A(0) = 9400, r = 0.143.

The population after t years is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 9400(1 - 0.143)^t[/tex]

[tex]A(t) = 9400(0.857)^t[/tex]

The tax status will change when:

[tex]A(t) < 6000[/tex]

Hence the inequality is:

[tex]9400(0.857)^t < 6000[/tex]

Then:

[tex](0.857)^t < \frac{6000}{9400}[/tex]

[tex]\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}[/tex]

[tex]t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}[/tex]

Since both logs are negative:

[tex]t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}[/tex]

t > 2.9.

The solution is t > 2.9, hence the tax status will change within the next 3 years.

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Going by the rules of the game to pick a random card and then multiply it by a roll of a number cube, we can find that:

If the die is rolled, it will land on a number between 1 and 6 while there are only four cards that can be picked.

The sample space is:

                  Dice             Card            Product        

                      1                 5                         5

                      1                 6                         6

                      1                 7                         7

                      1                 8                         8

                      2                 5                         10

                      2                 6                         12

                      2                 7                         14

                      2                 8                         16  

                      3                 5                         15

                      3                 6                         18

                      3                 7                         21

                      3                 8                         24

                      4                 5                         20

                      4                 6                         24

                      4                 7                         28

                      4                 8                         32

                      5                 5                         25

                      5                 6                         30

                      5                  7                         35

                      5                  8                         40

                      6                 5                         30                        

                      6                 6                         36

                      6                 7                         42

                      6                 8                         48

Based on the products, we can come up with the following frequency table:

                                 Frequency table

                          Product                     Frequency

                              5                                      1

                              6                                      1

                              7                                      1

                              8                                      1

                              10                                      1

                              12                                      1

                              14                                      1

                              16                                      1

                              15                                      1

                              18                                      1

                              21                                      1

                              24                                      2

                              20                                      1

                              28                                      1

                              30                                      2

                              32                                      1

                              25                                      1

                              35                                      1

                              40                                      1

                              36                                      1

                              42                                      1

                              48                                      1

                              Total                                24

The frequency table shows that to get 28 or more, a person will have a relative frequency of:

= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1

= 9

Probability is:

= 9 / 24

= 3/8

= 37.5%

The number of products required to win 25% of the time is:

= 25% x 24

= 6

To find the winning number, count down from the highest product 6 times to get 32.

The probability of getting 36 or higher is:

= ∑(Probabability of picking 36 and above numbers)

= 1 / 24 + 1/24 + 1/24 + 1/24

= 1 / 6

The probability of repeating this 4 consecutive times is:

= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6

= 1 / 1,296

= 0.0007716

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Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

V=⅓b²h

16=⅓*16*h

16=16h/3

h=3cm

Answer:

[tex]x = \frac{-7 +\sqrt{489} }{2}[/tex]

[tex]x = \frac{-7 - \sqrt{489} }{2}[/tex]

Step-by-step explanation:

2x² +21x-61 = (x+7)²

expand

2x² + 21x - 61 = x² + 14x +49

move everything to one side

x² + 7x - 12 = 0

use quadratic formula

[tex]x = \frac{-b +- \sqrt{b^{2}-4ac } }{2a}[/tex]

plug in the values

[tex]x = \frac{-7 +- \sqrt{7^{2}-4(1)(-110) } }{2(1)}[/tex]

solve

[tex]x = \frac{-7 +- \sqrt{49-4(1)(-110) } }{2}[/tex]

[tex]x = \frac{-7 +- \sqrt{49 + 440 } }{2}[/tex]

[tex]x = \frac{-7 +- \sqrt{489} }{2}[/tex]

Answer:

B

Step-by-step explanation:

given f(x) then f(x ± a ) is a horizontal translation of f(x)

• if + a , then a shift left of a units

• if - a then a shift right of a units

here g(x) is the graph of f(x) moved 2 units right , then

g(x) = (x - 2)²

Part (i)

1. ABCD is a quadrilateral in which AD=BC and ∠DAB=∠CBA (given)

2. AB = AB (reflexive property)

3. Triangles ABD and BAC are congruent (SAS)

Part (ii)

4. BD=AC (corresponding sides of congruent triangles are equal)

Part (iii)

5. ∠ABD = ∠BAC (corresponding angles of congruent triangles are equal)

Answer:

Hey!

In △ABD and△BAC,

AD = BC (it's given)

∠DAB = ∠CBA (it's given)

AB = BA (Common)

By SAS congruence rule,

∴△ABD≅△BAC

=> BD = AC (By C.P.C.T) (ii)

And, ∠ABD = ∠BAC (By C.P.C.T) (iii)

Hope it helps, any confusions you may ask.

Answer:

C

Step-by-step explanation:

P = S1t - S2t ← factor out t from each term on the right side

P = t(S1 - S2) ← isolate t by dividing both sides by S1-S2

[tex]\frac{P}{S1-S2}[/tex] = t