The height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet. Find the length of the base and the height of the triangle

Answer:

[tex]x\leq -3[/tex]

Step-by-step explanation:

I can't write interval notation on Brainly but I can solve the inequality.

[tex]5x+4\leq x-8[/tex]

Subtract [tex]x[/tex] from both sides

[tex]4x+4\leq -8[/tex]

Subtract 4 from both sides

[tex]4x\leq -12[/tex]

Divide both sides by 4

[tex]x\leq -3[/tex]

Answer: i) 12.5%       ii) 87.5%        iii) 23.4%

Step-by-step explanation:

There are two die, each with 8 sides so the total number of outcomes is 8²

i) Product is a prime number --> 2, 3, 5, 7

Since it is a prime we only have the option of one die being a 1 and the other being the prime number.

So possible successful outcomes is: (1, 2), (1, 3), (1, 5), (1, 7), (7, 1), (5, 1), (3, 1), and (2, 1) = 8 options.

[tex]\dfrac{successful\ outcomes}{total\ possible\ outcomes}=\dfrac{8}{8^2}=\dfrac{1}{8}=\large\boxed{12.5\%}[/tex]

ii) Not a perfect square.  Let's find the probability that it IS a perfect square and subtract that value from the total (64).

Product IS a perfect square --> 1, 4, 9, 16, 25, 36, 49, 64

Possible successful outcomes of a perfect square: (1, 1) (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8) = 8 options.

Product is NOT a perfect square = 64 - 8 = 56 options

[tex]\dfrac{successful\ outcomes}{total\ possible\ outcomes}=\dfrac{56}{8^2}=\dfrac{7}{8}=\large\boxed{87.5\%}[/tex]

iii) Product is a multiple of 5 --> 5, 10, 15, 20, ,25, 30, 35, 40,

Possible successful outcomes of a multiple of 5: (1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (7,5), (8, 5), (5, 8), (5, 7), (5, 6), (5, 4), (5, 3), (5, 2), (5, 1) = 15 options

[tex]\dfrac{successful\ outcomes}{total\ possible\ outcomes}=\dfrac{15}{8^2}=\dfrac{15}{64}=\large\boxed{23.4\%}[/tex]

You are limited to 3 questions on Brainly so hopefully you can follow what I did to answer the last two questions (less than or equal to 21) and (divisible by 4 or 6). If not, please post this question again and state "Need iv and v only".

Answer:

+6-6=0

so we need -6 to add in +6 to get 0

Step-by-step explanation:

i hope this will help you

[tex]solution \\ let \: the \: number \: be \: x \\ x + 6 = 0 \\ or \: x = 0 - 6 \\ x = - 6[/tex]

hope this helps...

Good luck on your assignment...

Answer:

1

Step-by-step explanation:

=> [tex]\sqrt[3]{1}[/tex]

=> [tex]\sqrt[3]{1*1*1}[/tex]

=> [tex]\sqrt[3]{1^3}[/tex]

=> 1

Answer:

The system of equations is consistent and independent

Step-by-step explanation:

Given system of equations :

[tex]y=x+4\\y= -x-4[/tex]

Consistent : For a two variable system of equations to be consistent the lines formed by the equations have to meet at some point or they have to be parallel.

Inconsistent :If the system of equations is not consistent then it is inconsistent.

Dependent:A dependent system of equations has infinite solutions

Independent :An independent system has a single solution.

Plot the lines on graph

y=x+4 --- Blue line

y=-x+4 ---- Green line

Refer the attached graph

The lines formed by the equations intersect at one point

So the lines are consistent

Now the given system of equations has single solution . So, it is independent

So, Option C is true

Hence The system of equations is consistent and independent

Answer:

[tex]9[/tex]

Step-by-step explanation:

[tex](-1)^4-(-1)^3+(-1)^2+6[/tex]

[tex]1-(-1)+1+6[/tex]

[tex]1+1+1+6[/tex]

[tex]3+6=9[/tex]

Answer:

Option 2

Step-by-step explanation:

p(t) = [tex]t^4-t^3+t^2+6[/tex]

Putting t = -1

p(-1) = (-1)⁴-(-1)³+(-1)²+6

p(-1) = 1-(-1)+1+6

p(-1) = 1+1+7

p(-1) = 9

Answer:

give me the rest of the question/ a picture or something then i can answer

Step-by-step explanation:

Answer:

±3

Step-by-step explanation:

y is directly proportional to the square of x.

[tex]y \propto x^{2}[/tex]

[tex]y = kx^{2}[/tex]

Find the value of k constant when y=32 and x=4.

[tex]32=k(4)^2[/tex]

Square the number 4.

[tex]32=16k[/tex]

Divide both sides with 16.

[tex]32/16=k[/tex]

[tex]k=2[/tex]

The value of k constant is 2.

Find the value of x when y=18

[tex]y=2x^2[/tex]

[tex]18=2x^2[/tex]

[tex]18/2=x^2[/tex]

[tex]9=x^2[/tex]

[tex]x= \± \sqrt{9}[/tex]

[tex]x=\± 3[/tex]

The value of x when y = 18 is ±3.

Answer:

hi i did calculations and my ans is coming (A) 8x - 12

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

A pentagon is a polygon that has 5 sides.

Answer:

A pentagon has 5 sides

Step-by-step explanation:

penta, often means 5.

Answer:

Either £16 or £26.32 depending on what you meant in the question

Step-by-step explanation:

I'm going to answer the question in 2 ways, since I'm not sure if you mean £14 or 14%

If its £14, then the original price is 30-14 = £16

If its 14% then that means after the increase, the shirt will be 100%+14% of the original price or 114% of the original price.

This means that

£30 = 114%

To make it easier, reduce the 114% to 1 %

1% = 30/114

1% = £0.26316

100% = £26.32 (rounded to 2 decimal places)

Therefore the original price was £26.32

Answer:

4/3

Step-by-step explanation:

9 1/3 ÷ 7

Convert the mixed fraction to improper fraction.

28/3 ÷ 7

Reciprocal second fraction.

28/3 × 1/7

Multiply the fractions.

28/21

Simplify the fraction.

4/3

Answer:

[tex]1\frac{1}{3}[/tex]

Step-by-step explanation:

=> [tex]9 \frac{1}{3} / 7[/tex]

=> [tex]\frac{28}{3} * \frac{1}{7}[/tex]

=> [tex]\frac{4}{3}[/tex]

=> [tex]1\frac{1}{3}[/tex]

Answer:

a(8) = -49152

Step-by-step explanation:

Step 1: Find r

-12/3 = 4

Step 2: Write geometric explicit formula

[tex]a_{n} = 3(4)^{n-1}[/tex]

Step 3: Plug in 8th term for n

[tex]a_{8} = 3(4)^{7}[/tex]

a(8) = -49152

Alternatively you can find r then multiply 3 by -4 8 times.

Answer: The answer is provided below

Step-by-step explanation:

A price markdown is a reduction that is deliberate when selling a product. From the question, we are informed that a video game that usually costs $30.65 is marked down 60%.

The find the new price of the video game, we have to subtract the amount reduced from the original price. The amount reduced is:

= 60% of $30.65

= 60/100 × $30.65

= 0.6 × $30.65

= $18.39

The new selling price = $30.65 - $18.39

= $12.26

The error that Kelvin made when he determined that the new price of the game would be $18.39 was that he didn't subtract the value from the original price of the video game.

Answer:

6(x +8)

Step-by-step explanation:

Factorising:

6x + 48

Take 6 as common, Therefore:

6(x +8)

Because:

6 * x = 6x

6 * 8 = 48

therefore:

6x + 48 = 6(x + 8)

Hope it helped!!!

Answer:

12ab / 4a - 8ab

= 4a(3b)/ 4a(1 - 2b)

= 3b / 1 - 2b

Hope this helps

Answer:

5/8

Step-by-step explanation:

Step 1: Add

1/16 + 9/16 = 10/16

Step 2: Divide both numerator and denominator by 2

10/2 = 5

16/ 2 = 8

Our answer is 5/8!

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

1 + 9 = 10

same denominator so it stays the same

[tex]\frac{10}{16}[/tex] ÷ [tex]\frac{2}{2} = \frac{5}{8}[/tex]

Answer:

43,45

Step-by-step explanation:

43+45=88

Answer:

43 & 45

Step-by-step explanation:

Let the numbers be x, x+2 (because they are consecutive i.e. coming one after another)

Condition:

x + x+2 = 88

2x = 88-2

2x = 86

Dividing both sides by 2

x = 43

Now, the numbers:

x = 43

x+2 = 45

Answer:

[tex] = ( - \frac{2}{3} \times \frac{3}{4}) \times ( - 1) [/tex]

[tex] = \frac{( - 2) \times ( - 1)}{4} [/tex]

[tex] = \frac{ + 2}{4} [/tex]

[tex] = + \frac{1}{2} [/tex]

Here's your answer girlfriend

Please follow me

Answer:

-6 < y < ∞

Step-by-step explanation:

The range is the value of the output, in this case the value of y

The value is from -6 not including -6 to infinity

-6 < y < ∞

Answer:

C. from -6 to infinity

Step-by-step explanation:

The range is the set of the y-coordinates of the points of the function.

The lowest value of y is -6 or just greater than -6.

All values greater than y are also part of the range.

Answer: Choice C. from -6 or just greater than -6 to infinity

Hey there! :)

Answer:

125.

Step-by-step explanation:

When g(x) = -1:

g(-1) = 2(-1) + 7

g(-1) = -2 + 7

g(-1) = 5

Plug this into f(x) since the question is asking for f(g(x)):

f(x) = x³

f(5) = 5³

f(5) = 125.

Answer:

-1

Step-by-step explanation:

f(x) = x^3

g(x) = 2x + 7

f(g(x)] =

Let g(x) = -1

Replace g(x) with -1

f(g(x) = f(-1) = (-1)^3 = -1

Answer:

d. The two triangles are not congruent because dilation is not a rigid motion.

Step-by-step explanation:

Triangle ABC is dilated about the origin b a factor of 2. It is then reflected and translated to form Triangle XYZ.

The new triangle formed is not congruent to ABC because the image is not the same size as the pre-image. It is only rigid transformations that preserve length, however dilation is not a rigid transformation.

Answer:

The length of BC is 15 units.

Solution,

Hypotenuse(h)=?

perpendicular(p)=12

base(b)=9

Using Pythagoras theorem,

[tex] {h}^{2} = {p}^{2} + {b}^{2} \\ or \: {h}^{2} = {12}^{2} + {9}^{2} \\ or \: {h}^{2} = 12 \times 12 + 9 \times 9 \\ or \: {h}^{2} = 144 + 81 \\ or \: {h}^{2} = 225 \\ or \: h = \sqrt{225} \\ or \: h = \sqrt{ {15}^{2} } \\ h = 15[/tex]

hope this helps...

Good luck on your assignment....

Answer:

252 bags of maize

Step-by-step explanation:

From the question, we are told that a farmer harvested maize

In the year 2012 = 144 bags of maize

In the year 2013(following year) the harvest decreased in the ratio 3:4

This means

3:4 = 2013: 2012.

Where number of bags harvested in 2013 = unknown = x

3/4 = x/ 144

Cross multiply 4x = 3 × 144

x = 3 × 144/ 4

× = 108

This means 108 bags of maize was harvested in 2013

The total number of bags harvested is = 108 + 144

= 252 bags of maize.

Answer:

The transformation is

reflection in the x axis

That's ( x , - y)

Hope this helps.

Answer:

25x + 5y + z cents

Step-by-step explanation:

1 quarter is worth 25 cents.

1 nickel is worth 5 cents.

1 penny is worth 1 cent.

Therefore, x quarters, y nickels and x pennies will be worth:

(x * 25) + (y * 5) + (z * 1)

= 25x + 5y + z cents

Answer:1/11

Step-by-step explanation:

Let the yellow cubes be x

yellow = x

blue = 2x                // Blue cubes is twice of yellow

Green = 8x              // Green is four times of blue

Ratio:

Yellow : Blue : Green

  1       :   2    :     8

P(Yellow) = 1/11