Help me please im trying to do this but dont understand it at all.

The length of the base of the triangle is 12m

The formula for calculating the area of a triangle is expressed as:

A = 0.5 * base * height

If the height of a triangle is 4 m less than its base, then;

h = b - 4

Substitute

A = 0.5(b)(b-4)

48 = 0.5b²-2b

b²-4b - 96 = 0

Factorise

b² - 12b + 8b - 96 = 0

b(b-12)+8()b-12) = 0
b - 12 = 0

b = 12

Hence the length of the base of the triangle is 12m

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Answer:

here

Step-by-step explanation:

Answer:

(-2 , 8)

Step-by-step explanation:

[tex]\begin{cases}y=-4x&\\ y=4x+16&\end{cases}[/tex]

We substitute y by -4x in the second equation of the system:

-4x = 4x + 16

⇔ -8x = 16

⇔ x = 16/(-8)

⇔ x = -2

Now ,we substitute x by -2 in the first equation of the system:

y = -4 × (-2) = 8

then

the solution of the system is {(x = -2 , y = 8)}

The value of the function h(-4) is (a) -2

The function is given as

h(x) = -2x - 10

When x = -4, we have:

h(-4) = -2 * -4 - 10

Evaluate the product

h(-4) = 8 - 10

Evaluate the difference

h(-4) = -2

Hence, the value of the function h(-4) is (a) -2

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x + 3x + 5x ( the variables are same you can add them immediately )

9x ( the answer is 9x for adding terms with the same variable just add the numbers and write the variable as itself)

HOPE IT HELPS

Answer: 9x

Step-by-step explanation:

As the variables are of same power (1) we can add it

x+3x+5x=9x

Answer:

-3

Step-by-step explanation:

Equation: (x + 6) - 5 = -2

we want to isolate x

(x + 6) - 5 = -2              

          + 5    + 5      (add 5 to start getting x on its own)

x + 6 = 3                

  - 6      - 6                 (subtract 6 to isolate x)

x = -3

so, this answer was not provided, but is the correct answer.

The solution to this equation is -3,

so, the correct answer is: -3.

Here, we have,

given that,

Equation is:

(x + 6) - 5 = -2

we want to isolate x

(add 5 to start getting x on its own)

(x + 6) - 5+ 5 = -2 + 5                          

(subtract 6 to isolate x)

x + 6 - 6 = 3   - 6              

so, we get,                  

x = -3

so, the solution to this equation is -3,

so, the correct answer is: -3.

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Answer:

x = 2; y = -1

Step-by-step explanation:

We can solve (first for y, then for x) using substitution:

[tex]x+y=1\\7x+4y=10\\(x+y=1)-y\\x=1-y\\\\7(1-y)+4y=10\\7-7y+4y=10\\(7-3y=10)-7\\(-3y=3)/-3\\y=-1\\\\(x-1=1)+1\\x=2[/tex]

Answer:

/.............................../././///////////////////////////////////////

Step-by-step explanation:

.

Answer: 6

Step-by-step explanation: 3 + 6 = 9,  9 + 6 = 15,  15 + 6 = 21,  21 + 6 = 27

Answer:

356000000

Step-by-step explanation:

1. Simplify the expression

Calculate the expression inside the parentheses.

[tex](1.5*10^8)+(2.06*10^8)[/tex]

Simplify exponents and square roots

[tex](1.5*10^8)+(2.06*10^8)[/tex]

[tex](1.5*100000000)+(2.06*10^8)[/tex]

Perform any multiplication or division, from left to right:

[tex](1.5*100000000)+(2.06*10^8)\\[/tex]

[tex](150000000)+(2.06*10^8)[/tex]

Simplify exponents and square roots

[tex]150000000+(2.06*10^8)[/tex]

[tex]150000000+(2.06*100000000)[/tex]

Perform any multiplication or division, from left to right:

[tex]150000000+(2.06*100000000)[/tex]

[tex]150000000+(206000000)[/tex]

Calculate any addition or subtraction, from left to right.

[tex]150000000+206000000[/tex]

[tex]356000000[/tex]

Why learn this

Order of operations is a basic rule of algebra. It tells us what to solve first when we have an equation with multiple functions, which is something that you will likely encounter throughout your maths studies. The order is: Parentheses, Exponents, Multiplication and Division, then finally Addition and Subtraction. Remember that when you're solving within the parentheses, the Order of Operations applies!

Terms and topics

Answer:

x = 36°

y = 66°

z = 78°

Step-by-step explanation:

Setup equations:

Allowing the first angle to be x, the second to be y, and the third to be z, the three sentences describing the relationships between angle measures are given below:

Substituting equation 3, into equations 1 and 2

Eq1:  x + y + z = 180°

x + y + (y+12°) = 180°

x + 2y + 12° = 180°

x + 2y = 168°

x = 168° - 2y

Eq2:  y + z = 4x

substituting the result from equation 1, and Equation 3...

y + (y+12°) = 4*(168° - 2y)

2y + 12° = 672° - 8y

10y = 660°

y = 66°

Substituting back into Equation 3...

Eq3:  z = y + 12°

z = (66°) + 12°

z = 78°

Substituting both y, and z into Equation 1...

x + y + z = 180°

x + (66°) + (78°) = 180°

x + 144° = 180°

x = 36°

So, the three angle measures are:

x = 36°

y = 66°

z = 78°

"The sum of the measures of the angles of a triangle is 180."

x + y + z = 180°

36° + 66° + 78° = 180°

True

"The sum of the measures of the second and third angles is four times the measure of the first angle"

y + z = 4x

66° + 78° = 4*(36°)

144° = 144°

True

"The third angle is 12 more than the second"

z = y + 12°

78° = 66° + 12°

True

The number of the blue marbles are in the box will be 102.

The solution of the equation means the value of the unknown or variable.

A box contains 162 marbles which are either red (r) or blue (b).

r + b = 162 ...1

There are 42 more blue marbles than red marbles.

b = r + 42 ...2

Then from equation 1 and 2, we have

r + r + 42 = 162

           2r = 120

             r = 60

Then the number of blue marble will be

b = 60 + 42

b = 102

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Considering the given graph, the profit during the period was of -2 dollars.

We add all the negative numbers, all the positive numbers, then keep the signal of the higher absolute value, and subtract the values.

From the graph, we have that:

8 > 6, hence the profit is negative given by:

-(8 - 6) = -2 dollars.

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Final answer:

Since absolute values determine the distance between the number and the value whether the value is positive or negative. As distance is always positive.

Thus, |a| is always nonnegative, even though |a|=-a for negative values of a.

Step-by-step explanation:

Step 1

It is said that |a| is always nonnegative even though even though |a|=-a for negative values of a.

Step 2

This is because by the definition of an absolute value, any real number inside an absolute value symbol || will always be positive.

Answer:

answer is the second option  m<-2 7/12

Step-by-step explanation:

process:

convert -2 1/4 into an improper fraction

m+1/3 < -9/4

m <-9/4 -1/3

calculate the difference

m<-31/12

turn into a mixed fraction

The most effective in controlling the confounding variables is matched pairs design.

A matched pairs design is when participants are matched based on shared characteristics that is of importance to the experiment. One member of the pair is put in the control group while the other is put in the experimental group.

Here are the options:

A completely randomized design experiment

A longitudinal observational study

A retrospective observational study

A matched-pair design experiment

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Answer:

Yes, because the p-value of the independent variable is less than 0.05

Step-by-step explanation:

The relationship between Red Sox away games and average daily revenues significant at the 95% confidence level because the p-value ( X) < 0.05 , Option C is the correct answer.

Probability is the study of chances of an event to happen.

It has a range form 0 to 1 , where 0 indicates uncertainty while 1 indicates certainty.

The data is given and on the basis of it

It can be seen that for 95 % confidence Level

P value =0.0005

So , the relationship between Red Sox away games and average daily revenues significant at the 95% confidence level because the p-value of the independent variable is less than 0.05.

Therefore Option C is the correct answer.

The complete question is

Is the relationship between Red Sox away games and average daily revenues significant at the 95% confidence level? Choose the correct answer with the corresponding correct reasoning.

No, because R Square is less than 50%

Yes, because the slope is positive.

Yes, because the p-value of the intercept is less than 0.05

Yes, because the p-value of the intercept is less than 0.95

Yes, because the p-value of the independent variable is less than 0.05

Yes, because the p-value of the independent variable is less than 0.95

The data table is attached with the answer.

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Answer:

A.

Step-by-step explanation:

so, the equation is

h(t) = -t² + 7t

so, we need to find the solutions for t (the time when the ball is exactly 10 ft in the air). there had to be 2 solutions, as the ball first goes up passing the 10 ft height, and then comes back down again, passing the 10 ft mark a second time. and between these 2 times the ball is higher (but not equal, so, we can only use < or > as inequality signs) than 10 ft.

10 = -t² + 7t

-t² + 7t - 10 = 0

the generation solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = t

a = -1

b = 7

c = -10

t = (-7 ± sqrt(7² - 4×-1×-10))/(2×-1) =

= (-7 ± sqrt(49 - 40))/-2 = (-7 ± sqrt(9))/-2

t1 = (-7 + 3)/-2 = -4/-2 = 2 seconds

t2 = (-7 - 3)/-2 = -10/-2 = 5 seconds

so, between 2 and 5 seconds airtime the ball is higher than 10 ft.

and remember : HIGHER THAN.

so, we cannot use any equality (like <= or >=).

t must be higher than 2 and lower than 5 :

2 < t < 5

The two compositions for the functions are:

[tex](p\°q)(2) = -6\\\\(q\°p)(2) = 6[/tex]

When we have two functions q(x) and p(x), the composition is:

[tex](q\°p)(x) = q(p(x))[/tex]

Here we have:

[tex]p(x) = -x\\\\q(x) = 2x^2 - 2[/tex]

The first composition is:

[tex](q\°p)(2) = q(p(2)) = 2*(p(2))^2 - 2 = 2*(-2)^2 - 2 = 6[/tex]

The other composition is:

[tex](p\°q)(2) = p(q(2)) = -(q(2)) = -(2*2^2 - 2) = -(8 - 2) = -6[/tex]

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The pOH of a solution is 5.70. The correct option is C; 2.5 x 10-7 is the hydroxide ion concentration.

The pOH of the solution is the negative logarithm of hydroxide ions concentration in a solution. The lower the value of pOH more alkaline will be the solution.

Mathematically written as:

pOH = - Log[OH-]

The sum of ph and pOH is equal to 14.

pH + pOH = 14

The pOH of a solution is 5.70.

pOH = - Log[OH-]

5.70 =  - Log[OH-]

[OH-] = 2.5 x 10-7 is the hydroxide ion concentration.

The solution has a pH value of more than 7 which means that it is base.

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The amount further by which Kate can see across the horizon than Paul is; 3.33 times farther

Formula for volume of a cone is;

V = ¹/₃πr²h

For Kate:

Height (h) = 50 m

Radius (r) = 6,371,000 m

Thus;

V = ¹/₃ * π * (6,371,000)² * 50

V = 2.12526863 × 10¹⁵ m³

To determine how much further can kate see across the horizon than Paul, we have:

⇒ (2.12526863 × 10¹⁵ m³)/6.3758059 × 10¹⁴ m³

= 3.33 times further.

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Answer:

Let the greater number be x and the smaller number be y

A.T.Q,

x+y=32 ...(1)

x=3y ...(2)

putting the value of x from (2) in (1)

(3y)+y=32

4y=32

y= 32/4=8

x=3y

x=3(8)=24

x=24 , y=8

An equation is formed when two equal expressions. The cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the cost of a pound of wheat flour be x and the cost of a pound of rye flour be y.

A baker purchased 13 lb of wheat flour and 14 lb of rye flour for a total cost of $14.85.

13x + 14y = $14.85

x = (14.85-14y)/13

A second purchase, at the same prices, included 15 lb of wheat flour and 12 lb of rye flour.

15x + 12y = $14.85

Substitute the value of x from the above equation and solve for y,

[tex]\dfrac{15(14.85-14y)}{13} + 12y = 14.85\\\\222.75-210y+156y = 193.05\\\\y = 0.55[/tex]

Substitute the value of y in any one of the equations formed,

13x + 14(0.55) = 14.85

13x = 7.15

x = 0.55

Hence, the cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.

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Answer:

======================

Since the given is the GP, find the common ratio in terms of given values:

Equate the two values and solve for x to find the missing term:

Considering the given stem-and-leaf plot, the quartiles are given as follows:

There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, which are 83 and 86, hence:

Me = (83 + 86)/2 = 84.5.

The first half has 12 elements, hence the first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:

Q1 = (67 + 68)/2 = 67.5.

The third half also has 12 elements, starting at the second 86, hence the third quartile is the mean of the 6th and 7th elements of this half, hence:

Q3 = (91 + 92)/2 = 91.5.

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