2. The height of a triangle is 5 m less than its base. The area of the triangle is 42 m2. Find the length of the base.(Points : 1)

Answers

Answer 1

Answer: Let's start with what we know

Area:
$42 = (1)/(2)bh$ where 42 is the area, b = base, and h = height

Height:
Since we know the height is 5 less than the base, we can write that as an equation.
$h = b - 5$

Now let's go and plug $h = b - 5$ into $42 = (1)/(2)bh$

$42 = (b)/(2)(b-5)$
Let's distribute b over (b-5)

$42 = ( b^(2) - 5b )/(2)$
Let's move 42 over to the right side to make a quadratic formula

$0 = (1)/(2) b^(2) - (5)/(2)b - 42$

Let's plug that into the quadratic equation, which is:

$\frac{-b +/- \sqrt{ b^(2) - 4ac } }{2a}$
And we can now plug the pieces in to calculate b

$\frac{- (-(5)/(2)) +/- \sqrt{ (-(5)/(2))^(2) - 4 ((1)/(2))(-42) } }{2 ((1)/(2)) }$
$\frac{(5)/(2) +/- \sqrt{ (25)/(4) +84 } }{1 }$
${(5)/(2) +/- \sqrt{ (361)/(4) } }$
${(5)/(2) +/- { (19)/(2) }$
Since we can't have a negative value for b (a base can't be negative meters), let's add:

${(5)/(2) + { (19)/(2) }$
${ (24)/(2) }$
$12 = b$

So the base of the triangle is 12m

Answer 2

Answer:

Answer:

took the quiz and it is correct the answer is 12

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Find the coordinates of the vertices after the given transformation. Reflection across x=-2. W(-4,-4)

Answers

Answer:

To reflect a point across the vertical line x = -2, we can use the formula:

(x, y) → (2c - x, y)

where c is the x-coordinate of the line of reflection. In this case, c = -2. Let's apply this formula to the point W(-4, -4):

W' = (2(-2) - (-4), -4)

= (-4 + 4, -4)

= (0, -4)

Therefore, after the reflection across x = -2, the coordinates of W(-4, -4) become W'(0, -4).

Step-by-step explanation:

A triangle with a perimeter of 13 centimeters is rotated and reflected in the coordinate plane. What is the perimeter of the resulting image?

Answers

Answer:

13 centimeters

Step-by-step explanation:

Rotation and reflection will not affects the shape

Out of a survey of 49 randomly chosen students 12 said they were going to attend a concert predict the number the number of students who attend the school

Answers

Answer:

Option C is correct.

The number of students who attend the school is approximately 980.

Step-by-step explanation:

The complete question is presented in the attached image to this question

It is known that 240 students bought concert tickets. That is, 240 students are attending the concert.

But out of a randomly chosen 49 students, 12 say that they are going for the concert.

Using the sample for a prediction or an approximation, the proportion of total number of students going for the concert = (12/49) = 0.245

Let x be the total number of students that attend the school.

This translates to the fact that

(0.245 × x) = 240

x = (240/0.245)

x = 979.6 = 980 to the nearest whole number.

Hope this Helps!!!

Answer: 613 students.

Step-by-step explanation:

Your question does not include the number of tickets sold as that will enable us to find out the number of students.

For that reason I will assume a number and you will then get a reference on how to solve this question.

Let us assume that 150 tickets were sold.

Now if 12 students out of a sample of 49 said they were going to attend and 150 tickets were sold, that means 150 tickets is the number of students that went from the general population.

This means that 12/49 should give us the same as 150/x with x being the total population of the school.

Solving for x,

12/49 = 150/x

12x = 150 * 49

12x = 7,350

x = 7,350 / 12

x = 612.5

x = 613 students.

Please help with the math problem shown in the image

Answers

Answer would be b=.25,-.25

A cone has a volume of 24 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of? 8 in3
24 in3
48 in3
72 in3

Answers

Answer:

72 cubic inches

Step-by-step explanation:

Volume of cone = $(1)/(3)\pi r^(2) h$ --1

Volume of cylinder = $\pi r^(2) h$ --2

We are given that a cylinder should fit exactly inside the cone

On comparing 1 and 2 we can see:

$\text{Volume of cone}= (1)/(3) \text{Volume of cylinder}$

Since we are given the volume of cone is 24 cubic inches .

So, $24= (1)/(3) \text{Volume of cylinder}$

$24 * 3= \text{Volume of cylinder}$

$72= \text{Volume of cylinder}$

Hence the volume of cylinder is 72 cubic inches

Option D is correct.

The correct answer is letter D. 72 in3

One milliliter of water weighs one gram. Explain the relationship between the conversion. Then draw a conversion chart to show the relationship between one milliliter of water and grams, milligrams, kilograms, and metric tons.

Answers

Well, one mililiter is one gram, 1000 miligrams, .001 kilograms and $10^(-6)$ metric tons.

Answer:

one square millimeter of water weighs one gram. That's the relationship

Step-by-step explanation:

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