The area of a triangle is given by A = 1/2bh, where b is the base and h is the height of the triangle

We have the following quadratic Function in a graph:

Now, we solve one aspect at a time:

Zeros

Let's remember that the zeros or roots of the quadratic function are those values of x for which the expression is 0. Graphically, the roots correspond to the abscissae of the points where the parabola intersects the x-axis.

By looking at the graph we can identify these, which in this case it is:

Axis of symmetry

Recall that the graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola.

By looking at the graph we can identify this, which in this case it is:

Max or min

In mathematical analysis, the maxima and minima of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range or on the entire domain.

By looking at the graph we can identify this, which in this case it is:

Vertex

Remember that the vertex of a quadratic equation or parabola is the highest or lowest point of the graph corresponding to that function. The vertex lies in the plane of symmetry of the parabola; whatever happens to the left of this point will be an exact reflection of what happens to the right.

By looking at the graph we can identify this, which in this case it is:

The graph of 6x + 4y = 4 can be sketched as shown in the image attached below.

A linear equation can be expressed in standard form as Ax + By = C, where A, B, and C are integers. Also, it can be rewritten in slope-intercept form as y = mx + b, where b is the y-intercept and m is the slope of the equation.

In order to graph an equation, we can easily determine what the slope (m) and the y-intercept (m) of the graph would be when we rewrite the equation in slope-intercept form.

Given the equation in standard form as, 6x + 4y = 4, rewrite it in slope-intercept form:

6x + 4y = 4

4y = -6x + 4

y = -6x/4 + 4/4

y = -3/2x + 1

This means that the slope of the graph you'd sketch will be -3/2, and the line must intercept the y-axis at 1, because the y-intercept is 1.

The graph is shown below.

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1.09 × 10^-4 in standard form is

A centroid divides each median in a ratio 2:1, in this case, the segment FC is the sum of the segments FG and GC:

By solving for GC, we get:

Then, the part of the median that goes from C to G has a length of 12 and the part that goes from the centroid to F has a length of 6, then we can express their ratio as 12:6, which is equivalent to 2:1.

Then the answer is:

Point G can be the centroid because 12:6 equals 2:1

The value of the length AB xcm = -3½ which is derived using the completing the square method, and satisfies the expression 2x² - 5x - 42 = 0.

To solve for the unknown value of a quadratic equation; say ax² + bx + c = 0:

From the derived quadratic equation, applying the method of completing the square as follows;

2x² - 5x - 42 = 0

divide through by 2

x² - (5/2)x - 21 = 0

add 21 to both sides

x² - (5/2)x = 21

divide the coefficient of x, square the result and add it to both sides

x² - (5/2)x + (5/4)(5/4) = 21 + (5/4)(5/4)

factor the left hand side of the equation

(x - 5/4)² = 21 + (25/16)

simplify the right hand side

(x - 5/4)² = 361/16

take the square root of both sides

x - 5/4 = (+ or -)(19/4)

then;

x = 5/4 + 19/4 or 5/4 - 19/4

x = 3 or x = -3½

The quadratic equation 2x² - 5x - 42 = 0 is true for the value of x = -3½.

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Answer: 4/7

Step-by-step explanation:

There are 7 students with brothers, 4 of which have sisters.

So, the probability is 4/7.

The given expression 3x^2 +14x-49=0

we will de factorization tos solve for x

The value of x is -7 and 7/3

Answer : x = -7 and x = 7/3

To visualize the solution of a system of equations, a graph is ideal, as we can see whether the functions intersect or not.

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem. The pair/tuple/... containing these values is called the solution of the system.

The equations that construct a system are functions, and the solution of a system is at the point of intersection of these functions. The intersection of two points is easier to visualize graphically then calculating, hence a graph is ideal, as we can see whether the functions intersect or not, while for the function we would have to calculate.

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Answer:

Step-by-step explanation:

3.75 is a2 x (b-c)

4.85 gose with the b + c -a

3.3 gose to the a - b + c

you should now know the last one

Answer:

1. A² × ( B - C ) = 3.75

2. B + C - A = 3.65

3. A - B + C = 4.85

4. B × ( A - C ) = 3.3

Step-by-step explanation:

1. (5 × 5) × (4.4 - 4.25)

    25 × .15 = 3.75

2. (4.4 + 4.25) - 5

     8.65 - 5 = 3.65

3. (5 - 4.4) + 4.25

     .6 + 4.25 = 4.85

4.  4.4 × ( 5 - 4.25 )

      4.4 × .75 = 3.3

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to solve this question, we need to difine our variables

we have values for end points as

x1 = -8

y1 = 4

x2 = -4

y2 = -8

next we can find the slope of the equation

step 2

let's find the mid-point using mid-point formula

mid-point = (-6, -2)

now we know the perpendicular line travels (-6 , -2) and has a slope of -3

equation of a straight line => y = mx + c

we can solve for c to find the equation.

note: m = slope

c = intercept

the equation of the perpendicular bisector can be written as

y = -3x - 20

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Explanation:

Define these two events

A = father born in Michigan

B = mother born in Michigan

The notation ~A and ~B represent the opposite of each defined event above.

According to the table

P(A) = 0.48

P(B) = 0.73

If A and B were independent, then P(A and B) = P(A)*P(B) = 0.48*0.73 = 0.3504 = 35.04% but this contradicts the 29% in the "father born in Michigan" column and "mother born in Michigan" row. The table states that P(A and B) = 0.29 should be the case instead of 0.3504.

Because of this contradiction, this means P(A and B) = P(A)*P(B) is false and therefore A and B are NOT independent

--------------------------------------

Another way to look at it:

P(A) = 0.48

P(A given B) = P(A and B)/P(B)

P(A given B) = 0.29/0.73

P(A given B) = 0.39726 approximately

If A and B were independent, then P(A) and P(A given B) would be the same value. However, they are not. This is another way to see why the events are NOT independent

Through similar calculations, P(B given A) = P(A and B)/P(A) = 0.29/0.48 = 0.6042 approximately which doesn't match with P(B) = 0.73; if A and B were independent then P(B) needs to be equal to P(B given A).

(i) The vertex's x-coordinate is 25.

(ii) The maximum height of the cannonball is 12.48 meters.

(iii) Total horizontal distance that a cannon ball can travel is 50 meters.

(iv) Total horizontal distance that a cannon ball can travel with decreased angle is 22.5 meters.

(v) Distance the cannonball traveled before reaching the maximum height is 25 meters.

What is coordinate?

A pair of values is used to specify a point's placement on a coordinate plane using both horizontal and vertical distinctions from the two separate axes. usually represented by a pair of x-values and y-values (x,y).

(i) They are both at y = 4 and separated by (40-10) = 30

The symmetry line is halfway between 40 and 10

Consequently, the vertex's x-coordinate is 25.

(ii) y = -0.01x2 + 0.5x, 

a = -0.01, 

b = 0.5,

-b/2(a) = -0.5/(2X-0.01) = 0.5/0.02, and so on.

y=-0.01*2+0.5(25) =12.48 meters

The maximum height of the cannonball is 12.48 meters.

(iii) Total horizontal distance that cannon ball can travel is (0,0)-(50,0)= 50 meters.

(iv)Total horizontal distance that cannon ball can travel with decreased angle is (0,0)-(22.5,0) =22.5 metres

(v) Distance cannon ball travelled before reaching the maximum height is [(0,0)-(50,0)]/2 =25 meters

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The scale of the map is 1 square inches = [tex]10^{13}[/tex] square inches.

Given that:-

Area of the desert = 25,000 square miles

Area of the desert in the map = 10 square inches

We have to find the scale of the map.

We know that,

1 mile = 63360 inches

Hence, conversion of square miles to square inches:-

1 mile * 1 mile = 63360 inches *63360 inches

1 square mile = 4,01,44,89,600 square inches

25,000 square miles = 40144893600*25000 = 10,03,62,24,00,00,000 square inches =[tex]10.036224 *10^{13}[/tex] ≈ [tex]10*10^{13}[/tex] square inches.

Now, we can say that [tex]10*10^{13}[/tex] square inches is scaled to 10 square inches.

Hence, the scale of the map is :-

1 square inches = [tex]10^{13}[/tex] square inches.

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The given number is

Which is equal to 6,0827625302982196889996842452021...

However, rounded to the nearest tenth is

The image below shows the number graphed on a number line.

Answer:

  2.×10^-2 cm/h . . . . rounded to 2 dp

  2.26×10^-2 cm/h . . . . rounded to 3 sf

Step-by-step explanation:

You want the difference in growth rates between 6.849×10^-4 cm per hour and 2.329×10^-2 cm per hour.

The difference of two numbers written in scientific notation requires that they have the same power-of-ten multiplier.

  2.329×10^-2 - 6.849×10^-4

  = 2.329×10^-2 - 0.06849×10^-2 = 2.26051×10^-2 = 0.0226051

The question asks for the answer rounded to 2 decimal places and expressed in scientific notation.

  0.0226051 ≈ 0.02 = 2×10^-2 . . . . cm per hour

It makes more sense to round the mantissa to 2 decimal places, meaning the value is rounded to 3 significant figures.

  2.26051×10^-2 ≈ 2.26×10^-2 . . . . cm per hour

Given

we are given numbers 4, 9, 15, 3, 5

Required

we need to find which of the above numbers are composite.

Explanation

Here

clearly 4, 9, 15 have factors other than 1 and itself.

so 4, 9 and 15 are composite numbers

Answer:

I wasn't too sure of your question, but this is what made sense to me.

Step-by-step explanation:

cross multiplication seems to be the best fit for this.

Like this:

[tex]\frac{9}{2}=\frac{x}{24}\\ 2(x)=9(24)\\ 2x=216\\x= \frac{216}{2}\\ x=108[/tex]

Hope this helped in any way.

Answer:

4.0738636

Step-by-step explanation:

Answer:

Step-by-step explanation:

63 and 117

Answer:

She can fill five boxes with 20 pencils left over.

Step-by-step explanation:

17x10=170

170/50=3.4

50x3=150

170-150=20

THE PROPERTY OF SUBSTITUTION IS USED. IF x=2 IT MEANS IN THE PLACE OF X IN THE EXPRESSION 4X-3 YOU WILL PLUG IN THE VALUE 2 AND SIMPLIFY.

[tex] = 4(2) - 3 \\ = 8 - 3 \\ = 5[/tex]

JUST AS I HAVE DONE ABOVE.

HOPE THIS HELPS

Hello

The sample which she has to study is 200

The answer to this question is option A

Given is a right angled triangle. Consider the figure,

Using the trignoetric funcyion tan, we have,

Now, as we have base, a = 3.89 and height c = 12, the perimeter can be calcualted as,

Now, the area can be calculated as,

1. -14/2 = -7 Integer, Rational

2. √64 = 8 Natural, Whole, Integer, Rational

3. 0 Whole, Integer, Rational

4. π Irrational

5.

can be expressed as a fraction, then it's rational

6. 3/8 Rational

Answer:

[tex]2.573 \times 10^7[/tex]

Step-by-step explanation:

[tex]92960000-67230000=25730000=2.573 \times 10^7[/tex]

We have to solve:

We can not write a explicit expression to find the value of x, but we can test each option to see which one is correct:

Answer: x=3

Answer:

The triangle has sides of 36 feet, 72 feet, and 49 feet.

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

x = shortest side

2x = second side

x+13 = third side

The three sides add up to the perimeter of 157

(x)+(2x)+(x+13) = 157

4x+13 = 157

4x = 157-13

4x = 144

x = 144/4

x = 36

The shortest side is 36 feet.

The second side is 2x = 2*36 = 72 feet.

The third side is x+13 = 36+13 = 49 feet.

Check:

side1+side2+side3 = 36+72+49 = 157

The answers are confirmed.

EXPLANATION

Price of shoes = $5.50

Markup= 40%

Let's call x to the unknown final price.

The markup percentage relationship is given by the following formula:

Replacing terms:

Multiplying both sides by 5.5:

Dividing both sides by 100:

Adding 5.5 to both sides:

Simplifyng the fraction:

Adding numbers:

Switching sides:

Answer: The final price of the shoes in the deparment store is $7.7

The number of red balloons is 5.

The number of blue balloons is 7.

The number of yellow balloons is 12.

To find the probability of randomly selected a yellow balloon

Hence the correct option is C that is 1/2.