In frequency curve the points are joined by bits of a straight line. True/False​

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Answer:

Step-by-step explanation:

I find it useful to graph the function using a graphing calculator. That answers most of the questions.

This function is written in standard form (terms have decreasing powers of x). It is a 2nd degree function, because the highest power of x is 2. A second-degree function is also called a quadratic. The leading coefficient is the coefficient of the term with the highest power of x. Here the leading coefficient is 4. The sign of it is positive, which tells you which way the graph opens (when the degree is even).

Opening

When the leading coefficient is positive, the function's graph opens upward. (If it were negative, the graph would open downward.)

Vertex

The vertex is the extreme point on the graph. If you want to find it algebraically, its coordinates are ...

  (-b/(2a), c -b^2/(4a))

where 'a', 'b', and 'c' are the coefficients of ax² +bx +c. In this function, a=4, b=-2, c=-3, so the vertex is ...

  (-(-2)/(2(4)), -3 -(-2)^2/(4(4)))  = (1/4, -3 1/4)

Axis of Symmetry

The axis of symmetry is the vertical line through the vertex. It will have the equation x=constant. Of course, the constant must be the x-value of the vertex (which is why we found the vertex first).

  x = 1/4

x-intercepts

The x-intercepts are where the graph crosses the x-axis. The attached graph shows an approximation of them, rounded to thousandths. You can compute the x-intercepts algebraically from the vertex and the leading coefficient.

  x-intercepts = (vertex x-value) ± √(-(vertex y-value)/(leading coefficient))

  x-intercepts = 1/4 ± √((3 1/4)/(4)) = 0.25 ±√0.8125 ≈ {-0.651388, 1.151388}

y-intercept

The y-intercept is the value of f(0), the point where the graph crosses the y-axis. It is always the constant in the polynomial, named 'c' above. The y-intercept is ...

  y-intercept = -3

_____

Additional comment

Sometimes you want the x- and y-intercepts written as coordinates. Of course the y-coordinate of the x-intercepts is 0. Similarly, the x-coordinate of the y-intercept is 0. The coordinate ordered pairs are shown on the graph.

These are fairly standard questions that are asked about quadratic functions. It can be worthwhile to get familiar with the way they are answered. (The computation of the x-intercepts shown here is perhaps a bit unusual, but is very effective once you have the function vertex. The values it gives are correct even when the "x-intercepts" are complex numbers.)

The answer is the last one, [tex]2\frac{11}{12}[/tex]

Answer:

The second one.

Step-by-step explanation:

With the equation -4/5x=80, you need to multiply the reciprocal of the fraction in order to isloate x so that you can solve. Therefore, the second answer seems to best represent this.

Answer:

Increasing on the interval(s) [tex]-2\leq x\leq -4[/tex]

Decreasing on the interval(s) [tex]-1\leq y\leq 1[/tex]

Step-by-step explanation:

Anytime the graph is going upward, the function is increasing. However, anytime the graph goes down, the function is decreasing. Look at the image below for further reference. Also, when the function is increasing, the slope is positive, and when the function is decreasing the slope is negative.

The increasing interval of the graph is -3

The decreasing interval of the graph is 0.5

Since the values are in the middle of the interval, it automatically becomes the answer.

9514 1404 393

Answer:

  x = ab/c

Step-by-step explanation:

The applicable theorem tells you the product of chord lengths is the same for the two crossing chords:

  ab = cx

  x = ab/c . . . . . divide by the coefficient of x

9514 1404 393

Answer:

Step-by-step explanation:

The sum of angles in a triangle is 180°. We are told the measures of the three angles are ...

  x + x + 94 = 180

  2x +94 = 180 . . . . . . equation to solve for x

  2x = 86 . . . . . . . subtract 94

  x = 43 . . . . . . divide by 2

The congruent angles each measure 43°.

Answer:

See below.

Step-by-step explanation:

The top is a square 3 cm by 3 cm.

The other 4 sides are rectangles. Each one is 4 cm by 3 cm.

Front: 4 cm * 3 cm = 12 cm^2

Back: 4 cm * 3 cm = 12 cm^2

Right: 4 cm * 3 cm = 12 cm^2

Left: 4 cm * 3 cm = 12 cm^2

Top: 3 cm * 3 cm = 9 cm^2

TOTAL: 12 cm^2 + 12 cm^2 + 12 cm^2 + 12 cm^2 + 9 cm^2

TOTAL: 57 cm^2

Bottom prism (blue):

Front: 5 cm * 6 cm = 30 cm^2

Back: 5 cm * 6 cm = 30 cm^2

Right: 5 cm * 6 cm = 30 cm^2

Left: 5 cm * 6 cm = 30 cm^2

Bottom: 5 cm * 5 cm = 25 cm^2

Top: 5 cm * 5 cm - 3 cm * 3 cm = 25 cm^2 - 9 cm^2 = 16 cm^2

TOTAL: 30 cm^2 + 30 cm^2 + 30 cm^2 + 30 cm^2 + 25 cm^2 + 16 cm^2

TOTAL: 161 cm^2

Explanation for area of top of bottom (blue) prism.

Notice that the entire bottom of the top (yellow) prism is connected to the bottom prism, so there is no area of the bottom of the top prism that adds to the total surface area of the composite solid. With the bottom prism's top surface it is different. Since the top surface of the blue prism is larger than the bottom surface of the yellow prism, there is a bit of top surface of the blue prism that is seen. That area is the area of the top surface of the blue prism minus the area of the bottom surface of the top prism.

5 cm * 5 cm = 3 cm * 3 cm = 25 cm^2 - 9 cm^2 = 16 cm^2

The area of the top surface of the blue prism is 16 cm^2

Total surface area of the composite solid:

57 cm^2 + 161 cm^2 = 218 cm^2

Answer:

57 cm^2

Step-by-step explanation:

4 (4x3) + (3x3) = 48 + 9 = 57 cm^2

Front: 12 cm2

Back: 12 cm^2

Right: 12 cm^2

Left: 12 cm2

Top: 9 cm^2

Answer:

92

Step-by-step explanation:

they must sell at least 92 because 92 times 5 equals 460 and so 460 is more than 455 so they made a profit

Answer:  $5.50

Step-by-step explanation: because adding all the shampoo together

The cost of one bottle of shampoo is $ 7.8

The cost is $ 7.8

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of one bottle of shampoo be = x

Let the cost of one bottle of body wash be = y

Now ,

The total cost of a bottle of shampoo and a bottle of body wash = $ 14.50

Substituting the values in the equation , we get

x + y = 14.50   be equation (1)

And ,

The cost of 3 bottles of shampoo and 5 bottles of body wash = $ 56.90

Substituting the values in the equation , we get

3x + 5y = 56.90   be equation (2)

On simplifying equation (1) and equation (2) , we get

Multiply equation (1) with 5 , we get

5x + 5y = 72.5   be equation (3)

Subtract equation (2) from equation (3) , we get

2x = 15.6

Divide by 2 on both sides of the equation , we get

x = $ 7.8

Therefore , the value of x is $ 7.8

Hence , The cost of one bottle of shampoo is $ 7.8

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Answer:

Step-by-step explanation:

measure angle b

add it with 90

90 + b = A

and create an angle with the measure of sum (A)

Answer:

90

Step-by-step explanation:

the question sat sum of A'angle and B'angle.

so A+B=180  

so when you subtract 180-90=90

36.25 miles

Answer:

p: True, q: False, r: True

Step-by-step explanation:

Truth value only has two answer choices: true or false

p: True (there are 7 days in a week)

q: False (there are 31 not 30 days in March)

r: True (Halloween is on Oct. 31)

If not correct, write a message and I will try to help further.

Answer - its 31

step by step

Answer:

your answer is 7,15,60

Step-by-step explanation:

15-8=7

15*4=60

7+15+60=82

Hope it helps u

Two numbers that equal 130 when rounded by the nearest tenth are 129 and 131

Answer:

W < 7

Step-by-step explanation:

1.

Step 1: Subtract 5 from both sides.

2. Check out the image below to see the graphed solution.

Answer:

[tex]x \geqslant 3[/tex]

[3, infinity)

Step-by-step explanation:

-3n + 4 < n-8

get all of the n's to the same side

-3n + 4 < n-8

+3n + 4 < +3n-8

4 < 4n-8

send the number (-8) off to the other side

4 < 3n-8

+8< 3n +8

12 < 3n

isolate variable

12/3 < 3n/3

4 < n

so

[tex]x \geqslant 3[/tex]

Answer:

it is the last one

Step-by-step explanation:

Answer:

[tex] \frac{162.5}{325} = \frac{156}{x} \\ x = (325 \times 156) \div 162.5 = 312[/tex]

Answer:

This can solve by using corresponding triangles.

(TS/RT) = (VU/RV)

[tex](156 \div 162.5) \times 325 = vu[/tex]

VU = 309.12

= 309 m

Answer:

We need to know how many miles it takes to get to school

Edit:

100 miles

Explanation:

5 x 20 = 100  

Answer:

100mile

Step-by-step explanation:

5miles a day multiplied by 20 school days

9514 1404 393

Answer:

  4%

Step-by-step explanation:

The multiplier for computing simple interest over a 3-year period is ...

  I = Prt . . . . . interest on principal P at rate r for t years

  I/P = rt = 3r

The multiplier for computing compound interest over a 3-year period is ...

  A = P(1 +r)^t . . . . amount with interest

  A/P -1 = (1 +r)^3 -1 . . . . multiplier for computing interest only

Then the multiplier for the difference in amounts of interest is ...

  ((1 +r)^3 -1) -3r = (1 +3r +3r^2 +r^3) -1 -3r = r^2(3 +r)

This means we need to solve the cubic ...

  r^2(3 +r) = 2.432/500

__

This can be solved a variety of ways. Perhaps my favorite is a graphical solution.  For that, we would rewrite the equation to the form ...

  f(x) = x^2(3 +x) -0.004864

so the solution is found where f(x) = 0. The graph shows the solution to be ...

  x = 0.04

The rate of interest is 0.04 = 4%.

_____

Additional comment

Using the above f(x) to develop a Newton's Method iterator, we find it to be ...

  x' = (x²(2x +3) +0.004864)/(3x(x +2))

This needs a starting value, so we need an initial clue as to the approximate interest rate.

That can be offered by rearranging the cubic we first developed:

  r = √(0.004864/(r +3))

Starting with r=0, this gives r ≈ 0.0402. At this point, we can either use this equation as an iterator, or use the Newton's method iterator above. Both will give an interest rate accurate to 4 or 5 decimal places in one iteration.

__

You may be aware from the development above that the polynomial that must be solved will have a degree equal to the number of years over which interest is computed. That is, solving the same question for a 10-year period would involve finding the root of a 10th-degree polynomial.

Answer:

9.5

Step-by-step explanation:

Probably wrong, but to find average you add up 12+7 then divide by 2, that is 19/2 which is 9.5

The average value of the time is 9.5 minutes.

"The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set".

For the given situation,

Time to walk in the stadium are 12 minutes and 7 minutes.

Number of values = 2

Formula to find average,

Average = Sum of Values/ Number of values

⇒ [tex]Average = \frac{12+7}{2}[/tex]

⇒ [tex]Average = \frac{19}{2}[/tex]

⇒ [tex]Average = 9.5[/tex]

Hence we can conclude that the average value of the time is 9.5 minutes.

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Answer:

45 degrees, 135 degrees, 225 degrees, 315 degrees

Step-by-step explanation:

x = 45 degrees + k * 90 degrees

t^3-4t^2-.5t+2=0

t = 4

t = 2^.5/2

cosx=2^.5/2

Answer:

25thousand six hundred

Answer and Step-by-step explanation::

250 grams.

Is that 0.25 kg converted to grams? the picture is way too small.

Every kg has 1000 grams. Because it is 0.25 kilograms, you need to take 0.25  of 1000.

1000

x

0.25

= 250.

Answer:

100/5 = 20

so 20 is 5% of 100

This is the same as writing [tex]-18w^7[/tex]

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

Explanation:

The three terms we are multiplying are:

The coefficients of those terms are: 3, 2, -3

Multiplying the coefficients gets us 3*2*(-3) = -18 which is the coefficient of the final answer.

As for multiplying the w terms, we add the exponents: -2+6+3 = 7, and this is the exponent of the final answer.

Wrapping everything up, that's how we end up with -18w^7

Answer:

neither

Step-by-step explanation:

If the graph is symmetric by the y-axis the function is even OR we can say that

f(x) = f(-x) for the function to be even

for f(3) = 2 and f(-3)= 2  works yet

for f(2) = 0 and f(-2) = 1 NOT an even function

f(-x) = -f(x) will make the function odd

f(-3) = 2 and -f(3) = -2 NOT an odd function

f(-x) ≠ -f(x) will make the function neither

f(-3) = 2 ≠ -f(3) = -2 the function is neither odd or even

9514 1404 393

Answer:

  p = 1.2

Step-by-step explanation:

From here, it is a 2-step linear equation.

Step 1:

Identify the constant term on the side of the equation with the variable. Subtract that constant from both sides.

  -10.9p = -13.08

Step 2:

Divide both sides by the coefficient of the variable.

  p = -13.08/-10.9 = 1.2

The solution is p = 1.2.

9514 1404 393

Answer:

  10%

Step-by-step explanation:

We assume the "sum" being referred to in both cases is the principal amount invested. The simple interest formula tells you ...

  I = Prt . . . . . . interest on P invested at annual rate r for t years

We have ...

Filling in these values, we get ...

  0.3P = Pr(3)

  0.1 = r . . . . . . . . divide by 3P

The interest rate is 0.1×100% = 10% per year.