The image of a parabolic lens is traced onto a graph. The function f(x) = (x + 8)(x – 4) represents the image. At which points does the image cross the x-axis?

Answer:

A-40

B-140

C-140

Step-by-step explanation:

b and c are supplementary angles to angle 40.

Therefore 180-40= 140.

and opposite angles in a quadrilateral are congruent to each other.

Answer:

(x,y) = (5,15)

Step-by-step explanation:

y = 3x

2x + 3y = 55

2x + 3(3x) = 55

2x + 9x = 55

11x = 55

x = 5

y = 3(5)

y = 15

Set up two equations:

Let a = adults and c = child:

a +  c = 289 ( rewrite as a = 289 - c)

1.50c + 4a = 746

Replace a with the rewritten formula:

1.50c + 4(289-c) = 746

SImplify:

1.50c + 1156 - 4c = 746

Combine like terms:

-2.50c + 1156 = 746

Subtract 1156 from both sides:

-2.50c = -410

Divide both sides by -2.50

c = -410 / -2.50 = 164

Number of children = 164

Number of adults = 289 - 164 = 125

Answer:

[tex] x+y = 289[/tex] (1) total people entered

[tex] 1.50 x +4 y = 746[/tex] (2) total amount collected

From the first equation we can solve for x and we got:

[tex] x = 289-y[/tex] (3)

Replacing (3) into (2) we got:

[tex] 1.5(289-y) +4y = 746[/tex]

And solving for y we got:

[tex] 433.5 -1.5 y +4y = 746[/tex]

[tex] 2.5 y= 312.5[/tex]

[tex]y=\frac{312.5}{2.5}= 125[/tex]

And then using (3) we can solve for x and we got:

[tex] x= 289-125= 164[/tex]

So then we have:

number of children = 164

number of adults = 125

Step-by-step explanation:

Let x the number of children and y the number of adults. From the info given we can set up the following equations:

[tex] x+y = 289[/tex] (1) total people entered

[tex] 1.50 x +4 y = 746[/tex] (2) total amount collected

From the first equation we can solve for x and we got:

[tex] x = 289-y[/tex] (3)

Replacing (3) into (2) we got:

[tex] 1.5(289-y) +4y = 746[/tex]

And solving for y we got:

[tex] 433.5 -1.5 y +4y = 746[/tex]

[tex] 2.5 y= 312.5[/tex]

[tex]y=\frac{312.5}{2.5}= 125[/tex]

And then using (3) we can solve for x and we got:

[tex] x= 289-125= 164[/tex]

So then we have:

number of children = 164

number of adults = 125

Answer:

It means the left side of the equation equals the right side of the equation regardless of the value of the variables. The solution is all real numbers for each variable

Step-by-step explanation:

Hi there! :)

Answer:

2nd choice. f(x) = 4 sin x + 2

Step-by-step explanation:

Recall that the transformations form of a sine function is:

y = ±a sin(b(x-h)) + k

Where:

'a' changes the amplitude

'b' changes the period

'h' is a horizontal shift

'k' is a vertical shift, or a change in the midline.

In this instance, the function has a midline of y = 2, which means an equation representing this must have a 'k' value of 2.

The only equation that contains this value is:

f(x) = 4 sin x + 2.

Answer:

I'm pretty positive the answer is B.   f(x) = 4sinx + 2

Step-by-step explanation:

Since d = 2 and the amplitude is 4 and there is nothing else effecting the function you are going up the graph 2 vertically and the amplitude will just go up and down 4 with you midline being at y = 2.

Step-by-step explanation:

Let the original price be x

After increasing by 20% the price is 3000

Thus,

x + ( x × 20%) = 3000

x + 20x/100 = 3000

x + x/5 = 3000

(5x + x)/5 = 3000

6x/5 = 3000

x = 3000 * 5/6

x = 2500

Hope it helps :)

the slope of the line is 3

Answer:

ln(2000) = 7.601

Step-by-step explanation:

For this we need to know the rules of logarithms, specifically the product rule and the power rule.  The product rule is simply ln(a*b) = ln(a) + ln(b).  The power rule is simply ln(a^b) = b ln(a).

With these rules, let's begin to simplify the expression:

4 ln(2) + 3 ln(5)

= ln(2^4) + ln(5^3)

= ln(16) + ln(125)

= ln(16 * 125)

= ln(2000)

= 7.601

Hope this helps.  Cheers.

A logarithm is a power to which a number must be raised in order to get some other number.

The value of the expression 4 log 2 + 3 log 5 as a single number is 3.30102.

A logarithm is a power to which a number must be raised in order to get some other number.

Example:

log 10 = 1

log 100 = log 10² = 2 log 10 = 2 x 1 = 2
log 1000 = log 10³ = 3 log 10 = 3 x 1 = 3

log 0 = undefined

log 1 = 0

We have,

Some formulas for log:

log[tex]x^{n}[/tex] = n log x

log mn = log m + log n

Given,

4 log 2 + 3 log 5

= log [tex]2^{4}[/tex] + log [tex]5^{3}[/tex]

= log 16 + log 125

= log (16 x 125)

= log 2000

= 3.30102

Thus the value of the expression 4 log 2 + 3 log 5 as a single number is

3.30102.

Learn more about log here:

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Answer: B or square root 2^5

Step-by-step explanation: I checked on my calculator

Answer:

See below

Step-by-step explanation:

Proof:

Statements                                    |  Reasons

AD ≅ BC                                         | Given

AD ║ BC                                         | Given

AC ≅ AC                                         |  Reflexive Property

∠DAC ≅ ∠ACB                               | If 2 || lines are cut by a trans., the                                                                       |  alternate interior ∠s are congruent.

ΔADC ≅ ΔBCA                               | S.A.S  Postulate

BA ≅ DC                                         | Corresponding sides of congruent Δs

So, quad. ABCD is a ║gm             | If a quad. has its opposite sides

                                                       | congruent, the quad. is a parallelogram.

It is prove that given quadrilateral is a parallelogram.

            AD ≅ BC      and AD ║ BC              

            AC ≅ AC            

       So that,   ∠DAC ≅ ∠ACB                              

            ΔADC ≅ ΔBCA    

        So that, BA ≅ DC                                        

Hence, opposite sides of given quadrilateral are equal. Therefore, given quadrilateral are parallelogram.

Learn more:

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Answer:

Well Plan D

Step-by-step explanation:

Answer:

plan D.

Step-by-step explanation:

2021 edge

Answer:

[tex]tan(-1) \approx -0.02[/tex]

Step-by-step explanation:

The given expression is

[tex]tan(-1)[/tex]

The tangent of -1 is defined, it's around -0.02.

The tangent is a trigonometric function with a period of [tex]\pi[/tex], where each period is separated by a vertical asymptote which indicates that the function is not determined through all its domain, that's what the question refers to when it says "if is undefined, enter undefined".

However, at [tex]x=-1[/tex], the tangent is determined, that means, there's no asymptote on that coordinate, that's why it has a "determined value", which is -0.02 approximately.

[tex]tan(-1) \approx -0.02[/tex]

Answer:

y = -(1/2)x+1

Step-by-step explanation:

-2Y - X = -2

Add x to both sides:

-2Y = X - 2

Divide both sides by -2:

Y = -(1/2)x+1

You could also use the shortcuts:

For Ay+Bx=C, the slope is -B/A and the y-intercept is C/A.

Slope = -B/A = -(-1)/(-2) = 1/-2 = -(1/2)

Y-intercept = C/A = (-2)/(-2) = 1

y = mx + b ---> y = -(1/2)x + 1

Answer:

y = -1/2x +1

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

-2y -x = -2

Solve for y

Add x to each side

-2y = x-2

Divide by -2

-2y/2- = x/-2 -2/-2

y = -1/2x +1

Answer:

area = 1800 m²

Step-by-step explanation:

area of one triangle = 900 m²

if a parallelogram has the same height and base as the triangle, then that means the area or the two triangle and shaped as a parallelogram

is twice the area given.

area = 900 * 2

area = 1800 m²

Answer:

AB = 20 tan55°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )

20 tan55° = AB

Answer:

(a) The mean weight of beer used to fill each bottle is 16 ounces.

(b) The answer of part (a) would not change.

Step-by-step explanation:

A local bottler, Fossil Cove, wants to ensure that an average of 16 ounces of beer is used to fill each bottle.

Ben takes a random sample of n = 48 bottles and finds the average weight to be [tex]\bar x=[/tex] 15.8 ounces. Also it is known that the standard deviation is, σ = 0.8 ounces.

(a)

The hypothesis can be defined as follows:

H₀: The mean weight of beer used to fill each bottle is 16 ounces, i.e. μ = 16.

Hₐ: The mean weight of beer used to fill each bottle is not 16 ounces, i.e. μ ≠ 16.

Assume that the significance level of the test is, α = 0.05.

As the population standard deviation is provided, we will use a z-test for single mean.

Compute the test statistic value as follows:

 [tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]

   [tex]=\frac{15.8-16}{0.80/\sqrt{48}}\\\\=-1.732[/tex]

The test statistic value is -1.732.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

[tex]p-value=2\cdot P(Z>-1.732)[/tex]

               [tex]=2\times [1-P(Z<1.732)]\\\\=2\times [1-0.04182]\\\\=0.08364\\\\\approx 0.084[/tex]  

*Use a z-table for the probability.

The p-value of the test is 0.084.

p-value = 0.084 > α = 0.05

The null hypothesis will not be rejected.

Thus, it can be concluded that the mean weight of beer used to fill each bottle is 16 ounces.

(b)

The standard deviation of a random variable is the square root of the variance.

[tex]SD=\sqrt{Variance}[/tex]

So, if the variance was 0.64, then the standard deviation will be:

[tex]SD=\sqrt{Variance}=\sqrt{0.64}=0.80[/tex]

Thus, the answer of part (a) would not change.

Step-by-step explanation:

x² + 11x + 121/4 = 125/4

x² + 11x + 121/4 - 125/4 = 0

x² + 11x - 1 = 0

after that apply quadratic formula

x = ( -b + or - √b² - 4ac ) ÷ 2a

x = (-11 + or - √11² - 4×1×-1 ) ÷ 2×1

+ = 0.090169....

- = -11.090168.....

x = 0.090 or x = -11.09

Answer:

The height of the box with the smaller base is 4  times that of the box with the larger base

Step-by-step explanation:

The volume of a box is the product of the base area and the height of the box, it is given as:

Volume = base area × height

For the smaller base box, it has a base of 5 cm by 5 cm, therefore the base area of the smaller base box = 5 cm × 5 cm  = 25 cm². Let the height of the smaller base box be [tex]h_1[/tex]The volume of the small box = [tex]25*h_1[/tex]

For the larger base box, it has a base of 10 cm by 10 cm, therefore the base area of the larger base box = 10 cm × 10 cm  = 100 cm². Let the height of the large base box be [tex]h_2[/tex]The volume of the larger base box = [tex]100*h_2[/tex]

Since both boxes have the same volume, therefore:

[tex]100*h_2[/tex] = [tex]25*h_1[/tex]

[tex]\frac{h_1}{h_2} =\frac{100}{25} \\\\\frac{h_1}{h_2}=4\\\\h_1=4h_2[/tex]

The height of the box with the smaller base is 4  times that of the box with the larger base

We can use the formula V=lwh to compare the volume in the two boxes.

First let's compare the volume of both boxes to see if they have the same height. To make it simple, let's use a height of 1 centimeter.

First the box with the smaller base.

V=lwh

V=5⋅5⋅1

V=25

Now the box with the larger base

V=lwh

V=10x10x1

V=100

We can set up an equation to find out how many times as tall the smaller box needs to be to have the same volume as the box with the larger base.

25·h=100

h=4

The boz with the smaller base is 4 times tall

hope it helped :)

​

​

Answer: 6

Step-by-step explanation:

Lets re- write the numbers in growing order.

2,3,4,6,7,10,10

The number that stays exactly in the middle of the the sequence is the median.

Number 6 stays in the middle. So 6 is the median

Answer

Step by step explanation

Given data : 4 , 3 , 2 , 10 , 10 , 6 , 7

Arranging the data in ascending order, we have,

2 , 3 , 4 , 6 , 7 , 10 , 10

Here, n ( total number of items) = 7

Now, position of median:

[tex] {( \frac{n + 1}{2}) }^{th} [/tex] item

plug the value

[tex] = {( \frac{7 + 1}{2} )}^{th} [/tex] item

Add the numbers

[tex] =( { \frac{8}{2} )}^{th} [/tex] item

Divide

[tex] = {4}^{th} [/tex] item

i.e 4th item is the median

Median = 6

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

Further more explanation:

Let's take another example:

please see the attached picture.

In the above series, the numbers are arranged in ascending order. Here, the fourth item 17 has three items before it and three items after it. So, 17 is the middle item in the series. 17 is called the median of the series.

Thus, Median is the value of the middle - most observation, when the data are arranged in ascending or descending order of magnitude.

Hope I helped..

Best regards!!

Answer:

bar graphs

Step-by-step explanation:

as in a bar graph, we don't do any calculations to graph on a paper,

so the data values, are taken RAW while graphing.

Answer:

He stitched 1 shirt in 6 hours.

He can stitch 1/6 of a shirt in one hour

Step-by-step explanation:

Given Mike can stitch 7 shirts in 42 hours

No. of shirt stitch in one hour = total no of shirt stitch/total time taken

No. of shirt stitch in one hour = 7/42 = 1/6

Thus, he can stitch 1/6 of a shirt in one hour

Time taken to stitch 1 shirt = total time taken by him to stitch 7 shirts/ total no. of shirt stitch(i.e 7)  = 42/6 = 6 hours.

Thus, he stitched 1 shirt in 6 hours.

Answer:

He can stitch 1/6 of a shirt in one hour

Step-by-step explanation:

Because he stitched  7 shirts in 42 hours

42/7 = 6

so 6 hours per shirt

In one hour:

1/6

Answer:

(a)The x-intercepts are 3, -4 and 1.

(b)f(x)=-0.5

Step-by-step explanation:

Given the function:

[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}[/tex]

x-Intercepts

When y=f(x)=0

[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}=0\\(x - 3)(x + 4)(x - 1)=0\\x - 3=0$ or $ x + 4=0 $ or $ x - 1=0\\x=3$ or $ -4$ or $ 1[/tex]

The x-intercepts are 3, -4 and 1.

y-intercepts

When x=0

[tex]f(x) = \dfrac{(x - 3)(x + 4)(x - 1)}{(x + 2)(x - 12)}\\f(x) = \dfrac{(0 - 3)(0 + 4)(0 - 1)}{(0 + 2)(0 - 12)}\\= \dfrac{(- 3)( 4)( - 1)}{( 2)( - 12)}\\= \dfrac{12}{-24}\\\\=-0.5[/tex]

The y-intercept is -0.5

Answer:

 -7x⁴+5x³-10x²-4x-7 - 4/4x+7

Step-by-step explanation:

Given the division problem, (28x⁵ + 29x⁴ + 5x³ + 86x² + 56x + 53) by (–4x – 7), find the solution in the attachment below.

The polynomial of a function is expressed as P(x) = Q(x) + R(x)/D(x)

Q(x) is the quotient

R(x) is the remainder

D(x) is the divisor

Accordin gto the divsion, Q(x) = -7x⁴+5x³-10x²-4x-7

R(x) = 4

D(x) = -4x-7

Substituting this functions in the polynomial P(x);

P(x) =  -7x⁴+5x³-10x²-4x-7 - 4/4x+7

Answer:

The  class width is  [tex]C_w \approx 13[/tex]

Step-by-step explanation:

From the question we are told that

 The  upper class limits is [tex]max = 121[/tex]

  The  lower class limits is  [tex]min = 14[/tex]

   The number of classes is  [tex]n = 8 \ classes[/tex]

The class width is mathematically represented as  

       [tex]C_w = \frac{max - min}{n }[/tex]

substituting values

       [tex]C_w = \frac{121 - 14}{8 }[/tex]

       [tex]C_w = 13.38[/tex]

      [tex]C_w \approx 13[/tex]

Since

Answer:

8.1% decrease

Step by step

To find precentage decrease we use formula:

Percent decrease= original amount-new amount/original amount(100%)

percent decrease= 7,400-6,800/7,400(100%)=300/37=8.1%

Step-by-step explanation:

Hello there!!

no need to be panic we will help you, alright.

look solution in picture ok...

sorry for cutting in middle.

Hope it helps...

Answer: THe slope is 2

SO answer d

Step-by-step explanation:

-4X + 2Y = 16 add 4x to the other side so equation is

2y=16+4x divided by 2

y=8+2x

Answer:

B. [tex]\frac{6}{2x^{2} - 5x}[/tex]

Step-by-step explanation:

The product of the ratioal expressions given above can be found as follows:

[tex] = \frac{2}{x} * \frac{3}{2x - 5} [/tex]

Multiply the denominators together, and the numerators together, separately to get a single expression

[tex] \frac{2(3)}{x(2x - 5)} [/tex]

[tex] = \frac{6}{x(2x) - x(5)} [/tex]

[tex]= \frac{6}{2x^{2} - 5x}[/tex]

The product of the expression [tex]\ = \frac{2}{x}*\frac{3}{2x - 5}[/tex] = [tex]\frac{6}{2x^{2} - 5x}[/tex]

The answer is B.

Answer:

14.05

Step-by-step explanation:

We have the following:

Current Dividend = D0 = $ 1.40

g = growth rate = 2%

r = discount rate = 13%

Dividend in Year 5

= D5 = D0 * (1 + g) ^ 5

= $ 1.40 * (1 + 2%) ^ 5

= $ 1.40 * (1.02) ^ 5

Firm Stock Price at the end of year 4 = Dividend in Year 5 / (r - g)

= $ 1.40 * (1.02) ^ 5 / (13% -2%)

= $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02)

Therefore, firm stock at the end of year 4 is

P4 = $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02) = 14.05