Solving exponential functions

Answer:

[tex]\boxed{x = 4}[/tex]

Step-by-step explanation:

=> 5x-4+2(x-4) = 16

Expanding the brackets

=> 5x-4+2x-8 = 16

Combining like terms

=> 5x+2x-4-8 = 16

=> 7x - 12 = 16

Adding 12 to both sides

=> 7x = 16+12

=> 7x = 28

Dividing both sides by 7

=> x = 4

Answer:

x = 4

Step-by-step explanation:

5x - 4 + 2(x-4) = 16

Expand the equation by multiplying 2 to x and -4 separately:

5x - 4 + 2x - 8 = 16

Collect like terms:

5x + 2x - 4 - 8 = 16

7x -12 = 16

Add 12 to both sides:

7x = 16 + 12

7x = 28

Divide both sides by 7 :

x = 28/7

x = 4

Answer:

If the correlation coefficient is 1, then the slope must be 1 as well.

Step-by-step explanation:

Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.

Answer:

The point of interception of the graph and x axis are -2.366 and -0.634.

The only graph that satisfy this conditions is Graph A

Step-by-step explanation:

Given the equation;

[tex]y = 2x^2 + 6x + 3\\[/tex]

at y = 0

[tex]2x^2 + 6x + 3=0\\[/tex]

the roots of the quadratic equation (at y =0) can be calculated using the quadratic formula;

[tex]x = \frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]

Using the quadratic equation to solve for the roots;

[tex]x = \frac{-6\pm \sqrt{6^2 -4*2*3}}{2*2}\\x = \frac{-6\pm \sqrt{36 - 24}}{4}\\x = \frac{-6\pm \sqrt{12}}{4}\\so, we have \\x = -2.366\\or\\x = -0.634\\[/tex]

Therefore, the point of interception of the graph and x axis are -2.366 and -0.634.

The only graph that satisfy this conditions is Graph A

Answer:

L = 45°

Step-by-step explanation:

1. 82° + 53° = 135°

2. 180° - 135° = 45°

3. Angle L is 45°

I hope this helps.

Answer:

The  number expected to pass that test is  [tex]k = 14 \ employees[/tex]

Step-by-step explanation:

From the question we are told that

      The probability of  success is  p  =  0.91

       The sample size is  n  =  15  

 The number of employee that will pass the test is mathematically represented as

          [tex]k = n * p[/tex]

substituting values

        [tex]k = 15 * 0.91[/tex]

      [tex]k = 14 \ employees[/tex]

surface area of a equilateral by hand a 140.4 cm and 9cm

Answer:

Hope it helps <3

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▹ Answer

Use a graphing calculator. Attached is an image.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer: B

Step-by-step explanation:

Answer:B

Step-by-step explanation: I took the edge quiz and it was right.

Answer:

A = 59.63cm^2

Step-by-step explanation:

You have the following function for the surface area of the container:

[tex]A=\pi r^2+\frac{100}{r}[/tex]                (1)

where r is the radius of the cross sectional area of the container.

In order to find the minimum surface are you first calculate the derivative of A respect to r, to find the value of r that makes the surface area a minimum.

[tex]\frac{dA}{dr}=\frac{d}{dr}[\pi r^2+\frac{100}{r}]\\\\\frac{dA}{dr}=2\pi r-\frac{100}{r^2}[/tex]         (2)

Next, you equal the expression (2) to zero and solve for r:

[tex]2\pi r-\frac{100}{r^2}=0\\\\2\pi r=\frac{100}{r^2}\\\\r^3=\frac{50}{\pi}\\\\r=(\frac{50}{\pi})^{1/3}[/tex]

Finally, you replace the previous result in the equation (1):

[tex]A=\pi (\frac{50}{\pi})^{2/3}+\frac{100}{(\frac{50}{\pi})^{1/3}}}[/tex]

[tex]A=59.63[/tex]

The minimum total surface area is 59.63cm^2

the answer is 36.36 but the closest to it is 37

Given:

D=165 feet and the frequency of the motion is 1.6 revolutions per minute.

Solution:

The radius is half of the diameter.

The radius of the wheel is 82.5 feet.

[tex]T=\frac{1}{1.6} \text{ minutes}[/tex]

As we know: [tex]\omega=\frac{2\pi}{T}[/tex]

Substitute the value of T in the above formula.

[tex]\omega=\frac{2\pi}{\frac{1}{1.6}}\\\omega=3.2\pi[/tex]

If the center of the wheel is at the origin then for [tex]t=0[/tex] the rest position is [tex]-a[/tex].

This can be written as:

[tex]h(t)=-a\cos(\omega t)\\h(t)=-82.5cos(32.\pi t)[/tex]

The actual height of the rider from the ground is:

[tex]h(t)=\text{ Initial height from bottom}+\text{ radius}-82.5\cos(3.2\pi t)\\h(t)=15+82.5-82.5\cos(3.2\pi t)\\h(t)=97.5-82.5\cos(3.2\pi t)[/tex]

The required equation is [tex]h(t)=97.5-82.5\cos(3.2\pi t)[/tex].

Answer:

SAS

Step-by-step explanation:

SAS

two side 1 angle

if not that try SSA

Answer:

SAS

Step-by-step explanation:

We have two  sides are equal and the angle between the two sides are equal so we can use the side angle side

Answer:

8 servings

Step-by-step explanation:

Spice required for one serving, using the rice-to-spice ratio to calculate:

David can make servings according to amount of spice he has:

Answer: David will be able to make 8 servings

Answer: 8

Step-by-step explanation:

Step-by-step explanation:

RD=BL

RE=BU

ED=UL

Please mark brainliest!!!

Answer:

The concert starts at 7:45 pm and ended at 1:35 am which mean the concert going on 5 hours and 50 minutes.

Answer:

A.) Even.

Step-by-step explanation:

If a function is an even function, then

F(-x) = f(x)

Also, if a function is an odd function, then, f(-x) = -f(x)

You are given the below function

f(x) = 1 + 3x^2 − x^4

Let x = 2

Substitute 2 for x in the function

F(x) = 1 + 3(2)^2 - (2)^4

F(x) = 1 + 3(4) - 16

F(x) = 1 + 12 - 16

F(x) = -3

Also, Substitute -2 for x in the function

F(x) = 1 + 3(-2)^2 - (-2)^4

F(x) = 1 + 3(4) - 16

F(x) = 1 + 12 - 16

F(x) = -3

Since f(-x) = f(x), we can conclude that

F(x) = 1 + 3x^2 - x^4 is even

Answer:

  The y-intercept is the number of minutes for producing vegetable cans when no minutes are used for fruit cans

Step-by-step explanation:

The problem statement tells you y is the number of minutes for producing vegetable cans. The y-intercept is the y-value when x = 0.

The y-intercept is the number of minutes for producing vegetable cans when no minutes are used for fruit cans.

Answer:

The y-intercept, at the point (0, 6), designates the choice to compose vegetables for 6 minutes. In 6 minutes, making 64 cans of vegetables per minute, 384 cans for the order decree performed. The 0 for the x-value designs that no time spent producing cans of fruit.

Step-by-step explanation:

I got it right on edgenuity

Answer

B. 27

firist divide 9÷2=4.5

the formula

=1/2×4.5×6

=13.5

cause there are 2 triangles. let's multiply 13.5 with 2

13.5×2= 27²

Answer:

[tex] 11 quarts *\frac{946.353 ml}{1 quarter}= 10409.883 ml[/tex]

And for this case we can create the following proportion rule:

[tex]\frac{29 gr}{200 ml} =\frac{x}{10409.883 ml}[/tex]

And solving for x we got:

[tex] x= 10409.883 ml *\frac{29 gr}{200ml}= 1509.433 gr[/tex]

Step-by-step explanation:

For this problem we know that A hemoglobin test measures 29 grams of hgb per 200 milimiters of blood. and we want to know how many grams of Hgb are present in 11 quarts

First we need to convert the quarts to ml and we have:

[tex] 11 quarts *\frac{946.353 ml}{1 quarter}= 10409.883 ml[/tex]

And for this case we can create the following proportion rule:

[tex]\frac{29 gr}{200 ml} =\frac{x}{10409.883 ml}[/tex]

And solving for x we got:

[tex] x= 10409.883 ml *\frac{29 gr}{200ml}= 1509.433 gr[/tex]

Answer:

x=-7, y= -20

Step-by-step explanation:

2x - y =6

x - y = 13

when I subract (x-y =13 ) from (2x-y =6)

2x -y =6

-x +y=-13

______________

x = -7

substitute x=-7 in the second equation

-7 - y =13

-y = 13 +7

-Y = 20

Y=-20

x=-7, y= -20

Answer:

x= -7/6

y= -25/3

Step-by-step explanation:

2x-y =6

4 x-y =13

Firstly, 4x-y=13(-)  =>> - 4x+y=-13

Then we make the sum and result 6x= -7. Result x= -7/6.

We need to find y. So:  

-y= 6-2x =>>  y= -6 +2x =>> y= -6 +2*(-7/6) =>> y= -6-7/3 =>> y=(-18-7)/3 =>>y= -25/3

Answer:

[tex]0.51 - 1.96 \sqrt{\frac{0.51(1-0.51)}{557}}=0.468[/tex]

[tex]0.51 + 1.96 \sqrt{\frac{0.56(1-0.56)}{1507}}=0.552[/tex]

And the 95% confidence interval would be given (0.468;0.552).

Step-by-step explanation:

The estimated proportion of people who say that were underpaid is given by:

[tex]\hat p=\frac{284}{557}=0.510[/tex]

The confidence interval would be given by this formula

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.

[tex]z_{\alpha/2}=1.96[/tex]

And replacing into the confidence interval formula we got:

[tex]0.51 - 1.96 \sqrt{\frac{0.51(1-0.51)}{557}}=0.468[/tex]

[tex]0.51 + 1.96 \sqrt{\frac{0.56(1-0.56)}{1507}}=0.552[/tex]

And the 95% confidence interval would be given (0.468;0.552).

Answer:

Five-number summary in ascending order: [tex] 0.58, 0.89, 0.98, 1.26, 1.42 [/tex]

Step-by-step Explanation:

The number summary, in ascending order, includes the minimum value, maximum value, median value, upper quartile and lower quartile.

To find each of the above values, first, order the data set in ascending order. Our values given, when ordered, would be:

0.58, 0.59, 0.89, 0.96, 0.97,| 0.98|, 1.07, 1.14, 1.26, 1.28, 1.42

1.The minimum value (the least value or lower value in the given data set).

From the ordered data set, minimum value = 0.58

2. The maximum value is the highest value in the data set = 1.42

3. Median value is the middle value of the data set. The middle value is the 6th value = 0.98.

The median value divides the data set into lower and upper region, as shown below.

0.58, 0.59, 0.89, 0.96, 0.97,|0.98|, 1.07, 1.14, 1.26, 1.28, 1.42

4. Lower Quartile (Q2) is the middle value of the lower region = 0.89, as shown below,

0.58, 0.59, [0.89], 0.96, 0.97,|0.98|, 1.07, 1.14, 1.26, 1.28, 1.42

5. Upper Quartile (Q3) is the middle value of the upper region = 1.26, as shown below.

0.58, 0.59, 0.89, 0.96, 0.97,|0.98|, 1.07, 1.14, [1.26], 1.28, 1.42

: this is the middle value of lower region, after our median divides the data set into two.

0.58, 0.59, 0.89, 0.96, 0.97,|0.98|, 1.07, 1.14, 1.26, 1.28, 1.42

Therefore, the five-number summary in ascending order is as follows: [tex] 0.58, 0.89, 0.98, 1.26, 1.42 [/tex]

Min = 0.58

Q1 = 0.89

Median = 0.98

Q3 = 1.26

Max = 1.42

A box plot has been constructed using the five-number summary. Check the attachment below.

The min value is represented by the whisker that starts from your left and connects to the rectangular box.

The max value is indicated at the extreme end of the other whisker that you have from the end of the rectangular box to your far right.

The median value is indicated by the vertical line that divides the rectangular box into 2.

The lower quartile is indicated at the beginning of the rectangular box, while the upper quartile is located at the end of the rectangular box.

Answer:

length= 42

width = 7

Step-by-step explanation:

Answer:

Hey there!

The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.

The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.

The circumference of the circle is 50.24 yards.

Hope this helps :)

Answer:

[tex]A +B+C+D = 3[/tex] is the correct answer.

Step-by-step explanation:

Given:

[tex]$\frac{5}{2+\sqrt{6}}$[/tex]

To find:

[tex]A+B+C+D = ?[/tex] if given term is written as following:

[tex]$\frac{A\sqrt{B}+C}{D}$[/tex]

Solution:

We can see that the resulting expression does not contain anything under [tex]\sqrt[/tex] (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

[tex]\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}[/tex]

Comparing the above expression with:

[tex]$\frac{A\sqrt{B}+C}{D}$[/tex]

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, [tex]A +B+C+D = 5+6-10+2 = \bold3[/tex]

Answer:

woman is 37, girl is 7

Step-by-step explanation:

7(x-2) = y-2

4(x+3) = y+3

7x - 14 = y - 2

7x - 12 = y

4x + 9 = y

3x - 21 = 0

x = 7

y = 37

Answer:

16 km

Step-by-step explanation:

From Washington, as the question asks, will now be considered 0 aka the starting point.

So as of now, we know Washington from Oakdale is 6.2 km.

And from Stanford to Salem is 11.9 km, also Salem to Washington is 10.3 km. Hence the addition of 11.9 km and 10.3 km to figure out the whole distance between Stanford and Washington.

11.9 km + 10.3 km = 22.2 km

Now we subtract 22.2 km to 6.2 km for the product of 16 km.

Answer:

The graph at the bottom left in your group of possible answers.

Step-by-step explanation:

Notice that the original given graph corresponds to the equation:

[tex]y=2x+1[/tex]

since the line's slope is 2/1 = 2 and the y-intercept is at the point (0, 1).

So if one modifies the equation multiplying the current slope by 1/2, and the y intercept increased by 3 units, Then the new function would be:

[tex]y=x+4[/tex]

A line of slope 1 and y-intercept at (0, 4)

Notice that the graph at the bottom left in your possible answers is representing such function.

Answer:

Answer Y: or Bottom Left of Given Answers

Step-by-step explanation:

Answer:

It is the first graph

Step-by-step explanation:

Just got it right on the test review :)

Inequalities help us to compare two unequal expressions. The graph shows that all the values of x that satisfies the given inequality are x>7. Thus, the correct option is A.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequality can be solved as,

[tex]\dfrac29(x+3) > 4(\dfrac59)\\\\\dfrac{2x+6}{9} > \dfrac{20}{9}\\\\2x + 6 > 20\\\\2x > 20 - 6\\\\x > \dfrac{14}{2}\\\\x > 7[/tex]

Hence, the graph shows that all the values of x that satisfies the given inequality are x>7. Thus, the correct option is A.

Learn more about Inequality:

https://brainly.com/question/19491153

#SPJ2

Answer:

1. Y= 7t^5 +C

2. Y= 35/12x^(12/7)+C

Step-by-step explanation:

The general solution will be determined by integrating the equations as the integration is a simple integration.

For dy/dt = 35t^4

The general solution y

= integral (35t^4)dt

The general solution y

=( 35/(4+1))*t^(4+1)

= 35/5t^5

= 7t^5 +C

To prove by differentiating the above.

Y= 7t^5 +C

Dy/Dt= (5*7)t^(5-1) +0

Dy/Dt= 35t^4

For dy/dx = 5x^(5/7)

Y=integral 5x^(5/7)Dx

Y= 5/(5/7 +1)*x^(5/7+1)

Y= 5/(12/7) *x^(12/7)

Y= 35/12x^(12/7)+C

To prove by differentiating

Y= 35/12x^(12/7)+C

Dy/Dx= (35/12)*(12/7) x^(12/7-1) +0

Dy/Dx=(35/7)x^(5/7)

Dy/Dx= 5x^(5/7)