What is the value of x if 2 + 4x = 10?

[tex]\vec r(t)=14t^4\,\vec\imath+t^6\,\vec\jmath[/tex]

[tex]\mathrm d\vec r=(56t^3\,\vec\imath+6t^5\,\vec\jmath)\,\mathrm dt[/tex]

[tex]\vec f(x,y)=xy\,\vec\imath+6y^2\,\vec\jmath\implies\vec f(x(t),y(t))=14t^{10}\,\vec\imath+6t^{12}\,\vec\jmath[/tex]

Then the line integral is

[tex]\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^1(14t^{10}\,\vec\imath+6t^{12}\,\vec\jmath)\cdot(56t^3\,\vec\imath+6t^5\,\vec\jmath)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^1(36t^{17}+784t^{13})\,\mathrm dt=\boxed{58}[/tex]

The line integral c f dot dr for the given parameters can be calculated by substituting values of functions r(t) and f(x, y) into the line integral, then integrating over t from 0 to 1.

To solve this problem, we start by writing the vector valued function r(t) and the vector field f(x, y) in component form. Given that r(t) = 14t4i + t6j and f(x, y) = xyi + 6y2j, the line integral c f dot dr becomes a definite interval where we integrate over t from 0 to 1.

In this case, we're essentially finding the work done by the vector field f as a particle moves along the path described by r(t). To calculate this, we need to find dr/dt which in our case evaluates to 56t3i + 6t5j.

Subsequent substitution of x = 14t4 and y = t6 into f will provide a new vector ft for f dot dr. Now we can find f dot dr by multiplying corresponding components of ft and dr/dt, add them up, and then integrate over t from 0 to 1.

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[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{15}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{15-8}{9-5}\implies \cfrac{7}{4}[/tex]

Check the picture below.

If these two shapes are combined then the new shape is generated. Then the new shape will be given below.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A cube and a cylinder are given.

If these two shapes are combined then the new shape is generated. Then the new shape will be

The shape is given below.

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Answer:

Step-by-step explanation:

Of the 20 trials, 18 of them ended up between 60 and 75.  So most likely, 60% to 75% of the town rides a bike.

The true statement about the dot plot is (c) Most likely, 60% to 75% of the town rides a bike.

From the dot plot, we have the following sample between 60 and 75%

Sample = 3 + 4 + 6 + 5

Evaluate

Sample = 18

The above means that 18 out of the 20 trials fall between 60 and 75%

This means that between 60 and 75% of the town rides a bike

Hence, the true statement about the dot plot is (c)

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Answer:

Tan <A = 1/2

Step-by-step explanation:

SOH CAH TOA

TOA (opposite/adjacent)

So, the answer is 1/2

because the opposite of <A is 1 and the adjacent is 2.

For this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle. Then, according to the figure we have:

[tex]tg (A) = \frac {1} {2}[/tex]

Answer:

[tex]tg (A) = \frac {1} {2}[/tex]

You can't in theory. Only a few "nice" values are known, because they lead to particular triangles. For example, we have

You can add other angles using symmetries, for example, you can compute sin(60) using sin(90-x) = cos(x), or similar stuff.

You can also use the double/half angles identities to add another couple of angles in our list, but that's it.

Simplify brackets

7 + 1

Simplify

8

Answer: C. 8

Answer:

minus and minus is plus

7+ 1 is 8 :)

Answer:

[tex]AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm[/tex]

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

[tex]AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm[/tex]

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

[tex]\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD[/tex]

Consider right triangle CAH.By the Pythagorean theorem,

[tex]CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8[/tex]

The length cannot be negative, so CD=8 cm and

[tex]CA=\sqrt{3}CD=8\sqrt{3}\ cm[/tex]

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

[tex]AB=2CA=16\sqrt{3}\ cm[/tex]

By the Pythagorean theorem,

[tex]BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm[/tex]

Answer:

Use the hyper link

Step-by-step explanation:

I took a picture on the unit.

Answer:

A.The longer leg is √3 times as long as the shorter

B. The hypotenuse is twice as long as the shorter leg

Step-by-step explanation:

The 30-60-90 is a special triangle with two acute angles 30° and 60°

The side across from the 30°= shorter leg

The side across from 60°=longer leg

The side across from 90°=hypotenuse

If we take the shorter side to be x and hypotenuse to be 2x then the  longer leg will be;

Apply Pythagorean relationship

a² + b² =c²

c²-a²=b² where-----------c=2x and a=x

(2x)² - x² = b²

4x² - x² =b²

3x² = b²

√3x²=b

x√3 =b

Hence longer leg is √3 times longer than the shorter leg which is x and the hypothenuse 2x is twice the shorter leg which is x

[tex]

y-15=3x \\

-2x+5y=-3 \\ \\

-2x+y-15=0 /\cdot2 \\

-2x+5y-3=0 /\cdot(-2) \\ \\

-4x+2y-30=0 \\

4x-10y+6=0 \\ \\

-8y-24=0 \\

\boxed{y=-3} \\ \\

-3-15=3x \\

\boxed{x=-6}

[/tex]

The answer is C. (-6, -3)

Hope this helps.

r3t40

For this case we have the following system of equations:

[tex]y-15 = 3x\\-2x + 5y = -3[/tex]

We multiply the first equation by -5:

[tex]-5y + 75 = -15x[/tex]

Now we add the equations:

[tex]-2x-5y + 5y + 75 = -3-15x\\-2x + 75 = -3-15x\\-2x + 15x = -75-3\\13x = -78\\x = \frac {-78} {13}\\x = -6[/tex]

We find the value of the variable "y" according to the first equation:

[tex]y = 3x + 15\\y = 3 (-6) +15\\y = -18 + 15\\y = -3[/tex]

The solution of the system is: (-6, -3)

Answer:

(-6, -3)

Option C

Answer:

The answer is the second choice.

Step-by-step explanation:

The value of the domain which is not part of the function is x = -2.

Given data:

The domain of a function is the set of values that are allowed to plug into the function which are the inputs.

The domain of the three line segments is represented as:

Domain of line 1 ranges from [ -5 , -2 ).

Domain of line 2 ranges from ( -2 , 2 ).

Domain of line 3 ranges from [ 2 , 5 ].

So, the value -2 is not included in the domain values of the function.

Hence, x = -2 is not in the domain of function.

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[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-6}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-6-(-7)}{-8-(-5)}\implies \cfrac{-6+7}{-8+5}\implies \cfrac{1}{-3}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-7)=-\cfrac{1}{3}[x-(-5)]\implies y+7=-\cfrac{1}{3}(x+5)[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-(-6)=-\cfrac{1}{3}[x-(-8)]\implies y+6=-\cfrac{1}{3}(x+8)[/tex]

if you add 3 to it it would be 6

First number = 23+x

Second number = 2(23+x)-18 = 46 +2x -18 = 2x +28

Now multiply each term by each term :

23 +x * 2x +28

23 * 2x + 23 * 28 + x *2x + x*28=

46x + 644 + 2x^2 + 28x =

Final answer = 2x^2 +74x +644

The answer is D.

Answer:

The product of two numbers is  [tex]P(x)=2x^2+74x+644[/tex]

Step-by-step explanation:

We are given that The first number is the sum of 23 and x,

First number = 23+x

The second number is 18 less than two times the first number.

Second Number = [tex]2(23+x)-18[/tex]

The product of two numbers :  [tex](23+x)(2(23+x)-18)[/tex]

                                                    [tex](23+x)(46+2x-18)[/tex]

                                                    [tex](23+x)(28+2x)[/tex]

                                                    [tex]2x^2+74x+644[/tex]

Let P(x) denotes the product

So, The product of two numbers is  [tex]P(x)=2x^2+74x+644[/tex]

Hence Option D is true .

The product of two numbers is  [tex]P(x)=2x^2+74x+644[/tex]

Answer:

  9.4 days

Step-by-step explanation:

Filling in the given numbers, we can solve for t:

  0.18 = 1·(1/2)^(t/3.8)

  log(0.18) = (t/3.8)log(1/2)

  t = 3.8·log(0.18)/log(0.50) ≈ 9.4 . . . . days

The best estimate of the age of the sample is 9.4 days.

Answer:

9.4 days

Step-by-step explanation:

2x+x = 2x^2

X(2+1) = 2x^2

2x^2 stays the same

Therefore the answer is d 3x is not the same as the rest

Answer:

2x^2

Step-by-step explanation:

2x+x=3x

x(2+1)=2x+x=3x

3x

Answer:

(-.5, 0)

Step-by-step explanation:

y ---- 2÷2=1, y-1= 1-1=0

x ---- 3÷2 =1.5, x-1.5= 1-1.5= -.5

Answer:

( -0.5, 0 )

Step-by-step explanation:

Add the 0 before 5, it matters if its right or wrong. The Answer is ( -0.5 , 0 ). ADD THE 0 !!!!!

The graph of inequality have many solution .

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.

According to the question

The system of inequalities:

y ≥ 2x – 4

x + 2y ≤ 7

y ≥ -2

x ≤ 1  

values to the graph of inequalities we will have to make inequalities into equal sign

y ≥ 2x – 4

y = 2x – 4

x                    y

0                  -4

1                   -2

2                  0

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≥ or > is used, shade above the line.

x + 2y ≤ 7

x + 2y = 7

x                    y

0                  3.5

1                   3

2                  2.5

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≤  or < is used, shade below the line.

y ≥ -2

y = -2

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≥ or > is used, shade above the line.

x ≤ 1

x = 1

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≤  or < is used, shade below the line.

Therefore, the darker part in graph  is  common part of all 4 inequalities with point (1,-2) and (1,3) .

Hence, The graph of inequality have many solution .

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Answer:

x=4

Step-by-step explanation:

16-4=12

3x=12

3*4=12

Answer: [tex]x=4[/tex]

Step-by-step explanation:

You need to find the value of the variable "x".

To solve for "x", the first step is to apply the Subtraction property of equality, which states that:

[tex]If\ a=b\ then\ a-c=b-c[/tex]

Then, you need to subtract 4 from both sides of the equation:

[tex]3x + 4 = 16\\3x + 4-4 = 16-4\\3x=12[/tex]

And finally, you can apply the Division property of equality, which states that:

[tex]If\ a=b\ then\ \frac{a}{c}=\frac{b}{c}[/tex]

Then you can divide both sides of the equation by 3, getting:

[tex]\frac{3x}{3}=\frac{12}{3}\\\\x=4[/tex]

The answer is:

The maximum height before landing will be 69.7804 feet.

Since there is no information about the angle of the launch, we can safely assume that it's launched vertically.

So, we can calculate the maximum height of the pumpkin using the following formulas:

[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]

[tex]v=vo-gt[/tex]

Where,

y, is the final height

[tex]y_o[/tex], is the initial height

g, is the acceleration of gravity , and it's equal to:

[tex]g=32.2\frac{ft}{s^{2} }[/tex]

t, is the time.

Now, we are given the following information:

[tex]y_{o}=12ft\\\\v=61\frac{ft}{s}[/tex]

Then, to calculate the maximum height, we must remember that at the maximum height, the speed tends to 0, so, calculating we have:

Time calculation,

We need to use the following equation,

[tex]v=vo-gt[/tex]

So, substituting we have:

[tex]v=61\frac{ft}{s}-32.2\frac{ft}{s^{2}}*t\\\\-61\frac{ft}{s}=-32.2\frac{ft}{s^{2}}*t\\\\t=\frac{-61{ft}{s}}{-32.2\frac{ft}{s^{2}}}=1.8944s[/tex]

We know that it will take 1.8944 seconds to the pumpkin to reach its maximum height.

Maximum height calculation,

Now, calculating the maximum height, we need to use the following equation:

[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]

Substituting and calculating, we have:

[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]

[tex]y=12ft+61\frac{ft}{s}*1.8944s-\frac{1}{2}32.2\frac{ft}{s^{2}}*(1.8944s)^{2}[/tex]

[tex]y=12ft+61\frac{ft}{s}*1.8944s-\frac{1}{2}32.2\frac{ft}{s^{2}}*(1.8944s)^{2}\\\\y_{max}=12ft+115.5584ft-16.1\frac{ft}{s^{2}}*(3.5887s^{2})\\\\y_{max}=127.5584ft-57.7780ft=69.7804ft[/tex]

Hence, we have that the maximum height before the landing will be 69.7804 feet.

Have a nice day!

The answer will be D. 7/10 because you have 10 numbers and you want to have a number greater than 3 so it would be 10-3=7 and 7 would go over 10 because there are 7 numbers greater than 3 but less than 10.

The probability he chooses a number greater than 3 is 7/10, the correct option is D.

Probability is the likeliness of an event to happen.

Jalen randomly chooses a number 1-10

Probability = ( No. of favourable outcomes)/ Total Outcomes

The chances of getting the number more than 3 is 7

Total numbers are 10

The probability he chooses a number greater than 3 is 7/10.

Therefore, the correct option is D.

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Answer:

4 and -4

Step-by-step explanation:

> means greater than

x² > 10

4² > 10 → True, 16 is greater than 10

-4² > 10 → True, 16 is greater than 10

Im pretty sure this is the answer F (x) = e^2x + 1

Answer:

Step-by-step explanation:

The sample is not biased.  The members were selected at random from the gym's female population.

The question is biased.  It described the weight lifting machines as "easy" and the free weights as "harder".

The second and third choices are correct.

Answer:

Part 1: Answer C) There is not enough evidence to reject H0

Part 2: Answer C) There is not enough evidence to accept or reject his claim.

Step-by-step explanation:

Just did it on edge

The z-statistic of 1.41 means the sample mean is 1.41 standard deviations to the right of the population mean, if we assume the null hypothesis is true. The corresponding p-value is approximately 0.1587, which is greater than the commonly used threshold (0.05), leading us to not reject the null hypothesis.

The z-statistic of 1.41 in the sample of Delmar's practice times can be used to draw conclusions about the sample's relationship to the population in a hypothesis test. It represents how many standard deviations an element (or group of elements, like a sample mean) falls from the mean or average of a population. A z-statistic of 1.41 means that the sample mean falls 1.41 standard deviations to the right of the population mean, assuming the null hypothesis to be true.

This information is useful in determining the p-value, which is the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true. If the p-value is smaller than the predetermined significance level (let's assume α=0.05), we would reject the null hypothesis. The p-value corresponding to z=1.41 in a two-tailed test is approximately 0.1587. Since this p-value is greater than 0.05, we would not reject the null hypothesis and state that we do not have enough evidence to suggest that Delmar's practice times are significantly different from the population.

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Zoe will need 84 pieces if they are 6” by 6”

For this case we have that by definition, 1 foot equals 12 inches.

So:

[tex]3 \ ft = 36 \ in\\7 \ ft = 84 \ in[/tex]

So, the area of the Zoes carpet is:

[tex]A = 36 * 84 = 3024 \ in ^ 2[/tex]

If the cardboard pieces are[tex]6 \ in\ by\ 6 \ in[/tex], then the area is:

[tex]36 \ in ^ 2[/tex]

To indicate the number of necessary pieces we divide:

[tex]\frac {3024} {36} = 84[/tex]

Thus, 84 pieces of cardboard are needed

Answer:

84

Answer:

f(x) < –x2 + x – 1

Step-by-step explanation:

The graph is going down so we know that there is a maximum, therefore the A value has to be negative. This rules out f(x) < x2 + x – 1 and f(x) > x2 + x – 1 . The shaded area of the graph is below which indicates that f(x) has to be less than the function. This means the correct answer is f(x) < –x2 + x – 1 .

Answer:

[tex]y>-x^2 +x-1[/tex]

Step-by-step explanation:

Lets find the inequality that best describes the given statement

The graph of the parabola is upside down so the value of 'a' is -1

It means the equation for the parabola becomes [tex]y=-x^2 +x-1[/tex]

Now to get inequality , lets pick a point from the shaded part .

Lets pick (0,0), plug in 0 for x and 0 for y

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

[tex]0=-(0)^2 +(0)-1[/tex]

[tex]0=-1[/tex]

0 is greater than -1

[tex]y>-x^2 +x-1[/tex]

Answer:

Your answer should be 4 pounds 6 ounces.

Step-by-step explanation:

If you subtract how much the potato sack was before she made the potato salad from how much it was after, this gives you how much the potato she used weighed.

Answer:

Step-by-step explanation:

sum of angle of triangle is 180 degree

5x+8x+50degree =180 degree

13x= 180-50

13x= 130

x= 130/13

x=10

5x= 5*10=50degree

8x= 8*10 =80degree

The value of other two angles of triangle are 50 and 80 degrees.

Let us consider that other two angles of triangle are 5x and 8x.

Given that, one angle of triangle is 50 degree.

By property of triangle, sum of all three angles is equal to 180 degrees.

                [tex]5x+8x+50=180\\\\13x=130\\\\x=130/13=10[/tex]

Other two angles of triangle are,

             [tex]5x=5*10=50\\\\8x=8*10=80[/tex]

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ANSWER

[tex] \lim_{x \to \: a}(x) = a[/tex]

[tex]\lim_{x \to \: a}(a) = a[/tex]

[tex]\lim_{x \to \: 5}(x) = 5[/tex]

EXPLANATION

For real number 'a',

[tex] \lim_{x \to \: a}(x) = a[/tex]

is true because we have to plug in 'a' for x.

[tex]\lim_{x \to \: a}(a) = a[/tex]

This is also true because limit of a constant is the constant.

[tex]\lim_{x \to \: 5}(4) = 5[/tex]

is false. The correct value is

[tex]\lim_{x \to \: 5}(4) =4[/tex]

[tex]\lim_{x \to \: 5}(x) = 5[/tex]

is also true because we have to substitute 5 for x.

[tex]\lim_{x \to \: a}(a) = x[/tex]

is also false

The limit should be

[tex]\lim_{x \to \: a}(a) = a[/tex]

Answer:

A, B, D

Step-by-step explanation:

Answers for the rest of the quick check

1. A,B,D

2. 16, D

3. 10a, B

4. 3, D

Good Luck :)