Find the area of the triangle. Round the answer to the nearest tenth. A. 4.4 square units B. 5.2 square units C. 6.8 square units D. 8.8 square units

Answer:

Step-by-step explanation:

f(x)=3x+15

let  f(x)=y

y=3x+15

flip x and y

x=3y+15

3y=x-15

y=1/3 x-5

or f^{-1}x=1/3 x-5

Answer:

[tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].

Step-by-step explanation:

It is given that a and 46° are complementary angles.

[tex]a+46^{\circ}=90^{\circ}[/tex]

[tex]a=90^{\circ}-46^{\circ}[/tex]

[tex]a=44^{\circ}[/tex]

It is given that a and b are supplementary angles.

[tex]a+b=180^{\circ}[/tex]

[tex]44^{\circ}+b=180^{\circ}[/tex]

[tex]b=180^{\circ}-44^{\circ}[/tex]

[tex]b=136^{\circ}[/tex]

Angle conjugate to c is 283°.

[tex]c+283^{\circ}=360^{\circ}[/tex]

[tex]c=360^{\circ}-283^{\circ}[/tex]

[tex]c=77^{\circ}[/tex]

Sum of all angles at a point is 360 degrees.

[tex]a+b+c+d+46^{\circ}=360^{\circ}[/tex]

[tex]44^{\circ}+136^{\circ}+77^{\circ}+d+46^{\circ}=360^{\circ}[/tex]

[tex]d+303^{\circ}=360^{\circ}[/tex]

[tex]d=360^{\circ}-303^{\circ}[/tex]

[tex]d=57^{\circ}[/tex]

Therefore, [tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].

Answer:

dy/dx = 3/√1-(3x+1)²

Step-by-step exxplanation:

Given the inverse function y = sin^-1(3x+1), to find the derivative of the expression, we will use the chain rule as shown;

Let u = 3x+1 ...1

y = sin⁻¹u ...2

From equation 1, du/dx = 3

from equation 2;

Taking the sin of both sides;

siny = sin(sin⁻¹u)

siny = u

u = siny

du/dy = cosy

dy/du = 1/cosy

from trig identity, cos y = √1-sin²y

dy/du = 1/√1-sin²y

Ssince u = siny

dy/du = 1/√1-u²

According to chain rule, dy/dx = dy/dy*du/dx

dy/dx = 1/√1-u² * 3

dy/dx = 3/√1-u²

Substituting u = 3x+1 into the final equation, we will have;

dy/dx = 3/√1-(3x+1)²

Answer:

-2.05

Step-by-step explanation:

From the given information,

Let consider [tex]\mu[/tex] to represent the population mean

Therefore,

The null and alternative hypothesis can be stated as :

[tex]H_o :\mu=9[/tex]

[tex]H_1 :\mu<9[/tex]

From the hypothesis , the alternative hypothesis is one tailed (left)

when the level of significance = 0.020, the Z- critical value can be determined from the standard normal distribution table

Hence, the Z-critical value at ∝ = 0.020 is -2.05

The answer is (180,80)

To solve this problem, we have to plot the graph, using a tool. This question relates to an inequality and graphical method is a reliable approach to solve inequality problem.

The given question is an inequality situation where we are asked to use graph to solve.

The data given are

The inequality for this problem is given is as

[tex]12x + 8y > 2500\\x + y < 280[/tex]

Kindly find the attached image as the graph and solution to this problem.

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Answer:

The  probability is   [tex]P(A') = 0.485[/tex]

Step-by-step explanation:

Let assume that the number of computer produced by factory C is  k = 1  

 So  From the  question we are told that

       The number produced by  factory A is  4k =  4

        The  number produced by factory B is  7k  = 7

        The  probability of defective computers from A is  [tex]P(A) = 0.04[/tex]

        The  probability of defective computers from B is  [tex]P(B) = 0.02[/tex]

        The  probability of defective computers from C is [tex]P(C) = 0.03[/tex]

Now the probability of factory A producing a defective computer out of the 4 computers produced is  

       [tex]P(a) = 4 * P(A)[/tex]

substituting values

        [tex]P(a) = 4 * 0.04[/tex]

        [tex]P(a) = 0.16[/tex]

The probability of factory B producing a defective computer out of the 7 computers produced is  

       [tex]P(b) = 7 * P(B)[/tex]

substituting values

        [tex]P(b) = 7 * 0.02[/tex]

        [tex]P(b) = 0.14[/tex]

The probability of factory C producing a defective computer out of the 1 computer produced is  

       [tex]P(c) = 1 * P(C)[/tex]

substituting values

        [tex]P(c) = 1 * 0.03[/tex]

        [tex]P(b) = 0.03[/tex]

So the probability that the a computer produced from the three factory will be defective is  

     [tex]P(t) = P(a) + P(b) + P(c)[/tex]

substituting values

     [tex]P(t) = 0.16 + 0.14 + 0.03[/tex]

     [tex]P(t) = 0.33[/tex]

Now the probability that the defective computer is produced from factory A is

      [tex]P(A') = \frac{P(a)}{P(t)}[/tex]

       [tex]P(A') = \frac{ 0.16}{0.33}[/tex]

        [tex]P(A') = 0.485[/tex]

Answer:

$7

Step-by-step explanation:

Simple interest formula:

I = Prt

6 months = 6 * 30 days = 180 days

1 year = 360 days

t = (180 days)/(360 days) = 0.5

I = $7000 * 0.002 * 0.5

I = $7

Answer:

$7

Step-by-step explanation:

Recall that simple interest is given by

I = Prt,

Where :

I = interest (we are asked to find this)

P = principal amount = given as $7000

r = rate = given as 0.2% = 0.002

t = time in years = given as 6 months = 0.5 years

SImply substitute the known values into the equation above:

I = Prt

= (7000)(0.002)(0.5)

= $7

Range is [tex]y\in[-3,+\infty)[/tex].

Hope this helps.

Answer:

A. x <= 2

Step-by-step explanation:

The domain of a real function should be all real numbers. In

f(x) = sqrt(2-x)

we need 2-x to be non-negative, therefore

2-x >= 0

which implies

x <= 2

Answer:

[tex]\Huge \boxed{{x\leq 2}}[/tex]

Step-by-step explanation:

The function is given,

[tex]f(x)=\sqrt{2-x}[/tex]

The domain of a function are all possible values of x.

There are restrictions for the value of x.

2 - x cannot be equal to a negative number, because the square root of a negative number is undefined. 2 - x has to equal to 0 or be greater than 0.

[tex]2-x\geq 0[/tex]

[tex]-x\geq -2[/tex]

[tex]x\leq 2[/tex]

The domain of the function is x ≤ 2.

Answer:

a.  $75.60

b.  $1335.60

Step-by-step explanation:

A.  First convert the percentage to a decimal.

6% = 0.06

Multiply the cost of the computer by the decimal to find the tax paid.

$1260 × 0.06 = $75.60

B.  To find the total cost, add the cost of the computer with the tax.

$1260 + $75.60 = $1335.60

Answer:

x=5

Step-by-step explanation:

2 − x = −3

Subtract 2 from each side

2-2 − x = −3-2

-x = -5

Multiply by -1

x = 5

Answer:

Step-by-step explanation:

y=4x

Answer:

The answer is B. 40 inches.

Step-by-step explanation:

The question starts by telling you that line VW is equal to 40 in. If you look at the picture you can see it is divided into 2 equal parts of 20 in each. If you look at line CT, you can see that there are the same marks meaning that those segments are also 20 in. That means that line CT and line VW are equal and that line CT is equal to 40 in.

Answer:

(12.141, 14.059)

Step-by-step explanation:

Explanation is provided in the attached document.

Answer:

quadratic

Step-by-step explanation:

This graph has a parabola form wich is a propertie for qaudratic functions

Answer:

A

Step-by-step explanation:

Answer:

D. 4x − 6

Step-by-step explanation:

f(x) = 4x − 2

f(x−1) = 4(x−1) − 2

f(x−1) = 4x − 4 − 2

f(x−1) = 4x − 6

Answer:

Chain rule: [tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex], u-Substitution: [tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]

Step-by-step explanation:

Differentiation and integration are reciprocal to each other. The chain rule indicate that a composite function must be differentiated, describing an inductive approach, whereas u-substitution allows integration by simplifying the expression in a deductive manner. That is:

[tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex]

Let integrate both sides in terms of x:

[tex]f[u(x)] = \int {\frac{df}{du} \frac{du}{dx} } \, dx[/tex]

[tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]

This result indicates that f must be rewritten in terms of u and after that first derivative needs to be found before integration.

Answer: -4/3

Step-by-step explanation:

Formula to find a slope of two given points is

y(sub2) - y(sub1) / x(sub2) - x(sub1)

Plug the values in to get the answer.

-2 - 2 / -1 - (-4)

-4/3

Answer:

[tex]\large \boxed{\sf \text{The rate of the boat is } 53 \ km/h \text{, the rate of the current is }8\ km/h \ \ }[/tex]

Step-by-step explanation:

Hello, let's note v the rate of the boat and r the rate of the current. We can write the following

[tex]\dfrac{135}{v-r}=3=\dfrac{183}{v+r}[/tex]

It means that

[tex]135(v+r)=183(v-r)\\\\135 v + 135r=183v-183r\\\\\text{ *** We regroup the terms in v on the right and the ones in r to the left***}\\\\(135+183)r=(183-135)v\\\\318r=48v\\\\\text{ *** We divide by 48 both sides ***}\\\\\boxed{v = \dfrac{318}{48} \cdot r= \dfrac{159}{24} \cdot r}[/tex]

But we can as well use the second equation:

[tex]3(v+r)=183\\\\v+r=\dfrac{183}{3}=61\\\\\dfrac{159}{24}r+r=61\\\\\dfrac{159+24}{24}r=61\\\\\boxed{r = \dfrac{61*24}{183}=8}[/tex]

and then

[tex]\boxed{v=\dfrac{159*8}{24}=53}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Correct option: D

Step-by-step explanation:

In the figure we have a right triangle, that is, one of the angles is a 90° angle. Therefore, we can use the Pythagoras' theorem to find the relation between the sides of the triangle:

[tex]a^2 = b^2 + c^2[/tex]

Where b and c are cathetus of the triangle (sides adjacent to the 90° angle) and a is the hypotenuse (opposite side to the 90° angle).

So in our case, we have that x is the hypotenuse, and 40 and 42 are cathetus, so we have:

[tex]x^2 = 40^2 + 42^2[/tex]

[tex]x^2 = 1600 + 1764[/tex]

[tex]x^2 = 3364[/tex]

[tex]x = 58[/tex]

So the correct option is D.

Recall the Pythagorean identity,

[tex]1-\cos^2t=\sin^2t[/tex]

To get this expression in the fraction, multiply the numerator and denominator by [tex]1+\cos t[/tex]:

[tex]\dfrac{t\sin t}{1-\cos t}\cdot\dfrac{1+\cos t}{1+\cos t}=\dfrac{t\sin t(1+\cos t)}{\sin^2t}=\dfrac{t(1+\cos t)}{\sin t}[/tex]

Now,

[tex]\displaystyle\lim_{t\to0}\frac{t\sin t}{1-\cos t}=\lim_{t\to0}\frac t{\sin t}\cdot\lim_{t\to0}(1+\cos t)[/tex]

The first limit is well-known and equal to 1, leaving us with

[tex]\displaystyle\lim_{t\to0}(1+\cos t)=1+\cos0=\boxed{2}[/tex]

Answer:

[tex]d \approx 5.8[/tex]

Step-by-step explanation:

Just use the distance formula.

[tex]d=\sqrt{(x_2-x_{1})^2+(y_2-y_{1})^2}[/tex]

[tex]d=\sqrt{(3-0)^2+(5-0)^2}}[/tex]

[tex]d=\sqrt{(3)^2+(5)^2}}[/tex]

[tex]d=\sqrt{9+25}[/tex]

[tex]d=\sqrt{34[/tex]

[tex]d \approx 5.8[/tex]

Answer:

7 children

Step-by-step explanation:

Answer:

7 children is the correct answer

and you follow me if you can't I will unfollow you

Answer:

f(x)= -3x + 400

Step-by-step explanation:

[tex]\frac{x-x_{1} }{x_{2}-x_{1} } = \frac{y-y_{1} }{y_{2}-y_{1} }[/tex]

[tex]\frac{x-3}{13-3} =\frac{y-391}{361-391}[/tex]

-3 ( x-3 ) = (y - 391 )

-3x + 400

Answer:

he is correct

Step-by-step explanation:

Step-by-step explanation:

look at the picture and if you still need help let me know or if this doenst help then well im sorry lol

Step-by-step explanation:

brain list me please......

Answer:

Jacob:

Alive 69-70

alive 79-80

alive 62-63

alive 73-74

alive 78-Died 79

Carol:

alive 88-89

alive 67-68

alive 99-100

alive 73-74

alive 94- Died 95

Step-by-step explanation:

Answer:

3.27 hours

Step-by-step explanation:

Calculate the difference in speed and distance between the trains.

The relative speed:

101 - 90 = 11 mph

Difference in distance:

42 - 6 = 36 miles

[tex]time=\frac{distance}{speed}[/tex]

[tex]t=\frac{36}{11}[/tex]

[tex]t = 3.27[/tex]

Answer:

yeah she is correct

Step-by-step explanation:

Answer:

B. Circumference of a circle

Step-by-step explanation:

The circumference of a circle can be found using formula 2πr where r is the radius of circle.

A circle's or an ellipse's circumference is its perimeter. The circumference would be the length of the circle's arc, if the circle were opened up and straightened out to a line segment, in other words.

Here, we have,

Suppose the radius of a circle is 5cm

So, we can find the circumference by using formula 2πr

    Circumference = 2 × π × 5 = 10π cm.

Hence, The circumference of a circle can be found using formula 2πr where r is the radius of circle.

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complete question;

The circumference of a circle can be found using the formula c 2r

Answer:

r = 90/30

r = 3

T12 = 10 × 3¹¹

T12 = 1771470