Y=2/3x-4 and y=-3/2x+1 are perpendicular lines. Jack notices that the product of the two perpendicular slopes is -1. If a line has a slope of a/b, determine the perpendicular slope, and then show that the product is-1.

Final answer:

The surface area of the rectangular prism is 376 square inches.

Explanation:

To find the surface area of an object, we need to calculate the sum of the areas of all its faces. Given the dimensions 10 in., 6 in., 8 in., and 7 in., we can assume that these are the lengths of the sides of a rectangular prism. The formula to find the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism, respectively.

Using the given values, we can substitute 10 in. for l, 6 in. for w, and 8 in. for h to find the surface area:

Surface Area = 2(10 in.)(6 in.) + 2(10 in.)(8 in.) + 2(6 in.)(8 in.)

Surface Area = 120 in² + 160 in² + 96 in²

Surface Area = 376 in²

Answer:

C.E=18 cm

Step-by-step explanation:

we know that

If the circle O is inscribed in triangle ABC

then

A.F=A.D=6 cm

B.D=B.E=14 cm

C.F=C.E=?

The perimeter of triangle is equal to

P=2(6)+2(14)+2(C.E)

P=76 cm

so

76=2(6)+2(14)+2(C.E) -----> solve for C.E

76=12+28+2C.E

2C.E=76-40

C.E=36/2

C.E=18 cm

Answer:

[tex]\large\boxed{Surface\ Area=63\ cm^2}[/tex]

Step-by-step explanation:

We have

square  with sides s = 3cm

four triangles with base b = 3cm and height h = 9cm.

The formula of an area of a square:

[tex]A_\square=s^2[/tex]

The formula of an area of a triangle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_\square=3^2=9\ cm^2\\\\A_\triangle=\dfrac{(3)(9)}{2}=\dfrac{27}{2}=13.5\ cm^2[/tex]

The Surface Area:

[tex]S.A.=A_\square+4A_\triangle\\\\S.A.=9+4(13.5)=9+54=63\ cm^2[/tex]

Answer:

Step-by-step explanation:

x= cost of 1 adult ticket

y=cost of 1 kid ticket

so 1 adult+4 childeren=x+4y=19

2 adults and 2 childern=2x+2y=17

elimination

x+4y=19

2x+2y=17

multiply firest equation by -2

-2x-8y=-38

add to first equatuion

-2x-8y=-38

2x+2y=17 +

0x-6y=21

-6y=-21

multiply -2

6y=21

divide by 6

y=21/6=7/2

subsitute

2x+2y=17

2x+2(7/2)=17

2x+14/2=17

2x+7=17

subtract 7 from both sides

2x=10

divide by 2

x=5

1 adult ticket costs £5

1 kid ticket costs £7/2 or £3 and 1/2 or £3.5

hope this helps and give me brainliest pls

Using the law of sines:

Sin (angle) = opposite leg / hypotenuse

Sin(30) = 14 /x

x = 14 * sin(30)

x = 28

Answer:

the answer is 28

Step-by-step explanation:

Answer:

Step-by-step explanation:

Radius is half diameter so you have to multiply the radius by 2 to find diameter.

3 1/2 * 2 = 7

Answer:

7π

Step-by-step explanation:

The circumference (C) of a circle is

C = 2πr = 2π × [tex]\frac{7}{2}[/tex] = [tex]\frac{14\pi }{2}[/tex] = 7π

Answer:

Option D

Step-by-step explanation:

step 1

Find the equation of the inequality A (quadratic equation)

The quadratic equation is

[tex]y=x^{2}-3x[/tex]

we know that

The solution of the inequality A is the shaded area above the solid line of the quadratic equation

so

The inequality is equal to

[tex]y\geq x^{2}-3x[/tex]

step 2

Find the equation of the inequality B (linear equation)

The linear equation is

[tex]y=-x+3[/tex]

we know that

The solution of the inequality B is the shaded area below the solid line of the linear equation

so

The inequality is equal to

[tex]y\leq -x+3[/tex]

Answer: it’s c

Step-by-step explanation:

Answer:

[tex]x\in (-2,0)\cup (2,\infty)[/tex]

Step-by-step explanation:

Find the derivative of the function [tex]y=x^4 -8x^2 +16:[/tex]

[tex]y'=4x^3 -8\cdot 2x\\ \\y'=4x^3 -16x[/tex]

The function is increasing when [tex]y'>0,[/tex] so solve the inequality

[tex]4x^3-16x>0\\ \\4x(x^2-4)>0\\ \\4x(x-2)(x+2)>0\\ \\x\in (-2,0)\cup (2,\infty)[/tex]

You can see from the graph that the function increases for [tex]x\in (-2,0)\cup (2,\infty)[/tex]

Final answer:

To determine the intervals where the function y = x⁴ - 8x² + 16 is increasing, calculate the first derivative, find its critical points, and analyze the sign changes. The function is increasing on the intervals (-∞, -2), (0, 2), and (2, ∞).

Explanation:

Intervals Where the Function is Increasing

To determine on which intervals the function y = x⁴ - 8x² + 16 is increasing, we need to analyze the function's first derivative. The first derivative, y', indicates the slope of the tangent to the function at any point. When y' > 0, the function is increasing. Let's find the first derivative of the given function:

Take the derivative of the function y with respect to x: y' = 4x³ - 16x.

Set the derivative equal to zero to find critical points: 4x³ - 16x = 0.

Factor out the common term (4x): 4x(x² - 4) = 4x(x + 2)(x - 2) = 0.

Solve for x to find critical points: x = 0, x = -2, and x = 2.

Analyze the sign of y' around these points to determine where the function is increasing and decreasing.

Through analyzing the signs, you will find that the function is increasing on the intervals (-∞, -2), (0, 2), and (2, ∞).

Note that these intervals are determined by looking at the sign changes of the first derivative around the critical points and selecting the intervals where the derivative is positive.

Answer:

The balance sheet consists of three major elements: assets, liabilities and owners' equity. The object of the statement is to prove true the accounting equation, "Asset = Liabilities + Owner's Equity."

Hope this helps!! :)

Answer:

Area of equilateral triangle = 43.3 units^2

Step-by-step explanation:

An equilateral triangle is a triangle in which all three sides of triangle are equal.

So,Length = 10 units

Area of triangle = [tex]\frac{\sqrt{3} }{4}*(side)^2[/tex]

                           = [tex]\frac{\sqrt{3} }{4}*(10)^2[/tex]

                           = [tex]\frac{\sqrt{3} }{4}*(100)[/tex]

                          = [tex]43.3units^2[/tex]

So, Area of equilateral triangle = 43.3 units^2.

The answer is:

The area of the triangle is equal to  [tex]A=43.30units^{2}[/tex]

To calculate the area of an equilateral triangle, we need to use the following formula:

[tex]A=\frac{s^{2} *\sqrt{3}}{4}[/tex]

Now, we are given an equilateral triangle, so we know that all of its sides are equal to 10 units.

So, calculating the area we have:

[tex]A=\frac{s^{2} *\sqrt{3} }{4}\\\\A=\frac{(10units)^{2} *\sqrt{3} }{4}\\\\A=\frac{100units^{2} *\sqrt{3} }{4}=43.30units^{2}[/tex]

Have a nice day!

Answer:

O.53 is the answer.

Step-by-step explanation:

Since standard form is more like number form, fifty three hundredths would be 0.53 in standard form.

Answer:

$45/h

Step-by-step explanation:

So, we have a total maximum cost for the finished product and we have the raw material costs... but we need to figure out the maximum labor cost (for 2 hours).

We can express this as follows (remember it takes 2 hours of labor):

98.62 + 2x <= 189.27

2x <= 90.65

x <= 45.325

Rounded to the nearest dollar: $45

The maximum cost Ethan can afford in labor is $45/h for the 2 hours machining of the parts.

Step-by-step explanation:

try surfing how to divide a function by the long division method

ANSWER

C) 16

EXPLANATION

Using the Pythagoras Theorem, we obtain:

QR² =PR²+ PQ²

From the diagram,

[tex]PQ = 8 \sqrt{3} [/tex]

[tex]PR=8[/tex]

We substitute into the formula to get;

[tex]|QR| ^{2} = {8}^{2} + {(8 \sqrt{3} )}^{2} [/tex]

[tex]|QR| ^{2} = 64+ 192[/tex]

[tex]|QR| ^{2} = 256[/tex]

Take square root

[tex]|QR| = \sqrt{256} [/tex]

[tex]|QR| = 16[/tex]

Answer:

The length of side QR is 16 units.

Option C is correct.

Step-by-step explanation:

Given a right angled triangle QPR in which length of sides are

[tex]PQ=8\sqrt3 units[/tex]

[tex]PR=8 units[/tex]

we have to find the length of side QR

As QPR is right angled triangle therefore we apply Pythagoras theorem

[tex](hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]

[tex]QR^2=PQ^2+PR^2[/tex]

[tex]QR^2=(8\sqrt3)^2+8^2[/tex]

[tex]QR^2=192+64=256[/tex]

Take square root on both sides

[tex]QR=16 units[/tex]

Hence, the length of side QR is 16 units.

Option C is correct.

Answer:

the domain of this function is [0, 27]

Step-by-step explanation:

One way of answering this question would be to make a table of x and y values.  Your x-values would be [0, 4] (that is, all x values between 0 and 4, including end points.

 x      y = 3x² - 6x + 3

 0                             3

 1                               0

 2                              3

 4                              27

From this table, it appears highly likely that the smallest y value would be 0, at x = 1, and that the largest would be 27 at x = 4.  Thus, the domain of this function is [0, 27].

If the circumference of a pizza is 81 inches, the radius would be 12.89155 inches.

The answer is:

The correct answer is:

d. [tex]f(m)=10+0.25*m[/tex]

From the statement we know that he begins at 10 miles away from his house riding at a speed of 0.25 miles per hour (h)

We have that:

[tex]x_{f}=x_{o}+v*t[/tex]

Where,

[tex]x=FinalPosition\\x_{o}=InitialPosition\\v=speed\\t=time[/tex]

Now, using the given information we have that=

[tex]x_{f}=x_{o}+v*t[/tex]

[tex]x_{f}=10miles+0.25mph*m[/tex]

We have that:

[tex]x_{f}=f(m)[/tex]

So,

[tex]f(m)=10miles+0.25mph*m[/tex]

Hence, we have that the correct answer is:

d. [tex]f(m)=10+0.25*m[/tex]

Have a nice day!

Final answer:

The function that represents Joe's distance from his house after riding for m minutes is f(m) = 10 - 0.25m. Hence, the answer is B.

Explanation:

The correct function to represent the distance Joe is from his house after riding for m minutes is f(m) = 10 - 0.25m. This is because Joe starts 10 miles away from his house and rides towards it, reducing the distance by 0.25 miles every minute.

To form the function, you need to start with the initial distance, which is 10 miles. Since Joe is moving closer to his house, the distance decreases over time. Therefore, for every minute m that Joe rides, he covers 0.25 miles. Thus, the distance from home after m minutes is the initial distance minus the product of the speed and time, which gives us f(m) = 10 - 0.25m.

Answer:

9 cupcakes and 64$

Step-by-step explanation:

try the math

So first, set up an equation for each shop, for the first one you can write 4x+28 (since it is 4 dollars for each cupcake and 28 dollars for the cake) and for the second shop you can write 55+x ( 55 dollars for cake and a dollar for each cupcake.) now you can set the 2 equations equal to each other because they want the number for cupcakes where the price will be equal. So 4x+28=55+x and then solve. I don’t want to completely tell you the answer but if you are stuck, you can tell me and I will gladly help.

Use rules of logarithms to condense. log ( y 3 x 2 z 4 )

The given expression 3 log y - 2 log x - 4 log z can be combined into one logarithm using rules of logarithms. We obtain the single logarithm: [tex]log [(y^3)/(x^2*z^4)][/tex]. Feel free to apply these rules to other similar problems.

The problem asks you to write the given expressions 3 log y - 2 log x - 4 log z as a single logarithm. From the rules of logarithms, we know that:

Using these rules, our expression simplifies as such:

3 log y - 2 log x - 4 log z

is equivalent to:

[tex]log(y^3) - log(x^2) - log(z^4)[/tex]

This can further be combined, using the second rule into:

[tex]log [(y^3)/(x^2*z^4)][/tex]

This method can be used to simplify any given logarithmic expression.

https://brainly.com/question/33159023

#SPJ2

Answer:

Step-by-step explanation:

It's a trapezoid.

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

b₁, b₂ - bases

h - height

(look at the picture)

Use the Pythagorean theorem to calculate the length x:

[tex]x^2+12^2=15^2[/tex]

[tex]x^2+144=225[/tex]            subtract 144 from both sides

[tex]x^2=81\to x=\sqrt{81}\\\\x=9[/tex]

Substitute:

[tex]b_1=9+12+9=30\\b_2=12\\h=12[/tex]

[tex]A=\dfrac{30+12}{2}\cdot12=(42)(6)=252[/txt]

Answer:

x = 8

3rd choice

Step-by-step explanation:

https://mathbitsnotebook.com/Geometry/Trigonometry/TGTrigSineCosine.html

Answer:

7: 9 times 8: 108

Answer:

7. 9 times

8. 108 people

Step-by-step explanation:

7. The probability of winning is 25%

So, if a person plays 36 times, the probability will be:

25% of 36

=> 36 * 25/100

=> 36 * 0.25

=> 9 times

So, option 3 is correct .

8. Total number of people asked are 300

and

The percentage of people who prefer two-door cars are 36%

So, the number of people who prefer two-door car are:

300 * 36/100

=> 300 * 0.36

=> 108 people

So, option 1 is correct ..

Answer:

The answer is x = -45 and y = 5

X is -45 and y is 5

Answer:

b  = 6

Step-by-step explanation:

In (y^b)^4=1/y^24 we can re-write (y^b)^4 as y^(4b) and then equate this result to y^24.  Setting the exponents equal to one another, we get 4b = 24, or b = 6.

Simplify= 4r+3

Because 8r plus -4r which is 4r and then 3 can’t be simplified so u keep it the same

Then the answer if r=5 is 23

Because the equation looks like 4(5)+3

5 times 4 is 20 plus 3 is 23

Final answer:

The expression 8r+(-4r)+3 simplifies to 4r + 3. Substituting r=5 into the simplified expression gives you 4(5) + 3, which equals 23.

Explanation:

To simplify the expression 8r+(-4r)+3, you combine the like terms which are 8r and -4r. They are like terms because they both contain the variable r.

Simplifying the like terms:

8r + (-4r) = 8r - 4r = 4r

So now the expression simplifies to 4r + 3. To solve for r = 5, you substitute the value of r into the simplified expression:

4r + 3 becomes 4(5) + 3,

20 + 3 = 23.

Therefore, when r = 5, the simplified expression evaluates to 23.

18 and 35. The numbers whose sum 53 are 18 and 35.

The key to solve this problem is using a system of equations.

There are two numbers whose sum is 53. This number can be represented as x and y. So:

x + y = 53

Three times the smaller number is equal to 19 more than the larger. Let's set x as the smaller number and y the larger number. So:

3x = 19 + y

Clear y in both equations and let's use the equalization method to solve for x:

y = 53 - x and y = 3x - 19

Then,

53 - x = 3x - 19

53 + 19 = 3x + x ---------> 3x + x = 53 + 19 -------> 4x = 72

x = 72/4 = 18

To find y, let's substitute x = 18 in the equation x + y = 53

18 + y = 53 --------> y = 53 - 18

y = 35

Answer:

20 miles with an error margin of  ± 8 miles

Step-by-step explanation:

The margin of error of a result is the range in which an error can vary. To find the margin of error between both distances we have to

28-12 = 16, that is, the variation of the result has a range of 16 miles. So we will look for the midpoint of both distances

(X2-X1)/2+X1=(28-12)/2+12=16/2+12=8+12=20

So from this midpoint the value can vary between 8 points below and 8 points above that would cover the difference of 16 miles that we observed at the beginning

In this way, the correct answer is 20 miles with an error margin of  ± 8 miles

Done

The quotient of 78,600 and 12 is 6,550

Answer:

6,550

Step-by-step explanation:

Answer:

Step-by-step explanation: Step

1. Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.

2. Multiply both top and bottom by that number.

3. Then write down just the top number, putting the decimal point in the correct spot

 Hey there!

 Turning fractions into decimals is very easy! You simply divide the numerator by the denominator and then you have your answer.

For example, we have 1/2. If we divide, we get 0.5, which is the decimal form.

I hope this helps!

Answer:

482

Step-by-step explanation:

Their 2nd difference is 12

[tex]2,20,50,92,...\\ \\ a_1 = 2\\ a_2 = a_1+18=a_1+6\cdot 3 \\ a_3 = a_2+30=a_2+6\cdot 5\\ a_4 = a_3 +42 = a_3+6\cdot 7\\ a_5 =a_4+54 = a_4+6\cdot 9\\...\\a_n = a_{n-1}+6\cdot (2n-1) \\ \\ a_1+a_2+...+a_n = \\ =a_1+a_2+...+a_{n-1}+2+6\cdot \Big(3+5+7+...+(2n-1)\Big)\\ \\ a_n = 2+6\cdot \Big(3+5+7+...+(2n-1)\Big)\\ a_n = 6\cdot \Big(1+3+5+7+...+(2n-1)\Big)-4 \\ a_n = 6\cdot n^2-4 \\ \\ \Rightarrow \boxed{a_n = 6n^2-4}[/tex]