calculate the angle between the longest side and the diagonal of a 577mm by 1000mm rectangle

Answer:

-72

Step-by-step explanation:

Divide by 3 on both sides (x and -216) and you get x= -72. It's negative because the three is positive and the product is negative, so x must be negative.

Answer:

-72

Step-by-step explanation:

-72 times 3=-216

Answer:

Option B: [tex]y=log_2(x-3)[/tex]

Step-by-step explanation:

To obtain the inverse of the function [tex]y= 2^x + 3[/tex], you need to solve the equation for the variable "x":

[tex]y= 2^x + 3\\\\y-3=2^x\\\\log_2(y-3)=log_2(2^x)\\\\x=log_2(y-3)[/tex]

Now you need to exchange the variable "x" with the variable "y". Then:

[tex]y=log_2(x-3)[/tex]

Finally, you get that the inverse of the function [tex]y= 2^x + 3[/tex] is:

[tex]y=log_2(x-3)[/tex]

This matches with the option B.

Answer:

(x, y) = (1, 1)

Step-by-step explanation:

[tex] -27x + 6y = -21 [/tex] --- (1)

[tex] -12x +3y = -9 [/tex] --- (2)

Multiplying (2) by -2 to get:

[tex] 24 x - 6 y = 1 8 [/tex] --- (3)

Adding (1) and (3) to get:

[tex]-27x + 6y = -21[/tex]

[tex]24x-6y=18[/tex]

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

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

x = 1

Finding y:

[tex]-12(1) +3y = -9[/tex]

[tex]3y=-9+12[/tex]

[tex]3y=3[/tex]

y = 1

Therefore, (x, y) = (1, 1).

(X,Y)= (1,1)

Explanation:

Answer:

C, (x - 4)(x - 2)

Step-by-step explanation:

to factor x² - 6x + 8, you need to find 2 numbers that multiplied together are equal to 8 and added together that are equal to -6

we can already eliminate answers B and D, since B added together does not equal -6, and D multiplied together does not equal 8

we are left with choices A and C

in order to get a positive 8 through multiplication, we need either two positive numbers, or two negative numbers

to get a -6 through addition, we need negative numbers

lets test (x - 4)(x- 2) to see if this works in the equation, we can use FOIL to expand the equation and we get:

x² -4x - 2x + 8

x² -6x + 8

our answer would be C, (x-4)(x-2)

The factored form of x^2 - 6x + 8 is (x - 2)(x - 4), which is option c.

To factor the expression x^2-6x+8 into its factored form, we are looking for two binomials (x - a)(x - b) such that when multiplied out, the result will be our original quadratic expression. The factors need to multiply to give the constant term 8, and add up to give the middle term -6. Starting with the constant term, the pairs of factors of 8 are (1, 8), (2, 4), and (-2, -4). We need to find the pair that adds up to -6, which is (-2, -4).

So, the factored form of x^2-6x+8 is (x - 2)(x - 4), and the correct choice here is option c.) (x - 4)(x - 2).

Answer:

[tex]\large\boxed{144^\frac{3}{2}=1728}[/tex]

Step-by-step explanation:

[tex]\sqrt[n]{a^m}=a^\frac{m}{n}\\\\144^\frac{3}{2}=144^{1\frac{1}{2}}=144^{1+\frac{1}{2}}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=144^1\cdot144^{\frac{1}{2}}=144\sqrt{144}=144\cdot12=1728[/tex]

Simplify using [tex]a\frac{n}{m} =\sqrt[m]{a^{n} } =\sqrt{144^{3} }[/tex]

Now, we will factor it and rewrite the radicand in exponential form:

                                  [tex]\sqrt{144^{2}*144 }[/tex]

Rewrite the expression using:

[tex]\sqrt[n]{ab} =\sqrt[n]a}*\sqrt[n]{b} =\sqrt{144^{2} } *\sqrt{144}[/tex]

Now, we will simplify the radical expression:

                        [tex]144*\sqrt{144}[/tex]

Now, factor it and rewrite the radicand in exponential form:

                       [tex]144*\sqrt{12^{2} }[/tex]

simplify the radical expression: [tex]144*12[/tex]

                                               [tex]=1728[/tex]

The expression which is equivalent to [tex]144^{\frac{3}{2} }[/tex] is 1728.

The exponential form is an easier way of writing repeated multiplication involving base and exponents. For example, we can write 5 × 5 × 5 × 5 as 54 in the exponential form, where 5 is the base and 4 is the power. In this form, the power represents the number of times we are multiplying the base by itself. 1.

2*2*3 will be its exponential form.

Hence, we have represented 243 as a product of prime given as 243=3×3×3×3×3, and in the exponential form as 243=35.

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Answer:

hope it helps you!!!!!!!!!

Answer:

Volume of cylinders in terms of pie is [tex\V= 896inc^3\pi[/tex]

Step-by-step explanation:

Volume of cylinder = V = π r^2 h

where r is radius and h is height

In the given question:

r= 8 and h = 14

Putting values in the formula:

[tex]V= \pi *(8^2)*(14)\\V = \pi * 64 * 14\\V = \pi *896\\or\\ V= 896\pi[/tex]

So, Volume of cylinders in terms of pie is [tex\V= 896inc^3\pi[/tex]

Answer:

The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches

Step-by-step explanation:

we know that

The Triangle Inequality Theorem. states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x -----> the possible lengths of the third side

Applying the Inequality Theorem

1) 12+8 > x

20 > x

Rewrite

x < 20 in

2) 8+x > 12

x> 12-8

x > 4 in

therefore

4 in < x < 20 in

The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches

Let [tex]x[/tex] be the amount of the 35% solution that will be added. The resulting solution will have a total volume of [tex]15+x[/tex], 38% of which is alcohol. 40% of 15 is 6, so the 40% solution contributes 6 oz of alcohol. So

[tex]0.35x+6=0.38(15+x)\implies x=10[/tex]

oz of the 35% solution need to be added.

[tex]\text{Hey there!}[/tex]

[tex]\bf{\frac{2}{3}=0.6\overline{6}7}\\\\ \bf{\frac{3}{5}=0.60}[/tex]

[tex]\text{Reason: if you use a fraction pie chart and compare}\frac{2}{3} \text{to}\frac{3}{5}, \text{you'd see that}\frac{2}{3}[/tex] [tex]\text{has more shaded areas than as for}\frac{3}{5}\text{has the least amount}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

[tex]\large\boxed{h>2\ \vee\ h<1\to h\in(-\infty,\ 1)\ \cup\ (2,\ \infty)}[/tex]

Step-by-step explanation:

[tex]|2h-3|>1\iff2h-3>1\ \vee\ 2h-3<-1\qquad\text{add 3 to both sides}\\\\2h>4\ \vee\ 2h<2\qquad\text{divide both sides by 2}\\\\h>2\ \vee\ h<1\to h\in(-\infty,\ 1)\ \cup\ (2,\ \infty)[/tex]

The solution of the absolute value inequality |2h-3| > 1 is h > 2 or h < 1. Two cases are considered based on whether the expression inside the absolute value is greater than 1 or less than -1.

To solve the inequality |2h-3| > 1, you need to consider two cases because an absolute value inequality represents two separate inequalities.

Case 1: The expression inside the absolute value (2h-3) is greater than 1. This gives us the inequality 2h - 3 > 1. Solving for h, we get h > 2.

Case 2: The expression inside the absolute value (2h-3) is less than -1. This gives us the inequality 2h - 3 < -1. Solving for h, we get h < 1.

Thus, the solution of the absolute value inequality is h > 2 or h < 1.

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Answer:

21 articles of clothing are clean.

Step-by-step explanation:

If 2/5 clothes, or 40% of them, are dirty, then 3/5, or 60% of them are clean.

Multiply 35 by 0.60, and you get your answer.

35 x 0.60 = 21.

We can check this answer by multiplying 0.40 by 35 to get the amount of dirty clothes and adding that amount to 21, which should equal 35.

35 x 0.40 = 14

14 + 21 = 35

To find out how many articles of clothing were clean, we set up a ratio equation using the given ratio of 2 to 5. By representing the number of clean clothes with a variable and using the total count of 35 clothes, we determined that Meredith found 10 clean articles of clothing.

When Meredith cleaned her room, she found that the ratio of clean clothes to dirty clothes was 2 to 5. If there were 35 articles of clothing in total, the problem can be approached by assigning a variable to represent the number of clean clothes. Let's denote the number of clean clothes by c and the number of dirty clothes by d.

Based on the given ratio, we can write the equation as 2/5 = c/d. Since we know that c + d = 35, we can use these two equations to solve for c.

We express d in terms of c as d = 35 - c.

Substituting this into the ratio equation, we get 2/5 = c/(35 - c). Cross multiplying gives us 5c = 2(35 - c), which simplifies to 5c = 70 - 2c.

Solving for c, we add 2c to both sides to get 7c = 70. Dividing both sides by 7 gives us c = 10. Therefore, Meredith found 10 clean articles of clothing.

Answer:

x = 20

Step-by-step explanation:

Adjacent angles on straight line add up to 180º

7x + (x + 20) = 180

7x + x + 20 = 180

8x + 20 = 180

8x = 160

x = 20

Two angles whose sum is 180° are called supplementary angles. The value of x is 20°.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

The sum of the measure of the angle will be supplementary to each other because the two angles together will be a line. Therefore, the sum will be,

7x + (x+20°) = 180°

7x + x + 20° = 180°

8x = 160°

x = 20°

Hence, the value of x is 20°.

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Answer:

s = ∛756

Step-by-step explanation:

The volume of a cube is found by V = s³. To solve for the side of a cube with a specific volume, we use inverse operations to find it. s = ∛V. If the volume is 756 then the s = ∛756.

Answer:

x= -7 , y= 9

Steps:

4x+3y=-1

5x+4y=1

First, multiply the top equations by -5, and the bottom by 4 to get :

-20x-15y=5

20x+16y=4

Then, you’re going to add the two equations with them being on top of each other so you can easily see what cancels out :

-20x-15y=5

+ 20x+16y=4

———————

0+1y=9

From this, you get :

y=9

Now that you have one variable, find x by substituting 9 for y in one of the equations, I choose :

4x+3y=-1

So :

4x+3(9)=-1

Then simplify by multiplying 3 and 9 :

4x+27=-1

Then subtract 27 on each side :

4x=-28

Then, divide by 4 to get that :

x= -7

Hope this helps!!

Answer:

8 7/20

Step-by-step explanation:

2+5=7

3/4+3/5=15/20+12/20=1 7/20

7+1 7/20=8 7/20

Answer:

11 + 28   For sure 100 %

4     5

Step-by-step explanation:

Plz MARK BRAINLIST!!!!!!!!!!!plzzz

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Answer:

If you are looking for what the total is at the end of the week, it is $270.

Step-by-step explanation:

Subtract the values where it says withdraw, and add the values where it says deposit.

Answer:

See picture

Step-by-step explanation:

The equation f(x)=x+4 becomes f(3x) = 3x +4. The graphs are attached below. The original is in red and the blue is the new function.

the answer is { } "an empty set or phi"

Answer:

the empty set { }

Step-by-step explanation:

A ∩ C represents the intersection of sets A and C, that is the members of set A which are also members of set C.

In this case there are no common members, thus

A ∩ C = { }

Answer:

Jon

Step-by-step explanation:

Jon: 3/5 (divide)

=0.6

Pasha: 0.65

Marie: 7/10 (divide)

=0.7

Karen: 0.62

After analyzing the values, of the smallest amount belongs to Jon that is 3/5 or $0.6.

The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.

As per the data provided in the question,

Jon = 3/5 = $0.6

Pasha = $0.65

Marie = 7/10 = $0.7

Karen = $0.62

Compare all the values, Jon has got the smallest amount.

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[tex]

x+1=x-1-1\Longrightarrow x+1=x-2 \\

x=x-3\Longrightarrow x\notin\mathbb{C}\Longrightarrow x=no solution

[/tex]

Answer:

True ~apex

Step-by-step explanation:

a point has zero dimension

True

A point has zero dimension.

Because every open cover in the space has a refinement made up of just one open set, a point is zero-dimensional in relation to the covering dimension.

So, A point is just a position in space and has no dimensions.

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Answer:

Variance σ² having standard deviation 2.5 is 6.25.

Step-by-step explanation:

The standard deviation is basically the square root of the variance.

So, if want to find the variance of the data we simply take square of standard deviation to get the variance of data.

standard deviation = σ = 2.5

taking square on both sides

(σ)² = (2.5)²

σ² = 6.25

So, variance σ² having standard deviation 2.5 is 6.25.

Answer:

D

Step-by-step explanation:

D, because 2.5 squared is 6.25; which rounds up to 6.3

Answer:

1. B

A. Not true because the peak of the data is 2

B. True because 0-2 contains the most dots on the graph and they're bunched together

C. Not true because from 2-5 there is a big gap

D. Not true because there is an outlier

Thus, B. is the answer

2. F.

1 yard = 3 feet

So, divide 6,615 by 3 to get 2,205

I hope this helps! :)

Answer:

Your picture is not clear enough.

Step-by-step explanation:

For this case we have that by definition, the volume of the prism shown is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex]It is the area of the base of the prism

h: It is the height of the prism

Substituting the values:

[tex]A_ {b} = 10 \ cm ^ 2\\h = 6 \ cm[/tex]

Then, the volume is:

[tex]A_ {b} = 10 \ cm ^ 2\\h = 6 \ cm[/tex]

ANswer:

60

Answer:

B. line segment

because without the point A it would be a ray

or without the arrow after point a it would be a line

The figure a(n) represents a line segment Option(B)

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane.

In geometry, a ray is usually taken as a half-infinite line (also known as a half-line) with one of the two points and. taken to be at infinity.

A line segment is bounded by two distinct points on a line. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.

The given figure is a line segment as it has two end points a and b and also it is bounded by the similar two extended point .

Therefore a(n) is a line segment, Option (B.)

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Answer:

Step-by-step explanation:

first solve for x

x-16=8

add 16 to both sides to isolate x, you now have:

x=8+16

x=24

soooo...now you have to plug in x into the other equation.

3(x+7) turns into 3(24+7)

so now we solve.

3(24+7)

3 x 31

93=x

Hope this was helpful!

The value of x in the equation x-16=8 is found to be 24. Substituting x into the expression 3(x+7) yields a final result of 93.

The equation given in this question is: x-16=8. To find the value of x, add 16 to both sides of the equation. So, x = 8 + 16, which simplifies to x = 24.

Next, to find the value of 3(x+7), you first replace the x with the value we have just found. That gives you 3(24 + 7) which equals 3(31). Multiplying this out gives the final answer, 3(31) = 93.

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120 be cause it is not a straight line

Answer:

9090

Step-by-step explanation:

Answer:

I = $ 90.90

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 4.5%/100 = 0.045 per year,

then, solving our equation

I = 505 × 0.045 × 4 = 90.9

I = $ 90.90

The simple interest accumulated

on a principal of $ 505.00

at a rate of 4.5% per year

for 4 years is $ 90.90.

Answer:

Step-by-step explanation:

1.  Replace F(x) with y.

2.  Interchange x and y in  y = 2x + 1:  x = 2y + 1

3.  Solve this result for y:  2y = x - 1, or y = (x - 1)/2

4.  Replace y with:

   -1

F     (x):

   -1             x - 1

F     (x) = -----------

                     2

Answer:

f-1(x) = (x - 1)/2.

Step-by-step explanation:

Let f(x) = y

y = 2x + 1

2x = y - 1

x = (y - 1)/2

Now replace x by the inverse of f(x) ( that is f-1(x) ) and y by x:

f-1(x) = (x - 1)/2.