Given: f(x) = 2/3x-4 and g(x) = x + 1
Four statements about this system are written
below.
I.f(4) = g(4)
II.When x = 12, f(x) = g(x).
III. The graphs of f(x) and g(x) intersect at
(12,4).
IV. The graphs of f(x) and g(x) intersect at
(4, 12).
Which statement(s) are true?
A. II, only
C. I and IV
B. IV, only
D. II and III

The equation is written as x + 25° + 25° = 90°. Then the value of the variable 'x' is 40°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

AB and BC are perpendicular lines. Then the equation is given as,

x + 25° + 25° = 90°

x + 50° = 90°

x = 90° - 50°

x = 40°

The equation is written as x + 25° + 25° = 90°. Then the value of the variable 'x' is 40°.

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The complete question is given below.

Answer:

-9

Step-by-step explanation:

First combine like terms.

-8x+5-2x-4+5x       -8x-2x+5x=-5x

-8x+5-2x-4+5x       5-4=1

Now plug in 2 for x

-5x+1

   ↓

-5(2)+1= -10+1=-9

If this is wrong, I'm sorry for the misguidance.

In a case whereby a number has the same digits in its hundreds place and it’s hundredths place the number of times that the value is greater in the hundreds place than the value of the digit in the hundreds place is 10,000 times.

The question can be interpreted that the particular number has the same digit  which is seen in hundreds place  hence  hundredths place.

we can then represent the digit  as '1'.

The value of number's hundreds place can be represented as  100

we can as well represent the number's hundredths place as 0.01

the number of times the value of the hundreds place digit exceeds the value of the hundredths place digit can be expressed as 100/0.01 =(100*100)/1 = 10, 000

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missing options:

A. 100,00

B. 100

C. 1,000

D. 10,000

There's no need to turn it into a mixed number since 378/9 = 42 is entirely a whole number.

I suppose you could write  42  0/9 or 42 & 0/9 or [tex]42 \frac{0}{9}[/tex], but that isn't really necessary.

The combined area of all the circles to the nearest hundredth would be = 14,519.36cm³

The formula for the area of a circle = πr²

The radius for one circle = 68/2 = 34cm

π = 3.14

The area of one circle = 3.14× 34²

= 3.14× 1156 = 3629.84

Therefore the combined area of the 4 circle = 4× 3629.84 = 14,519.36cm³.

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A. 9 students offer all three subjects.

B. The only possible value of m is 8.

A. We can use the Principle of Inclusion-Exclusion (PIE) to find the number of students who offer all three subjects.

Let's call the number of students who offer all three subjects "x".

The total number of students who offer Biology is 35, but we have to subtract the number of students who offer only Biology and Economics (12) and only Biology and Physics (7) to avoid counting them twice.

So, the number of students who offer Biology only is 35 - 12 - 7 + x = 16 + x.

Similarly, the number of students who offer Economics only is 28 - 12 - 5 + x = 11 + x.

And the number of students who offer Physics only is 15 - 7 - 5 + x = 3 + x.

The total number of students who offer at least one of the three subjects is 58, so:

16 + x + 11 + x + 3 + x = 58

30 + 3x = 58

3x = 28

x = 9

So, 9 students offer all three subjects.

B. In a regular polygon with (2m + 1) sides, each interior angle is equal to (2m + 1 - 2) * 180 / (2m + 1) = (2m - 1) * 180 / (2m + 1).

We know that this value is equal to 1440, so:

(2m - 1) * 180 / (2m + 1) = 1440

Expanding the right side:

2m - 1 = 1440 * (2m + 1) / 180

Dividing both sides by (2m + 1) and rearranging:

2m = 1440 * 2 / 180 + 1

2m = 16 + 1

m = 8.5

Since m must be a positive integer, the only possible value of m is 8.

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A line has a slope of –9 and includes the points (–7,u) and (9,9).

The value of u is 153.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

A line has a slope of –9 and includes the points (–7,u) and (9,9).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

-9 = (9 - u)/(9 + 7)

-9 = (9- u)/16

9 - u = -144

u = 153.

Therefore, the value of u is 153.

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Answer:

One number is equal to 4228 and the other is equal to 1057

Step-by-step explanation:

1. Let's consider the number that four times the other X, and the other as N

2. We can write X as 4N to make it easier

3. Next, we can form a simple equation X + N = 5285 and substitute the value of X to get 4n + n = 5285

4. We get 5n = 5285

5. To get N we divide 5285 by 5 to get 1057

6. 5285 - 1057 = 4228

Therefore, one number is equal to 4228 and the other is 1057

18x+26.6

18x+133/5

1/5(90x+133)

The length of the remaining sides is a = 57.50 and b = 61.93.

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle.

Given a triangle ABC, and ∠B = 90°

∠A = 68.2° and c = 23.0

so ∠C = 90 - ∠A

∠C = 90 - 68.2

∠C = 21.8°

according to the law of sines,

sinA/a = sinB/b = sinC/c

for a,

sinA/a = sinC/c

substitute the values

sin(68.2)/a = sin(21.8)/c

a = 23(sin68.2)/(sin21.8)

a = 57.50

and for b,

sinB/b = sinC/c

substitute the values

b = csinB/sinC

b = 23(sin90/sin21.8)

b = 61.93

Hence a = 57.50 and b = 61.93.

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A straight line defines the intersection of the two planes.

Given is that Points {X} and {Y} lie in both plane P and plane Q.

Two common points can only lie on a straight line. So, a straight line defines the intersection of the two planes.

Therefore, a straight line defines the intersection of the two planes.

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Answer:

the answer is y≤1

Step-by-step explanation:

i hope it is right sorry if wrong

The scientific notation is [tex]3.7 \times10 ^8[/tex] in a blood volume of 60 ml. Take note that the power of 10 is evaluated using the product of power property.

The reliability of a value, which is frequently an estimation affected by the item's decimal bit count. Beginning with the first non-zero digit, count the decimal places.

Up to the quel decimal place, all zeros are allowed. For example, the number 0.0079800 has five three-digit digits. When present, any digits to the right of the measurement's final non-zero number are required. equivalently increases an integer by three significant digits and three places.

After three, move upward, and start measuring at the first non-zero digit. The final digit must then be removed. The last two numbers are multiplied by zeros to the right of the decimal point.

given

If there are 6,200,000 red blood cells per cubic millimeter of blood,

then there are

[tex]60 \times 6,200,000=60 \times 6.2 \times 10^ 6=372 \times 10^6[/tex]

= [tex]3.7 \times10 ^8[/tex]

= [tex]3.7 \times10 ^8[/tex] in a blood volume of 60 ml. Take note that the power of 10 is evaluated using the product of power property.

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Answer:

78

Step-by-step explanation:

312 divided by 4 equals 78

Answer:

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

Since P is incenter, we have properties of incenter applicable to given questions:

Since JN is angle bisector of ∠J, set up equation:

Angle measures of the triangle are:

Then, according to triangle sum:

Then, find the missing angle:

Sides are equidistant from incenter:

Set up equation and solve or x:

Find one of equal segments:

Hence, MP = 38

ΔMPJ and ΔOPJ are congruent right triangles as MP = OP and JP is common hypotenuse, therefore JM and JO are congruent as corresponding sides:

Then JM is:

We know MP = NP = 22.

Find JP using Pythagorean:

Answer: 2:5

Step-by-step explanation:

Given,

Number of sunfish = 12

Number of rainbow shiner = 30

To find,

The ratio of sunfish to rainbow shiner.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Ratio of sunfish to rainbow shiner :

= Number of sunfish : Number of rainbow shiner

= 12 : 30

= 6 : 15

= 2 : 5

(This ratio cannot be for the simplified so we will have to assume this as the final answer of this question.)

Hence, the ratio is 2:5

Answer:

2:5

Find the number both sides can be divided by in this case, it is 6. Diving both sides by a common number gives us 2 from 12 and 5 from 30.

Answer:

49/3 or 16 1/3

Step-by-step explanation:

Answer:

Jacob uses 5.67 yards of fabric for the cape.

Step-by-step explanation:

The simplest form of the expression is -3x³ + 2x² + 13x -10

An algebraic expression in mathematics is an expression that is made up of letters and numbers, along with algebraic operations (addition, subtraction, multiplication, etc).

-(x − 2)(3x² + 4x − 5) can be expressed in simplest form as follows:

-(x − 2)(3x² + 4x − 5) = (-x +2)(3x² + 4x − 5)

                                 = -x(3x² + 4x − 5) + 2(3x² + 4x − 5)      

                                 = -3x³-4x²+5x + 6x²+8x-10

                                 = -3x³ + 2x² + 13x -10

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Therefore , the solution of the given problem of limit comes out to be it is the definition of the limit f(x,y).

A function's limit is a value that the function takes on as its input approaches or approaches a certain number. Continuity, integrals, & derivative are defined by limits. A function's limit is always interested in how the function behaves at a specific location.

Here,

Given :

If f(x,y) is a function that depends on x and y, then we have this function. Then, assuming that  ϵ>0,∃ δ > 0  positive definite

|f (x,y)C| whenever, this given function does have the limit of C as (x,y) (a,b). 0 < ( x − a ) 2 + ( y − b ) 2 < δ

It's described as. lim (a, b) f (x, y) => ( x , y )

Thus , it is the definition of the limit f(x,y).

Therefore , the solution of the given problem of limit comes out to be it is the definition of the limit f(x,y).

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The fraction of their money remains for other expenses each month is 5/12.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

Williams spend 1/3 of their total monthly income for rent and 1/4 for food.

The fraction of their money remains for other expenses each month,

= 1 - 1/3 - 1/4

= 5/12

Therefore, 5/12 is the remaining money.

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Answer:

b=8

Step-by-step explanation:

5(b-1)=30

5b-5=35

5b=40

b=8

The value for b is 7.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

Darryl had 5 boxes of books with b books in each box.

If one 1 book remove from each box then total number of books

= (b-1) +  (b-1) +  (b-1) +  (b-1) +  (b-1)

= 5(b-1)

and, After giving away 1 book from each box, he had 30 total books left.

Then, 5(b-1)= 30

b-1 = 6

b = 7

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Answer:

Slope is -2

Y-intercept is 8

Step-by-step explanation:

The given equation is in the form:

y = mx + b

It is called Slope-Intercept form of an equation. This is because you can look at the equation and automatically see/know the slope and the y-intercept.

The m is the slope, it is the number right next to the x. In your question it is -2. This is the slope -2/1 or 2/-1 (which are the same) It tells you how steep or flat a line is.

The b is the y-intercept, it is the number tacked on to the end of the equation. In your question it is the 8. It tells you where on the y-axis the line crosses.

Slope: m = -2

Y-int: b = 8

Answer:

[tex]\displaystyle{x = \dfrac{\log 7}{\log 5}}[/tex]

Step-by-step explanation:

Given the equation:

[tex]\displaystyle{2\left(5^x\right)=14}[/tex]

Divide both sides by 2:

[tex]\displaystyle{\dfrac{2\left(5^x\right)}{2}=\dfrac{14}{2}}\\\\\displaystyle{5^x=7}[/tex]

Apply common logarithm both sides:

[tex]\displaystyle{\log 5^x = \log 7}[/tex]

From the property:

[tex]\displaystyle{\log a^n = n\log a}[/tex]

Thus:

[tex]\displaystyle{x\log 5 = \log 7}[/tex]

Divide both sides by log5:

[tex]\displaystyle{\dfrac{x\log 5}{\log 5} = \dfrac{\log 7}{\log 5}}\\\\\displaystyle{x = \dfrac{\log 7}{\log 5}}[/tex]

The greatest possible number of pansies in each row is 9.

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.

Given that, a gardener has 27 pansies and 36 daises.

Here, factors of 27 and 36 are

27 =3×3×3

36 =2×2×3×3

So, the GCF of 27 and 36 is 3×3 =9

Therefore, the greatest possible number of pansies in each row is 9.

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The solution is Option D.

The limit of the infinite series diverges and the limit goes off to infinity

If a series is convergent then it has bounded partial sums. Equivalently, if a series fails to have bounded partial sums then it is divergent.

When the series' limits reach its finite range of values, the series is said to be convergent. It is important that, partial sum of series, there should be a limit existed and that is finite in nature then only series converges

An infinite series is one that doesn't converge at any point , had a series of incomplete sums that went on forever and had no end. A series diverges when each sum does not approach zero.

Given data ,

Let the infinite series be represented as A

Now , the value of A is

A = ∑n=1 to ∝ ( 3n⁴ / ( 15n⁴ + 5 )

On simplifying the equation , we get

A = 3 ∑n=1 to ∝ ( n⁴ / ( 15n⁴ + 5 )

In the equation , where the limit goes to infinity, there will finally be no exact solution because the sum of the series will be infinity and the infinite series diverges

Hence , the limit of the equation is infinity

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Answer: 14

Tap to view steps...

Step-by-step explanation:

Answer:

[tex]\displaystyle y=-\frac{3}{8}x+2[/tex]

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes. So, we must first determine our slope of the original equation by converting to slope-intercept form:

[tex]-8x+3y=-6\\3y=8x-6\\y=\frac{8}{3}x-2[/tex]

Hence, because the slope of the original line is 8/3, then the slope of the perpendicular line is -3/8. We are not done, however, as we need to account for the point that the perpendicular line passes through by solving for the new y-intercept:

[tex]y=-\frac{3}{8}x+b\\ \\8=-\frac{3}{8}(-16)+b\\\\8=6+b\\\\2=b[/tex]

Thus, the perpendicular line equation is [tex]y=-\frac{3}{8}x+2[/tex]. See below for a graph.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]-8x+3y=-6\implies 3y=8x-6\implies y=\cfrac{8x-6}{3} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{8}{3}}x-2\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{8}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{8}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{8} }}[/tex]

so we're really looking for the equation of a line whose slope is -3/8 and it passes through (-16 , 8)

[tex](\stackrel{x_1}{-16}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{8} \\\\\\ \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-\stackrel{y_1}{8}=\stackrel{m}{- \cfrac{3}{8}}(x-\stackrel{x_1}{(-16)}) \implies y -8= -\cfrac{3}{8} (x +16) \\\\\\ y-8=-\cfrac{3}{8}x-6\implies {\Large \begin{array}{llll} y=-\cfrac{3}{8}x+2 \end{array}}[/tex]

The equation of the line of Kaya’s line in slope-intercept form is y = 15x  + 25.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given this, Kaya babysits to add money to her savings. She draws a graph to show how much she can earn by babysitting.

To calculate the equation of the line we at least need Two points on the line.

Two points on the graph (0, 25) and (5, 100) and also the y-intercept of the given line is 25(where x is 0)

From the general formula of the slope-intercept form of an equation:

y=mx+b,

where m is the slope

b is the y-intercept,

Since. m = (y - y')/ (x -x')

In our case m = (100 - 25)/5-0)

m = 75 /5

m = 15

and b = 25

Thus, the equation of a line:

y = 15x  + 25

Therefore, The equation of the line of Kaya’s line in slope-intercept form is y = 15x  + 25.

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Answer:

192,753

Step-by-step explanation:

    194,753

 -     2,000

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

    192,753

194,753 - 2,000 = 192,753

The first three terms for the sequence, which have x₁ = 3 and xₙ₊₁ = xₙ -5 are respectively,  3, -2, -7,

In the arithmetic sequence  the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any nth term in AP,

T = a + nd

d = T₂-T₁

Where, a is first term , n is nth term and d is common difference

Given that,

The Sequence,

Having a relation,

x₁ = 3

And xₙ₊₁ = xₙ -5

Let,  n = 1

Then,

x₁₊₁ = x₁ - 5

x₂  =  x₁ - 5

x₂  =  3 - 5

x₂  =  - 2

x₂₊₁ = x₂ - 5

x₃   =  -2 -5

     =  -7

x₃₊₁ = x₃ - 5

x₄  =  -7 -5

     = - 12

Therefore, the first three terms are 3, -2, -7

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