According to the fundamental theorem of algebra, how many zeros does the function f(x) = 5x - 9 have?

The dimension of the rectangle of the largest area in an equilateral triangle is √3/4L.

Here we have to find the dimension of the rectangle of the largest area.

Let the distance from the tip of the base of the triangle to the point that the top of the rectangle meets the triangle be x.

The width of the rectangle is √3/2 x.

By this, we can find the area of the rectangle

Area = √3/2x ( L -x) = √3/2 xL - √3/2x²

To find the maximum area we have:

dA/ dx = 0

dA / dx = √3/2L - √3x = 0

From we have to find the value of x,

√3 x = √3/2L

x = L/2

The dimension of rectangle is √3/2x = √3/2(L/2)

                                                             = √3/4 L

Therefore the dimension of the rectangle is √3/4 L.

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Answer:

5

Step-by-step explanation:

divide.

[tex]a=-5(-3)-2=13\\\\b=-5(-1)-2=3\\\\c=-5(1)-2=-7\\\\d=-5(2)-2=-12[/tex]

Answer:

A = 13 B = 3 C = -7 D = -12

Step-by-step explanation:

Just insert the x values for a, b, c, and d. for example if we were to find a.

The x value for a is -3 so we would put -3 in place of x in the equation.

-5(-3) - 2

Remember: Two negative numbers multiplied with each other equal a positive.

15 - 2 = 13

The range of the function is [0, 960]

From the question, we have the equation of the function to be

f(x) = 16x

Where

When the dispenser is empty, it means that f(x) = 0

When the dispenser is full, it means that f(x) = 960

When these values are combined, they represent the range

In other words, the range is 0 to 960

This can be rewritten as [0, 960]

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Answer:

big black men

Step-by-step explanation:

(i have your search history)

26.2% is the total percent of discount offered by the merchant.

Let us assume that each item is $100.

As it is given that 18% is off, we have an amount after off is:

Amount after 18% off = 100 × (100 - 18)/ 100

                           = 100 × 0.82

                           = 82

Next, there is 10% off

So the amount become = 82 ×( 100 - 10) / 100

                                        = 82 ×0.9

                                        = 73.8

So the final price of an item is $73.8

The discount = (100 - 73.8) / 100

                      = 26.2%

Therefore the total percent of discount is 26.2%.

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Answer:

Step-by-step explanation:

You have to multiply both sides by 3 so its -9>-5+n. Then add each side by 5. The answer is n<-4 (D)

Answer:

D) n<-4

Step-by-step explanation:

Using the theories of probability, we got that 0.0260 is the probability  of choosing 4 spades and 2 cards that are not spades and 0.1202 is the probability of choosing 2 red face cards  from a well shuffled deck of 52 playing cards..

We know a deck of 52 playing cards has  13 hearts, 13 clubs, 13 spades,

13 diamonds.

∴  The possibility that she chooses 4 spades and 2 cards that are not spades is,

= ([tex]^1^3C_4[/tex]×[tex]^3^9C_2[/tex])/([tex]^5^2C_6[/tex])

As from the 13 spade cards 4 are chosen, so now we are left with (52 - 4) = 48

and 2 cards that are not spades means out of 9 spades that are left after choosing 4 that is 9 will also be subtracted (48 - 9) = 39.

= (13!/(13 - 4)!×4!)×(39!/(39 - 2)!×2!)/52!/(52 - 6)!×6!

= (13!/9!×4!)×(39!/37!×2!)/(52!/46!×6!)

= (13×12×11×10)/(4×3×2)×(39×38)/2)/(52×51×50×49×48×47)/(6×5×4×3×2)

= (529815)/(20358520)

= 0.026.

Similarly, the probability of choosing 2 red face card is given by

=([tex]^6C_2[/tex]×[tex]^4^6C_4[/tex])/([tex]^5^2C_6[/tex])

=[ [(6! / (2!.4!)] × [46! / (4!.42!)] ]/ [52! / (6!.46!)]

=(15×163185)/20358520

=0.1202.

Hence, the probability of choosing 4 spades and 2 cards by carrie that are not spades is 0.026 and the probability of choosing 2 red face cards by carrie is 0.1202.

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Step-by-step explanation:

in order to be able to decide each case we need the slopes of all involved lines.

and that means we need to bring all of the equating into a "y = ..." form, because then the slope is always the factor of x.

parallel lines have the same slope.

the slopes of perpendicular lines (intercept at a right angle) have the y/x ratio turned upside-down and a flipped sign : -x/y.

"neither" is everything else.

our reference line

x + 2y = 6

2y = -x + 6

y = -1/2 x + 3

so, the reference slope is -1/2.

y = -1/2 x - 5 is parallel (same slope).

-2x + y = -4

y = 2x - 4 perpendicular (2/1 vs. -1/2)

-x + 2y = 2

2y = x + 2

y = 1/2 x + 1 neither

x + 2y = -2 parallel (as the structure except for the constant part is the same as our reference line).

2y = -x - 2

y = -1/2 x - 1

For the given triangles ΔTRS and ΔQRP , the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.

As given in the question,

Two triangles ΔTRS and ΔQRP,

It is given that :

Line segment SR ≅ Line segment PR

Line segment SP bisects Line segment TQ

⇒ line segment TR ≅ line segment RQ

∠TRS ≅ ∠PRQ ( by vertically opposite angle )

By Side angle side theorem we have ,

ΔTRS ≅ ΔPRQ

Therefore, for the given triangles ΔTRS and ΔQRP ,the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.

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The equation of straight line having

(a) gradient -4 and coordinates (-2,1) is  4x + y [tex]=[/tex] -7

(b) gradient 0 and coordinates (-1,21) is y = 21 .

In the question ,

the gradient and coordinates of the point on the line is given .

we have to find the equation of the straight line .

Part(a)

the gradient of the line [tex]=[/tex] -4 ,

the coordinates of a point on the line = (-2,1)

So , the equation of the line is

(y - 1) = (-4)*(x -(-2))

y - 1 = -4(x + 2)

y - 1 = -4x - 8

4x + y = -8 + 1

4x + y = -7

the equation is 4x + y = -7  .

Part(b)

the gradient of the line = 0 ,

the coordinates of a point on the line = (-1 , 21)

So , the equation of the line is

(y - 21) = 0(x-(-1))

y - 21 = 0

y = 21

the equation of the line is y = 21  .

Therefore , The equation of straight line having  (a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7  and (b) gradient 0 and coordinates (-1,21) is  y = 21  .

The given question is incomplete , the complete question is

Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.

(a) -4, (-2 , 1)

(b) 0, (-1, 21)

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Step-by-step explanation:

3 units right = x + 3

12 units down = y - 12

E = (-5, 4) -> E' (-2, -8)

F = (-5, 9) -> F' (-2, -3)

G = (1, 9) -> G' (4, -3)

H = (1, 4) -> G' (4, -8)

Answer: y=3x-5

Step-by-step explanation:

This was the answer i got after solving

Hope that helped :)

Screenshot is the proof of the answer btw :)

The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.

If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.

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The slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a equation of a straight line as -

4x - 1 = 3y + 5

We have the equation as follows -

4x - 1 = 3y + 5

Rearranging the equation -

3y = 4x - 1 - 5

3y = 4x - 6

y = (4/3)x - 2

Refer to the graph attached.

The slope of the line is [m] = 4/3

The [y] intercept is at [c] = -2

Therefore, the slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2

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Answer:

f(x) = 4x + 10

Step-by-step explanation:

The given information is in the form f(x) = y.

f(0) = 10 means if x is 0, y is 10. This is the point (0,10)

Likewise, f(6) = 34

means when x is 6, y is 34. That is the point (6,34).

Slope is y-y / x-x

34-10 / 6-0

is 24/6.

The slope is 4.

The y-intercept is where x is 0, that is 10.

y=mx+b is slope-intercept form. Fill in the slope, 4 for m and the y-intercept, 10, for b.

y = 4x + 10

but they also asked to call it f, so for function notation, use f(x) instead of y.

f(x) = 4x + 10

The monthly payment for a 25-year loan is $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1

What is compound interest?

When you earn interest on both the money you've saved and the interest you've earned, this is known as compound interest.

what is the monthly payment?

The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original amount borrowed, but also the interest that accrues, must be repaid.

Here,

We know that the monthly payment is given as

MP = [Pr(1 + r)¹²ⁿ] / [(1 + r)¹²ⁿ - 1]

Where MP monthly payment, P is the initial amount, r is the rate of interest, and n is the number of years.

we have

r = 0.0115

P = $150,000

n = 25 * 12

n = 300

Then we have

MP = $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1

Hence, the monthly payment for a 25-year loan is $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1

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Answer:

For the first equation, it is "True for one value of x."

For the second equation, it is "True for no value of x."

For the third equation, it is "True for all values of x."

Step-by-step explanation:

Just solve the equation and check the numbers:

If both numbers are the same, it is "true for all values of x"

If there is a variable and a number, it is "true for one value of x"

If there are two numbers and they are different, it is "true for no values of x"

Hope this helps!

Please give brainliest

We need to check whether the given equations are true for all values of [tex]x[/tex] , one value of [tex]x[/tex] , or no values of [tex]x[/tex] .

The equations are ,

solve this equation for x ,

[tex]\longrightarrow 3x +9=-4.5x+20\\[/tex]

[tex]\longrightarrow 3x+4.5x =20-9\\[/tex]

[tex]\longrightarrow 7.5x =11\\[/tex]

[tex]\longrightarrow \underline{\underline{x =\dfrac{11}{7.5}}}[/tex]

Hence the equation is true for one value of x .

solve out for x ,

[tex]\longrightarrow 9x +27=9x-12\\ [/tex]

[tex]\longrightarrow 9x -9x =-27-12\\ [/tex]

[tex]\longrightarrow 0 = -39[/tex]

This can never to true , so the equation is true for no values of x .

solve out for x ,

[tex]\longrightarrow 8x+12=12+8x \\[/tex]

[tex]\longrightarrow 12-12=8x-8x\\[/tex]

[tex]\longrightarrow 0=0 [/tex]

Hence this equation is true for all values of x .

And we are done!

Answer:

x=7

Step-by-step explanation:

2(2x - 7) = 14

Solve for x

Divide each side by 2

2/2(2x - 7) = 14/2

2x-7 = 7

Add 7 to each side

2x-7+7 = 7+7

2x = 14

Divide each side by 2

2x/2 = 14/2

x = 7

Answer:

b) x = 7

Step-by-step explanation:

Given equation,

→ 2(2x - 7) = 14

Now the value of x will be,

→ 2(2x - 7) = 14

→ 4x - 14 = 14

→ 4x = 14 + 14

→ x = 28/4

→ [ x = 7 ]

Hence, the value of x is 7.

For the given figure, angle 3 will be equal to angle 2.

According to the question,

We have the following information:

We have a figure where some angles are marked in form of numbers and  the measure of angle 3 is equal to the sum of the measures of angle 6.

Now, we know that vertically opposite angles are equal and angle 1 and angle 4 are vertically opposite angles like angle 2 and angle 3.

(More to know: the sum of three angles of a triangle is equal to 180°.)

Hence, for the given figure, angle 3 will be equal to angle 2.

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The equation, in vertex form, of the graph in the diagram is determined as: y = 1|x - 3| + 5.

The formula that represents the equation in vertex form of an absolute value function is y = a|x - h| + k, where:

Vertex = (h, k).

Therefore, we will need to determine what the values of a, h, and k is using the information derived from the graph.

Thus:

(h, k) = (3, 5)

a = 1 (this is because the graph opens upward)

To write the equation of the graph, substitute a = 1, h = 3, and k = 5 into:

y = 1|x - 3| + 5

The equation is, y = 1|x - 3| + 5.

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The required price of almond and expression are $32.75 and c= $7.25P - $3.5 respectively.

Pound is unit used to measure weight of quantity. It is used by the English speaking peoples.It equal to the 16 ounces and 0.454 kilogram.

Alonso has a coupon of $3.5, let us consider P pound of almond. And price per pound of almond is $7.25

So, equation for the cost,

Cost(c) = $7.25P - $3.5

Then, the price of 5 pound of almond = $7.25×5 - $3.5

⇒ $36.25 - $3.5 = $32.75

Thus, the price of 5 pounds of almond is $32.75.

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The required equation for the given condition is 50x + 100y = 1000.

What is an algebraic expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number).

Given, the charge for every birthday party =$50

number of birthday parties = x

So, the total charge for birthday parties = 50x

the charge for every wedding  = $100

the number of weddings = y

So, the total charge for the wedding = 100y

Then,

Total amount achieve = $1000

or, 50x + 100y = 1000

Hence, the required equation is 50x + 100y = 1000.

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Answer:  y  =  160/q   -a

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

4x

Step-by-step explanation:

the quotient of x and 2 is [tex]\frac{x}{2}[/tex] , then

8 × [tex]\frac{x}{2}[/tex] ( cancel 8 and 2 by 2 )

= 4 × x

= 4x

The points (2, 3)  (6, 3), and  (2, 7) sides corresponds to length of 4 : 4 : 5 and do not form Pythagorean triple hence they do not form a right angle

The distance between the points is calculated and Pythagoras theorem is used to determine if the triple  forms a right angle

let the points be

A (2, 3)  B (6, 3), and  C (2, 7)

using the equation

d = √{(x₁ - x₂)² + (y₁ - y₂)²}

AB = √{(2 - 6)² + (3 - 3)²} = 4

BC = √{(6 - 2)² + (3 - 7)²} = 5

CA = √{(2 - 2)² + (3 - 7)²} = 4

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The number that should be on the bottom left stamp is 1. It was gotten by dividing 2 by 2.

From the first picture, we have 82 and the number below it is 4. This was gotten as:

= 8 ÷ 2

= 4

The second picture has 93 and the number below it is 3. This was calculated as:

= 9 ÷ 3

= 3

The third picture has 61 and the number below it is 6. This was calculated as:

= 6 ÷ 1

= 6

The fourth picture will be:

= 2 ÷ 2

= 1

Therefore the value is 1.

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For the given triangle and the measures of the given angle the value of x is equal to -11° .

As given in the question,

For the given triangle,

Let us consider the triangle name ABC,

Where,  m ∠A = x + 51° ,

m ∠ABC = 80° ( vertically opposite angle of given 80° angle.)

m ∠ACB = 60° ( vertically opposite angle of given 60° angle.)

To get the value of x we have,

Sum of all the interior angles of a triangle is equal to 180°

m ∠A + m ∠B + m ∠C = 180°

⇒ x + 51° + 80° + 60° = 180°

⇒ x + 191° =  180°

⇒ x = 180° - 191°

⇒ x = - 11°

Therefore, for the given triangle and the measures of the given angle the value of x is equal to -11° .

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Answer: 30[tex]\pi \\[/tex] or 94.247

Step-by-step explanation:

Circumference=2[tex]\pi[/tex]r

2·[tex]\pi[/tex]·15=30[tex]\pi[/tex]=94.247

Answer:

94.2in.

Step-by-step explanation:

The formula for circumference is 2radius x π

π≈3.14

So we can say:

30in.x3.14=circumference

30x3.14=94.2

94.2in=circumference

(i.e. I don't know what you mean by using T.)

Answer:

Line 1 is considered perpendicular

Line 2 is considered parallel

Line 3 is also parallel

Step-by-step explanation:

This should be right if this is the rest to your problem:

1. Line AB formed by A(-1,3) and B(1,5); Line CD formed by C(2,3) and D(-2,7)

2. Line AB formed by A(3,8) and B(-6,5); Line CD formed by C(-6,7) and D(-3,8)

3. Line AB formed by A(2,-7) and B(2,3); Line CD formed by C(-4,0) and D(-4,-5)