y=x^2-4x-1 in vertex form

The rotations that will carry the equilateral triangle in discuss onto itself are;

It follows from the task content that the rotation which produces the desired output in which case, the rotation maps exactly unto the equilateral triangle is required.

On this note, when the rotation is 90° and 270° about the center P in which case, the rotation can be clockwise or anticlockwise, the desired result is obtained.

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Answer: 240 and 120

Step-by-step explanation:

Answer:

y = 2x + 8

Explanation:

Equation: y = 2x - 4

Comparing it with slope intercept form "y = mx + b" where 'm' is slope and 'b' is y-intercept. This function has slope: 2 and y intercept of -4

Parallel lines has same slope.

Passes through (-2, 4)

[tex]\sf y - y_1 = m(x - x_1)[/tex]

[tex]\sf y - 4 = 2(x - (-2))[/tex]

[tex]\sf y - 4 = 2(x + 2)[/tex]

[tex]\sf y = 2x + 4 + 4[/tex]

[tex]\sf y = 2x + 8[/tex]

Answer: y = 2x + 8

Step-by-step explanation:

This is a fairly simple problem. I hope this helps!

So, to find a line parallel, it's simple, and it only requires that for the other line to have the same slope and a different y-intercept (or same "m" and different "b" in the equation y = mx + b).

To find a line parallel to a point is slightly harder, but don't worry, I'll teach you how.

To do this, we have to recognize the point. The point given is (-2, 4) where -2 is the x-value and 4 is the y-value. Remember, points always go by (x, y).

So, we set y to 4, and we set x to -2.

When testing out lines that are parallel to a point, you must always be careful that you end up with the same value. Such as 4 = 4 or 8 = 8, etcetera.

We get:

4 = 2 × (-2) + 8

Simplifying, we get:

4 = -4 + 8

Adding -4 to 8, we get 4:

4 = 4

Thus, y = 2x + 8 is parallel to the point (-2, 4)

Answer:

C

Step-by-step explanation:

a = 4

b = 5

c = 2

C = arccos((a² + b² - c²) / 2ab)

C = arccos((16 + 25 - 4) / 2(4)(5))

C = arccos(37 / 40)

C = 22.33°

2abcosC

2(4)(5)cos(22.33)

40(0.925)

37

Option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have from law of cosines that a² + b² - 2abcosC = c²

We have to find the value of 2abcosC.

Now let us find the value of C

C = arccos((a² + b² - c²) / 2ab)

C = arccos((16 + 25 - 4) / 2(4)(5))

C = arccos(37 / 40)

C = 22.33°

Now plug in the value of C in  2abcosC.

2abcosC

=2(4)(5)cos(22.33)

=40(0.925)

=37

Hence, option C is correct, if the law of cosines is a² + b² - 2abcosC = c² then the value of 2abcosC is 37.

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Answer:576

Step-by-step explanation:

24 squared is 576

The simplified form of the expression 2/5 x (-7)x 5/2 would be -7.

When two fractions are multiplying each other, the numerator of both fractions multiplies each other, likewise the denominator of both fractions respectively.

Use the property of real numbers to write the expression

[tex]\dfrac{2}{5} \times (-7) \times \dfrac{ 5}{2}\\\\\dfrac{10}{10} \times (-7) \\\\-7 \times 1\\\\= -7[/tex]

Therefore, The simplified form of the expression would be -7.

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After 85 minutes of calls, there are $27.25 left on the card.

A linear equation in slope-intercept form is:

y = a*x + b

Where a is the slope.

If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)

(points of the form (time, dollars)).

So the slope is:

[tex]a = \frac{32.2 - 36.7}{52 -22} = -0.15[/tex]

The linear equation is then:

y = -0.15*x + b

To find the value of b, we use the point (22. 36.7)

36.7 = -0.15*22 + b

36.7 + 0.15*22 = b = 40

Then the linear equation is:

y = -0.15*x +40

The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.

y = -0.15*85 + 40 = 27.25

This means that after 85 minutes of calls, there are $27.25 left on the card.

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Answer:

x≥11

Step-by-step explanation:

4x-3≥41

4x≥41+3   -44

x≥44/4 = 11

Answer:

d.

Step-by-step explanation:

Left line is defined when x < 1 (x is less than 1). The point is not full and that means that x = 1 is not included.

Right line is defined when x is greater or equal to one x ≥ 1.

Options that have x < 1 and x ≥ 1 are b and d, so the answer is one of those.

Equations of the lines are in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

Right line has steeper slope than left line, so the slope of right line will have bigger absolute value. That is the case with option d. (Left line has slope -1 and right one has slope -2, absolute value of right slope is bigger.)

You could also check with y-intercepts. Left line has y-intercept at y = 2 and left line is defined when x < 1. Only option d meets these conditions.

Answer:

1279.5mg

Step-by-step explanation:

103 pound man takes -1292mg of medicines

102 pound woman will take -xmg of medicine

cross multiply

102x1292=103x

131784=103x

x=131784/103

x=1279.5mg

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Women will have 1279.5mg of medicine in a day.

103-pound man takes -1292mg of medicines.

102-pound woman will take x mg of the medicine.

By cross multiply

102x1292=103x

131784=103x

x=131784/103

x=1279.5mg

Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?

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Explanation:

The white rectangle is 3 by 6 with area of 3*6 = 18 square inches.

The larger rectangle is 8 by 5 with area of 8*5 = 40 square inches.

The difference of these will get us the shaded area:

40 - 18 = 22 square inches

Step-by-step explanation:

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Answer:

option N is the correct option, apply Formula of area of rectangle and triangle by splitting figure into 2 parts

Answer:

23.1 years  (nearest tenth)

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 1200=600\left(1+\dfrac{0.03}{12}\right)^{12t}[/tex]

[tex]\implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf 2=\left(1.0025\right)^{12t}[/tex]

Take natural logs:

[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]

[tex]\implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]

[tex]\implies t=23.13377513...[/tex]

[tex]\implies t=23.1\: \sf years \:\:(nearest\:tenth)[/tex]

The money will double in value in approximately [tex]\boxed{\sf 23.1}[/tex] years.

Used formula

[tex]\boxed{\sf A=P(1+\dfrac{r}{n})^{nt}}[/tex]

[tex]\\ \implies \sf 1200=600\left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf \dfrac{1200}{600}=\left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf 2=\left(1.0025\right)^{12t}[/tex]

[tex]\implies \sf \ln 2=\ln \left(1.0025\right)^{12t}[/tex]

[tex]\\ \implies \sf \ln 2=12t\ln \left(1.0025\right)[/tex]

[tex]\\ \implies t=\dfrac{ \ln 2}{12 \ln (1.0025)}[/tex]

[tex]\\ \implies t=23.1years[/tex]

Answer:

The Answer is 50 or 50x

Answer: 15x^2+35x ✅

Step-by-step explanation:

Hii, do you need to distribute [tex]\boldsymbol{5x(3x+7)}[/tex]? No problem! (:

We can solve problems like this one by using what is known as the "distributive property". What it says is: If you have a term that comes before the parentheses, you multiply it times every single term in the parentheses. Let me show you what I mean...

[tex]\twoheadrightarrow\sf 5x(3x+7)[/tex]

[tex]\bullet[/tex] Multiply 5x tmes 3x and 7 - you will obtain

[tex]\twoheadrightarrow\sf 15x^2+35x[/tex] (if we multiply x times x we obtain x²)

Voila! There's our solution, cheers! (:

--

Hope that this helped! Best wishes.

[tex]\it Reach\quad far.\:Aim\quad high. \,Dream\quad big.[/tex]

[tex]\bigstar\underbrace[/tex]

--

The total negative terms are 4 which are greater than -6000 if the geometric sequence 1.5, -3, 6, -12 ... with a common ratio -3.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

A geometric sequence 1.5, -3, 6, -12 ....

The common ratio r = -3/1.5 = -2

1.5, -3.6, 6, -12, 36, -108, 324, -972, 2916, -8748

The total negative terms = 4

Thus, the total negative terms are 4 which are greater than -6000 if the geometric sequence 1.5, -3, 6, -12 ... with a common ratio -3.

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The water level increases by 0.608 meters per minute when the water is 3.5 m deep

The given parameters are:

The relationship between the radius and height is:

r/h = 3/7

Make r the subject

r = 3h/7

The volume of a cone is;

[tex]V = \frac 13\pi r^2h[/tex]

This gives

[tex]V = \frac 13\pi (\frac{3h}{7})^2h[/tex]

Expand

[tex]V = \frac{3h^3}{49}\pi[/tex]

Differentiate

[tex]V' = \frac{9h^2}{49}\pi h'[/tex]

Make h' the subject

[tex]h' = \frac{49}{9\pi h^2}V'[/tex]

When the water level is 3.5.

We have:

[tex]h' = \frac{49}{9\pi * 3.5^2}V'[/tex]

Also, we have:

V' = 4.3

So, the equation becomes

[tex]h' = \frac{49}{9\pi * 3.5^2} * 4.3[/tex]

Evaluate the products

[tex]h' = \frac{210.7}{346.36}[/tex]

Evaluate the quotient

h' = 0.608

Hence, the water level increases by 0.608 meters per minute

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The equation of the line is y = 0.8x - 1.4 if the  slope of the line is 0.8 and line passes through coordinates (-2,-3)

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The slope m = 0.8

The line passing through coordinates (-2,-3)

y = mx + c

y = 0.8x + c

Plug the point in the equation.

-3 = 0.8(-2) + c

c = -1.4

y = 0.8x - 1.4

Thus, the equation of the line is y = 0.8x - 1.4 if the  slope of the line is 0.8 and line passes through coordinates (-2,-3)

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Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

From the information given, the cost of sales is $65,000. See the explanation below.

Add your initial inventory to the purchases made over the time period, remove that amount from your ending inventory, and that is your cost of sales.

Cost of Sales = (Bi + P) - Ei

Where Bi is Beginning Inventory

P is Purchases; and

Ei is Ending Inventory.

Beginning Inventory = 8,000

(add)          Purchase = 70,000

Bi + P                          = 78,000

Ending Inventory  = 13,000

Cost of sales = 78,000 - 13,000

= $65,000

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The  probability that more than 562 drivers is 0.9328

It is a branch of mathematics that deals with the occurrence of a random event.

Given: p = 0.60

n = 900

Let X denote the number of drivers that wear a seat belt,

P(X > 562)

[tex]\mu[/tex] = n*p = 900(0.60) = 540

[tex]\sigma^{2}[/tex]= n*p*(1-p)

=900*0.60*0.40

=216

P(X >562) = Pr( Z > 1.4976)

                = 0.9328

Hence, the probability that more than 562 drivers is 0.9328

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The graph is attached with the answer, This is looking like a horizontal staircase

A step function is a piece wise function whose all pieces are horizontal line or a point.

It is given in the question to graph the interval

-2 ≤x≤2

for f(x) = |x+3|

-2    1

-1     2

0     3

1      4

2     5

The graph is attached with the answer.

This is looking like a horizontal staircase

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Answer:

-4

Step-by-step explanation:

The equation for slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

m: Slope

(6, 2) = [tex](x_1, y_1)[/tex]

(4, 10) = [tex](x_2, y_2)[/tex]

Substitute these values into the equation:

[tex]m=\frac{10-2}{4-6}=\frac{8}{-2}=-4[/tex]

Therefore the slope is -4.

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the slope of the line that passes through the points? 2 points given

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The formula used here, is [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{\dfrac{10-2}{4-6}}[/tex] | subtract

[tex]\bf{\dfrac{8}{-2}}[/tex] | evaluate

[tex]\bf{-4}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

           [tex]\bf{=Slope\;-4}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Answer: C, 5, 5√3

Step-by-step explanation:

The short leg of a 30-60-90 triangle equal half the hypotenuse, 10/2 = 5. The long leg equals √3 times the short leg, 5*√3 = 5√3.

Answer:

7/4 meters

Step-by-step explanation:

the tallest plant is 19/8

since they have all the same denominaters we can just compare the top numbers

so

the smallestp lant is 5/8

19/8 - 5/8 = 14/8

7/4 is your final answer after simplifying

a. 2n^4b, neither a volume nor an area

b. 2Iw + 2wh + 2Ih, It is an area

c. 80 y^4, neither a volume nor an area

a. n(4) 2 x b

n * n * n* n* 2 * b

2n^4b

It is neither an area nor a volume

b.  lw+lw+wh+wh+lh+lh

Collect like terms

2Iw + 2wh + 2Ih

It is an area

c. 8y2(10y2)
8y^2 * 10 * y^2

80 y^4

It is neither a volume nor an area

Thus, the expressions are simplified as a. 2n^4b, b. 2Iw + 2wh + 2Ih, c. 80 y^4

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Step-by-step explanation:

108 = 60%

1% = 60%/60 = 108/60 = 1.8

100% = 1%×100 = 1.8×100 = 180

how many do not study French ?

the remainder of the students. that is 40% (100% - 60%) or 72 students (40×1.8 or simply 180-108).

Answer:

72 students do not study French.

Step-by-step explanation:

60% = 108 students

1. 108 ÷ 60 = 1.8 ( this is to find 1% of the students)

2. 1.8(1%) × 40 = 72

To check the answer:

108 + 72 = 180

180 × 60% = 108

Answer:

y = -2x + 64

Explanation:

The x represents the time in minutes and y represents distance in km.

Determine coordinates: (0, 64), (17, 30)

Find slope:

[tex]\sf slope : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) : \dfrac{30-64}{17-0} = -2[/tex]

Find equation:

[tex]\sf y- y_1 = m(x - x_1)[/tex]

[tex]\sf y - 64 = -2(x - 0)[/tex]

[tex]\sf y = -2x + 64[/tex]

Answer:

Using the concept of number line, we find that Libby owes more than Daniel.

Step-by-step explanation:

Given that the account balance of Daniel is -$1.25 and of Libby is -$2.00. Sandra has as much savings in her account as the amount Daniel owes the bank. So, her account balance is +$1.25.

The numbers to be plotted on the number line are -2.00, -1.25 and 1.25.

The number line is in the attachment.

These numbers are related as: -2 < -1.25 < 1.25.

From the number line, all the names that come left to the origin owe some amount to the bank while all the names that come right to the origin have some money as savings in their account.

Clearly, Daniel and Libby owe the bank.

But since Libby comes before Daniel, Libby owes more than Daniel.

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If we want the slope to be -6/7, then the value of x must be -5.

Remember that if a linear equation passes through (x₁, y₁) and (x₂, y₂), then the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we have the points (x, 9) and (9, -3), and the slope must be -6/7, so we need to solve:

[tex]\frac{- 3 - 9}{9 - x} = \frac{-6}{7} \\\\\frac{-12}{9 - x} = \frac{-12}{14}[/tex]

Where on the second line we multiplied and divided the right fraction by 2.

Comparing the fractions, we see that we must have:

9 -x = 14

9 - 14 = x

-5 = x

So the value of x must be -5.

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