What is the expression in factored form?
5x² - 7x-6
O
(5x-2)(x-3)
(x + 3)(5x - 2)
O (5x + 3)(x - 2)
O (5x + 3)(x + 2)

The pair of triangles can be proved to be congruent using the ASA postulate of congruency.

In the two triangles , let the first right angled triangle be ABC and the second right angled triangle be DEF.

In ΔABC and ΔDEF

∠ABC = 90° and ∠DEF = 90°

∠ACB = ∠DFE

therefore by using the angle sum property of the triangle we can say that:

∠CAB = ∠FDE

Therefore in the pair of triangles: ΔABC and ΔDEF we have :

∠ACB = ∠DFE

∠CAB = ∠FDE

AC = DF is given which is also the common side to both the angles.

Hence we can say

ΔABC ≅ ΔDEF  ( By angle-side -angle postulate of congruency)

Therefore the two triangles are congruent by the ASA postulate of congruency.

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Answer:

y = 2m -1

Step-by-step explanation:

y = mx + b is the slope intercept form of a line.

Perpendicular slopes are opposite reciprocals of each other.  That means that you flip the fraction and take the opposite sign.  The slope will be 2.

Now us the slope, the x value and the y value from the give point to find the y-intecept (b)

Slope = 2 (m)

y = 7 from the point (4,7)

x = 4 from th point (4,7)

y = mx + b

7 = 2(4) + b

7 = 8 + b  Subtract 8 from both sides

-1 = b

y = 2x - 1

Answer:

Step-by-step explanation:

y = 2x - 1

$ 1.31 should pay for the chance to win if it is a fair game.

Probability is simply how likely something is to happen.

Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

It is a fair game if what we gain equals what we stake.

There are 13 clubs in a standard deck of 52 cards.

Probability of 3 clubs = 13C3 / 52C3 = 286/22100 = 0.01294

For a fair game,

$100(0.01294) = x(1-0.01294)

Solving for x,

1.294 = x(0.98706)

x = 1.31

$ 1.31 should pay for the chance to win if it is a fair game.

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Answer:

a) x=5

b) x=4

Step-by-step explanation:

4x-3=2x+7

-2x.  -2x

2x-3=7

   +3. +3

2x=10

x=5

2x+6=7x-14

-2x.   -2x

6=5x-14

+14. +14

20=5x

/5. /5

4=x

Hopes this helps please mark brainliest

Answer:

[tex]\textsf{1.} \quad (x-1)^2=12(y+2)[/tex]

     See attachment 1.

2.  See attachment 2.

Step-by-step explanation:

Given values:

As the x-value of the vertex and focus is the same, the parabola has a vertical axis of symmetry.

The focus is always on the inside of the parabola.

Since p represents the distance from the vertex to the focus, and the distance from the vertex to the focus is 1 - (-2) = 3, then p = 3.

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.  Therefore, as p > 0, the parabola opens upwards.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a parabola}\\(with a vertical axis of symmetry)\\\\$(x-h)^2=4p(y-k)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h,k+p)$\\ \phantom{ww}$\bullet$ Directrix: \; $y=(k-p)$\\ \phantom{ww}$\bullet$ Axis of symmetry: \; $x=h$\\\end{minipage}}[/tex]

Therefore:

Substitute the values into the formula:

[tex]\implies (x-h)^2=4p(y-k)[/tex]

[tex]\implies (x-1)^2=4\cdot 3(y-(-2))[/tex]

[tex]\implies (x-1)^2=12(y+2)[/tex]

See attachment 1 for the graph of the parabola.

Given equation of a parabola:

[tex](y-4)^2=8(x+2)[/tex]

As the y-variable is contained within the squared part of the equation, the parabola has a horizontal axis of symmetry.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a parabola}\\(with a horizontal axis of symmetry)\\\\$(y-k)^2=4p(x-h)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h+p,k)$\\ \phantom{ww}$\bullet$ Directrix: \; $x=(h-p)$\\ \phantom{ww}$\bullet$ Axis of symmetry: \; $y=k$\\\end{minipage}}[/tex]

Therefore:

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.   Therefore, as p > 0, the parabola opens to the right.

Find the y-intercepts of the graph by substituting x = 0 into the equation:

[tex]\implies (y-4)^2=8(0+2)[/tex]

[tex]\implies (y-4)^2=16[/tex]

[tex]\implies y-4=\pm4[/tex]

[tex]\implies y=4\pm4[/tex]

[tex]\implies y=0, y=8[/tex]

To sketch the graph of the parabola, plot:

Draw a curve through the vertex and y-intercepts, opening to the right.

Use the axis of symmetry to ensure the curve is symmetric.

See attachment 2 for the graph of the parabola.

Miguel's sister's red gumdrops weigh 0.5 pounds.

Formulate based on the conditions stated: [tex]\frac{3}{8} + x = \frac{7}{8}[/tex]

Unknown terms should be moved to the left side of the equation: [tex]x = \frac{7}{8} - \frac{3}{8}[/tex]

Numerators written over common denominator: [tex]x = \frac{7-3}{8}[/tex]

Determine the total or difference: [tex]x = \frac{4}{8}[/tex]

Remove the connecting element: [tex]x = \frac{1}{2}[/tex]

get the outcome: or x = 0.5 or 50%

A fraction is a mathematical symbol representing any quantity of equal parts, and it also represents a portion of a whole. In common English, the word "fraction" is used to describe the quantity of parts of a particular size. Fractions speed up and simplify calculations by making it easier to divide and evaluate numbers.

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The probability that tails appears on the next toss is 0.5

Given,

In the question:

If I toss a fair coin five times and the outcomes are TTTTT,

To find the probability that tails appears on the next toss is.

Now, According to the question:

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.

A sequence of five fair coin flips has a sample space that contains all potential outcomes. [tex]2^3[/tex] {H, T}  is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .

The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH}  or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5

Hence,  the probability that tails appears on the next toss is 0.5

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The most likely to generalize to it's population of interest is a stratified random sample of 120

a stratified random sample 120

Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members’ shared attributes or characteristics, such as income or educational attainment. Stratified random sampling has numerous applications and benefits, such as studying population demographics and life expectancy.

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The G.P. of a term is 256/243.

To find out the G.P. for the 3rd term:

Let us consider the 1st term to be 'a'.

So, [tex]ar^{2}=18[/tex] ....... Equation (1)

Also [tex]ar^{6} = \frac{32}{9}[/tex] .....  Equation (2)

Dividing (2) by (1), we get,

[tex]\frac{ar^{6}}{ar^{2}} = \frac{32}{162}[/tex]

[tex]r^{4}[/tex] = 16/81.

r = 2/3.

Putting r in equation (1) than we will get

a = 81/2.

So, 10th term = [tex]ar^{9}[/tex]

= (81/2) ×(512/19683)

= 256/243.

Hence the answer is the G.P. of a term is 256/243.

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Answer: 745.31 cm²

Total area of the figure can be obtained by adding area of the semi circle and rectangle.

The radius of the semi circle is given as 12.5cm and it's area is equal to (πr²)/2

I hope you understand It's simple!

The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

A linear function is a function that varies linearly with respect to the changing variable.

4.1)

The linear equation is given as y = mx + c

Here, m is the slope while c is the y-intercept.

Given line has a y-intercept of 12.

Slope m = (12 - 24)/(0 - 4) = 3

Thus, h = 3t + 12

4.2)

Time is taken to bamboo to 66 inches tall,

66 = 3t + 12

3t = 54

t = 3 months.

Hence "The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months".

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Answer:

$325

Step-by-step explanation:

t +b = 582

t = b - 68

b - 68 + b = 582

2b = 582 + 68

2b = 650

2/2 b = 650 / 2

b = 325

The length of side x is 6cm

We need to find the scale factor of the shapes below are mathematically similar.

it can be found using the two bases given.

The base of the smaller triangle is 9  and that of large triangle is 12

9/12 = 3/4

The smaller triangle is 3/4 of the larger one.

Multiply the known side by 3/4

X = 8 x 3/4 = 6

X= 6

Therefore, the length of side x is 6cm

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sin y =12/13 but can't find cos x as sin x can't exceed from 1.

It can be solved by using identities of trigonometry.

What are the  trigonometric identities?

These are the equivalent ways to define trigonometric functions.

Basic identities are:

sin²x + cos²x = 1

1 + tan²x = sec²x

1 + cot²x = cosec²x

For cos x:
cos²x = 1 - sin²x

          = 1 - (5/3)²

          = 1- (25/9)

          = -16/9

i.e. not possible

For sin y:

sin²y = 1 - cos²y

         = 1 - (5/13)²

         = 1 - 25/169

         = 144/169

So, sin y = ±(12/13)

but as mentioned x and y are in 1st quadrant ,

so, sin y = 12/13.

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The value of x that makes m║n is 40°

In geometry, the line that intersects two straight lines at distinct points is known as a transversal.

The angles that are formed when two parallel lines are intersected by a third line i.e a transversal are corresponding angles.

Note:

Two corresponding angles are formed by a transversal with two parallel lines that are equal

Here we have

The angle made by the intersecting line with line m is 120°

And the angle made by the same line with line n is 3x°

Let us assume that m║n  

From above observations

The given angle are corresponding angles

=> 3x° = 120°

=> x° = 40°  

Therefore,

The value of x that makes m║n is 40°

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The statement can you use to conclude that quadrilateral xyzw is a parallelogram

The statement to conclude that quadrilateral XYZW is a parallelogram is

XY = WZ and XW = YZ

Quadrilateral :

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.

Parallelogram :

A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other , where the pair of parallel sides are equal in length.

So we can conclude that :

XY is parallel to WZ  and XW is parallel to YZ .

so ,

XY = WZ and XW = YZ is the conclusion .

Hence , the answer is XW = YZ and XY = WZ

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The possible outcomes in the sample space of this experiment are

{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}

Jo flips a coin sample space for a coin = {h, t}

and rolls a 6-sided die sample space for a die = {1,2,3,4,5,6}

at a time coin is tossed and the die is rolled

the possible outcomes in the sample space of this experiment are

{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}

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The set of ordered pairs that represent dilation factor of -3 is

c. A' (-3, -18) B' (-18, -18) C' (-3, -6)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

From the graph the coordinates are read and following the given transformation rule we have

preimage                           image

A (1, 3)   → (2 * -3, 4 * -3) →   A' (-3, -8)

B (6, 6)  → (4 * -3, 4 * -3) →    B' (-18, -18)  

C (1, 6)  → (3 * -3, 2 * -3) →    C' (-3, -6)

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Answer:20

Step-by-step explanation: my man

Answer:

20

Step-by-step explanation:

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

= 20

The expression can be represented in terms of exponent as 4³ b² c³ if the expression is 4 · 4 · 4 · b · b · c · c · c.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The expression is:

=  4 · 4 · 4 · b · b · c · c · c

By using the properties of exponent:

= 4³ b² c³

4³ = 64

=  64b² c³

Thus, the expression can be represented in terms of exponent as 4³ b² c³ if the expression is 4 · 4 · 4 · b · b · c · c · c.

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Answer:

B. 700+200

Step-by-step explanation:

691+208=899

A. 600+200=700

B.700+200=900

C.700+300=1000

D.900+200=1100

B is closest to 899

Answer:

700+200

Step-by-step explanation:

we round these numbers to the closest hundreds by looking at the tenth place

5 or more we round up

4 or less we let it rest and round down

691 since it is 9 in the tenths place we round up to 700

208 since the tenths place is 0 we round down to get 200

700+200 is the answer hopes this helps please mark brainliest

Answer:

if you don't mind is there a starting number or a chart so i can calculate and solve this for you!

Answer:

x ≥ 5

Step-by-step explanation:

3x - 8 ≥ 7 ( add 8 to both sides )

3x ≥ 15 ( divide both sides by 3 )

x ≥ 5

The equation  that can be used to find the number of hotdogs

and sodas sold at the swim meet.

a)x+0.50y=150

b)  y=-2x+300

c)Number of soda sold y =220 if hot dog is 40.

d)  x intercept=150. It is related to the total earnings of soda and hot dogs sold.

f) y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.

What is x-intercept and y-intercept?

An equation's or a function's graph that contacts the x axis is said to have a "X intercept." This is comparable to a point having a value of zero. Given that it is located on the horizontal axis, this is sometimes referred to as the horizontal intercept. The y value at the point where the line meets the y axis is known as the y intercept. By examining the graph and identifying the point that crosses the y axis, we may determine the y intercept. This point's x coordinate will always be 0. It will be recorded as (0,y). Given that it is on the vertical axis, this is also referred to as a vertical intercept.

Let us take number of hot dogs sold as x and number of soda sold as y.

Cost of one hot dog = $1.00

Cost of one soda = $0.50

Then , cost of x number of hot dogs sold = 1x

cost of y number of soda sold = 0.50y

Then, . At the end of the day you made $150.

=> 1x+0.50y= 150

a) standard form of the equation is ,

=> x+0.50y=150 ------->1

b) x+0.50y=150

=> x+[tex]\frac{1}{2}[/tex]y=150

=>2x+y=150*2

=>2x+y=300

Then slope intercept form is  y=-2x+300------->2

c) Number of hot dogs sold x=40 and put into 2 ,

then ,  y=-2(40)+300

=> y=-80+300

=>y=220

Number of soda sold y =220

d) To find x intercept put y=0 into 1 , then

=> x+0=150

=>x=150

Here x intercept=150. It is related to the total earnings of soda and hot dogs sold.

e)To find y intercept put x=0 into 1,

=> 0+0.50y=150

=> y = 150/0.50

=> y =300

Here y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.

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Answer: __________________________________________

3x + 9

Answer: 3x + 9

Step-by-step explanation:

The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .

In the question ,

it is given that ,

the quadratic equation is cos²x + 2 cosx - 3 = 0 ,

let cosx = a ,

So , the equation becomes , a² + 2a - 3 = 0

writing the factors using the splitting the middle term method ,

we get ,

a² [tex]+[/tex] 3a -a - 3 = 0

a(a + 3) -1(a [tex]+[/tex] 3) = 0

(a - 1)(a [tex]+[/tex] 3) = 0

which means a - 1 = 0      or    a + 3 = 0

a [tex]=[/tex] 1    or     a [tex]=[/tex] -3 ,

Substituting a = cosx , we get

cosx [tex]=[/tex] 1   or cosx [tex]=[/tex] -3 ,

Therefore , The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .

The given question is incomplete , the complete question is

Solve the given quadratic equation for Cosx , cos²x + 2 cosx - 3 = 0 .

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The proportion of the pan of leftover brownies that now has icing is of 0.21 = 21%.

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations to find the desired amounts in whichever context of the problem.

In the context of this problem, these amounts are given as follows:

Hence the part of the pan of leftover brownies that now has icing is obtained by the multiplication presented as follows:

0.7 x 0.3 = 0.21.

It can be interpreted by the multiplication of 7 and 3 = 21, and then the result moves two decimal places to the left as each factor of the multiplication has one decimal digit.

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The dynamic power consumption of your chip if it has an area of 70 mm² and runs at 450 MHz at vdd = 0.9V is 1.08 W.

It is given that,

The average activity factor = 0.1

The Average switching capacity = 450 pF/mm²

We know that,

              p = aCV²f

putting the values in the above equation:

   = 0.1× (450e⁻¹² × 70) × (0.9)² × 450e⁶

   = 1.08 W

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