Factor the following expression
x²- 15 x 56 =

Answer:

4x^2

Step-by-step explanation:

2x(2x) It is a square so we multiply the side by the side to get the area.

=2*x*2*x

=4*x2

=4x^2

Answer:

Step-by-step explanation:

Solution :  

hello :

note :

Use the point-slope formula.

y - y_1 = m(x - x_1)   when : x_1= -1      y_1= 5  

     m= the slope is : (YC - YA)/(XC -XA)

(-1-2)/(0-3) = -3/-3 =1

( parallel to AC means same slope)

an equation in the point-slope form is : y -5 = 1(x+1)

y=x+6

The expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.

The slope at any point of the function can be found by definition of derivative following algebraic handling:

[tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex]

[tex]m = \lim_{h \to 0} \frac{\frac{x+1 - x - h - 1}{(x + h + 1)\cdot (x + 1)} }{h}[/tex]

[tex]m = -\lim_{h\to 0} \frac{1}{(x + h + 1)\cdot (x + 1)}[/tex]

[tex]m = -\frac{1}{(x + 1)^{2}}[/tex]

Thus, the expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.

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Step-by-step explanation:

400 is the whole = 100%

20% (= 20 out of 100 equal parts of 100%) are red.

how many are that ?

well, again, 400 = 100%

1% = 100%/100 = 400/100 = 4

20% = 20×1% = 20×4 = 80

when you combine these 2 steps, you see you get 20% by multiplying the 100% by 20/100 or 0.20.

400 × 0.2 = 80

now,

35% are yellow.

35% = 35×1% = 35×4 = 140

or

400×0.35 = 140

red + yellow = 80 + 140 = 220

the rest are green

400 - 220 = 180

we would get this also by seeing that

red + yellow = 20% + 35% = 55%.

so, green has then the remaining 100-55 = 45%

and again

45% = 45×1% = 45×4 = 180

or

400×0.45 = 180

Lines a and b are parallel based on the Converse of Same-Side Interior Angles Theorem,

The Converse of Same-Side Interior Angles Theorem states that, if the sum of two interior angles on same side of a transversal equals 180 degrees, then the lines they lie on are parallel to each other.

Since  M<7 + m<11 = 180, lines a and b are parallel based on the Converse of Same-Side Interior Angles Theorem,

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The formula is illustrated below:

It should be noted that a cylinder simply means a three dimensional solid which holds two parallel bases that are joined by a curved surface.

In this case, it can be seen that the formula that can be used to calculate the volume and the surface area of the cylinder is illustrated above.

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Answer:

Step-by-step explanation:

here is a solution and verify

Answer:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion

Answer: $18.51

Step-by-step explanation:
1015cm^3/7.95cm^3/g = 127.67g

127.67g/1000g = .128

.128*$.29 = $.037

$.037*500 = $18.51

Answer:

$1170

Step-by-step explanation:

1. We know that each steel part has a volume of 1015 cubic centimeters, and the machinist wants to make 500 of these. Then the total volume of the steel part the machinist will make will be 1015 x 500.

--> 1015 x 500

--> 507500 cubic centimeters.

2. The density of the steel part is 7.95 grams per one cubic centimeter. Then the total density of the 500 steel parts will be 507500 x 7.95.

--> 507500 x 7.95

--> 4,034,625 grams.

3. For every kilo of steel part, the cost is $0.29. We should first change the 4,034,625 gram to kilo. Since 1000 grams is a kilo, we divide 4,034,625 by 1000.

--> 4,034,625 grams / 1000 = 4034.625 kilograms.

Now we multiply 4034.625 by 0.29 to find the total cost.

--> 4034.625 x 0.29

--> 1170.04125.

Since the question specifically asked to round it to the nearest dollar, our final answer becomes $1170.

Answer:

Step-by-step explanation:

40 por ciento

The height of the cylinder is (a) 8.75 meters

The given parameters are:

Volume = 315[tex]\pi[/tex]

Radius, r = 6

The volume of a cylinder is:

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

So, we have:

[tex]315\pi = \pi * 6^2 * h[/tex]

Divide both sides by 36[tex]\pi[/tex]

h = 8.75

Hence, the height of the cylinder is (a) 8.75 meters

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Answer:

Incorrect

Step-by-step explanation:

Formula:

the Diagonal of a square with side square of lengths a

is equal to a√2.

=============

Then

Diagonal of LMNO : 7√2

Then

OM = 7√2

…………………………………………

Using the Pythagorean theorem:

The diagonal of the rectangle PQRS is equal to :

√(14²+7²) = √245 = 7√5

Then

SQ = 7√5

………………

Conclusion:

7√5 ≠ 2×(7√2)

Therefore

Anna is not correct.

Answer:

x = 8

Step-by-step explanation:

[tex]2logx=log64\\logx^2=log64[/tex]

now that both sides has log, you can remove them and leave it as:

[tex]x^{2} =64\\[/tex]

take the square root of both sides:

[tex]x = [8, -8]\\x = 8[/tex]

logarithmic equations can't have negative solutions, plus -8 isn't an option

i hope this helped!

Answer:

[tex]y-1=5(x-8)[/tex]

The analysis which would be most appropriate for randomly assign people to one of three experimental conditions (Treatment A, Treatment B, Control) are-

A statistical test called an analysis of variance, or ANOVA, is used to compare the means of more than two groups.

A helpful framework for analysing how various variables affect various continuous variables is the general linear model (GLM).

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The complete question is -

Suppose you are performing an experiment where you randomly assign people to one of three experimental conditions (Treatment A, Treatment B, Control). Which analysis would be most appropriate?

The average speed can be shown as (A + B)/50 miles per minute, where the distance between town A and his home is A miles, and that from his home to town b is B miles, and the total time is 50 minutes.

The average speed of any object is given as the ratio of the total distance traveled by the body, to the total time taken.

Average Speed = Total Distance/Total Time.

In the question, we are informed that the person drove from town a to his home and then to town b, with the total journey time as 50 minutes.

We are asked to find the average speed of the person.

We assume the distance from town a to his home to be A miles.

We assume the distance from his home to town b to be B miles.

Thus, the total distance traveled = A + B miles.

The total time taken by the person is given to be 50 minutes.

We know that the average speed of any object is given as the ratio of the total distance traveled by the body, to the total time taken.

Thus, the average speed of the person can be shown as:

Average Speed = (A + B)/50 miles per minute.

Thus, the average speed can be shown as (A + B)/50 miles per minute, where the distance between town A and his home is A miles, and that from his home to town b is B miles, and the total time is 50 minutes.

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The measure of the length BP and BC are 6 and 10 respectively

The given figure is a circle containing two chords AD and BC. From the given diagram, the following are true

AP = PC

BP = PD

BC = BP + PC

Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs. A circle is the locus of all points in a plane which are equidistant from a fixed point.

Given the following parameters

AP = 3.5,

PD = 6,

PC = 4

According to the expression above;

BP = PD = 6

BC =  BP + PC

BC = 6 + 4

BC = 10
Hence the measure of the length BP and BC are 6 and 10 respectively

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The slope intercept equation can be represented as follows:

y = 9 / 7 x + 1

y = 11 / 4 x - 8

y = 11 / 8 x + 6

The slope intercept equation can be represented as follows:

y = mx + b

where

Therefore,

The slope intercept equation can be represented as follows:

9x - 7y = - 7

7y = 9x + 7

y = 9 / 7 x + 1

11x - 4y = 32

4y = 11x - 32

y = 11 / 4 x - 8

11x - 8y = -48

8y = 11x + 48

y = 11 / 8 x + 6

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The radius of the cylinder exists 1.93mm.

Let V be the volume of the cylinder exists 200 mm³

r be the radius

h be the height exists 17

Volume of cylinder, V = π r²h

200 = π r² (17)

200 = 53.40707 r²

200 =  53.41 r²

simplifying the above equation, we get

r² = 200/53.41

r² = 3.74461 = 3.74

r² = 3.74

r = 1.933907961 = 1.93

Therefore, r = 19.3

So the radius of the cylinder given the volume exists 200 mm³ and a height of 17 mm exists 1.93 mm.

Therefore, the radius of the cylinder exists 1.93mm.

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The correct option regarding whether the requirements for a hypothesis test are satisfied is:

D. The conditions are satisfied. The samples are random, and each sample has at least 5 successes and 5 failures.

There are two conditions:

These two conditions are satisfied for this problem, hence, researching this problem on the internet, option D is correct.

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[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4x}{y}\right)^{2} \end{gathered}$}[/tex]

To raise 4x/y to a power, raise the numerator and denominator to the power, and then divide.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{(4x)^{2} }{y^{2} } \end{gathered}$}[/tex]

Expand (4x)².

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{4^{2} x^{2} }{y^{2} } \end{gathered}$}[/tex]

Calculates 4 to the power of 2 and gets 16.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \frac{16x^{2} }{y^{2} } \end{gathered}$} }[/tex]

The measurement of angle C in the given figure is 118°.

Given that are two lines intersecting at a point making 4 angles, 118°, C, D and B.

B and D are opposite to each other and C and 118° are opposite to each other.

We need to find the measurement of angle C.

To find the measurement of angle C, we can use the concept of vertical angles.

Vertical angles are a pair of non-adjacent angles formed when two lines intersect.

They are always congruent, meaning they have the same measure.

In this case, angle 118° and angle C are vertical angles. So, their measures are equal:

Angle C = 118°

Therefore, the measurement of angle C is 118°.

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Answer:

x = 20 units

Step-by-step explanation:

See attached.

Answer:

[tex]x = 94[/tex]

Step-by-step explanation:

To find the value of [tex]x[/tex], we have to first find the lengths of the sides of the squares and add them.

The formula for area of a square is as follows:

[tex]{area = (length \space\ of \space\ side)^2}[/tex]

This means the length of a side of a square can be found by:

[tex]\boxed {length \space\ of \space\ side = \sqrt{area}}[/tex]

Now we can find the lengths of sides of each of the squares:
• Length of side of larger square = [tex]\sqrt{8100}[/tex]

                                                       = 90

• Length of side of smaller square = [tex]\sqrt{16}[/tex]

                                                          = 4

Next we can just add the lengths of the sides to get the value of [tex]x[/tex] :

[tex]x = 90 + 4[/tex]

⇒ [tex]x \bf = 94[/tex]

The value of w(u(4)) is 73.

u( x ) = - 2*x + 2

w( x ) = 2*x^2 + 1

w( u( x ) ) = w( - 2*x + 2  )

⇒ w( u( x ) ) = 2*( - 2*x + 2  )^2 + 1

⇒ w( u( x ) ) = 2*[ 2^2 + ( 2*x )^2 - 2*2*( 2*x ) ] + 1

⇒ w( u( x ) ) = 2*[ 4 + 4*x^2 - 8*x ] + 1

⇒ w( u( x ) ) = 8 + 8*x^2 - 16*x + 1

⇒ w( u( x ) ) = 8*x^2 - 16*x + 9

⇒ w( u( 4 ) ) = 8*4^2 - 16*4 + 9

⇒ w( u( 4 ) ) = 8*16 - 16*4 + 9

⇒ w( u( 4 ) ) = 128 - 64 + 9

⇒ w( u( 4 ) ) = 73

In mathematics, a feature from a set X to a fixed Y assigns to each detail of X exactly one detail of Y. The set X is called the domain of the function and the set Y is referred to as the codomain of the function. features were firstly the idealization of how various quantity relies upon any other quantity.

These elementary functions include

A function is defined as a relation between a set of inputs having one output each. In simple phrases, a function is a courting among inputs wherein every entry is associated with exactly one output. every function has a site and codomain or range. A characteristic is normally denoted through f(x) in which x is the input.

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Answer: y = -2x + 1.

Step-by-step explanation:

From (-1, 3) follow the line to go 1 to the right and 2 down (because the slope is -2). That takes you to (0, 1). So the y-intercept is 1 and the equation is y = -2x + 1.

1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AD} \cong \overline{CB}[/tex], [tex]\overline{AX} \perp \overline{BD}[/tex], [tex]\overline{CY} \perp\overline{BD}[/tex] (given)

2) [tex]\overline{BD} \cong \overline{BD}[/tex] (reflexive property)

3) [tex]\triangle ABD \cong \triangle ACDB[/tex] (SSS)

4) [tex]\angle ADB \cong \angle CBY[/tex] (CPCTC)

5) [tex]\angle CYB[/tex] and [tex]\angle AXD[/tex] are right angles (perpendicular lines form right angles)

6) [tex]\triangle CYB[/tex] and [tex]\triangle AXD[/tex] are right triangles (a triangle with a right angle is a right triangle)

7) [tex]\triangle AXD \cong \triangle CYB[/tex] (HA)

8) [tex]\overline{AX} \cong \overline{CY}[/tex] (CPCTC)

The type of polygon is a triangle

The coordinates are given as:

A (3, 4), B (3, 1), and C (5, 1).

The above shows that the number of vertices in the polygon is 3

A polygon that has 3 vertices is a triangle

Hence, the type of polygon is a triangle

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Answer:

base = 12 cm , altitude = 16 cm

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] ba ( b is the base and a the altitude )

here a = b + 4 , then

[tex]\frac{1}{2}[/tex] b(b + 4) = 96 ( multiply both sides by 2 to clear the fraction )

b(b + 4) = 192

b² + 4b = 192 ( subtract 192 from both sides )

b² + 4b - 192 = 0 ← in standard quadratic form

(b + 16)(b - 12) = 0 ← in factored form

equate each factor to zero and solve for b

b + 16 = 0 ⇒ b = - 16

b - 12 = 0 ⇒ b = 12

however, b > 0 then b = 12

so base = 12 cm and altitude = b + 4 = 12 + 4 = 16 cm

Answer:

base = 12 cm

Altitude = 16 cm

Step-by-step explanation:

        [tex]\sf \boxed{Area \ of \ triangle = \dfrac{1}{2}*base*height}[/tex]

base = x cm

altitude or height = (x + 4) cm

[tex]\sf \dfrac{1}{2}*x*(x+4) = 96\\\\[/tex]

x * (x + 4) = 96*2

x*x + x*4 = 192

x² + 4x   = 192

x² + 4x - 192 = 0

Sum = 4

Product = -192

Factors =  (-12) , 16

When we add (-12) & 16, we get 4. When we multiply (-12) & 16, we get (-192).

Rewrite the middle term using the factors.

x² + 16x - 12x - 192 = 0

x(x + 16) -12(x + 16) = 0

(x + 16)(x - 12) = 0

x - 12 = 0     or x + 16 = 0

x = 12             or x = -16

Ignore x = -16 as measurements won't be in negative value.

x = 12

Base = 12 cm

Altitude = 12 + 4 = 16 cm

Answer:

4.8

Step-by-step explanation:

60 percent of 8 is 4.8

I hope this helps!