True or False ? A remainder of 1 or more in the process of doing synthetic division tells you that you have found a root of the polynomial function and a factor of the polynomial.

[tex]A_{\triangle}=\dfrac{1}{2}bh\\\\\text{We have}\ b=7cm,\ h=4cm\\\\\text{Substitute:}\\\\A_{\triangle}=\dfrac{1}{2}(7)(4)=\dfrac{28}{2}=\boxed{14\ cm^2}[/tex]

Answer: B: 56

Step-by-step explanation: First find f(g(x)). Where f(x) = -3x-4 and

g(x) = 2x-6. Replace X in f(x) with the equation for g(x)

f(g(x)) = -3(2x-6) -4. Then use the foil method and simplify.

= -6x+18-4

=-6x+14

Now sub. in the value of x with -7 and evaluate.

=-6(-7)+14

=42+14

=56

The slope of the equation x + 2y = 4, is -1/2 and y-intercept of the equation is 2.

When any equation is represented in the y = m x +c form, it is called the slope intercept form of the equation.

Here m is slope and c is constant.

The given equation of line,

x + 2y = 4,

To find the slope,  represent the equation in slop intercept form,

Simplify the equation,

x + 2y = 4

2y = -x + 4

y = -(1/2)x + 2

The slope of the equation is -1/2.

To find y-intercept, substitute x = 0,

y = -(1/2). 0 + 2

y = 2

The y-intercept of the equation is 2.

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Answer:

None of the Above

Step-by-step explanation:

As it is given that

cosФ= 3/2

and Ф lies in quadrant 4

Now in quadrant 4 we know that by the rules of trigonometry that

cos Ф is positive in 4th quadrant also in 4th quadrant

and sinФ is negative in 4th quadrant

also we know that by simple rules of trigonometry in a right angled triangle

cos Ф=[tex]\frac{Base}{Hypotenuse}[/tex] =[tex]\frac{3}{2}[/tex]

now from the law of trigonometry

cos²Ф+sin²Ф=1

From this we derive the value of sinФ

solving the equation

sin²Ф=1-cos²Ф

Putting in the values of cos Ф

sin²Ф=1-[tex](\frac{3}{2})^{2}[/tex]

sin²Ф=1-[tex](\frac{9}{4})[/tex]

solving the fraction

sin²Ф=[tex](\frac{4-9}{4})[/tex]

sin²Ф=[tex](\frac{-5}{4})[/tex]

so taking square root of both sides

[tex]\sqrt{sin^{2}\alpha}=\sqrt{\frac{-5}{4} }[/tex]

here

[tex]\alpha[/tex]=Ф

so it becomes

sin Ф=[tex]\frac{\sqrt{-5} }{2}[/tex]

as we know that in imaginary numbers

[tex]\sqrt{-1}[/tex] = ι

so the given becomes

sin Ф=[tex]\frac{{-5ι} }{2}[/tex]

Which is the value of sin Ф

And in the given values we can see that it is none of the values

Also seeing the question we can see that the question is absurd because

cos Ф= base / hypotenuse

in our question we can see that base =3 and hypotenuse = 2

but in real geometry this is the rule that hypotenuse can never be smaller then base either it is equal to base or greater then base

the formula for finding value of finding hypotenuse is

hypotenuse ² = base ² + perp ²

so this formula shows that if perp is 0 then hypotenuse will be equal to base

in other cases it would be greater then base

Answer:

- 1/ 2

Step-by-step explanation

-1\ 2

Use the Pythagorean identity, sin2Θ + cos2Θ = 1 to get sinΘ = ±1 - cos2Θ, then solve for sinΘ.

Answer: sqrt(19)/10

Step-by-step explanation:

sinx=0.9

x=arcsin(0.9)

Insert x for cos(x):

cos(arcsin(0.9)=

Use identify [tex]cos(arcsin(x))=\sqrt{1-x^{2} }[/tex], so

[tex]\sqrt{1-(\frac{9}{10})^{2}} =\sqrt{\frac{19}{100} } =\frac{\sqrt{19}}{10}[/tex]

Sorry if this is confusing.

Final answer:

To find cos X given sin X = 0.9, use the Pythagorean identity, solve for cos2 X, take the square root, and round to the nearest thousandth to get cos X ≈ 0.436.

Explanation:

To calculate the value of cos X when sin X= 0.9, we can use the Pythagorean identity which states that sin2X + cos2X = 1. First, square the sine value: (sin X)2 = 0.92 = 0.81. Then, we subtract this value from 1 to find (cos X)2: 1 - 0.81 = 0.19. Finally, we take the square root of 0.19 to find the value of cos X. Since sin X is positive and assuming X is an angle in the first quadrant, cos X will also be positive. So, cos X = √0.19 ≈ 0.436.

Therefore, the value of cos X, rounded to the nearest thousandth, is 0.436.

We know that : Sin²θ + Cos²θ = 1

Given : Sinθ [tex]\bf{= \frac{4}{7}}[/tex]

[tex]\bf{\implies (\frac{4}{7})^2 + Cos^2(\theta) = 1}[/tex]

[tex]\bf{\implies Cos^2(\theta) = 1 - \frac{16}{49}}[/tex]

[tex]\bf{\implies Cos^2(\theta) =(\frac{49 - 16}{49})}[/tex]

[tex]\bf{\implies Cos^2(\theta) =(\frac{33}{49})}[/tex]

[tex]\bf{\implies Cos(\theta) = (\pm)(\frac{\sqrt{33}}{7})}[/tex]

Given : θ lies in Quadrant II

We know that : Cosθ is Negative in Quadrant II

[tex]\bf{\implies Cos(\theta) = (-)(\frac{\sqrt{33}}{7})}[/tex]

Option 3 is the Answer

Answer:

Use point slope form, by finding the slope between two of the points given on the line you can then input it with one of the points into the formula. Then simplify to convert to slope-intercept form. You can then graph it easily. After which, you can convert to standard form by getting the variables to one side. Be sure in standard form to clear negatives x may have or any fractions x or y may have through multiplication.

Step-by-step explanation:

To write an equation for linear equations, we use one of three forms: standard, slope intercept, and point slope. Slope intercept and point slope are the most common. After we choose our form, we need to find the information required for that form. Point slope is easiest since it requires the slope/rate of change and any point on the line.

Point slope:[tex]y-y_1=m(x-x_1)[/tex]

We must find the slope using the slope formula.

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

We substitute [tex]x_1=-3\\y_1=1[/tex] and [tex]x_2=3\\y_2=5[/tex]

[tex]m=\frac{5-1}{3-(-3)}[/tex]

[tex]m=\frac{4}{3+3}=\frac{4}{6} =\frac{2}{3}[/tex]

We will substitute [tex]m=\frac{2}{3}[/tex] and [tex]x_1=-3\\y_1=1[/tex].

[tex]y-1=\frac{2}{3} (x-(-3))[/tex]

We can simplify to get slope intercept form:

[tex]y-1=\frac{2}{3} (x+3))[/tex]

[tex]y-1=\frac{2}{3}x+\frac{2}{3}(3)[/tex]

[tex]y-1=\frac{2}{3}x+2[/tex]

[tex]y-1+1=\frac{2}{3}x+2+1[/tex]

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

This is the slope intercept form. We can graph it by finding 3 on the y-axis. Plot a point there.  Then move up two units and to the right three units. Plot a point. Connect the points.

To convert to Standard Form, we will rearrange the equation with x and y on the same side.

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

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

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

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

[tex] 2x-3y=-9[/tex]

This is the standard form.

Answer:

angle(ADB)=angle(CBD)

ADC+DCB=180

AE=CE

Step-by-step explanation:

we will verify each options

option-A:

we know that

ABCD is a parallelogram

so, AD and BC are parallel

and alternate interior angles are always equal

so,

angle(ADB)=angle(CBD)

so, this is TRUE

option-B:

we know that

ABCD is a parallelogram

so, AD and BC are parallel

so, we get

ADC+DCB=180

so, this is TRUE

option-C:

Since, AC is a diagonal of parallelogram

so, E is the mid-point between AC

AE=CE

[tex]angle(DEC)\neq angle(DEA)[/tex]

so, this is FALSE

option-D:

Since, AC is a diagonal of parallelogram

so, E is the mid-point between AC

AE=CE

so, this is TRUE

option-E:

Since, AC and DB are diagonals of parallelogram

so, they can not be equal

so, this is FALSE

[tex]a_n=n^2-n\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}.\\\\n=1\to a_1=1^2-1=1-1=0\\\\n=2\to a_2=2^2-2=4-2=2\\\\n=3\to a_3=3^2-3=9-3=6\\\\n=4\to a_4=4^2-4=16-4=12\\\\n=5\to a_5=5^2-5=25-5=20\\\\Answer:\ \boxed{0,\ 2,\ 6,\ 12,\ 20}[/tex]

Answer: -1, 2, 7, 14, 23

Step-by-step explanation:

aₙ = n² - 2

for n=1

a₁ = 1² - 2 = 1-2= -1

for n=2

a₂ = 2² - 2 = 4-2 =2

for n= 3

a₃ =3² - 2 = 9-2=7

for n=4

a₄= 4² - 2 = 16-2=14

for n=5

a₅= 5² - 2=25-2=23

Therefore, the first five terms of the sequence are; -1, 2, 7, 14 and 23

Answer:the answer is D. All of the above

Step-by-step explanation:

Answer:

D) ALL OF THE ABOVE

Explanation:

In today's world, banks offer various variety of services at door-steps to attract customers However, some basic today's services offered by the banks to its customers are discussed below:

1. Home banking:

Home banking is the procedure of finishing financial affairs from an individual's own home as opposed to using a branch of a bank. It compromises actions such as transferring money, applying for loans, paying bills, making financial inquires and directing deposits.

2. Online banking:

Online banking is one of the famous service offered by banks nowadays that allows customers to access their account data by using the internet. Online banking is also known as “Internet banking”.

3. Priority banking:

Priority banking may include various services, but some of the famous services include online bill pay, financial consultation, free checking of account amount and information.

Answer:

∠NET = 63°

Step-by-step explanation:

We are given a figure with a circle A and a line ET which is tangent to the circle at the point T. Also, the measure of the angle TNG is given to be 27° and we are to find the measure of angle NET.

If we recall the point of tangency, we will remember that the point where a tangent touches the radius of a circle is always a right angle.

That makes the angle NTE to be 90°.

Putting the sum of these angles equal to 180 to get:

90 + 27 + ∠NET = 180

∠NET = 180 - 90 - 27

∠NET = 63°

Answer:

This means the function touches the x-axis at -1 but does not cross.

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

This means the function touches the x-axis at -1 but does not cross.

The value of x is -101/4 or the simplified form of the expression can be given as -1/2x = 101/8

This question relates to equation in mathematics and all we need to do is solve for x. But this requires some step by step process which are

The given equation is

[tex]2(\frac{x}{2} - 5) - \frac{3}{2} (x+\frac{7}{4} )\\[/tex]

[tex]2(\frac{x}{2} - 5) - \frac{3}{2} (x+\frac{7}{4} )\\\\(\frac{2}{2}x-10)-(\frac{3}{2}x-\frac{21}{8}) \\x- 10 -\frac{3}{2}x-\frac{21}{8}\\[/tex]

[tex]x-\frac{3}{2}x-10-\frac{21}{8}=0\\-\frac{1}{2}x =10+\frac{21}{8}\\-\frac{1}{2}x=101/8\\[/tex]

We have to divide through by coefficient of x

[tex]-\frac{1}{2}x =\frac{101}{8}\\(-1/2x)/(-1/2)=(101/8)/(-1/2)\\x=\frac{-101}{4} \\[/tex]

from the above calculation, the value of x is -101/4. The simplified form of the expression is -1/2x = 101/8

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Answer:

area = 6m + 51 feet²

Step-by-step explanation:

area = length × width = 3(2m + 17) = 6m + 51

Answer:

Let x represents the ounces of first spice.

From the given statements, you draw a table as shown below:

                           ounces of spice         Percentage           ounces of salt

First spice                 x                              3%                            0.03x

Second spice           175                            6%                          175(0.06)

Final  mixture          x+ 175                         5%                        (x+175)(0.05)

Now, to solve for x;

Final spice = First spice + second spice

[tex]0.03x+175(0.06) = (x+175)(0.05)[/tex]

[tex]0.03x + 10.5 = 0.05x + 8.75[/tex]

Subtract 10.5 on both sides we have;

[tex]0.03x + 10.5 -10.5= 0.05x + 8.75-10.5[/tex]

Simplify:

[tex]0.03x= 0.05x -1.75[/tex]

Subtract 0.05x on both sides;

[tex]0.03x - 0.05x= 0.05x -1.75-0.05x[/tex]

Simplify:

[tex]-0.02x= -1.75[/tex]

Divide both sides by -0.02, we get;

x = 87.5 ounces

Therefore, 87.5 ounces of spices i.e 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt

Step-by-step explanation:

[tex]4csc(2x) = 2csc^2(x) tan(x)[/tex]

We start with Left hand side

We know that csc(x) = 1/ sin(x)

So csc(2x) is replaced by 1/sin(2x)

[tex]4 \frac{1}{sin(2x)}[/tex]

Also we use identity

sin(2x) = 2 sin(x) cos(x)

[tex]4 \frac{1}{2sin(x)cos(x)}[/tex]

4 divide by 2 is 2

Now we multiply top and bottom by sin(x) because we need tan(x) in our answer

[tex]2\frac{1*sin(x)}{sin(x)cos(x)*sin(x)}[/tex]

[tex]2\frac{sin(x)}{sin^2(x)cos(x)}[/tex]

[tex]2\frac{1}{sin^2(x)} \frac{sin(x)}{cos(x)}[/tex]

We know that sinx/ cosx = tan(x)

Also  1/ sin(x)= csc(x)

so it becomes 2csc^2(x) tan(x) , Right hand side

Hence verified

Answer:

5y + 4 and 7y + 4 - 2y

Step-by-step explanation:

Look at  the second choice:-

5y + 4  and 7y + 4 - 2y

Simplifying the second expression:-

7y + 4 - 2y

= 5y + 4

So both expressions are equivalent . Therefore if you plug in 2 or 5 the results will be the same.

Answer:

Second option:

5y+4 and 7y+4-2y

Step-by-step explanation:

1. y=2→2y-1=2(2)-1=4-1→2y-1=3

y=2→3y-5+y→3(2)-5+2=6-5+2→3y-5+y=3

y=5→2y-1=2(5)-1=10-1→2y-1=9

y=5→3y-5+y→3(5)-5+5=15-5+5→3y-5+y=15

2y-1 is not equivalent to 3y-5+y when y=2 and y=5

2. y=2→5y+4=5(2)+4=10+4→5y+4=14

y=2→7y+4-2y→7(2)+4-2(2)=14+4-4→7y+4-2y=14

y=5→5y+4=5(5)+4=25+4→5y+4=29

y=5→7y+4-2y→7(5)+4-2(5)=35+4-10→7y+4-2y=29

5y+4 is equivalent to 7y+4-2y when y=2 and y=5

3. y=2→y+7=2+7→y+7=9

y=2→y+2+y→2+2+2→y+2+y=6

y+7 is not equivalent to y+2+y when y=2 and y=5

4. y=2→3y-4=3(2)-4=6-4→3y-4=2

y=2→3y-2+y→3(2)-2+2=6-2+2→3y-2+y=6

3y-4 is not equivalent to 3y-2+y when y=2 and y=5

[tex]adj(x) = \frac{\sqrt{7}}{3}[/tex]

[tex]opp(y) = \frac{\sqrt{2}}{3}[/tex]

adj² + opp² = hyp²

[tex](\frac{\sqrt{7}}{3})^{2} +(\frac{\sqrt{2}}{3})^{2} = hyp^{2}[/tex]

[tex]\frac{7}{9} +\frac{2}{9} = hyp^{2}[/tex]

1 = hyp²

1 = hyp

sin = [tex]\frac{opp}{hyp} =\frac{\sqrt{2}}{3}[/tex]

cos = [tex]\frac{adj}{hyp} =\frac{\sqrt{7}}{3}[/tex]

tan = [tex]\frac{opp}{adj} =\frac{\sqrt{2}}{sqrt\{7}=\frac{\sqrt{14}}{7}}[/tex]

csc = [tex]\frac{hyp}{opp} =\frac{3}{sqrt\{2}=\frac{3\sqrt{2}}{2}}[/tex]

sec = [tex]\frac{hyp}{adj} =\frac{3}{sqrt\{7}=\frac{3\sqrt{7}}{7}}[/tex]

cot = [tex]\frac{adj}{opp} =\frac{\sqrt{7}}{sqrt\{2}=\frac{\sqrt{14}}{2}}[/tex]

****************************************************************

Answer: 8052

Step-by-step explanation:

[tex]A = Pe^{kt}[/tex]

[tex]5500 = 5000e^{k(3)}[/tex]

[tex]\frac{5500}{5000} = e^{3k}[/tex]

[tex]1.1 = e^{3k}[/tex]

[tex]ln1.1 = lne^{3k}[/tex]

ln1.1 = 3k

[tex]\frac{ln1.1}{3}=k[/tex]

0.03177 = k

[tex]A = Pe^{0.03177t}[/tex]

[tex]A = 5500e^{0.03177(12)}[/tex]

[tex]A = 5500e^{0.3812}[/tex]

[tex]A = 5500(1.4641)}[/tex]

A = 8052.55

****************************************************************

Answer: (2, 9)

Step-by-step explanation:

3x - 8y = -66   →   2(3x - 8y = -66)   →   6x - 16y = -132

2x - 7y = -59   →  -3(2x - 7y = -59)   →  -6x + 21y = 177

                                                                        5y = 45

                                                                          y  = 9

2x - 7y = -59

2x - 7(9) = -59

2x - 63 = -59

2x         = 4

x          = 2

Answer: 27 grams

Step-by-step explanation:

m(x) = 64(0.75)ˣ

m(3) = 64(0.75)³

      = 64(.421875)

      = 27

Answer:

16

Step-by-step explanation:

sum of x and 14 is 18

x+14 = 18

Subtract 14 from each side

x+14-14 = 18-14

x = 4

product of x and 4

x*4

4*4

16

Answer:

16

18 minus 14 is 4. 4 times 4 is 16.

Answer:

240 pennies occupy (2/5 minus 1/10) the penny bank volume.

2/5 - 1/10 = 3/10 = .3

240 pennies .3 * the volume

Volume = 240 / .3 = 800 pennies

Step-by-step explanation:

A scale factor of 1/2 makes the triangle half the size of the original.

The original is 4 units tall, so 1/2 scale makes the new one 2 units tall.

It is 6 units long, so 1/2 would be 3 units long.

Now since the scale factor is centered at (-1,3) fine the midpoint between The top left corner of the triangle and the center point:

Midpoint ( -1-5/2 , 3+7/2)

Midpoint = (-6/2 , 10/2)

Midpoint = -3,5

This is where the top left corner of the scaled triangle would be.

See attached picture:

Answer: C) 1

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

One way is to graph the function f(x) = ln(x)/(x-1) and you'll see the curve slowly approach y = 1 when x approaches 1 from either side. Check out the attached image labeled "figure 1" for this graph.

---------

You can use a table to see this in action. See figure 2 (attached below as well).

-----------

Another alternative is to use L'Hospital's rule. This is because we get the indeterminate form 0/0 after plugging x = 1 into the original function.

if y = ln(x), then dy/dx = 1/x

If y = x-1, then dy/dx = 1

So f(x) = ln(x)/(x-1) becomes (1/x)/1 = 1/x

If you plug in x = 1, you get 1/x = 1/1 = 1.

Regardless of which method you use, the limiting value is 1

Answer:

C

Step-by-step explanation:

The lines drawn have the following features:

Since the equation of a line has the form y=mx+b where b is y-intercept and m is the slope, we can write

y=-2x+1

y=2x-3

This is the system of equations and is answer choice C.

Answer: C

Step-by-step explanation:

Slope-Intercept form of an equation is y = mx + b

Red line:

It crosses the y-axis at -3 so b = -3

Now count the rise over run from the b (0, -3) to another point (I chose (1, -1) because it was the next point on a lattice line). The rise is 2 and the run is 1. So. rise over run is 2/1  ⇒ m = 2

Equation: y = 2x - 3

Yellow line:

Follow the same steps as the Red line to get b = 1 and m = -2

Equation: y = -2x + 1

See the attached picture.

Answer:

5. 20

6. 30

7. 22

Step-by-step explanation:

5. The median is indicated by the line (and dot) in the middle of the box.

6. The maximum value is indicated by the extreme right end of the whisker.

7, The upper quartile is indicated by the right end of the box.

Answer:

5. 20

6. 30

7. 22

Step-by-step explanation:

5. The median is indicated by the line (and dot) in the middle of the box.

6. The maximum value is indicated by the extreme right end of the whisker.

7, The upper quartile is indicated by the right end of the box.

[tex]QR=\sqrt{68^2-60^2}\\QR=\sqrt{4624-3600}\\QR=\sqrt{1024}\\QR=32\\\\sinS=\frac{32}{68}\\sinS=\frac{8}{17}[/tex]

For this case, we have that by definition:

Be a rectangular triangle and an "x" angle.

[tex]Sine (x) = \frac {CO} {H}[/tex]

CO is the leg opposite the angle and H the hypotenuse

We want to find the Sine (S) according to the figure shown:

[tex]Sine {S} = \frac {QR} {68}[/tex]

We do not have the opposite leg, we must apply the Pythagorean theorem, which states:

[tex]H = \sqrt {(CO) ^ 2 + (CA) ^ 2}[/tex]

Where:

H: Hypotenuse

CO: Opposite leg

CA: Adjacent leg

In this case, we must find CO:

[tex]CO = \sqrt {H ^ 2- (CA) ^ 2}[/tex]

Where:

[tex]H = 68\\CA = 60[/tex]

Substituting:

[tex]CO = \sqrt {68 ^ 2-60 ^ 2}\\CO = \sqrt {4624-3600}\\CO = \sqrt {1024}\\CO = 32[/tex]

So, we have:

[tex]Sine (S) = \frac {32} {68}[/tex]

Answer:

[tex]Sine (S) = \frac {32} {68}[/tex]

[tex]Sine (S) = \frac {8} {17}[/tex]