If a triangle’s original dimensions are 24 cm by 40 cm, which triangle would be an enlargement of the original by a scale factor of 2.2? A triangle with a base of 18.18 centimeters and a height of 10.9 centimeters. A triangle with a base of 42.2 centimeters and a height of 26.2 centimeters. A triangle with a base of 88 centimeters and a height of 52.8 centimeters. A triangle with a base of 200 centimeters and a height of 120 centimeters.

Answer:

f(x - n) - shift the graph n units right

f(x + n) - shift the graph n units left

f(x) - n - shift the graph n units down

f(x) + n - shift the graph n units up ----------------------------------------------------------------------------

Answer: shift the graph of y = 2(3)ˣ one unit right and four units up.

Answer:

a) [tex]cos(\alpha)=-\frac{3}{5}\\[/tex]

b)  [tex]\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

c) [tex]\frac{4+3\sqrt{3} }{10}\\[/tex]

d)  [tex]\alpha\approx 53.1^o[/tex]

Step-by-step explanation:

a) The problem tells us that angle [tex]\alpha[/tex] is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

[tex]tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}[/tex]

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

[tex]cos(\alpha)=-\frac{3}{5}[/tex]

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

[tex]cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find [tex]sin(\alpha -\beta)[/tex] by using the identity:

[tex]sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\[/tex]

Notice that we need to find [tex]sin(\alpha)[/tex], which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

[tex]sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}[/tex]

Then:

[tex]sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}[/tex]

d)

Since [tex]sin(\alpha)=\frac{4}{5}[/tex]

then  [tex]\alpha=arcsin(\frac{4}{5} )\approx 53.1^o[/tex]

Answer:

≈ 5.8

Step-by-step explanation:

Step 1: Round the fractions

29 1/5 = 146/5 = 29.2 ≈ 29

4 6/7 = 34/7 = 4.85714 ≈ 5

Step 2: Divide

29/5 = 5.8

The answer is under

Answer:

You can verify if lines are parallel if they have the same slope and different y-intercepts and if they don't intersect each other. You can also graph the 2 equations to see if they ever intersect.

Step-by-step explanation:

Answer:

C. Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles. Took the test just now and got it right

Step-by-step explanation:

Answer:

A number line is used in the mathematical positioning of real numbers that include the numbers from positive infinity to negative infinity. This includes rational, irrational, fractions, and whole numbers. In this case, we are given with an expression that we have to reduce to lowest terms: negative seven and one over two and +1. The first one is equal to -7.5 while the other one is equal to +1. Positive numbers lie on the right side of zero (center of the line) while negative numbers lie on the left on the other hand. -7.5 lies between -8 and -7 while +1 lies exactly between 0 and 2. Both of which are positive numbers

I hope that is what your asking...

Answer:

On which number line do the points represent negative seven and one over two and +1? The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of

Step-by-step explanation:

Hey there! :)

Answer:

56.7 kg.

Step-by-step explanation:

Use the density formula to solve for the mass:

D = m/V.

Rearrange in terms of mass, or 'm':

DV = m.

Solve for the volume:

0.06 × 0.9 × 1.5 = 0.081 m³.

Plug this into the equation along with the density:

700 × 0.081 = 56.7 kg.

Answer:

(1) N or n = 20

(2) [tex]\bar X \text{ or } \mu[/tex] = 43.4

(3) σ = 9.78 and s = 10.04.

Step-by-step explanation:

We are given with the following data set below;

{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}

(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.

(2) The formula for calculating Mean of the data, i.e. [tex]\bar X \text{ or } \mu[/tex] is given by;

        Mean  =  [tex]\frac{\sum X}{n}[/tex]

              =  [tex]\frac{51 +48+ 42+ 43+48+48+ 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42}{20}[/tex]

              =  [tex]\frac{868}{20}[/tex]  = 43.4

So, the value of [tex]\bar X \text{ or } \mu[/tex] is 43.4.

(3) The formula for calculating population standard deviation ([tex]\sigma[/tex]) is given by;

        Standard deviation, [tex]\sigma[/tex] =  [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{N} }[/tex]

             =  [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20} }[/tex]

             =  9.78

Similarly, the formula for calculating sample standard deviation (s) is given by;

        Sample Standard deviation, s =  [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex]

             =  [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20-1} }[/tex]

             =  10.04

Answer:

C. -3

Step-by-step explanation:

Plugging both of those points into the slope formula gets you a slope of -3.

Answer:27.5

Step-by-step explanation:

Answer:

B. 27.5

Step-by-step explanation:

37 is the Q2, which is the median,

Q1 is 27 + 28 / 2 = 27.5

Answer:

price paid of speakers= £40.5

price paid of headphones=£ 5.6

price paid of book=£6.65

price paid of mobile phone=£42

price paid of mouse=£ 15.75

price paid of DVD=£11.05

solution,

1. Cost of speakers:

Discount percent=10 %

Marked price=£45

discount amount= discount % of MP

=10% of 45

=£4.5

Selling price= MP - discount amount

=£45-£4.5

=£ 40.5

2. cost of headphones:

discount amount= discount% of MP

=20% of 7

=£1.4

Selling price= MP- Discount amount

=£7-£1.4

=£ 5.6

3. cost of books:

discount amount= discount percent of MP

= 30% Of 9.50

=£ 2.85

selling price= MP- Discount amount

= £ 9.50-£2.85

=£ 6.65

4. cost of mobile phone:

discount amount= discount% of MP

=40% of 70

=£ 28

selling price= MP- Discount amount

=£70-£28

=£ 42

5. cost of mouse:

discount amount= discount% of MP

= 25% of 21

=£ 5.25

selling price= MP- Discount amount

=£21-£5.25

=£ 15.75

6. cost of DVD:

discount amount= discount % of MP

= 15% of 13

= £ 1.95

selling price= MP- discount amount

=£ 13 -£ 1.95

=£ 11.05

Hope this helps...

Good luck on your assignment..

Answer:

[tex]5\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\sqrt{2\sqrt{8^2+15^2}+\sqrt{9^2+40^2}}=?\\\\1)\sqrt{8^2+15^2}=\sqrt{289}=17\\2)\sqrt{9^2+40^2}=\sqrt{1681}=41\\3)2\times17=34\\4)\sqrt{34+41}=5\sqrt{3}[/tex]

All Done!

Answer:

Your correct answer is 8.660254

Step-by-step explanation:

√2√82 + 152 + √92 + 402 = 8.660254

Answer:

The found values are:

A = 1/3

B = -8/3

Step-by-step explanation:

We know that general equation is given by:

y = mx + c

where m is the slope and c is a constant.

x + 3y = -5

y = -(1/3)x - 1/3(5)

Slop of the equation is -(1/3). As parallel line have same slope substitute it in the first equation:

Ax + By = 3

By = -Ax - 3

By = (1/3)x - 3

Hence, A = 1/3

Substitute point (-7,2) into the equation:

B(2) = (1/3)(-7) -3

B(2) = -7/3 - 3

B(2) = -16/3

B = -16/6

B = -8/3

Answer:

The value of a + 2z/ 2 in terms of a is (3a+4)/2

Step-by-step explanation:

least of 3 consecutive integers is a, and the greatest is z

if a is the least one

we know that integers differ by value of 1.

example -2, -1, 0, 1,2

they all differ by

then next consecutive integer will be a+1

third integer will be  second integer +1 = a+1 + 1 = a+2

Thus, 3 consecutive integer

a , a+1, a+2

but given that greatest is z

thus, a+2 is greatest and hence

a+2 = z

we have to find   value of a + 2z/ 2 in terms of a

a + 2z/ 2 = a + 2(a+2)/2 = (a+ 2a +4)/2 = (3a+4)/2.

The value of a + 2z/ 2 in terms of a is (3a+4)/2

Answer:

Park Q has greatest percentage of pink butterflies.

Step-by-step explanation:

Butterfly Park Survey Park           P     Q      R       S

No, of Pink Butterflies                  25    35   37      23

Total Number of Butterflies          53    64   75     55

Now we are supposed to find which park had the greatest percentage of pink butterflies

So, Percentage of pink butterflies in park P =[tex]\frac{25}{53} \times 100=47.169\%[/tex]

Percentage of pink butterflies in park Q =[tex]\frac{35}{64} \times 100=54.68\%[/tex]

Percentage of pink butterflies in park R= [tex]\frac{37}{75} \times 100=49.33\%[/tex]

Percentage of pink butterflies in park S= [tex]\frac{23}{55} \times 100=41.81\%[/tex]

So, Park Q has greatest percentage of pink butterflies.

So, Option B is true

Hence Park Q has greatest percentage of pink butterflies.

Answer:

11,8,5

Step-by-step explanation:

an=11-3(n-1)

Let n=1

a1 = 11 - 3(1-1)

    = 11 -0

    =11

Let n=2

a2 = 11-3(2-1)

     = 11 -3(1)

     = 8

Let n=3

a3 = 11-3(3-1)

    = 11 -3(2)

    = 11 -6

    =5

Answer:

The answer is 11,8,5

Step-by-step explanation:

that's the correct answer

Answer:

(a) y = -3/5 x + 13/5

(b) y = 5/3 x + 1/3

Step-by-step explanation:

(a) The slope of the tangent line is dy/dx.  Use implicit differentiation:

x² + y² + 4x + 6y − 21 = 0

2x + 2y dy/dx + 4 + 6 dy/x = 0

2x + 4 + (2y + 6) dy/dx = 0

x + 2 + (y + 3) dy/dx = 0

(y + 3) dy/dx = -(x + 2)

dy/dx = -(x + 2) / (y + 3)

At the point (1, 2), the slope is:

dy/dx = -(1 + 2) / (2 + 3)

dy/dx = -3/5

Using point-slope form of a line:

y − 2 = -3/5 (x − 1)

Simplifying to slope-intercept form:

y − 2 = -3/5 x + 3/5

y = -3/5 x + 13/5

(b) The normal line is perpendicular to the tangent line, so its slope is 5/3.  It also passes through the point (1, 2), so point-slope form of the line is:

y − 2 = 5/3 (x − 1)

Simplifying to slope-intercept form:

y − 2 = 5/3 x − 5/3

y = 5/3 x + 1/3

Answer: B

Step-by-step explanation:

Makes the most sense out of all the options because it’s the most random or unpredictable

Answer:

[tex]mGH=80^\circ[/tex]

Step-by-step explanation:

Circle F and J are congruent.

[tex]\angle DFE \cong \angle GJH[/tex]

Given that: m∠DFE = 80°

DFE is the central angle of the circle F.

The measure of arc GH is equal to the central angle of Circle J.

Since both circles are congruent

[tex]mGH=\angle DFE = 80^\circ[/tex]

The measure of arc GH is 80 degrees.

Answer:

Arc GH=80°

Step-by-step explanation:

Edge 2020

Step-by-step explanation:

Area 1 = the rectangle

8×3=24cm²

Area 2= semi circle

3.14r² 314/100×4×4 = 50.24cm²

add. 24+50.24 = 74.24cm² ( 10th)

Answer:

0.16 P(Yellow or Brown)=0.16

Answer: 0.44

Step-by-step explanation:

0.4 + 0.28 = 0.68

1.00 - 0.68 = 0.32

0.32 divided by 2.0 = 0.16

Total answer is 0.44

GLAD TO HELP:)

HAVE A NICE DAY!

BTW: I WAS DOING A TEST, BUT TOOK MY TIME TO HELP YOU! :)

PLEASE BRAINLEST ME!

Answer:

The third and fourth options.

Step-by-step explanation:

You simplify the inequality first...

-6x + 15 < 10 - 5x

-x < -5

x > 5

The first option is incorrect since it is less than.

The second option is basically -5x < 15; x > -3; that's incorrect.

The third option is basically -x < -5; x > 5; that is correct!

The fourth option is correct since it shows more than 5.

The fifth option is incorrect because it shows less than -5.

Hope this helps!

Answer: The answer is C and E

Step-by-step explanation:

Hope this helps;)

Answer:

1. equilateral triangle

2. rectangle

3. circle area

4. trapezoid

5. circle circumference

6. parallelogram

7. regular polygon

8. triangle

Hope that helps.

Answer:

D

Step-by-step explanation:

4x^4+3x^2-3x^3-3x+1

Answer: 5x + 1

Step-by-step explanation:

f(x) - g(x)

(3x + 2) - (-2x + 1)       Here you distribute the negative sign to (-2x + 1)

3x + 2 + 2x - 1            Here you combine like terms

5x + 1                         This is the answer.

Answer:

19.625 cm^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = 3.14 * 5^2 * .25

V =19.625 cm^2

Answer:

B

Step-by-step explanation:

The independent variable is the variable who's variation doesn't depend on the other. Therefore the answer is B because the amount of rooms doesn't depend on the charge, the charge depends of the amount of rooms.

Answer:

Step-by-step explanation:

find the slope

[tex]\frac{4-8}{-5-(-3)} =\frac{-4}{-2} \\\\slope=2\\y=mx+b\\y=2x+b\\[/tex]

take a coordinate to fill in

[tex](-5,4)\\y=-5\\x=4\\-5=2(4)+b\\-5=8+b-8 -8\\-13=b\\[/tex]

this means that the equation is y=2x-13

and if you add m and b

you get :-11

I HOPE THIS HELPS

Answer:

7/2

Step-by-step explanation:

Let $A = (-3,8)$ and $B = (-5,4)$. The midpoint of $\overline{AB}$ is $\left( \frac{(-3) + (-5)}{2}, \frac{8 + 4}{2} \right) = (-4,6)$.

The slope of $\overline{AB}$ is $\frac{8 - 4}{(-3) - (-5)} = 2$, so the slope of the perpendicular bisector of $\overline{AB}$ is $-\frac{1}{2}$. Therefore, the equation of the perpendicular bisector is given by

\[y - 6 = -\frac{1}{2} (x + 4).\]Isolating $y,$ we find

\[y = -\frac{1}{2} x + 4.\]

Answer:

I think it's A but I could be wrong

Answer: B

Step-by-step explanation:

A graph or table is a function if it passes the vertical line test. That means, each x and only 1 y. One x cannot have more than 1 y because, that means it does not pass the veritcal line test. In the vertical line test, the vertival line only passes through 1 point, not 2. Since we know that this graph does not pass the vertical in test, we can eliminate C and D. We can eliminate A because 2 y-values can be the same as lone as there have different x. B fits the description of what we see on the table. Therefore, the answer is B.