Lynn tried to solve the equation 1/2 (×+14)=2. Explain where she made her mistake?

Answer:

7, 14, 21

Step-by-step explanation:

for n as term number

n = 1

7n = 7

n = 2

7n = 14

n = 3

7n = 21

hence the first 3 terms are 7, 14, 21

Answer:

Yes

Step-by-step explanation:

5 - 2 / 4 - 2 ---> Rise Over Run (first two coordinates)
3/2 --> Slope

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

-1 --> y-intercept

Answer:

x° = 26.5

Step-by-step explanation:

Each triangle is a right triangle; one angle = 90°, second angle = x° , and the   third angle = 63.5° because the 53° + the two angles adjacent to 53° is will = 180° which is the measure of a straight angle and those two angles are equal because the triangles are congruent by HA ; 180° - 53° =  127° ÷ 2 = 63.5°.

Now each triangle angles = 180° so 90° + x° + 63.5° = 180°; 153.5° + x° = 180;

x° = 180 - 153.5; x° =26.5°

Answer:

0.59

Step-by-step explanation:

The mechanical advantage of the pulley is 1.

The ratio of the force produced by a machine to the force applied to it.

[tex]\rm M.A. = \dfrac{F_o}{F_i}[/tex]

Here,  [tex]\rm F_o[/tex] is output force and [tex]\rm F_i[/tex] input force.

A pulley is given.

The mechanical advantage of the pulley.

We know by Newton's first law.

P = W

where P is applied force

and W is the weight of the object.

Then

[tex]\rm M.A. = \dfrac{F_o}{F_i}\\\\M.A. = \dfrac{P}{W}\\\\M.A. = \dfrac{P}{P}\\\\M.A. = 1[/tex]

The mechanical advantage of the pulley is 1.

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Step-by-step explanation:

It is assumed EF and CB are parallel.

The triangles ACB and AEF are similar by SAS as:

Confirm if corresponding sides have same ratios:

Confirmed

Answer:

[tex]x= \frac{9}{7}[/tex] ; [tex]y= -\frac{17}{7}[/tex]

Step-by-step explanation:

-3x - 1 = 2(2x-5)

-3x-1=4x-10

7x=9

x=9/7

y=2× [tex]\frac{9}{7}[/tex] - 5 = -17/7

Answer:

there are 2

Step-by-step explanation: happy to help

Answer:

B)

Step-by-step explanation:

Given f(x) = ( 7 - 8x )²

let f(x) be y,

y =  ( 7 - 8x )²  .............to find inverse we have to make x the subject.

±√y = 7 - 8x

-8x = √y  - 7

x = (±√y  - 7 ) / -8

Then,

Inverse of ( 7 - 8x )² is  [tex]-\frac{\sqrt{x}-7}{8},\:-\frac{-\sqrt{x}-7}{8}[/tex] and is a  function.

1) The measures of angles H and F are 121°, respectively.

2) The measures of angles U and V are 65° and 139°, respectively.

3) The missing angles are [tex]m \angle 1 = 72^{\circ}[/tex], [tex]m\angle 2 = 72^{\circ}[/tex], [tex]m\angle 3 = 47^{\circ}[/tex], [tex]m\angle 4 = 90^{\circ}[/tex], [tex]m\angle 5 = 18^{\circ}[/tex], [tex]m\angle 6 = 47^{\circ}[/tex] and [tex]m\angle 7 = 43^{\circ}[/tex].

4) The missing angles are [tex]m \angle 1 = 55^{\circ}[/tex], [tex]m\angle 2 = 35^{\circ}[/tex], [tex]m\angle 3 = 35^{\circ}[/tex], [tex]m\angle 4 = 90^{\circ}[/tex], [tex]m \angle 5 = 55^{\circ}[/tex], [tex]m \angle 6 = 67^{\circ}[/tex], [tex]m\angle 7 = 67^{\circ}[/tex], [tex]m\angle 8 = 23^{\circ}[/tex] and [tex]m \angle 9 = 23^{\circ}[/tex], respectively.

5) The measure of side [tex]QT[/tex] is [tex]\sqrt{105}[/tex].

6) The measure of side [tex]DF[/tex] is [tex]4\sqrt{26}[/tex].

7) The measure of side [tex]NP[/tex] is [tex]3\sqrt{65}[/tex].

8) The value of [tex]x[/tex] is 17.

9) The value of [tex]x[/tex] is 6.

10) The measure of angle EDC is 107°.

11) The measure of angle RST is 122°.

1) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the measures of angles H and F are 121°, respectively. [tex]\blacksquare[/tex]

2) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the measures of angles U and V are 65° and 139°, respectively. [tex]\blacksquare[/tex]

3) According to geometry, the sum of internal angles in a triangle equals 180° and the sum of internal angles in a quadrilateral equals 360°. The missing angles are [tex]m \angle 1 = 72^{\circ}[/tex], [tex]m\angle 2 = 72^{\circ}[/tex], [tex]m\angle 3 = 47^{\circ}[/tex], [tex]m\angle 4 = 90^{\circ}[/tex], [tex]m\angle 5 = 18^{\circ}[/tex], [tex]m\angle 6 = 47^{\circ}[/tex] and [tex]m\angle 7 = 43^{\circ}[/tex], respectively. [tex]\blacksquare[/tex]

4) According to geometry, the sum of internal angles in a triangle equals 180° and the sum of internal angles in a quadrilateral equals 360°. The missing angles are [tex]m \angle 1 = 55^{\circ}[/tex], [tex]m\angle 2 = 35^{\circ}[/tex], [tex]m\angle 3 = 35^{\circ}[/tex], [tex]m\angle 4 = 90^{\circ}[/tex], [tex]m \angle 5 = 55^{\circ}[/tex], [tex]m \angle 6 = 67^{\circ}[/tex], [tex]m\angle 7 = 67^{\circ}[/tex], [tex]m\angle 8 = 23^{\circ}[/tex] and [tex]m \angle 9 = 23^{\circ}[/tex], respectively. [tex]\blacksquare[/tex]

5) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

[tex]QT = \sqrt{PQ^{2}-PT^{2}}[/tex]

[tex]QT = \sqrt{13^{2}-8^{2}}[/tex]

[tex]QT = \sqrt{105}[/tex]

The measure of side [tex]QT[/tex] is [tex]\sqrt{105}[/tex]. [tex]\blacksquare[/tex]

6) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

[tex]DF = 2\cdot DH[/tex], [tex]DH = \sqrt{DE^{2}-EH^{2}}[/tex]

[tex]DF = 2\cdot \sqrt{DE^{2}-EH^{2}}[/tex]

[tex]DF = 2\sqrt{15^{2}-11^{2}}[/tex]

[tex]DF = 4\sqrt{26}[/tex]

The measure of side [tex]DF[/tex] is [tex]4\sqrt{26}[/tex]. [tex]\blacksquare[/tex]

7) In this case we need to apply Pythagorean theorem and triangle and quadrilateral properties to determine the missing side:

[tex]NK = 7\cdot x - 1[/tex], [tex]NM = 10\cdot x - 13[/tex], [tex]KM = 24[/tex], [tex]NK = NM[/tex], [tex]KP = \frac{KM}{2}[/tex]

[tex]NP = \sqrt{NK^{2}-KP^{2}}[/tex]

[tex]NP = \sqrt{[7\cdot (4)-1]^{2}-12^{2}}[/tex]

[tex]NP = 3\sqrt{65}[/tex]

The measure of side [tex]NP[/tex] is [tex]3\sqrt{65}[/tex]. [tex]\blacksquare[/tex]

8) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the value of [tex]x[/tex] is 17. [tex]\blacksquare[/tex]

9) According to geometry, the sum of internal angles in a quadrilateral equals 360°. Since the given figure is a kite-type rhombus, the value of [tex]x[/tex] is 6. [tex]\blacksquare[/tex]

10) According to geometry, the sum of internal angles in a triangle equals 180°. Hence, we have the following expressions:

[tex]m\angle EDC = 180^{\circ}-90^{\circ}-[2\cdot (2)+13][/tex]

[tex]m\angle EDC = 107^{\circ}[/tex]

The measure of angle EDC is 107°. [tex]\blacksquare[/tex]

11) According to geometry, the sum of internal angles in a triangle equals 180°. Hence, the angle RST is:

[tex]m\angle RST = 2\cdot (3\cdot 12 +25)[/tex]

[tex]m \angle RST = 122^{\circ}[/tex]

The measure of angle RST is 122°. [tex]\blacksquare[/tex]

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Answer:

s>761

Step-by-step explanation:

I think

Answer:

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

Step-by-step explanation:

[tex]\sqrt{6}[/tex] · [tex]\sqrt{6}[/tex] · [tex]\sqrt{5}[/tex] = 6[tex]\sqrt{5}[/tex]

Answer:

How do you calculate standard deviation without a data set?

You can calculate from other information.

For example, if you roll a standard die, you’re equally likely to get results 1, 2, 3, 4, 5 or 6. The mean result is 1+2+3+4+5+66=3.5 . The variance is 12+22+32+42+52+626−3.52=916−12.25≈2.9167 . Therefore the standard deviation is 2.9167−−−−−√=1.7078 .

Or suppose you know that the chance that a scratch-off lottery ticket returns some prize is 1 in 10. If you buy 900 tickets, on average you will get 90 that return some prize. The standard deviation of the number is 900×0.1×(1–0.1)−−−−−−−−−−−−−−−√=81−−√=9 .

In many other situations you can calculate standard deviation from the information you have. In other situations you can estimate a subjective standard deviation from what you don’t know. You might look at someone and guess their age at 35, with a subjective standard deviation of 4 years.

I Don't know the answer to this maths

Answer:

(10x - 9y)(10x + 9y)

Step-by-step explanation:

100x² - 81y² ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

100x² - 81y²

= (10x)² - (9y)²

= (10x - 9y)(10x + 9y)

Answer:

Step-by-step explanation:

Answer:

2 2/5 cubic cm

Step-by-step explanation:

to find a volume of a rectangular prism you multiply the length width and height together

so our equation looks like this

3 * (4/3) * (3/5)

we can split this equation up into

[3(4/3)] * 3/5

and do the 3 * (4/3) first

3 * (4/3) is 4 when you cross reduce

then multiply 4 by (3/5) and you get 12/5

12/5 or 2 2/5 is your answer

Answer:

The second option is correct.

Step-by-step explanation:

[tex]Solution,\\Breadth(b)=5cm\\Length (l)=4cm+6cm=10cm\\Now ,\\Area=l*b=5cm*10cm=50cm^{2}[/tex]

Answer:

um

Step-by-step explanation:

i dont know

Answer:

80.

Step-by-step explanation:

Hope it helps

my first answer was 125% but then I realised I seen the wrong number sorry my eyes are not very good lol

Answer:

(2, 5)

Step-by-step explanation:

The x coordinate is the number inside the parentheses, but with the opposite sign, 2

The y coordinate is the number at the end

Answer:

vertex: (2, 5)

Step-by-step explanation:

y=3(x−2)2+5

this is a parabola because of one variable squared and the other one is not so now write it in the standard form of parabolas which it is = to

______

Vertical :

(x−h)2=4p(y−k)

Horizontal:

(y−k)2=4p(x−h)2

vertex = (h, k)

______

this y=3(x−2)2+5 equation is vertical since x is squared

subtract 5 from both sides:

y−5=3(x−2)2

divide both sides by 3:

(y−5)13=(x−2)2

vertex:

(2,5)

Answer:

6 minutes per mile

Step-by-step explanation:

72 divided by 12 equals 6

Polynomials are algebraic expressions represented by variables and coefficients.

This is the interval, where the open seats increase the same time the time in minutes increases.

From the graph, the open seats increases at the interval (100, 600)

This is the first point where the curve changes its direction from decreasing values to increasing values

From the graph, the curve changes its direction at point (25,100)

Hence, the first meeting ended at 10:25 AM

From the graph, we have:

(x,y) = (5, 700)

Hence, there were 700 open seats at 10:05 AM

At 10:00 AM, we have:

(x,y) = (0,800)

At 10:25 AM, we have:

(x,y) = (25,100)

So, the average rate of change is:

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

This gives

[tex]m = \frac{100 - 800}{25 - 0}[/tex]

[tex]m = \frac{-700}{25 }[/tex]

[tex]m = -28[/tex]

Hence, the average rate of change from 10:00 AM to 10:25 AM is -28 people per minute

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Answer:

RP/QR = OP/NO

Step-by-step explanation:

RP corresponds to OP, QR corresponds to NO. So, RP/QR = OP/ON

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &3.6\\ t=\textit{elapsed time}\dotfill &45\\ h=\textit{half-life}\dotfill &14.4 \end{cases} \\\\\\ A=3.6\left( \frac{1}{2} \right)^{\frac{45}{14.4}}\implies A=3.6\left( \frac{1}{2} \right)^{3.125}\implies A\approx 0.41265[/tex]

After 45 years, approximately 0.225 grams of the original 3.6 grams of plutonium-241 will remain.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

To solve this problem, we can use the formula for radioactive decay:

[tex]N = N_0 \times (\dfrac{1}{2})^{\frac{t}{T}[/tex]

Where:

N = the amount of radioactive material remaining after time t

N₀ = the initial amount of radioactive material

t = time

T = the half-life of the radioactive material

We know that the half-life of plutonium-241 is 14.4 years, and we want to find the amount of plutonium-241 remaining after 45 years. We also know that the initial amount of plutonium-241 is 3.6 grams. So we can plug these values into the formula:

[tex]N = 3.6 \times (\dfrac{1}{2})^\frac{45}{14.4}[/tex]

N ≈ 0.225 grams

Therefore, after 45 years, approximately 0.225 grams of the original 3.6 grams of plutonium-241 will remain.

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