1. State the expression by which you would multiply each side of the equation in order to solve the equation. What value(s) of x cannot be a solution? x/x+4 + 1/2 =1

Answer:

Step-by-step explanation:

Since the figure is symmetrical, angle MOA will be half of angle BOA, so will be 130°/2 = 65°. The tangent ratio is useful here. It tells you ...

  tan(MOA) = MA/OA

  AM = OA·tan(MOA) = 6·tan(65°)

  AM ≈ 12.87 . . . cm

__

Similarly, ...

  CM = 4·tan(65°)

  CM ≈ 8.578 . . . cm

__

The cosine ratio is useful for finding OD.

  cos(MOA) = OA/OM

  OM = OA/cos(MOA) = 6/cos(65°)

Similarly, ...

  DM = 4/cos(65°)

The length we want is OD, so ...

  OD = OM +DM = 6/cos(65°) +4/cos(65°) = 10/cos(65°)

  OD ≈ 23.66 . . . cm

Answer:

Area: 7, because there are 7 squares.

Perimeter: 14.

Step-by-step explanation:

Answer:

-2²

Explanation:

Doing -k² is the same thing as -(k²), so the answer will be negative. However, (-k)² will still be positive. -2² will equal -4.

Answer: The answer would be A.

The coordinates of the line are (0, 3) and (3, 0) hence, the line will pass through these points so, option A is correct.

A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Given:

y = negative x + 3

The above phrase can be written as,

y = -x + 3

Calculate the slope as shown below,

Slope = -1

The x-intercept can be calculated as,

0 = -x + 3  (y is zero at the x-axis)

x = 3

The x-intercept can be calculated as,

y = 0 + 3 (y is zero at the x-axis)

y = 3

Mark the coordinates (0, 3) and (3, 0) on the graph and join the points you will get the graph.

The graph is attached below.

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Answer:

768

Step-by-step explanation:

let C represent cost and w weight, then the equation relating them is

C = kw² ← k is the constant of variation

To find k use the condition w = 20, C = 4800, that is

4800 = k × 20² = 400k ( divide both sides by 400 )

12 = k

C = 12w² ← equation of variation

When w = 8, then

C = 12 × 8² = 12 × 64 = 768

Answer:

The estimated number of times the spinner will land on 3 is 20.

Step-by-step explanation:

The complete question is:

A four-sided spinner is provided. If Tom spins the spinner 80 times then work out an estimate for the number of times the spinner will land on 3.

Solution:

Assume that the four-sided spinner is unbiased.

That is all the four outcomes are equally likely to be selected.

The probability that the spinner lands on any of the four numbers is:

P(1) = P (2) = P (3) = P (4) = 0.25

It is provided that Tom spins the spinner n = 80 times.

The spinner can land on any of the four numbers independently.

The random variable X, defined as the number of times the spinner lands on 3, follows a Binomial distribution with parameters n = 80 and p = 0.25.

The expected value of X is:

[tex]E(X)=np[/tex]

        [tex]=80\times 0.25\\=20[/tex]

Thus, the estimated number of times the spinner will land on 3 is 20.

Answer:

There are 8 quarters and 2 nickels

Step-by-step explanation:

4 quarters for every 1 nickel

This means that for every 1 dollar, there are 5 cents

Double the statement above

1.05 x 2 = 2.10

There are 8 quarters and 2 nickels

Answer:

x = 60 and y = 100

Step-by-step explanation:

As shown in the table, you have: x + y = 160

Otherwise, you have x:y = 3:5 or x = 3y/5

=> 3y/5 + y = 160

or 8y/5 = 160

or y/5 = 20

or y = 20*5 = 100

=> x = 160 - y = 160 - 100 = 60

=> x = 60 and y = 100

Answer:

3 acute angles.

Step-by-step explanation:

Triangles have three angles. If any one angle is obtuse or right-angle, then the remaining two angles must be acute. Or else, all the 3 angles can be acute.

An example can be an equilateral triangle because it has 3 acute angles. Each angle is 60 degrees.

Answer:

Just count the unit squares

Step-by-step explanation:

If you learn this they may call u dumb but if your beginner then count the squares

Answer:

Mean: 12.9

Standard deviation: 14.8

Step-by-step explanation:

The mean is calculated adding all of the values and dividing by the number of elements:

[tex]m=\frac{2+3+7+12+1+4+27+49+11}{9}=\frac{116}{9}=12.9[/tex]

to find the standard deviation, we first find the variance (which is defined as the sum of all the elements subtracting the mean and squared and then dividing by the total amount of elements):

[tex]v=\frac{(2-12.9)^2+(3-12.9)^2+(7-12.9)^2+(12-12.9)^2+(1-12.9)^2+(4-12.9)^2+(27-12.9)^2+(49-12.9)^2+(11-12.9)^2}{9}\\[/tex]

[tex]v=\frac{1978.89}{9}\\[/tex]

[tex]v=219.88[/tex]

Noe that we have the variance, we can calculate the standard deviation.

The stardard deviation is defined as the squared root of the variance:

[tex]standardDeviation=\sqrt{v}[/tex]

we substitute the variance:

[tex]standardDeviation=\sqrt{219.88} \\standardDeviation=14.8[/tex]

Thus, the answer is:

Mean: 12.9

Standard deviation: 14.8

Answer:

250

Step-by-step explanation:

1000/4000

Answer:

∛50 cm, 2∛50 cm, 3∛50 cm

Step-by-step explanation:

V= wlh

V=300 cm³

w= 1/3l

h= 2/3l

---------

Answer:

Length is 11.052cm

Width is 3.684cm

Height is 7.386cm

Step-by-step explanation:

Let length be x, width y and height Z

Width (y) = X/3 , height (z) = 2x /3

volume =xyz

volume = x(x/3)(2/3)x

Volume = (2/9)x³

But Volume =300

300= (2/9)x³

300/(2/9) = x³ (make x³ the subject to find x )

1350 = x³

x=3√(1350)

x=11.052cm

Length is 11.052cm

Width = x/3 =11.052 /3

= 3.684cm

Height = 2x/3 = 2(11.052) /3

= 7.368cm

You can check it by multiplying LWH to see if you get 300 (the volume)

Answer: 22%

Step-by-step explanation: First, you have to add the percetages of the white and blue towels.

20+58=78

Now, you can simply subtract 78% from 100% to get your answer, 22%

Answer:

25.5x

Step-by-step explanation:

Simply convert the fraction into a decimal and add.

21/2x = 10.5x

10.5x + 15x = 25.5x

If you want to keep it in fraction form, 15 is 30/2, so,

30x/2 + 21x/2 = 51x/2

Answer:

51x/2

Step-by-step explanation:

Add it like a normal fraction equation

Have them both with the same denominator of 2

30/2 + 21/2

Add the numerators

51/2

Now put the x into the numerator since it started as in the numerator

Answer: 51x/2

Hope this helps!

Answer:

7.9km

Step-by-step explanation:

(a)See attached for the diagram representing this situation.

(b)

In Triangle ABC

[tex]\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ[/tex]

Next, we determine the value of Angle B.

[tex]\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ[/tex]

Finally, we find b.

[tex]\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)[/tex]

The distance between the small plane and the observation tower is 7.9km.

Answer:

Step-by-step explanation:

D is the answer

Answer:

see below

Step-by-step explanation:

2/3y + 15 = 9

Subtract 15 from each side

2/3y + 15-15 = 9-15

2/3y = -6

Multiply each side by 3/2 to isolate y

3/2 * 2/3y = -6 *3/2

y = -9

Answer:

y = - 9

Step-by-step explanation:

2/3y + 15 = 9

Subtract 15 on both sides.

2/3y = 9 - 15

2/3y = - 6

Multiply both sides by 3/2.

y = - 6 × 3/2

y = -18/2

y = -9

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete answer.

A given line has the equation 2x + 12y = −1.

What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?

General formula of equation of a line is exspressed as y = mx+c

m = gradient or slope  

c = intercept

Step 1: we need to first get the slope of the given equation of a line by rewriting the equation in standard form y = mx+c

2x + 12y = −1

12y = -1-2x

y = -1/12-2x/12

y = -1/6 x - 1/12

From the equation above, it can be seen that the slope (m) of tghe line is -1/6.

Since both lines are perpendicular, the slope of the unknown line will be;

M = -1/m

M = -1/(-1/6)

M = 6

Step 2: We will find the intercept c by substituting the point (0,9) and the slope into the equation y = mx+c

9 = 6(0)+ c

c = 9

Stwp 3: We will find the equation of the line perpendicular to the given line by substituting the value of m and c into the equation y = mx+c

y = 6x+9

y-6x = 9

The equation in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9) is y-6x = 9

Answer:

y-6x=9

Step-by-step explanation:

Answer:

-6,6

Step-by-step explanation:

x^2=36

6*6=36

-6*-6=36

Answer:

3

Step-by-step explanation:

=> 5xyz

Degree of polynomial is summing up the powers of the variable, so it will give you the degree of polynomial

=> Degree of this polynomial = 1+1+1

=> 3

Answer:

Step-by-step explanation:

After one year

A=p(1+r/n)^nt

=2000(1+0.03/12)^12*1

=2000(1+0.0025)^12

=2000(1.0025)^12

=2000(1.0304)

=$2060.8

After two-years

A=p(1+r/n)^nt

=2060.8(1+0.03/12)^12*2

=2060.8(1+0.0025)^24

=2060.8(1.0025)^24

=2060.8(1.0618)

=$2188.157

After three years

A=p(1+r/n)^nt

=2188.157(1+0.03/12)^12*3

=2188.157(1+0.0025)^36

=2188.157(1.0025)^36

=2188.157(1.0941)

=$2394.063

Amount in account after one year, two and three years are respectively  $2,060 , $2,121.8 and $2,185.45

Given:

Principal amount = $2,000

Rate of interest = 3% = 0.03

Amount in account after one year

A = P(1+r)ⁿ

A = 2,000(1+0.03)¹

A = 2,000(1.03)¹

A = 2,000(1.03)

A = $2,060

Amount in account after two year

A = P(1+r)ⁿ

A = 2,000(1+0.03)²

A = 2,000(1.03)²

A = 2,000(1.0609)

A = $2,121.8

Amount in account after three year

A = P(1+r)ⁿ

A = 2,000(1+0.03)³

A = 2,000(1.03)³

A = 2,000(1.092727)

A = $2,185.45

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Answer:

1

Step-by-step explanation:

PODMAS:-

16-3(8-3)²/5

=16-3(5)²/5

=16-3(25)/5

=16-3(5)

=16-15

= 1

Answer:

65

Step-by-step explanation:

=> [tex]\frac{16-3(8-3)^2}{5}[/tex]

=> [tex]\frac{13(5)^2}{5}[/tex]

=> [tex]\frac{13(25)}{5}[/tex]

=> 13 × 5

=> 65

Answer:

The variance rounded to the nearest tenth is 691.8

Step-by-step explanation:

Xavier's bowling scores:

135, 140, 130, 190, 112, 200, 185, 172, 163, 151, 149

No. of observations n = 11

[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{135+140+130+190+112+200+185+172+ 163+ 151+149}{11}\\Mean =157[/tex]

Formula of variance : [tex]\sigma^2=\frac{\sum(x_i-\bar{x})^2}{n}[/tex]

[tex]\sigma^2=\frac{(135-157)^2+(140-157)^2+(130-157)^2+(190-157)^2+(112-157)^2+(200-157)^2+(185-157)^2+(172-157)^2+(163-157)^2+(151-157)^2+(149-157)^2}{11}[/tex]

[tex]\sigma^2=\frac{7610}{11}[/tex]

[tex]\sigma^2=691.81[/tex]

Hence the variance rounded to the nearest tenth is 691.8

Answer:  A) 7 real zeros and 6 turning points at 0, 2, 4

Step-by-step explanation:

x⁷ - 6x⁶ + 8x⁵

The degree (largest exponent) is 7 so the maximum number of real zeros is 7.

Factor out x⁵

x⁵(x² - 6x + 8)

Factor the quadratic

x⁵(x - 2)(x - 4)

Set each factor equal to 0 and solve for x

x⁵ = 0         --> x = 0  (multiplicity of 5)

x - 2 = 0     --> x = 2

x - 4 = 0     --> x = 4

Answer:

A.) It is not in standard form because the degree of the first term is not greater than six.

Step-by-step explanation:

Answer:

230 cm squared

Step-by-step explanation:

Split the shape into a triangle and a rectangle

The area of a triangle is base x height / 2

20 x 9= 180/2= 90             (9 because you do 16-7 to find height of triangle)

Find the area of the rectangle=

7 x 20= 140

Add them up

140+90= 230cm squared

I hope this helped :)

Answer:

230 cm squared

Step-by-step explanation:

Answer:

x ≥ 2

Step-by-step explanation:

Step 1: Isolate x

6x ≥ 12

Step 2: Divide both sides by 6

x ≥ 2

And we have our answer!

Answer:

x ≥ 2

Step-by-step explanation:

6x+1 ≥ 13

Subtracting both sides by 1

6x ≥ 13-1

6x ≥ 12

Dividing both sides by 6

=> x ≥ 2