Follow the steps to solve for the variable in this two step equation 5x-10=0

[tex]\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 = \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 = -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}[/tex]

Answer:

AC = 20°

Step-by-step explanation:

180° (total angle amount of a triangle) - 70° + 90° (right angle) = ac

AC = 20°

Hope this helps!

Answer:

For sample size n = 39 ; P(X < 31.6) = 0.9756

For sample size n = 76 ; P(X < 31.6) = 0.9970

Step-by-step explanation:

Given that:

population mean μ = 31

standard deviation σ = 1.9

sample mean  [tex]\overline X[/tex] = 31.6

Sample size n                 Probability

39

76

The probabilities that the sample mean is less than 31.6 for both sample size can be computed as  follows:

For sample size n = 39

[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]

[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{6.245}})[/tex]

[tex]P(X < 31.6) = P(Z< 1.972)[/tex]

From standard normal  tables

P(X < 31.6) = 0.9756

For sample size n = 76

[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]

[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{8.718}})[/tex]

[tex]P(X < 31.6) = P(Z< 2.75)[/tex]

From standard normal  tables

P(X < 31.6) = 0.9970

Answer:

5400 cycles

Step-by-step explanation:

You have the following function:

[tex]V(t)=220sin(180\pi t)[/tex]

where t is in seconds.

In order to find the number of cycles in 1 minute, you first  calculate the frequency of the function, which is given by:

[tex]f=\frac{180\pi}{2\pi}=90s^{-1}[/tex]

The number of cycles is then given by:

[tex]n=ft=(90s^{-1})(60s)=5400\ cycles[/tex]

There are 5400 cycles in 1 minute

Answer: £4

Step-by-step explanation:

From the question, we are informed that when the normal price of a book is reduced by 30%, then the sale price of the book is £2.80.

Since the normal price of a book is reduced by 30%, that means the book is sold at (100% - 30%) = 70% of its normal price.

Let the normal price of the book be y.

70% of y = £2.80

70/100 × y = £2.80

0.7 × y = £2.80

0.7y = £2.80

y = £2.80/0.7

y = £4

The normal price of the book is £4.

Answer:

q = 108-n

Step-by-step explanation:

Given: 108 coins containing only quarters and nickels

q = 108-n

since total number of coins is 108, and n= number of nickels

If you want to know how many of each kind of coin, read on:

First solve the number of quarters and nickels.

If all 108 coins are quarters, the value is 108*0.25 = $27

Since this value exceed the actual by 27-21 = $6,

we replace a number of quarters by nickels.

Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.

So it will take 6/0.2 = 30 replacements.

Therefore there are 108-35 = 78 quarters and 30 nickels.

The solution is : q = 108-n, is the value could replace q on the chart.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Given:

108 coins containing only quarters and nickels

q = 108-n

since total number of coins is 108, and n= number of nickels

If you want to know how many of each kind of coin, read on:

First solve the number of quarters and nickels.

If all 108 coins are quarters, the value is 108*0.25 = $27

Since this value exceed the actual by 27-21 = $6,

we replace a number of quarters by nickels.

Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.

So it will take 6/0.2 = 30 replacements.

Therefore there are 108-35 = 78 quarters and 30 nickels.

The solution is : q = 108-n, is the value could replace q on the chart.

To learn more on multiplication click:

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Answer: The store must sell 40 bikes.

Step-by-step explanation:

y=60x+2400

y=120x

120x=60x+2400

-60x on both sides

60x=2400

divide 60 on both sides

2400/60=40

x=40  

Answer:

$96.00

Step-by-step explanation:

Perimeter formula, 2w+2l

2(23)+2(25)=96 feet

1$ per foot

96 feet,

so $96

Answer:

I think it 96.00

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Greetings from Brasil...

Here we have application of Trigonometry

COS β = adjacent side ÷ hypotenuse (H)

bringing to our problem....

COS A = AC ÷ H

But we dont have AC.... We have to use Pitagoras:

AB² = AC² + BC²

AC² = AB² - BC²

AC = √(AB² - BC²)

AC = √(10² - 8²)

AC = √(100 - 64)

AC = √36

So

COS A = AC ÷ H  ⇔ COS A = AC ÷ AB

COS A = 6/10

Answer: B) 3/5

Step-by-step explanation:

Cos = adjacent/hypotenuse

Thus, the cos is AC/AB.

Because of Pythagorean Theorem, AC^2=AB^2-BC^2.  Let AC be x.

[tex]x^2=10^2-8^2\\x^2=100-64\\x^2=36\\x=6[/tex]

Thus, the cos is 6/10, or 3/5

Answer:

1. a. b = - 8

b. x = 8

c. x = 11

d. x = 5

2. 12 soccer balls and 8 basketballs can be purchased.

Step by step explanation

a. [tex] - 14 + 6b + 7 - 2b = 1 + 5b[/tex]

Calculate the sum

[tex] - 7 + 6b - 2b = 1 + 5b[/tex]

Collect like terms

[tex] 7 + 4b = 1 + 5b[/tex]

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S and change its sign

[tex]4b - 5b = 1 + 7[/tex]

Collect like terms

[tex] - b = 8[/tex]

Change the signs on both sides of the equation

[tex]b = - 8[/tex]

-----------------------------------------------------------------

b. [tex] \frac{5x + 10}{ - 6} = - 5[/tex]

Apply cross product property

[tex]5x + 10 = - 5 \times ( - 6)[/tex]

Multiply the numbers

[tex]5x + 10 = 30[/tex]

Move constant to R.H.S and change its sign

[tex]5x = 30 - 10[/tex]

Calculate the difference

[tex]5x = 20[/tex]

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{20}{5} [/tex]

Calculate

[tex]x = 4[/tex]

----------------------------------------------------------------

c. [tex] - 15 = \frac{ - 8x - 17}{7} [/tex]

Apply cross product property

[tex] - 15 \times 7 = - 8x - 17[/tex]

Multiply the numbers

[tex] - 105 = - 8x - 17[/tex]

Swap the sides of the equation

[tex] - 8x - 17 = - 105[/tex]

Move constant to R.H.S and change its sign

[tex] - 8x = - 105 + 17[/tex]

Calculate

[tex] - 8x = - 88[/tex]

Change the signs on both sides of the equation

[tex]8x = 88[/tex]

Divide both sides of the equation by 8

[tex] \frac{8x}{8} = \frac{88}{8} [/tex]

Calculate

[tex]x = 11[/tex]

------------------------------------------------------------------

D. [tex]5 = 6x + 5(x - 10)[/tex]

Distribute 5 through the parentheses

[tex]5 = 6x + 5x - 50[/tex]

Collect like terms

[tex]5 = 11x - 50[/tex]

Swap both sides of the equation

[tex]11x - 50 = 5[/tex]

Move constant to R.H.S and change its sign

[tex]11x = 5 + 50[/tex]

Calculate the sum

[tex]11x = 55[/tex]

Divide both sides of the equation by 11

[tex] \frac{11x}{11} = \frac{55}{11} [/tex]

Calculate

[tex]x = 5[/tex]

------------------------------------------------------------------

2.

Solution,

No.of students in soccer = x

No.of students in basketball = y

Total no.of students = 20

i.e x + y = 20 → equation ( i )

Cost of soccer ball = $ 7

Cost of basketball = $ 10

Total budget = $ 164

i.e 7x + 10 y = 165 → equation ( ii )

In equation ( i ),

x + y = 20

Move 'y' to R.H.S and change its sign

x = 20 - y

Put the value of x in equation ( i )

[tex]7(20 - y) + 10y = 164[/tex]

[tex]140 - 7y + 10y = 164[/tex]

[tex]3y = 164 - 140[/tex]

[tex]3y = 24[/tex]

[tex]y = \frac{24}{3} [/tex]

[tex]y = 8[/tex]

Now, put the value of y in equation ( i ) ,

x + y = 20

[tex]x + 8 = 20[/tex]

[tex]x = 20 - 8[/tex]

[tex]x = 12[/tex]

Hence, 12 soccer balls and 8 basketballs can be purchased.

Hope this helps...

Best regards!!

Answer:

1. b = -8

2. x = 8

3. x = 11

4. x = 5

hope that helpwd

Answer:

a) More.

b) Less.

c) More.

Step-by-step explanation:

a) If you invest $10 with an interest rate of 50% (that's very high I know XD), you would earn 10 / 2 = $5 in interest. If you invest $100 with an interest rate of 50%, you would earn 100 / 2 = $50 in interest. So, the more principal invested, the more interest earned.

b) Let's say you are investing $100. If there is an interest rate of 50%, as stated before, you would earn $50 in interest. If the interest rate were lowered to 25%, you would earn 100 / 4 = $25 in interest. So, the lower the interest rate, the less the interest.

c) The same exact thing as part a.

Hope this helps!

Answer:

Step-by-step explanation:

the upper left graph is the correct answer

because "... or equal to" always represents a filled dot, while just "greater/less than" represents blank dot

Answer:

Shaded area: 70cm^2

Step-by-step explanation:

Whole=120cm^2

White Square=

10-2.5-2.5=5

12-1-1=10

5✖️10=50cm^2

Whole-white=70cm^2

Answer:

C= 3g

Step-by-step explanation:

Answer:

Length of first leg = 1.4feet

Hypotenuse = 4.2feet

Explanation:

Since we are dealing with a right angled triangle, we will apply the Pythagoras theorem to solve the question. According to Pythagoras theorem, the square of the hypotenuse is equal to the sum if the square of the other two legs.

Mathematically, a² = b²+c² where a is the hypotenuse and b, c are the other two legs.

From the question, since hypotenuse of a right triangle is three times the length of its first leg, then a = 3b.

Also the other leg is four feet i.e c= 4

Substituting this values into the Pythagoras formula;

a²=b²+c²

(3b)² = b²+4²

9b² = b²+16

9b²-b² = 16

8b² = 16

b² = 16/8

b² = 2

b = √2

b = 1.4

Since a = 3b

a = 3(1.4)

a = 4.2

Hence, the length of the first leg is 1.4feet and that of the hypotenuse is 4.2feet both to the nearest tenth.

Answer:

(0,-7)

Step-by-step explanation:

If nay point is form (x,y)

x is abscissa can be also called x axis coordinate

y is ordinate can be also called y axis coordinate

ordiantes are points lying on y axis.

For any point lying on y axis, its x-axis coordinate will be 0

given that ordinate is -7. it means that value of y coordinate is -7

Thus,  coordinates of the point is (0,-7)

Answer:

2, 3 , 5, 7

Step-by-step explanation:

2(x - 2)/3 < (x + 1)/2 < 3(5x + 6)/4

Considering:

    2(x - 2)/3 < (x + 1)/2

<=>(2x - 4)/3 < (x + 1)/2

<=> (2x - 4)*2 < (x + 1)*3

<=> 4x - 8 < 3x + 3

<=> 4x - 3x < 8 + 3

<=> x < 11

Considering:

     (x + 1)/2 < 3(5x + 6)/4

<=>(x + 1)/2 < (15x + 18)/4

<=>(x + 1)*4 < (15x + 18)*2

<=> 4x + 4 < 30x + 36

<=> 4x - 30x < 36 - 4

<=> -26x < 32

<=> 26x > -32

<=> x > -32/26

=> -32/26 < x < 11

The prime numbers satisfy the above inequalities: 2, 3 , 5, 7

Answer:

x=1/4c+1/4k

Step-by-step explanation:

4x-c=k

move c over

4x=c+k

then divide by 4

x=1/4c+1/4k

hope this helps

Answer:

12.65

Step-by-step explanation:

In the case of the blue triangle, to calculate the rise, which would be the increase, therefore it would be the hypotenuse formed by the arrow.

We have to Pythagoras is:

h ^ 2 = a ^ 2 + b ^ 2

In this case:

a (x-axis) = 4

b (y-axis) = 12

replacing:

h ^ 2 = 4 ^ 2 + 12 ^ 2

h ^ 2 = 160

h = 12.65

Which means that the rise in the blue triangle is 12.65 units

Answer:

80

Step-by-step explanation:

t is important to note that a square of any non-zero integer is positive, and therefore there is no advantage in using negative integers instead of positive integers to attain the greatest difference of squares. So we will not consider negative integers.

The greatest value of a^2 - b^2 occurs when a^2 is at its largest and b^2 is at its smallest.

The larger a, the larger a^2:

8 ^ 2 = 64

9 ^ 2 = 81

10 ^ 2= 100

Since a^2 can have at most two digits, a=10 is too large, and so a=9 is the largest integral value of a we can use.

Now, b^2 is at its smallest when b is closest to zero on the number line (the further b gets from zero, the larger its square becomes):

2 ^ 2 = 4

1 ^ 2 =1

0 ^ 2 = 0

Remember to go back to the original problem sometimes, to make sure you are taking everything into account. It states b doesn't =0, and therefore the b=1 is the closest b can get to zero as an integer. So, the greatest difference between b^2 and a^2 is when b=1 and a=9, giving the result:

a^2-b^2 =9^2-1^2 =81-1= 80.

So, 80 is your answer.

Answer:

942.5 in²  

Step-by-step explanation:

The formula for the area (A) of a sector of a circle is

A = ½r²θ

where θ is the angle in radians.

1. Convert the angle to radians

θ = 125°  

[tex]\theta = 125^{\circ} \times \dfrac{\pi \text{ rad }}{180^{\circ}} =\frac{25}{36} \pi\text{ rad}[/tex]

2. Area swept out by wiper arm

A = ½r²θ = ½ × (30 in)² × θ = ½ × 900 in²× θ = 450 θ in²

3. Area missed by wiper

A = ½r²θ = ½ × (6 in)² × θ = ½ × 36 in²× θ = 18 θ in ²

4. Area covered by wiper

A = 450 θ in² - 18 θ in² = 432 θ in²

5. Insert the value of θ

A = 432 × 25/36 π in² = 300π in² ≈ 942.5 in²

The area swept out by the wiper blade is 942.5 in².

Answer:

0.5333333333 or 0.53 when simplified.

Step-by-step explanation:

8/15 is simply 8÷15

15 into 8 is not possible so you annex a zero and write a decimal point.The 8 now becomes 80. We now say 80÷15,the answer is 5 because 15x5=75.The remainder is five.We annex another zero and it becomes 50,50÷15=3

I hope this helps.

Answer:

0.2

Step-by-step explanation:

it works out to be 0.2 as a decimal and 20% as a percentage.

Answer:

.2

Step-by-step explanation:

Answer:

9 and 23

Step-by-step explanation:

Let x be smaller length in inches.

x+3x-4=32

4x=36

x=9

9*3-4=23

So they're 9 and 23 inches long.

The lengths of the two parts of the pipe are 9 and 23 inches long.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Let x be the smaller length in inches.

x + 3x - 4 = 32

4x = 36

x  =9

Now substitute;

9*3 - 4 = 23

Hence, the lengths of the two parts of the pipe are 9 and 23 inches long.

Learn more about the unitary method;

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Answer:

25.52791653032955454422437424679625318128649677442393276098...

Step-by-step explanation:

You can just paste this into wolframalpha.

Answer: 970.72312

Step-by-step explanation:

Straightforward operation.

Answer:

the long diagonal d=15.49 ( rounded to the nearest hundredth)

the shortest d=√136-120(cos 30)=5.663 ( rounded to the nearest hundredth)

Step-by-step explanation:

Area=height * base

30=h*6

h=30/6=5 cm

height=asinФ

sinФ=5/10=1/2 (Ф=30)

alternate angle=180

180-30=150 degrees

diagonal²=a^2+b^2-2abcos150

d²=10²+6²-2(10)(6)(-√3/2)

d=√136+60(√3)

the long diagonal d=15.49 ( rounded to the nearest hundredth)

the shortest d=√136-120(cos30)=5.663

Answer:

your answer is k

Step-by-step explanation:

not all the isosceles triangles are similar

Answer:

5.65%

Step-by-step explanation:

Principal=$600

Time=20 years

FV=600*3=$1800

n=1

r=?

r= n[(A/P)^1/nt - 1]

=1{(1800/600)^ 1/1*20 - 1}

={(3)^1/20-1}

=3^0.05-1

=1.0565-1

=0.0565

rate=0.0565*100

=5.65% to the nearest hundredth percent

Answer:

86

Step-by-step explanation:

We can set the first digit as (10x+y)

We can interchange it to be (10y+x)

X is the second digit and Y is the first.

1) (10x+y) +(10y+x) =154

2) 11x+11y=154

3) 11(x+y) =154

4) x+y=14

5) x+x+2=14

6) 2x=12

7) x=6

8) y=6+2=8 , so y =8