When dividing exponents with the same base, what operation do we use
with the exponents? (the quotient rule)

Answer:

x= -8 , y = 5

x= 25/4 , y = 1/4

Step-by-step explanation:

substitute first eqn into the second eqn:

(7 - 3y)^2 -y^2 = 39

49 - 42y + 9y^2 - y^2 = 39

8y^2 - 42y +10 =0

4y^2 - 21y + 5 = 0

(4y-1) (y-5) = 0

y= 1/4 , 5

when y=1/4

x = 7- 3/4

=25/4

when y= 5

x = 7- 15

= -8

The required solution of the given simultaneous equations are x = -8, 25/4 and y = 5, 1/4.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
x = 7 – 3y - - - - -(1)
x² - y² = 39 - - - - (2)

Put x from equation 1 in equation 2

(7 - 3y)² -y² = 39

49 - 42y + 9y² - y² = 39

8y² - 42y +10 =0

4y² - 21y + 5 = 0

(4y-1) (y-5) = 0

y= 1/4 , 5

Substitute this values in the equation 1,
x = -8 and 25/4

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Answer:

I am not good at word problems but I think I found some good examples

Step-by-step explanation:

Durain beans cost $9 per pound and they sold 11 pounds.

Multiply the cost by the amount sold: 9 x 11 = $99

Subtract that from the total sold:

196 - 99 = $97

Now divide the amount left by the cost per pound for Ice cream beans:

97 / 10 = 9.7 pounds.

The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:

It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.

Based on the information given, the correct expression that can be used to solve the question should be:

65 - (5.50b + 7.5)

In conclusion, the correct options are B and C.

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Answer:

B and C

Step-by-step explanation:

Answer:

I think it should be (C)

Answer:

B

Step-by-step explanation:

The fastest way to solve this would to plug in a number for x such as 1 in both equations to find which 2 are equivalent.

When you plug 1 into the top equation it equals 3.5, so now we need to find the correct equation below that equals 3.5 when 1 is plugged in for x.

When you plug 1 into equation B you are also left with 3.5.

Answer: 2x2−3x−8

Step-by-step explanation:

Answer:

117.79

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

If the scale factor is 2/7 divide 12 by 2 which is 6. 6 is 1/7 and if Figure a is 7/7

multiply 6 by 7 to get x. That would be 42.

Answer:

42

Step-by-step explanation:

Since the scale factor is [tex]\frac{2}{7}[/tex], we know that the bigger shape went to the smaller shape.

If we know that the smaller shape's side, 12, is [tex]\frac{2}{7}[/tex] of the bigger one, we can make the equation

[tex]\frac{2}{7}x = 12[/tex].

To solve for x, we can divide both sides by  [tex]\frac{2}{7}[/tex].

[tex]x = 12\div{\frac{2}{7}}[/tex]

We can multiply by the reciprocal:

[tex]\frac{12}{1} \cdot \frac{7}{2} = \frac{84}{2} = 42[/tex]

Hope this helped!

Answer:

3/5 + 2 3/4 = 3 7/20

Step-by-step explanation:

2 = 8/4

2 3/4 = 2 + 3/4

then:

3/5 + 2 3/4 = 3/5 + 8/4 + 3/4

= 3/5 + (8+3)/4

= 3/5 + 11/4

3/5 = 12/20

11/4 = 55/20

then:

3/5 + 11/4 = 12/20 + 55/20 = 67/20

67/20 = 60/20 + 7/20 = 3 + 7/20

= 3 7/20

Answer:

[tex]f(x) = x^{2}\cdot (x^{2}+9)\cdot (x^{3}+2\cdot x)[/tex] is an odd function.

Step-by-step explanation:

Let be [tex]f(x) = x^{2}\cdot (x^{2}+9)\cdot (x^{3}+2\cdot x)[/tex], by Algebra this expression can be rewritten as:

[tex]f(x) = x^{3}\cdot (x^{2}+9)\cdot (x^{2}+2)[/tex]

Where [tex]x^{2} + 9[/tex] and [tex]x^{2}+ 2[/tex] are even functions, because they satisfy the condition that [tex]g(x) = g(-x)[/tex], whereas [tex]x^{3}[/tex] is an odd function, as the condition of [tex]h(-x) = - h(x)[/tex] is observed. Then, the overall function is odd.

Answer:

D. 9%, 440.36 million

Step-by-step explanation:

w = 221(1.09)t

9%, 440.36 million

if [tex] x\times e=x[/tex] for all x, then e is the Multiplicative Identity.

is this enough for you to get the answer?

Answer:

FALSE.

Step-by-step explanation:

1 is the multiplicative identity of the set of rationals.

Answer:

14)  answer is 4

15) proved

Step-by-step explanation:

x=7-4√3 , √x +1/√x

√(7-4√3) +1/√7-4√3)=

8-4√x/√(7-4√3)= 4 ( use calculator)

Answer:

The 2 values that makes the function equal to 18 is 3 and -6

Step-by-step explanation:

First you can convert the quadratic equation from standard form to root form

Step 1: Substitute f(g) = 18

Step 2: Move 18 to the other side to create

0 = g² + 3g - 18

Step 3: Now we rearrange equation from standard form into root form

Step 4: Find what adds to 3 and multiples to -18

-3 and 6 adds to 3 and multiples to -18

Step 5: Now we substitute -3 and 6 into the root equation

0 = (g-3)(g+6)

Step 6: Set the brackets to 0 and solve

g - 3 = 0

g = 3

g + 6 = 0

g = -6

Answer:

15x+6=10x+21

15x-10x=21-6

5x=15

divide by 5

5x/5=15/5

x=3

Answer:

x=3

Step-by-step explanation:

15x+6=10x+21

-10x

5x+6=21

-6

5x=15

divided by 5

x=3

Answer:

[tex]\huge\boxed{10.4\ units\²}[/tex]

Step-by-step explanation:

Area of circle:

=> [tex]\pi r^2[/tex]

Where r = 2.8

=> [tex](3.14)(2.8)^2[/tex]

=> (3.14)(7.84)

=> 24.6 units²

Area of Triangle:

=> 1/2 (Base)(Height)

=> 1/2 (10)(7)

=> 5 * 7

=> 35 units²

Area of the shaded region:

=> 35 - 24.6

=> 10.4 units²

Pregunta completa:

En una empresa trabajan 60 personas. Usan gafas el 16% de los hombres y el 20% de las mujeres. Si el numero total de personas que usan gafas es 11. ¿Cuantos hombres y mujeres hay en la empresa?

Responder:

Hombres = 25

Mujeres = 35

Explicación paso a paso:

Dado lo siguiente:

Número de personas que trabajan en la empresa = 60

Porcentaje de hombres que usan anteojos = 16%

Porcentaje de mujeres que usan anteojos = 20%

Número total de personas que usan anteojos = 11

Suponga, Número de hombres en la empresa = m

Número de mujeres = número total - número de hombres = 60 - m

Por lo tanto,

16% de los hombres = 0,16 m

20% de mujeres = 0,2 (60 - m) = 12 - 0,2 m

Por lo tanto,

0,16 m + 12 - 0,2 m = 11

- 0,04 m = 11 - 12

-0,04 m = - 1

m = 1 / 0.04 = 25

Por tanto, Número de hombres en la empresa = m = 25

Número de mujeres en la empresa = (60 - m) = (60 - 25) = 35 mujeres

Answer:

3 - b=12

4- b=14.1

Step-by-step explanation:

Area of the bookshelf=864 square inches

the book shelf is a rectangular prism

if we have height=4b, width=3b, length=b

then the area=length * width

A=(l*w)*2 ( we have 2 shelves)

864=(b*3b)*2

864=6b²

b²=864/6=144

b=√144= 12 inches

4- to cover the sides :

(height * length)*2   ( we have 2 sides)

(4b*b)×2=1600

8b²=1600

b²=1600/8=200

b=√200=14.1

Answer:

Question #3:  b = 12 in

Question #4:  b = 14.1 in

Step-by-step explanation:

Please see in the image attached the actual proportions that the furniture manufacturer uses to build the furniture in question:

Height = 4 b

Width = 3 b

Depth = b

So for question #3, given that the customer wants a total surface of the shaded shelves to be 864 [tex]in^2[/tex]

we can write that one wants twice the area of each rectangle of width 3 b and depth b to total 864:

[tex]2\,(3b\,*\,b)=864\\6 b^2=864\\b^2=864/6\\b^2=144\\b=12\,\,in[/tex]

Question # 4:

The total lateral surface to be covered by the silk is 1600 [tex]in^2[/tex], therefore if we consider the surface of each lateral plank as:

Area of each lateral plank :

[tex](4b)\,(b) = 4\,b^2[/tex]

Then twice these is: [tex]8\, b^2[/tex]

So we can solve for be requesting that these total surface equal the amount of silk:

[tex]8\,b^2=1600\\b^2=1600/8\\b^2=200\\b=\sqrt{200} \\b\approx 14.1421\,\,in[/tex]

which rounded to the nearest tenth of an inch gives:

[tex]b\approx 14.1\,\,in[/tex]

Answer:

x = 7.5

Step-by-step explanation:

Step 1: Create a fraction with the known sides

[tex]\frac{x}{10}[/tex]

Step 2: Set the fraction equal to the scale factor

[tex]\frac{x}{10}=\frac{0.75}{1}[/tex]

Cross multiple to solve for x

[tex]x = 7.5[/tex]

Therefore x is equal to 7.5

Answer:

7.5

Step-by-step explanation:

did it on khan

Answer:

Step-by-step explanation:

Area of a rectangle = Length * Width

Given parameters

Area A = 8x2 – 10x – 12

Length of the rectangle = 4x+3

Required

Width of the rectangle.

Substituting the given parameters into the formula

8x2 – 10x – 12  = (4x+3)*width

width = 8x2 – 10x – 12 /4x+3

S

Factorizing the numerator

8x² – 10x – 12

= 2(4x²-5x-6)

= 2(4x²-8x+3x-6)

= 2(4x(x-2)+3(x-2))

= 2(4x+3)(x-2)

Width = 2(4x+3)(x-2)/4x+3

Width = 2(x-2)

Width = 2x-4

Hence the width of the rectangle is 2x-4

Answer:

59.5 feet

Step-by-step explanation:

The second tree is 59.5 feet tall.

Two trees are growing in a clearing.

The first tree is 17 feet tall and casts a 10-foot shadow.

The second tree casts a 35-foot shadow.

Let x be the tall is the second tree.

Then,

The ratio of the height of the tree is;

[tex]\rm \dfrac{17}{10} = \dfrac{x}{35}\\\\17 \times 35 = x \times 10\\\\595 = 10x\\\\x = \dfrac{595}{10}\\\\x = 59.5 \ feet[/tex]

Hence, the second tree is 59.5 feet tall.

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Answer:

Hey There!! The Correct answer C: ) is the average number of days a house stays on the market before being sold for price p in $1,000s

A little more clearer explanation:

p is the price in $1000s, and

f(p) is the number of days before its sold for p

Hence, f(250) would be the number of days before its sold for 250,000 (since p is in $1000s)

Answer choice C is the correct one.

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer: C

Step-by-step explanation:  This is the average number of days the house stayed on the market before being sold for $250,000

Answer:

Fail to reject the null hypothesis.

Step-by-step explanation:

The hypothesis test is conducted for Boston public school. They have used z-value table and the value of test statistics is 1.20. AT the significance level of 0.05, the null hypothesis is accepted. We cannot reject the null hypothesis. The p-value is greater than alpha so there is no evidence to support the claim of Boston Public School.

Answer:

The probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42 is 0.3115

Step-by-step explanation:

From the question, we can deduce the following;

n = 75

p = 0.35

where q = 1-p = 1-0.35 = 0.65

To compute the probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42, we start by calculating the standard deviation of sample proportion.

Mathematically;

Standard deviation of sample proportion = √pq/n

SD = √(0.35)(0.65)/75 = 0.055 which is approximately 0.06

Let’s now compute the z-scores

For 0.36, we have ; (0.36-0.35)/0.06 = 0.01/0.06 = 0.17

For 0.42, we have; (0.42-0.35)/0.06 = 0.07/0.06 = 1.17

So the probability we want to calculate is :

P(0.17<z<1.17) = P(z<1.17) - P(z < 0.17) = 0.8790 - 0.5675 = 0.3115

Answer:

4.6225

Step-by-step explanation: It would be too long to get an exact

Answer:

Step-by-step explanation:

Area of square = 18.49 square yards

side² = 18.49

side = √18.49

side = 4.3 yards

Answer:

probably the 2.38 seconds answer

Step-by-step explanation:

start by setting the entire equation equal to 8, since h(t) is the height and 8m is the height we are looking at right now.

[tex]8=-5t^{2}+14t+3[/tex]

subtract 8 from both sides to get: [tex]0=-5t^{2}+14t-5[/tex]

use the Quadratic equation to find the time, the negative answer does not count.

when you do the quadratic equation you get [tex]\frac{7+2\sqrt{6} }{5},\frac{7-2\sqrt{6} }{5}[/tex]

In decimal form that's about  2.38 and 0.42 You'd probably go with the 2.38 seconds because the ball starts at 0 seconds, so the lower number is probably to close to the start point.

The solution of the problem is

Given that:

      The equation is  [tex]h(t)=-5t^2+14t+3[/tex] , where  [tex]h(t)[/tex]  is height .

     The ball is [tex]8m[/tex] above the ground so [tex]h=8m[/tex] .

     Now,

      Substitute the value of height in given equation,

      [tex]h=-5t^2+14t+3\\\\8=-5t^2+14t+3[/tex]

     Subtract [tex]8[/tex] on both side to obtain the quadratic equation,

     [tex]-5t^2+14t+3-8=8-8\\\\-5t^2+14t-5=0[/tex]

   Multiply minus sign in both sides,

    [tex]5t^2-14t+5=0[/tex]

    Solve the quadratic equation ,

     Where,

    [tex]a=5,b=-14,c=5[/tex]

    [tex]x=-b +\frac{\sqrt{b^{2}-4ac } }{2a} \\\\ x=-b -\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]

   Substitute the known values in the formula,

   [tex]x=\frac{14+\sqrt{(-14)^2-4(5)(5)} }{2(5)} \\x=\frac{14+\sqrt{196-100} }{10} \\\\x=\frac{14+\sqrt{96} }{10} \\\\x=\frac{14+\sqrt{2*2*2*2*2*3} }{10} \\\\x=\frac{14+(4\sqrt{6}) }{10} \\\\x=\frac{7+2\sqrt{6} }{5}[/tex]

Similarly,

[tex]x=\frac{7-2\sqrt{6} }{5}[/tex]

Answer:

a) m∠BPD = 120°

b) m∠BC + m∠AD = 120°

Step-by-step explanation:

a) To solve for question a, we make use of a theorem called the intersecting chord theorem. This states that:

The measure of the angle formed by two chords that intersect inside a circle is the average of the measures of the intercepted arcs.

The Interior angle =( The larger exterior arc + The smaller exterior arcs) ÷ 2

The larger exterior arc (m∠BD) = 170°

The small exterior arc (m∠CA) = 70°

m∠BPD = m∠BD + m∠CA/2

m∠BPD = 170° + 70°/2

= 240°/2

= 120°

b) We are to find m∠BC + m∠AD

The sum of exterior angles in a circle = 360°

360° = m∠BD + m∠CA + m∠BC + m∠AD

360° = 170° + 70° + m∠BC + m∠AD

360° = 240 + m∠BC + m∠AD

360 - 240° = m∠BC + m∠AD

Thererefore,

m∠BC + m∠AD = 120°

Answer:

1. m∠BPD = 120°

2. m∠BC + m∠AD = 120°

Answer:

x = 2

Step-by-step explanation:

Probability that the marble comes to rest in the shaded region is equal to the ratio of the shaded area to the total area.

Probability 'P' = [tex]\frac{A'}{A}[/tex]

Area of the shaded region (A')= (x + 1)(x + 2)

Total area of the figure (A) = (2x + 1)(3x + 2)

P = [tex]\frac{(x+1)(x+2)}{(2x+1)(3x+2)}=\frac{3}{10}[/tex]

10(x + 1)(x + 2) = 3(2x + 1)(3x + 2)

10(x² + 3x + 2) = 3(6x² + 7x + 2)

10x² + 30x + 20 = 18x² + 21x + 6

(18x² - 10x²) + (21x - 30x) + (6 - 20) = 0

8x² - 9x - 14 = 0

x = [tex]\frac{9\pm\sqrt{(-9)^2-4(8)(-14)} }{2(8)}[/tex]

x = [tex]\frac{9\pm \sqrt{81+448}}{16}[/tex]

x = [tex]\frac{9\pm 23}{16}[/tex]

x = -[tex]\frac{7}{8}, 2[/tex]

Therefore, positive value of x = 2 will be the answer.

Answer:

Step-by-step explanation:

a=3400t+600, we put in 21,000 for a. Because we have to find 't' when 'a' is 21,000.

which will give us  21,000 = 3400t+600.

Then,Subtract 600 to both sides to get 20,400 = 3400t

Divide both sides by 3,400 and you get 6 = t.

The ans is 6 minutes. The plane will take 6 min to reach the altitude 21,000 feet

[tex](-3+5,10-7)=(2,3)[/tex]

Range: 71.9

Spread out above the median

The range is the biggest number minus the smallest number. This makes sense. The range here is 81.3 - 9.4 = 71.9.

Next, see the two middle groups? You can see the median, 45.5. Does the left or right side seem more spread out? It's the right side. 34.7 is closer to 45.5 than 63.6 is to 45.5.

Hope that helped,

-sirswagger21