Graph the inequality below on a number line
[tex]x < - 2[/tex]
​

Answer:

42.5

Step-by-step explanation:

x                      15

_                       _

85                   100

15x85=1275

1275/100=127.5

127.5-85=42.5

Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.

As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.

One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.

Case 1: 82% gold + 50% gold

Let x grams of 82% gold and y  grams of 50% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 50% of y

[tex]\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times y \\\\[/tex]

[tex]\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times (14-x)[/tex]  [as x+y=14]

[tex]\Rightarrow 75 \times 14 = 82 \times x + 50 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 50 \times14-50\times x \\\\\Rightarrow 75 \times 14 = 32 \times x + 50 \times14 \\\\\Rightarrow 32 \times x =75 \times 14 - 50 \times14 \\\\[/tex]

[tex]\Rightarrow x =(25 \times 14)/32=10.9375[/tex] grams

and [tex]y = 14-x= 14-10.9375=3.0625[/tex] grams.

Hence, 10.9375 grams of 82% gold and 3.0625  grams of 50% gold added to make 14 grams of 75% gold.

Case 2: 82% gold + 25% gold

Let x grams of 82% gold and y  grams of 25% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 25% of y

[tex]\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times y \\\\\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times (14-x) \\\\ \Rightarrow 75 \times 14 = 82 \times x + 25 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 25 \times14-25\times x \\\\\Rightarrow 75 \times 14 = 57 \times x + 25 \times14 \\\\\Rightarrow 57 \times x =75 \times 14 - 25 \times14 \\\\[/tex]

[tex]\Rightarrow x =(50 \times 14)/57=12.28[/tex] grams

and [tex]y = 14-x= 14-12.28=1.72[/tex] grams.

Hence, 12.28 grams of 82% gold and 1.72  grams of 50% gold added to make 14 grams of 75% gold.

Answer:

Step-by-step explanation:

1. use the slope formula --> (y2-y1)/(x2-x1)

2. (8 - 4)/(13 -(-3))

3. 4/16

4. m = 1/4

Answer:

7

Step-by-step explanation:

7 is not a factor of 48, since 7 can not be multiplied by another whole number to get 48. (48 divided by 7 is 6.8)

Answer:

7

Step-by-step explanation:

3 is 13 more than 10, and 3 is 30% of 10, so 30% im pretty sure

Answer:

130%

Step-by-step explanation:

It's 130% because 10*130% is 13.

Answer:

A, B, and C

Step-by-step explanation:

We can substitute each number into each equation

2 < -1 + 5 true

2 > 1 true

1 > 0 true

A is correct

4 < -1 + 5 true

4 > 1 true

1 > 0 true

B is correct

3 < -0 + 5 true

3 > 0 true

0 > 0 true

C is correct

5 < -2 + 5 false

D is incorrect

Answer:

-8 and 3

Step-by-step explanation:

The asked numbers are -8 and 3.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, two numbers multiply to -24 and add up to -5

Let the two numbers be x and y

x+y = -5...(i)

xy = -24

x = -24/y...(ii)

Put eq (ii) in eq (i)

-24/y + y = -5

-24 + y² = -5y

y²+5y-24 = 0

Factorizing,

y = 8 and 3

Taking y = 3, put it in eq(ii)

x = -24/3

x = -8

Hence, the asked numbers are -8 and 3.

Learn more about equations, click;

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Answer:

x=19/4

Step-by-step explanation:

The product of 5 and a number x is 1/4

Answer:

5/2

Step-by-step explanation:

25 and 10 so 25/10 or 5/2 or 2 1/2

Answer:

a= (Z + 2b)/24

Step-by-step explanation:

given:

Z = 24a - 2b

to solve for a, we will try to move "a" to one side of the equation and all other terms to the other side:

Z = 24a - 2b    (add 2b to both sides)

Z + 2b = 24a -2b +2b

Z + 2b = 24a  (switch sides)

24a = Z + 2b (divide both sides by 24)

a/24 = (Z + 2b)/24

a= (Z + 2b)/24

Answer:

The correct answer is -6x⁶

Step-by-step explanation:

Given that:

[tex]3x^2 ( - 2x^4 ) \\ \\ =3(-2)x^{2.4} \\ \\ = 6x^8[/tex]

From the second step above, using the law of indices the correct format should be

[tex]= (3\times -2)x^{2+4}[/tex]

So, the problem lies where we have 2.4, it is not supposed to be (2*4). It supposed to be 2+4 because the law of indices states that we multiply the index together and add their power.

Then the result of that yields

= -6x⁶

In the third step, they also omit the negative sign, when multiplying (3 * -2).

Thus, the correct answer is -6x⁶

Answer:

d=25 or d=2

Step-by-step explanation:

hope that helps!

Answer:

d=2/5 or d=2

Step-by-step explanation:

Step 1: Subtract -6d^2 from both sides.

−d2−12d+4−−6d2=−6d2−−6d2

5d2−12d+4=0

Step 2: Factor left side of equation.

(5d−2)(d−2)=0

Step 3: Set factors equal to 0.

5d−2=0 or d−2=0

d= 2/5 or d=2

Answer:

it is D.... PERIODT

Step-by-step explanation:

Step-by-step explanation:

the regular form of r=8

Answer:

The solution is too long. So, I included them in the explanation

Step-by-step explanation:

This question has missing details. However, I've corrected each question before solving them

Required: Determine the inverse

1:

[tex]f(x) = 25x - 18[/tex]

Replace f(x) with y

[tex]y = 25x - 18[/tex]

Swap y & x

[tex]x = 25y - 18[/tex]

[tex]x + 18 = 25y - 18 + 18[/tex]

[tex]x + 18 = 25y[/tex]

Divide through by 25

[tex]\frac{x + 18}{25} = y[/tex]

[tex]y = \frac{x + 18}{25}[/tex]

Replace y with f'(x)

[tex]f'(x) = \frac{x + 18}{25}[/tex]

2. [tex]g(x) = \frac{12x - 1}{7}[/tex]

Replace g(x) with y

[tex]y = \frac{12x - 1}{7}[/tex]

Swap y & x

[tex]x = \frac{12y - 1}{7}[/tex]

[tex]7x = 12y - 1[/tex]

Add 1 to both sides

[tex]7x +1 = 12y - 1 + 1[/tex]

[tex]7x +1 = 12y[/tex]

Make y the subject

[tex]y = \frac{7x + 1}{12}[/tex]

[tex]g'(x) = \frac{7x + 1}{12}[/tex]

3: [tex]h(x) = -\frac{9x}{4} - \frac{1}{3}[/tex]

Replace h(x) with y

[tex]y = -\frac{9x}{4} - \frac{1}{3}[/tex]

Swap y & x

[tex]x = -\frac{9y}{4} - \frac{1}{3}[/tex]

Add [tex]\frac{1}{3}[/tex] to both sides

[tex]x + \frac{1}{3}= -\frac{9y}{4} - \frac{1}{3} + \frac{1}{3}[/tex]

[tex]x + \frac{1}{3}= -\frac{9y}{4}[/tex]

Multiply through by -4

[tex]-4(x + \frac{1}{3})= -4(-\frac{9y}{4})[/tex]

[tex]-4x - \frac{4}{3}= 9y[/tex]

Divide through by 9

[tex](-4x - \frac{4}{3})/9= y[/tex]

[tex]-4x * \frac{1}{9} - \frac{4}{3} * \frac{1}{9} = y[/tex]

[tex]\frac{-4x}{9} - \frac{4}{27}= y[/tex]

[tex]y = \frac{-4x}{9} - \frac{4}{27}[/tex]

[tex]h'(x) = \frac{-4x}{9} - \frac{4}{27}[/tex]

4:

[tex]f(x) = x^9[/tex]

Replace f(x) with y

[tex]y = x^9[/tex]

Swap y with x

[tex]x = y^9[/tex]

Take 9th root

[tex]x^{\frac{1}{9}} = y[/tex]

[tex]y = x^{\frac{1}{9}}[/tex]

Replace y with f'(x)

[tex]f'(x) = x^{\frac{1}{9}}[/tex]

5:

[tex]f(a) = a^3 + 8[/tex]

Replace f(a) with y

[tex]y = a^3 + 8[/tex]

Swap a with y

[tex]a = y^3 + 8[/tex]

Subtract 8

[tex]a - 8 = y^3 + 8 - 8[/tex]

[tex]a - 8 = y^3[/tex]

Take cube root

[tex]\sqrt[3]{a-8} = y[/tex]

[tex]y = \sqrt[3]{a-8}[/tex]

Replace y with f'(a)

[tex]f'(a) = \sqrt[3]{a-8}[/tex]

6:

[tex]g(a) = a^2 + 8a- 7[/tex]

Replace g(a) with y

[tex]y = a^2 + 8a - 7[/tex]

Swap positions of y and a

[tex]a = y^2 + 8y - 7[/tex]

[tex]y^2 + 8y - 7 - a = 0[/tex]

Solve using quadratic formula:

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

[tex]a = 1[/tex] ; [tex]b = 8[/tex]; [tex]c = -7 - a[/tex]

[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes

[tex]y = \frac{-8 \±\sqrt{8^2 - 4 * 1 * (-7-a)}}{2 * 1}[/tex]

[tex]y = \frac{-8 \±\sqrt{64 + 28 + 4a}}{2 * 1}[/tex]

[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 * 1}[/tex]

[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 }[/tex]

Factorize

[tex]y = \frac{-8 \±\sqrt{4(23 + a)}}{2 }[/tex]

[tex]y = \frac{-8 \±2\sqrt{(23 + a)}}{2 }[/tex]

[tex]y = -4 \±\sqrt{(23 + a)}[/tex]

[tex]g'(a) = -4 \±\sqrt{(23 + a)}[/tex]

7:

[tex]f(b) = (b + 6)(b - 2)[/tex]

Replace f(b) with y

[tex]y = (b + 6)(b - 2)[/tex]

Swap y and b

[tex]b = (y + 6)(y - 2)[/tex]

Open Brackets

[tex]b = y^2 + 6y - 2y - 12[/tex]

[tex]b = y^2 + 4y - 12[/tex]

[tex]y^2 + 4y - 12 - b = 0[/tex]

Solve using quadratic formula:

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

[tex]a = 1[/tex] ; [tex]b = 4[/tex]; [tex]c = -12 - b[/tex]

[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes

[tex]y = \frac{-4\±\sqrt{4^2 - 4 * 1 * (-12-b)}}{2*1}[/tex]

[tex]y = \frac{-4\±\sqrt{4^2 - 4 *(-12-b)}}{2}[/tex]

Factorize:

[tex]y = \frac{-4\±\sqrt{4(4 - (-12-b))}}{2}[/tex]

[tex]y = \frac{-4\±2\sqrt{(4 - (-12-b))}}{2}[/tex]

[tex]y = \frac{-4\±2\sqrt{(4 +12+b)}}{2}[/tex]

[tex]y = \frac{-4\±2\sqrt{16+b}}{2}[/tex]

[tex]y = -2\±\sqrt{16+b}[/tex]

Replace y with f'(b)

[tex]f'(b) = -2\±\sqrt{16+b}[/tex]

8:

[tex]h(x) = \frac{2x+17}{3x+1}[/tex]

Replace h(x) with y

[tex]y = \frac{2x+17}{3x+1}[/tex]

Swap x and y

[tex]x = \frac{2y+17}{3y+1}[/tex]

Cross Multiply

[tex](3y + 1)x = 2y + 17[/tex]

[tex]3yx + x = 2y + 17[/tex]

Subtract x from both sides:

[tex]3yx + x -x= 2y + 17-x[/tex]

[tex]3yx = 2y + 17-x[/tex]

Subtract 2y from both sides

[tex]3yx-2y =17-x[/tex]

Factorize:

[tex]y(3x-2) =17-x[/tex]

Make y the subject

[tex]y = \frac{17 - x}{3x - 2}[/tex]

Replace y with h'(x)

[tex]h'(x) = \frac{17 - x}{3x - 2}[/tex]

9:

[tex]h(c) = \sqrt{2c + 2}[/tex]

Replace h(c) with y

[tex]y = \sqrt{2c + 2}[/tex]

Swap positions of y and c

[tex]c = \sqrt{2y + 2}[/tex]

Square both sides

[tex]c^2 = 2y + 2[/tex]

Subtract 2 from both sides

[tex]c^2 - 2= 2y[/tex]

Make y the subject

[tex]y = \frac{c^2 - 2}{2}[/tex]

[tex]h'(c) = \frac{c^2 - 2}{2}[/tex]

10:

[tex]f(x) = \frac{x + 10}{9x - 1}[/tex]

Replace f(x) with y

[tex]y = \frac{x + 10}{9x - 1}[/tex]

Swap positions of x and y

[tex]x = \frac{y + 10}{9y - 1}[/tex]

Cross Multiply

[tex]x(9y - 1) = y + 10[/tex]

[tex]9xy - x = y + 10[/tex]

Subtract y from both sides

[tex]9xy - y - x = y - y+ 10[/tex]

[tex]9xy - y - x = 10[/tex]

Add x to both sides

[tex]9xy - y - x + x= 10 + x[/tex]

[tex]9xy - y = 10 + x[/tex]

Factorize

[tex]y(9x - 1) = 10 + x[/tex]

Make y the subject

[tex]y = \frac{10 + x}{9x - 1}[/tex]

Replace y with f'(x)

[tex]f'(x) = \frac{10 + x}{9x -1}[/tex]

Answer: 35 minutes

Step-by-step explanation:

For us to solve the question, we have to calculate the amount of gallons of water that is drained every minute. This will be:

= (1320 - 1040) / (9 - 2)

= 280/7

= 40 gallons per minute

Since we are told that 1,320 gallons of water remain in the pool after 2 minutes. This means that the total water in the pool at the beginning was:

= 1320 gallons + (40 × 2)

= 1320 gallons + 80 gallons

= 1400 gallons

The time taken for the pool to be completely drained will be:

= Total water in pool / Gallons drained per minute

= 1400 / 40

= 35 minutes

Answer:

rise : atmospheric pressure increases

fall : atmospheric pressure decreases

Step-by-step explanation:

In the context, it is given that a weather forecaster takes the help of the barometer to check the air pressure and predicts the weather. The column of mercury level in the barometer shows a rise or fall in the glass tube as the weight of the atmosphere falling on the mercury surface changes.

Here it is given that the mercury rises for 0.02 in, then it falls 0.09 in,  it then rises by 0.07 in and then again falls by 0.18 in. The word "rise" here shows that the weight of the atmosphere is more. In other words, increase in atmospheric pressure increases the level of mercury in the glass tube and the decrease in or "fall" in the mercury level shows the drop in atmospheric pressure.

Answer:

202 miles per day

Step-by-step explanation:

Answer:

165

Step-by-step explanation:

A 2-column table with 3 rows. Column 1 is labeled Days, x with entries 3, 4, 5. Column 2 is labeled Miles, y with entries 771, 973, 1,175.

The Bodens drove for awhile before they made a plan to drive a set number of miles each day. Days 3, 4, and 5 are displayed in the table. Assume the relationship is linear.

Determine the initial number of miles that the Boden family drove before they made their plan.

771 miles

367 miles

165 miles

135 miles

This is your correct answer 165, oops this is the wrong question sorry

Answer:

-2

Step-by-step explanation:

Answer:

niwebfasfbjsdfb

Step-by-step explanation:

jsdfhsdbfjhadsjbdsfhb

Answer:

0.00462962962

Step-by-step explanation:

Answer for #5:

7 friends

Step-by-step explanation:

convert fraction into 4ths:

1/4, 2/4, 3/4, 1/4

add together:

7/4ths

if each friend ate 1/4 of the pizzas, then there are 7 friends

Answer:

C

Step-by-step explanation:

430 feet above sea level

Answer:

C. 430 feet above sea level

Answer:           0.875

Step-by-step explanation:

Answer:

z=kx/y

zy=kx

zy/x=kx/x ( divided both side by x. to find k)

k=zy/x

k=6×4/3(z=6,y=4,x=3)

k=24/3

k=8

so z=kx/y

z=8×5/2(replace the numbers in the place of variables,k=8,x=5,y=2)

z=40/2

z=20

Answer:

Matching the population trend to a contributing factor:

Contributing Factors                                                 Population Trends

government-sponsored family control programs    Low birth rate

agricultural economies                                              increase in food supply

medical advancements                                             low death rate

Industrial Revolution                                                 high birth rate

Step-by-step explanation:

a) Contributing factors are some negative or positive factors that influence or cause a single event or chain of events that result to the incident.

b) Defining population trends:

1) High birth rate: the industrial revolution triggered high birth rate, following increased food supply and medical advancements.

2) Low death rate: medical advancements brought about low death rate as better healthcare is provided to the sick.

3) Increase in food supply: large-scale agricultural economies ensured increasing food production and supply.

4) Low birth rate: when governments started sponsoring family control programs, the resulting effect was low birth rate.

Answer:

The first one is children and adolescents

the second one is adults

the third one is pregnancy

the last one is indivisuals with brittle bones

Step-by-step explanation:

hope this helps :D