Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a not-equals 1 and b not-equals 1?

Question 5

Vertical angles are congruent. Therefore, [tex]3y=\boxed{150}[/tex]. The sum of two supplementary angles equals [tex]\boxed{180^{\circ}}[/tex].

Therefore, [tex]6x+150=\boxed{180}[/tex]

Question 6

[tex]\angle b-14=90-\angle b\\\\2\angle b=104\\\\\angle b=\boxed{52^{\circ}}[/tex]

Question 7

[tex]\angle d+32=180-\angle d\\\\2\angle d=146\\\\\angle d=\boxed{73^{\circ}}[/tex]

Question 8

[tex]7x-80=3x\\\\-80=-4x\\\\x=20\\\\\implies \boxed{m\angle 1=m\angle 3=60^{\circ}}[/tex]

The value of b is -16 and the value of ac is 60 after comparing with the standard equation.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic function:

= 3x² - 16x + 20

On comparing with standard function:

b = -16

a = 3

c = 20

ac = 3(20) = 60

Thus, the value of b is -16 and the value of ac is 60 after comparing with the standard equation.

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The equation to model the situation is [tex]\mathbf{y = \dfrac{k}{x^2}}[/tex]. The constant for the variation is 2250.

The intensity of light from a lantern varies inversely to the square of the distance from the lantern.

From the given information:

Then:

[tex]\mathbf{y \alpha \dfrac{1}{x^2} }[/tex]

[tex]\mathbf{y = \dfrac{k}{x^2} }[/tex]   here, k = constant.

2.

If y = 90 W/m² when the distance x = 5m

Then:

[tex]\mathbf{90 = \dfrac{k}{(5)^2}}[/tex]

k = 90 × 25

k = 2250

c.

The equation to model the situation by using the constant variation is:

[tex]\mathbf{y = \dfrac{2250}{x^2}}[/tex]

d.

If the light intensity y = 40, then x is determined as:

[tex]\mathbf{40 = \dfrac{2250}{x^2}}[/tex]

[tex]\mathbf{x = \sqrt{\dfrac{2250}{40}}}[/tex]

x = 7.5 m

e.

The light is needed in (225 × 1000)m = 225000 km of illumination.

f.

The lantern required for the new light estimation is:

y = 2250/225000

y = 0.01 intensity

Therefore, we can conclude that to get an intensity of 1 W/m², we need to put 100 lanterns.

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The equivalent expression of [tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex] is [tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]

The complete question is in the attached image

We have:

[tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex]

Take the LCM

[tex]\frac{\frac {2y - 4x}{xy}}{\frac{-5x + 3y}{xy}}[/tex]

Divide through by xy

[tex]\frac {2y - 4x}{-5x + 3y}[/tex]

Rewrite as:

[tex]\frac {2y - 4x}{ 3y-5x}[/tex]

Factor out 2

[tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]

Hence, the equivalent expression of [tex]\frac{\frac 2x - \frac 4y}{-\frac 5y + \frac 3x}[/tex] is [tex]\frac {2(y - 2x)}{ 3y-5x}[/tex]

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Answer:

Quadrants 1 and 4 EDIT: Quadrants 2 & 4

Step-by-step explanation:

Quadrant 1  : Edit: no

Quadrant 2  : Edit: yes

Quadrant 3 : No

Quadrant 4 : Yes

The equation of line passing through points (4.5. 0) and (0, 9) is y = -2x + 9.

Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

The graph of the picture shows two clear points (4.5. 0) and (0, 9)

[tex](y - 0) = \dfrac{9 - 0}{0 - 4.5} (x -4.5)\\\\\\(y - 0) = \dfrac{9 }{- 4.5} (x -4.5)\\\\\\-4.5y = 9(x -4.5)\\\\-4.5y = 9x - 40.5\\\\y = -2x + 9[/tex]

Hence, the equation of line passing through points (4.5. 0) and (0, 9) is y = -2x + 9.

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The chocolate will last for 1 day, if she gets 4 more dragons

The expression can be represented using the following ratio:

Ratio = Dragons : Days : Chocolate

For the 2 dragons she has, we have:

Ratio = 2 : 12 : 300

When she gets 4 more dragons, we have:

Ratio = 6 : days : 300

Equate both ratios

6 : days = 12 : 2

Express as fraction

days/6 = 2/12

Multiply both sides by 6

days = 6 * 2/12

Evaluate

days = 1

Hence, the chocolate will last for 1 day

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A significance level of 5% (more commonly referred to as 95%) corresponds to a statement that (only) a probability of 5% or less is that a particular randomly generated observation is accepted as significant.

In this example, the p-level (the true probability that the observations are randomly generated) is less than 5% (0.0421 <0.05), so we can draw the conclusion that the observations are significant.

p = 0.0421 means that the probability is only 0421/1000. The choice of significance level to reject the null hypothesis is optional. Traditionally, 5%, 1%, and 0.1% levels have been used. In rare situations, a 10% significance level is also used.

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In order to make the new flag, Lauren decided to triple the sides of the old flag in order to get a new one.

The old triangle is the smaller one. We can see that this triangle has increased by a factor of 3 on all sides.

We have 4 x 3= 12

2 x 3 = 6

7 x 3 = 21

The calculated values above is what produced the new larger flag.

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Answer:

-6,0 & -3,0

Step-by-step explanation:

Answer:

19 inches

Step-by-step explanation:

So the perimeter of a triangle is the sum of the three sides. So the perimeter is [tex]\sqrt{65} + \sqrt{35} + \sqrt{26}[/tex] which is approximately 19.077 inches but in this case the answer is 19 inches

the constant variation, K= 4

Step-by-step explanation:

i have replace the constant variation by the letter K

First step is to write down the information

y directly proprotional to x

So, y= Kx

Replace the value given for x and y to find k

y= -4 and x = -1

Kx= y

K( -1) = -4

K = -4 ÷ -1

K= 4

Further answer

if you are asked the connecting equation between y and x just replace the value of K in the equation

y= Kx

y= 4x

Answer:

128.4°, 51.6°

Step-by-step explanation:

x + x - 76.8 = 180

2x = 256.8

x = 128.4

x - 76.8 = 51.6

Answer:

It's A and C

Step-by-step explanation:

the angles are 45, which is less than 90

Answer:

25.5 mph

Step-by-step explanation:

So Bradley's speed can be modeled by the equation y=2x+40 where y=speed, x=time in hours after noon, and b=initial speed

So 12:15 is 15 minutes after noon, which is also 0.25 or 1/4 of an hour after noon. This is the x-value. Plug this into the equation to get his speed at 12:15

y=2(0.25)+40

y=0.5+40

y=40.5

So his speed was 40.5 at the time and since he was going 15 miles over the speed limit, the speed limit is 15 less than his speed

40.5 - 15 = 25.5

Answer:

25.5 mph

Step-by-step explanation:

Given information:

Calculate Bradley's speed at 12.15 pm:

60 minutes = 1 hour

⇒ 15 minutes = 1/4 hour

⇒ speed at 12.15 pm = speed at 12.00pm + 1/4 of 2 mph

                                  = 40 mph + 0.5 mph

                                  = 40.5 mph

If he was 15 miles over the speed limit at 12.15 pm then:

⇒ speed limit = speed at 12.15pm - miles over the limit

                       = 40.5 mph - 15

                       = 25.5 mph

Therefore, the speed limit was 25.5 mph.

From the given recursive definition,

[tex]a_1 = 3[/tex]

[tex]a_2 = a_1 + 5 = 3 + 5 = 8[/tex]

[tex]a_3 = a_2 + 5 = 8 + 5 = 13[/tex]

[tex]a_4 = a_3 + 5 = 13 + 5 = 18[/tex]

[tex]a_5 = a_4 + 5 = 18 + 5 = 23[/tex]

Answer:

x = - 6

Step-by-step explanation:

By using the definitions of distance and number line, the distance between a and b on the number line is 10.97 units, not 0.47 units. (Right choice: A)

Herein we must determine what choice is false with respect to two integers, one negative and other positive. The first choice represents a false proposition as:

|a - b| = |- 5.72 - 5.25| = |- 10.97|

|a - b| = 10.97

By using the definitions of distance and number line, the distance between a and b on the number line is 10.97 units, not 0.47 units. (Right choice: A)

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The house would have slid 910 yards in 15 days.

A geometric progression is a sequence in which successive terms differ by a common ratio.

It is a sequence in which the ratio of two consecutive terms is a constant.

Analysis:

first term, a= 1

second term, ar = 2

third term, ar^2= 4

common ratio = ar/a = 2/1 = 2

Sum of the G.P where n = 15

sum of G.p = a([tex]\frac{r^{n} - 1}{r-1}[/tex])

= 1([tex]2^{15}[/tex] - 1)/2 - 1 = 32768 - 1 = 32768 inches

converting the inches to yard, where 1 yard = 36 inches

so 32768/36 = 910 yards

In conclusion, the house would slide 910 yards in  15 days.

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Answer:

not moving any spaces

Hope this helps you

.......

Answer:

A. 0.068

Step-by-step explanation:

First, 3 inches to miles. 3 inches in a mile is 0.00004735.

The snail moves 0.00004735 miles per minute.

Next, search how many minutes are there in a day. There is 1440 minutes in a day.

Multiply the 1440 and 0.00004735.

1440*0.00004735=0.068

The snail can move 0.068 miles per day if it doesn't take a break.

Hope this helps!

If not, I am sorry.

You can by 24 combinations of items from the store

The given parameters are:

Cups = 3

Bowl = 4

Spoon = 2

The number of combination is:

Combination = Cups * Bowl * Spoon

So, we have:

Combination = 3 * 4 * 2

Evaluate

Combination = 24

Hence, you can by 24 combinations of items from the store

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Using a system of equations, it is found that the lengths of the sides of the triangle are given as follows:

0.91 feet, 0.73 feet, 1.23 feet.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are the lengths, given by x, y and z.

The length of one side of a triangle is 2 feet less than three times the length of its second side, hence:

y = 3x - 2.

The length of the third side is 3/4 of the sum of the lengths of the first two sides, hence:

[tex]z = \frac{3(x + y)}{4} = \frac{3(4x - 2)}{4}[/tex]

The perimeter of the triangle is 17.5 feet, hence:

[tex]x + y + z = 17.5[/tex]

[tex]x + 3x - 2 + \frac{3(4x - 2)}{4} = 17.5[/tex]

[tex]4x + \frac{3(4x - 2)}{4} = 19.5[/tex]

[tex]16x + 12x = 25.5[/tex]

x = 25.5/28

x = 0.91.

Then the other sides are:

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Answer: Exponential

Step-by-step explanation:

Because every time x increases by 1, y increases by a factor of 3.

6/2 = 3

18/6 = 3

54/18 = 3

162/54 = 3

P.S.: I ANSWERED ONE OF YOUR PROBLEMS WITH EXACTLY THE DATA IN THIS TABLE BY COINCIDENCE HAHA

Answer:

see explanation

Step-by-step explanation:

sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{\sqrt{119} }{12}[/tex]

cosX = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{XZ}{XY}[/tex] = [tex]\frac{5}{12}[/tex]

40.2 percent of the customers at the beauty supply store choose brand B.

An equation is an expression that shows the relationship between two or more numbers and variables.

The percent of customers that choose brand B = (number of  brand B customers / total number of customers) * 100%

The percent of customers that choose brand B = (402/1000) * 100% = 40.2%

40.2 percent of the customers at the beauty supply store choose brand B.

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Answer:

the inclination of the line will decrease

Step-by-step explanation:

If Cassandra changes the amount she deposits from 18 to 14, the slope changes to 14. So the new equation is M=14n + 224. The 224 is still the same, because that is the initial amount, and the new situation hasn't said anything about changing that, so it will not have any vertical translations. With that being said, as a result the slope will be less, so you can see it as "less vertical", so the inclination of the line will decrease

Answer:

24

Step-by-step explanation:

140 times .25 = 35

140 + 35 = 175

4,200 divided by 175 =

24

jobtestprep

The number of TV bought post-raise for $4,200 is 24 if the store manager decides to raise the TV price by 25% in order to increase the store's profits.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

A home appliance store has recently seen an increase in TV sales.

The store manager decides to raise the TV price by 25% in order to increase the store's profits.

Original price of TV = $140

Price after increasing:

= 140 + 25% of 140

= $175

The number of TV bought post-raise for $4,200 = 4200/175

= 24

Thus, the number of TV bought post-raise for $4,200 is 24 if the store manager decides to raise the TV price by 25% in order to increase the store's profits.

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Answer:

For plan B to save money car rental need to drive 111.1 miles as [tex]\frac{x}{y}[/tex] expresses the average amounts of miles per day car rental drive and its obtained value is 111.1.

Step-by-step explanation:

In the question it is given that a car rental company offers two plans for renting a car.

Plan A: $30 per day and [tex]$\$ 0 \cdot 18$[/tex] per mile.

Plan B: $50 per day with free unlimited mileage

It is required to find that how many miles would be needed to drive for plan B to save money. be needed to drive for plan B to save money.

Step 1 of 5

In Plan A $30 per day and [tex]$\$ 0 \cdot 18$[/tex] per mile are costed so the cost of Plan A is given by following equation,

[tex]$$A=30 y+0 \cdot 18 x$$[/tex]

In Plan B $50 per day with free unlimited mileage are costed so the cost of Plan B is given by following equation,

[tex]$$B=50 y$$[/tex]

Step 2 of 5

Now comparing the obtained equations [tex]$A=30 y+0 \cdot 18 x$[/tex]

and B=50y.

[tex]$$30 y+0 \cdot 18 x=50 y$$[/tex]

Step 3 of 5

Subtract 30y from both the sides of the obtained equation 30 y+0.18x=50y and simplify using subtraction properties.

[tex]$$30 y+0 \cdot 18 x-30 y=50 y-30 y$$\\ $0 \cdot 18 x=20 y$[/tex]

Step 4 of 5

Divide both the sides of the obtained equation [tex]$0 \cdot 18 x=20 y$[/tex] by [tex]$0 \cdot 18$[/tex] and simplify using division properties.

[tex]$$\begin{aligned}&\frac{0 \cdot 18 x}{0 \cdot 18}=\frac{20 y}{0.18} \\&x=\frac{1000 y}{9}\end{aligned}$$[/tex]

Step 5 of 5 save money car rental need to drive 111.1 miles.

[tex]$$\begin{aligned}&\frac{x}{y}=\frac{1000 y}{9 y} \\&\frac{x}{y}=111.1\end{aligned}$$[/tex]