Solve the following inequalities,express the solution in interval notation and graph it 4.a)

Answer:

Step-by-step explanation:

The first thing you need to do, is find the total amount of gorillas.
to do this, you are going to use the equation:

24 + g = 7g

Both sides are equal, since the wallabies and the buffalo are equal. This makes the equation true.
you subtract g from 7g, and you should get:

24= 6g

Divide by six:

4 = g  

That is the # of gorillas.

Now, if you add 24 + 4

You get the # of buffalo.

Which is: 28

Since the buffalo and wallabies are the same, the # of wallabies is also 28.
if you want to check, multiply 4x7 to get the amount of wallabies.

The range of the equation of the function given as y = x^2 + 4x + 7 is y >= 3

The equation of the function is given as

y = x^2 + 4x + 7

Differentiate the function with respect to x

So, we have

y' = 2x + 4

Set the differentiated function to 0

So, we have

2x + 4 = 0

This gives

2x = -4

Divide by 2

x = -2

Substitute x = -2 in the equation y = x^2 + 4x + 7

So, we have

y = (-2)^2 - 4 x 2 + 7

Evaluate

y = 3

The leading coefficient is positive

This means that the vertex is a minimum

So, we have the range to be

y >= 3

Hence, the range is y >= 3

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The bulb is 5 inches far from the vertex of the cross section.

A portion of the right cone known as a parabola is one that runs parallel to the generating line on one side of the conic figure.

The standard equation for a parabola is typically expressed as y² = 4ax if the directrix is parallel to the y-axis, and y² = 4ax if the parabola is in the negative quadrants. The conventional equation of a parabola is x² = 4ax if the parabola is sideways, or if the directrix is parallel to the x-axis. If the parabola is in the negative quadrants, the equation is x² = 4ax.

Given, The equation x = 1/20y² can be used to model the cross section of a parabolic spotlight (with units in inches).

We must determine the distance between the bulb and the cross section's vertex.

Equation x = 1/20y² is alternatively denoted by the expression y² = 20x.

Now, comparing the equation to the parabola's conventional form, y²=4ax

So, 4a=20

a=5

Consequently, a=5 represents the distance from the cross section's vertex to the bulb.

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The correct graph that represents the solution set of the system of inequalities is in Option(b).

Inequality is a  statement of an order relationship (greater than, greater than, or equal to, less than, or less than or equal to) between two integers or algebraic expressions in mathematics.

The given system of inequalities are,

y < -3x - 2

y ≤ x - 2

We have to select the graph that represents the solution set of the system of inequalities.

y < -3x - 2

Let, y = -3x - 2

Now, plot the graph of the line y = -3x - 2 with a Dotted line ( as < is a strict inequality).

y ≤ x - 2

Let, y = x - 2

Now, plot the graph of the line y = x - 2 on the graph.

The area between the two lines of inequalities on the graph represent the solution set.

Upon comparison with the graphs in the options, the correct graph is present in Option(b).

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Moving waves can be described either as a function of time or as a function of position

A wave is a dynamic disturbance of one or more quantities that propagates in physics, mathematics, and related sciences. When waves oscillate frequently around an equilibrium value at a certain frequency, they are said to be periodic.

In a medium, a wave is a disturbance or variation that gradually transfers energy from one point to another. It can be an elastic deformation or a change in pressure, electric or magnetic strength, electric potential, or temperature.

It should be noted that it can be a function of the position as well as the time.

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Answer:

C.

Step-by-step explanation:

as M is right over the middle of LN, this is an isoceles triangle (both legs are equally long).

so, we need to calculate only one leg and then double it fit both legs.

we get e.g. LM via Pythagoras.

LM is the Hypotenuse of the right-angled triangle with half of LN and the height to M being the legs.

so,

LM² = height² + (LN/2)² = 3² + 6² = 9 + 36 = 45

LM = sqrt(45) = 6.708203932... units

the perimeter is the sum of all 3 sides :

LN + LM + MN = LN + 2×LM = 12 + 2×sqrt(45) =

= 25.41640786... units

Answer: (0,3)

Step-by-step explanation:

The y-intercept for f(x)=x would be (0,0). Therefore, if we translate it up by three to get g(x), then the y coordinate would go up by 3, resulting in (0,3).

So we need to solve the following equation for x:

We can apply a square root to both sides but it is important to remember the following property. For any given number a we have:

Which means that:

So for our case we have:

Then the solutions are 7 and -7.

If the temperature is 13 degrees at midnight, then the temperature will be 6 degrees at 3:00 AM.

Temperature at midnight = 13 °

Temperature drop per hour = 2 °

We need to find the temperature at 3:00 AM

Number of hours till then = 3 hours.

Temperature drop will be calculated by using multiplication.

Temperature drop = 2 × 3 = 6°

Temperature ate 3:00 AM = 12 - 6 = 6°

Therefore, we get that, if the temperature is 13 degrees at midnight, then the temperature will be 6 degrees at 3:00 AM.

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Answer:$346.8

Step-by-step explanation:

1. X - 70% = 204

Want to get the value of X

2. X + 70% = 204 + 70%

= X = 204 x 1.7

= X = $346.8

Answer:

Original Price = $680

Step-by-step explanation:

Think about what a 70% reduction in price means.

If the original price of an item is $100 then a 70% reduction would mean that it costs 70% less from the original price. This means you would be paying only 30% of the original price

Let the original price be $P

Then the price you pay after 70% reduction is 30% of P
= P x 30/100

= P x 0.3                  (30% = 30/100 = 0.3)

= 0.3P

We are given that this sale price = $204

--> 0.3P = 204

Dividing both sides by 0.3 gives us the value for P
0.3P/0/3 = 204/0.3

P = 204/0.3 = 680

So

Original Price = $680

We can double check our computations as follows

If original price = 680, then a reduction of 70% would be a discount of
0.7 x 680 = 476

Price after discount = Original Price - Discount

= 680 - 476 = 204

So our results are consistent

Given the system of equations:

To solve it by substitution, follow the steps below.

Step 1: Solve one linear equation for x in terms of y.

Let's choose the second equation. To solve it for x, add 3y to each side of the equations.

Step 2: Substitute the expression found for x in the first equation.

Step 3: Isolate y in the equation found in step 2.

To do it, first, add 48 to both sides.

Then, divide both sides by 15.

Step 4: Substitute y by 5 in the relation found in step 1 to find x.

Answer:

x = -9

y = 5

or (-9, 5)

Also, you can graph the lines by choosing two points from each equation, according to the picture below.

Side BC is opposite to angle BAC, in the picture.

Answer: Angle BAC - first option

Answer: 3 17/20 is bigger than 3 13/28

Step-by-step explanation:

2 ways:

1) Turn the fractions into decimal form.

13/28 = 0.464

0.464 + 3 = 3.464

17/20 = 0.85

0.85 + 3 = 3.85

2) Check which one is bigger

3.85 is bigger than 3.464 because the tenth place is bigger than the second number.

Second way:

1) Remove the 3s.

Both equations have three, so you could remove both sides three

3 13/28  ?  3 17/20

13/28 ? 17/20

2) Multiply both bottom expressions by itself.

(The numbers that its multiplying equals to 1. When multiplying a number by 1, it stays the same.)

13/28 * 20/20 = 260/560

17/20 * 28/28 = 476/560

3) Compare the fractions

260/560  ?  476/560

260/560  <  476/560

The number in the fraction is bigger

Answer:

No, 3 ¹³/₂₈ is smaller than 3 ¹⁷/₂₀.

Step-by-step explanation:

Convert both mixed numbers into improper fractions:

[tex]\implies 3 \frac{13}{28}=\dfrac{3 \times 28+13}{28}=\dfrac{97}{28}[/tex]

[tex]\implies 3 \frac{17}{20}=\dfrac{3 \times 20+17}{20}=\dfrac{77}{20}[/tex]

The lowest common multiple of 28 and 20 is 140.

Therefore, multiply the numerator and denominator of each improper fraction by the same number to make both denominators 140:

[tex]\implies \dfrac{97 \times 5}{28 \times 5}=\dfrac{485}{140}[/tex]

[tex]\implies \dfrac{77 \times 7}{20 \times 7}=\dfrac{539}{140}[/tex]

Therefore, as 539 > 485:

[tex]\implies \dfrac{539}{140} > \dfrac{485}{140}[/tex]

[tex]\implies \dfrac{77}{20} > \dfrac{97}{28}[/tex]

[tex]\implies 3 \frac{17}{20} > 3 \frac{13}{28}[/tex]

Therefore, 3 ¹³/₂₈ is smaller than 3 ¹⁷/₂₀.

In the picture there is a cylinder with height 5 inches and diameter 4 inches. The surface area of cylinder is 87.62.

Given that,

In the picture there is a cylinder with height 5 inches and diameter 4 inches.

The surface area of a cylinder is the area that is enclosed by the flat bases and the curving surface of the cylinder. The cylinder's total surface area includes the area of the curving surface as well as the areas of the two circle-shaped bases of the cylinder.

The surface area of cylinder is 2πr²+2πrh

r is radius which is diameter/2

r=4/2=2

h is 5

Surface area of cylinder= 2πr²+2πrh

=2π×2²+2π×2×5

=8π+20π

=28π

=28×3.14

=87.92

Therefore, the surface area of cylinder is 87.62.

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Answer:

Measure of Angle A is 100°

Step-by-step explanation:

The sum of interior angles of a polygon is given by the formula :

(n-2)×180  (where n is the number of sides)

n = 6

(6-2)×180 =  

4 × 180 = 720

So :

A + B + C + D + E + F = 720

Substitute values given in diagram (angle d is 90 as the little square indicates a right angle) (Calling angle a as x)  :

x + 135 + 115 + 90 + 110 + 170 = 720

Simplify :

x + 620 = 720

Subtract 620 from both sides :

x = 720 - 620

x = 100

Measure of Angle A is 100°

Hope this helped and have a good day

Answer:

approximately 1,375 feet

Step-by-step explanation:

Set up and solve this proportion:

[tex] \frac{881}{66} = \frac{h}{103} [/tex]

[tex]66h = 90743[/tex]

[tex]h = 1375[/tex]

So the height of building b is about 1,375 feet.

Given the patient consumption rate on his diet:

(a) Average energy per day consumed will be since the number of days = 4

The average energy per day consumed = 850 Cal(b) The unit symbol for the answer = calorie

Answer:

Question 1:

x + y = 97

$1.55x + $1.09y = $120.45

Question 2:

32

Question 3:

65

Step-by-step explanation:

phew, way to long to explain why. A brainliest would be nice :)

Given

Scale Factor of 2:7

When the scale factor is a:b

Recall the following

Given that the ratio is is 2:7 then we have the following

Mapping diagram (D) is not a function.

So, an option which is not a function:

Therefore, mapping diagram (D) is not a function.

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Answer:

p = 18, q = 0

Step-by-step explanation:

The expression on the left side of the equation is
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} $}[/tex]

Multiply the denominators to get a common denominator:

[tex]\text{$\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)$}[/tex]

= [tex]\left(\sqrt{5}\right)^2-2^2[/tex]                           ∵ (a + b)(a - b) = a² - b²

[tex]=5-4\\\\= 1[/tex]

[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} $}\\\\[/tex]

[tex]=\dfrac{\left(\sqrt{5}+2\right)\left(\sqrt{5}+2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)} + \dfrac{\left(\sqrt{5} - 2\right)\left(\sqrt{5} - 2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}[/tex]

Since denominator
[tex]\text{$\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)$} = 1,[/tex]

the expression becomes

[tex]=\left(\sqrt{5}+2\right)^2 + \left(\sqrt{5}-2\right)^2\\\\= 5 + 4\sqrt{5} + 4 + 5 - 4\sqrt{5} + 4\\\\[/tex]

[tex]= 10 + 8 = 18[/tex]

Therefore  
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} = p + q\sqrt{5}$}\\\\\\= > \large \text{$ 18 = p + q\sqrt{5}$}[/tex]

Now [tex]\sqrt{5}[/tex] is an irrational number and p = rational so since there is no [tex]\sqrt{5}[/tex] term on the left side, q = 0 and p = 18

Answer:290

Step-by-step explanation:

first look at the ones place it is greater than 4 so round up  

286 to the nearest tenth is 290.

Place value, which is related to a digit's location in a number, is the amount that each digit is worth.

Given:

The number is 286.

The digit in tenth place is 6.

And the number 6 is greater than the number 4.

And 6 > 4.

So, the number will round off to the nearest tenth.

6 becomes zero.

And the number left to 6 will increase by 1.

That means 8 + 1 = 9.

So,

286 to the nearest tenth is 290.

Therefore, 290 is the nearest ten of the required number.

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Explanation

Lets first find the slope:

Now let's use the point-slope formula:

Answer

Answer:

(0,7]

Step-by-step explanation:

It is an open circle at 0 and a closed circle at 7.

a . After stopping for lunch Elena has travelled 50 miles.

b . She is less than 9 / 10 to her grand mother's location after travelling for 110 miles.

She is  traveling to visit her grandparents who live 125 miles away.

a.

She stops for lunch 2/3 of the way.

The distance she has travelled after she stopped for lunch can be calculated as follows:

distance in miles = 2 / 5 × 125

distance in miles = 2 × 25

distance in miles = 50 miles

b.

She enters the city where her grandmother lives after 110 miles.

Hence,

9 / 10 × 125 = 1125 / 10 = 112.5 miles

Therefore, she is less than 9 / 10 of her way there.

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If the second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. The number of  phone calls did she receive each evening is: 30, 80, 20.

Let x , y, z represents the 1st , 2nd, and 3rd evenings respectively

X + Y + Z = 130

Y = 4Z  

X = z+10

Substituting the second and third equations into the first:

z+10 + 4z + z = 130

Combine like terms

6z + 10 = 130

Subtract 10 from both sides

6z +10 -10 = 130 -10

6z =130 -10

6z =120
Divide both side by 6z

z = 120/6

z = 20

Solving for y

y = 4z

y = 4×20

y = 80

Solving for x

x = z+10

x = 20 +10

x = 30

Check:

x + y + z =130

30 +80 + 20 =130

Therefore they each received 30 phones, 80 phones and 20 phones.

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Answer

Selling price = $ 925

Mark percentage = 62%

The cost price is 570.

Answer:

150

Step-by-step explanation:

Answer:

[tex]-12w + x[/tex]

Step-by-step explanation:

question:

[tex]-3w - 3x - 7w + 4x - 2w[/tex]

first you add all the 'w' together.

(-3)+(-7)+(-2) = -10+(-2)=-12

so, [tex]-12w - 3x + 4x[/tex]

second you add all the 'x' together

(-3)+(4) = 1

so, [tex]-12w+1x[/tex]

then simplify:

[tex]-12w + x[/tex] <--answer

hope this helps!

Answer:

c. 250 miles

Step-by-step explanation:

[tex]d=(50)(5)=250[/tex]