Solve the system of equations given below.
8x + 4y = 16
7y = 15
-
1
OA. (4,-2)
B. (-2,4)
C. (1.2)
:
D.
(2,1)
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Answer:

triangle; area = 90 ft2

Step-by-step explanation:

THe type of two dimensional solid created by a vertical cross section of the cone that passes through the apex is a triangle, as you can see in the picture, if you draw a line that cuts the cone in half passing through the apex it would just be a triangle, and the area of the cross section is given by the formula:

[tex]a=\frac{b*h}{2}[/tex]

Since you have the radius of the base of the cone, you need the diameter to calculate the area, the diameter is given by the next formula:

[tex]D=2r[/tex]

[tex]D=2(6)[/tex]

[tex]D=12[/tex]

Now you just put your values into the formula of the triangle:

[tex]a=\frac{(12)(15)}{2}[/tex]

[tex]a=\frac{(180}{2}[/tex]

[tex]a=90[/tex]

So the area of the triangle formed is:

[tex]90ft^{2}[/tex]

Answer:

B

Step-by-step explanation:

correct on ed2020

Exponential functions model growth patterns such as population growth under ideal conditions, while the logistic model accounts for resource limits. The standard exponential equation is Y=abˣ, while logistic growth has a more complex form that includes the carrying capacity.

Exponential functions model various real-world phenomena in which growth occurs at a rate proportional to the current amount. For example, in natural populations, exponential growth is observed when resources are abundant and organisms can reproduce without constraints.

The standard form of an exponential function is Y = abx, where 'a' is the initial amount, 'b' is the growth factor, and 'x' represents time or another independent variable. In the context of population growth, 'a' would be the initial population size, 'b' is the growth rate per time period, and 'x' is the time elapsed.

Logistic growth is another pattern that is observed when resources become limited. It starts off similar to exponential growth but eventually slows down as the population reaches the carrying capacity of the environment.

Environmental conditions represented by the exponential growth model imply unlimited resources and space, whereas the logistic growth model includes the effects of limiting factors such as space, food, and other resources.

Answer:

B.44 mph and 46 mph

Step-by-step explanation:

This question is on relative speed

when cars move towards each other, you add their individual speeds to get their relative speed

Lets have two cars , A and B

Let  car A to have an average speed of x m/h towards the right hand side

Let car B to have an average speed of x+2 m/h towards the opposite direction

The distance between the cars is 270 miles

Time of meeting is 3 hours

The relative speed will be x+x+2=2x+2 miles per hour

Apply the formula for time=Distance/speed =D/S

[tex]t=\frac{D}{S} \\\\\\3=\frac{270}{2x+2} \\\\\\3(2x+2)=270\\\\\\6x+6=270\\\\\\6x=270-6\\\\\\6x=264\\\\\\x=\frac{264}{6} =44[/tex]

x=44 miles per hour

x+2=44+2=46 miles per hour

solution

44 mph and 46 mph

Final answer:

Two cars are traveling towards each other at speeds where one car is 2 mph faster than the other. They meet after 3 hours covering 270 miles. By setting an equation with the distance formula, we find that the slower car's speed is 44mph and the faster car's speed is 46mph. (Option B)

Explanation:

The question involves calculating the average speed of two cars traveling towards each other on the same road and meeting after a certain time. To solve this, we can set up an equation using the formula for speed, which is distance divided by time.

Let's denote the speed of the slower car as ‘s’ mph (miles per hour). Consequently, the faster car travels at ‘s+2’ mph. When they meet after 3 hours, both cars together will have covered a distance of 270 miles. Thus, the total distance covered by both cars can be written as:

Total distance = (speed of car A)×(time) + (speed of car B)×(time)

270 miles = s×3 hours + (s+2)×3 hours

This simplifies to:

270 = 3s + 3s+ 6

Combining like terms and simplifying, we get:

270 = 6s + 6

Subtract 6 from both sides to find:

264 = 6s

Dividing both sides by 6 yields:

s = 44 mph

Therefore, the slower car travels at 44 mph and the faster car at 44+2 = 46 mph.

The correct answer is B. 44 mph and 46 mph.

Answer:

QT = RT

Step-by-step explanation:

When drawing triangle PQR the perpendicular bisector cuts the triangle in half, which results in two sides that are congruent. This makes QT and RT congruent.

Based on the triangle QPR  option C) PQ = PR and A) QT = RT

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In QPR

∠Q = ∠R (∵ PT is a bisector)

∴QT = RT (∵ PT is a bisector of QR)

PT is a common  between PQT and RQT

∴PQ = PR ( by congruent part of congruent triangle)

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Answer:

The vertex of the parabola is (105 , 7)

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation of the parabola is y = a(x - h)² + k, where (h , k) are

  the coordinates of the vertex point of the parabola

- The points (0 , 27) , (52.5 , 12) , (105 , 7) ,  (157.6 , 12) , (210 , 27) are

 the points lie on the parabola

- We have three unknown a , h , k to find them we will substitute the x

 and y in the equation by the coordinates of some point on the

 parabola

- Lets start with point (0 , 27)

∵ x = 0 and y = 27

∴ 27 = a(0 - h)² + k

∴ 27 = ah² + k ⇒ (1)

- Lets use point (210 , 27)

∵ x = 210 and y = 27

∴ 27 = a(210 - h)² + k ⇒ (2)

- Equations (1) and (2) have the same L.H.S, so we can equate them

∴ ah² + k = a(210 - h)² + k ⇒ subtract k from both sides

∴ ah² = a(210 - h)² ⇒ divide both sides by a

∴ h² = (210 - h)² ⇒ take √ for both sides

∴ h = ± (210 - h)

∵ h = 210 - h ⇒ add h to both sides

∴ 2h = 210 ⇒ divide both sides by 2

∴ h = 105

∵ h = - (210 - h)

∴ h = -210 + h ⇒ no value of h from this equation so we will ignore it

∴ The value of h is 105

- Lets substitute this value of h in the equation

∴ y = a(x - 105)² + k

- Lets use the point (105 , 7)

∵ x = 105 and y = 7

∴ 7 = a(105 - 105)² + k

∴ 7 = a(0) + k

∴ k = 7

- The coordinates of the vertex point are (h , k)

∵ h = 105 and k = 7

∴ The vertex of the parabola is (105 , 7)

Answer:

105, 7 and then for the next one y= 0.0018(x – 105)2 + 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

Put the given y-intercept b = 7 and the coordinates of the point (-2, 1) to the equation:

[tex]1=-2m+7[/tex]          subtract 7 from both sides

[tex]-6=-2m[/tex]       divide both sides by (-2)

[tex]3=m\to m=3[/tex]

We have the equation:

[tex]y=3x+7[/tex]

Convert it to the general form [tex]Ax+By+C=0[/tex]:

[tex]y=3x+7[/tex]              subtract 3x and 7 from both sides

[tex]-3x+y-7=0[/tex]           change the signs

[tex]3x-y+7=0[/tex]

Answer:

Her average speed = 7.5 miles/hour

Explanation:

First, since the required speed unit is miles/hour, we need to make sure that all units given are in miles (for distance) and hour (for time)

We are given that:

Distance covered = 2400 miles

Times taken = 13 days and 8 hours

We know that 1 day has 24 hours

Therefore:

13 days = 13 x 24 = 312 hours

Time taken = 13 days and 8 hours = 312 + 8 = 320 hours

Now, average speed is calculated as the total distance divided by the total time

This means that:

[tex]Average Speed=\frac{Total Distance}{Total Time} = \frac{2400}{320}=7.5[/tex] miles/hour

Hope this helps :)

To find the average speed, convert the total migration time of 13 days and 8 hours to hours, which is 320 hours. Then divide the total distance, 2400 miles, by the total time to get an average speed of 7.5 miles per hour.

To calculate the average speed of the Canada goose on its $2400$-mile migration completed in $13$ days and $8$ hours, we must first convert the total time into hours. There are $24$ hours in a day, so $13$ days is equal to $13 \times 24 = 312$ hours. Adding the additional $8$ hours, we have a total travel time of $320$ hours. The average speed is then calculated by dividing the total distance by the total time.

The average speed of the goose is:

The average speed is $\frac{2400}{320} = 7.5$ miles per hour.

Answer:

12.

Step-by-step explanation:

First arrange in ascending order:

2 5 8 10 14 17 21

The median is 10.

the lower quartile is the middle number of 2 5 and 8 which is 5.

Similarly the upper quartile is 17.

IQR = 17 - 5 = 12.

Answer:

12

Step-by-step explanation:

Answer:

Ratio: 20:36

Rate: 20 squids per 36 eels

Simplified ratio:

[tex] = \frac{20}{36 } = \frac{10}{18} = \frac{5}{9} [/tex]

Unit ratio:

20/36 squids per eel (dividing by 36)

Please mark Brainliest if this helps!

Answer:

Step-by-step explanation:

Number of squid in the tank = [tex]20[/tex]

Number of eels in the tank = [tex]36[/tex]

Rate of squids to eels will be obtained by creating a fraction of number of squids over number of eels

Rate of squid to eels = [tex]\frac{20}{36}[/tex]

also ratio of squid to eels will be written as [tex]20:36[/tex]

Simplified ratio = [tex]\frac{20}{36} = \frac{5}{9} = 5:9[/tex]

Unit rate will be defined as number of squid per eels

Unit rate = [tex]\frac{20}{36} = 0.55[/tex]

Answer:

220 miles

Step-by-step explanation:

Joe got $301 for an overnight trip.

As the employees get $125 for lodging. The lodging expense will be subtracted from the total amount to get the amount for the miles he drove.

So,

Expense by company for miles driver = 301 - 125 = $176

So, Joe received $176 for miles driven

Now,

amount for one mile = $0.80

Miles driven in $176 = 176/0.80 = 220 miles

Joe drove 220 miles ..

Joe drove 220 miles for his company to be reimbursed $301 for an overnight trip, after considering the fixed lodging cost and the per mile reimbursement rate.

The student wishes to know how many miles Joe drove if his company reimbursed him $301 for an overnight trip wherein he receives $125 for lodging plus $0.80 per mile driven. To solve this problem, we start by subtracting the fixed lodging cost from the total reimbursement to find the total amount reimbursed for mileage. Let's denote the number of miles driven by Joe as m.

Total reimbursement for mileage = Total reimbursement - Lodging cost
$301 - $125 = $176

Now, since Joe gets reimbursed $0.80 per mile, we can calculate the number of miles driven as follows:

$176 / $0.80 per mile = 220 miles

Therefore, Joe drove 220 miles for his company to be reimbursed $301 for an overnight trip.

let's recall that, arc's angle measures come from the central angle they're in.

if this intercepted arc is 80°, and is intercepted by an angle stemming from the center, namely a central angle, then the angle is also 80°.  Check the picture below.

If angle with its vertex at the center of a circle intercepts an 80° arc of that circle then the measure of the angle is  80°.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that angle with its vertex at the center of a circle intercepts an 80° arc of that circle

We have to find the measure of the angle.

When an angle is formed at the center of a circle, it intercepts an arc of the circle that is equal in measure to the angle.

Since the given angle intercepts an 80° arc of the circle, we know that its measure is also 80°. so the measure of the angle is 80°.

Hence, if angle with its vertex at the center of a circle intercepts an 80° arc of that circle then the measure of the angle is  80°.

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Answer:

Radius of circle is 4

Step-by-step explanation:

The standard equation of circle is

(x-h)^2+(y-k)^2=r^2

where (h,k) is the center and r is the radius.

We are given:

(x² - 10x + 25) + (y² - 16y + 64) = 16

we know that a^2-2ab+b^2 =(a-b)^2

Using the above formula and converting the given equation into standard form, we get:

(x-5)^2+(y-8)^2=(4)^2

So, radius of circle is 4.

Answer:

it should be 1/2

Step-by-step explanation:

because the sequence is going down by 0.05 each time;

7/10= 0.70

13/20= 0.65

3/5= 0.6

11/20= 0.55

so to continue the pattern,

1/2= 0.5

Answer:

The correct answer is first option

u² - 11u + 24 = 0

When u = (x² - 1)

Step-by-step explanation:

It is given that,

(x² - 1)² - (x² - 1) + 24 = 0

To find the correct answer

Substitute u = x² - 1

The equation becomes,

u² - 11u + 24 = 0 Where u = (x² - 1)

Therefore the correct answer is first option

u² - 11u + 24 = 0

When u = (x² - 1)

Answer:

u² - 11u + 24 = 0 is equivalent to (x²-1)² - 11(x²-1) + 24 = 0

Step-by-step explanation:

(x²-1)² - 11(x²-1) + 24 = 0

Evaluate each equation by substituting the value of u to match the equation above.

1) u² - 11u + 24 = 0 where u = (x² - 1)

(x²-1)² - 11(x²-1) + 24 = 0

This equation matches (x²-1)² - 11(x²-1) + 24 = 0

2) (u²)² - 11(u²) + 24 where u = (x² - 1)

[(x²-1)²]² - 11(x²-1)² + 24

This equation does not match (x²-1)² - 11(x²-1) + 24 = 0

3) u² + 1 - 11u +24 = 0 where u = (x² - 1)

(x² - 1)² + 1 - 11(x²-1) + 24 = 0

This equation does not match (x²-1)² - 11(x²-1) + 24 = 0

4) (u² - 1)² - 11(u² - 1) + 24 where u = (x² - 1)

[(x²-1)²-1]² - 11(u² - 1)² + 24

This equation does not match (x²-1)² - 11(x²-1) + 24 = 0

Therefore, the first quadratic equation is equivalent to (x²-1)² - 11(x²-1) + 24 =0.

!!

[tex]\bf (\stackrel{x_1}{9}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{-5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-(-9)}{10-9}\implies \cfrac{-5+9}{1}\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=4(x-9)\implies y+9=4(x-9) \\\\\\ y+9=4x-36\implies y=4x-45\implies \stackrel{\textit{standard form}}{-4x+y=-45}[/tex]

just a quick note

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

now, however the inappropriate choices here, do have it with a negative "x".

Answer:

y + 9 = 4(x - 9); -4x + y = -45

Step-by-step explanation:

According to the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, so put the coordinates into their correct positions, depending on the signs. In the equation, there is a 9 in it [-(-9) = 9], according to the formula. By the way, this is its y-coordinate. The x-coordinate is 9, which is normal, according to the formula (see part of above answer in parentheses). So now, this is how your work will look:

y + 9 = 4x - 36 [Point-Slope Form]↷

- 9 - 9

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

y = 4x - 45 [Slope-Intercept Form]↷

-4x -4x

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

-4x + y = -45 [Standard Form]

Here we are at this second equation.

I am joyous to assist you anytime.

Add the bases together, divide that by 2 then multiply by the height.

15.8 + 21.8 = 37.6

37.6/2 = 18.8

18.8 x 11.7 = 219.96 yd^2

Answer:

B) 219.96 yd2

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

(a + b) /2*h

Now you would plug in the numbers

(15.8 + 21.8) /2*11.7

Now solve this in order of operations

(15.8 + 21.8) /2*11.7

37.6/2*11.7

18.8*11.7

219.96

Answer:

y=3x+1  (slope-intercept form)

-3x+y=1 (standard form)

3x-y=-1 (another version of standard form)

y-7=3(x-2) (point-slope form)

Step-by-step explanation:

y=mx+b is slope intercept form where m is slope and b is y-intercept.

The slope of perpendicular lines are opposite reciprocals.

The opposite reciprocal of -1/3 is 3.

So we are looking for a line of the form y=3x+b going through (2,7)

y=3x+b with (x,y)=(2,7)

7=3(2)+b

7=6+b

7-6=b

1=b

b=1

So the equation is y=3x+1.

Now you can also put it in standard form:

Subtract 3x on both sides:

-3x+y=1

You can also multiply both sides by -1:

3x-y=-1

ax+by=c is standard form.

We can also use point slope form.

y-y1=m(x-x1) where (x1,y1) is a point contained by our line and m is the slope.

We have m=3 and (x1,y1)=(2,7)

y-7=3(x-2)

Answer:

its a)the first sequence is geometric bc of the common ratio of 2. the second sequence is arithmetic bc of the common difference of 7.

Option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.

Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.

For the given situation,

First sequence: 5, 10, 20, 40..

Second sequence: 8, 15, 22, 29, ...

Now consider the first sequence: 5, 10, 20, 40..

Here, when we divide the second number by first number, we get the common ratio as 2.

⇒ [tex]\frac{10}{5}=2[/tex]

⇒ [tex]\frac{20}{10}=2[/tex]

⇒ [tex]\frac{40}{20}=2[/tex]

Thus the first sequence follows a geometric progression with common ratio 2.

Now consider the second sequence: 8, 15, 22, 29, ...

Here, when we subtract the first term is subtracted from the second term, the common difference is 7.

⇒ [tex]15-8=7[/tex]

⇒ [tex]22-18=7[/tex]

⇒ [tex]29-22=7[/tex]

Hence we can conclude that option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.

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Answer:

[tex]\large\boxed{3m+(m+5)=4m+5}[/tex]

Step-by-step explanation:

[tex]3m+(m+5)=3m+m+5\qquad\text{combine like terms}\\\\=(3m+m)+5=4m+5[/tex]

Answer:

-1/4

Step-by-step explanation:

You can find the slope from a graph several ways.

Here are two ways of doing it.

Method 1. Slope formula

Find two points, then apply the slope formula, m = (y2 - y1)/(x2 - x1)

We read two easy  to read points of the graph: (0, -2) and (4, -3)

m = (y2 - y1)(/(x2 - x1) = [-3 - (-2)]/(4 - 0) = (-3 + 2)/4 = -1/4

Method 2. Rise/Run

Slope = m = rise/run

Pick two points. Start at one point and go to the other point by going vertically (rise) and horizontally). The vertical distance is the rise, and the horizontal distance is the run. Up is positive, and down is negative. Right is positive, and left is negative.

Pick points (0, -2) and (4, -3).

Start at (0, -2). To go to (4, -3), move 1 unit down. That is a rise of -1. Now go horizontally 4 inits to the right. That is a run of 4.

slope = rise/run = -1/4

e = Euler's constant

e ≈ 2.718281828459045, rounded up e = 2.7183.

= 4.17356

the number after the line is lower than 5, round the number down (keep it the same). If the number is 5 and more than it round the number upwards. therefore in example 1 you need to round 4.17356 to 4 decimal places. This means you have 2 choices, either 4.17356 or 4.17357.

When we say round to 4 it means to fewer the digits to 4 to the right of the decimal point. The basic rule of remember is, if the number in the 5th place ( to round it any decimal place, consider this next digit) is > 5 then add 1 on the 4th digit and else remains the same.

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Answer:

Alonzo baseball

Your question is incomplete and lacks a graph. Please check below for the full content.

Chase and Alonzo stand next to each other and throw baseballs in the air. The path of Chase's ball is described by the equation y = - 4x²+ 5x+ 7. The path of Alonzo's ball is shown by the graph. In each function, x is the horizontal distance the ball travels in meters, and y represents its height. Whose baseball reaches a greater height?

A. Both baseballs reach the same height.

B. Chase's baseball

C. Alonzo's baseball

The misssing graph is shown below.

The correct option is option C: Alonzo's baseball

The equation whose highest degree of the variable used in the equation is 2 and has 2 roots, is called quadratic equation.

Here the quadratic equation of the path of Chase's ball is given by y = - 4x²+ 5x+ 7

To compare the height of both paths followed by the ball

we have to first calculate the height of the path of Chase's ball.

the path of Chase's ball is f(x)=-4x²+ 5x+ 7

The function will have the highest value when f'(x) will be 0.

f'(x)=-8x+5

f'(x)=0

⇒-8x+5=0

⇒-8x=-5

⇒x=5/8

at x=5/8, function value is

f(x)=-4x²+ 5x+ 7

=-4(5/8)²+ 5(5/8)+ 7

=-4(25/64)+(25/8)+7

=(-25/16)+25/8+7

=8.5625

There maximum value of f(x) is 8.5625.

The maximum height reached by Chase's ball will be 8.5625m.

From the graph of the path of Alonzo's ball, it is clear that

The maximum height reached by Alonzo's ball will be 9m.

As 8.5625m < 9m

Alonzo's baseball will reach greater height.

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Answer:

5 < √32 < 6.

Step-by-step explanation:

√25 = 5 and √36 = 6 so

5 < √32 <  6.

Answer:

[tex]a_{20} = 12+3(20-1)[/tex]

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Anything multiplied by 0 gives you an answer of 0, therefore 2*2*2*2*0=0

Answer:

0

Step-by-step explanation:

In most cases, zero times anything is zero.

Here we have 2*2*2*2 = 2^4 = 16.  Thus,

2*2*2*2*0 = 16(0) = 0

You meant pi, pi is a irrational number, but they use 3.14 for approximation, so that is your answer.

Hope this helped!

Nate

[tex]\pi-\bold{pi}\\\\\pi\ \text{it's the ratio of a circle's circumference to its diameter}\\\\\pi=\dfrac{\text{circumference of a circle}}{\text{circle diameter}}\\\\\pi\ \text{it's irrarional number}\\\\\pi=3.14159265358979323846264338327...\\\\\text{Approximation of}\ \pi:\\\\\pi\approx3.14\\\\\pi\approx\dfrac{22}{7}\\\\\pi\approx\dfrac{355}{113}[/tex]

The number pi occurs when calculating the surface area or volume of the rotational solids.

Cylinder:

[tex]S.A.=2\pi r^2+2\pi rH\\\\V=\pi r^2H[/tex]

Cone:

[tex]S.A.=\pi r^2+\pi rl\\\\V=\dfrac{1}{3}\pi r^2H[/tex]

Sphere:

[tex]S.A.=4\pi R^2\\\\V=\dfrac{4}{3}\pi R^3[/tex]

The number pi occurs when calculating the area and the circumference of a circle.

[tex]C=\pi d=2\pi r\\\\A=\pi r^2[/tex]

It is also used to convert angle measure in degrees to radians.

[tex]x^o=\dfrac{x\pi}{180}\ rad[/tex]

WHAT IS A COMPLEMENTARY ANGLE?

Complementary comes from the word complement. When two angles sum a total of 90°, they 'complement' each other. A complementary angle is a combination of two angles whose sum is equal to 90°.

BACK TO THE QUESTION

The question is asking what the measure of the other angle is. The given angle is 28°.

HOW TO FIND YOUR ANSWER

When you're given the measure of one of the angles, it's easy to find the other. All you have to do is subtract the measure of the angle from 90°.

In this question, you are given that the angle is 28°. That means you have to subtract 28 from 90.

[tex]90\°-28\°=62\°[/tex]

a. 14° ✘

b. 28° ✘

c. 62° ✓

d. 152° ✘

The answer to your question is 62°, also known as choice c.

Answer:

Step-by-step explanation:

the answer is 4/5

Because there are 5 section and the blueberry takes up 4 of the sections it is 4/5

Answer:

4/5

Step-by-step explanation:

So he divided something into 5 sections.

He fills one section with graph jelly and 4 sections with blueberry jelly.

Since there are 5 sections and 4 are filled with blueberry, then 4/5 is the fraction of the table he filled will blueberry.

Answer:

A

Step-by-step explanation:

all we need to do is to plug the point (6,4) in the inequality and see if it satisfies it :

pay attention that here we have x=6  y=4

4<[tex]\frac{3}{4} (6) - 3[/tex]

we simplify we get :

4<4.5-3  

4<1.5  which is incorrect  so (6,4) is not a solution. moreover

notice that 4 is > than 1.5  so the point lies above the line

thus the answer is : A

you can also solve this problem by graphing the line [tex]y= [/tex][tex]\frac{3}{4} x-3[/tex]  and plotting the point (6,4)  and hence you will notice that the point is above the line

Answer:

Step-by-step explanation:

[tex]y<\dfrac{3}{4}x-3\\\\\text{Put the coordinates of the point and check the inequality:}\\\\(6,\ 4)\to x=6,\ y=4\\\\4<\dfrac{3}{4}\cdot6-3\\\\4<\dfrac{18}{4}-3\\\\4<4.5-3\\\\4<1.5\qquad\bold{FALSE}\\\\\text{Therefore your answer is NO, because (6, 4) is above the line.}[/tex]

[tex]\text{Other mathod:}\\\\\text{Show this inequality in the coordinate system.}\\\\\text{Draw the dotted line}\ y=\dfrac{3}{4}x-3.\\\\for\ x=0\to y=\dfrac{3}{4}(0)-3=0-3=-3\to(0,\ -3)\\\\for\ x=4\to y=\dfrac{3}{4}(4)-3=3-3=0\to(4,\ 0)\\\\\text{shaded region below the line}\\\\\text{Mark point (6, 4) and check if it lies in the shaded region.}[/tex]

To find the cost of buying 15 baseball caps, we set up a proportion using the information about the cost per cap from last year. The cost of buying 15 caps is $75.

To write a proportion that gives the cost of buying 15 baseball caps, we can use the fact that the cost per cap is the same as last year. Let c represent the cost of buying 15 caps. We can set up the proportion as follows:

11 caps / $55 = 15 caps / c

To solve for c, we can cross-multiply and solve for the unknown variable:

11c = 15 * $55

c = (15 * $55) / 11 = $75

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To find the cost of buying 15 baseball caps, set up a proportion of 11 caps for $55 and 15 caps for (c). Solve for (c) by cross multiplying and dividing by 11. The cost of buying 15 baseball caps would be $75.

To write a proportion that gives the cost (c) of buying 15 baseball caps, we can set up the ratio of the number of caps to the cost of the caps in two scenarios: 11 caps for $55 and 15 caps for (c). Since the cost per cap is the same in both scenarios, the proportion would be:

11/55 = 15/(c)

To solve for (c), we can cross multiply:

11 * c = 15 * 55

Dividing both sides of the equation by 11, we find:

c = 15 * 55 / 11 = 75

Therefore, the cost of buying 15 baseball caps would be $75.

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