Find the focus for y=x^2+4x-7

Answer: 72and 108

Step-by-step explanation: that is the correct answer don’t be a fool

Answer:

The solution of the equation f (x) = g (x) is the same as the coordinates of the intersection.

Exaple in the attachment.

f(x) = g(x) → x = -2, y = -1 or x = -1 and y = 0 or x = 1 and y = 2.

Answer:

119.45 meters

Step-by-step explanation:

This question can be solved using one of the three trigonometric ratios. The height mentioned is 298.5 + 1.5 = 300 m and the angle of depression is 28 degrees for Boat D and 34 degrees for Boat C. It can be seen that the required distance is given by x feet, which is the distance between the two boats. This forms two right angled triangle, as it can be seen in the diagram. The perpendicular is given by 300 m, the base is the unknown, and the angles 28 degrees for boat A and 34 degrees for boat B is is given, as shown in the attached diagram. Therefore, the formula to be used is:

tan θ = Perpendicular/Base (For the distance between the mountain and Boat D)

Plugging in the values give:

tan 28 degrees = 300/d.

d = 300/tan 28.

d = 564.22 m (to the nearest hundredth).

tan θ = Perpendicular/Base (For the distance between the mountain and Boat C)

Plugging in the values give:

tan 34 degrees = 300/c.

c = 300/tan 34.

c = 444.77 m (to the nearest hundredth).

The difference between d and c will be x, i.e. that distance between the boats. So 564.22 - 444.77 = 119.45 meters (to the nearest hundredth).

Therefore, the boats are 119.45 meters apart from each other!!!

To calculate the distance between the two boats, we can use the concept of angles of depression and trigonometry. The distance to boat D is calculated using the tangent function with the angle of depression and the height of the observer. The same process is used to find the distance to boat C. The distance between the boats is then the difference between these two distances.

To calculate the distance between the two boats, we can use the concept of angles of depression. Let's consider the boat D first. The angle of depression is the angle that the line of sight makes with the horizontal when looking down. In this case, the angle of depression for boat D is 28 degrees. Similarly, the angle of depression for boat C is 34 degrees.

Now, let's use trigonometry to find the distances. We can use the tangent function, which is the opposite side divided by the adjacent side. The opposite side represents the height difference between the observer and the boat, while the adjacent side represents the distance between the observer and the boat.

For boat D, we have:

tan(28 degrees) = opposite/adjacent

opposite = 1.5 m (height of the observer)

adjacent = distance between the observer and boat D

distance between the observer and boat D = 1.5 m / tan(28 degrees)

We can use the same process to find the distance between the observer and boat C:

distance between the observer and boat C = 1.5 m / tan(34 degrees)

Therefore, the distance between the boats is the difference between the distance to boat D and the distance to boat C.

Answer:

Exact Form:

1190/ 3

Decimal Form:

396. 6

Mixed Number Form:

396  2 /3

Step-by-step explanation:

Final answer:

The volume of the triangular prism with a triangle base of 14 units and height of 17 units and a prism height of 5 units is 595 cubic units.

Explanation:

To find the volume of a triangular prism, we need to first find the area of the base triangle and then multiply it by the height of the prism. The formula for the volume of a triangular prism is given by V = (base area)  imes (prism height). However, we need to be clear about what the given 14 and 17 represent. Assuming they stand for base and height of the triangle, respectively, the area of the base triangle is A = (1/2)  imes base  imes height = (1/2)  imes 14  imes 17. Multiplying this area by the prism height of 5 units gives us the volume of the prism.
Calculating the base area: A = (1/2)  imes 14  imes 17 = 119 square units. The volume is then V = 119  imes 5 = 595 cubic units. Therefore, the volume of the triangular prism is 595 cubic units.

Answer:

After 2.9 years the town's tax status will change

The towns tax status change within the next 3 years

Step-by-step explanation:

The question below is

Will the towns tax status change within the next 3 years ?

Let

y -----> the population of a small town

t ----> the number of years

we have a exponential function of the form

[tex]y=a(b)^{t}[/tex]

where

a is the initial value

b is the base

In this problem

[tex]a=9,400\ people[/tex]

[tex]b=100\%-14.3\%=85.7\%=85.7/100=0.857[/tex]

substitute

[tex]y=9,400(0.857)^{t}[/tex]

Remember that

The town's tax status will change once the population is below 6,000 people

so

The inequality that represent this situation is

[tex]9,400(0.857)^{t}< 6,000[/tex]    

Solve for t

[tex](0.857)^{t}< 6,000/9,400[/tex]

Apply log both sides

[tex](t)log(0.857)< log(6,000/9,400)[/tex]

[tex]-0.067t< -0.1950[/tex]

Multiply by -1 both sides

[tex]0.067t > 0.1950[/tex]

[tex]t > 2.9\ years[/tex]

so

After 2.9 years the town's tax status will change

therefore

The answer is

Yes, the towns tax status change within the next 3 years

the town's tax status will change a little over 7 years from the current time, assuming the rate of population decline remains constant.

To find out after how many years the population of the town would decrease to below 6,000 people, we start with the current population and apply the annual exponential decrease. The population decreases at a rate of 14.3% each year, which means the remaining population each year is 85.7% (100% - 14.3%) of the previous year. Starting with a population of 9,400 people, we need to solve for t in the inequality 9400  × (0.857)^t < 6000. We take the natural logarithm of both sides to solve for t:

ln(9400 × (0.857)^t) < ln(6000)

t × ln(0.857) < ln(6000) - ln(9400)

t > (ln(6000)-ln(9400)) / ln(0.857)

Using a calculator, we find that:

t > 7.17

Therefore, the town's tax status will change a little over 7 years from the current time, assuming the rate of population decline remains constant.

Answer:

с. 57°

Step-by-step explanation:

The measure of the exterior angle of a triangle is equal to sum of the opposite interior angles

114 = y+y

114 = 2y

Divide by 2

114/2 = 2y/2

57 =y

57° is the value of y.

A triangle has three sides, three angles, and three vertices. The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle. The sum of the length of any two sides of a triangle is greater than the length of the third side

Given

The measure of the exterior angle of a triangle is equal to the sum of the opposite interior angles

114 = y+y

114 = 2y

Divide by 2

114/2 = 2y/2

57 =y

To know more about the properties of triangles refer to :

https://brainly.com/question/17228179

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Answer:

The slope is [tex]m=\frac{5}{4}[/tex]   or  [tex]m=1.25[/tex]

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]A(9,7)\ B(5,2)[/tex]

Substitute the values

[tex]m=\frac{2-7}{5-9}[/tex]

[tex]m=\frac{-5}{-4}[/tex]

[tex]m=\frac{5}{4}=1.25[/tex]

Heyyyyyyyyyyyy

12 is to 7 is the answer

Idlkkk

The probability of hitting the soccer goal drawn onto the wall is approximately 45%, given that the soccer shots are completely random.

The subject of this question is probability, which is part of mathematics. The scenario describes a soccer training drill where the aim is to hit a goal that has been drawn onto a wall. The goal's dimensions are 21 feet by 7 feet, and the wall's dimensions are 36 feet by 9 feet.

In order to calculate the probability of hitting the target goal, we first need to calculate the area of the goal and the area of the wall. The area of the goal is obtained by multiplying the length by the height (21ft x 7ft = 147ft^2). Similarly, the area of the wall is 36ft x 9ft = 324ft^2.

Now that we have the areas, the probability of hitting the goal can be calculated by dividing the area of the goal by the area of the wall. That is, 147ft^2/324ft^2 = 0.4537, or approximately 0.45 or 45% when converted into a percentage.

Therefore, given that the shots are completely random, there is a 45% probability that the soccer ball will hit the drawn goal on the wall.

https://brainly.com/question/32117953

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Answer:

The total area is [tex]16\sqrt{3}\ units^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the regular pyramid is equal to the area of its four triangular faces

Each face is an equilateral triangle

so

Applying the law of sines

The surface area is equal to

[tex]SA=4[\frac{1}{2}b^{2}sin(60\°)][/tex]

we have

[tex]b=4\ units[/tex]

[tex]sin(60\°)=\frac{\sqrt{3}}{2}[/tex]

[tex]SA=4[\frac{1}{2}(4)^{2}\frac{\sqrt{3}}{2}][/tex]

[tex]SA=16\sqrt{3}\ units^{2}[/tex]

Answer:

16 sqrt 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

You need an x value to determine what number to multiply that will give you three numbers that are in the ratio of 3:1:4

Let the number = x

Set the equation up as 3x + x + 4x = 500

3x + x + 4x = 500           Combine the left

8x = 500                         Divide both sides by 8

x = 500/8                        Divide by 8.  

x = 62.5

So 3x = 3*62.5 = 187.5

1x       = 1 * 62.5 =  62.5

4x      = 4 * 62.5 = 250    The total should be 500

Answer:

{187.50, 62.50, 250}

Step-by-step explanation:

Add up the numbers in the ratio:  Add up 3, 1 and 4.  We get 8.

Then we divide up 500 into eight parts, each 62.5.

The ratio we are to follow is 3:1:4.

3 parts of 62.5 each comes out to 187.5;

1 part of 62.5 each comes out to      62.5; and

4 parts of 62.5 each comes out to 250.

If we have done this correctly, these 3 results add up to 500:

187.50

 62.50

250

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

   500

So, 500 divided up in the ratio 3:1:4 is {187.50, 62.50, 250}

Answer:

90 degree Clockwise Rotation

Step-by-step explanation:

Look at the figure and its points. When you rotate the paper clockwise, you will see that D'E'F is in the same position as DEF.

Answer:

90 degree anti-clockwise rotation

Step-by-step explanation:

if you turn the paper anti-clockwise, u can see that DEF is turned into D'E'F.

Answer:

B (6,12)

Step-by-step explanation:

The distance from point A (6,5) to point B should be 7.

A- (6,5)-> (7,5) is 1 unit right

B- (6,5)-> (6,12) is 7 units up

C- (6,5)-> (6,7) is 2 units up

D- (6,5)-> (12,5) is 6 units up

Answer: r = -10

Step-by-step explanation:

Move variable to the left , collect like terms, then divide both sides by 2.

Answer:

r = -10

Step-by-step explanation:

Your equation is 6r = 4r - 20

To solve this equation, find out r's value.

To do that, you must get r alone on one side of the equation

6r = 4r - 20

[Subtract 4r from both sides]

2r = -20

[Now divide both sides by 2]

r = -10

So, the answer to this equation is r = -10

I hope this helps! :)

Answer:

The approximate measure of the largest angle formed by these streets is [tex]99.2\°[/tex]

Step-by-step explanation:

we know that

Applying the law of cosines

[tex]c^{2}=a^{2}+b^{2} -2(a)(b)cos(C)[/tex]

In this problem we have

[tex]a=300\ ft[/tex]

[tex]b=250\ ft[/tex]

[tex]c=420\ ft[/tex] ----> is the greater side

substitute and solve for angle C

[tex]420^{2}=300^{2}+250^{2} -2(300)(250)cos(C)[/tex]

[tex]176,400=152,500 -150,000cos(C)[/tex]

[tex]cos(C)=[152,500-176,400]/150,000[/tex]

[tex]cos(C)=-0.1593[/tex]

[tex]C=arccos(-0.1593)=99.2\°[/tex]

Answer:

He will run 31.6 miles in two weeks.

Step-by-step explanation:

6 days a week = 2.3 miles

6 days · 2 weeks = 12 days total running 2.3 miles

1 day a week = 2 miles

1 day · 2 weeks = 2 days total running 2 miles

(12 · 2.3) + (2 · 2)

27.6 + 4

31.6 miles

The triangles cross the center of the circle CAD is the same as CBD.

The answer is B) 40 degrees.

Answer:

3(3a - 6b + 7c )

Step-by-step explanation:

The greatest common factor of 9, 18 and 21 is 3

Factor out 3 from each term

9a - 18b + 21c

= 3(3a - 6b + 7c) ← in factored form

Answer:

3(3a - 6b + 7c)

Step-by-step explanation:

Write each term as a multiplication of its factors. Then see which factors are in common to all terms.

9a - 18b + 21c =

= 3 * 3 * a - 2 * 3 * 3 * b + 3 * 7 * c

The common factors are shown below in bold:

= 3 * 3 * a - 2 * 3 * 3 * b + 3 * 7 * c

The only common factor is 3.

Now use the distributive property to factor out a 3.

= 3(3 * a - 2 * 3 * b + 7 * c)

Now multiply each term in parentheses again.

= 3(3a - 6b + 7c)

Answer:

15836

Step-by-step explanation:

Formula

Minor Earthquakes = (%) * Total Earthquakes.

Givens

Minor Earthquakes = ??

% = 89.6

Total Earthquakes = 17674

Solution

Minor Earthquakes = 89.6 / 100 * 17674

Minor Earthquakes = 1583590.4/100

Minor Earthquakes = 15836

Answer: There are 14940 minor earthquakes occurred in the world in 2014.

Step-by-step explanation:

Since we have given that

Number of earthquakes occurred world wide = 16674

Percentage of minor tremors with magnitude of 4.9 or less = 89.6%

So, Number of minor earthquakes occurred in the world in 2014 is given by

[tex]\dfrac{89.6}{100}\times 16674\\\\=0.896\times 16674\\\\=14939.90[/tex]

Hence, there are 14940 minor earthquakes occurred in the world in 2014.

Answer:

1. [tex]m=1\frac{1}{14}[/tex]

2. undefined

3. [tex]-6[/tex].

4. [tex]2\frac{1}{3}[/tex].

5. [tex]2[/tex].

6.  [tex]\frac{7}{2}[/tex]

Step-by-step explanation:

1. The required line passes through [tex](3,0),(-11,-15)[/tex]. The slope of the line joining the points  [tex](x_1,y_1),(x_2,y_2)[/tex] is given by the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] or [tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]

Either of them yields the same result.

Substitute [tex]x_1=3,y_1=0,x_2=-11,y_2=-15[/tex] into the first formula to get,

[tex]m=\frac{-15-0}{-11-3}[/tex] [tex]\implies m=\frac{-15}{-14}=\frac{15}{14}[/tex]

You can write this as a mixed number to obtain:

[tex]\implies m=1\frac{1}{14}[/tex]

2. The given line passes through [tex](4,-8),(4,13)[/tex].

Observe that the first coordinates are the same for both points. This implies that, the line is vertical.

The slope of all vertical lines are undefined.

3. The average rate of change of the function [tex]y=f(x)[/tex] on the interval [tex][a,b]\:\:or\:\:a\le x\le b[/tex] is given by:

[tex]ARC=\frac{f(b)-f(a)}{b-a}[/tex].

The given function is [tex]f(x)=x^2-4x[/tex]

[tex]f(-2)=(-2)^2-4(-2)=12[/tex]

[tex]f(4)=(4)^2-4(4)=0[/tex]

[tex]ARC=\frac{f(4)-f(-2)}{4--2}[/tex].

[tex]ARC=\frac{0-12}{6}=-6[/tex].

4. The given function is [tex]f(x)=2^x-1[/tex]

[tex]f(0)=2^0-1=0[/tex]

[tex]f(3)=2^3-1=7[/tex]

[tex]ARC=\frac{f(3)-f(0)}{3-0}[/tex].

[tex]ARC=\frac{7-0}{3}=2\frac{1}{3}[/tex].

5. From the graph

[tex]f(3)=7,f(0)=1[/tex]

[tex]ARC=\frac{f(3)-f(0)}{3-0}[/tex].

[tex]ARC=\frac{7-1}{3}[/tex].

[tex]ARC=\frac{6}{3}=2[/tex].

6. The given equation is :

[tex]2y-7x=-4[/tex]

Add [tex]7x[/tex] to both sides.

[tex]2y=7x-4[/tex]

Divide through by 2.

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

Compare this function to [tex]y=mx+b[/tex]

The slope is [tex]m=\frac{7}{2}[/tex]

Answer:

1. k(x) = (3g + 5h)(x) = -24x+40

2. k(x) = (h - g)(x)  = 0

3. k(x) = (g + h)(x) = -6x+10

4. k(x) = (5g + 3h)(x) = -24x+40

5. k(x) = (3h - 5g)(x) = 6x-10

6. k(x) = (5h - 3g)(x) = 10-6x

Step-by-step explanation:

Given

h(x) = 5 - 3x

and

g(x) = -3 x + 5

1. k(x) = (3g + 5h)(x)

3*g(x) = 3(-3 x + 5)

=> -9x+15

5*h(x) = 5(5 - 3x)

=>25-15x

(3g + 5h)(x)=3*g(x)+5*h(x)

= -9x+15+25-15x

=-9x-15x+15+25

=-24x+40

2. k(x) = (h - g)(x)

(h - g)(x) = h(x) - g(x)

= 5 - 3x -(-3 x + 5)

=5-3x+3x-5

= 0

3. k(x) = (g + h)(x)

(g+h)x = g(x) + h(x)

= -3 x + 5 + 5 - 3x

= -6x+10

4. k(x) = (5g + 3h)(x)

5*g(x) = 5(-3 x + 5)

=-15x+25

3*h(x) = 3(5 - 3x)

=15-9x

(5g + 3h)(x) = 5*g(x) + 3*h(x)

= -15x+25+15-9x

= -15x-9x+25+15

=-24x+40

5. k(x) = (3h - 5g)(x)

(3h - 5g)(x) = 3*h(x)-5*g(x)

=15-9x-(-15x+25)

=15-9x+15x-25

=-9x+15x+15-25

=6x-10

6. k(x) = (5h - 3g)(x)

5*h(x)-3*g(x) = 25-15x - (-9x+15)

= 25-15x+9x-15

= 25-15-15x+9x

=10-6x

Answer:

1. k(x) = (5g + 3h)(x) ---------------- 5. k(x)=40-5(3^x)-9x

2. k(x) = (3h - 5g)(x) ---------------- 6. k(x)=5(3^x)-9x-10

3. k(x) = (3g + 5h)(x) ---------------- 1. k(x)=40-3^x+1-15x

4. k(x) = (5h - 3g)(x) ----------------- 3. k(x)=10+3^x+1-15x

5. k(x) = (h - g)(x) ----------------- 2. k(x)=3^x-3x

6. k(x) = (g + h)(x) ----------------- 4. k(x)=10-3^x-3x

The difficulty between theorems and proofs in geometry is subjective. Theorems are proven true statements, while proofs are the logical processes used to establish the truth of theorems. Students may find one harder than the other depending on their individual abilities and understanding.

In the study of geometry, students often ask which are harder: theorems or proofs. To address this, it's important to understand the nature of both. A theorem is a statement that has been proven to be true through a logical sequence of statements, starting from agreed-upon assumptions, known as axioms. The Pythagorean Theorem, for instance, states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem provides a consistent and reliable outcome as long as the arithmetic is carried out correctly.

On the other hand, a proof is the process by which a theorem is shown to be true. Proofs involve a series of logical deductions from accepted principles and previously proven theorems. They are essentially the 'work' or argument that establishes the truth of a theorem. In any proof, each step must logically follow from the previous ones based on established geometric postulates and existing theorems. Therefore, a proof can be viewed as a bridge that connects the basic assumptions of geometry to the theorem being proven.

Whether theorems or proofs are harder is subjective and depends on the student's strengths. Some students find memorizing theorems challenging, while others may struggle with the logical sequence and creativity required to craft proofs. Nonetheless, the study of geometry contributes valuable reasoning skills and knowledge that connects fundamental truths of mathematics to practical applications in the real world, like engineering and physics.

Answer:

WoodChuck-Prairie Dog

WoodChuck-Beaver

WoodChuck-Chipmunk

PrairieDog-Beaver

PrairieDog-Chipmunk

Beaver-Chipmunk

Answer:

A chipmunk and a beaver

Answer:

x = 95 - 4y

Step-by-step explanation:

Let the pieces he has now be a variable x

The number of students in his class be y

According to the question he gave every student 4 pieces in the class

The pieces he gave to everyone become 4y.

Note that 4 here means he had given four to each

and as he had won 95 pieces at the fair in the starting,

therefore the equation becomes:-

x = 95 - 4y....

Answer:

51 in² is the area of the shape.

Step-by-step explanation:

Note that there is a triangle, as well as a Parallelogram.

First, solve for the measurement for the Parallelogram. The Parallelogram has sides that measure 6 in. & 7 in. respectively.

Note the measurement of the left length, which is 13. The right length is 7. To solve for the length of the triangle, subtract the two:

13 - 7 = 6

The triangle length is 6.

To solve for the triangle width, subtract the part from the total:

6 - 3 = 3

The triangle width is 3.

Note that the area of the triangle is found using the formula: Area = 1/2base x height (or length x width). Plug in the corresponding numbers to the corresponding variable.

A = 1/2(3)(6)

A = (3)(3)

A = 9

The triangle's area is 9 in².

Solve for the area of the parallelogram:

6 x 7 = 42

The parallelogram's area = 42 in².

Add the two measurements together:

42 + 9 = 51

51 in² is the area of the shape.

~

The above composite shape can be divided into :

●  A Rectangle with Length 7 in. and Width 6 in.

●  A Right angled Triangle with base 3 in. and height 6 in.

Let us first find the Area of Rectangle :

We know that - Area of a Rectangle is given by : Length × Width

[tex]:\implies[/tex]  Area of Rectangle = (7 × 6) in²

[tex]:\implies[/tex]  Area of Rectangle = 42 in²

Now, Let us find the Area of Right angled Triangle :

[tex]\mathsf{We\;know\;that - Area\;of\;a\;Triangle\;is\;given\;by : \dfrac{1}{2} \times base \times height}[/tex]

[tex]\implies \mathsf{Area\;of\;Right\;angled\;Triangle = \dfrac{1}{2} \times 3 \times 6\;(in^2)}[/tex]

[tex]:\implies[/tex]  Area of Right angled Triangle = (3 × 3) in²

[tex]:\implies[/tex]  Area of Right angled Triangle = 9 in²

Area of the Composite shape :

●  Area of Rectangle + Area of Right angled Triangle

[tex]:\implies[/tex]  Area of the Composite shape = (42 + 9) in²

[tex]:\implies[/tex]  Area of the Composite shape = 51 in²

Answer: 9

Step-by-step explanation:

Answer:

the remainder is 9

Step-by-step explanation:

find the remainder in the synthetic division

1         4       6        -1

Take down the first number 4 as it is. then multiply it with divisor 1 and put it below 6. then add it and do the same till we get remainder

1         4       6        -1

         0        4        10

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

         4        10       9 -> Remainder

So the remainder is 9

Answer:

B. 1.81

Step-by-step explanation:

Simply divide [tex]\frac{6.98}{3.86}[/tex] to get [tex]1.8082...[/tex].

This is closer to [tex]1.81[/tex] than it is to [tex]1.80[/tex], so that is how it is rounded.

Then, you have your answer.

Answer:

the answer is that D is false

Step-by-step explanation:

the relative frequency chart shows that 0.35 of her total freshman and sophomores take biology (Bottom left corner of the chart).

Answer: D

Step-by-step explanation: Apex said so

Answer:

t = 13.1576  years

Step-by-step explanation:

The situation can be modeled as

P = Po.(1-r)^t

Where

t is the years transcurred

Po is the initial amount

r is the rate of change

Po = 40000

r = 10% equivalent to 0.1

Now

A quarter of the original amount

(1/4)*Po = Po.(1-r)^t

(1/4) = (0.9)^t

t = 13.1576

Please, see attached picture