a² + b²
______
a-b

if a = -3 and b = -5

Answer:

48000

Step-by-step explanation:

260000*5%=13000

35000+13000=48000

[tex]111.2[/tex]

Step-by-step explanation:

As per the question, 15 times 15 i.e. 225

[tex]15 \times 15 = 225[/tex]

225 divide by 20 i.e. 11.25

[tex] \frac{225}{20} = 11.25[/tex]

take away five from the 11.25 then it will be 11.2

Add 100 to 11.2 i.e

[tex]11.2 + 100 = 111.2[/tex]

Answer: 115

Step-by-step explanation:

[tex]\displaystyle\\\frac{15*15}{20-5} +100=\\\\\frac{15*15}{15} +100=\\\\15+100=\\\\115[/tex]

She ran 15 miles at a quicker speed based on the information supplied. See explanation below. This is a distance time problem.

The distances between the two "half" of the race are our unknowns here. We must assign them to variables - Alicia ran x miles in the first half of the race and y miles in the second.

Since the race is 21 miles in total, x and y together must add up to 21.

Hence,

x + y = 21

The speeds at which she raced and the total time involved are then given; we can link this to the distances using the speed and distance equation

d = st, or t = d/s.

Because she completed in two hours, the hours spent running the first and second parts must sum up to two hours, or:

x/8 + y/12 = 2

Two equations are sufficient to solve for two unknowns. We can approach this by multiplying the second equation by the LCM, 24

3x + 2y = 48

And rearrange the first to get y = 21 - x, which we can plug into the above. This gives us:

3x + 2(21 - x) = 48

3x + 42 - 2x = 48

x = 6

Use y = 21 - x again:

y = 21 - (6) = 15.

Recall that the question asks how long she ran at the faster speed - this would be the second half of the race, which we've labeled y, so 15 miles. But first, let's make sure our solution works.

Obviously, 15 + 6 = 21, thus the overall distance is correct.

In terms of time, 6 miles at 8 mph takes

6/8 =.75 hours = 45 minutes, whereas

15 miles at 12 mph takes 15/12 = 1.25 hours = 75 minutes.

As stated in the question, the total time to complete would be.

75 + 1.25 = 2 hours.

As a result, this solution is correct, as Alicia ran 15 miles at a quicker rate.

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Given that the distance AB is (260), let A be the points (a,2a-1) and B be the places (2a+4,3a+9) where "a" is a constant.

discover the several meanings of "a." noting that an is an integer An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.

Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, a specific value, or a thing. Fractions are represented in the form of p/q. For example, ¼, ½, ¾, and so on.

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As  given Chole and Tinos age , the present age of Tino is equal to 15 years.

As given,

Let x and y be the present age of Chole and Tino. respectively.

Combined age = 48

Given condition,

x + y = 48 _______(1)

Three years ago

x - 3 = 2y

⇒x =2y +3 _______(2)

Substitute the value of x in (1),

2y+3 +y =48

⇒ 3y = 45

⇒ y = 15years

Therefore , as given Chole and Tinos age , the present age of Tino is equal to 15 years.

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The correct answer to the exponential expression which is as given in the task content is; 8³.

Based on the given task content, Gina's error from her workings is dividing the bases of the exponent.

Gina's working:

8^12 / 8^9

= 0^12 / 0^9

The Correct workings:

8^12 / 8^9

= 8^(12-9)

= 8³

So therefore, the correct answer to the exponential expression which is given in the above expression is 8³.

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We get A' as { 2, 6, 8, 16}. B' as {12, 18}, (AUB)' as ∅ and A' U B' as {2, 6, 8, 12, 16, 18}.

We are given the sets as:

U= { 2, 4, 6, 8, 10, 12, 14, 16, 18}

A = {4, 10, 12, 14, 18}

B = { 2, 4, 6, 8, 10, 14, 16}

We first will find out A':

A' = U - A

A' = { 2, 4, 6, 8, 10, 12, 14, 16, 18}  - {4, 10, 12, 14, 18}

A' = { 2, 6, 8, 16}

Now, we will find B':

B' = U - B

B' = { 2, 4, 6, 8, 10, 12, 14, 16, 18}  - { 2, 4, 6, 8, 10, 14, 16}

B' = { 12, 18}

Now, we have to find:

(AUB)' = U - (AUB)

AUB = {4, 10, 12, 14, 18} U { 2, 4, 6, 8, 10, 14, 16}

AUB = { 2, 4, 6, 8, 10, 12, 14, 16, 18}  = U

(AUB)' = U - U = ∅.

Now, we will find A' U B':

A' U B' = { 2, 6, 8, 16} U { 12, 18}

A' U B' = {2, 6, 8, 12, 16, 18}

Therefore, we get A' as { 2, 6, 8, 16}. B' as {12, 18}, (AUB)' as ∅ and A' U B' as {2, 6, 8, 12, 16, 18}.

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Answer: 13512

100332

Step-by-step explanation:

The shortest time for her run is approximately 36 minutes and the longest time is approximately 67 minutes.

To represent Kenzie's situation, we can use an absolute value equation. Let x represent the length of her run in miles.

The equation would then be |x - 6| ≤ 1, which means the distance between x and 6 is less than or equal to 1.

To find the shortest or longest amount of time for Kenzie's run, we need to consider the speed.

The time can be found by dividing the distance by the speed, so the minimum time would be (6 - 1)/6.25 hours,

which is approximately 0.6 hours or 36 minutes.

The maximum time would be (6 + 1)/6.25 hours,

which is approximately 1.12 hours or 67 minutes.

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The equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]

To find the equation:

When we differentiate the function [tex]y=6 \sec (x)-12 \cos (x)[/tex], we get:

[tex]\begin{aligned}y^{\prime} &=\frac{d}{d x}(6 \sec (x)-12 \cos (x)) \\&=6 \frac{d}{d x}(\sec (x))-12 \frac{d}{d x}(\cos (x)) \\&=6 \sec (x) \tan (x)+12 \sin (x)\end{aligned}[/tex]

The slope of the tangent line is given by this derivative at the point [tex]x=\frac{\pi}{3}[/tex]:

As a result, this tangent line has the equation: [tex]y-6=18 \sqrt{3}\left(x-\frac{\pi}{3}\right)[/tex]

Therefore, the equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]

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The correct question is given below:

Find the equation of the tangent line to the curve y = 6 sec (x) at the point ([tex]\pi[/tex]/3, 6). Give your answer in the form y = mx + b where m is the slope and b is the y--intercept.

When the velocity of the car is zero. Then the time will be 1 second.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The position of a car is given, for positive t, by x = 9t - 3t³. x is in meters and t is in seconds.

We know that velocity is the rate of change of displacement. Then we have

v = dx / dt

v = 9 - 9t²

When the velocity of the car is zero. Then the time will be

v = 0

9 - 9t² = 0

1 - t² = 0

(1 - t)(1 + t) = 0

t = 1, -1

When the velocity of the car is zero. Then the time will be 1 second.

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The probability value indicates that there is statistical significance in 0.015 option (b) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

The p-values are:

As we know,

Statistical significance is commonly defined as a probability value of 0.05 or even less. P-value can be used in replacement of or in additional to preset levels of confidence when testing the claim.

Thus, the probability value indicates that there is statistical significance in 0.015 option (b) is correct.

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Step-by-step explanation:

a/b = 5/6

a + b = 44

a = 44 - b

so, the first equation is

(44 - b)/b = 5/6

44 - b = 5b/6

264 - 6b = 5b

264 = 11b

b = 24

a = 44 - b = 44 - 24 = 20

the fraction is a/b = 20/24.

Also 2+4 as sum of the digits of the denominator = 6 is correct.

Given ~

[tex] \: [/tex]

[tex] \tt \: f(x) = −3x² − x – 15[/tex]

[tex] \: [/tex]

now , put x= -8 in the function ~

[tex] \: [/tex]

[tex] \tt \: f( - 8) = −3( - 8)² − ( - 8) – 15[/tex]

[tex] \: [/tex]

[tex] \tt f(-8) = −3(64) − (-8) – 15[/tex]

[tex] \: [/tex]

[tex]\tt f(-8) = −192 − (-8) – 15[/tex]

[tex] \: [/tex]

[tex] \tt f(-8) = −192 − (-8) – 15[/tex]

[tex] \: [/tex]

[tex]\tt f(-8) = −184 – 15 [/tex]

[tex] \: [/tex]

[tex] \underline{\boxed{\red {\tt f(-8) = - 199}}}{\green ✓} [/tex]

[tex] \: [/tex]

hope helps ~

Answer:

Step-by-step explanation:

                          [tex]\boxed{x^2-y^2=(x+y)(x-y)}[/tex]

[tex]c^2-(d+2)^2=\\(c+(d+2))(c-(d+2))=\\(c+d+2)(c-d-2)[/tex]

Answer:

See below

Step-by-step explanation:

The first one scales UP from 4 to 6     F'G'/FG =    factor is  6/4 = 1.5

second one scales DOWN from 4 to 3  

        F'G' / FG = scale factor is 3/4

Third one is scaled DOWN

F'G' / FG =    2/4 = 1/2

Note when scale is DOWN the factor is less than one

  when scale is UP , factor is more than one

Answer:

2x-1=3×+8

Step-by-step explanation:

2×-3x=8+1

-x=9

x=-9

Answer: Non-rectangular Parallelogram

The opposite sides are parallel, but the figure is not a rectangle. It's also not a square either since those figures have an axis of symmetry.

Answer:

Option 3

Step-by-step explanation:

First tke lcm i.e. 6 then multiply the dinominator to make six.

Multiply tje above no. With the same digit the sub. The numerators

Answer:

c) 7/6

Step-by-step explanation:

The difference will be,

→ (5/3) - (1/2)

→ (10/6) - (3/6)

→ (10 - 3)/6

→ 7/6

So, the answer is 7/6.

The distance between the point A and point B is 9.5 units

The formula for calculating the distance between two points is expressed according to the formula shown below;

AB = √(x₂-x₁)²+(y₂-y₁)²

Using the given coordinates points A(5, -3) and B (-4, -6)

Substitute to have:

AB = √(5-(-4))²+(-3-(-6))²

AB = √(5+4)²+(-3+6))²

AB = √81+9

AB =  √90

AB = 9.5 units

Hence the distance between the point A and point B is 9.5 units

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The radius of the pool with height as 0.5 cm and volume as 12,000 cm³ is 87.39 cm.

We have that:

Radius of the water pipe = 0.74 cm

r = 0.74 cm

It fills a 12 L bucket in 4 minutes

1 L = 1000 cm³

12 L = 12,000 cm³

Volume of water put in the pool = 12,000 cm³

Height of the pool that rise = 5 mm = 0.5 cm.

H = 0.5 cm

Let the radius of the pool be R.

Volume = π r² h

Substituting the values, we get that:

12,000 = ( 22 / 7 ) R² ( 0.5 )

R² = 7636.36

R = 87.39 cm

Therefore, we get that, the radius of the pool with height as 0.5 cm and volume as 12,000 cm³ is 87.39 cm.

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The difference between the two points ; (-3,10 )

given

(-4,-1)  and (1,-9)

here we have to find the difference between -4 and -1

which is -3 so u go -3 spaces left so it would be -3

then , find the difference between 1 and -9 which is 10 so u go 10 spaces down so the difference between is;

(-3,10).

therefore the distance between two point are (-3,10)

Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates.to know more about distance.

We will use the distance formula in order to find the distance between points a and b. By substituting the points A(3, 4) and B(1, 2) in the above formula we get our required distance d. Hence, distance d = 2√2 units

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You can just try out all the answers but I'll give you a solution.

We will expand out the middle term to 5x^2 - 30x - 6x + 36, then we group the first 2 terms together, and the last 2 terms together.

= 5x (x - 6) - 6(x - 6)

And we put x-6 out : (x-6)(5x-6) = 0

Now, we can just set the value of one bracket to 0 and find out the value of x, and do the same for the other one

x - 6 = 0 -> x = 6
5x - 6 = 0 -> x = 6/5

Because 6 is not a possible option, the answer is x = 1.2

The final length of Juanita recording after editing was completed was 7/6

To solve this exercise, we have to state the equation using the information of the problem:

Information about the problem:

Transforming the mixed number to fraction, we get:

1 1/2 =

[(2*1)  +1]  /2

(2+1)/2

3/2

Calculating the final length of the recording, we have:

Final length = Recorded - deleted

Final length = 3/2 - 1/3

Final length = (9-2) / 6

Final length = 7/6

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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The sphere's equation that passes through the given point is:

To find the equation of the sphere:

So,

Now,

[tex]\begin{aligned}&=\sqrt{\left(x_c-x_p\right)^2+\left(y_c-y_p\right)^2+\left(z_c-z_p\right)^2} \\&=\sqrt{(3-4)^2+(8-3)^2+(1-(-1))^2} \\&=\sqrt{(-1)^2+(5)^2+(2)^2} \\&=\sqrt{1+25+4} \\\therefore r &=\sqrt{30}\end{aligned}[/tex]

Supplement the center point and radius into the standard sphere equation:

[tex]\left(x-x_c\right)^2+\left(y-y_c\right)^2+\left(z-z_c\right)^2=r^2\\(x-3)^2+(y-8)^2+(z-1)^2=(\sqrt{30})^2\\(x-3)^2+(y-8)^2+(z-1)^2=30[/tex]

Therefore, the sphere's equation that passes through the given point is:

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The correct question is given below;

Find an equation of the sphere that passes through the point (4, 3,−1) and has to center (3, 8, 1).

After simplifying the equation we acquire the value of x as:

x = 1.225 or x = ₋12.225

Given the equation is x² ₊ 11x ₊ 15 = 30

arrange the constants on one side.

x² ₊ 11x = 30 ₋ 15

x² ₊ 11x = 15

x² ₊ 11x ₋ 15 = 0

now simplify the equation using the formula: -b±√b²₋4ac / 2a

in the equation we have the values for a = 1 , b = 11 and c = ₋15

substitute the values and get the value of x.

= ₋11 ± √(11)² ₋ 4(1)(₋15) / 2(1)

= ₋11 ± √121 ₊ 60 / 2

= ₋11 ± √181 / 2

= ₋11 ± 13.45 / 2

= ₋11 ₊ 13.45 / 2 or ₋11 ₋ 13.45 / 2

= 2.45/2 or ₋24.45/2

= 1.225 or ₋12.225

Therefore x value is 1.225 or ₋12.225

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Considering the definition of an equation and the way to solve it, it will take 4 hours for both companies to equal the same price and it will cost $90 at that time.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

First, you define the variable "t" as the time for the landscaping company to work on the backyard renovation. You know that:

So the price of each company is:

If both companies equal the same price, the equation in this case is:

Price of company A= Price of company B

50+ 10t= 30 + 15t

Solving

50 - 30= 15t - 10t

20= 5t

20÷5= t

4=t

At this time, the price of both companies is

In summary, it will take 4 hours for both companies to equal the same price and it will cost $90 at that time.

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Answer: x = 7 ft, DO = 25 ft, OG = 35 ft

Step-by-step explanation:

        We will write an equation using the segment addition postulate.

Given by segment addition postulate:

   DO + OG = DG

Substitute known values:

   (4x - 3) ft + (2x + 21) ft = 60 ft

Combine like terms and simplify:

   6x + 18 ft  = 60 ft

Subtract 18 ft from both sides of the equation:

   6x  = 42 ft

Divide both sides of the equation by 6:

   x = 7 ft

        Now, we will "plug" this value in and solve for the segments.

DO ➜ (4x - 3)ft ➜ (4(7) - 3) ft ➜ 28 - 3ft = 25 ft

OG ➜ (2x + 21) ➜ (2(7) + 21) ft ➜ 14 + 21 = 35 ft