Simplify the following expression

The speed of Sali is 18.75 km/hr.

Given,

Total distance travelled by Jane and Sali =63 km.

The total time is taken by Jane=3.5 hours.

Sali started to cycle 4 minutes after Jane started to cycle [tex]=\frac{4}{60}=\frac{1}{15}[/tex] hours.

The formula to find speed is [tex]Speed=\frac{Distance}{Time} \ km/hr[/tex].

The speed of Jane[tex]=\frac{63}{3.5}=18 \ km/hr[/tex].

Let the speed of Sali be [tex]x \ km/hr[/tex].

Sali caught up with Jane when they had both cycled 30 km.

Thus, [tex]\frac{30}{18}-\frac{30}{x}=\frac{1}{15}[/tex]

[tex]\implies \ \frac{30x-540}{18x} =\frac{1}{15}[/tex]

[tex]\implies \ 15(30x-540)=18x[/tex]

[tex]\implies \ 5(30x-540)=6x[/tex]

[tex]\implies \ 150x-2700=6x[/tex]

[tex]\implies \ 144x=2700\implies \ x=18.75[/tex]

Therefore, the speed of Sali is 18.75 km/hr.

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Answer: ∠PQR = 130°

Step-by-step explanation:

      The word bisects means that angle PQS and SQR are equal to each other.

           3x + 5 = 2x + 25

           3x = 20

           x = 20

      Now, we will plug this value back in and solve for angle PQR. There are three ways we could do this.

      [1]

             (3x + 5) + (2x + 25)

             (3(20) + 5) + (2(20) + 25)

             (60 + 5) + (40 + 25)

             (65) + (65)

                 130 degrees

      [2]

             (3x + 5) * 2

             (3(20) + 5) * 2

             (65) * 2

                 130 degrees

      [3]

             (2x + 25) * 2

             (2(20) + 25) * 2

             (65) * 2

                 130 degrees

Answer:

1

Step-by-step explanation:

 12+[2-(4 × a²)] ÷ 7+b

= 12+[2-(4 × 5²)] ÷ 7+ 1

= 12+[2-(4 × 25)] ÷ 7+ 1

= 12 + (2 - 100)÷ 7 + 1

= 12 - 98 ÷ 7 + 1

= 12 - 14 + 1

= 1

Answer:

-1

Step-by-step explanation:

Answer: 80 miles

Step-by-step explanation:

- 400/5 = 80

- so 80 is 1/5 of 400

hope this helps :)

Answer:

80 miles

Step-by-step explanation:

The whole journey is 400 miles, so we say that he traveled x miles, where x equals 400.
if we multiple 1/5 by x miles, then we will get how much he travels
1/5*x = 1/5*(400), since x = 400, so you can replace x with 400
1/5*x=1/5*400=400/5=80 miles

Answer:

a = 2

Step-by-step explanation:

given x = - 1 is a zero then f(- 1) = 0 , that is

a(- 1)³ - (- 1)² - 1 + 4 = 0

- a - 1 - 1 + 4 = 0

- a + 2 = 0 ( subtract 2 from both sides )

- a = - 2 ( multiply both sides by - 1 )

a = 2

Answer:

40. 50c goes into 200 40 times

Answer:

x₁ = 4

(x₂ = -3)

Step-by-step explanation:

√(x + 12) = x

x + 12 = x²

x² - x - 12 = 0

Δ = 49

x = (1 ±√Δ)/2

x₁ = 4

x₂ = -3

the right solution is 4 this can be seen by inserting the solutions found in the starting equation

[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]

★ Radius of first sphere [tex]\sf r_{1}[/tex] = 6cm.

★ Radius of second sphere [tex]\sf r_{2}[/tex] = 8cm.

★ Radius of third sphere [tex]\sf r_{3}[/tex] = 10cm.

[tex] {\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]

★ The radius of the resulting sphere formed.

[tex] {\large{\textsf{\textbf{\underline{\underline{Formula \: used :}}}}}}[/tex]

[tex]\star \: \tt Volume \: of \: sphere = {\underline{\boxed{\sf{\red{ \dfrac{ 4}{3}\pi {r}^{3} }}}}}[/tex]

[tex] {\large{\textsf{\textbf{\underline{\underline{Concept :}}}}}}[/tex]

★ As, three spheres are melted to from one new sphere. Therefore, volume of three old sphere is equal to volume of new sphere.

i.e, Volume of first sphere + volume of second sphere + volume of third sphere = Volume of new sphere.

[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]

Let,

The radius of resulting sphere be [tex]R[/tex]

According to the question,

• Volume of first sphere + volume of second sphere + volume of third sphere = Volume of new sphere.

[tex] \longrightarrow \sf \dfrac{4}{3} \pi {(r_{1})}^{3} + \dfrac{4}{3} \pi {(r_{2})}^{3} + \dfrac{4}{3} \pi {(r_{3})}^{3} = \dfrac{4}{3} \pi {(R)}^{3} [/tex]

• here

☆[tex]\: \sf r_{1}[/tex] = 6cm

☆[tex]\: \sf r_{2}[/tex] = 8cm

☆[tex]\: \sf r_{3}[/tex] = 10cm

Putting the values,

[tex] \longrightarrow \sf \dfrac{4}{3} \pi {(6)}^{3} + \dfrac{4}{3} \pi {(8)}^{3} + \dfrac{4}{3} \pi {(10)}^{3} = \dfrac{4}{3} \pi {(R)}^{3} [/tex]

Taking " [tex]\dfrac{4}{3} \pi [/tex]" common,

[tex] \longrightarrow \sf \dfrac{4}{3} \pi \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = \dfrac{4}{3} \pi {(R)}^{3} [/tex]

[tex]\longrightarrow \sf \cancel{ \dfrac{4}{3} \pi} \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = \cancel{ \dfrac{4}{3} \pi } {(R)}^{3} [/tex]

[tex]\longrightarrow \sf \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = {(R)}^{3} [/tex]

[tex]\longrightarrow \sf \bigg[ 216 +512 + 1000 \bigg] = {(R)}^{3} [/tex]

[tex]\longrightarrow \sf 1728 = {(R)}^{3} [/tex]

[tex]\longrightarrow \sf \sqrt[3]{1728} = R[/tex]

[tex]\longrightarrow \sf \sqrt[3]{ 12 \times 12 \times 12 } = R[/tex]

[tex]\longrightarrow \sf \sqrt[3]{ {(12)}^{3} } = R[/tex]

[tex]\longrightarrow \sf R = \red{12 \: cm} [/tex]

Therefore,

Radius of the resulting sphere is 12cm.

[tex]{\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}[/tex]

★ Figure in attachment.

[tex]{\underline{\rule{290pt}{2pt}}}[/tex]

Answer:

A. -3

Step-by-step explanation:

Use slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]

Use the points given, (-1, 6) and (2,-3)

[tex]\frac{-3-6}{2+1}=\frac{-9}{3}[/tex]

Simplify the answer.

[tex]\frac{-9}{3}=-3[/tex]

The slope of the line is -3.

Hope this helps!

If not, I am sorry.

The value of x is the length GH, which is determined as 6.

The value of x is the length GH and can be calculated from Pythagoras theorem.

|OG|² = |OS|² + |SG|²

|OG|² = 9² + 12²

|OG|² =  225

|OG| = √225

|OG| = 15

x + H = |OG|

where;

x + 9 = 15

x = 15 - 9

x = 6

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The options w > x, w > y, and x + y = w are correct because the sum of the two interior angles is equal to the exterior angle.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

From the figure,

The interior angle of a triangle is w

w > x (true)

w > y (true)

x + y = w (sum of the two interior angles is equal to the exterior angle)

Thus, the options w > x, w > y, and x + y = w are correct because the sum of the two interior angles is equal to the exterior angle.

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Given :

Subtract 5 from each side :

Take the root on each side :

Hence, the values of x are :

[tex]x^2+5=6\\x^2=1\\x=1 \vee x=-1[/tex]

The probability that a person wins the game is 32.1%

Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.

Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:

= 24 + 4 = 28

The frequency table will be such that 28 or more has a relative frequency of 9. Therefore, the probability that a person wins the game will be:

= 9/28 = 32.1%

When you win 25% of the time, this illustrates that the number of products picked will be:

= 25% × 28

= 7 products.

The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:

= 1/6⁴

= 1/1296

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Answer:

17th term

Step-by-step explanation:

Substitute [tex]a_{n}[/tex] with the value 107

107=11+6(n-1)

96=6n-6

102=6n

n=17

17th term !!

Hope it helps!

Answer:

[tex] \boxed{\bf A. \: x - 2}[/tex]

Step-by-step explanation:

[tex] \sf ( x + 1)^2-9/ x + 4 [/tex]

First, we need to factor the expressions that are not already factored.

Now, let's Cancel out x+4 in both numerator and denominator.

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

Considering the given probability distributions, distribution D is valid.

A probability distribution is valid if:

In this problem, only distribution D has a sum of 1, hence it is the only valid distribution.

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Answer:

Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.

Step-by-step explanation:

The answer above is correct.

Answer:

Hence the expression [tex]$$(6p+5)(p+1)=6p^2+11p+5$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ \times & {} & p & + & 1 \\ \end{matrix}}[/tex]

_____________

[tex]{\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ 6{{p}^2} & + & 5p & {} & {} \\ \end{matrix}}{\begin{matrix}6{{p}^2} & + & 11p & + & 5 \\ \end{matrix}}}$$[/tex]

The graph is concave has two curved part as follows;

The direction the concave part of the graph faces is given as follows;

The graph is concave up when the concave part faces up

It is concave down when the concave part faces down

From the given diagram, we have;

The graph is concave up between;

(0, 1), and (1, 0)

The graph is concave down between; (0, 1), and (-a, 2)

Where a is in the range; 1 < a < 2

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0 ≤ x ≤ 60

0 ≤ y ≤ 40

Definition of Domain and Range

The set of  all the possible input values for which the provided function is defined is termed as the domain of that function.

The set of all the possible values that a given function can generate as an output is termed as the range of that function.

Forming the Relation

It is given that,

Thus, the relation formed is given by,

[tex]2x + 3y \leq 120[/tex]

Domain and Range of the Given Relation

We have,

[tex]2x + 3y \leq 120[/tex]

⇒ [tex]2x \leq 120[/tex]

⇒ [tex]x\leq60[/tex]

Thus, the domain is given by,

⇒ [tex]0\leq x\leq 60[/tex]

Similarly,

[tex]3y\leq 120[/tex]

⇒ [tex]y\leq 40[/tex]

Thus, the range is given by,

⇒ [tex]0\leq y\leq 40[/tex]

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Answer: 25.6

Step-by-step explanation:

[tex](d-3) \tan 37^{\circ}=17\\\\d-7=\frac{17}{\tan 37^{\circ}}\\\\d=\frac{17}{\tan 37^{\circ}}+3 \approx \boxed{25.6}[/tex]

Answer:

C

Step-by-step explanation:

you know the drill

Answer:

the answer is 0.

Step-by-step explanation:

When you are adding two of the same numbers together, and one of them is positive while the other is negative, they cancel each other out.  

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\mathsf{-6 \dfrac{4}{5} + 6 \dfrac{4}{5}}[/tex]

[tex]\mathsf{= \dfrac{-6 \times 5 + 4}{5}+ \dfrac{6 \times 5 + 4}{5}}[/tex]

[tex]\mathsf{= \dfrac{-30 + 4}{5}+ \dfrac{30 + 4}{5}}[/tex]

[tex]\mathsf{= \dfrac{-34}{5} + \dfrac{34}{5}}[/tex]

[tex]\mathsf{= 0}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{0}}}\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

x = 6, y = 5

Step-by-step explanation:

5x - 4y = 19 -------> equation 1

x + 2 = 8 --------> equation 2

Step 1 : Subtract 2 on both sides in equation 2.

x + 2 - 2 = 8 - 2

x = 6

Step 2 : Substitute the value of x is equation 1.

5 ( 6 ) - 4y = 19

( 5 * 6 ) - 4y = 19

30 - 4y = 10

Step 3 : Subtract 30 on both sides.

30 - 30 - 4y = 10 - 30

- 4y = - 20

Step 4 : Multiply - 1 on both sides.

- 1 * - 4y = - 1 * - 20

4y = 20

Step 5 : Divide 4 on both sides.

4y / 4 = 20 / 4

y = 5

Hence,

x = 6

y = 5

Answer:

x = 5, y = 3/2.

Step-by-step explanation:

5x-4y=19

x+2y =8               Multiply this by 2:

2x + 4y = 16       Adding this to first equation 1:

7x = 35

x = 5

So

5 + 2y = 8

2y = 3

y = 3/2.

Answer:

mean: 2.6, mode: 1, median: 1

Step-by-step explanation:

The mean is essentially the average of the data set which can be defined as: [tex]\frac{\text{sum of data set}}{\text{amount of data in data set}}[/tex]. So adding all the values together you get: [tex]26[/tex]. and counting all the numbers in the data set you find the data set has 10 numbers. This gives you the equation: [tex]\frac{26}{10} = 2.6[/tex] which is the mean

To find the mode, you find which number occurs most frequently, this is of course 1, which can really be determined by just looking at the data set for a second. all the other numbers only occur once, while 1 is in the data set 5 times. So 5 is the mode

To find the median you sort the data, from min to max, and then find the middle number. Sorting the data set gives you. -2, 1, 1, 1, 1, 1, 4, 5, 6, 8. Since this data set has an even amount of numbers, there is not going to be an exact middle. If you go the "middle" which is the 5th and 6th number, you add these two numbers and divide the sum by 2. This gives you: (1+1)/2 = 1 So the median is 1

Answer:

So now,

you know the formula for simple interest is P×R×T divided by a hundred?

So 2500 times 3.55 times 2.75 divided by 100

Answer:

1386m cubic

Step-by-step explanation:

hope it helps.in case of any other question, you can count on me.good day.

The area of the circular field in square meters will be equal to, 1386 m².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass a compact figure's surface. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Total number of posts = 66

Distance between two posts = 2 meters

Then, the circumference of the area will be,

= 66 × 2 = 132 meters

Now, let's find the radius of the circle,

C = 2πr

132 = 2 × 3.14 × r

r = 132/(2 × 3.14)

r = 21.01 m

Use the formula for the area of the circle:

A = πr²

A = 3.14 × (21.01)²

A = 441.420 × 3.14

A = 1386 m²

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Answer:

[tex]4x^{2} -8x+4[/tex]

Step-by-step explanation:

The average profit expression is for 1 piece of furniture

The amount of furniture is another expression

So we have to multiply both expressions to get the total profit.

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

                    = 4x^2 - 8x + 4

Answer:

C

Step-by-step explanation:

When x is negative    1/2 ^x  becomes   1 / ( 1/2 ^x)   meaning it is quite large as x becomes more negative

   when x = 0  the value is 1  

  as x increases from 0 to + inf   the value becomes smaller...but never negative

   the only graph that fits is C

The initial value of the function f(x) = 3(18)ˣ is 3. The domain of the function is all real numbers and the range is y > 0

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

Given the function f(x) = 3(18)ˣ, hence:

The initial value of the function f(x) = 3(18)ˣ is 3. The domain of the function is all real numbers and the range is y > 0

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