A system of equations is shown below:
n = 3m + 7
n - 2m = 1
What is the solution, in the form (m, n), to the system of equations?
O (3,7)
(1,8)
O(-3,-2)
O(-6, -11)

Answer:

The probability that the fruits will be selected in the order of banana then apple then orange is 0.1094

Step-by-step explanation:

The given information are;

The number of bananas = 4

The number of apples = 3

The number of oranges = 5

The total number of fruits are 4 + 3 + 5 = 12

The probability of selecting a banana, p(b) = 4/12 = 1/3

The probability of selecting an apple, p(a) = 3/12 = 1/4

The probability of selecting an oranges, p(o) = 5/12

The probability of selecting one banana, then one apple, then one orange, in that order, from the basket with replacement is the product of the individual probabilities found as follows;

p(p(b) then p(a) then p(o)) =

The number o

The probability that the first fruit is a banana = ₁₁C₃×(1/3)^(3)×(2/3)^8 = 0.2384

The probability that the second fruit is an apple = ₁₁C₃×(1/4)^(3)×(3/4)^8 = 0.258

The probability that the third fruit is an apple = ₁₁C₃×(5/12)^(3)×(7/12)^8 = 0.16

The total probability = 0.2384 + 0.285 + 0.16 = 0.657

The number of ways in which the three can be selected = 3 × 2 × 1 = 6 ways

Therefore, the probability that the fruits will be selected in the order of banana then apple then orange = 0.657/6 = 0.1094.

Answer:

∠A ≅ ∠E

Step-by-step explanation:

The AAS (Angle-Angle -Side) congruence theorem implies that triangles ABC and EDC are congruent if both have equal two angles and a non included side.

In the given figures,

<ACB ≅ <ECD (vertical opposite angles)

BC ≅ DC (congruence property)

<ABC ≅ <EDC (alternate angles property)

∠A ≅ ∠E (alternate angle property)

With respect to AAS congruence theorem, ∠A ≅ ∠E is the correct option.

Answer:

67.5 degrees, and 112.5 degrees.

Step-by-step explanation:

Let's make the second angle "x"

Supplementary angles always add up to 180 degrees.

So the first angle is 45 degrees more than the second, so you do:

x+x+45=180

Solve that and you get 67.5. That is the second answer. To find the first answer, add 45 to that. The answer is correct. Please give me branliest.

Answer:

C. 2mn and mn^2

Step-by-step explanation:

All of the other options are like terms.

Option A: -x+3x=2x

Option B: 4a+7a=11a

Option D. 3p^2q+(-p^2q)=2p^2q

Option C: These terms are not like terms since 2mn is not squared while mn^2 is squared.

Hence,

the correct option would be C.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

The thrid option or 2mn and mn^2

Step-by-step explanation:

Like terms are sets of terms that have the same variables and powers. All these answer choices have the same variables but answer c are not like terms because the second term is raised to the power of 2 and the first is not. Coefficients do not matter for like terms.

Answer:

There is no error, Amad is correct.

Step-by-step explanation:

Khan Academy Checked.

Amad had done no error. His conclusion is true.

Two triangles are said to be congruent if their sides are equal in length, the angles are of equal measure, and they can be superimposed on each other.

For example,

In the figure given above, Δ ABC and Δ PQR are congruent triangles. This means that the corresponding angles and corresponding sides in both the triangles are equal.

Sides: AB = PQ, BC = QR and AC = PR;

Angles: ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.

Therefore, Δ ABC ≅ Δ PQR

The following are the congruence theorems or the triangle congruence criteria that help to prove the congruence of triangles.

As, from the given cases the prediction of congruency of two triangles is correct. There is no error he made.

Hence, Amad had not made any error.

Learn more about congruency here:

https://brainly.com/question/14011665

#SPJ2

There are 4060 different groups of runners.

It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

The formula of combination is [tex]^nC_r[/tex] = n!/r!(n - r)!

We have,

Number of runners = 30

Number of runners in the group = 3

The number of different groups of runners.

= [tex]^{30}C_3[/tex]

= 30 x 29 x 28 / 3 x 2

= 5 x 29 x 28

= 4060

Thus,

The number of different groups of runners is 4060.

Learn more about combination here:

https://brainly.com/question/14355408

#SPJ2

Answer:

a. Domain = All real numbers

Range = y ≥ 2

b. Domain = -4 < x ≤ 4

Range = 0 ≤ y < 4

Answer

y= 12.5x + 210,000

Step-by-step explanation:

This is a linear function because it is increasing constantly by 12.5 percent so it will me written as y=mx+b

The value of function that represents the situation is,

⇒ P = 210,000 (1.125)ⁿ

Where, n is number of years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The situation is,

⇒ A population of 210,000 increases by 12.5% each year​.

Now, Let number of years = n

Hence, The value of function that represents the situation is,

⇒ P = 210,000 (1 + 12.5%)ⁿ

⇒ P = 210,000 (1 + 0.125)ⁿ

⇒ P = 210,000 (1.125)ⁿ

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ5

Answer:

To find a we Pythagoras theorem

That's

[tex] {a}^{2} = {6}^{2} + {11}^{2} \\ {a}^{2} = 36 + 121 \\ \\ {a}^{2} = 157 \\ \\ a = \sqrt{157} \\ [/tex]

[tex] {11}^{2} = {b}^{2} + {6}^{2} \\ \\ {b}^{2} = 121 - 36 \\ \\ {b}^{2} = 85 \\ \\ \\ b = \sqrt{85} [/tex]

Hope this helps you

Answer:

Below in bold.

Step-by-step explanation:

The first one  a^2 = 6^2 + 11^2    ( By the Pythagoras Theorem)

a^2 =  157

a = √157.

The second triangle:

b^2 = 11^2 - 6^2

b^2 = 85

b = √85.

Answer:

Answer:

four and six one hundredths

406/100

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total surface area of the bite= total surface area of the sphere + total surface area of the rectangular prism

Total surface area of a sphere Ss = 4πr²

r = radius of the sphere = diameter/2

Given diameter of the sphere= 3cm; r = 3/2 cm

Ss = 4π(3/2)²

Ss = 4π*9/4

Ss = 9πcm²

For the rectangular prism

Total surface area   Sr = 2WL + 2LH + 2HW

W = width of the prism

L = length of the prism

H = height of the prism

Given W = 4cm, L = 4cm, H = 0.5cm

Sr = 2(4)(4) +  2(4)(0.5) +  2(0.5)(4)

Sr = 32+4+4

Sr = 40cm²

Surface area of the bite = 9π + 40

Surface area of the bite = 68.27cm²

Surface area of the bite = 68cm² (to nearest square of a centimetre)

Answer:

B. 3\sqrt(x)-2

Step-by-step explanation:

A polynomial cannot have a variable in the denominator

A constant is a polynomial

3\sqrt(x)-2 and this cannot be simplified to get rid of the variable in the denominator so it is not a polynomial

Answer:

C. 3√7

Step-by-step explanation:

As we know, the product of projections is equal to square of altitude in the right triangle. Applied to the given triangle, we get:

Choice C. 3√7 is the correct one

Answer: C. 3√7

Step-by-step explanation:

Answer: No. Choosing two dimes are dependent events. The probability of choosing the first dime is 1/4 and the probability of choosing the second dime is 1/7. The probability that both coins are dimes is (1/4)(1/7) = 1/28.

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/8×1/7=1/28

Answer:

The height of the building is approximately 18 meters.

Step-by-step explanation:

The question is:

FROM THE HIGH PART OF A WALL OF 8M HEIGHT, YOU CAN SEE THE LOW AND HIGH PART OF A BUILDING WITH ELEVATION AND DEPRESSION ANGLES OF 37° AND 45° RESPECTIVELY. CALCULATE THE HEIGHT OF THE BUILDING A.18 B.14 C.12 D.24 E.16

Solution:

Consider the diagram below.

Consider the triangle ABC.

Compute the value of y as follows:

[tex]tan\ 37^{o}=\frac{AB}{BC}[/tex]

  [tex]0.754=\frac{8}{y}[/tex]

        [tex]y=\frac{8}{0.754}[/tex]

           [tex]=10.61\\\approx 11[/tex]

Thus, the length of side AD is also 11 meters.

Now consider the triangle AED.

Compute the value of x as follows:

[tex]tan\ 45^{o}=\frac{AE}{ED}[/tex]

        [tex]1=\frac{11}{x}[/tex]

        [tex]x=11[/tex]

Then the height of the building is:

[tex]\text{Height of the Building}=x+8[/tex]

                                 [tex]=11+8\\=19[/tex]

From the options provided it can be concluded that the height of the building is approximately 18 meters.

Answer:

x=4

Step-by-step explanation:

Answer:

6x³ - 4x² - 8x - 16

Step-by-step explanation:

Step 1: Distribute the 2x

6x³ + 8x² + 8x

Step 2: Distribute the -4

-12x² - 16x - 16

Step 3: Combine the 2 distributions

6x³ + 8x² + 8x - 12x² - 16x - 16

Step 4: Combine like terms

6x³

8x² - 12x² = -4x²

8x - 16x = -8x

-16

Step 5: Rewrite

6x³ - 4x² - 8x - 16

━━━━━━━☆☆━━━━━━━

▹ Answer

6x³ - 4x² - 8x - 16

▹ Step-by-Step Explanation

(3x² + 4x + 4) (2x - 4)

Distribute

3x²(2x - 4) + 4x(2x - 4) + 4(2x - 4)

Remove parentheses

6x³ - 12x² + 4x(2x - 4) + 4(2x - 4)

Collect like terms

6x³ - 12x² + 8x² - 16x + 8x - 16

6x³ - 4x² - 16x + 8x - 16

Solve

6x³ - 4x² - 8x - 16

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

C.

Step-by-step explanation:

You are looking for an equation that, when you input 0 for x, you get 4 for y, and when you input -5 for x, you get -1 for y.

That only works for Option C.

Hope this [sorta] helps!

Answer:

C

Step-by-step explanation:

C

Answer:

1/2

Step-by-step explanation:

Square root as a exponent or power with a base is 1/2.

z^1/2 = √z

Answer:

y = 1/2x + 2

Comparison: The black and blue line haver the same y-intercept, however they have different slopes. The slope of the black line is 2/3 and the slope of the blue line is 1/2.

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Answer:

Check it below, please

Step-by-step explanation:

Hi there!

Let's prove segment AB is perpendicular to CD. Attention to the fact that a two column proof has to be concise. So all the comments can't be exhaustive, but as short as possible.

Let's recap: An isosceles triangle is one triangle with at least 2 congruent angles.

Statement                     Reason

[tex]\overline{AB} \cong \overline{AC}\\[/tex]                     Given

[tex]\widehat{ACB} \:bisects\: \overline{AB}[/tex]        Isosceles Triangle the altitude, the bisector coincide.          

[tex]\overline{AD} \cong \overline{DB}[/tex]               Bisector equally divide a line segment into two congruent      

[tex]m\angle CDA =m \angle CBD=90^{\circ}[/tex] Right angles, perpendicular lines.                  

[tex]\overline{CD}\perp \overline{AB}[/tex]                    Perpendicular Line segment      

Answer:

15

Step-by-step explanation:

[tex]y = 4x + 15 \\ equating \: it \: with \\ y = mx + b \\ we \: find \\ b = 15 \\ \implies \: y - intercept = 15[/tex]

Answer:

Y intercept = 15

Step-by-step explanation:

Formula we use,

→ y = mx + b

→ b = y intercept

Then the y intercept will be,

→ y = mx + b

→ y = 4x + 15

→ [ b = 15 ]

Thus, required answer is 15.

Answer:

y = 5  1/4

Step-by-step explanation:

For direct or inverse variation relation

relation between two variable and y can be expresses in form of

y = kx  where k is constant of proportionality .

Only thing happens in inverse relation is that when x increases then y decreases and vice versa. That is care by constant of proportionality

__________________________________

Thus, let the inverse relation be

y = kx

given

when y = 6 then x = 8

we will plug this value in y = kx

6 = k*8

=>k = 6/8 = 3/4

Thus,

relation is

y = 3/4 x

we have to find y when x = 7 ,

lets put x = 7 in y = 3/4 x

y = 3/4 *7 = 21/4 = 5 1/4

Thus, when x = 7 then y = 5 1/4

Answer:

Question 1:

a. The answer is B because the graph inclined really quickly and then it inclined at a much slower pace, suggesting that the person was running and then walking.

b. The answer is C because you can see on the graph that after a while, the distance from the starting point goes back to 0, indicating that the person forgot something at home.

Question 2:

a. The dashed line reaches the bottom at 15:30 so the answer is C.

b. Siobhan travels 8 km to go from home to school so the answer is 2 * 8 = 16 which is option D.

Question 3:

The answer is C because after the distance from the starting point increased, it then decreased and came back to the original point suggesting that he walked, turned around and walked back to the starting point.

Answer:

first page : a) A because it is the shortest time with no stop

b) C the graph goes up and return to the start point after a while

second page : it is at 3:30 0r 15:30

b): 8 km going to schools and 8 coming back is 16

third page it is C because he walk up a certain distance and come back to the starting point

Answer:

Basketball players are generally taller.

Basketball player heights vary slightly more.

Step-by-step explanation:

I hope this helps!

Basketball players are taller because the average (mean) of basketball players is greater than soccer players.

Basketball player heights vary more because the MAD is greater or more than the soccer players.

Basketball players are generally taller. Basketball player heights vary slightly more.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

Basketball players are taller because the average (mean) of basketball players is greater than soccer players.

Basketball player heights vary more because the MAD is greater or more than the soccer players.

Therefore, basketball players are generally taller. Basketball player heights vary slightly more.

To know more about mean follow

https://brainly.com/question/414254

#SPJ2

Answer:

Step-by-step explanation:

7 + 8 = 15

5 - 2 = 3

∴ 7 + 8 ÷ 5 - 2

= 15 / 3

= 5

Hope this helps

plz mark as brainliest!!!!!!

Answer:

5

Step-by-step explanation:

:)

Answer:

7.5 years

Step-by-step explanation:

P = $5000,

R = 4.25%,

A = $6593.75,

N =?

SI = A - P = 6593.75 - 5000 =$1593. 75

[tex] \because \: SI = \frac{ PNR}{100} \\ \\ \therefore \: 1593.75 = \frac{5000 \times N \times 4.25}{100} \\ \\ \therefore \: 1593.75 \times 100 = 21,250 \times N \\ \\ N = \frac{159375}{21250} \\ \\ N = 7.5 \: years \: [/tex]