Two numbers have a sum of 1,212 and a difference of 518. What are the two numbers?

The coordinates of points are: (11/7 , 4)

Step-by-step explanation:

The formula for a point which divides a line in ration m:n is given by:

[tex]P(x,y) = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]

Here

(x1,y1) = (-1,4)

(x2,y2) = (5,4)

m = 3

n = 4

So putting the values in the formula

[tex]P(x,y) = (\frac{(3)(5)+(4)(-1)}{3+4},\frac{(3)(4)+(4)(4)}{3+4})\\=  (\frac{15-4}{7},\frac{12+16}{7})\\=(\frac{11}{7}, \frac{28}{7})\\=(\frac{11}{7} , 4)[/tex]

The coordinates of points are: (11/7 , 4)

Keywords: Ratio, fraction

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Answer:

(x, y ) → (x + 6, y + 12 )

Step-by-step explanation:

We require to determine the horizontal and vertical shift to go from one of the points on the line to the corresponding point on the image

Consider point V with x- coordinate - 8 and y- coordinate - 2

The corresponding point is V'

with x- coordinate - 2 and y- coordinate 10

Thus V → V' is 6 units right in the horizontal direction and 12 units up in the vertical direction.

These are the same shifts for W → W'

Thus the translation rule is

(x, y ) → (x + 6, y + 12 )

The requried batch of sugar that can be made by 6.5 cups of sugar is 8.67 batches.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Mateo has 6.5 cups of sugar.
Each batch requires 3/4 cup of sugar,
Batches of cookies can he make,
= total cups of sugar/ 1 beach requires cups of sugar

= 6.5 / [3/4]
= 8.67 batches of cookies can be made.

Thus, the requried batch of sugar that can be made by 6.5 cups of sugar is 8.67 batches.

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Answer:

16.43

Step-by-step explanation:

(6% /100%)* 15.50

= 16.43

Answer: $16.43

Step-by-step explanation:

Answer:

27 miles

Step-by-step explanation:

Find the rate or speed that Shawn hikes at. Find this reduced to lowest terms.

speed = distance / time

speed = 12 miles / 4h

speed = 3miles / h

Every hour, Shawn hikes 3 miles.

Multiply speed by time to find distance.

3mph X 9h = 27 miles

Therefore Shawn could hikes 27 miles in 9 hours.

Answer:

Kyle

Step-by-step explanation:

Kyle:

Kyle’s parents told him that for every 5 hours of homework or reading he completes, he will be able to play 3 hours of video games.

Victor:

Victor’s parents told their son that he can play 30 minutes for every hour of homework or reading time he completed. If Victor spends 5 hours doing homework or reading, then he could play

[tex]30\cdot 5=150[/tex] minutes

that is

[tex]120+30=2[/tex] hours [tex]30[/tex] minutes (less than 3 hours).

Hence, if both boys spend the same amount of time on homework and reading this week, then Kyle will have more time to play video games.

Divide miles ran by speed to get time:

2 miles / 8 miles per hour = 0.25 hours = 15 minutes.

2 miles / 6 miles per hour = 0.33 hours = 20 minutes.

20 minutes - 15 minutes = 5 minutes longer.

Final answer:

After calculating the time taken by each runner to complete the 2-mile race, we find that Arif took 5 minutes longer than Sharif to finish.

Explanation:

To determine how many minutes longer Arif took to complete the race compared to Sharif, we need to calculate the time each runner took to complete the 2-mile race. First, we calculate Sharif's time. Since speed is distance divided by time, we can rearrange the formula to find time: time = distance/speed.

For Sharif:

Distance = 2 miles

Speed = 8 miles per hour

Time = 2 miles / 8 mph = 0.25 hours

Convert Sharif's time from hours to minutes by multiplying by 60 minutes per hour (0.25 hours * 60 minutes/hour = 15 minutes).

For Arif:

Distance = 2 miles

Speed = 6 miles per hour

Time = 2 miles / 6 mph = 0.333... hours

Convert Arif's time from hours to minutes (0.333... hours * 60 minutes/hour = 20 minutes).

Now, to find the difference in time, subtract Sharif's time from Arif's time:

Difference = Arif’s time - Sharif's time = 20 minutes - 15 minutes = 5 minutes

Arif took 5 minutes longer than Sharif to complete the race.

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The average rate of change of h(x) in the closed interval [ a, b ] is

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

Here [a, b ] = [ - 2, 2 ], thus

f(b) = f(2) = [tex]\frac{1}{8}[/tex] × 2³ - 2² = 1 - 4 = - 3

f(a) = [tex]\frac{1}{8}[/tex] × (- 2)³ - (- 2)² = - 1 - 4 = - 5

average rate of change = [tex]\frac{-3-(-5)}{2-(-2)}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

The average rate of change of h over the interval −2≤x≤2 is 1/2.

Here,

The function is [tex]h(x)= \frac{1}{8} x^3-x^2[/tex] and the interval −2≤x≤2.

We have to find, the average rate of change of h over the interval −2≤x≤2.

What is Average rate?

The  Average rate of change of function f( x ) in the close interval [a, b ]

is, [tex]\frac{f(a)-f (b)}{b-a}[/tex]

Now,

The function is [tex]h(x)= \frac{1}{8} x^3-x^2[/tex] and the interval −2≤x≤2.

Hence, [tex]h(-2) = \frac{1}{8} *(-2)^{3} -( -2)^{2} = -5[/tex]

And, [tex]h(2) = \frac{1}{8} *(2)^{3} -( 2)^{2} = -3[/tex]

So, Average rate of change of function h(x) = [tex]\frac{-3-(-5)}{2-(-2)} = \frac{2}{4} = \frac{1}{2}[/tex]

The average rate of change of h over the interval −2≤x≤2 is 1/2.

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Answer:

Therefore the value of x is 8 unit.

Step-by-step explanation:

Given:

In Right Angle Triangle ABC

angle B = 90°

angle C = 30°

AB = 4

To Find:

AC = Hypotenuse = ?

Solution:

In Right Angle Triangle ABC Sine Identity we have

[tex]\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\[/tex]

Substituting the given values we get

[tex]\sin 30 = \frac{AB}{AC}[/tex]

[tex]\dfrac{1}{2} =\dfrac{4}{x}\\\\\therefore x=4\times 2=8\\\\\therefore x =8[/tex]

Therefore the value of x is 8 unit.

area of triangle = 1/2bh

area = 1/2(120)(252) = 15120 in²

answer: C

Answer:

C) 15,120 square inches

Step-by-step explanation:

To solve this problem we first need to convert both legs of the triangle to inches. 10 ft * 12 is 120 and 7 yards is roughly 21 ft and that times 12 is 252. All we have to do now is to plug these values into the formula for area of a triangle: 1/2(b x h) = 1/2(252 * 120) = 1/2(30240) = 15,120 square inches.

Answer:

154 small cubes.

Step-by-step explanation:

We are given the dimensions of the cuboid as 72 cm × 66 cm × 56 cm.

So, length of the cuboid, l = 72 cm

Breadth of the cuboid, b = 66 cm

Height of the cuboid, h = 56 cm

Capacity of cuboid = l × b × h = 72 × 66 × 56 = 266112 cm³

Now, we have to find the number of small cubes of side 12 cm each that can be placed in the given cuboid.

Now, length of each side of each small cube, s = 12 cm

Volume of each small cube = s³ = (12)³ = 12 × 12 × 12 = 1728 cm³

For calculating the number of small cubes that can be placed in the given cuboid, we will divide the capacity of given cuboid by volume of each small cube.

Required number of cubes = [tex]\frac{Capacity\; of\; cuboid}{volume\; of\; each\; small\; cube}[/tex]

⇒ Number of cubes = [tex]\frac{266112}{1728}=154[/tex]

∴ 154 small cubes each of side 12 cm can be placed inside the given cuboid of dimensions 72 cm × 66 cm × 56 cm.

Answer:

The segment is 6 units long.

Step-by-step explanation:

The points (–2, 4) and (–2, –2) are vertices of a heptagon. We have to explain how to find the length of the segment formed by these endpoints.

If two points at the ends of a straight line PQ are P([tex]x_{1},y_{1}[/tex]) and Q([tex]x_{2},y_{2}[/tex]), then the length of the segment PQ will be given by the formula  

[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]

Now, in our case the two points are (-2,4) and (-2,-2) and the length of the segment will be  

[tex]\sqrt{(- 2 - (- 2))^{2} + (4 - (- 2))^{2}} = 6[/tex] units. (Answer)

The length of the segment is 6 units.

It is given that,

To find the length of the segment formed by these endpoints.

Explanation:

The distance formula is used to find the length of the segment formed by two endpoints.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d=\sqrt{(-2-(-2))^2+(-2-4)^2}[/tex]

[tex]d=\sqrt{(0)^2+(-6)^2}[/tex]

On further simplification, we get

[tex]d=\sqrt{36}[/tex]

[tex]d=6[/tex]

Thus, the length of the segment is 6 units.

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Answer:

[tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex]

Step-by-step explanation:

We have been given an expression [tex]q^2+11q[/tex]. We are asked to complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

We know that a perfect square trinomial is in form [tex]a^2+2ab+b^2[/tex].

To convert our given expression into perfect square trinomial, we need to add and subtract [tex](\frac{b}{2})^2[/tex] from our given expression.

We can see that value of b is 11, so we need to add and subtract [tex](\frac{11}{2})^2[/tex] to our expression as:

[tex]q^2+11q+(\frac{11}{2})^2-(\frac{11}{2})^2[/tex]

Upon comparing our expression with [tex](a+b)^2=a^2+2ab+b^2[/tex], we can see that [tex]a=q[/tex], [tex]2ab=11q[/tex] and [tex]b=\frac{11}{2}[/tex].

Upon simplifying our expression, we will get:

[tex](q+\frac{11}{2})^2-\frac{11^2}{2^2}[/tex]

[tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex]

Therefore, our perfect square would be [tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex].

Adding 121/4 to the equation will make it a perfect square to have [tex]q^2+11q + \frac{121}{4}[/tex]

The standard form of a quadratic equation is expressed as [tex]ax^2+bx+c=0[/tex]

Given the equation [tex]q^2+11q[/tex], we need to add a constant value that will make the expression a perfect square.

To complete the square, we will add the square of the half of the coefficient of q to the equation

Coefficient of q = 11

Half of the coefficient = 11/2

Square of the result = (11/2)² = 121/4

Adding 121/4 to the equation will make it a perfect square to have [tex]q^2+11q + \frac{121}{4}[/tex]

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Question:

Which statements are true regarding the area of circle D? Select two options.

The area of the circle depends on the square of the radius.

The area of circle D is 36Pi centimeters squared.

The area of circle D is 324Pi centimetres squared

The area of the circle depends on the square of pi.

The area of the circle depends on the central angle.

Answer:

The following statements are true regarding the area of circle D:

Step-By-Step Explanation:

As we know, the formula for area of the circle is given by,

             [tex]A=\pi r^{2}[/tex]

Where, r = radius of the circle. In figure, CD = radius = 18 cm

So, the circle area can be measured as

            [tex]A=\pi(18)^{2}=324 \pi \mathrm{cm}^{2}[/tex]

From this, concluding that the circle area depends on radius square and its value is [tex]324 \pi \mathrm{cm}^{2}[/tex]. Hence, the statement given in option A and C are correct (reveals that option B is incorrect).  

As the Pi is constant, the circle radius cannot depend on Pi value and Option D also incorrect. The area of sector of circle only depends on ratio of central angle to entire circle (So option E also incorrect).

Answer:

x=-1, -7

Step-by-step explanation:

x^2+8x+7=0

factor out the trinomial,

(x+1)(x+7)=0

zero property,

x+1=0, x+7=0

x=0-1=-1,

x=0-7=-7

Answer:

The required co-ordinate is (-2, -5).

Step-by-step explanation:

For a given point, reflection of a point (x, y) across a horizontal line y = k, the reflected co-ordinates will be: [tex]$ R_{y = k} = (x, 2k - y) $[/tex].

Here, (x, y) = (-2, 7) then reflection along the line y = 1, we get:

[tex]$ R_{y = 1} (-2, 7) = (-2, 2(1) - 7) $[/tex]

= (-2, -5)

The reflected point is (-2, -5).

Answer:

[tex]P=\$9,174.31[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested  or present value

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=6\ years\\ P=?\\ A=\$10,000\\r=1.5\%=1.5/100=0.015[/tex]

substitute in the formula above

[tex]10,000=P(1+0.015*6)[/tex]

solve for P

[tex]10,000=P(1.09)[/tex]

[tex]P=10,000/(1.09)[/tex]

[tex]P=\$9,174.31[/tex]

Final answer:

To find the dimensions of Bill's sand box, use the given constraints and solve for the width and length using a simple equation.

Explanation:

Bill's sand box dimensions:

Let the width be x.

Length = x + 2.

Given 20 feet of boards, 2x + 2(x + 2) = 20.

Solving the equation, x = 4 feet (width) and length = 6 feet.

Given number is 369. The number 3 is made of 5 match sticks, 6 is made of 6 match sticks and 9 is also made of 6 match sticks.

Let us try the possibilities of moving 1 match stick to make the biggest number.

(a) If the left upper match stick from 9 is moving to right upper position of 6, then the number will be 383.

(b) If the left bottom match stick from 6 is moving to left bottom position of 9, then the number will be 358.

(c) If the right upper match stick from 9 is moving to right upper position of 6, then the number will be 385.

(d) If the right upper match stick from 9 is moving to left upper position of 3, then the number will be 965.

The above four trials are shown in the below attachment.

Among these four possibilities, 965 is the biggest number.

Answer:

Step-by-step explanation:

In a figure like this, the largest angle is formed from the two outermost points, which are D and A. Since the vertex is X, the angle is DXA.

Answer:

45

Step-by-step explanation:

533÷12=44R5

44R5≈45

Answer:

55

Step-by-step explanation:

13+6*7=13+42=55

Answer:

B

Step-by-step explanation:

9000-500 = 8500

8500 × (3/100) =255

8500 + 255 = 8755

8755 × (3/100) = 262.65

8755 + 262.65 = 9017.65

hence, the answer is B

*please correct me if im wrong ^^

Answer:

b) 2 years

Step-by-step explanation:

If you have $9000 in the saving account, and you take $500, you are left with:

$9000 - $500 = $8500

in one year you will have 3% more of the 8500 which is:

8500/100*3 = $255

so in one year the number on your savings account is:

8500 + 255 = $8755

and by the next year you will have 3% more of the 8755 which is:

8755/100*3 = $262.65

so in two years the number on your savings account is:

8755 + 262.65 = $9017.65

which is a little bit more than the $9000.

so it will take 2 years until the calance again reaches $9000

Good evening ,

Answer:

A. 2n-1

Step-by-step explanation:

It’s an arithmetic series

with first term 1

Un = U₁ + r×(n-1)

     = 1 + 2× (n-1)

     = 1 + 2n -2

     = 2n - 1.

:)

Answer:

A. 2n-1

Step-by-step explanation:

Answer:

110°

Step-by-step explanation:

Angles of a quadrilateral add up to 360:

70 + 40 + ∠B + ∠O = 360

∠B + ∠O = 250

The central angle between A and C is double the angle B.  And, it plus angle O add up to 360.

Therefore:

2∠B + ∠O = 360

Solve the system of equations.  Subtracting the first equation from the second:

∠B = 110

Answer:6 of her counters are yellow.

9-3=6

Answer:

Step-by-step explanation:

A: a number divided by ten.  **g/10**

B: a number to the third power times by ten.  **10g³**

C: a number to the third power divided by ten.   **g³/10**

D: a number to the second power divided by ten. **g²/10**

answer: C

Answer:

42. Graph a

43. Not possible.

44. Graph e

45. Graph c

46. Graph b.

Step-by-step explanation:

42. 7x + 13 ≥ 55

⇒ x ≥ 6

So, it matches graph a.

43. 12x - 8 > 4(3x + 2)

⇒ 12x - 8 > 12x + 8

Hence, d. not possible.

44. [tex]\frac{x}{- 4} - 3 < - 1[/tex]

⇒ [tex]\frac{x}{- 4} < 2[/tex]

⇒ x > - 8

Hence, graph e matches.

45. - 4(- 2x + 3) ≤ 5 + 8x

⇒ 8x - 12 ≤ 5 + 8x

⇒ - 12 ≤ 5

This is true for all values of x, hence that matches graph c.

46. - 4(x + 3) > 8(x + 3)

⇒ - 4x - 12 > 8x + 24

⇒ 12x < - 36

⇒ x < - 3

Hence, graph b matches the situation. (Answer)

The range of Jennifer's math scores for the third quarter is 26.

The range of Jennifer's math scores for the third quarter can be determined by subtracting the lowest score from the highest score. In this case, the lowest score is 73 and the highest score is 99. Therefore, the range is 99 - 73 = 26.

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