Rectangle A: 2 * 3 Rectangle B: 8 * 12 Rectangle C: 5 * 7 Rectangle D: 10 * 12 Which pair of rectangles is similar?

Answer:x intercept (2,0)

Yintercept (0,-10)

Step-by-step explanation:

y=mx+b b= y intercept

To find x you just solve

Y=5x-10

10=5x

2=x

By proving the two triangles as similar triangles , the value of x in the triangles is x = 5 cm .

By using the proportions, for the two triangles which are similar because they contain three equal angles ;

The One angle due to connected by the vertex (oppose by the vertex), another angle as marked with the tick, and

the third angle one has to be same because of the sum of the three internal angles of a triangle must equal 180 degrees.

So , the proportions of the sides are written as :

⇒ 4/32 = x/40  ;

Cross multiplying , and solving for "x" ,

we get ;

⇒ x = (4 × 40)/32 ;

⇒ x = 5 .

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The given question is incomplete , the complete question is

What is the value of x in the polygon given below ?

The next term in the sequence of number 8, 4, 2, 1, 1/2 is 1/4

From the question, we have the following parameters that can be used in our computation:

The sequence of number 8, 4, 2, 1 -1/2

Express properly

The sequence of number 8, 4, 2, 1, 1/2

The above definitions imply that we simply divide the previous term by 2 to get the current term

Using the above as a guide,

Next term = (1/2)/2

Evaluate

Next term = 1/4

Hence, the next term is 1/4

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Answer:

where’s the options??

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

3+2+7=12

Hope this helps! Please give brainliest!

The average of the three weighted points, A, B, and C, is (-1, 2.875).

A technique known as a weighted average accounts for the varied levels of significance of the values in a data collection. Each number in the data set is multiplied by a predefined weight before the final computation is completed when calculating a weighted average.

weighted average = (w1 × x1 + w2 × x2 + w3 × x3) / (w1 + w2 + w3),

where wi is the weight of the ith point, and xi is the coordinate of the ith point.

Substituting the given values, we get:

weighted average = (1 × (-8, 5) + 3 × (8, 2) + 4 × (5, 4)) / (1 + 3 + 4)

= (-8, 5 + 3 × 2 + 4 × 4) / 8

= (-8, 23) / 8

= (-1, 2.875)

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The procedure for angle measurement by the protractor is mentioned below:

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

To measure an angle using a protractor, follow these steps:

1. Place the protractor on the angle you want to measure, with the base of the protractor aligned with one side of the angle.

2. Make sure the protractor is centered and level, with the zero-degree mark on the protractor aligned with the vertex (corner) of the angle.

3. Read the measurement of the angle from the protractor, where the second side of the angle intersects with the protractor scale. The measurement is usually given in degrees.

If the angle is larger than 180 degrees, you may need to use a full-circle protractor or measure the angle in two parts and add the measurements together.

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The equations used are:

Longest side = a

Shortest side = 1/2 x a = 1/2a

Third side = a - 1

The shortest side is 8 inches, the longest side is 16 inches and the third side is 15 inches.

The perimeter of a triangle is the sum of the length of the three sides of the triangle.

Let the following expressions represent the lengths of the sides of the triangle:

Longest side = a

Shortest side = 1/2 x a = 1/2a

Third side = a - 1

Perimeter = a + 1/2a + a - 1 = 39

a + 1/2a + a = 39 + 1

2a + 1/2a = 40

2 1/2a = 40

5/2a = 40

a = 40 x 2/5

a = 16 inches

Shortest side = 1/2 x 16 = 8 inches

Third side = 16 - 1 = 15 inches

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Answer:

choice C.  y = -4/3x + 2

Step-by-step explanation:

slope of a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the first line.

m = -4/3  (negative reciprocal of 3/4)

Now use point-slope form to find the y-intercept (b):

y-2 = -4/3(x-0)

y = -4/3x + 2

Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then  R(t) = 20 + 1.6sin(2πt/5.2).

The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.

In this case, the amplitude is 1.6.

Since the radius changes by a maximum of 1.6 million miles.

The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)

The phase shift is 0, since when t = 0 the radius is increasing.

The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)

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Answer:

12

Step-by-step explanation:

First find the missing angle S

Three angles of a triangle add up to 180°

So m∠S + 81 + 42 = 180

m∠S + 123 = 180

m∠S = 180 - 123 = 57°

Using the law of sines which states that the ratio of each side to the opposite angle is the same for both sides we get

[tex]\dfrac{r}{\sin 42} = \dfrac{q}{\sin81} = \dfrac{15}{\sin 57}\\\\\sin 57 = 0.83867\\\\ \dfrac{15}{\sin 57}= \dfrac{15}{0.83867}\\\\= 17.88545\\\\[/tex]

Hence
[tex]\dfrac{r}{\sin 42} = 17.88545\\\\r = 17.88545 \times \sin 42\\\\r = 17.88545 \times 0.66913\\\\r = 11.9677\\\\r = 12 \textrm{ rounded to the nearest tenth}[/tex]

The location of Kris' signature on the $601.73 check Elmo wrote to Kris and which Kris deposited into her checking account is on the back of the check. The correct option is option C.

C. Only on the back of the check

A checking account is an account opened at a financial institution into which deposits and withdrawals can be made by a customer. A checking account can also be referred to as a transaction account, a credit unions share draft account, demand deposit account or current account.

The amount of check Elmo wrote Kris = $601.73

The amount Kris deposited into her checking account = The check Elmo issued to her

The location to sign before depositing a check into a checking account is at the back of the check, including informing the cashier that the specified  check is to be deposited into the checking account.

The correct option is therefore option C.

C. Only on the back of the check

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Answer:

Below

Step-by-step explanation:

Instead of x , I assume you want the angle For RIGHT triangles, remember

cos (angle ) = adjacent leg / hypotenuse

cos ( angle ) = 5 /12    

      angle = arccos( 5/12) = 65 °

You could also use pythagorean theorem to calculate the misssing side....then use cos law to calculate the angle.

In the absence of trade between Glacier and Sequoia, Glacier would consume 8 million pairs of shorts and 48 million pounds of almonds, and Sequoia would consume 15 million pairs of shorts and 20 million pounds of almonds. However, if both countries decide to engage in trade, Glacier could specialize in producing shorts, using 1 million hours of labor per week, and Sequoia could specialize in producing almonds, using 1 million hours of labor per week. This specialization would result in Glacier producing 12 million pairs of shorts and Sequoia producing 24 million pounds of almonds. This would enable each country to consume more of both goods than they could produce in the absence of trade.

Answer:

Standard form of the equation for the circle

(x + 3)² + (y + 5)² = 40

Step-by-step explanation:

The equation of a circle in standard form is
[tex]\boxed{(x - a)^2 + (y-b)^2= r^2}[/tex]

where (a, b) is the center of the circle and r is the radius

To find center of circle

The end points of the diameter are (-5, -11) and (-1, 1)

The center of the circle is midway between these two points

The x-coordinate of the midpoint = (-5 + -1)/2 = -6/2 = -3

The y-coordinate of the midpoint is (-11 + 1) /2 = -10/2 = -5

So the center of the circle is at (-3, -5)

To find the radius,

Calculate the distance from (-3, -5) to any of of the endpoints.

Let's take the endpoint (-1, 1) and find its distance from (-3, -5)

The distance between any two points (x₁, y₁) and (x₂, y₂) is calculated from the formula

[tex]d^2 = {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2[/tex]

Substituting
(x₁, y₁) = (-1, 1)
(x₂, y₂)  = (-3, -5)

and r for distance

we get

[tex]r^2 = {(-3 - (-1))^2 + (-5 - 1)^2[/tex]

[tex]r^2 = {(-2)^2 + (-6)^2}[/tex]

[tex]r^2 = {{4} + {36}}[/tex]

[tex]r^2 = {40}[/tex]

So the center (a, b) is (-3, -5) and r² =40

Plugging this into the circle equation:
(x - (-3))² + (y - (-5))² = 40

(x + 3)² + (y + 5)² = 40

The lengths of the sides of the pentagon are;

12 Inches

13 inches

14 inches

15 inches

16 inches

The formula for the perimeter of a pentagon is expressed with the formula;

P = 5a

Given that the parameter are;

Since the sides are consecutive integers, then;

60 = 5(a)

expand the bracket

60= 5a

Make 'a' the subject

a = 12In

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Answer:

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

Let the number of pizzas be x.

The average cost per pizza is:

If we need the average cost be at most $3.50, we need an inequality:

This is translated as:

The blanks are:

The y-intercept of the line passing through the given points is -26 and the slope is -13/17

The y-intercept is the point where the graph intersects the y-axis.

Given that, the pair of coordinates of some points, we need to find the y-intercept,

To find the same, we will firstly find the equation of the line passing through these points,

We know that, the equation of a line passing through two points is given by,

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Considering the points, (34, -52) and (51, -65)

The equation will be,

y+52 = -65+52 / 51-34 (x-34)

y+52 = -13/17(x-34)

y+52 = -13x/17+26

y = -13x/17-26

Hence, the y-intercept of the line passing through the given points is -26.

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The required Length of the DC is 30.47 Units.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

We have;

In ΔABD, ∠BAD = 54° and in ΔBDC, ∠BCD = 28°.

Then, In ΔABD

Sin∅ = BD/20

Sin(54°) = BD/20

BD = 0.809(20)

BD = 16.18

in ΔBDC

tan(28°) = BD/DC

DC = BD/tan(28°)

DC = 16.18/0.531

DC = 30.47 Units.

Thus, required Length of the DC is 30.47 Units.

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Answer:

26 kangaroos on the farm
32 goats on the farm

Step-by-step explanation:

To find the number of goats and kangaroos on the farm, we need to determine the number of legs each animal has. Let's say that there are 'g' goats and 'k' kangaroos.

Since each goat has 4 legs, the total number of legs for all the goats is 4g. Similarly, since each kangaroo has 2 legs, the total number of legs for all the kangaroos is 2k.

Adding these two quantities, we have:

4g + 2k = 180

Since each goat has 1 head, the total number of heads for all the goats is g. Similarly, since each kangaroo has 1 head, the total number of heads for all the kangaroos is k.

Adding these two quantities, we have:

g + k = 58

Now, we have two equations and two unknowns. To solve for 'g' and 'k', we can use substitution or elimination method.

Let's use substitution method:

From the second equation, we can find g:

g = 58 - k

Substituting this in the first equation, we get:

4(58 - k) + 2k = 180

Expanding and solving, we get:

232 - 4k + 2k = 180

232 - 2k = 180

-2k = -52

k = 26

So, there are 26 kangaroos on the farm. To find the number of goats, we can use the first equation:

g = 58 - k = 58 - 26 = 32

Therefore, there are 32 goats on the farm.

Answer: the enswer is c the range is 46

Step-by-step explanation:

Answer: A = 5

Step-by-step explanation:

So, we are given a function, with a point: we can substitute (x,y) from the coordinate into x and f(x) in the function. (recall that f(x) is just a fancy way of saying y).

so:

[tex]-1 = \frac{2(0) + 5}{0 - A}[/tex]

[tex]-1 = \frac{5}{-A}[/tex], (we can drop the negative sign from both sides here)

[tex]\frac{5}{5} = \frac{5}{A}[/tex], (recall 1 = x/x where x is literally any number)

hence we can see that A = 5

Ask questions in the comments if this doesn't make sense :)

The number of pieces of candy that will be left on day 4 would be 2, 560 candies .

The number of pieces of candy left on day 8 would be 66 candies .

To find the number of candy left on the fourth day, given that Augustus only gives candies after the pile of 100, 000 candies is reached, the formula is:

= Number of starting candy x ( 1 - Percent given away ) ^ number of days

= 100, 000 x ( 1 - 60 % ) ⁴

= 100, 000 x 40 % ⁴

= 2, 560 candies

On Day 8, this would be:

= 100, 000 x ( 1 - 60 % ) ⁸

= 66 candies

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The question is:

How many pieces of candy will be left on day 4? On day 8?

Answer:

Step-by-step explanation:

The Rational Zeroes Theorem states that if a polynomial equation has a rational solution (a solution that can be expressed as a fraction of two integers), then that rational solution must be of the form p/q, where p is a factor of the constant term (in this case 36) and q is a factor of the leading coefficient (in this case 4).

Step 1: Find the factors of 36. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Step 2: For each factor of 36, divide it by each factor of 4 to get a list of possible rational solutions.

Step 3: Test each of the possible rational solutions by plugging them into the polynomial equation and seeing if they make the equation equal to zero. If a solution makes the equation equal to zero, it is a root of the polynomial.

Step 4: Once you have found all of the roots of the polynomial, you can use them to write the polynomial in factored form.

Note: This method only works for polynomials with real coefficients and will only give you the real solutions of the equation. If the polynomial has complex solutions, you will need to use a different method to find them.

The vertical asymptotes of y = 6tan(0.2x) is [tex]\:x=\frac{\pi }{0.4}+\frac{\pi }{0.2}n[/tex]

From the question, we have the following parameters that can be used in our computation:

y = 6tan(0.2x)

The equation is a trigonometry function

The best way to determine the vertical asymptotes is with the use of a graphing tool

Using the above as a guide, we have the following:

From the graphing tool, we have

[tex]\:x=\frac{5\pi }{2}+\frac{\pi }{0.2}n[/tex]

This gives

[tex]\:x=\frac{\pi }{0.4}+\frac{\pi }{0.2}n[/tex]

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You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second,  64.23 feet/second long it will take for the object to hit the ground below. This can be solved using the concept of law of conservation of energy.

Three fundamental quantities all maintain their original values. Energy, momentum, and angular momentum are these. Energy is a conserved quantity, which could surprise you if you've read instances in previous pages, such the kinetic energy of charging elephants. The first law of thermodynamics, generally known as the law of conservation of energy, stipulates that the energy of a closed system must remain constant and cannot rise or fall on its own without external intervention.

Given that,

Height of the cliff, h= 55 Foot

Initial speed of the projectile, u = 85 m/s

Let, the projectile hit the ground with velocity "v"

Applying the law of conservation of energy,

mgh + 1/2 mu² = 1/2 mv²

or, m (gh + 1/2 u²) = 1/2 mv²

or, (gh + 1/2 u²) = 1/2 v²

or, 10 × 55 + (1/2 × (55)²) = 1/2 v²

or, 550 + 1512.5 = 1/2 v²

or, 2062.5 = 1/2 v²

or, 4125 = v²

or, v = 64.23 feet/second

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3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).

3.2. it would take approximately 6.67 years to pay off the vehicle through instalments.

A deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit

3.1 The cash price of the NISSAN NP300 is R221,180 (incl. VAT).

3.2 The given information does not explicitly state the number of years for the instalment plan, but it does provide the number of months (80) and the total payment amount (R303,007). Assuming a monthly payment plan, we can calculate the number of years as follows:

Number of years = Number of months / 12

Number of years = 80 / 12

Number of years ≈ 6.67 years

So it would take approximately 6.67 years to pay off the vehicle through instalments.

To calculate the deposit needed, we need to subtract the residual amount from the total cash price. From the given information, the total payment is R303,007 and the residual is R80,180, so:

Cash price = Total payment - Residual

Cash price = R303,007 - R80,180

Cash price = R222,827

So the cash price is slightly higher than the advertised price of R221,180, likely due to financing fees or interest. To determine the deposit needed, we can assume a specific percentage of the cash price that must be paid upfront. For example, if the deposit required is 10% of the cash price, then:

Deposit = 0.1 x Cash price

Deposit = 0.1 x R222,827

Deposit = R22,282.70

So a deposit of approximately R22,282.70 would be needed if the financing plan requires a 10% deposit.

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The graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.

What is a quadratic equation?

The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and  a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f(x). Where it equals zero is where the quadratic equation finds its solutions. They are also known as the equation's roots.

Assuming the question is to graph the quadratic function y = 6x².

The x-intercept can be found by substituting y = 0

0 = 6x²

x = 0

x-intercept = (0,0)

y-intercept can be found by substituting x=0

y = 6 * 0

y = 0

y-intercept = (0,0)

The given quadratic equation is the equation of an upward parabola with the vertex as (0,0).

The axis of symmetry is x = 0 i.e y-axis.

Hence the graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.

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Jenny's average jogging speed in the distance covered is; 10 miles/hr

Let x miles/hr be the speed that Jenny walks at

Then, 2x miles/hr is the speed that Jenny runs at

She jogs for  9.5 miles

2x miles = 1 hours

9.5 miles = a hours

a = 9.5/2x hours

She walks for 2.5 miles

x miles = 1 hour

2.5 miles = b

b = 2.5/x hours

Thus;

(9.5/2x) + (2.5)/x = 1.45

Multiply through by 2x to get;

9.5 + 5 = 2.9x

14.5/2.9 = x

x = 5 miles/hr

Jogging speed = 2 * 5 = 10 miles/hr

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