which of these characteristics do a rhombus and a rectangle always have in common?

A. all angles are right angles

B. opposite sides with equal length

C. all sides with equal lenght ​

im pretty sure its 85

please correct me if im wrong!

Answer:

x = 4

Step-by-step explanation:

We require to find RT

Since ΔRST is right use the sine ratio to find RT

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{RT}[/tex]

Multiply both sides by RT

RT × sin60° = 2[tex]\sqrt{3}[/tex] ( divide both sides by sin60° )

RT = [tex]\frac{2\sqrt{3} }{sin60}[/tex] = 4

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

Since ΔRTQ is right use the tangent ratio to find x

tan45° = [tex]\frac{RQ}{RT}[/tex] = [tex]\frac{x}{4}[/tex]

Multiply both sides by 4

4 × tan45° = x, hence

x = 4 × 1 = 4

That is x = 4

Answer:

The distance would be 4 units and you would go 4 to the right

I hope this helps :)

Step-by-step explanation:

Answer: First option

Step-by-step explanation:

The distance between two points is calculated using the following formula

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

In this case we have the following points

W(0, 8) and X(0, 12)

Therefore

[tex]x_1 = 0\\x_2 = 0\\y_1=8\\y_2=12[/tex]

[tex]d=\sqrt{(0-0)^2 +(12-8)^2}[/tex]

[tex]d=\sqrt{(12-8)^2}[/tex]

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

[tex]d=4[/tex]

Answer:

1.25

Step-by-step explanation:

Calculate the scale factor as the ratio of corresponding sides of the image to the original.

here the corresponding sides are

image = 5 and original = 4

scale factor = [tex]\frac{5}{4}[/tex] = 1.25

To solve the given system of equations, one can utilize matrix operations, specifically finding the inverse of the coefficient matrix and multiplying it by the constants matrix to solve for the variables x, y, and z.

Solving a System of Equations

To solve the system of linear equations: 3x+4y+3z=5, 2x+2y+3z=5, and 5x+6y+7z=7, we can use methods such as substitution, elimination, or matrix operations. In this case, matrix operations may be more efficient for finding the values of x, y, and z.

Firstly, we must write the system of equations in matrix form (Ax = b), with A being the coefficient matrix, x the variable matrix, and b the constant terms matrix:

A =
| 3 4 3 |
| 2 2 3 |
| 5 6 7 |,
x =
| x |
| y |
| z |,
b =
| 5 |
| 5 |
| 7 |

Next, we find the inverse of matrix A, if it exists, and then multiply it by b to solve for x:

x = A-1 * b

Through matrix operations, we can find A-1. The existence of an inverse is dependent on the determinant of A not being zero. If the determinant is non-zero, the inverse can be used to compute the variables' values. Therefore, we proceed with calculating the determinant and, if possible, the inverse to solve for x, y, and z.

Finally, we multiply the inverse of A (if it exists) by b to get the values for x, y, and z. This involves algebraic steps and matrix multiplication. If any mistake is made, the process requires careful checking and rechecking.

Answer:

y = -3 or (0,-3)

Step-by-step explanation:

y intercept is when x is 0 so substitute 0 for x:

y=-6(0)-3=0-3=-3

y = -3

In order to find the y intercept you must substitute 0 for x and solve for y, and also simplify if needed.

[tex]y=-6x-3[/tex]

[tex]y=-6\times0-3[/tex]

[tex]-6\times0-3[/tex]

[tex]y=0-3[/tex]

[tex]-6\times 0 = 0[/tex]

[tex]0-3=-3[/tex]

[tex]= -3[/tex]

[tex]y = (0,-3)[/tex]

Therefore your answer is " y = (0,-3)."

Hope this helps.

Answer:

x=3/4

Step-by-step explanation:

0=8(8x-7)+8

0=64x-56+8

0=64x-48

48=64x

x=48/64

x=6/8

x=3/4

[tex]8(8x - 7) + 8=0\\64x-56=-8\\64x=48\\x=\dfrac{48}{64}=\dfrac{3}{4}[/tex]

Answer:

5cm

Step-by-step explanation:

okay what you need to know is that:

1cm:5km

5km times 5 is the distance you traveled, 25km

1cm times 5 is 5

Don't get confused with 5km to 5.

It's totally different.

Using the map scale of 20cm to 100km, it is calculated that 25 kilometers in reality is represented by 5 centimeters on the map. This is determined by setting up a proportion between the distance on the map and the actual distance and solving for the unknown value.

To find out how many centimeters on the map represent 25 kilometers of actual distance, we use the map's scale. The scale given is 20cm:100km, which means that for every 20 centimeters on the map, the actual distance represented is 100 kilometers. To solve the problem, we need to set up a proportion.

First, convert the actual distance you want to find on the map from kilometers to centimeters using the scale. So, for every 100 kilometers, we have 20 centimeters on the map. Hence, for 1 kilometer, the distance on the map would be 20 cm divided by 100 km.

20 cm/100 km = X cm/25 km

To find the value of 'X', our unknown value which represents how far you've travelled on the map, we perform cross-multiplication.

100 km * X cm = 20 cm * 25 km

X = (20 cm * 25 km) / 100 km

X = 500 cm / 100

X = 5 cm

So, you have travelled 5 centimeters on the map.

Answer:

Surface Area = 283

Step-by-step explanation:

Radius = 3

Height = 12

Formula for suface area is SA= 2πrh+2πr^2

let "r" be for radius

let "h" be for height

SA=2*π*3*12+2*π*3^2

SA=282.74

round to the nearest ones spot and that will make the surface area = 283

The surface area of a right cylinder with a radius of 3 and a height of 12 is calculated using the formula S = 2πr(h + r), resulting in S = 90π or approximately 282.6 square units.

The question is asking to calculate the surface area of a right cylinder with a known radius and height. The formula to find the surface area of a cylinder is S = 2πr(h + r), where r is the radius, and h is the height.

To calculate the surface area of the given cylinder with a radius of 3 and a height of 12, we plug in these values into the formula:

S = 2 × π × 3 × (12 + 3)

This simplifies to S = 2 × π × 3 × 15, which further simplifies to S = 2 × π × 45, and hence S = 90π. By multiplying this by the approximate value of π (3.14), we get S = 282.6 square units as the surface area of the cylinder.

The cross-sectional area (base area) of the cylinder is πr², which is the area of a circle with the same radius as the cylinder. The side surface area, which is the area of the rectangle that would be formed if you 'unrolled' the outer surface of the cylinder, is 2πrh. Adding two times the base area and the side surface area gives you the total surface area of the cylinder.

Answer:

Step-by-step explanation: The first step is to divide this shape into multiple other shapes. First, let's start with the smaller rectangle. It has a height of 10 centimeters and a width of 9 centimeters, giving us 90 centimeters in total.

Now, lets do the bigger rectangle. The height is 12 centimeters, and the width is 24 centimeters. [tex]12*24=288[/tex]

[tex]288+90 = 378[/tex], so our answer will be 378.

Answer:  [tex]\bold{\dfrac{1}{(x+1)(x-2)}}[/tex]

Step-by-step explanation:

[tex]\dfrac{x+2}{4x^2+5x+1}\times \dfrac{4x+1}{x^2-4}\\\\\\\text{Factor the quadratics:}\\\dfrac{x+2}{(4x+1)(x+1)}\times \dfrac{4x+1}{(x-2)(x+2)}\\\\\\\text{Simplify - cross out (4x+1) and (x+2):}\\\dfrac{1}{(x+1)(x-2)}[/tex]

Answer:

[tex]\frac{1}{x^2 - x - 2}[/tex]

Step-by-step explanation:

The given expression is

[tex]\frac{x+2}{4x^2+5x+1}\times \frac{4x+1}{x^2-4}[/tex]

Factorize the denominators.

[tex]\frac{x+2}{4x^2+4x+x+1}\times \frac{4x+1}{x^2-2^2}[/tex]

[tex]\frac{x+2}{4x(x+1)+1(x+1)}\times \frac{4x+1}{(x-2)(x+2)}[/tex]             [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]\frac{x+2}{(x+1)(4x+1)}\times \frac{4x+1}{(x-2)(x+2)}[/tex]

Cancel out common factors.

[tex]\frac{1}{(x+1)}\times \frac{1}{(x-2)}[/tex]

[tex]\frac{1}{(x+1)(x-2)}[/tex]

On further simplification we get

[tex]\frac{1}{x^2 - x - 2}[/tex]

Therefore, the simplified form of the given expression is [tex]\frac{1}{x^2 - x - 2}[/tex].

Answer:

x = 3 and -2 are the two solutions.

Step-by-step explanation:

2x^2 -2x -12 = 0

First factor out a 2

2(x^2 - x - 6) = 0

2(x - 3)(x + 2) = 0

2 = 0 x - 3 = 0 x + 2 = 0

2 does not equal zero so this is an extraneous solution

x - 3 = 0 so x = 3

x + 2 = 0 so x = -2

Answer:

L=130 while W=39

Step-by-step explanation:

Let's setup some equations.

W=.3L  from first sentence

2L+2W=338 from second sentence

I'm going to plug equation 1 into equation 2:

2L+2[.3L]=338

2L+.6L=338

2.6L=338

L=338/2.6

L=130

so W=.3L=.3(130)=39

Answer L=130 while W=39

Length of the rectangle = 130

Width of the rectangle = 39.

Given: that the width of a rectangle exists 30% of the length.

Where Perimeter = 338 ft

Width of the rectangle = 0.3L

Perimeter = 2(Length + Width)

Substitute the value of perimeter in the above equation, we get

2L + 2W = 338

2L + 2[0.3L] = 338

2L + 0.6L=338

2.6L = 338

L = 338/2.6

L = 130

Length of the rectangle = 130

So, Width of the rectangle = 0.3L

= 0.3(130) = 39

The length of the rectangle is 130 and the width of the rectangle is 39.

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Answer: 16 units

Step-by-step explanation:

Answer:

m = 12

Step-by-step explanation:

[tex]\frac{m+18}{m}[/tex]=[tex]\frac{5}{2}[/tex]

2(m+18) = 5(m)

2m + 36 = 5m

2m - 5m = -36

-3m = -36

m = 12

Answer:

Step-by-step explanation:

(m + 18) / m = 5/2

Do you know what cross multiplication is for a proportion? It means that you take the top of one fraction and multiply it by the bottom of the other fraction.

So for this question

5 (top right) * m (bottom left)

and put an equal sign

5*m =

Now take the top left and multiply by the bottom right.

2 * (m + 18)

Now equate the two results.

5m = 2*(m + 18)          Remove the brackets.

5*m = 2*m + 2*18       Combine the right.

5m = 2m + 36             Subtract 2m from both sides.

5m-2m=2m-2m+36    Combine

3m = 36                       Divide both sides by 3

3m/3 = 36/3

m = 12

Answer:

10rs

Step-by-step explanation:

C.P. - 120  

S.P. - 130  

cp < sp  

120 < 130  

so , profit = sp - cp  

= 130-120  

= 10 rs.

Profit=10rs

please mark me brainiest

Answer:

7.5 Miles.

Step-by-step explanation:

3 + 4.5 = 7.5 Miles.

Answer: [tex]x=2[/tex]

Step-by-step explanation:

According to the Intersecting Secants Theorem, when two secants intersect each other outside a circle, then the products of their segments are equal.

Based on this, we can write this expression:

[tex](3)(3+5)=(4)(4+x)[/tex]

Knowing this, we can solve for "x". Therefore, this is:

[tex](3)(8)=(4)(4+x)\\\\24=16+4x\\\\24-16=4x\\\\8=4x\\\\\frac{8}{4}=x\\\\x=2[/tex]

ANSWER

[tex]c = 5[/tex]

EXPLANATION

A quadratic equation is said to be in standard form when it is in the form

[tex]a {x}^{2} + bx + c = 0[/tex]

where a, b, c are real numbers.

The given quadratic equation is

[tex] - 6 = {x}^{2} + 4x - 1[/tex]

When we add 6 to both sides, we obtain,

[tex]-6 + 6= {x}^{2} + 4x - 1 + 6[/tex]

[tex] \implies \: 0= {x}^{2} + 4x + 5[/tex]

Or

[tex]\implies \: {x}^{2} + 4x + 5 = 0[/tex]

This is what Alexandra got after he wrote the quadratic equation in standard form.

By comparing this equation to

[tex]a {x}^{2} + bx + c = 0[/tex]

we have a=1, b=4 and c=5.

Answer:

Debit Card

Step-by-step explanation:

It is not a credit card, but you can use it to purchase anything, but you have your own money to use. Credit cards are used to purchase anything as well, but that is the bank's money you are borrowing and eventually, you have to pay them back the EXACT same money.

The type of card that is not really a credit card but is sometimes used for credit purchases is a primary sales credit card.

A primary sales credit card is a type of card that is issued by a merchant or retailer, rather than a bank. It can be used to make purchases at that particular merchant, and the cardholder is typically given a line of credit that they can borrow against. However, primary sales credit cards are not considered to be true credit cards because they are not issued by a licensed financial institution.

There are a few reasons why someone might choose to use a primary sales credit card. One reason is that they may not be able to qualify for a traditional credit card from a bank. Another reason is that primary sales credit cards often offer special benefits, such as discounts on purchases or rewards programs.

However, it is important to be aware of the risks associated with using primary sales credit cards. One risk is that the interest rates on these cards can be very high. Another risk is that the cardholder may be liable for the full balance of their account, even if the merchant goes out of business.

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Answer:

20

Step-by-step explanation:

24/3=8

36/3=12

8+12=20

he'll have 20 3' ropes

The probability that a first roll is an even number and a second role is a number greater than 4 when a six-sided number cube is rolled twice is 1/6.

The probability of an event is the fractional value determining how likely is that event to take place. If the event is denoted by A, the number of outcomes favoring the event A is n and the total number of outcomes is S, then the probability of the event A is given as:

P(A) = n/S.

When the occurrence of one event, doesn't affect the occurrence of the other event, then the two events are independent of each other.

If we have two independent events A and B, then the probability of A and B is given as:

P(A and B) = P(A) * P(B).

We are informed that a six-sided number cube is rolled twice. We are asked what is the probability that a first roll is an even number and a second roll is a number greater than 4.

Let the event of getting an even number on a first roll be A.

∴Number of outcomes favorable to event A (n) = 3 {2, 4, 6}

Total number of outcomes (S) = 6 {1, 2, 3, 4, 5, 6}

∴ The probability of getting an even number on a first roll is:

P(A) = n/S = 3/6 = 1/2.

Let the event of getting a number greater than 4 on a second roll be B.

∴Number of outcomes favorable to event B (n) = 2 {5, 6}

Total number of outcomes (S) = 6 {1, 2, 3, 4, 5, 6}

∴ The probability of getting a number greater than 4 on a second roll is:

P(B) = n/S = 2/6 = 1/3.

∵ Our two events, A and B, are independent of each other, that is, the occurrence of one doesn't affect the occurrence of the other, the probability that a first roll is an even number and a second roll is a number greater than 4 is given by:

P(A and B) = P(A)*P(B) = (1/2)*(1/3) = 1/6.

∴ The probability that a first roll is an even number and a second role is a number greater than 4 when a six-sided number cube is rolled twice is 1/6.

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Answer: A) [tex]18, 0, -10, -10[/tex]

Step-by-step explanation:

Given the quadratic function [tex]y=x^2-x-12[/tex], you need to substitute each value of "x" into the function to find the corresponding value of "y":

For [tex]x=-5[/tex]:

[tex]y=(-5)^2-(-5)-12\\\\y=18[/tex]

For [tex]x=-3[/tex]:

[tex]y=(-3)^2-(-3)-12\\\\y=0[/tex]

For [tex]x=-1[/tex]:

[tex]y=(-1)^2-(-1)-12\\\\y=-10[/tex]

For [tex]x=2[/tex]:

[tex]y=(2)^2-(2)-12\\\\y=-10[/tex]

The correct option is: A

Answer:

Step-by-step explanation:

The sum of x and 25 is less than 75. Inequality form shows x+25<75. To solve x, subtract 25 from both sides. x<50. X must be less than 50.

Answer:

y = 6 (pieces)

Step-by-step explanation:

y = (48 inches) / (8 inches per piece) = 6 pieces.

y = 6 (pieces)

Jerry will have to grow 24 more inches in order to reach his max Hight of 72 inches. If you put this into a inequality it would be 48 plus a number is greater that or equal to 72.

48+X_>72

The  expression for g(x) is g(x) = x^3, a cubic function that passes through the origin and is slightly narrower than the graph of f(x) = x^2.

 Certainly! Let's walk through the step-by-step calculation to determine the expression for g(x) based on the given information.

Given Information:

f(x) = x^2 (quadratic function)

Coordinate marked for g(x) is (2, 8)

g(x) is a parabola slightly narrower than f(x)

The curve g(x) passes through the origin

Expression for g(x):

Since g(x) is a parabola, we consider it as g(x) = ax^2 initially.

The coordinate (2, 8) helps determine the value of a.

g(2) = a(2)^2 = 4a = 8

Solving for a, we get a = 2.

So, g(x) = 2x^2 is the initial expression.

Adjusting for Narrowness:

If g(x) is slightly narrower than f(x), we need to make it narrower than 2x^2.

To achieve this, we can use g(x) = x^3.

Verification:

Check the coordinate (2, 8) in g(x) = x^3:

g(2) = 2^3 = 8

The coordinate (2, 8) satisfies the expression.

Answer:

The inequality is  [tex]6x+4,885.78\leq 9,750.05[/tex]

[tex]x\leq 810.71\ gal[/tex]

Step-by-step explanation:

Let

x -----> amount of water that can be used by only one family member for the rest of the month

we know that

[tex]6x+4,885.78\leq 9,750.05[/tex]

Solve for x

Subtract 4,885.78 both sides

[tex]6x\leq 9,750.05-4,885.78[/tex]

[tex]6x\leq 4,864.27[/tex]

Divide by 6 both sides

[tex]x\leq 4,864.27/6[/tex]

[tex]x\leq 810.71\ gal[/tex]

Answer:

Each member can use, x = 810.71 gallons of water for the remaining month.

The equation is 6x + 4885.78 [tex]\leq[/tex] 9750.05

Step-by-step explanation:

Total number of members in Green's family = 6

Let one member uses = x gallons of water

Therefore six member will use = 6x gallons of water

Given the Green's family can use only 9750.05 gallons of water in one month. And they have use so far 4885.78 gallons of water.

Therefore the equation becomes

6x + 4885.78 [tex]\leq[/tex] 9750.05

6x [tex]\leq[/tex] 9750.05 - 4885.78

6x [tex]\leq[/tex] 4864.27

x [tex]\leq[/tex] 4864.27 / 6

x [tex]\leq[/tex] 810.71 gallons

Hence, the equation is 6x + 4885.78 [tex]\leq[/tex] 9750.05

and each member can use 810.71 gallons of water for the remaining days of the month.

Answer:

[0, 2, 5]

Step-by-step explanation:

Find z, plug in 5 for every "z" you see, then solve by Elimination to find y and x.

The solution to the given system of linear equations is x = 1, y = 3, z = 5. The problem is resolved by first solving the simplest equation and using its answer to simplify and solve the next, allowing us to find the final answers.

To solve the given system of linear equations, we need to find the values for variables x, y and z that satisfy all the three equations. Start by solving the simplest equation which is '2z = 10'. By dividing both sides by 2, we find that z = 5.

Next, substitute z = 5 into the other two equations. The first equation 'x + 2y + z = 9' becomes 'x + 2y + 5 = 9', which simplifies to x + 2y = 4. The second equation 'x - y + 3z = 13', becomes 'x - y + 3*5 = 13', simplifying to x - y = -2.

We now have two equations with two variables, which we can solve simultaneously. By adding the equations together '(x + 2y = 4) + (x - y = -2)', we get 2x + y = 2, hence, x = 1. Substituting x = 1 into 'x - y = -2' yields y = 3.

Therefore, the solution to the system is x = 1, y = 3, z = 5.

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Answer:

A

Step-by-step explanation:

Between 4 and 5 where the vertex is. The axis of symmetry is a line going through the vertex. For a while it will be of the form x = a

In this case, the axis of symmetry is x = 4.5

Answer:

=6000 m/min

Step-by-step explanation:

There are 60 seconds in 1 minute.

The speed of the race car is 100 m/s. If it covers 100 m in one second,  then in one minute it will cover a longer distance calculated as follows.

100 m/s × 60 second/min = 6000 m/min

Answer: Last Option

6,000 meters per minute

Step-by-step explanation:

We know that 60 seconds is equal to one minute.

Then we use this data as a conversion factor.

The speed of the car is 100 meters per second, this is:

[tex]s = 100\ \frac{meters}{seconds}[/tex]

Now we multiply this amount by the conversion factor in the following way:

[tex]100\ \frac{meters}{second} * \frac{60\ second}{1\ minute}= 6000\ \frac{meters}{minute}[/tex]

The answer is:

6,000 meters per minute

Answer:

=42

Step-by-step explanation:

The expression 8×7×9×49×3 can be written in its simplest factor form as follows.

8=2³

49=7²

9=3²

Thus the expression becomes:2³×7×3²×7²×3

Combine the indices to the same base.

2³×3³×7³

Finding the cube root involves dividing the index by three.

Thus ∛(2³×3³×7³)= 2×3×7

=42