To prove triangles similar, we only need to prove corresponding angles congruent OR corresponding sides are proportional. However, with a quadrilateral we need to prove corresponding angles congruent AND corresponding sides are proportional. Explain in your own words why it takes more to prove that quadrilaterals are similar. Include examples demonstrating how “just angles” or “just sides” is not enough.

Answer:

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Step-by-step explanation:

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The complete question is :

Question: What is the coefficient in the expression 10x²-7?

The coefficient in the expression [tex]10x^{2} -7[/tex] is 10

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

According to the question,

The expression given is [tex]10x^{2} -7[/tex]

The variable given is x

We need to find the coefficient in the expression.

In the given expression x is the variable and the number before the x is coefficient which is 10 .

Hence the coefficient in the expression is 10.

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When reflected over ry-axis (x, y) (-x, y) , rx-axis (x, y) (x,-y) , Option A and D is the correct answer.

The rule for reflection is when an object or a coordinate point is reflected over x axis then the coordinate of the x axis remains the same while the y coordinate changes to be additive inverse.

Vice Versa happens when reflected over y axis.

So,

rx-axis (x, y) - (-x, y) --> (x,-y)

ry-axis (x, y) (-x, y)

Therefore Option A and D is the correct answer.

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Answer: its A not A & D

Step-by-step explanation:

Answer: Hope this helps you

1/2

Step-by-step explanation:

To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.

8x+2y = 4 ➨ 8x+2*0 = 4

Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:

8x = 4

Now I will divide both sides by 8, which isolates our x.

x = 1/2

The x-int is 1/2.

Answer:

25

Step-by-step explanation:

you first solve for the expontes. 5 to the power of 2 is 25 plus 5 is 30. subtract 5 from that and we're back at 25

Answer:

25

Step-by-step explanation:

When we plug in 5 for x, we get 25+5-5=25.

Note that

108° = 90° + 18°

so

sin(108°) = sin(90° + 18°) = sin(90°) cos(18°) + cos(90°) sin(18°) = cos(18°)

Then

sin²(108°) + sin²(18°) = cos²(18°) + sin²(18°) = 1

by the Pythagorean identity.

The value of the expression sin²(108°) + sin² (18°) ​will be 0.9986.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. The six - trigonometric functions are -

We have the following trigonometric equation -

sin²(108°) + sin² (18°) ​

We have the following expression -

sin²(108°) + sin² (18°) ​

(0.95)² + (0.31)²

0.9025 + 0.0961

0.9986

Therefore, the value of the expression sin²(108°) + sin² (18°) ​will be 0.9986.

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Answer:

y-4=-1/2(x-4)

Step-by-step explanation:

point slope form: y-y1=m(x-x1)

every time x increases by 8, y decreases by 4. slope can be found by rise/run. the slope is -4/8 which is -1/2, which means m=-1/2. in the given equation, it said y-4. It plugged in 4 for y1, meaning it was talking about the second given point, which was (4,4). plug in 4 for x and you get y-4=-1/2(x-4)

The probability of 6 years or more, so we want the complement,

1 - 0.98533 = 0.01467                        1.467% chance, not very likely.

A z score is a type of statistical measurement that gives an idea of how far a raw score is from the mean of a distribution. A z score is used in a z test for hypothesis testing.

Here, Because you are looking for the mean of a group of 7.8, the standard deviation will shrink by a factor of √6

Old standard deviation = 0.7,

new standard deviation = 0.7/√6 = 0.64254

You need to find a z-score and then convert your z-score to a probability.

z-score = (your score - average)/ std dev

z-score = (7.8 - 6)/0.64254

z-score = 2.1789

To convert a z-score either look it up on a table or use a calculator.

But z-tables are designed to shade to the left, which means this is the probability that the mean life is 6 years or less. We want the probability of 6 years or more, so we want the complement, 1 - 0.98533 = 0.01467

1.467% chance, not very likely.

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Answer:

3 gallons

Step-by-step explanation:

For every value of green ( 'x') ....white is 3 times as much

  for 1 gallon green     ====> 3 gallons white

Answer: 1.3062

Step-by-step explanation:

0.311 * 4.2 = 1.3062

Answer:

(-3, -13)

(-1, -7)

(1, -1)

(3, 5)

(5, 11)

Step-by-step explanation:

Plug x into the equation y = 3x - 4 for each value of x to obtain the y value.

For example:

y = 3(3) - 4

y = 9 - 4

y = 5

Answer:

The relationship between the scale factor and perimeter of an image and its pre-image is a, b = perimeter = 2a + 2b. the relationship between the scale factor and area of an image and its pre-image is k∧2 (ab).

Step-by-step explanation:

Relationship between the scale factor and perimeter of an image and its pre-image.

Scale factor = k

Pre-image lengths: a, b = perimeter = 2a + 2b

Image lengths: ka, kb = perimeter = 2ka + 2 kb = k (2a + 2b) = 2 * preimage perimeter.

She has to say that the perimeter of the image is the perimeter of the preimage times the same scale factor.

What should she say about the relationship between the scale factor and area of an image and its pre-image?

area of the pre-image = ab

are of the image = (ka)(kb) = k^2 (ab)

The area of the image is the area of the preimage times the square of the scale factor.

Support her statements using scale factors of 5 and 6.

Scale factor 5

length of the pre-image = 3 x 4 = perimeter = 2 (3 + 4) = 2(7) = 14

length of the image = 3*5 x 4*5 = 15 x 20 = perimeter = 2 (15 + 20) = 2 (35) = 70

14 * 5 = 70 which shows the prediction

area of the pre-image = 3 * 4 = 12

area of the image = 15 * 20 = 300

12 * (5^2) = 12*25 = 300 which is the value predicted.

Now you can do the same using scale factor 6.

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Answer

(0,3)

Step-by-step explanation:

Answer:

Solution:

Here,

[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}[/tex]

Weight of 13 m of rod=23.4 kg

Weight of 1 m of rod=23.4/13 kg

[less length,less weight]

Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg

[more length,more weight]

Thus,the weight of 6 m of rod is 10.8 kg.

Alternative method:

Let,the required weight be x kg.

Then,

[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}[/tex]

We know that,

More length of iron rod([tex]\red{\uparrow}[/tex]) will have the more weight([tex]\red{\uparrow}[/tex]).

So,using the rule of direct proportion;

i.e. Ratio of length=Ratio of weight

[tex] \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }[/tex]

[tex] \rm{13x = 6 \times 23.4}[/tex]

[tex] \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}[/tex]

[tex] \therefore{x = 10.8}[/tex]

Thus,the weight of 6 m long iron rod is 10.8 kg.

Your question translates to computing [tex]3^{2020} \pmod {13}[/tex].

Recall Euler's theorem: if [tex]\gcd(a,n)=1[/tex] (that is, [tex]a[/tex] and [tex]n[/tex] are relatively prime), then [tex]a^{\varphi(n)}\equiv1\pmod n[/tex], where [tex]\varphi(n)[/tex] denotes Euler's totient function, which counts the number of positive integers relatively prime to [tex]n[/tex].

Since 13 is prime, we have [tex]\phi(13)=12[/tex]. Then by Euler's theorem,

[tex]3^{12} \equiv 1 \pmod{13}[/tex]

Now, observe that 2020 = 168×12 + 4, so that

[tex]3^{2020} \equiv 3^{168\times12+4} \equiv \left(3^{12}\right)^{168} \times 3^4 \equiv 1^{168} \times 3^4 \equiv 3^4 \pmod{13}[/tex]

and since 3⁴ = 81 = 6×13 + 3, we end up with

[tex]3^{2020} \equiv 81 \equiv 3 \pmod{13}[/tex]

so the remainder upon dividing 3²⁰²⁰ by 13 is 3.

Answer:

The account has $18,795.02.

Step-by-step explanation:

The account has $18,795.02.

3 years * $535 = $1,605

$1,605 * .0034 = $5.481

$5.481 * 36 (months) = $197.146

$18,795.02 = $1,605 + $197.146

Answer:

3 miles

2.73 miles=3 miles

The equation for the red graph will be g(x) = x² + 3.

A statement, principle, or policy that creates the link between two variables is known as a function.

The function f(x) is given below.

f(x) = x²

Then the function g(x) will be given as

g(x) = x² + 3

Then the equation for the red graph will be g(x) = x² + 3.

The missing graph is given below.

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The question is incomplete. Below you will find the missing contents.

The correct match of events with order are,

When two events A and B are independent then,

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

when A and B are dependent events then,

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

When two events A and B are mutually exclusive events then,

P(A and B)=0

So, P(A or B) = P(A) + P(B) - P(A and B) = P(A) + P(B)

P(A) + P(B) = P(A or B)

When events are not mutually exclusive then the general relation is,

P(A or B) = P(A) + P(B) - P(A and B)

If the probability of the event B conditioned by A is given by,

[tex]\mathrm{P(B|A)=\frac{P(A~and~B)}{P(A)}}[/tex]

Hence the correct match are -

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Answer:

14x + 8

Explanation:

⇒ 4(5x+5) - 3(2x + 4)

distribute inside parenthesis

⇒ 4(5x) + 4(5) - 3(2x) - 3(4)

multiply the variables

⇒ 20x + 20 - 6x - 12

collect like terms

⇒ 20x - 6x + 20 - 12

subtract like term

⇒ 14x + 8

4 x 5x = 20x

4 x 5. = 20

-3 x 2x = - 6x

-3 x 4 = - 12

Line them up, collect like terms & simplify

20x + 20 - 6x - 12

20x - 6x = 14x

20 - 12 = 8

Thus, answer is 14x + 8

Hope this helps!

The answer to the question on Parallelograms being rectangles is that; No; the diagonals may not be congruent

1) We cannot conclude that the parallelogram is a rectangle but we can say that all rectangles are parallelograms.

2) The explanation for number 1 above is that the parallelogram's diagonals may not be equal or congruent but in rectangles diagonals are always equal and bisect each other.

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The standard deviation of the data to the nearest hundredth is 173.01.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation: 185

Determine the difference between each value and the mean and then square the result:

Determine the mean of the sum of the squared differences and then find the square root of the mean:

Following these steps, the standard deviation is 173.01

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Answer:

please provide the diagram

Step-by-step explanation:

for the solution figure is necessary so provides us to solve this problem

Answer:

A = 13 degrees

B = 65.3 degrees

C = 180 - (13 + 65.3) = 101.7 degrees

Side a = 35 km

Side b = 141.4 km

Side c = 152.4 km

The length of the rectangle is 100cm.

The breadth of the rectangle is 4cm.

The square encloses more area than the rectangle.

The first step is to determine the area of the square.

Area of a square = length² = 50² = 2500 cm²

Area of a rectangle = length x width

length = area / width

2500 / 25 = 100cm

The first step is to determine the perimeter of the square.

Perimeter = 4 x length

4 x 5 = 20cm

Perimeter of a rectangle = 2(length + width)

breadth = (perimeter / 2) - length

(20 / 2) - 6

10 - 6 = 4cm

Area of the square = 5 x 5 = 25

Area of the rectangle = 6 x 4 = 24

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There are 540 fuses in total and the original price of the internet is $55.91

a) We know that 5% of the fuses are faulty, and there are 27 faulty fusses, then we can write:

5% = 27

100% = x

We want to find x, to do that, we can write:

x = 27*(100%/5%) = 27*20 = 540

There are 540 fuses in total.

b) Now we know that the original price is P, and when we decrease it by 7%, then new price is $52.00

Then we can write:

$52.00 = P*(1 - 7%/100%)

$52.00 = P*(0.93)

$52.00/0.93 = P = $55.91

The original price is $55.91

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