\(5x+3=3x+7\)

Answer:

Step-by-step explanation:

42:7=ED:24

cross multiply 42 into 24.

Then divide by 7

you will get ED

Then use pythageorous theorem.

Ed square + 42 square=Ef square

Then do square root of Ef square

The function family based on the information is a linear function.

A linear function is a type of mathematical function that has the form:

f(x) = ax + b

where a and b are constants, and x is a variable. The variable x is often called the independent variable, and the variable f(x) is called the dependent variable.

The value of a determines the slope of the line, while the value of b determines the intercept of the line with the y-axis. The slope of the line represents the rate of change of the dependent variable with respect to the independent variable, and the intercept represents the value of the dependent variable when the independent variable is zero.

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After using the formula for the sum of an infinite geometric series, we conclude that the given infinite series does not converge to 1.

To prove that the infinite series ∑(i=1 to ∞) 2^(i-1) equals 1, we can use the formula for the sum of an infinite geometric series.

The sum of an infinite geometric series with a common ratio r (|r| < 1) is given by the formula:

S = a / (1 - r)

where 'a' is the first term of the series.

In this case, our series is ∑(i=1 to ∞) 2^(i-1), and the first term (a) is 2^0 = 1. The common ratio (r) is 2.

Applying the formula, we have:

S = 1 / (1 - 2)

Simplifying, we get:

S = 1 / (-1)

S = -1

However, we know that the sum of a geometric series should be a positive number when the common ratio is between -1 and 1. Therefore, our result of -1 does not make sense in this context.

Hence, we conclude that the given infinite series does not converge to 1.

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Answer:

true

Step-by-step explanation:

Answer:

The speed increases (45—>47—>49) then decreases (48—>47) over time.

Step-by-step explanation:

The table that represents the speed of the car that increases and decreases as time increases is Table B.

Option B is the correct answer.

Speed is the ratio of the given distance and time.

It shows how fast an object is moving at a given time.

The formula is Distance / Time.

We can find the distance or time when the required values is given using this formula.

We have,

From the table,

We see that,

Time      5     6     7      8     9

Speed   45   47   49   48   47

This indicates that,

As time increases, the speed increased from 5 minutes to 7 minutes and decreases from 7 minutes to 9 minutes.

Thus,

The table that represents the speed of the car that increases and decreases as time increases are in Table B.

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The answers for all triangle problems are:

10. ΔABC is a equilateral triangle, then:

∠A = ∠B = ∠C = 8x - 44

3 (8x - 44) = 180

24x - 132 = 180

24x = 48

x = 2

11. ΔRST is an isosceles triangle, then:

∠R = ∠T

15x - 31 = 9x + 11

6x = 42

x = 7

∠S + ∠R + ∠T = 180°

∠S + 2∠T = 180°

∠S + 2( 9x + 11) = 180°

∠S + 2(9(7) + 11) = 180°

∠S + 2 (63 + 11) = 180°

∠S + 2 (74) = 180°

∠S = 180 - 144

∠S = 36°

12. Based on the given data:

∠P = 5x - 14

∠Q = x - 5

∠R = 2x - 9

Since ΔPQR is a triangle, then:

∠P + ∠Q + ∠R = 180°

(5x - 14) + (x - 5) + (2x - 9) = 180°

8x - 28 = 180°

8x = 208

x = 26

∠P = 5x - 14 --> 5(26) - 14 = 116°

∠Q = x - 5 --> (26) - 5 = 21°

∠R = 2x - 9 --> 2(26) - 9 = 43°

13. ΔJKL is a triangle, where:

∠J = ∠L - 7

∠K = 2∠L - 21

∠J + ∠K + ∠L = 180

(∠L - 7) + (2∠L - 21) + ∠L = 180°

4∠L - 28 = 180°

4∠L = 208

∠L = 51°

∠J = ∠L - 7 --> (51) - 7 = 44°

∠K = 2∠L - 21 --> 2(51) - 21 = 81°

14. In a triangle ΔBCD:

BD = BD

∠B = 13x - 35

∠C = 5x - 19

∠D = 2x + 14

Since BC = BD; then:

∠C = ∠D

5x - 19 = 2x + 14

3x = 33

x = 11

∠C = ∠D = 2x + 14 --> 2(11) + 14 = 36°

∠B + ∠C + ∠D = 180°

∠B + 36° + 36° = 180°

∠B = 108°

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Answer:

c. 6

d. 3

Step-by-step explanation:

:-)

Reserve Requirement

Took the test got 100

Answer:

Its D

Step-by-step explanation:

Reserve Requirement I got it right on my test

These two triangles are congruent by angle angle side(AAS) congruency theorem.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

From the given figure line segment AB is similar to line segment CD.

Angle E is congruent to angle D hence line segment AB is congruent to line segment BC.

So, These two triangles are congruent by angle angle side congruency theorem.

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a. The chart did not maintain consistent scaling

b. The graph is not the appropriate graph type to display such data

c.  The display had inaccurate or distorted visual representations

When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.

The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.

So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.

It also advisable to make use of  clear and accurate labeling with descriptive titles and units of measurement.

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Answer:

D

Step-by-step explanation:

If you plot both points on a graph you can see the angle is much larger than 58 degrees so it must be 122 degrees. The square root of 13 is less than 4, and you can see that the two points are further than four units apart. Sorry for a non-mathematical explanation, this is just how I solve these things lol.

Answer:

d

Step-by-step explanation:

Answer: The answer is A: 1:2.

From the calculations, we can see that the number of beetles after three years is 11618 beetles.

The term "exponential problem" has to do with any problem in which the increase or decrease occurs exponentially.

In this case we have P = Poe^rt

Po = 10,000

r = 0.05

t = 3

P =  10,000 e^(0.05 * 3)

P= 11618 beetles

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Answer:

47/2

Step-by-step explanation:

you take 22 times 2 and get 46. then you add 1 and get 47. we know this is the correct answer because when you are converting a mixed number to a fraction, you take the denominator (bottom) and multiply it to 22, getting 46. then you add the numerator (top) to the answer that you got from the previous step. this step will end you with 47. you keep the denominator (bottom) as 2, therefore getting 47/2.

Answer:

B. 7-r212

Step-by-step explanation:

The coefficient should be in front of the variable.

Answer:

it's 80.

Step-by-step explanation:

120-40= 80

....

Answer: 80

Step-by-step explanation:

hope this helps

Answer:

One possibility is to work for (10) hours as a babysitter, and (10) hours as a cashier.

Step-by-step explanation:

An easy way to solve this problem is to set up a system to model the situation. Create one equation to model the money make, and the other to model the time spent. Let parameters (x) and (y) represent the time one spends at each job.

Since one cannot spend more than (20) hours a week working, set the first equation, for time, equal to (20),

x + y = 20

Now multiply each unit for the time by the money earned at each job, set this new equation equal to (150), the minimum amount of money one wishes to earn,

6(x) + 9(y) = 150

Thus the system is the following,

\(\left \{ {{x+y=20} \atop {6x+9y=150}} \right.\)

Now use the process of elimination. The process of elimination is when one multiplies one of the equations by a term such that when one adds the two equations, one of the variables cancels. One can solve for the other variable, and then backsolve for the first variable. Multiply the first equation by (-6) so that the variable (x) cancels.

\(\left \{ {{-6x-6y=-120} \atop {6x+9y=150}} \right.\)

Add the two equations,

\(3y=30\)

Use inverse operations to solve for (y),

\(y=10\)

Now substitute the value of (y) back into one of the original equations and solve for (x),

\(x+y=20\)

\(x+10=20\)

\(x=10\)

1. (-y, x)

2. (-x, -y)

3. (y, -x)

4. (x, -y)

5. (-x, y)

Step-by-step explanation:

option b is the correct answer

On solving the provided question, we can say that Slope is 1/2, so  equation is y=1/2x+0 or y=1/2x.v

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

We can utilize the slope-intercept version of the equation. It is written as y=mx+b. B is the y-intercept, and m stands for the slope. The line intersects the y-axis at (0,0). the y-intercept is consequently 0.

the slope by equation, we have

m = y2 - y1 / x2 - x1

m = 2-1/4-2

m = 1/2

Slope is 1/2, so  equation is y=1/2x+0 or y=1/2x.

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The correct question is

Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus 5

https://photomath.app/en/

Just use this app to help you if your really really really stuck. It is free and is very useful. Or you can use Khan academy or Ixl. :P

From this graph , it takes 0.75 seconds to reach the highest position.

A graph is a visual representation of the relationship between two sets of data or variables, typically via lines or curves. A diagram or pictorial representation of facts or values that is arranged might be referred to as a graph in mathematics. The relationship between two or more items is frequently represented by the points on the graph

The graph indicates that the peak is at (0.75, 9)

The x-axis displays the time in seconds, while the y-axis displays the height in feet.

Consequently, it takes 0.75 seconds to reach the highest position.

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Answer: -0.26, 1, 1.75, 1.9

To order the given numbers from least to greatest, first convert the numbers to the same format, such as decimals:

|-1.75| = 1.75
|1| = 1
|1 9/10| = 1.9
-0.26

Now, arrange them in ascending order:

-0.26, 1, 1.75, 1.9

Your answer: -0.26, 1, 1.75, 1.9

Answer: 16

Step-by-step explanation:

y² - 1 should be multiplied on both sides to solve the equation.

Option B is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

(y² - 5) / (y² - 1) = (y² + y + 2) / (y + 1)

This can be written as,

y² - 1 = (y + 1) (y - 1)

So,

Multiplying y² - 1 on both sides.

(y² - 1) x (y² - 5) / (y² - 1) = (y² - 1) x (y² + y + 2) / (y + 1)

(y² - 5) = (y² + y + 2) (y - 1)

y² - 5 = y³ + y² + 2y - y² - y - 2

y² - 5 = y³ + y - 2

y³ - y² + y - 2 + 5

y³ - y² + y + 3

Thus,

Multiplying y² - 1 on both sides will solve the equation.

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Answer:She should plant 32 daisies.

Step-by-step explanation:4:2 can be expressed as 2:1 .

2+1 =3

48/3 = 16(value of one)

16 x 2 = 32

The probability of being dealt a 3, 4, 5, 6, 7, all in the same suit is approximately 0.0000031.

To calculate the probability of being dealt a 3, 4, 5, 6, 7, all in the same suit, we can use the following formula:

P = (number of favorable outcomes) / (total number of possible outcomes)

the order in which the cards are chosen does not matter, so we need to divide by the number of ways we can arrange 5 cards, which is 5! (5 factorial).

Therefore, the total number of possible outcomes is (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1), which simplifies to 2,598,960.

Finally, we can calculate the probability of being dealt a 3, 4, 5, 6, 7, all in the same suit:

P = 8 / 2,598,960

P = 0.00000308 (rounded to seven decimal places)

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The probability that Kelsi will eat a custard filled donut and then a chocolate donut is approximately 0.1455.

To calculate the probability of Kelsi eating a custard filled donut and then a chocolate donut, we need to use the concept of conditional probability.

The probability of Kelsi eating a custard filled donut first is 4/12 (since there are 4 custard filled donuts out of a total of 12 donuts).

After Kelsi eats a custard filled donut, there are only 11 donuts left, and 6 of them are chocolate donuts. So the probability of Kelsi eating a chocolate donut second, given that she already ate a custard filled donut, is 6/11.

To find the probability of both events happening together (Kelsi eating a custard filled donut first and a chocolate donut second), we multiply the probabilities:

P(custard first and chocolate second) = P(custard first) * P(chocolate second | custard first)

P(custard first and chocolate second) = (4/12) * (6/11)

P(custard first and chocolate second) = 0.1455

Rounding to 4 decimal places, we get:

P(custard first and chocolate second) ≈ 0.1455

Therefore, the probability that Kelsi will eat a custard filled donut and then a chocolate donut is approximately 0.1455.

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