BEFORE solving an equation, how do you know if it is a 1-step or Multi-step
equation?


Solve the following equation
-4(x + 5)-2 = 6x



Explain how you solved the equation above./

The distance between the two points is [tex]\sqrt{61}[/tex]

Explanation:

Given that the two points are [tex](-4,-6)[/tex] and [tex](2,-1)[/tex]

We need to determine the distance between the two points in simplest radical form.

The distance between the two points can be determined using the

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

Let us substitute the coordinates [tex](-4,-6)[/tex] and [tex](2,-1)[/tex] in the above formula, we get,

[tex]d=\sqrt{(2+4)^2+(6+1)^2}[/tex]

Simplifying the terms, we get,

[tex]d=\sqrt{(6)^2+(7)^2}[/tex]

Squaring the terms, we get,

[tex]d=\sqrt{36+49}[/tex]

Adding, we get,

[tex]d=\sqrt{85}[/tex]

Simplifying, we have,

[tex]\sqrt{61}[/tex]

Thus, the distance between the two points in simplest radical form is [tex]\sqrt{61}[/tex]

(a) The transformation that maps ΔSTU to ΔLMN is a translation of three units to the right and one unit up, followed by a counterclockwise rotation of 90° around the origin

What is transformation?

A dilation with respect to the origin by a scale factor of 1/3.

To map ΔSTU to ΔLMN, we need to perform a combination of transformations: a translation, a rotation, and a dilation.

First, we translate triangle STU three units to the right and one unit up to get triangle S'T'U', where S'(1,3), T'(-2,5), and U'(0,-2).

Next, we rotate triangle S'T'U' 90 degrees counterclockwise around the origin to get triangle S''T''U'', where S''(3,1), T''(-5,2), and U''(2,0).

Finally, we dilate ΔS''T''U'' by a scale factor of 1/3 with respect to the origin to get ΔLMN, where L(1/3,1/3), M(-5/3,2/3), and N(2/3,0).

Therefore, the transformation that maps ΔSTU to ΔLMN is a translation of three units to the right and one unit up, followed by a counterclockwise rotation of 90° around the origin, and finally a dilation with respect to the origin by a scale factor of 1/3.

(b) The side overline SU corresponds to the side overline LN.

(c) Yes, corresponding sides are congruent. the triangles are congruent by the Side-Side-Side (SSS) congruence criterion.

What is congruent?

We can see this by calculating the length of each side of the two triangles:

Length of ST = distance between points S and T = √(((-5) - (-2))² + ((4) - (2))²) = √(10)

Length of LM = distance between points L and M = √(((-5/3) - (1/3))² + ((2/3) - (1/3))²) = √(10)/3

Length of TU = distance between points T and U = √(((-5) - (-3))² + ((4) - (-3))²) = √(74)

Length of MN = distance between points M and N = √(((-5/3) - (2/3))² + ((2/3) - 0)²) = √(10)/3

Length of US = distance between points U and S = √(((-3) - (-2))² + ((-3) - (2))²) = √(26)

Length of NL = distance between points N and L = √(((2/3) - (1/3))² + ((0) - (1/3))²) = √(2)/3

All corresponding sides have the same length, so the triangles are congruent by the Side-Side-Side (SSS) congruence criterion.

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Answer:

price of the juice increased by 15%, then the new price of the juice is: New price = Old price + (Percent increase * Old price) Percent increase = 15% Old price = $9.40 New price = $9.40 + (0.15 * $9.40) New price = $9.40 + $1.41 New price = $10.81 Therefore, the new price of the juice after the increase is $10.81.

Answer:

a. already done

b. x=3, x=4, and x=5

c. x=2, x=3, x=4, and x=6

Step-by-step explanation:

The < symbol means less than, so all values of x less than what is stated are correct

The ≤ symbol means less than or equal to, so all values of x less than, and what is stated are correct

The answer is in the screenshot.
Let me know if it helps

The least positive integer that will be divisible by both 15 and 35 will be 105.

The given integers are 15 and 35.
As we know that the least positive integer will be divisible by both 15 and 35 will be LCM ( least common factor) of 15 and 35.
The least common multiple of LCM of two integers is the common multiple of two numbers such that it is the least among all common multiples.
For example, LCM of 3 and 5 will be 15 because among all common multiples of 3 and 5, 15 will be least common multiple.
For LCM of 15 and 35, let's write multiples of both the numbers.
Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180,195,210,....
Multiples of 35= 35,70,105,140,175,210,...
We can see that 105 and 210 are two common multiples out of which 105 is the least multiple.
Therefore, the least positive integer that will be divisible by both 15 and 35 will be 105.

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Center - radius equation for circle of radius r ,centered at (h,k) is :

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]

you have r = √21

[tex]r^{2} =[/tex] (√21)^2 = 21

centre (h,k) = (0,0) so h =0 and k =0

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]

[tex](x-0)^{2} + (y -0)^2 = 21[/tex]

[tex]x^{2} + y^{2} = 21[/tex]

Answer:

x = 21

Step-by-step explanation:

Given exponential equation:

[tex]7^{3-5x}=\left(\dfrac{1}{49}\right)^{2x+9}[/tex]

Rewrite 49 as 7²:

[tex]7^{3-5x}=\left(\dfrac{1}{7^2}\right)^{2x+9}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad \dfrac{1}{a^n}=a^{-n}[/tex]

[tex]7^{3-5x}=\left(7^{-2}\right)^{2x+9}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad (a^b)^c=a^{bc}[/tex]

[tex]7^{3-5x}=7^{-2(2x+9)}[/tex]

Simplify the exponent:

[tex]7^{3-5x}=7^{-4x-18}[/tex]

[tex]\textsf{Apply the exponent rule:} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]3-5x=-4x-18[/tex]

Add 4x to both sides:

[tex]3-5x+4x=-4x-18+4x[/tex]

[tex]3-x=-18[/tex]

Subtract 3 from both sides:

[tex]3-x-3=-18-3[/tex]

[tex]-x=-21[/tex]

Divide both sides by -1:

[tex]x=21[/tex]

Therefore, the value of x is 21.

Answer:

Will mark Brainliest

Solve the exponential equation for x:

7^3-5x=(1/49)^2x+9

Answer:

Step-by-step explanation:

The expression p² - 10p + 25 can be factored as follows:

p² - 10p + 25 = (p - 5)²

This is an example of perfect square trinomial. It can be recognized as such because the first and last terms are perfect squares (p² and 25), and the middle term (-10p) is twice the product of the square roots of the first and last terms (2√(p²×25) = 2p×5 = 10p).

So, the factored form of the expression is (p - 5)².

Step-by-step explanation:

The answer to this question is (p-5)^2

Answer:

If you spent $56 on candy, she'd buy 8 pounds.

Step-by-step explanation:

the statement is true.the success-failure condition is satisfied and we can conclude that simple random sample gets us independence.

Simple random sampling is a type of probability sampling technique wherein every member of the population has an equal and independent chance of being selected. Independence means that the selection of one unit does not affect the selection of any other unit. The success-failure condition is an important condition of simple random sampling, which states that the size of each of the two groups (i.e., success and failure) should be at least 10. In this case, the two groups are 289 and 111, which are both greater than 10. Therefore, the success-failure condition is satisfied and we can conclude that simple random sample gets us independence.

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Answer:

y = 2x + 10

Step-by-step explanation:

What we know:

10 dollar entrance fee

2 dollars PER ride

"per" is an important word since it tells us that the x will be there.

That means that, if its a 10 dollar entrance fee and 2 dollars per ride, it will be 2x + 10.

[tex]y=2x+10[/tex]

Answer 24 do you enderstand?

Answer:

2x-3x=-45

-x=-45

x=45

by simple method

Equation for the regression line is given as y = -0.95X + 8.99.

When the wind is blowing at a speed of 27 mph, the chill factor is -16.66.

Regression coefficients are estimates of specific unknown properties that explain the relationship between a predictor variable and the related response.

In order to extrapolate the value of an unknown variable from a known variable, regression coefficients are used. The effect of a one-unit change in an independent variable on the dependent variable can be measured via linear regression by determining the equation of the best-fitted straight line. The procedure in question is regression analysis.

Calculation Overview

X's total is 45.

Total Y = 20

Mean X = 6.4286

Mean Y = 2.8571

Square sum (SSX) equals 113.7143.

Product total (SP) = -108.5714

Regression Equation = ŷ = bX + a

b = SP/SSX = -108.57/113.71 = -0.95477

a = MY - bMX = 2.86 - (-0.95*6.43) = 8.99497

y = -0.95477X + 8.99497

y = -0.95X + 8.99

The wind speed chill factor when it is 27 mph.

Using the output of the regression line shown above, we would solve for this.

y=-0.95X+8.99 

y=-0.95X+8.99 

y = -0.95 * 27 + 8.99

y = -25.65 + 8.99

y = -0.95 * 27 + 8.99

Conclusion: y = -16.66

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Answer:

True.

Step-by-step explanation:

True.

Let's say A = 5, and B = 10.

We need to swap the contents of A and B, so A will end up with 10 and B will end up with 5.

A = 5

B = 10

Introduce variable C.

C = A (now C contains 5)

A = B (now A contains 10)

B = C (now B contains 5)

In the last two steps above, you see that the values of A and B were swapped.

The new variance is 0.41.

Given that the mean cost of a box of Cheerios oat crunch is $4.00 and the variance is 0.35.

The variance represents the average of the squared deviations from the mean, so we can write:

variance = (standard deviation)^2

The standard deviation is the square root of the variance, so we have:

standard deviation = sqrt(variance) = sqrt(0.35) = 0.59

Now, if the price of a box of Cheerios oat crunch increases by 25 cents, the new mean cost will be:

new mean = $4.00 + $0.25 = $4.25

To find the new variance, we need to calculate the new squared deviations from the mean and take their average. The squared deviation of each observation is given by:

(new cost - new mean)^2

We can simplify this expression by substituting the new mean and the original standard deviation:

(new cost - $4.25)^2 = (old cost - $4.00 + $0.25)^2 = (old cost - $4.00)^2 + 2($0.25)(old cost - $4.00) + $0.25^2

The first term on the right-hand side is the squared deviation of the original cost, the second term represents the change in the squared deviation due to the increase in price, and the third term is a constant that does not affect the variance.

To find the new variance, we need to take the average of these squared deviations. Since the original variance was 0.35, we have:

new variance = (1/n) * [sum of (new cost - new mean)^2]

where n is the number of observations (we assume it is large enough to use the normal distribution approximation). Using the expression above for the squared deviation, we can write:

new variance = (1/n) * [sum of (old cost - $4.00)^2 + 2($0.25)(old cost - $4.00) + $0.25^2]

We can simplify this expression by using the properties of summation:

new variance = (1/n) * [sum of (old cost - $4.00)^2] + (2/$n) * ($0.25) * [sum of (old cost - $4.00)] + ($0.25^2)

The first term is the original variance, the second term is zero (since the sum of deviations from the mean is always zero), and the third term is a constant that does not affect the variance. Therefore, the new variance is:

new variance = 0.35 + ($0.25)^2 = 0.41

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Answer:

B) The distance between -2.2 and x is greater than 3.

Step-by-step explanation:

The comparison of the volume of a cone relative to the volume of a cylinder with the same dimensions is given as follows:

4 The volume of the cone is 1/3 as large.

The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.

V = πr²h/3.

For the volume of the cylinder, the equation is given as follows:

V = πr²h.

The volume of the cylinder is triple the volume of the cone, hence the volume of the cone is one third of the volume of the cylinder.

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Step-by-step explanation:

Here are the graphs of the two functions:

y

|

|

|

| (1) (2)

| | |

------x------x-------

| | |

| (3) (4)

|

|

Function 1: y = -2x^2

The graph is a downward-facing parabola.

The vertex is located at (0, 0).

The y-intercept is 0.

The function is symmetric about the y-axis.

Function 2: y = -2x^2 + 4

The graph is also a downward-facing parabola.

The vertex is located at (0, 4).

The y-intercept is 4.

The function is symmetric about the y-axis.

Comparing and contrasting the two graphs:

Both functions are downward-facing parabolas.

Function 2 is a vertical shift of Function 1, as it has been shifted 4 units upwards.

The vertex of Function 2 is higher than the vertex of Function 1.

The y-intercept of Function 2 is higher than the y-intercept of Function 1.

The shape and symmetry of the two graphs are the same.

The test value is 0.636, and the critical z-value is 1.645. Since the test value (0.636) is greater than the critical z-value (1.645), we reject the null hypothesis and conclude that there is enough evidence.

It is usually represented by the number of errors or defects found in a system or component during a test phase.

For this test, we use the formula for a z-test for proportions.

Let p be the proportion of Wenatchee population that prefers Taco Bell.

Null hypothesis: p = 0.25

Alternative hypothesis: p > 0.25

The critical z-value for this test is 1.645, which is the z-value corresponding to a=0.05.

The test value is calculated by taking the sample proportion of people preferring Taco Bell

(63/200 = 0.315)

and subtracting the null hypothesis proportion of people preferring Taco Bell (0.25).This gives us 0.065.

This value is then divided by the standard error of the proportion, which is calculated as the square root of

(p*(1-p)/n), where p is the null hypothesis proportion (0.25) and n is the sample size (200). This gives us a value of 0.636.

Therefore, the test value is 0.636, and the critical z-value is 1.645.

Since the test value (0.636) is greater than the critical z-value (1.645), we reject the null hypothesis and conclude that there is enough evidence to support John's claim that more than 25% of Wenatchee population prefer TACO BELL.

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The frequency distribution table for the question is :

Grade 7 | 0.67 | 0.33 | 1.00

Grade 8 | 0.42 | 0.58 | 1.00

Total      | 1.09 | 0.91 | 2.00.

Frequencies refer to the number of times an event or a value occurs in a dataset. It is a count of the occurrences of a particular value or event. Frequencies are commonly used in statistics to summarize data and to help understand patterns in a dataset. The frequency of a value can be expressed as an absolute frequency (the number of times a value occurs) or a relative frequency.

The given table shows the results of a survey conducted among students in Grade 7 and Grade 8 about their preference for joining a movie club or a music club. The students want to make a two-way relative frequency table using row totals. In the table, the row totals represent the total number of students in each grade, and the column totals represent the total number of students who want to join each club.

To complete the table, we need to find the missing values. For example, in the row for Grade 7, the total number of students is 33. We know that 20 of these students want to join the movie club, so the relative frequency of Grade 7 students who want to join the movie club is 20/33, which is approximately 0.61. Similarly, we know that 13 Grade 7 students want to join the music club, so the relative frequency of Grade 7 students who want to join the music club is 13/33, which is approximately 0.39.

Likewise, we can find the missing values in the other rows and complete the table. The completed table shows the relative frequency of students in each grade who want to join each club. For example, 0.61 or approximately 61% of Grade 7 students want to join the movie club, while 0.25 or approximately 25% of Grade 8 students want to join the movie club.

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The expression which represents this condition is x=-15z/y

A link between two variables known as inverse variation occurs when one variable's value rises while the other one's value falls, and vice versa. Inverse variation can be represented mathematically as y = k/x, where y and x are the variables, k is the constant of proportionality, and the product of y and x is constant.

When the value of x increases the value of y decreases.

When the value of x decreases the value of y increases.

So for an inverse variation we have the expression

y=k/x   or

x=k/y

The expression which represents this condition is

x=-15z/y

Hence option b) or the second option is the right answer.

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The complete question is attached below.

The expression equivalent is 9+2x/6x

A fraction is a part of a whole. It is the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator

1/4x +1 3/4x - 2/3-1/2x

1/4x + (4x + 3/4x) - 2/3 - 1/2x

(1 + 4x + 3)/4x - (4x - 3)/6x

4 + 4x/4x - 4x - 3/6x

(3(4 + 4x) - 2(4x - 3))/12x

(12 + 12x - 8x + 6)/12x

(18 + 4x)/12x

(9 + 2x)/6x

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A combination of two or more simple statements is a compound statement. The connectives generally used in mathematics are ‘and’, ‘or’, ‘if ’, ‘if and only if’.

In mathematics, like in any language, compound statements are created by combining simpler ones using connectives. The truth value of a compound statement is determined by the truth value of its smaller components.

There are four compound statements:

1. ¬p , Not p (i.e. the negation of p)  : Negation

2. p ∧ q, p and q                                : Conjunction

3. p ∨ q, p or q                                   : Disjunction

4. p → q, If p then q                            : Conditional

Beginning with the premise that P (the hypothesis) is true, we create a chain of implications, each of which has previously been proven to be true, ultimately leading to Q. (the conclusion). Imagine the chain has six consequences. As a result, the direct proof technique may be expressed combination as follows:

        P, P ⇒ P1, P1 ⇒ P2, P2 ⇒ P3, P3 ⇒ Q1, Q1 ⇒ Q2, Q2 ⇒ Q.

If P and the implications in the previous chain are all true, we must derive that Q is likewise true logically. But, according to the truth table for          P ⇒ Q, knowing that P ⇒ Q is a true statement does not indicate that P or Q are true, just that the inference is true. Recall that P can be false, Q can be true or false, and the inference might be true or false.

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Question: What are Compound Statements? Write proof and logic for the statements.

The relation between x and y is defined by the equation: y = 5x, where % is constant of the equation and X and Y are variable.

It is given that y varies directly as x. It means y is proportional to x.

y ∝ x

y = kx

{Where k is constant of proportionality.}

It is given that y=30 when x=6. Put x=5 and y=25 in the above equation to find the value of k.

30 = k(6)

Divide both sides by 6.

The value of k is 5.

Hence The relation between x and y is defined by the equation: y = 5x.

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the disposal under the following assumptions are:  To Equipment   $78,200

   Being equipment is scrapped at a gain  

a)

Particulars Debit Credit

Loss on disposal $28,300  

Accumulate depreciation of $49,900  

   To Equipment   $78,200

   Being equipment scrapped with no value

b)

Particulars Debit Credit

Loss on disposal $8,800  

Accumulate depreciation of $49,900  

Cash $19,500  

   To Equipment   $78,200

   Being equipment disposed of at a loss

c)

Particulars Debit Credit

Accumulate depreciation of $49,900  

Cash $30,800  

   To Gain on disposal    $2,500

   To Equipment   $78,200

   Being equipment is scrapped at a gain  

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No, it is not possible to dilate a satellite in such a way that the number of square feet of surface area is equal to the number of cubic feet of volume.

In mathematics, the volume of an object is a measure of the amount of three-dimensional space that the object occupies. Volume is typically expressed in units such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or cubic feet (ft³), depending on the context. Volumes are used in a wide variety of fields, including physics, engineering, and architecture, among others. For example, the volume of a container can be used to determine how much liquid it can hold, or the volume of a room can be used to calculate how much air conditioning is needed to cool the space.

Here,

This is because the units of measurement for surface area and volume are fundamentally different, and therefore cannot be equated without introducing additional variables. For example, consider a cube with a side length of 1 foot. Its surface area would be 6 square feet (since there are 6 sides to the cube, each with an area of 1 square foot), while its volume would be 1 cubic foot (since it occupies a space with a volume of 1 cubic foot). These two measurements cannot be equated without introducing additional variables. Therefore, it is not possible to dilate a satellite in a way that would make the number of square feet of surface area equal to the number of cubic feet of volume.

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