4x-5+7(x+1)=6x+7
What is the solution to this problem

Answer:

y2=14y-24

y2-14y+24=0

y2-2y-12y+24=0

yx(y-2)-12(y-2)=0

(y-2)x(y-12)=0

y-2=0

y-12=0

y=2

y=12

y1=2,y2=12

x4-81=0

x4=81

x=+3

x=-3

x=3

x1=-3.x=3

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that the radius of the circle is √91 units and its centre is (-3,2) .

We know that the standard equation of circle is,

\(\longrightarrow (x-h)^2+(y-k)^2=r^2 \\\)

where,

On substituting the respective values, we have;

\(\longrightarrow \{ x-3\}^2+\{ y-(-2)\}^2= (\sqrt91)^2 \\\)

Simplify,

\(\longrightarrow \red{ (x-3)^2+(y+2)^2=91} \\\)

This is the required equation of the circle.

Answer:

(x - 3)² + (y + 2)² = 91

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (3, - 2 ) and r = \(\sqrt{91}\) , then

(x - 3)² + (y - (- 2) )² = ( \(\sqrt{91}\) )² , that is

(x - 3)² + (y + 2)² = 91 ← equation of circle

Answer:

x = -7

Step-by-step explanation:

Use the distibutive property on both side:

Right side:

4 ( 1 - x )

( 4 x 1 ) + 4 x -X )

4 - 4x

Left side:

-3 ( x + 1 )

( -3 x X ) + ( -3 x 1 )

-3x -3

4 - 4x + 2x = -3x - 3

Combine like terms:

( 2x + ( -4x ) ) + 4 = -3x - 3

-2x + 4 = -3x - 3

Add 3 to each side:

-2x + 7 = -3x

add 2x to each side:

7 = -x

Divide each side by -1:

-7 = x

Answer:

3(2+15)= 3(2) + 3(15)

Step-by-step explanation:

Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

Answer:

40.8 < x > 55.2 (if the number is between these two numbers, it is a solution)

Step-by-step explanation:

Hope this helped :)

Answer:

Possible: 46, 41 and 55.

Not possible: 58, 56, and 39

Step-by-step explanation:

First, you need to find the range of possible estimates, you can find this by multiplying 0.15 by 48 which equals 7.2, this means that the estimates have to be less than 7.2 pounds away from 48.

The lowest possible estimate is 48 - 7.2 which equals 40.8 and the highest possible estimate is 48 + 7.2 which equals 55.2.

If it is in between 40.8 and 55.2, then it's a possible estimate, if not, not possible.

Answer:

In general terms, if a is a positive real number, then the square root of a is a number that, when multiplied by itself, gives a. The square root could be positive or negative because multiplying two negative numbers gives a positive number.

Standard deviation of data represents hours worked per day by entry level employees is 2.9

The following set of data represents hours worked per day by entry level employees :

14, 7, 10, 9

First calculate the mean of the sample

Mean (\(\overline{X}\))= \(\frac{14+7+10+9}{4}\)

Mean = \(\frac{40}{4}\)

\(\overline{X}\)  = 10

Now, calculate the standard deviation:

Standard deviation = \(\sqrt\frac{\sum{(x_i - \overline{X}})^{2}}{N -1}\)

Standard deviation = \(\sqrt \frac{(14-10)^{2}+(7-10)^{2}+(10-10)^{2}+(9-10)^{2}}{3}\)

Standard deviation = \(\sqrt\frac{16+9+0+1}{3}\)

Standard deviation = \(\sqrt{8.66}\) = 2.9

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Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

The distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.

In other words, the distance between two points in space is the magnitude of the vector formed by said points.

So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:

distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

In this case, you know:

Replacing in the definition of distance:

distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)

distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)

distance= \(\sqrt{7^{2} +(-5)^{2} }\)

distance= \(\sqrt{49+25 }\)

distance= √74= 8.6023

Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

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The end behavior of the parent function is consistent.

As x approaches infinity, the y-values slowly get larger, approaching infinity. As x approaches 0 from the right (denoted as x → 0+), the y-values approach negative infinity.

Answer: 8 servings

Step-by-step explanation:

1/2 cup + 1/2 cup = 1 cup

                                              >  1 cup + 1 cup = 2 cups = one pint

1/2 cup + 1/2 cup = 1 cup

if 4 servings go in one pint then 8 servings goes in 2 pint

Answer:

8 cups/servings.

Explanation:

Can't explain further more because I'm not good in explaining things yet I'm sure that's the correct answer.

Without explicitly solving for x, we can conclude that the solution to the equation 2^x - 2 = 8^4 is x = 12.

To solve the equation 2^x - 2 = 8^4 without explicitly solving for x, we can simplify the equation using exponent rules and observe the relationship between the numbers.

First, let's simplify the equation:

2^x - 2 = 8^4

We know that 8 can be expressed as 2^3, so we can rewrite the equation as:

2^x - 2 = (2^3)^4

Applying the exponent rule (a^m)^n = a^(mn), we can simplify further:

2^x - 2 = 2^(34)

Simplifying the right side of the equation:

2^x - 2 = 2^12

Now, we can observe that both sides of the equation have the same base, which is 2. In order for the equation to hold true, the exponents must be equal:

x = 12

Therefore, we may deduce that the answer to the equation 2x - 2 = 84 is x = 12 without having to explicitly solve for x.

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Answer

Yes, zero is contained in the interval

For the hours is she going to do studying per day is 10 hours.

The Lagrangian method is a mathematical technique used to find the maximum or minimum value of a function subject to constraints. It is used in optimization problems where the objective is to maximize or minimize a function, but there are some constraints that limit the possible values of the inputs.

The Lagrangian method works by combining the objective function and the constraints into a single function, called the Lagrangian, which is then optimized. The Lagrangian is defined as the original objective function minus the product of the constraints and a set of Lagrange multipliers, which represent the trade-off between the objective and the constraints.

To maximize Julie's utility subject to the constraint of 15 hours of waking time, we need to find the optimal level of s (study time) that satisfies the constraint and maximizes the utility function.

We can start by using the Lagrangian method to find the optimal solution. The Lagrangian is given by:

L(s,λ) = S^(1/3)I^(2/3) + λ(15 - s - I)

Where λ is the Lagrange multiplier, representing the marginal rate of substitution between s and I. To find the optimal solution, we need to find the values of s and λ that satisfy the first-order conditions:

∂L/∂s = (1/3)S^(-2/3)I^(2/3) - λ = 0

∂L/∂λ = 15 - s - I = 0

Solving the first-order conditions for s and λ, we get:

s = (15 * (2/3)) / (1 + (2/3)) = 10 hours

I = 15 - s = 5 hours

So, Julie will spend 10 hours per day studying.

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Answer:

y-4=4(x-1)

Step-by-step explanation:

The perimeter of a square is 4 times the length of one side, so we can write the equation like this.

y=4x

To find the equation in point-slope form, we know that when x=1, y=4. This gives us the point, (1,4). We also know that the slope of the equation is 4.

Plug the coordinate point into the point slope formula.

y-y1=m(x-x1)

y-4=4(x-1)

The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.

In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.

The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.

Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°

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Joseph must invest approximately $110840.16 today to reach his retirement goal of $2 million, assuming a consistent rate of inflation of 7.5%.

To calculate the amount Joseph needs to invest today to reach his retirement goal of $2 million, we can use the future value formula for a lump sum investment:

\($FV = PV x (1 + r)^n\)

where FV is the future value, PV is the present value, r is the rate of return (in this case, the inflation rate of 7.5%), and n is the number of years.

In this case, we want to solve for PV, which represents the amount Joseph needs to invest today. We know that:

Joseph has 40 years until he retires (65 - 25 = 40)

His retirement goal is $2 million

The inflation rate is 7.5%

Plugging these values into the formula, we get:

\($2,000,000 = PV \times (1 + 0.075)^{40}\)

Simplifying, we have:

\($PV = \frac{2,000,000}{(1 + 0.075)^{40}}\)

PV = $2,000,000 / 18.044

Therefore, Joseph must invest approximately $110840.16 today to reach his retirement goal of $2 million, assuming a consistent rate of inflation of 7.5%.

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A graph of the cube root function g(x) = 1/2x³ is shown in the image below.

In Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would be stretched or shrunk depending on the scale factor that is applied.

When the parent cube root function f(x) = x³ is vertically shrunk by a scale factor of 1/2, the transformed function g(x) is given by;

g(x) = kf(x)

g(x) = 1/2f(x)

g(x) = 1/2x³.

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floor plan => It is the scale drawing that show the relationship between rooms, spaces, and physical features viewed from the above

THIS PIC WILL ALSO HELP U

The equation of the circle is given by (C) (x-3)² + (y + 4)² = 9

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. The radius of a circle is the separation between any point on the circle and its center.

The equation of the circle in the general form is given by the

(x-a)²+(y-b)²=r²

Where (a,b) is the co-ordinates of the center of the circle and the radius is r.

Now the center of the circle is given at (3,-4) and the radius is r.

We know that the general equation of a circle is  \({\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}}\)

Substituting the values in the equation we get:

(x-3)²+(y-(-4))²=(3)²

or, (x-3)²+(y+4)²=9

Hence the equation of the circle is (x-3)² + (y + 4)² = 9.

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The linear function there after 18 minutes of calls, then the credit was = $29

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Given that,

Slope = -0.16

There linear function is $29.00 in credit remaining on the card after 25 minutes of calls

There after 18 minutes of calls?

Slope m = -0.16

Let us assume,

x = 25 minutes

y = $29.00 in credit

Substitute this values,

So,

We can write,

y = mx + b

$29.00 = (-0.16) (25) + b

$29.00 = -24.84 + b

b = $29.00 + 24.84

b = $53.84

We can substitute b value,

y = mx + b

y = (-0.16) x + $53.84

y = \(-0.16x\) + $53.84

y = (-0.16)(25) + $53.84

y = -24.84 + $53.84

y = $29

Therefore,

The linear function there after 18 minutes of calls, then the credit was = $29

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Answer:

362%, 3.66, 3 2/3, 36

Step-by-step explanation:

Answer: 362%, 3.66, 3 2/3, 36

I hope this helps!

Answer:

−225x^6y^4

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

5/4x-2=3/2x-4

5/4x-3/2x = -4+2

(multiply both sides by 4)

5x-6x=-16+8

-x=-8

(multiply by -1)

x=8

Answer:

C

Step-by-step explanation:

\(\frac{5x}{2} +\frac{7}{2} =\frac{3x}{4} +14\\) isolate the terms with the variable x

\(\frac{5x}{2} -\frac{3x}{4} =14-\frac{7}{2}\) get the same denominator and combine like terms

\(\frac{10x-3x}{4} = \frac{28-7}{2}\) solve

\(\frac{7x}{4} =\frac{21}{2}\) crossmultiply and solve for x

\(x=\frac{4*21}{7*2} =6\) so is not the first option

try second

\(\frac{5x}{4} -9=\frac{3x}{2} -12\) same steps as before

\(\frac{5x-6x}{4}=9-12\\)

\(\frac{-x}{4} =\frac{-3}{1}\)  so  x=12 not the second option

try third option

\(\frac{5x}{4} -2=\frac{3x}{2} -4\)

\(\frac{5x-6x}{4} =2-4\)

\(\frac{-x}{4} =\frac{-2}{1}\) so x=8

Step-by-step explanation:

answer is one and half

Step-by-step explanation:

To find the value of y when z = 14 we must first find the relationship between them

The statement

y varies directly as z is written as

y = kz

where k is the constant of proportionality

when y = 180

z = 10

180 = 10k

Divide both sides by 10

k = 18

The formula for the variation is

y = 18z

When z = 14

y = 18(14)

Hope this helps you

Answer:

10- I can't really help you with that one you have to just draw it on your own.

11- a triangle can only have 1 obtuse angle because the other 2 need to be acute to connect 3 sides.

12- x=20 degrees,y=64 degrees,z=116 degrees

Step-by-step explanation:

11- 1 obtuse angle because the other 2 need to be acute to connect 3 sides.

12- x=20 degrees because of the other 20 degree angle opposite to it. y=64 degrees because 180-(20+96)=64 (all angles in a triangle add to 180). z=116 degrees because supplementary angles add to 180 degrees and Y and Z are supplementary.