Solve the inequality

-7x + 12 = 75

Answer:

Step-by-step explanation:          

\(49x^2-42x+(\frac{42}{2})^2=49x^2-42x+(\frac{42}{2} )^2\)    (completing the square)  

  \(49x^2-42x+441=49x^2-42x+21^2\)

                              \(=(7x-21)^2\)

So    \(49x^2-42x+441=(7x-21)^2\)

Solution: The required constant is 441.

Remember:    Completing the square IN \(ax^2+bx+c\) involves adding  \((\frac{b}{2} )^2\)     to both sides of the equation. THIS KEEPS IT BALANCED AND ALLOWS US TO MAKE A PERFECT SQUARE.    

Answer: 1, 3, 5 and 15

Step-by-step explanation:

trust me bro

you don't multiply

Step-by-step explanation:

you must divide it by itself to get the variable alone and then divide the other side hope this helps!

Answer:

57°F differences

Step-by-step explanation:

-14+57= 43

43-57= -14

Answer:

7x - 2y - 20 = 0

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = (4, 4 )

m = \(\frac{4-(-3)}{4-2}\) = \(\frac{4+3}{2}\) = \(\frac{7}{2}\) , then

y = \(\frac{7}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, 4 )

4 = \(\frac{7}{2}\) (4) + c = 14 + c ( subtract 14 from both sides )

- 10 = c

y = \(\frac{7}{2}\) x - 10 ← in slope- intercept form

multiply through by 2

2y = 7x - 20 ( subtract 2y from both sides )

0 = 7x - 2y - 20 , that is

7x - 2y - 20 = 0 ← required equation

Answer:

how will you give 15 points if it only says 8?

Step-by-step explanation:

a) required value of curl(F) is 0.

b) required value of ∫C F ⋅ dr is 0.

To solve this problem, we'll follow the steps given and calculate the curl of the vector field F and then evaluate the line integral ∫C F ⋅ dr.

(a) Calculating the Curl of F:

The curl of a vector field F = ⟨P, Q, R⟩ is given by the following determinant:

curl(F) =

| ∂/∂x ∂/∂y ∂/∂z |

| P Q R |

Let's calculate the individual partial derivatives first:

∂P/∂y = exy + yexy - z

∂Q/∂z = -yx

∂R/∂x = 0

Now, we can evaluate the curl:

curl(F) =

| ∂/∂x ∂/∂y ∂/∂z |

| 0 exy + yexy - z -yx |

Expanding the determinant, we have:

curl(F) = (∂R/∂y - ∂Q/∂z)i - (∂R/∂x - ∂P/∂z)j + (∂Q/∂x - ∂P/∂y)k

Plugging in the partial derivatives:

curl(F) = (-yx)i - 0j + (0 - (exy + yexy - z))k

= -yxi - (exy + yexy - z)k

Now we have the curl of F as a vector. To show that the curl is zero, we need to demonstrate that both components of the curl vector are zero:

-yx = 0

exy + yexy - z = 0

The first equation, -yx = 0, implies that y = 0 or x = 0. Since this is a 3D problem, it suggests that the vector field F is conservative.

The second equation, exy + yexy - z = 0, doesn't provide any additional information about the curl being zero. However, since we know that the vector field is conservative, this equation must hold true.

Therefore, we have shown that the curl of F is zero: curl(F) = 0.

(b) Calculating the Line Integral ∫C F ⋅ dr:

Since the curl of F is zero, we know that F is a conservative vector field. Therefore, the line integral of F over any closed curve will be zero. Since C is a closed curve (intersection of a cylinder and a paraboloid), we can conclude that:

∫C F ⋅ dr = 0

Hence, the value of the line integral is zero.

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Answer: radius is is 12.

Step-by-step explanation:

Explanation: A circle with equation of the form x2+y2=r2 will have radius r=√144=12 .

Sorry, I'm not sure on the bottom part

We know,

The general equation for circle is –

\( { \boxed{\bf{\rm \red {(x \: - \: a)² \: + \: (y \: - \: b)² \: = \: r²}}}} \)

\( \bf (a, \: b) \: = \: center \: coordinates \)

\( \bf r \: = \: radius \)

\( \bf a \: = \: 0 \: , \: b \: = \: 0 \: , \: r \: = \sqrt{144} \: = \: 12 \)

\( \bf Center \: coordinates \: = \: (0, \: 0) \) [Answer]

\( \bf Radius \: = \: 12 \) [Answer]

__________________________________________________

NOTE – Refer the above attachment.

__________________________________________________

Answer:

Lines a and b are parallel.

Because when 54 is added to 126, the answer is 180.

(SAME SIDE INTERIOR THEOREM)

90%

because 540,000/600,000 = 0.9

and 0.9 multiplied by 100 = 90

Hope this helps!

Answer:

90%

Step-by-step explanation:

540,000 x 100 / 600,000 = 90

Answer:

4

Step-by-step explanation:

at x=3

since x=3 means x>= 1

use x+1 = 3+1=4

Step-by-step explanation:

formula used is height= area×3/base

35.595×2/6.3

71.19/6.3

11.3mm2 is the answer

Answer:

\( \huge{ \fbox{ \sf{11.3 \: mm}}}\)

Step-by-step explanation:

\( \underline{ \sf Given} : \)

\( \star{ \sf{ \: Base \: of \: a \: triangle \: (b) \: = 6.3 \: mm}}\)

\( \star{ \sf{ \: Area \: of \: a \: triangle \: (a) = 35.595 \: {mm}^{2} }}\)

\( \star{ \sf{ \: Let \: height \: of \: a \: triangle \: be \: h}}\)

\( \underline{ \underline{ \sf{ \: Finding \: the \: height \: of \: a \: triangle}}} : \)

\( \boxed{ \sf{Area \: of \: a \: triangle = \frac{1}{2} * base \: * \: height}}\)

\(\sf{Plug \: the \: values}\)

\( \mapsto{ \sf{35.595 = \frac{1}{2} * 6.3 * h}}\)

\( \mapsto{ \sf{35.595 = \frac{6.3h}{2} }}\)

\( \sf{Apply \: cross \: product \: property}\)

\( \mapsto{ \sf 6.3h = 35.595 * 2}\)

\( \mapsto{ \sf{6.3h = 71.19}}\)

\( \sf{Divide \: both \: sides \: by \: 6.3}\)

\( \mapsto{ \sf{ \frac{6.3h}{6.3} = \frac{71.19}{6.3}}} \)

\( \mapsto{ \sf{h = 11.3 \: mm}}\)

The height of a triangle = 11.3 mm

Hope I helped!

Best regards! :D

~\( \sf{TheAnimeGirl}\)

The algebraic expression for the scenario is 15 + x = 60

From the question, we have the following parameters that can be used in our computation:

Amount saved up = $15

Cost of item = $60

Amount gifted by your grandma = x

The above parameters means that the mathematical statement is an equation statement

So, we have the following representation

Amount saved up + Amount gifted by your grandma = Cost of item

Substitute the known values in the above equation, so, we have the following representation

15 + x = 60

Hence, the algebraic expression is 15 + x = 60

The question does not require that the equation be solved

However, when it is solved, we have:

15 + x = 60

Subtract 15 from both sides

x = 45

So, the amount is 45

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The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter.

If the sample size is 28 and the population standard deviation is increased, there will be a direct impact on the confidence interval. This is because the confidence interval is calculated based on the sample mean and the standard deviation. If the population standard deviation is increased, it means that there is more variability in the population. This increase in variability will lead to wider confidence intervals.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. The width of the confidence interval is determined by the sample size, the standard deviation, and the level of confidence.
In this case, if the population standard deviation is increased, it means that the sample standard deviation will also increase. The sample mean will be relatively more variable than it would be if the population standard deviation was lower. This increase in variability will cause the confidence interval to become wider, as there is more uncertainty in the estimate of the population parameter.
In summary, if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter. It is important to note that increasing the sample size can help to reduce the impact of increased population standard deviation on the confidence interval, as a larger sample size provides more accurate estimates of the population parameter.

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Answer:

$1920.00

Step-by-step explanation:

You want to calculate the interest on $6000 at 4% interest per year after 8

year(s).

The formula we'll use for this is the simple interest formula, or:

I= P * r * t

Where:

• P is the principal amount, $6000.00.

• r is the interest rate, 4% per year, or in decimal form, 4/100=0.04.

• t is the time involved, 8.…..year(s) time periods

So, t is 8...year time periods.

To find the simple interest, we multiply 6000 x 0.04 x 8 to get that:

The interest is: $1920.00

Answer:

i don't know sorry :(

Step-by-step explanation:

The remainder when N is divided by 1000 is 106.

The Principle of Inclusion-Exclusion, often known as PIE, offers a method/formula for organizing information about the size of each set, the number of elements in the union of a given set of sets, and the size of all potential set intersections.

From the question,

First, we think about all the possible divisions of the 7×1 board. Since we require at least one tile of each color, we exclude the cases of just one or two pieces.

Three pieces = 5+1+1 , 4+2+1 , 4+1+2 etc (6C2) = 15 ways

Four pieces = 6C3 = 20

Five pieces = 6C4 = 15

Six pieces = 6C5 = 6

Seven pieces =6C6 = 1

Now, we apply the Principle of Inclusion-Exclusion to consider how many ways to color them:

Three pieces : 3³ - 3 × 2³ + 3 = 6

Four pieces: 3⁴ - 3 × 2⁴ + 3 = 36

Five  pieces : 3⁵ - 3 × 2⁵ + 3 = 150

Six pieces : 3⁶ - 3 × 2⁶ + 3 = 540

Seven pieces : 3⁷ - 3 × 2⁷ + 3 = 1806

Adding them together, we get

15×6 + 20×36 + 15×150 + 6×540 + 1×1806 = 8106

Hence, the remainder when it is divided by 1000 is 106.

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Answer:

106

Step-by-step explanation:

Answer:

Independent variable is the measurement that that changes and the dependent variable is the result of the independent variable (aka the one that is being measured).

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

3x - 5 is an exterior angle of the triangle, then

3x - 5 = x + 25 ( subtract x from both sides )

2x - 5 = 25 ( add 5 to both sides )

2x = 30 ( divide both sides by 2 )

x = 15

Answer:

40° and 115°

Step-by-step explanation:

x+3x-5+25°=180°(angle on a straight line)

4x+20=180°

4x=180°-20

4x=160°

x=160/4

x=40°

The other angle

3x-5=3(40)-5

120-5=115°

total

40°+25°+115°=180°

Answer:

11.03377918, which is 11.0 if rounded

Step-by-step explanation:

Since We have a leg and an angle we should use a trig

Soh cah toa

According to the angle we have opposite and we are looking for hypotenuse

meaning we'll need sin(X)

sin(x) = o/h   sin(65) = 10/x   x = 11.03377918

Answer:

-1 1/3

Step-by-step explanation:

You can see that if you subtract 1 1/3 from -1/3, you get -1 2/3, and so on

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

The expression fraction with negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 is simplified to give 8

The fraction: negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 is written in words

Rewriting the fraction

-4( (2 - ∛8 * 6) / 5)

The equation is simplified as

= -4( (2 - ∛8 * 6) / 5)

= -4( (2 - 2 * 6) / 5)

= -4( (2 - 12) / 5)

= -4( (-10) / 5)

= -4( -2)

= 8

Option C, 8 is the correct answer

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Answer:

BE / AB = HE / AH

Step-by-step explanation:

AE is angle bisector

BE / HE = AB / AH

BE / AB = HE / AH