Solve for x: −2x + 5 < 7 (1 point)

Group of answer choices

x > −1

x < −1

x > −6

x < −6

Answer:

The slope is 3/2

Step-by-step explanation:

Rise over run- up 3 and to the left 2.

Answer:

2 to the left and 3 down

Step-by-step explanation:

Answer:

[tex]\boxed { x = 4}[/tex]

Step-by-step explanation:

Solve for the value of [tex]x[/tex]:

[tex]2x + 4x + 6x - 2(x + 3) = 34[/tex]

-Combine like terms:

[tex]2x + 4x + 6x - 2(x + 3) = 34[/tex]

[tex]12x - 2(x + 3) = 34[/tex]

-Use Distributive Property:

[tex]12x - 2(x + 3) = 34[/tex]

[tex]12x - 2x - 6 = 34[/tex]

-Combine like terms:

[tex]12x - 2x - 6 = 34[/tex]

[tex]10x - 6 = 34[/tex]

-Add [tex]6[/tex] to both sides:

[tex]10x - 6 + 6 = 34 + 6[/tex]

[tex]10x = 40[/tex]

Divide both sides by [tex]10[/tex]:

[tex]\frac{10x}{10} = \frac{40}{10}[/tex]

[tex]\boxed { x = 4}[/tex]

Therefore, the value of [tex]x[/tex] is [tex]4[/tex].

Answer:

13, 16

Step-by-step explanation:

We need to find the common difference.

4 - 1 = 3

7 - 4 = 3

10 - 7 = 3

Find the next two terms.

10 + 3 = 13

13 + 3 = 16

Best of Luck!

Answer:

3

Step-by-step explanation:

6-3=3

9-6=3

13-16=3

333

Answer:  see proof below

Step-by-step explanation:

Since (a, b) is equidistant from (-a, 2) and (2, -b), then it is the midpoint of the those two points. Use Midpoint formula to find (a, b).

[tex]M_x=\dfrac{x_1+x_2}{2}\qquad \qquad \qquad M_y=\dfrac{y_1+y_2}{2}\\\\\\a=\dfrac{-a+2}{2}\qquad \qquad \qquad \quad b=\dfrac{2-b}{2}\\\\\\2a=-a+2\qquad \qquad \qquad \quad 2b=2-b\\\\\\3a=2\qquad \qquad \qquad \qquad \qquad 3b=2\\\\\\a=\dfrac{2}{3}\qquad \qquad \qquad \qquad \qquad b=\dfrac{2}{3}[/tex]

3(a + b) - 4 = 0

[tex]3\bigg(\dfrac{2}{3}+\dfrac{2}{3}\bigg)-4=0\\\\\\3\bigg(\dfrac{4}{3}\bigg)-4=0\\\\\\4-4=0\\\\0=0\qquad \text{TRUE!}[/tex]

Notice that I changed the equation to "negative 4" because the equation you provided did not make a true statement.

The mass of the wire is k(56π/3) and the center of mass of the wire is (0, 0, 2√3/π).

A helix is a three-dimensional curve that has a spiral form, such as a corkscrew.

We will be using the formula to find the mass and center of mass of the wire.

Formula to find mass and center of mass of a wire:

mass= ∫a b dm center of mass=(1/M)∫a b r dm

Given, the equation of the helix is x = t, y = 7 cos t, z = 7 sin t, 0 ≤ t ≤ 2π.

To find mass and center of mass of wire in the shape of helix, we need to use the formulae of mass and center of mass of a wire.

Here, the density at any point is equal to the square of the distance from the origin.

Mass: Let us consider a small element of the wire as shown in the below figure. A small element of the wire. The element is a small part of the helix with length ds and mass dm.

According to the question, the density at any point is equal to the square of the distance from the origin. So, the density of this element is equal to the square of its distance from the origin, i.e.,

dm = kx² + y² + z²ds = k(t² + 7²)dt

where k is the constant of proportionality.

So, the mass of the element can be written as

dm = k(t² + 7²)dt

Integrating both sides, we get

Mass of the helix = ∫₀^(2π)k(t²+7²)dt = k ∫₀^(2π)(t²+7²)dt = k[(t³)/3+7t]₀^(2π) = k(56π/3)

where the limits are 0 to 2π.

The mass of the helix is k(56π/3).

Center of Mass: Let us consider a small element of the wire at a distance r from the origin as shown in the below figure. A small element of the wire at a distance r from the origin. The element is a small part of the helix with length ds and mass dm.

The coordinates of the element can be written as

(x, y, z) = (t, 7 cos t, 7 sin t)

The distance of the element from the origin can be calculated as

r = (x² + y² + z²)½= [(t² + 7² cos² t + 7² sin² t)]½= [(t² + 49)]½= (t² + 49)½

The element is at a distance r from the origin and has mass dm.

The x-coordinate of the element can be written asx = t

The y-coordinate of the element can be written asy = 7 cos t

The z-coordinate of the element can be written asz = 7 sin t

So, the coordinates of the element are (t, 7 cos t, 7 sin t)

So, the position vector of the element isr = t i + 7 cos t j + 7 sin t k

The center of mass of the wire can be calculated as follows:

Center of Mass of Helix = (1/M)∫a b r dm = (1/M)∫a b r(kx²+y²+z²)ds

where M is the mass of the helix obtained in the first step.

So, the center of mass of the helix is

(1/M)∫₀^(2π)r(kx²+y²+z²)ds

where r = (t² + 49)½, and x = t, y = 7 cos t, z = 7 sin t.

Substituting the values, we get

(1/M)∫₀^(2π)r(kx²+y²+z²)ds = (1/kM)∫₀^(2π)[t²+k(7² cos² t+7² sin² t)](t i + 7 cos t j + 7 sin t k) (k(t² + 7²)dt)

where r = (t² + 49)½, and x = t, y = 7 cos t, z = 7 sin t.

(1/M)∫₀^(2π)r(kx²+y²+z²)ds = (1/kM) ∫₀^(2π)[t²+49k](t i + 7 cos t j + 7 sin t k) (k(t² + 7²)dt)

On solving, we get the center of mass of the helix as Center of Mass of Helix = (0,0,2√3/π)

So, the center of mass of the helix is (0, 0, 2√3/π).

Therefore, the mass of the wire is k(56π/3) and the center of mass of the wire is (0, 0, 2√3/π).

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The principal amount of $5500 is invested in a bank account with an interest rate of 6% per annum, compounded weekly.

The question asks how long it will take for the account balance to reach $5700. The correct answer, rounded to two decimal places, is 5.62.

To calculate the time it takes for the account balance to reach $5700, we can use the compound interest formula:

A = P(1 + r/n)^(n*t)

Where:

A is the final account balance

P is the principal amount

r is the interest rate (in decimal form)

n is the number of compounding periods per year

t is the time in years

In this case, the principal amount P is $5500, the interest rate r is 6% (or 0.06), and the account balance A is $5700. We need to solve for t, the time it takes for the account balance to reach $5700.

5700 = 5500(1 + 0.06/52)^(52*t)

To solve for t, we can take the logarithm of both sides:

log(5700/5500) = 52*t*log(1 + 0.06/52)

Using a calculator, we can solve for t:

t = log(5700/5500) / (52*log(1 + 0.06/52))

Calculating the above expression will give us the time t in years. Rounded to two decimal places, the correct answer is 5.62.

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Answer:

x = 15

Step-by-step explanation:

The equation for direct variation is

y = kx

y=21 when x=3

21 = k*3

Divide each side by 3

21/3 = 3k/3

7 =k

y = 7x

Let y=105

105 = 7*x

Divide by 7

105/7 = x

15 =x

a)  False.  the null hypothesized value could not fall within a 99% confidence interval . b) false ; c) false ; d) true ; e) true ; f) false.

(a) False. If a given value (for example, the null hypothesized value of a parameter) is within a 95% confidence interval, it will not always be within a 99% confidence interval.

The reason for this is that a 99% confidence interval is wider than a 95% confidence interval.

Hence, the null hypothesized value could fall within a 95% confidence interval but not within a 99% confidence interval.

(b) False. Decreasing the significance level (α) will reduce the probability of making a Type 1 error, not increase it. A Type 1 error occurs when we reject a true null hypothesis.

By decreasing the significance level, we make it more difficult to reject the null hypothesis, which reduces the probability of a Type 1 error.

(c) False. Suppose the null hypothesis is μ = 5 and we fail to reject H0. Under this scenario, we cannot conclude that the true population mean is 5.

The data may be consistent with a range of population means, including means that are different from 5.

(d) True. If the alternative hypothesis is true, then the probability of making a Type 2 error and the power of a test add up to 1. Power is defined as the probability of rejecting a false null hypothesis.

If the alternative hypothesis is true, then the null hypothesis is false, and the probability of rejecting it (i.e., the power) is equal to 1 minus the probability of failing to reject it (i.e., the Type 2 error rate).

(e) True. With large sample sizes, even small differences between the null value and the true value of the parameter, a difference often called the effect size, will be identified as statistically significant.

This is because large sample sizes increase the precision of our estimates, which makes it easier to detect even small differences.

(f) False. A cutoff of α = 0.05 is not the ideal value for all hypothesis tests. The choice of α depends on several factors, including the consequences of a Type 1 error and the sample size.

For example, if the consequences of a Type 1 error are severe, then a lower value of α may be more appropriate. Similarly, if the sample size is very large, then a lower value of α may be necessary to maintain the Type 1 error rate.

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When Jevonte pulls the ladder 3 feet farther from the house, the ladder will reach approximately 10.15 feet up the Side of the house.

To solve this problem, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the ladder, the distance from the house to the ladder, and the height along the side of the house form a right triangle.

Let's denote the distance Jevonte pulls the ladder as d. We want to find the new height, h, along the side of the house when the ladder is pulled 3 feet farther from the house.

According to the Pythagorean theorem, we have:

h^2 + (48 + d)^2 = 52^2

Simplifying the equation, we get:

h^2 + (48 + d)^2 = 2704

Expanding and rearranging the equation, we have:

h^2 + (d^2 + 96d + 48^2) = 2704

h^2 + d^2 + 96d + 2304 = 2704

h^2 + d^2 + 96d = 2704 - 2304

h^2 + d^2 + 96d = 400

Now we substitute the known values into the equation. We have d = 3 (since Jevonte pulls the ladder 3 feet farther) and h as the unknown.

h^2 + 3^2 + 96(3) = 400

h^2 + 9 + 288 = 400

h^2 + 297 = 400

h^2 = 400 - 297

h^2 = 103

Taking the square root of both sides, we get:

h = √103

Rounding to the nearest tenth of a foot, h ≈ 10.15 feet.

Therefore, when Jevonte pulls the ladder 3 feet farther from the house, the ladder will reach approximately 10.15 feet up the side of the house.

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The Hardware Shop in Subang Jaya is considering in-house production of brackets instead of buying them. The setup cost for in-house production is RM25.00, and the shop plans to produce 50 brackets.

In-house production of brackets involves setting up the necessary equipment and processes to manufacture the brackets within The Hardware Shop.

The shop is currently evaluating this option as an alternative to buying the brackets from an external supplier.

To initiate in-house production, there is a one-time setup cost of RM25.00.

This cost covers expenses related to acquiring the required machinery, tools, and materials, as well as setting up the production area.

In terms of production volume, the shop plans to produce 50 brackets. This quantity represents the number of brackets that the shop aims to manufacture within a given time period.

Producing brackets in-house gives the shop control over the quantity and timing of production.

By considering in-house production, The Hardware Shop can potentially reduce dependency on external suppliers, have more control over the production process, and potentially achieve cost savings in the long run. However, it is important for the shop to carefully evaluate the total costs, including setup costs, production costs, and any associated overhead costs, to make an informed decision about whether in-house production is the most viable option for the business.

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Answer:

5x

Step-by-step explanation:

Step-by-step explanation:

2x +31 = 9

2x = - 22

x = - 11

Thank you and please rate me as brainliest.

Answer:

x + y = 2

y = 2 - x

so it is a linear equation.

2x + 5 = 11

2x = 11 - 5

2x = 6

x = 3

it is not a function because for just one x we have many y

Answer:

An algebraic expression is a compact way of describing mathematical objects ... the three main components of algebraic expressions are numbers, variables, and ... to be successful in writing or interpreting any given algebraic expression. ... a number increased by 4, x + 4 ... 11 more than the product of 3 and y, 3y + 11.

Step-by-step explanation:

Answer:

10 is your answer

The desired basis of R³ in which the coordinates of vector v are (0, 2, 1) is {e₁, 2 * e₂, e₃}.

The given vector v = [1, -2, 5] has coordinates (0, 2, 1) in the desired basis. To find the basis, we can start by considering the standard basis vectors in R³: e₁ = [1, 0, 0], e₂ = [0, 1, 0], and e₃ = [0, 0, 1].

We want to find coefficients a, b, and c such that a * e₁ + b * e₂ + c * e₃ = [0, 2, 1], which represents the coordinates of vector v in the desired basis. This gives us the following system of equations:

a * 1 + b * 0 + c * 0 = 0

a * 0 + b * 1 + c * 0 = 2

a * 0 + b * 0 + c * 1 = 1

Solving this system of equations, we find that a = 0, b = 2, and c = 1. Therefore, the desired basis of R³ in which the coordinates of vector v are (0, 2, 1) is {e₁, 2 * e₂, e₃}. These three vectors are linearly independent and span R³, forming a basis for the space.

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Answer:

The vertex is (-2,1)

Step-by-step explanation:

The standard equation for the parabola is 4p(x-h)=(y-k)^2

Rewrite (y-1)^2=24(x+2) in standard form

4*6(x-(-2))=(y-1)^2

Therefore parabola properites are:

(h,k)=(-2,1)

Answer:

C

Step-by-step explanation:

NO CAP

Answer: The answer would be C

Step-by-step explanation:

Answer:

sure

Step-by-step explanation:

Answer:

1) 10,11,12

2)92,94

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

Let the number be x,

4/2 of x is equal to 64

=> 4/2 * x = 64

=> 4x = 64 * 2

=> x = 64 * 2/4

=> x = 128 / 4

=> x = 32

Therefore the number is 32

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Thank You!!

Answer:

32

Step-by-step explanation:

4/2 * x = 64

NB : x is the number we are finding

we can first solve 4/2

4/2 = 2

2 * x = 64

make x the subject of formula :

x = 64 / 2

x = 32

the number is 32

The answer is option c, the statement correctly identifies the part as "n," the whole as 750, and the percent as 15.

In the statement "part = n, whole = 750, percent = 15," the part is represented by the variable "n," the whole is 750, and the percent is 15.

In this scenario, we are given the percentage (15%) and the whole (750), and we need to determine the part. The part represents the portion or fraction of the whole that corresponds to the given percentage. In this case, the part is represented by the variable "n," and its value is unknown.

To find the value of the part (n), we can use the formula for calculating a percentage: part = (percent/100) * whole. In this case, it would be n = (15/100) * 750.

Therefore, in option c, the statement correctly identifies the part as "n," the whole as 750, and the percent as 15. The other options either have incorrect variable assignments or do not include all the necessary components to represent the part, whole, and percent.

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The population mean number of pounds per person per week is estimated to be between 35.764 pounds and 38.036 pounds.

a. To compute the confidence interval, we will use a t-distribution.

b. With 95% confidence, the population mean number of pounds per person per week is between **35.764 pounds** and **38.036 pounds**.

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / sqrt(Sample Size))

Given that we have a sample size of 241 residents, a sample mean of 37.4 pounds, and a standard deviation of 8.5 pounds, we need to determine the critical value associated with a 95% confidence level using the t-distribution. The degrees of freedom for this calculation are equal to the sample size minus 1, which is 240.

Looking up the critical value for a 95% confidence level and 240 degrees of freedom in the t-distribution table or using a statistical calculator, we find the critical value to be approximately 1.97.

Plugging in the values into the formula, we have:

Confidence Interval = 37.4 ± (1.97 * (8.5 / sqrt(241)))

Calculating this expression, we find:

Confidence Interval ≈ 37.4 ± 1.122

Lower Limit = 37.4 - 1.122 ≈ 36.278 pounds

Upper Limit = 37.4 + 1.122 ≈ 38.522 pounds

Therefore, with 95% confidence, the population mean number of pounds per person per week is estimated to be between 35.764 pounds and 38.036 pounds.

c. If many groups of 241 randomly selected members are studied, then approximately **95%** of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week, and approximately **5%** will not contain the true population mean. This is due to the nature of confidence intervals, which provide an estimated range for the population parameter with a certain level of confidence.

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Answer:

20

Step-by-step explanation:

4 times 5 is 20

Given that S is a nonempty subset of a vector space X. The span of S is a vector space.Proof:Let S be a nonempty subset of a vector space X. Now, we need to show that span(S) is a vector space in X.

To show that the span of S is a vector space, we need to verify the following axioms: Closure under addition: Let u, v ∈ span(S), and α, β ∈ F.

Then we have:αu + βv = α(c1u1 + c2u2 + ... + cnun) + β(d1v1 + d2v2 + ... + dmvn)= (αc1u1 + αc2u2 + ... + αcnun) + (βd1v1 + βd2v2 + ... + βdmvm)where ci, vi ∈ S, di, ui ∈ S.

Since S is a subset of X, then αu + βv ∈ span(S).Closure under scalar multiplication: Let u ∈ span(S), and α ∈ F. Then we have:αu = α(c1u1 + c2u2 + ... + cnun) = (αc1u1 + αc2u2 + ... + αcnun)

where ci ∈ S. Since S is a subset of X, then αu ∈ span(S).Contains zero vector: Since S is nonempty, there exists some v ∈ S. Now, we have:0 = 0v = 0(c1v1 + c2v2 + ... + cnvn) = 0u

where ci, ui ∈ S.

Therefore, span(S) contains the zero vector.Contains additive inverses: Let u ∈ span(S), then there exist ci, ui ∈ S, such that:u = c1u1 + c2u2 + ... + cnunThen, -u = -c1u1 - c2u2 - ... - cnunTherefore, -u ∈ span(S).Hence, span(S) is a vector space in X.

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To make the expression [tex]\(u^2 + 16u + \_\_\)[/tex]  a perfect square, we need to add 64. We know to use the number 8 because it is half the coefficient of the linear term, and squaring it ensures that the quadratic term is doubled, completing the square.

To make the expression [tex]\(u^2 + 16u + \_\_\)[/tex]  a perfect square, we need to determine the missing term that completes the square.

To determine this term, we take half of the coefficient of (u) (which is 16) and square it. Half of 16 is 8, and when we square it, we get 64.

So, the missing term to make the expression a perfect square is 64. Therefore, the complete expression as a perfect square is [tex]\(u^2 + 16u + 64[/tex].

We know to use the number 8 because we want to create a perfect square trinomial.

By taking half of the coefficient of the linear term, we ensure that the quadratic term is doubled, and when we add the square of half the linear term, it perfectly completes the square, resulting in a perfect square trinomial.

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Answer:

Y/k +6

Step-by-step explanation:

Answer:

x=k+6/y

Step-by-step explanation:

This is a literal equation, so x won't be an actual number.

First, move 6 to the other side (or add 6 to both sides)

xy=k+6

then, divide by y

x=k+6/y

Hope this helps!

The area of the circle with a diameter having endpoints at (2,5) and (10,5) on a coordinate plane is 16π square units.

The midpoint of the line segment connecting the endpoints of the diameter is the center of the circle.

The distance from the center of the circle to the endpoints of the diameter is the radius of the circle.

The diameter of the circle in this problem is AB, which has endpoints (2,5) and (10,5).

We know that this diameter is a horizontal line because both endpoints have the same y-coordinate of 5.

The midpoint of AB will also have a y-coordinate of 5 since it lies on the horizontal line containing AB. The x-coordinate of the midpoint is the average of the x-coordinates of A and B.  

It is easy to find the distance between the endpoints of the diameter, so the radius can also be found as follows:

r = AB/2 = 8/2 = 4

Therefore, the area of the circle is 16 π square units.

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Answer:

6, 4, 2, 0

Step-by-step explanation:

To find the first 4 terms, substitute n = 1, 2, 3, 4 into the n th term formula, that is

a₁ = 8 - 2(1) = 8 - 2 = 6

a₂ = 8 - 2(2) = 8 - 4 = 4

a₃ = 8 - 2(3) = 8 - 6 = 2

a₄ = 8 - 2(4) = 8 - 8 = 0

The first 4 terms are 6, 4, 2, 0