If {v1, v2, v3} is an orthogonal basis for W, then multiplying v3 by a scalar c gives a new orthogonal basis {v1, v2, cv3}. True or False

Answer: She had 167.57 remaining in her account

Step-by-step explanation:

You add all her expenses and then subtract it from the beginning balance

On solving the provided question, we got to know that ∠ H + ∠ K = 45°.

K therefore has a 135° measure.

A unique kind of quadrilateral created by parallel lines is a parallelogram. A parallelogram might have different angles between its neighboring sides, but it must have parallel opposite sides in order to be considered one. If a quadrilateral's opposite sides are parallel and congruent, it is a parallelogram. As a result, a parallelogram is a quadrilateral with both pairs of opposite sides being parallel and equal.

the K-value of the angle.

First of all, we should be aware that the sum of the adjacent angles in the parallelogram ABCD, which has the angles A, B, C, and D, is 180°.

[tex]angle A + angle B = 180\\ angle B + angle C = 180\\ angle C + angle D = 180\\ angle A + angle D = 180[/tex]

They're considered to be a linear pair.

As a result, the parallelogram HIJK, whose angle H = 45°, is what we have.

Therefore, ∠ H +∠K = 180° (linear pair),

∠ K = 180° - 45°

∠ K = 135°,

and

∠ H + ∠ K = 45°.

K therefore has a 135° measure.

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Answer:

1. Given

2. Subtraction P.O.E

3. Addition P.O.E

4. Division P.O.E

5. Symmetric P.O.E

Step-by-step explanation:

P.O.E stands for Property of Equality

The complete type of bipartite graphs ,[tex]K_{n.n}[/tex] and [tex]K_{n.n+1}[/tex] will have the maximum possible of all number incliding edges among all the present triangle-free nodes i.e., graphs with all same number of vertices.

Approach: The wide variety of edges can be most whilst each vertex of a given set has an aspect to each different vertex of the opposite set i.e. edges = m * n in which m and n are the wide variety of edges in each the sets. that allows you to maximize the wide variety of edges, m need to be same to or as near n as possible.

The two main sets are X = {A, C}, Y = {B, D}.

The vertices for the given set X join, with the vertices Y and vice-versa.

Similar proposition will always holds for bipartite planar type of  graphs: any n-vertex bipartite  graph (n ≥ 3) includes at most 2n − four edges, moreover, each n-vertex bipartite planar graph may be prolonged to an n-vertex bipartite planar graph with 2n − four edges.

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Correct Question:

Among what g will have a complete bipartite graphs  [tex]K_{n.n}[/tex] and [tex]K_{n.n+1}[/tex] have the maximum possible number of edges among it.

a. The equation is, P = 15m + 10

b. The graph of P = 15m + 10 can be seen in the image attached below.

c. The total number of pages written in 5 months, is, 85.

A linear equation is a straight line graph, which can be expressed in slope-intercept form as y = kx + b, where;

a. To write the equation for the total number of pages P written after any number of months m, we have the following defined variables:

Unit rate or slope (k) = 15

Initial value or y-intercept (b) = 10

Number of pages, y = P

Number of months, m = x.

Substitute k = 15 and b = 10 into P = km + b:

P = 15m + 10

b. The graph of the P = 15m + 10 is shown below.

c. Substitute m = 5 into the equation, P = 15m + 10:

P = 15(5) + 10

P = 85

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Answer: 1.3

Step-by-step explanation:

We know that in order to convert from percentages to decimals, we divide by 100. Therefore, 130 percent is the same as 1.3.

Answer: 1.3

Step-by-step explanation:

100% is equal to 1. Now we just have to find the value of 30%. Divide 1 by 10 and multiply by 3 to get 0.3. Since 0.3 is 30% and 1 is 100%, 130% = 1 + 0.3 = 1.3.

An easier way of converting is dividing the percentage by 100.

To find the range of a function: consider a function y = f(x). The spread of all the y values from minimum to maximum is the range of the function. In the given expression of y, replace all the values of x to investigate whether it is positive, negative or equal to other values.

The range of a function is the complete set of all possible resulting or output values of the dependent variable (usually labeled by y), after we have replaced the domain. Typically, this will be represented by the letter y or f(x). The range is any number that you can get when you plug in any number for x.

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If a model airplane takes off at a constant rate of 7 feet per second and the  initial velocity of 30 feet per second. The time it takes for the plane collision to occur is 1.437 sec.

Given data :

T seconds = h=7t

h=-16t^2+30x

Let t represent the time

Hence,

7t=-16t²+30x

7t=          -7t

0 =-16t² + 23t

0=-2t(8t +11.5)

0=-2t               0 =8t-11.5

0=t                   11.5/8 =8t/t

t = 11.5/8

t = 1.437 sec

Therefore the time is 1.437 sec.

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The complete question is:

a model airplane takes off at a constant rate of 7 feet per second.

At the same time, a ball is launched from ground level with an initial velocity of 30 feet per second. The height of the ball, in feet, after t seconds is given by h=-16t^2+30x Will the airplane and ball collide. Find the time it takes for the plane collision to occur .

The descending order of the polynomial is (x³ + 8y³)

The term polynomial in algebra is defined as  an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

Here we have given that (x+2y)(x²−2xy+4y²)

And we have to multiply the polynomial and write your answer in descending order.

Here we have the polynomial (x+2y)(x²−2xy+4y²).

Now, we have to use the identity

=> a³ + b³ = ( a² − ab + b² ) ( a + b ) ,

Now, we have to apply these identity one the given polynomial, then we get,

=> ( x + 2y ) ( x² − 2xy + 4y² )

=> (x³ + ( 2 y )³) = (x³ + 8 y³) .

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Community colleges in the United States play an important role in higher education. In United States, everyone monitors they community colleges are primarily her two-year institutions of higher education that focus on teaching and learning and workforce preparation.

Community colleges are open access institutions that offer economically affordable entry into higher education. About half of first-time college-going students enroll in community colleges, which serve as her transition route to four-year colleges (Beach, 2011). However, despite the important role and primary focus of community colleges, students may view community college instruction as inferior and undesirable to her four-year college (Dougherty, Lahr, & Morest, 2017; Twombly, 2001; Twombly & Townsend, 2008). This general dissatisfied view of community college instruction has much to do with the historical legacy of community colleges, where most two-year schools are either officially called "junior colleges" or "junior colleges." is called Community colleges have reason to brag about progress. It tends to have a higher proportion of female and minority teachers compared to traditional her four-year colleges (Antonio, 2002; Marcotte, Bailey, Borkowski, & Kientz, 2005; Turner, 2001). While the high recruitment rate of minority teachers is laudable, most higher education institutions are still predominantly white and male dominated (with the exception of those serving minorities). Overall, despite the high proportion of women and minority teachers, empirical studies show that such teachers experience high levels of stress and frustration with the way students are treated in the classroom. (Allen et al., 2002; Pittman, 2010). For many teachers and teachers of color, the classroom environment serves as a reminder of the unfortunate social ills that plague our society (Harlow, 2003; Seo & Hinton, 2009).

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In the given diagram, the arc length of the given arc is 10.46.

From the question, we are to determine the length of the arc.

From the formula for calculating the length of an arc, we have that

Length of an arc = θ/360° × 2πr

Where θ is the angle subtended by arc at the center of the circle

and r is the radius of the circle

In the given diagram,

Angle subtended = π/3 = 60°

Radius, r = 10

Thus,

The length of the arc = 60/360 × 2πr

Length of the arc = 1/6 × 2×3.14×10

Length of the arc = 10.46

Hence, the length is 10.46

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WR Answer: 10.46

Step-by-step explanation:

he length of the arc = 60/360 × 2πr

Length of the arc = 1/6 × 2×3.14×10

Length of the arc = 10.46

Hence, the length is 10.46

As per the confidence interval, the average weight gain for composites of this kind is smaller than 0.43% is 0.0006​

Confidence interval

In statistics, the probability that a population parameter will fall between two set values is known as Confidence interval.

Given,

Here the weight gains of a collection of n =21 samples of composite subjected to water diffusion were obtained. The sample mean is x=0.42% with a sample std. of S=0.04%

Here we need to find the 95% confident from the results of this experiment that the average weight gain for composites of this kind is smaller than 0.43% .

As per the given question, we have the following details,

=> x=0.337%,

=> s=0.025%,

=> n=18.

And then we use next test hypotheses 

=> H0​:μ≥0.36 versus HA​:μ<0.36.

And then first we will calculate t-statistic and then p-value to decide which hypotheses we will accept.

=> [(0.337−0.36)/ 0.025] x √18​

=> -3.903,

=> p = TDIST(∣t∣, n − 1 , 1)

=> p = TDIST(∣−3.903∣,17,1)=0.0006​

Therefore, p-value is smaller than 0.01, we reject H0​ and accept HA​.

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When an equation's discriminant is zero, the following is the given statement that is correct: There is just one viable solution.

Having the form ax2 + bx + c = 0, quadratic equations are second-degree algebraic expressions. The name "Quadratic" is derived from the word "Quad" which means square. A quadratic equation is an "equation of degree 2," to put it another way. A quadratic equation is employed in numerous situations.

There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are denoted as (α, β) and are also known as the roots of quadratic equations.

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Answer:

–3 4/15

or

3 4/15

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

There are No Real Roots possible for the Quadratic Equation

What is Quadratic Equation?

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The quadratic equation has the following general form: ax² + bx + c = 0. where x is an unknown variable and the numerical coefficients a, b, and c.

Solution:

x² - 12x + 52 = 0

Formula to Solve the equation is -b +- (D) / 2a

D is the discriminant

D = √b² - 4ac

D = √12*12 - 4*52

D = √144 - 208

D = √-64

Since the value of Discriminant is negative

Therefore there are no real roots possible for the equation

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To prove that the triangles are congruent by ASA, the statement and reason could be used as part of the proof is option (A) ∠FGH ≅ ∠KGJ because vertical angles are congruent.

Here we have two triangle FHG and KJG,

The sides HF and the side JK are parallel

The length of the side of the HG and the length of the side JG are equal

HG ≅ JG

According to the ASA property of congruent, if the two angle and one side of the triangle are equal to the two angle and one side of the other triangle, then the both triangles are congruent

Here we have to prove that angle FHG and angle KJG are vertical angles

Here the vertical angles are congruent

Therefore, the statement that can be the part of proof is option (a) angle FGH ≅ angle KGJ because vertical angles are congruent.

I have solved the question in general, as the given question is incomplete

The complete question is:

Given: HF || JK; HG ≅ JG

Prove: FHG ≅ KJG

To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

a) FGH ≅ KGJ because vertical angles are congruent.

b) JKG ≅ HFG because vertical angles are congruent.

c) FHG ≅ JKG because right angles are congruent.

d) HFG ≅ KJG because alternate interior angles are congruent.

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The coordinates of point G are (-8, -10)

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments

The midpoint of a line segment is the point on a segment that is at the same distance or halfway between the two ending points.

midpoint(M) = (-6, -3)

H = (-4, 4)

let the coordinates of G be (p,q)

taking the x coordinates for M, G and H

-6 = p -4/2

cross multiply

p -4 = -12

p = -12 + 4

p = -8

taking y-coordinates

-3 = q +4/2

q + 4 = -6

q = -6 -4

q = -10

coordinates of G (-8, -10)

in conclusion the coordinates of G is ( -8, -10)

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Condense the expression:

Used property:

Expand the expression:

Used property:

Answer:

[tex]\ln(3x)^{-4}[/tex]

[tex]\ln2 + \ln x[/tex]

Step-by-step explanation:

Given expression:

[tex]-4\ln(3x)[/tex]

[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]

[tex]\implies \ln(3x)^{-4}[/tex]

---------------------------------------------------------------------------------

Given expression:

[tex]\ln(2x)[/tex]

[tex]\textsf{Apply the product law}: \quad \ln xy=\ln x + \ln y[/tex]

[tex]\implies \ln2 + \ln x[/tex]

The market price in this economy equals to $9.

Basically, a market price is the amount of money for what an asset can be sold in a market. In other word, it is the cost of the products determined with respect to the point where the demand meets supply.

The value of marginal product of labor (VMPL) is equal to the marginal product of labor (MPL) multiplied by the market price (P).

In this case, to find market price, we will divide the the value of the marginal product of labor by the marginal product of labor:

= 90/10

= $9

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Distribution will be possible even if we do not know the true population distribution.

What is a frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

Here, the A5 sample size is infinite then the sample distribution becomes normal.  So as per the C.L.T n→∞  so distribution is normal.

Hence, Distribution will be possible even if we do not know the true population distribution.

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The corrected mean will be 17.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Helen took four tests, for which her mean score was 26.

Later on, it was found that her score in the English test was wrongly recorded as 51 instead of 15.

Now,

Since, Later on, it was found that her score in the English test was wrongly recorded as 51 instead of 15.

Hence, The correct mean = 26 - (51 - 15)/4

                                        = 26 - 36/4

                                        = 26 - 9

                                        = 17

Thus, The corrected mean will be 17.

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Using the conversion factor we know that the penguin gained 5,350 grams of weight from a chick to an adult.

A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.

The amount is often expressed as a fraction or ratio with a multiplication factor.

A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).

So, we know that:

1 kg = 100 g

Weight of the adult penguin: 5 1/2 kg that is,

5 1/2 = 10+1/2 = 11/2 = 5.5

5.5kg = 5500 g

Weight of the newborn penguin: 150 g

Weight gain from chick to adult:

5500 - 150

5,350 g

Therefore, using the conversion factor we know that the penguin gained 5,350 grams of weight from a chick to an adult.

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Answer:

Previous meter reading: 2090

Charge per unit: 12p per unit

Step-by-step explanation:

Answer:

£43.26

Step-by-step explanation:

Given readings:

Calculate the number of units used:

[tex]\begin{aligned} \textsf{Number of units used} &= \textsf{Present meter reading} - \textsf{Previous meter reading}\\&= \sf 2410 - 2090\\&= \sf 320\; units \end{aligned}[/tex]

Given charges:

Calculate the cost excluding VAT:

[tex]\begin{aligned}\textsf{Cost (exc. VAT)}&=\textsf{(\# of units $\times$ charge per unit)}+\textsf{(\# of days $\times$ service charge per day)}\\ & = \sf 320 \times \£0.12 + 14 \times \£0.20\\&= \sf \£38.4+\£2.8\\&= \sf \£41.20\end{aligned}[/tex]

To find the total cost including VAT at 5%, multiply the cost (exc. VAT) by 1.05:

[tex]\begin{aligned}\textsf{Cost (inc. VAT at 5\%)}&= \sf \£41.20 \times 1.05\\&= \sf \£43.26\end{aligned}[/tex]

Answer:

Below

Step-by-step explanation:

The probability of Z    given Y  would be

      7  out of (15+7) = 7/22

Answer:

Step-by-step explanation:

3/4x + 5 = 5 -2( x + 7 )

First, use Distributive Property.

-2 ( x + 7 ) --> -2x - 14

3/4x + 5 = 5 -2x - 14

Next, you can get rid of the fraction by multiplying EVERYTHING by 4...

3x + 20 = 20 - 8x - 56

Then, move x by subtracting 3x on BOTH sides...

20 = 20 - 11x - 56

Combine like terms...

20 = - 11x - 36

Add 36 on BOTH sides...

56 = - 11x

Divide -11 on BOTH sides...

56/11 = 5.09 repeating

x = 5.0909090909090909...

Correct me if I'm wrong, but there you go!

Answer:

option 1

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 )

y = 6x + 10 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex]

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{1}{6}[/tex] and (a, b ) = (5, - 8 ) , then

y - (- 8) = - [tex]\frac{1}{6}[/tex] (x - 5 ) , that is

y + 8 = - [tex]\frac{1}{6}[/tex] (x - 5) ← equation of perpendicular line

Answer:

B) -2x+y=8

Step-by-step explanation:

First I looked at the graph and found the y-intercept and slope.

Y-intercept = 8

I found that because the point was the on the y-axis line like (0,8)

To find the slope I identified the next point. From the Y-intercept (0,8), you have to go down 8 units. Then I saw the point go left 4 units which makes it negative.

Slope = -8/4, which is also -2

Slope Intercept Equation (y=mx+b) would be: y=-2x+8

Then I compared it to the options and that's what I got.

The equation of the line that passes through (2, 3) and is parallel to 2y = 5 - 3x is: y = -3/2x + 6.

Given that the line that is parallel to 2y = 5 - 3x passes through the point (2, 3), it means both lines will have the same slope (m).

Step 1: Rewrite the 2y = 5 - 3x in slope-intercept form and determine the slope.

2y/2 = 5/2 - 3x/2

y = -3/2 + 5/2

The slope (m) is -3/2. The slope of the line that is parallel to 2y = 5 - 3x is also -3/2.

Step 2: Substitute m = -3/2 and (x, y) = (2, 3) into y = mx + b to find the value of the y-intercept (b):

3 = -3/2(2) + b

3 = -3 + b

3 + 3 = b

b = 6

Step 3: Write the equation of the parallel line by substituting m = -3/2 and b = 6.

y = -3/2x + 6

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