The following two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally:

The cost of one ruler is $0.70

From the question, we are to determine the cost of one ruler

Let x represent the cost of a ruler

and

y represent the cost of a pen

From the given information, we can write that

y + x = $2.10 ----------- (1)

2y + 3x = $4.90  ----- (2)

From equation (1),

y + x = $2.10

Then,

y = $2.10 - x

Substitute this into equation (2)

2y + 3x = $4.90

2($2.10 - x) + 3x = $4.90

$4.20 - 2x + 3x = $4.90

$4.20 +x = $4.90

x = $4.90 - $4.20

x = $0.70

Hence, the cost of one ruler is $0.70

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Step-by-step explanation:

180 250 300 H.C.F by division method

The statements about the local maximums and minimums for the given function which are true include:

This is defined as the mathematical entities which assign unique outputs to given inputs and defines a relationship between the two variables.

According the the graph: over the interval [2, 4], the local minimum is –8 because the given minimum point is (3.4, -8) and over the interval [3, 5], the local minimum is –8.

Over the interval [1, 4], the local maximum is 0 and over the interval [3, 5], there is no maximum point hence why it is false.

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The central angle is 77 degrees mate.

The correct answer would be option(C) opposite angles of a parallelogram are congruent.

A parallelogram defined as a special type of quadrilateral which has both pairs of opposite sides parallel and equal.

Given that PQRS is a parallelogram.

PQ ≅ RS

QR ≅ PS

By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ.

Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.

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Answer:

"B"

Step-by-step explanation:

The rule that describes the second transformation is; Rotated at 90° clockwise

From the given diagram we can see that;

The transformation from Rectangle ABCD to A'B'C'D' follows the transformation sequence of;

Shift 1 unit downwards then translate 5 units to the right.

However, for the transformation of A'B'C'D' to A"B"C"D", we see that the transformation is; Rotated at 90° clockwise

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Answer:

The value of [tex]$(f \circ g)(x)$[/tex] is 17-18x and [tex]$(g \circ f)(x)$[/tex] is -7-18x.

Step-by-step explanation:

It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.

It is required to find [tex]$(f \circ g)(x)$[/tex] and [tex]$(g \circ f)(x)$[/tex].

To find [tex]$(f \circ g)(x)$[/tex], substitute g(x) for x in f(x) and simplify the expression.

To find [tex]$(g \circ f)(x)$[/tex], substitute f(x) for x in g(x) and simplify the expression.

Step 1 of 2

Substitute g(x) for x in f(x) and simplify the expression.

[tex]$$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$$[/tex]

Step 2 of 2

Substitute f(x) for x in g(x) and simplify the expression.

[tex]$$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$$[/tex]

Answer:

Therefore , 25 ans.

The probability that a two-digit number selected at random has a tens digit less than its units digit is 0.2667 (4/15).

[tex]A=24B=90\\\\P=A/B\\\\P=24/90\\p=4/15[/tex]

There are 90 two-digit numbers (99-9). Of these, six numbers are divisible by 15 (15, 30, 45, 60, 75, 90). This is also divisible by 5. Therefore, the preferred case is 30-6 = 24. Therefore, the required probability is 24/90 = 4/15.

The probability of an event can be calculated by simply dividing the number of favorable results by the total number of possible results using a probabilistic expression. Whenever you are uncertain about the outcome of an event, you can talk about the probability of a particular outcome, that is, its potential.

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Thus, we need information about the sides OQ and PQ to solve the triangle and find the area. The information given is not enough to determine the area of the triangle.

In this question we must analyze if the area of the triangle OPQ can be found by all information given. By the law of the cosines we understand that lengths of two sides and the measure of an angle should be known to construct a triangle and by the law of the sines we understand that either two angles and a side or two sides and an angle must be known.

Thus, we need information about the sides OQ and PQ to solve the triangle and find the area. The information given is not enough to determine the area of the triangle.

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Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).

expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

LHS,

    (-6)([tex]\frac{14}{3}[/tex]) = -28

RHS,

   (-6)()[tex]4+\frac{2}{3}[/tex]) = -28

LHS=RHS

Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).

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[tex]take \: some \: values \\ h(1) = 5.5 \times |1| = 5.5 \times 1 = 5.5 \\h(2) = 5.5 \times |2| = 5.5 \times 2 = 11 \\ h(4) = 5.5 \times |4| = 5.5 \times 4= 22[/tex]

The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.

Given that the circumference of a sphere is 76cm and error is 0.5cm.

The formula of the surface area of a sphere is A=4πr².

Differentiate both sides with respect to r and get

dA÷dr=2×4πr

dA÷dr=8πr

dA=8πr×dr

The circumference of a sphere is C=2πr.

From above the find the value of r is

r=C÷(2π)

By using the error in circumference relation to error in radius by:

Differentiate both sides with respect to r as

dr÷dr=dC÷(2πdr)

1=dC÷(2πdr)

dr=dC÷(2π)

The maximum error in surface area is simplified as:

Substitute the value of dr in dA as

dA=8πr×(dC÷(2π))

Cancel π from both numerator and denominator and simplify it

dA=4rdC

Substitute the value of r=C÷(2π) in above and get

dA=4dC×(C÷2π)

dA=(2CdC)÷π

Here, C=76cm and dC=0.5cm.

Substitute this in above as

dA=(2×76×0.5)÷π

dA=76÷π

dA=24.19cm².

Find relative error as the relative error is between the value of the Area and the maximum error, therefore:

[tex]\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end[/tex]

As above its found that r=C÷(2π) and r=dC÷(2π).

Substitute this in the above

[tex]\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end[/tex]

Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.

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Answer: 25% off

Step-by-step explanation:

1= 0.25 + 0.75

25% is off is the equivalency of multiplying the value of the original cost with 0.75.

20*0.75=15

Answer:

8+16+2= 24 legs on ground

Step-by-step explanation:

A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient.

To gauge how strongly two variables are related to one another, correlation coefficients are used.

A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient. The values are in the -1.0 to 1.0 range. There was a measurement error in the correlation if the estimated value was larger than 1.0 or lower than -1.0. Perfect negative correlation is shown by a correlation of -1.0, and perfect positive correlation is shown by a correlation of 1.0. A correlation of 0.0 indicates that there is no linear link between the two variables' movements. Finance and investing can benefit from the usage of correlation statistics.

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Answer:

3π

Step-by-step explanation:

arc length = radius x central angle in radians

π = radius x π/3

radius = 3π

since OMN is an equilateral triangle, radius = MN

thus MN = 3π

Answer:

Z = 90 degrees

Step-by-step explanation:

Reason is a diameter subtends angle of 90 degrees on the circumference

3 roots are exist, since the polynomial is of third degree.

According to statement

This follows immediately from the zero product property: if ab=0, then either a=0 or b=0. We have3 roots are exist, since the polynomial is of third degree.

(9x+ 7)(4x +1)(3x+ 4) = 0

from which it follows that each of which admits only one solution.

AND

using the fundamental theorem of algebra, expanding we have a polynomial that is of third degree:

(9x+ 7)(4x +1)(3x+ 4) = 0

108x^3 + 255 x^2 +169x + 28 =0

The theorem states that a polynomial will have up to n distinct roots. In this case, it follows that there are exactly 3, since the solutions to the system above are all distinct.

So, 3 roots are exist, since the polynomial is of third degree.

DISCLAIMER : The question was incomplete. Please find the full content below.

QUESTION

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 1 root 3 roots 4 roots 9 roots

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Answer: 4/12 or 1/3

Step-by-step explanation:

A whole cake is 12/12.

He gave away 1/12, 5/12, and 2/12s of the cake

1+5+2 = 8

So he gave out 8/12s of the cake, which means he has 4/12 left, or 1/3 if you want simplest form.

Hope this helps.

0.017559

It is given that:

Probability of Households Having cable TV, p₀ = 76% = 0.76

Therefore,

The probability that the Households not having cable TV = 1 - 0.76 = 0.24

Sample size, n = 225 households

sample proportions is less than 82% i.e p = 0.82

Now,

The standard error, SE = [tex]\sqrt{} \frac{0.76(1-0.76)}{225}[/tex]

= 0.02847

Z = [tex]\frac{0.82-0.76}{0.02847}[/tex]

Z = 2.107

therefore, P(sample porportions < 0.82) = P(Z < 2.107)

now from the p value from the Z table we get P(sample porportions < 0.82) =  0.017559

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The equation that matches the given situation is [tex]-2\frac{1}{2}+6\frac{3}{4}=?[/tex] . So, after two moves, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above.

We know that in mathematics, subtraction means removing something from a group or a number of things. What is left in the group gets smaller when we subtract. The minuend is the first element we use. The subtrahend is the part that is being removed. The difference is the portion that remains after subtraction.

Assume that "negative" means climbing down and "positive" means climbing up. We must locate the elevation change in this area.

Given that Eric climbed straight down [tex]2\frac{1}{2}[/tex] meters. So we can write [tex]-2\frac{1}{2}[/tex].

Again Eric climbed straight up [tex]6\frac{3}{4}[/tex] meters. So, we can write [tex]6\frac{3}{4}[/tex].

Then the change = [tex]-2\frac{1}{2}+6\frac{3}{4}[/tex]

=[tex]-\frac{(2*2+1)}{2}+\frac{6*4+3}{4}[/tex]

=[tex]-\frac{5}{2} +\frac{27}{4}[/tex]

=[tex]\frac{-(5*2)+27}{4}[/tex]

=[tex]\frac{-10+27}{4}[/tex]

=[tex]\frac{17}{4}[/tex]

=[tex]\frac{4*4+1}{4}[/tex]

=[tex]4\frac{1}{4}[/tex]

Therefore, the equation that matches the given situation is [tex]-2\frac{1}{2}+6\frac{3}{4}=?[/tex] . So, after two moves, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above.

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Answer:

0.5 t

Step-by-step explanation:

Since we know that 2,000lbs=1 t
1,000lbs is half a ton, which makes it 0.5 tons

Answer: 22

Step-by-step explanation:

Using the triangle midsegment theorem,

[tex]2(5x+2)=3x+32\\\\10x+4=3x+32\\\\7x+4=32\\\\7x=28\\\\x=4[/tex]

So, the length of the midsegment is 5(4) + 2 = 22

Answer:

b

Step-by-step explanation:

The set of all input values of a function is the domain of the function

A function relates an input to an output.

A function defines a relationship between one variable (the independent variable) and another variable.

The set of all input values of a function is the domain of the function.

The domain of a function are also called independent variables.

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Non-linear graph best describes this function.

As described in the question, Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. It is linear because the graph decreases over time. It is linear because there is both an independent and a dependent variable but it doesn't satisfies one condition of being linear. Thus, It's Nonlinear because linear functions are increasing functions. It is nonlinear because linear functions increase or decrease at the same rate.

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Answer:

B

Step-by-step explanation:

Answer:

B. more dense