Evaluate log6 base 10+ log45 base 10 - log27 base 10

In a Isosceles triangle, DEF , ∆DFB is congruent to ∆DEC by SAS Congruence criteria, i.e., ∆DFB ≅ ∆DEC.

SAS congruance Criteria : If two sides and the angle between these two sides of one triangle are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. We have a triangle DFE with base FE, see in above figure. The EC congruent to FB, i.e., FB ≅ EC. We have to prove ∆DFB ≅ ∆DEC.

Proof : It is known that ∆DEF is isocles triangle with base FE. So, two sides of triangle are equal.

In ∆DFB and ∆DEC,

=> DF = D E ( by definition of Isoceles triangle)

Also, base FB≅ EC ( since, we have)

Now, ∠DFE = ∠DEF => ∠DFB = ∠DEC ( because DE = DF in ∆DEF , corresponding angles of equal sides are equal) .

So, Two sides and the angle between the sides of one triangle, ∆DFB is congruent to the corresponding sides and angle of another triangle, ∆DEC. Therefore, by SAS Congruence criteria, Triangle DFB is congruent to triangle DEC, i.e., ∆DFB≅ ∆DEC. Hence proved..

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Complete question:

Given: ΔDFE is isosceles with base FE; FB ≅ EC. Prove: ∆DFB ≅ ∆DEC.Complete the missing parts of the paragraph proof. We know that triangle DFE is isosceles with base FE and that segment FB is congruent to segment EC because . Segment DF is congruent segment by the definition of isosceles triangle. Since these segments are congruent, the base angles, angles , are congruent by the isosceles triangle theorem. Therefore, triangles are congruent by SAS

Answer:

The equation that we most use to find how many chocolates Maggie bought would be:
6 x c = how many chocolates Maggie bought


Maggie bought c times as many chocolates as Tanner. This means to find how many chocolates Maggie bought we would multiply the c (Being how many times more chocolates Maggie bought) by 6 to find the number of chocolates Maggie bought`.






For example:
If the question stated Maggie bought 4 times as many chocolates as Tanner, the equation would be; 6 x 4 = how many chocolates Maggie bought. Which would be 24 chocolates.

Step-by-step explanation:

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Answer:

it is the vector

Step-by-step explanation:

The y-intercept is given by the value of y when x = 0, and the x-intercept is given by the value of x when y = 0.

The domain is all values of x the function can assume in order to y exist.

The axis of symmetry is the axis where the function is mirrowed.

a) y² = 8x -> y = √(8x)

b) x² = 8y

c) y² = -4x -> y = √(-4x)

d) x² = -4y

Answer:

40

Step-by-step explanation:

The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Answer:

-2, 5/3

Step-by-step explanation:

y=2/3(-2)+3

2/3(-2)=-4/3

y=-4/3+3

Stephanie earns $1.5 per hour more than what Marco earns.

Linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept.

Let w represent the wages after h hours.

From the table using the points:

The rate of change (m) for Stephanie is:

This means that Stephanie earn $10.5 per hour.

From the equation: w = 9h, Marco earns $9 per hour

Hence, Stephanie earns $1.5 per hour more than what Marco earns.

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Answer: The answer for the second one is solid figure

Step-by-step explanation: In geometry, three-dimensional shapes are solid figures.

Refer to the attachment

1).find the next number in the sequence (Answers in bold)

a). 3,6,9,12_15

b). 4,25,46,57_68

c). 4,25,46,67_88

d). 3,6,12,24,48_96



2). solve the following

a). 36×(18-3 + 5) exponent2 ÷5​

Answer:

2880

Answer:

Step-by-step explanation:

Answer:

(-infinity,+infinity)

Step-by-step explanation:

Any real value of x can be defined with a unique output in this function.

The two sequences of transformations that would show that triangles ABC and AED are similar are:

Dilating ΔABC by scale factor 1/2 and reflect A'B'C' over AD.

Reflect AED over line AB and Dilate A'E'D' by scale factor 2.

Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.

Given:

as, From the Figure we have to dilate the sides of ΔABC by scale factor 1/2.

Then, sides of Δ will be Similar with equal side ratio.

Then we can have,

Dilating ΔABC by scale factor 1/2 and reflect A'B'C' over AD.

or, Reflect AED over line AB and Dilate A'E'D' by scale factor 2.

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84.13% of the printing jobs will be acceptable.

The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.

The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.

The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.

To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

x = 1.25

Step-by-step explanation:

Givens

Area = L * w

L = 4x-1

w = 2x

Area = 10 cm^2

Formula

A = L * w

Area = 2x(4x - 1)

Solution

Area = 2x (4x - 1) = 10           Remove the brackets

2x * 4x - 2x = 10                    Subtract 10 from both sides

8x^2 - 2x - 10 = 0                  Factor

This factors into

(4x - 5)(2x + 2) = 0

4x - 5 = 0

4x  = 5

x = 5/4

x = 1.25

2x + 2 = 0

2x = -2

x = - 1      When talking about area, this is an impossible answer.

In the given figure, the measure of the central angle CAD is 80°, the major arc is arc CBD, and minor arc is arc CD. The measure of arc BEC is 2.27r and that of arc BC is 0.87r.

About the Central Angle:

An angle formed by two radii of a circle is known as a central angle. Thus, arc BC and arc CD both subtends central angles at the center.

Since BD is the diameter of the circle,

∠BAC + CAD = 180°

It is given that ∠BAC = 100°

⇒ ∠CAD = 180° - 100°

⇒ ∠CAD = 80°

About Major Arc:

The arc which subtends an angle greater than 180° at the center, is called a major arc.

Angle subtended by arc BEC = 360° - m(arc CD)

= 360° - 80°

= 280° > 180°

∴ Arc BEC is the major arc

About Minor Arc:

The arc which subtends an angle less than 180° at the center, is called a minor arc.

⇒ Arc CD is the minor arc.

Calculating arc BEC and arc BC:

Let us assume the radius of the circle is r.

Then, the formula of the measure of an arc is given by,

θ × (π/180) × r

Here, θ is the angle ( in degrees) subtended by the arc at the center.

Arc BEC = 260 × (π/180)r  ......... [Put π = 3.14]

= 2.27r

Similarly, arc BC = 100 ×(π/180) × r .......... [Put π = 3.14]

= 0.87r

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Answer:

146.9

Step-by-step explanation:

I'm not sure of the answer but if I'm wrong tell me I'll continue trying it is a pleasure to help you.

To make one cake, you would need 0.4 kg (or 400 grams) of flour.

To make 30 cakes, 12 kg of flour are needed.

We can find out how many kilograms of flour are needed for one cake by dividing the total amount of flour by the number of cakes.

Dividing 12 kg of flour by 30 cakes gives us:

12 kg / 30 cakes = 0.4 kg of flour per cake.

Therefore, to make one cake, you would need 0.4 kg (or 400 grams) of flour.

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Answer:

A polyhedron with 6 faces and 8 vertices has 12 edges.

Step-by-step explanation:

Euler Formula is given in the problem:

We are told that the polyhedron has 6 faces (F = 6) and 8 vertices (V = 8). The only unknown variable in Euler's Formula now is E = number of edges.

Substitute the known variables into the formula and solve for E.

A polyhedron with 6 faces and 8 vertices has 12 edges.

Answer:

no solutions

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 )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

(a) The reduced row echelon form of A is not necessarily I3.

(b) The rank of A is 3.

(c) The system [A | b] has a unique solution for any vector b in R3.

(a) The reduced row echelon form of A is not necessarily I3. In fact, the reduced row echelon form of A can be any invertible 3x3 matrix, as long as it is not equal to I3. This is because any invertible matrix can be obtained by row operations from the identity matrix, and these row operations do not change the linear independence of the columns of A.

(b) The rank of A is 3. This is because the three vectors a1, a2, and a3 are linearly independent, so none of them can be written as a linear combination of the others. Therefore, the span of the three vectors is the entire space R3, and the rank of A is the dimension of this span, which is 3.

(c) The system [A | b] has a unique solution for any vector b in R3. This is true, because the rank of A is 3, which means that the columns of A span the entire space R3. Therefore, for any vector b in R3, there exists a unique linear combination of the columns of A that equals b, and this linear combination gives the solution to the system [A | b].

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simplification of expression will be g - 2

Our expression is  g - 16/4 + 2

16/4 = 4

so we c will write it as

g - 4 + 2

which can be further simplified to

g - 2

Therefore, our simplified expression comes out to be g - 2.

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Answer:

Step-by-step explanation:

9/x

By the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

The Mean Value Theorem (MVT) states that if a function ƒ(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

ƒ(x) = 2lnx - 8 is continuous on the closed interval [1, 7], since it is the sum and composition of continuous functions.

ƒ(x) = 2lnx - 8 is differentiable on the open interval (1, 7), since its derivative ƒ'(x) = 2/x is defined and continuous on (1, 7).

Therefore, the Mean Value Theorem can be applied to ƒ(x) on [1, 7]. To find the value of c, we need to solve the equation:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

Substituting the given values, we get:

2/c = [ 2ln7 - 2ln1 ] / (7 - 1)

2/c = ln7

c = 2 / ln7

c ≈ 0.909

Therefore, by the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

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Answer:

$10.71

Step-by-step explanation:

\(\frac{3.75}{y} =\frac{35}{100}\)

y × 35 = 3.75 × 100

35y = 375

35y ÷ 35 = 375 ÷ 35

\(y=10\frac{5}{7}\)

y = 10.7142857143

10.7142857143 round to 10.71

Answer:

\((f+g) (x)=\mid 3x+5\mid+13\)

Step-by-step explanation:

Operation of Functions

Given:

\(f(x)=\mid 3x+5\mid+6\)

\(g(x)=7\)

The sum of (f+g) (x) is:

\((f+g) (x)=\mid 3x+5\mid+6+7\)

We cannot operate with the expression inside the absolute bars, thus:

\(\boxed{(f+g) (x)=\mid 3x+5\mid+13}\)

Answer:

f(1) = -7

Step-by-step explanation:

Step 1: Define

f(x) = -x² + x - 7

f(1) = x = 1

Step 2: Substitute and Evaluate

f(1) = -(1)² + 1 - 7

f(1) = -1 + 1 - 7

f(1) = -7