Which equation represents the line through (0, 0) and (4, 7)?
A. y = 7/4x
B. y = 4/7x
C. y = 7x
D. y = 4x

Solving the problem as per a linear equation, it can be proved that q = r.

A linear equation is an algebraic equation in the form of y = mx+ b. The highest power of a variable in a linear equation is always 1. Such equations always form a straight line on the graph.

From equation 1 we can write,

2q - r = 4p.................(1)

or, 2q - 4p = r ( side switched ) ................(2)

Now, 2p = r

or, 4p = 2r and we know 2r = q

Hence, we can write 4p = q ...............(3)

If we put equation (3) in (1)

we will get, 2q - q = r

or, q = r

q = r is proved.

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The axes of symmetry of the functions are f(x): x = 8 and  h(x): x = 3

The functions are given as

f(x) = -4(x - 8)^2 + 3

h(x) = -(x - 3)^2 + 2

A quadratic function is represented as

y = a(x - h)^2 + k

Where the equation of the axis of symmetry of the function is

x = h

This means that the axes of symmetry of the functions are

f(x): x = 8

h(x): x = 3

Hence, the axes of symmetry of the functions are f(x): x = 8 and  h(x): x = 3

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Answer:D

Step-by-step explanation:  3 over 9 = .333 repeating which is greater then .22 and lower then 33

The value of logarithmic expression x log₄m+1/y log₄n - log₄p is log₄(m^x  * n^1/4)/p.

By considering the given logarithmic expression

x log₄m+1/y log₄n - log₄p

log₄m^x+  log₄n^1/4- log₄p

log₄(m^x  * n^1/4)- log₄p

log₄(m^x  * n^1/4)/p

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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Answer:  addition

Step-by-step explanation:  add three to both sides to eliminate the 3 on the X side and isolate the X

Answer:

X=9

In order to find X u must subtract 3 from 12

12-3=9

so X=9

The required dimension of the longer side of the fencing is 18 ft.

As given in the question, there is an 18-ft fence on one side of a rectangular garden. the gardener has 43 ft of fencing to enclose the other three sides.

Perimeter is the measure of the figure on its circumference.

Here,
Total length of the fencing = 18 + 43
The total length of the fencing = 61
Perimeter of rectangle  = 2 length + 2 width
61 = 2 * 18 + 2 width
2 width = 61 - 36
2 width = 25
width = 12.5 ft

Thus, the required dimension of the longer side of the fencing is 18 ft.

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The equation 6 ⁸ = a + 1 in the logarithm form will be given as log ₆ ( a + 1 ) = 8 .

Logarithms are another form of  exponents.

For example, we know that 2 raised to which power is equal to 8,

this is expressed by the exponential form as follows 2³ = 8 is equal to log ₂ 8 = 3

Both equations describe the same relationship between the numbers 2, 3, 8 where 2 is the base and 3 is the exponent

The difference is that while the exponential form isolates the power 8,the logarithmic form isolates 3

So by writing given equation in logarithmic form we get -log₆ ( a + 1 ) = 8.

Therefore, the equation 6 ⁸ = a + 1 in the logarithm form will be given as log ₆ ( a + 1 ) = 8 .

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The value of (fof)(3) is 21.

When two or more functions are combined to form a new function, the new function is known as a composite function. For example- if there is a function f(x), then fof(x) is a composite function formed by repeating f(x) twice.

Here, we are given a function- f(x) = x + 9

if we put the value of x = 3, we get-f(3) = 3 + 9f(3) = 12

now, we need to find the value of (fof)(3)

This can also be written as- {f(f(3)}

we know that f(3) = 12

⇒ {f(f(3)} = f(12)

f(12) = 12 + 9f

(12) = 21

Thus, the value of (fof)(3) is 21.

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Your question was incomplete. Check for full content below-

f(x) = x + 9

What is (fof)(3)?

(F) 1 (G) 5 (H) 21 (I) 77

The logarithmic form of the given equation (5⁴=625)is  = log₅(625) = 4.

Logarithmic functions are the inverses of exponential functions. So a log is an exponent! y=logbx if and only if by=x for every x>0 and 0b1.

Logarithms depict changes in terms or multiplication: in the instances above, each step is 10x larger. Each step on the natural log is "e" (2.71828...) times longer. When dealing with a sequence of multiplications, logarithms let us "count" them in the same way that addition counts on our behalf when effects are added.

using the property of log:

5⁴=625

Apply logarithmic definition: aⁿ = b gives logₐᵇ = n

so,

a = 5

b = 625

n = 4

equation would be as follows:

log₅(625) = 4

The  logarithmic form of the given equation (5⁴=625)is  = log₅(625) = 4

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Answer: [tex]log_{5} 625 = 4[/tex]

Step-by-step explanation:

Answer: 100 million.

Step-by-step explanation:

It is 100 million because if you forget the K which means three zeros, it would be like this. 100000000. After three digits, you put a comma, so it would be 100,000,000.

Answer:

45o and 135o

Step-by-step explanation:

The sum of angles of a linear pair is always equal to 180°.

So if the first angle is x,

then the second angle is 3x

x + 3x = 180

4x = 180

x = 45

then 3x = 135

Calvin is incorrect. He should add 2 to each side not multiply each side by 2.

The correct answer is an option (C)

For given question,

Let l be the length of the rectangle and w be the width of the rectangle.

Assume that l = 10 units and w = 4 units

The perimeter of the rectangle is,

P = 2(length + width)

So, for above values the perimeter of the rectangle would be,

⇒ P1 = 2×(10 + 4)

⇒ P1 = 28 units

The length of each side is increased by 2 units.

so, l = 12 and w = 6 units

Then the perimeter of the rectangle would be,

P2 = 2(12 + 6)

P2 = 36 units

According to Calvin, if the length of each side of rectangle is increased by 2 units, the perimeter of the rectangle would double.

But from P1 and P2 we can clearly observe that, Calvin is incorrect.

Calvin possibly double the each side of the rectangle instead of increasing by 2 units.

If he double each side then l = 20 and w = 8

The perimeter of the rectangle would be,

P3 = 2(20 + 8)

P3 = 56

From P1 and P3, the perimeter of the rectangle is doubled.

Therefore,  Calvin is incorrect. He should add 2 to each side not multiply each side by 2.

The correct answer is an option (C)

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The stated logarithm equation log₇8 in changed by the Base Formula is logₓ8 - logₓ 7.

A logarithmic notation is one where variable x contains a logarithm.

The variable in an exponential equation is depicted by an exponent. To solve exponential equations, first see if both sides of the formula could be written as powers of the same number. If you can't, consider taking the common logarithm of both equation sides and solve the problem using property.

Now, as per the stated conditions;

The given equation is; log₇8

Apply the Base Rule and re-write the equation;

= logₓ8 / logₓ 7

This obtained equation can also be written on the form by applying product rule.

=  logₓ8 - logₓ 7

Therefore, the logarithm equation log₇8 in expressed by the Base Formula is logₓ8 - logₓ 7.

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Answer:

0.25

Step-by-step explanation:

group like terms: 0.42b+9.14b-8.3=-5.91

add similar elements: 9.56b-8.3=-5.91

multiply both sides by 100: 956b-830=-591

add 830 to both sides: 956b-830+830=-591+830

simplify: 956b=239

divide each side by 956: you know what that looks like

simplify: b=1/4

convert to decimal: 0.25

Answer:

b = 0.25

Step-by-step explanation:

Given:

[tex]\sf 0.42b - 8.3 + 9.14b = -5.91[/tex]

Collect like terms:

[tex]\implies\sf 0.42b+ 9.14b - 8.3 = -5.91[/tex]

Combine like terms:

[tex]\implies \sf 9.56b - 8.3 = -5.91[/tex]

Add 8.3 to both sides:

[tex]\implies \sf 9.56b - 8.3+8.3 = -5.91+8.3[/tex]

[tex]\implies \sf 9.56b=2.39[/tex]

Multiply both sides by 100:

[tex]\implies \sf 9.56b \times 100=2.39 \times 100[/tex]

[tex]\implies \sf 956b=239[/tex]

Divide both sides by 956:

[tex]\implies \sf \dfrac{956b}{956}=\dfrac{239}{956}[/tex]

[tex]\implies \sf b=\dfrac{239}{956}[/tex]

Write 956 as 4 × 239:

[tex]\implies \sf b=\dfrac{1 \times 239}{4 \times 239}[/tex]

Cancel the common factor 239:

[tex]\implies \sf b=\dfrac{1}{4}[/tex]

[tex]\implies \sf b=0.25[/tex]

The actual dimensions of the bookcase is 234 cm tall, 162 cm wide and 30 cm deep

An equation is an expression that shows the relationship between two or more numbers and variables.

The scale of 1:30 is used to produce a diagram of a bookcase in an instruction booklet.

If the diagram is 7.8 cm tall 5.4 wide and 1 cm deep, hence:

Height of bookcase = 7.8 cm * 30 = 234 cm

Width of bookcase = 5.4 cm * 30 = 162 cm

Depth of bookcase = 1 cm * 30 = 30 cm

The actual dimensions of the bookcase is 234 cm tall, 162 cm wide and 30 cm deep

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Answer:

y = 3/4x - 8

Step-by-step explanation:

The scale factor of △DEC to △RST is 13 : 3.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

A multiplicative inverse or reciprocal for a number y, denoted by 1/y or y⁻¹, is a number that when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction b/a is a/b.

The scale factor of △RST to △DEC is 3 : 13.

Now, △DEC to △RST is the inverse of  △RST to △DEC

Therefore,

[tex]\frac{\Delta RST}{\Delta DEC} = \frac{3}{13}[/tex]

[tex]\frac{\Delta DEC}{\Delta RST} =\frac{13}{3}[/tex]

Hence, the scale factor of △DEC to △RST is 13 : 3.

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Answer:

5/8

Step-by-step explanation:

3/4 = 6/8. so 6/8-1/8= 5/8. 5/8 is the answer.

No, it is not as a result of all whole numbers are integers, thus there's no number that's not associate degree whole number.

The whole numbers area unit the numbers while not fractions and it's a group of positive integers and nil. it's diagrammatical by the image “W” and also the set of numbers area unit . Zero as a full represents nothing or a null worth.These numbers area unit positive integers as well as zero and don't embody aliquot or decimal elements (3/4, 2.2 and 5.3 don't seem to be whole numbers). Also, arithmetic operations like addition, subtraction, multiplication and division area unit attainable on whole numbers.

 Hence , it is not possible.

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a) Since the new score is less than the average score, it will decrease the average.

a) Since the new score is less than the average score, it will decrease the average.

b) Sum of 27 scores = 27*79

Hence,

New average = (79*27 + 63)/28 = 78.43

c) Since the variability would increase in the overall data, the standard deviation increases.

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Answer:

speed

Step-by-step explanation:

speed is the right answer hope its right

The value of the given fraction 3/8 - 8/11 after the evaluation is -31/88.

So, evaluation of 3/8 - 8/11:

Now,

Therefore, the value of fraction 3/8 - 8/11 after the solution is -31/88.

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Answer:

Step-by-step explanation:

PS =5 because PS's line is parallel to 5 the line.

So now all that is left is the angle one

m∠Q =105° we can come to this conclusion because 105° is parallel to m∠Q

If you are still confused please, let me know! :)

Answer:

3.7

Step-by-step explanation:

Triangles BDE and BCE are congruent, so BC=BD=3.7.

Answer:

The answer is in the attached screenshot (I wanted to show properly formatted fractions)

Explanation:

The explanation is in the attached screenshot (I wanted to show a properly formatted fraction)

Answer:

The answer is -16175

Step-by-step explanation:

-First multiply 360 by -45, which equals -16200

-Then add 25 to -16200, and you get -16175

Answer:

Step-by-step explanation:4n+8-2n=0. 2n=-8. n=-4.

HOPE THIS HELPSSSS!!!!!!!!!!!!!+

Answer:

-4

Step-by-step explanation:

4n+8-2n=0 2n=-8.n=-4