Solve 3x 1 = 15 for x using the change of base formula log base b of y equals log y over log b. −0.594316 1.405684 1.464973 3.469743

Third triangle is congruent to triangle PQR.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

For triangles, there are five primary congruency rules:

Side-Side-Side is an SSS criterion.

The side-angle-side SAS criterion.

Angle, Side, Angle is an ASA criterion.

Angle-Angle-Side is an AAS criterion.

Right Angle Hypotenuse Side (RHS) Criteria

As Height of the triangle PQ is similar to triangle third

Angle 90° ≈ Angle 90° of third triangle

Angle 67° ≈ Angle 67° of third degree

So, By ASA, both the triangles are congruent.

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The value of the constant k in the equation of the division of g(x) by (x + 1); [tex]\frac{g(x)}{x + 1} = 2\cdot x - 3 + \frac{k}{x + 1}[/tex] obtained by the long division of g(x) = 2·x² - x by (x + 1) is 3.

The method or algorithm of finding the long division of a polynomial, p(x) known as the dividend, by a divisor, g(x) makes use of the equation;

p(x) = q(x) × g(x) + r(x)

Where;

q(x) = The quotient

r(x) = The remainder from the division;

The specified equation; [tex]\frac{g(x)}{x + 1} = 2\cdot x - 3+\frac{k}{x+1}[/tex], indicates that the remainder, r(x) = k.

The value of k in the specified equation, can be found by dividing the function g(x) = 2·x² - x, by (x + 1) as follows;

The expression obtained when g(x) is divided by (x + 1) using long division, is presented as follows;

 [tex]{}[/tex]        2·x - 3

(x + 1) |2·x² - x

[tex]{}[/tex]           2·x² + 2·x

[tex]{}[/tex]                    -3·x

     [tex]{}[/tex]            [tex]{}[/tex]  -3·x - 3

[tex]{}[/tex]                       [tex]{}[/tex]     3

The remainder obtained from the long division of 2·x² - x by (x + 1) is; 3

The result of the long division of 2·x² - x by (x + 1) is therefore;

[tex]\frac{g(x)}{x+1} =2\cdot x - 3 + \frac{3}{x + 1}[/tex]

Comparison of the equation; g(x)/(x + 1) = 2·x - 3 + k/(x + 1) and the equation; g(x)/(x + 1) = 2·x - 3 + 3/(x + 1), indicates that the value of k is 3

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When two lines are parallel, they do not intersect, so there will be no angle formed between them. Therefore, the number of 90° angles formed by the intersection of EF and the two parallel lines AB and CD is zero.

Answer:

2/3

Step-by-step explanation:

First divide the numerator by the denominator.

You then get the percentage and then you can judge from there.

Answer:

2/3

Step-by-step explanation:

first we have to equalise the denominators

we know 3 × 4 = 12 so we multiply both the denominator and the nominator by 4 which would give us 8/12

so the answer would be 2/3 since 8/12>7/12

The answer accurate to the nearest hundredth is 38.5

How to find the nearest hundredth?

To find the nearest hundredth of a number, you can round it to the nearest hundredth. To do this, you need to look at the third digit after the decimal point.

Regarding the rectangles, since the two rectangles are similar, we know that the ratio of their corresponding sides are equal.

W1/W2 = P1/P2 = k (where k is the proportionality constant)

So, P2 = (P1 * W2)/W1 = (34 * 14)/12 = 38.5

Hence, The answer accurate to the nearest hundredth is 38.5

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Answer:

[tex]\boxed{384}[/tex]

Step-by-step explanation:

The bar represent 120 bars The histogram shows information about 480 cars.

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The total length of the reel of thread is 5 meters, which is equal to 500 centimeters. Since Lahon used 300 centimeters of thread, he has 200 centimeters of thread left.

Lahon recently purchased a reel of thread that was 5 meters long. This is equivalent to 500 centimeters. He then used 300 centimeters of the thread for sewing. This leaves him with 200 centimeters of thread remaining. This can be expressed as 2 meters. Thus, Lahon has 2 meters of thread left from the reel of thread that he originally bought. This leftover thread can be used for other sewing projects or kept for future use. It is important to keep track of how much thread has been used and how much is left to ensure that an adequate amount of thread is available for future projects. The total length of the reel of thread is 5 meters, which is equal to 500 centimeters. Since Lahon used 300 centimeters of thread, he has 200 centimeters of thread left.

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When t = 3, the exponential function has a value of 809.0.

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.

Here,

Given the exponential function h (t) = 1250(0.865)^t

When t = 3

h(3) = 1250(0.865)^3

h(3) = 1250 (0.6472)

h(3) = 809.0

The exponential function when the value of t is 3 is 809.0.

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Answer:

  y = 1/4x +1/8

Step-by-step explanation:

You want to know the equation of the table showing a linear function and points (0, 1/8), (1, 3/8).

The y-intercept of the line described by this table is the y-value when x=0. That value is 1/8.

The slope of the line described by the table is the difference in y-values for a difference in x-values of 1. The difference between x=1 and x=0 is ...

  ∆y = 3/8 -1/8 = 2/8 = 1/4

The slope-intercept equation for the table is then ...

  y = mx +b . . . . . . . line with slope m and y-intercept b

  y = 1/4x +1/8 . . . . . line with slope 1/4 and y-intercept 1/8

The equation of the table is ...

  y = 1/4x +1/8

Answer:

A = 72 units²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

note that the middle section of the lower base = upper base = 6

here h = 8 , b₁ = 3 + 6 + 3 = 12 , b₂ = 6 , then

A = [tex]\frac{1}{2}[/tex] × 8 × (12 + 6) = 4 × 18 = 72 units²

We can write the linear equation:

y = x + 50

And evaluating it on the given values of x, we will get the table:

x        y

10     60

20    70

30    80

40    90

50    100

We know that there are x sparrows in a tree, and there are 50 sparrows on the ground beneath the tree.

y represents the total number of sparrows, then y is equal to the number of sparrows on the tree (x) plus the ones beneath (50) then we will get:

y = x + 50

B) Now we want to make a table. To make that table, we need to evaluate the linear equation in different values of x.

if x = 10

y = 10 + 50 = 60

if x = 20

y = 20 + 50 = 70

if x = 30

y = 30 + 50 = 80

if x = 40

y = 40 + 50 = 90

if x = 50

y = 50 + 50 = 100

Then the table will be:

x        y

10     60

20    70

30    80

40    90

50    100

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The scale factor of a similarity transformation is the ratio of the lengths of the corresponding sides of the two similar figures.

The scale factor is a ratio between two corresponding lengths, areas, or volumes of two similar figures. It is used to compare the size of one figure to another, as well as to enlarge or reduce the size of a figure. The scale factor is expressed as a ratio, such as 1:2, where the first number is the original size and the second is the new size.

It is usually represented as a decimal or fraction, and can be calculated by dividing the length of one of the sides of one figure by the length of the corresponding side of the other figure. For example, if we have two triangles with corresponding sides that measure 3 units and 6 units, then the scale factor of the dilation is 0.5 (3/6). This means that the second triangle is half the size of the first.

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When nine is divided by 60 , the quotient would be 0. 15 .

The quotient when nine is divided by 390 is 0. 023 or 3 / 130 .

The quotient refers to the result when a number is divided by another number as is the case with nine being divided by 60 .

The quotient is therefore :

= 9 ÷ 60

= 9 / 60

= 0. 15

The quotient for the division of nine by 390 is :

= 9 ÷ 390

= 9 / 390

= 0. 023

Another way to do this is to find the greatest common factor of nine and 390 which is 3 . Then use it to take the numbers to their simplest form. The quotient would then be :

= ( 9 / 3 ) / ( 390 / 3 )

= 3 / 130

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-3x=4y+8 is a continuous and linear equation and it can be written as y=-3/4x-2

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The given equation is -3x=4y+8

This equation can written in y=mx+b form

-3x=4y+8

Add 3x on both sides

0=4y+3x+8

Subtract 4y on both sides

-4y=3x+8

Multiply with minus

4y=-3x-8

y=-3/4x-2

The line is continuous and linear

Hence, -3x=4y+8 is a continuous and linear equation and it can be written as y=-3/4x-2

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The speed of spin of carousel is 0.286 miles/minutes. The The speed at which something moves in a specific direction is known as its velocity. as the speed of a car driving north on a highway or the speed at which a rocket takes off.

based on the distance traveled in a given amount of time. These cars can travel at speeds of more than 150 kilometers per hour (km/h). Meters per second (m/s) is the fundamental unit of speed in the metric system.

Given,

distance spinned=2 miles

time taken=7min

speed=distance/time

speed=2/7=0.286 miles/minute

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Table A represents a function, but Table B does not represent a function.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y, or vice versa. For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y. We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.

As, each element of X is associated with unique element of Y, so this is a function.

Table A    

           X               Y

           3                 1

            2                 0

            1                  0

As, each element of X is associated with a unique element of Y, so this is a function.

Table B

X            Y

3           -2

5              1

5              2

Hence, Table A represents a function, but Table B does not represent a function.

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Profit per kilogram = R1.90

The profit per kilogram is the difference between the selling price and the cost price per kilogram.

a) To find the profit per kilogram, we can use the following formula:

Profit per kilogram = Selling price per kilogram - Cost price per kilogram

Therefore,

Profit per kilogram = R2.80 - R0.90

Profit per kilogram = R1.90

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The coordinates of the orthocenter of ABC are (6,4).
The correct option is C) (6,4).

What is an orthocenter of a triangle?

In geometry, an orthocenter is a point in a triangle that is the intersection of the three lines containing the altitudes of the triangle. An altitude of a triangle is a line segment from a vertex of the triangle to the line containing the opposite side, and is perpendicular to that side. The orthocenter of a triangle is the point where all the altitudes of a triangle meet.

To find the orthocenter of a triangle, the first step is to find the equation of the altitudes from each vertex. Then, we can find the point of intersection of these three lines.

Given the triangle ABC with vertices A (2,6), B (8,6), and C(6,2),

The equation of altitude from vertex A is (x-2) = -2(y-6)

The equation of altitude from vertex B is (x-8) = -2(y-6)

The equation of altitude from vertex C is (x-6) = 2(y-2)

By solving the system of these three equations, we can find the coordinates of the orthocenter.

Hence, The coordinates of the orthocenter of ABC are (6,4).
The correct option is C) (6,4)

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The total money earned after working the given number of hours is $18.60.

When using the cross-multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa.

Given that to pick green peppers:

15 minutes = $3.20

45 minutes = x

Using cross multiplication solve the above equation:

[tex]x = \frac{(3.20)(45)}{15} \\\\x = 9.60\\[/tex]

For picking carrots:

20 minutes = $3. 00

1 hour = 60 minutes = x

Using cross multiplication solve the above equation:

[tex]x = \frac{(3)(60)}{20}\\ \\x=9[/tex]

The total amount made after all the work is:

A = 9.60 + 9

A = 18.60.

Hence, the total amount of money she earned after all the work is $18.60.

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The desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.

The discipline of finance is the study of money, money systems, and capital assets. It is associated with economics, which is the study of the production, distribution, and consumption of money, assets, products, and services, but is not the same thing

Let x be the cost of the desktop computer before finance charges.

We know that the laptop cost 150 more than the desktop, so the cost of the laptop is x+150

We also know that the total finance charge for one year is $303 and the interest rate of the desktop is 7% and the interest rate of the laptop is 9.5%

So we can set up the following equations using the information provided:

(x*0.07) + ((x+150)*0.095) = 303

Simplifying and solving for x:

0.07x + 0.095x + 14.25 = 303

0.165x = 288.75

x = $1750

Therefore, the desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.

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The value of y in the right triangle is found to be 3√3 units.

Given data:

So, apply trigonometric ratios:

cos 30 = y / 6

y = cos 30 * 6

y = √3 / 2 * 6

y = 3√3

Thus, the value of y in the triangle is found to be 3√3 units.

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The angle created by the two rays or arms at a shared vertex is known as the angle measure in geometry.

With a protractor, you can determine how large an angle is. Alternatively, the congruent angles could be indicated on the figure by an arc. Supplementary angles are two angles whose combined measurements are 180°, such as two right angles since 90° + 90° Equals 180°. the measurement of an angle wherein 1 degree equals 1/360 of a circle.

An angle (created by perpendicular lines) that is exactly 90 degrees is called a right angle. Less than 90 degrees is considered an acute angle. Revolutions, degrees, and radians are the three types of angles that can be measured. Degrees serve as a more widely used measurement unit. In order for a right angle to be 90 degrees, a circle must be divided into 360 equal degrees.

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The expression that is 0.5 times as large as 342 + 156 is (342 + 156) x 0.5

This is because 0.5 is a factor that multiplies the entire sum of 342 + 156.

So the correct answer is (Choice A) (342 + 156) x 0.5

Answer: The correct answer is (A) (342 + 156) × 0.5. This is because in mathematics, multiplication and division should be done before addition and subtraction. Therefore, the parenthesis is solved first, which results in 342 + 156 = 498. Then, 0.5 is multiplied to the result, 498 × 0.5 = 249.

Step-by-step explanation:

When a figure is dilated using a scale factor of 1, the resulting figure is the same as the original figure.

This is because a scale factor of 1 means that the dimensions of the original figure are not changed in any way.

Mathematically, this is represented by the equation:

Original Length x Scale Factor = Resulting Length

For a scale factor of 1, the equation simplifies to:

Original Length x 1 = Resulting Length

Therefore, the resulting length is equal to the original length.

For example, if a line had a length of 5 units before dilating, the resulting length would be 5 units after dilating.

5 units x 1 = 5 units

This is because the scale factor of 1 does not change the length of the line in any way.

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Answer:

y = 5x - 14

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

Given that the line passes through the point (1, -9) and has a slope of 5, we can use the point-slope form of a line, which is y - y1 = m(x - x1)

Substituting the point and slope we have:

y - (-9) = 5(x - 1)

y + 9 = 5x - 5

Now we can solve for y by adding 9 to both sides of the equation:

y = 5x - 14

So the equation in slope-intercept form for the line that passes through the point (1, -9) and has a slope of 5 is:

y = 5x - 14

Answer:

y = 5x - 14

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

Given that the line passes through the point (1, -9) and has a slope of 5, we can use point-slope form to write the equation of the line. Point-slope form is written as: y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

We know that the line passes through the point (1, -9) and has a slope of 5, so we can substitute these values into the point-slope form:

y - (-9) = 5(x - 1)

Simplifying, we get:

y + 9 = 5x - 5

Now we can add 9 to both sides to get:

y = 5x - 14

So the equation of the line in slope-intercept form is y = 5x - 14

We can confirm that the point (1,-9) belongs to the line by substitute the values x =1 and y = -9 into the equation y = 5x - 14, if the equation holds true then the point belongs to the line.

On solving the provided question, we can say that - Since the two triangle are similar and each sides are 3 times the others, so x= 3 X 4 = 12 cm

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Since the two triangle are similar

\and each sides are 3 times the other,

so x= 3 X 4 = 12 cm

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Answer:

x = 6 / sqrt(2)

Step-by-step explanation:

We are given the diagonal of a square

The side length is x

Using the Pythagorean theorem

x^2 + x^2 = h^2  where h is the length of the hypotenuse which is 6

x^2+x^2 = 6^2

2x^2 = 36

x^2 = 18

Taking the square root of each side

sqrt(x^2) = sqrt(18)

x = 3 sqrt(2)

This can be rewritten as

x = 3 sqrt(2) * sqrt(2)

    ------------------------

             sqrt(2)

x =    3*2  

        -------

          sqrt(2)

x = 6 / sqrt(2)

Answer:

Step-by-step explanation:

To find f(-6), we need to substitute -6 for x in the function f(x) = -4x² + 4x - 1.

f(-6) = -4(-6)² + 4(-6) - 1

f(-6) = -4(36) + (-24) - 1

f(-6) = -144 + (-24) - 1

f(-6) = -167

Therefore, f(-6) = -167