What are m∠1 and m∠2?

The equivalent equation of the logarithmic equation is [tex]5x + 4 = 8^{3x - 4}[/tex]

The logarithmic equation is given as

Log_8(5x+4)=3x-4

Rewrite properly as:

[tex]\log_8(5x+4)=3x-4[/tex]

Apply the following law of logarithm

[tex]\log_a(b) = x \to a = b^x[/tex]

So, we have:

[tex]5x + 4 = 8^{3x - 4}[/tex]

Hence, the equivalent equation of the logarithmic equation is [tex]5x + 4 = 8^{3x - 4}[/tex]

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The area of part 1 is 15√2 square in, the area of part 2 is 30 square in, and the area of the entire rectangle is (30 + 15√2) square in.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

The area of part 1 = 5√2×3 = 15√2 square in

The area of the part 2 = 5√2×3√2 = 15×2 = 30 square in

The area of the entire rectangle = area of part 1 + area of part 2

= (15√2 + 30) square in or

= (30 + 15√2) square in

Thus, the area of part 1 is 15√2 square in, the area of part 2 is 30 square in, and the area of the entire rectangle is (30 + 15√2) square in.

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Answer:

Step-by-step explanation:

x⁴ + 4y⁴

In order to factorize it, follow the steps:

Used identities:

In a circle H with a measure of angle ∠GKJ = 27°. Then the measure of angle ∠GHJ will be 54°

It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

In a circle H with a measure of angle ∠GKJ = 27°.

Then the measure of angle ∠GHJ will be

We know that a chord's slope in the centre is double that of the chord's slope at the perimeter.

Then we have

∠GHJ = 2 x ∠GKJ

∠GHJ = 2 x 27°

∠GHJ = 54°

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Answer:

211410

Step-by-step explanation:

234900x.10

23490

234900-23490

211410

Answer:

y = - x

Step-by-step explanation:

From the given table:-

( x_1,x_2): (5,-5)

( y_1,y_2): (6,-6)

1) Let's find the slope (m):-

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{ - 6( - 5)}{6 - 5} = \frac{ - 6 + 5}{1} = \frac{ - 1}{1} = - 1[/tex]

2) Substitute x_1= 5, y_1=-5 and m=-1 into y-y_1=m(x-x_1)

[tex]y - ( - 5) = - 1(x - 5)[/tex]

[tex]y + 5 = - x + 5[/tex]

[tex]y = - x + 5 - 5[/tex]

[tex]y = - x[/tex]

The Dimension of the Cylinder:    Height = 1.5 m and radius = 0.75 m

Volume of Cylinder = 2.649 m³

Surface Area = 10.59 m²

A cylinder is a three-dimensional solid figure which has two identical circular bases joined by a curved surface at a particular distance from the center which is the height of the cylinder.

Here, Trailer bed dimension = 1.5 m X 1.5 m

  So, height of the cylindrical = 1.5 m

         Radius = 1.5/2 = 0.75 m

Now, Volume of Cylinder = πr²h

                                          = 3.14 X (0.75)²X1.5

                                          = 2.649 m³

Surface area of cylinder = 2πrh + 2πr²

                                        = 2πr (h + r)

                                       = 2 X 3.14 X 0.75 ( 1.5 + 0.75)

                                       = 10.59 m²

Thus, The Dimension of the Cylinder: Height = 1.5 m and radius = 0.75 m

Volume of Cylinder = 2.649 m³

Surface Area = 10.59 m²

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Answer:

D

Step-by-step explanation:

are the same length and intersect at different angles

A circle is a curve sketched out by a point moving in a plane. The diameter of the circular poll is 12 inches. Thus, the correct option is A.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

The area of a circle is given as πR², where r is the radius of the circle. Since the area of the pool is 113 sq. inches, therefore, the radius of the circle will be,

Area of pool = πR²

113 sq. inches. = πR²

113/π = R²

R = √35.9690

R = 5.9974 ≈ 6 inches

Now, since the diameter of a circle is twice the radius of the circle, therefore, the diameter of the circle will be,

Diameter of the circle = 2 × 6 inches = 12 inches

Hence, the diameter of the circular poll is 12 inches. Thus, the correct option is A.

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Answer:

a. 12 inches

Step-by-step explanation:

113 ÷ 3.14 = 35.98726114649682

2√35.98726114649682 = 5.998938334947011

5.998938334947011 x 2 = 11.99787666989402

keyword approximate ;)

The value of x in the equation is -4.92

The equation is given as:

12x + 59 = 0

Add -59 to both sides of the equation

12x = -59

Divide by 12

x = -59/12

Evaluate

x = -4.92

Hence, the value of x in the equation is -4.92

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[tex]x^2-12x+59=0\\x^2-12x+36+23=0\\(x-6)^2=-23\\x\in\emptyset[/tex]

Step-by-step explanation:

it is a rectangle !

a straight road and its width.

so, the area is (as for any other rectangle)

length×width

in our case

1.4 km × 0.04 km = 0.056 km²

Answer:

Area formula= length x width

length of road= 1.4 km

width of road= 0.04 km

Area= 1.4 x 0.04

= 0.056 km

Answer:

6:5

Step-by-step explanation:

Answer:

70 cm^3; 1000 cm^3; 343 cm^3; 30 cm^3; 48 cm^3

Step-by-step explanation:

to find the volume to all of these shapes you can just multiply all the sides together

one looks like this

2 * 5 * 7 = 70

70 is the answer for the first one

you repeat this 4 more times

since a cube has all equal sides for 2 and 3 you can just cube your side length

10^3 = 1000

7^3 = 343

afterwards since they are all just rectangular prisms you can just multiply all the sides together

1 * 5 * 6 = 30

4 * 6 * 2 = 48

those are your answers

dont forget to add ^3 behind the cm

Step-by-step explanation:

70cm kr 5ko 12m y x W L H V

ksk

The value of the product [tex]\frac{2y}{y -3} \times \frac{4y - 12}{2y + 6}[/tex] is [tex]\frac{4y}{y + 3}[/tex]

The product expression is given as:

[tex]\frac{2y}{y -3} \times \frac{4y - 12}{2y + 6}[/tex]

Factorize each factor of the expression

[tex]\frac{2y}{y -3} \times \frac{4(y - 3)}{2(y + 3)}[/tex]

Cancel the common factors

[tex]\frac{y}{1} \times \frac{4}{y + 3}[/tex]

Evaluate the product

[tex]\frac{4y}{y + 3}[/tex]

Hence, the value of the product [tex]\frac{2y}{y -3} \times \frac{4y - 12}{2y + 6}[/tex] is [tex]\frac{4y}{y + 3}[/tex]

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Answer:

4y/y+3

Step-by-step explanation:

edge 2022

Answer:

3

Step-by-step explanation:

Answer:

(28)  61.5, or $61,500

(29) 49.25, or $49,250

(30) the median

Step-by-step explanation:

(28) the mean can be calculated by adding together the values and then dividing by the total number of values.

(45 + 47 + 47.5 + 51 + 53.5 + 125) / 6 = 61.5

(29) the median can be calculated by crossing off the values from the outside in, alternating sides

45, 47, 47.5, 51, 53.5, 125

47, 47.5, 51, 53.5

47.5, 51

you will end with two middle values since there are six values in the set, so average these to find the median

(47.5 + 51) / 2 = 49.25

(30) The median will better reflect the value of the homes because it is not as much influenced by the outlier value, 125, as the mean is.

Answer:

I. - 4

II. - 3

III. - 5

Step-by-step explanation:

All values are the solution to the inequality

Answer:

[tex]x= -\dfrac {9}2 +\dfrac{\sqrt{57}}{2},~~x = -\dfrac {9}2 - \dfrac{\sqrt{57}}{2}[/tex]

Step-by-step explanation:

[tex]~~~~~~~x^2 +9x +12 = 6\\\\\implies x^2 +9x = 6-12\\\\\implies x^2 +9x = -6\\\\\implies x^2 +2 \cdot \dfrac 92 \cdot x +\left(\dfrac 92\right)^2 -\left( \dfrac 92 \right)^2 = -6\\\\\implies \left(x+ \dfrac 92 \right)^2 -\dfrac{81}{4}= -6\\\\\implies \left(x +\dfrac 92 \right)^2 = -6 + \dfrac{81}4\\\\\implies \left(x + \dfrac92 \right)^2 = \dfrac{57}{4}\\\\\implies x+ \dfrac 92 = \pm\sqrt{\dfrac{57}4}\\\\\implies x = -\dfrac {9}2 \pm\dfrac{\sqrt{57}}{2}[/tex]

The equation of the number of pages Stephanie still needs to read will be n + 45 = 120. Then the correct option is A.

The missing options are given below.

A.  n + 45 = 120

B.  n - 45 = 120

C.  45ⁿ = 120

D.  n/45 = 120

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Stephanie read 45 pages from a book of 120 pages.

Let n be the number of remaining pages.

Then the equation, we have

n + 45 = 120

Then the correct option is A.

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Answer:

[tex]\sqrt 2[/tex]

Step-by-step explanation:

[tex]f(x) = 1-x\\\\|f(i)| = |1-i| = \sqrt{1^2 +1^2 } =\sqrt 2[/tex]

1. Disregard my comment. Since R is said to be a relation from A to B, we take both a ∈ A and b ∈ A. Then the set R is the pairs (a, b) whose entries' sum belongs to B.

We have

• 4 = 1 + 3 = 2 + 2 = 3 + 1, so R contains (1, 3), (2, 2), and (3, 1)

• 5 = 1 + 4 = 2 + 3 = 3 + 2 = 4 + 1, so R contains (1, 4), (2, 3), (3, 2), and (4, 1)

• 6 = 1 + 5 = 2 + 4 = … = 5 + 1, so R contains (1, 5), (2, 4), …, (5, 1)

Then

R = {(1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4),

…     (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)}

2. The domain of R is the set of all values a in the pairs (a, b) belonging to R :

dom(R) = {1, 2, 3, 4, 5}

3. The range of R is the set of all values b in those same pairs:

range(R) = {1, 2, 3, 4, 5}

4. The inverse of R is the set with the same elements as R, but the entries are swapped:

inv(R) = {(3, 1), (4, 1), (5, 1), (2, 2), (3, 2), (4, 2),

…            (1, 3), (3, 2), (3, 3), (1, 4), (2, 4), (1, 5)}

In this case, we have R = inv(R).

Answer:

6, 8, 10

Step-by-step explanation:

Where:

a = 6

b = 8

c = 10

Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]

[tex]6^2 + 8^2 = c^2[/tex]

[tex]36 + 64 = c^2[/tex]

[tex]100 = c^2[/tex]

c = [tex]\sqrt{100}[/tex]

c = 10

Step-by-step explanation:

I think you mean triangle XYZ. and angle XYZ.

so, the angle at Y is 90°.

that makes XZ the Hypotenuse (baseline opposite of the 90° angle) of the right-angled triangle.

so, we can actually use Pythagoras (we don't need the area of the triangle to solve) :

13² = 12² + YZ²

169 = 144 + YZ²

25 = YZ²

YZ = 5 cm

just to check - the area of this triangle is (remember, it is a right-angled triangle, so XY and YZ serve also as baseline and height) :

area = 12 × 5 / 2 = 60/2 = 30 cm²

correct, it fits.

All the numbers follow a pattern of division by 2

Therefore the next number is 3/2 which is equal to 1.5

i would recommend setting a schedule for each day. a to do list can also help. this can help you stay on track make a list of things you need to do and have set goals for every week or month. if you're studying something you dont like, i would recommend doing pomodoros. you can find videos to follow along to.

i hope this was helpful!

Step-by-step explanation:

the answer is true

the statement is true