I need help on both please

Answer:

x = -4.5

Step-by-step explanation:

We shall be using the following property of logarithms;

[tex]lna+lnb=ln(a*b)[/tex]

Therefore, In -x + In 8 can be re-written as;

[tex]ln-x+ln8=ln(-8x)\\\\ln(-8x)=ln36\\\\-8x=36\\\\x=-4.5[/tex]

Hey there! :)

Equation 1 : -5x + 3y = 2

Equation 2 : -5x - 5y = -30

Because both equations contain a like term (which in this case is 5x), we can easily subtract these equations from one another.

Subtract equation 1 from equation 2 :

-5x - (-5x) = 0

3y - (-5y) = 3y + 5y --> 8y

2 - (-30) = 2 + 30 --> 32

This leaves us with 8y = 32. Simplify this to get y by dividing both sides by 8.

8y ÷ 8 = 32 ÷ 8

Simplify.

y = 4

Now, plug in 4 for y in our first equation.

-5x + 3(4) = 2

Simplify.

-5x + 12 = 2

Subtract 12 from both sides.

-5x = 2 - 12

Simplify.

-5x = -10

Divide both sides by -5.

-5x ÷ -5 = -10 ÷ -5

Simplify.

x = 2

Therefore, our answer is :

(2, 4) where x = 2, y = 4

~Hope I helped!~

Answer:

see explanation

Step-by-step explanation:

Given

2x - [tex]\frac{3}{x}[/tex] = 1

Multiply through by x

2x² - 3 = x ( subtract x from both sides )

2x² - x - 3 = 0 ← in standard form

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

The factors are + 2 and - 3

product = 2 × - 3 = - 6 and sum = 2 - 3 = - 1

Use these factors to split the x- term

2x² + 2x - 3x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x + 1) - 3(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]

Answer:

C

Step-by-step explanation:

We know a straight angle is 180 degrees ( a straight line).

Looking at the figure, we can say that A + F + E = 180 (since it creates a straight line).

We know A = 45, E = 85, plugging these into the equation, we can solve for F:

A + F + E = 180

45 + F + 85 = 180

130 + F = 180

F = 180 - 130

F = 50

Answer choice C is right.

Answer:

Step-by-step explanation:

It seems that the question was cut off before it was completed. To provide an answer related to the domain in mathematical terms, the domain is an essential component of a function. Let me explain it in detail:
In mathematics, when we talk about a function, f(x), the domain of the function represents the set of all possible input values (x-values) for which the function is defined. It's essentially the set of "allowable" values that we can plug into our function to get an output.
To determine the domain of a given function, we have to consider the nature of the function itself and any mathematical rules or constraints that apply. Here are several examples that can come up:
1. **For a polynomial function**, such as f(x) = x^2 - 3x + 2, there's no restriction on the x-values. So the domain is all real numbers, often written as (-∞, ∞).
2. **For a rational function** (a ratio of two polynomials), like f(x) = (2x + 1) / (x - 3), we must exclude x-values that would make the denominator equal to zero, since division by zero is undefined. In this case, the domain is all real numbers except x = 3, or in interval notation: (-∞, 3) U (3, ∞).
3. **For a square root function**, such as f(x) = √(x - 4), the expression inside the square root must be non-negative, since we're typically considering real-valued functions. So the domain of this function is x ≥ 4, or in interval notation, [4, ∞).
4. **For a logarithmic function**, like f(x) = log(x), the argument of the logarithm must be positive. Therefore, the domain is x > 0, or in interval notation, (0, ∞).
5. **For trigonometric functions**, such as f(x) = sin(x), since there are no restrictions on the input of sine function in terms of real numbers, the domain is all real numbers.
In conclusion, to define the domain of a particular function, we need to consider the mathematical constraints such as not dividing by zero, keeping the radicand of square roots non-negative, and ensuring the arguments of logarithms positive, among others. Once these conditions are taken into account, we can specify the domain of the function, which is often expressed as an interval or a set of intervals on the real number line.

6 ft person casts 18 ft shadow

x ft tree casts 20 ft shadow

6*20 = 18x

120 =18x

x=120/18

×≈6.67

The height of the tree is 6.67 feet.

The term proportionality describes any relationship that is always in the same ratio.

Given that, a tree casts a 20-foot shadow at the same time the person who is 6 feet tall casts a shadow 18 ft, we need to find the height of the tree.

Here, using the concept of proportionality, since, the phenomena is happening at the same time, therefore, the ratio of the height and length if the shadow will be equal for all.

Let the height of the tree be x,

20 / x = 18 / 6

120 = 18x

x = 6.67

Hence, the height of the tree is 6.67 feet.

Learn more about proportionality, click;

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[tex]b=a+5[/tex]

Hope this helps.

Answer:

b=a+5

Step-by-step explanation:

6-1=5

7-2=5

8-3=5

9-4=5

Please rate brainliest! :D

Answer:

1. J=10

2. L<=7

3. h>32

4. O=15

5. q<=17

Step-by-step explanation:

J/10+4=5

subtract 4 from both sides

j/10=1

multiply 10 by both sides

j=10

-7L+5>=-49

subtract 5 from both sides

-7L>=-49

divide by -7 and change your symbol

L<=7

9+h/2>16

subtract 9 from both sides

h/2>16

multiply by 2 on both sides

h>32

O-5/2=5

multiply by 2 on each side

O-5=10

add 5 on each side

O=15

8q+2<=138

subtract 2 from both sides

8q<=136

divide by 8 on both sides

q<=17

Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = [tex]a_{2}[/tex] - [tex]a_{1}[/tex] = [tex]a_{3}[/tex] - [tex]a_{2}[/tex]

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

--------------------------------------------------------

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d

[tex]a_{1}[/tex] = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

[tex]a_{8}[/tex] = 4 + (7 × 5) = 4 + 35 = 39

Answer:

Area = 40

Step-by-step explanation:

The area of a rhombus is

Area = a*b/2

Where a and b are the lengths of the diagonals.

Area = 8 * 10/2

Area = 40

Answer:

40

Step-by-step explanation:

In a rhombus the two diagonals intersect perpendicularly. So you can see a rhombus as the union of two triangles whose base is one of the diagonals of the rhombus and whose height is the half of the other diagonal.

Therfor you can calculate the area of the rhombus calculating the area of the two triangles that are the same.

In this case the area of each triangle must be  [tex]\frac{4\times 10}{2}= 20[/tex] (if you take the 10-lenght-side as the basis of the triangles).

Hence the area of the rhombus is 40 because is the double of the area of each triangle.

Answer:

48xy+4

Step-by-step explanation:

Because we know that a square has 4 sides, we can multiply this expression by 4, thus ending in 48xy+4. Hope this helps :)

For this case we have by definition, that the perimeter of a square is given by the sum of its sides. As the sides measure the same, then the perimeter is:

[tex]p = 4l[/tex]

Where "l" represents the side of the square:

Then, they tell us that:

[tex]l = 12xy + 1[/tex]

So:

[tex]p = 4 (12xy + 1)\\p = 48xy + 4[/tex]

ANswer:

[tex]p = 48xy + 4[/tex]

Answer:

sqrt(61)

Step-by-step explanation:

The distance between two points is found by the following formula

d = sqrt (( x2-x1)^2 + (y2-y1)^2 )

   = sqrt( (-1--6)^2 + (1-7)^2)

  = sqrt( (-1+6)^2 + (1-7)^2)

= sqrt( (5)^2 + (6)^2)

= sqrt( 25 + 36)

= sqrt(61)

Answer:

The answer is D.The arrangement of words and phrases suggests a thought process that flits from thought to thought.

Step-by-step explanation:

The best description of the syntax in the given text indicates that the arrangement of words and phrases suggests a thought process that moves erratically from one thought to another, reflecting the text's stream-of-consciousness style and mixed sentence constructions.

The question involves analyzing an excerpt for the syntax used, which refers to the manner by which words are organized into sentences. Among the given choices, the best description that matches the details provided about the text would be D) The arrangement of words and phrases suggests a thought process that flits from thought to thought. This is supported by the description of the text which includes mixed sentence constructions, lack of consistency in grammatical paths, and an attempt by the author to meet or challenge conventional expectations in rhetorically effective ways. The text also mentions the replication of a child's growing awareness and a stream-of-consciousness style which implies a thought process that is not linear but more erratic and intuitive, which is characteristic of syntax that flits from thought to thought.

Answer:

The given quadrilateral is a rectangle.

Step-by-step explanation:

We are given the vertices of a quadrilateral,

We can use the slopes and modulus of all sides to determine whether it is a rectangle or not. The four sides of the quadrilateral are Ab, BC, CD and AD. So finding slopes of all sides using the formula

[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where x_1 and y_1 are the coordinates of firsst vertex and x_2 and y_2 are coordinates of second vertex.

So.

Slopes are:

Slope of AB = 2 and Length=2.23

Slope of BC = -1/2 and length = 4.47

Slope of CD = 2 and length = 2.23

Slope of AD = -1/2 and length = 4.47

As we can see that the slope of AB and CD is equal which means that they are parallel and their lengths are also same.

Similarly BC and AD have same slope which means that they are also parallel and their lengths are also equal.

More over the product of slopes of AB and CD, BC and CD, CD and AD and AD and AB is equal to -1 which indicated that these sides are parallel to each other so it can be concluded that as the opposite sides of the quadrilateral are equal and the interior angles are 90 degrees so the quadrilateral is a rectangle ..

Answer:

I am given that the vertices of quadrilateral ABCD are A(-1, 6), B(-2, 4), C(2, 2), and D(3, 4). The slope formula applied to each pair of adjacent vertices gives the slopes (m) of the sides:

slope of AB (m AB) = 4 - 6 / -2 - -1)  = -2 / -1 =2

slope of BC (m BC) = 2 - 4 / 2 - (-2)  = -2 / 4 = - 1 / 2

slope of CD (m CD) = 4 - 2 / 3 -2  = 2 / 1 =  2

slope of DA (m DA) = 6 - 4 / - 1 -3  = 2 / - 4 =  - 1 / 2

Because line segments with equal slopes are parallel, segment AB is parallel to segment CD and segment BC is parallel to segment DA.

Multiplying the slopes of one pair of adjacent sides, I find that.

mAB * mBC = 2 * - 1/2 = - 1

If the product of the slopes of two segments is -1, then they are perpendicular. Since both pairs of opposite sides have been proven parallel, proving one pair of adjacent sides perpendicular implies that the other pair of adjacent sides are also perpendicular. Therefore, by definition, quadrilateral ABCD is a rectangle.

Step-by-step explanation:

Answer:

None of the above

Step-by-step explanation:

2 r + ( t + r )

2 r + t + r

3 r + t

Answer:

880

Step-by-step explanation:

First we have to convert 1 mile into inches.

1 mi * 5280 ft/mi * 12 in/ft = 63,360 inches

Each rotation covers 72 inches, so the number of rotations is:

63,360 in / (72 in / rotation) = 880 rotations

Answer:

880

Step-by-step explanation:

I got it right on my test.

Answer:

The ratio between their surface areas = 49/9

Step-by-step explanation:

* Lets revise the similarity of to prism

- If two prisms are similar, then there is a ratio between their

 corresponding dimensions

- There is a ratio between their volumes and surface area

- The the ratio between their corresponding dimensions is a/b,

  then the ratio between their volumes is (a/b)³ and the ratio between

 their surface area is (a/b)²

* Lets solve the problem

∵ The two rectangular prisms are similar

∵ The ratio between their corresponding sides is 7/3

∴ The ratio between their surface areas = (7/3)² = 49/9

* Lets check our answer

∵ The surface area of the rectangular prism is :

  S.A = Perimeter of base × its height + 2 × area of its base

- Find the surface area of the large prism

∵ The base has dimensions 14 units and 21 units

∵ Its height = 7 units

∵ The base is a rectangle

∵ Perimeter the rectangle = 2L + 2W

∵ Area the rectangle = L × W

∴ S.A = (2×14 + 2×21) × 7 + 2(14 × 21) = 1078 unit²

- Find the surface area of the small prism

∵ The base has dimensions 6 units and 9 units

∵ Its height = 3 units

∴ S.A = (2×6 + 2×9) × 3 + 2(6 × 9) = 198 unit²

- Lets find the ratio between them

∴ The ratio between surface areas of them = 1078/198 = 49/9

- It is the same with the answer above so we are right

since this a 45 45 90 right triangle to get the side lengths you divide 2 times the square root of 2 and you get 2, since this has two congruent angles which makes it an Isosceles triangle. your a and b value are 2.

[tex](4t-\dfrac{8}{5})-(3-\dfrac{4}{3}t)---------------\dfrac{16t}{3}-\dfrac{23}{5}[/tex]

[tex]5(2t+1)+(-7t+28)--------------3t+33[/tex]

[tex](\dfrac{-9}{2}t+3)+(\dfrac{7}{4}t+33)-----------------\dfrac{-11t}{4}+36[/tex]

[tex]3(3t-4)-(2t+10)-------------7t-22[/tex]

a)

[tex](4t-\dfrac{8}{5})-(3-\dfrac{4}{3}t)[/tex]

Firstly we will open the parentheses term and then on combining the like terms and then solving them.

[tex]=4t-\dfrac{8}{5}-3+\dfrac{4}{3}t\\\\i.e.\\\\=4t+\dfrac{4}{3}t-\dfrac{8}{5}-3\\\\=\dfrac{4t\times 3+4t}{3}+\dfrac{-8-3\times 5}{5}\\\\=\dfrac{16t}{3}-\dfrac{23}{5}[/tex]

b)

[tex]5(2t+1)+(-7t+28)\\\\=5\times 2t+5\times 1-7t+28\\\\=10t+5-7t+28\\\\=10t-7t+5+28\\\\=3t+33[/tex]

( Here we used distributive property for first bracket and open the parentheses term and them we combined the like terms and finally simplified our terms )

c)

[tex](\dfrac{-9}{2}t+3)+(\dfrac{7}{4}t+33)[/tex]

We firstly open our parentheses term but there will be no change in the terms since the sign before parentheses is positive.

and then we will combine the like terms and simplify them.

[tex]=\dfrac{-9}{2}t+3+\dfrac{7}{4}t+33\\\\\\=\dfrac{-9}{2}t+\dfrac{7}{4}t+3+33\\\\\\=\dfrac{-9t\times 2+7t}{4}+36\\\\\\=\dfrac{-11t}{4}+36[/tex]

d)

[tex]3(3t-4)-(2t+10)[/tex]

i.e. we use the distributive property for first bracket and open second parentheses term. since the sign before the second parentheses is negative hence the sign of the terms will get interchanged.

i.e.

[tex]=3\times 3t+3\times (-4)-2t-10\\\\i.e.\\\\=9t-12-2t-10\\\\=9t-2t-12-10\\\\=7t-22[/tex]

ANSWER

C [0,9]

EXPLANATION

The number of bottled water on the shelf is modeled by the function

[tex]4x + y = 36[/tex]

We make y the subject to obtain;

[tex]y = 36 - 4x[/tex]

When no water is sold, then x=0.

When all the bottles are sold, then

[tex]4x - 36 = 0[/tex]

[tex]4x = 36[/tex]

[tex]x = \frac{36}{4} = 9[/tex]

Therefore the store cannot sell more than 9 bottles.

The domain is [0,9]

Answer:

B. 8.37 ft

Step-by-step explanation:

⇒This question is on circumference

⇒The water sprinkler covers a circular pattern as it moves to cover 300° and remain with 60° to cover so as to complete a single circular pattern.

⇒The remaining distance asked is the one represented by 60°

⇒Apply the formula for circumference of a circle with angle theta

[tex]c=2\pi r\alpha/360[/tex]   where alpha is the angle in degrees

Given that r=8ft and ∝=60°

c=3.14×2×8×60°/360°

c=8.37 ft

Your answer should be x < 0 or x > 4.

I'm 3 Brainliests away from ranking up, so one would be much appreciated. Thank you, and good luck!

Final answer:

The reference angle of -150 degrees is found by first determining the positive angle in standard position by adding 180 degrees, resulting in 330 degrees. Since 330 degrees is in the fourth quadrant, we subtract it from 360 degrees to get the reference angle, which is 30 degrees.

Explanation:

To find the reference angle of -150 degrees, we must determine the smallest angle between the terminal side of the given angle and the x-axis. A reference angle is always positive and measured between 0 to 90 degrees. Since -150 degrees is in the third quadrant when considering standard position in a coordinate system, where angles are measured counterclockwise from the positive x-axis, you add 180 degrees to determine its corresponding positive angle in the second quadrant. Therefore, the reference angle of -150 degrees is:

180° - (-150°) = 180° + 150° = 330°

Since 330 degrees is in the fourth quadrant, to find the reference angle, we subtract it from 360 degrees:

360° - 330° = 30°

Thus, the reference angle for -150 degrees is 30 degrees.

Answer:  B) y = -4 sin(x - π/2)

Step-by-step explanation:

The graph of a sine function is the cosine function shifted π/2 units to the right.

Similarly, the graph of a cosine function is the sine function shifted π/2 units to the left.

We have the function [tex]y = \frac{2}{3} x -3[/tex] and we want to find a function that has the same y-intercept than the previous function.

First, let's find the y-intercept by subtituting 0 for 'x'.

[tex]y = \frac{2}{3} (0) -3 = -3[/tex]

Now that we found that y-intercept =-3, any lineal function of the type: [tex]y = ax - 3[/tex] will have the same y-intercept. Where 'a' can take all the real values.

Also, any quadratic function of the type: [tex]y=ax^{2} + bx - 3[/tex] will have the same y-intercept. Where 'a' and 'b' can take all the real values.

Answer:

r=64°

Step-by-step explanation:

angles in a triangle = 180°

180 -37 -27 = 116

angles in a straight line = 180°

180 -116 = 64

r= 64

Answer:

d. 64

Step-by-step explanation: i had it on usa testprep

Answer:4/3

Step-by-step explanation:BY PHYTHAGORAS THEOREM

OPP=X,ADJ=3,HYP=5

5^2=3^2+X^2

25=9=X^2

25-9=X^2

16=X^2

4=X

BY TRIGONOMERTRY

SOHCAHTOA

TAN=OPP/ADJ

=4/3

The answer is:

[tex]Tan(\beta)=Tan(53.13)=1.33\°[/tex]

or

[tex]Tan(\beta)=\frac{4}{3}[/tex]

To find the answer, we first need to find the value of the given angle, we can calculate it since we already know the cosine of that angle.

So, solving we have:

[tex]Cosine(\beta)=\frac{3}{5} \\\\Cosine((\beta)^{-1}=Arccos(\frac{3}{5})\\\\\beta =53.13\°[/tex]

Now, that we know that the angle is equal to 53.13°, we can calculate the value of the tangent, so:

[tex]Tan(\beta)=Tan(53.13)=1.33\°[/tex]

Also, we can find it using the Pythagorean Theorem and the trigonometric identities:

We have that:

[tex]Cosine=\frac{Adjacent}{Hypothenuse}[/tex]

So, using the given information we have:

[tex]Cosine=\frac{3}{5}[/tex]

Where,

Hypothenuse, is equal to 5.

Adjacent, side is equal to 3.

So, we are looking for the opposite side.

Then, substituting it into the Pythagorean Theorem formula, we have:

[tex]Hypothenuse^{2}=Adjacent^{2}+Opposite^{2}\\\\5^{2}=3^{2}+Opposite^{2}\\\\Opposite^{2}=25-9=16\\\\Opposite=\sqrt{16}=4[/tex]

Now that we already know the opposite side, we can find the value of the tangent that will be:

[tex]Tan(\beta)=\frac{Opposite}{Adjacent}=\frac{4}{3}[/tex]

Have a nice day!

Answer: 48

96/2 = 48 cm

Answer:

ab = 48 cm

Step-by-step explanation:

Supposing ABC is a right angled triangle where m∠B = 90°, ac = 96 cm and c = 30°, we are to find the length of the side ab in cm.

For this, we will use the trignometric ratios to find ab.

[tex] sin B = \frac { a b } { a c } [/tex]

[tex] sin 30 = \frac { a b } { 9 6 } [/tex]

[tex]\frac{1}{2} =\frac{ab}{96}[/tex]

[tex]96=2ab[/tex]

[tex]ab=\frac{96}{2}[/tex]

ab = 48 cm

Answer:

2.  18 cubic cm.

3. 27 cubic cm

5. 90 cubic m

Step-by-step explanation:

2. Triangular prism

So, we have a triangular prism with a width of 3 cm, a height of 1.5 cm and a length of 4.  We'll take the triangle shape as the base.

Like for any prism, the volume is the base multiplied by the height.

So, the area of the base is found with the regular formula: base x height:

so, 3 x 1.5 = 4.5 sq cm for the base.

Then we multiply the base by the length to get the volume: 4.5 x 4 = 18 cubic cm.

3. Trapezoidal prism

Again, first step is to calculate the area of the trapezoid shape, then multiply by its depth.

The area of a trapezoid is calculated with the formula:

A = h/2 * (a + b) where a and b represent the short and long sides respectively.

So, for our given trapezoid:

A = 1.5/2 * (2+4) = 0.75 * 6 = 4.5 sq cm.

Then we multiply the base area by the height to get the volume:

V = 4.5 * 6 = 27 cubic cm

5. Triangular prism 2

The best way to approach this one is to consider it's a triangle prism with a height of 3 cm, and use the triangle shape (with sides of 13 and 5) as the base.

But to calculate the area of that triangle we need to find out the missing length. Using Pythagore's theorem, we can easily find the length of the other side with the hypotenuse formula:

hypotenuse² = sideA² + sideB²

In our case, we have:

13² = x² + 5²

169 = x² + 25

x² = 144

x = 12

Now we can calculate the area of the triangle easily:

A = (b x h)/2 = (5 x 12)/2 = 30 sq m

Then multiply by the thickness of the prism....

V = 30 x 3 = 90 cubic m

Answer:

y-axis The vertical number line in a coordinate graph. The line in the coordinate plane, usually vertical, or in space, containing those points whose first coordinates (and third, in space) are 0. y-coordinate The second coordinate of an ordered pair or ordered triple.

Step-by-step explanation: