Which is 5logx - 6log(x-8) written as a single logarithm?

ANSWER

5.5

EXPLANATION

We can use the cosine rule to find the missing side length.

The cosine rule is given as;

[tex] {a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos( A) [/tex]

Let the missing side be "a".

Then,

[tex] {a}^{2} = {9}^{2} + {6}^{2} - 2 \times 9 \times 6 \cos(37 \degree) [/tex]

[tex] {a}^{2} = 81+ 36- 86.253[/tex]

[tex] {a}^{2} = 30.74736[/tex]

[tex]a = \sqrt{30.747} [/tex]

[tex]a \approx5.5[/tex]

Therefore the missing side length is approximately 5.5 units to the nearest tenth.

Step-by-step explanation:

4/5x+5<-3

4/5x<-8

4x<-40

x<-10

Answer: option a.

Step-by-step explanation:

To solve the given exercise nad write the expression as a single logarithm, you must keep on mind the following properties:

[tex]ln(a)+ln(b)=ln(ab)\\m*ln(a)=ln(a)^m[/tex]

Therefore, by applying the properties shown above, you can rewrite the expression given, as following:

[tex]lnx^{2}+3lny=lnx^2+lny^3=ln(x^2y^3)[/tex]

Then, the answer is the option a.

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=7850 \end{cases}\implies 7850=2\pi r\implies \cfrac{7850}{2\pi }=r\implies 1249.37\approx r[/tex]

Answer:

1249.37 units

Step-by-step explanation:

Answer:

[tex]\$103.75[/tex]

Step-by-step explanation:

step 1

Find the area of the gate

The area of the gate is equal to the area of a trapezoid minus the area of the rectangular glass panel

[tex]A=\frac{1}{2}(10+7)(5)-(0.71)(1.43)= 41.5\ ft^{2}[/tex]

step 2

Find the cost

Multiply the total area by $2.50  

so

[tex]41.5*2.50=\$103.75[/tex]

Answer:

4.02

Step-by-step explanation:

4+0.02=4.02

The number represented by the expanded form (4 × 1) + (2 × 0.01) can be presented in other forms such as decimal form (4.02), fraction form (402/100), percentage form (402%), or scientific notation (4.02 x 100).

The expanded form of a number is a way of breaking down the number into its parts. In this specific question, the expanded form of the number given is (4 × 1) + (2 × 0.01). This form shows the number 4.02 in a decomposed format. To write the number 4.02 in another format, we can use the decimal form, fraction form, percentage form, or even scientific notation.

For instance:

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Answer: Third option.

Step-by-step explanation:

Calculate the area of the gate (including the glass panel) which has the shape of a trapezoid.

The formula for calculate the area of a trapezoid is:

[tex]A=\frac{h}{2}(B+b)[/tex]

Where h is the height, B is the larger base and b is the smaller base.

In this case:

[tex]B=10ft\\b=7ft\\h=5ft[/tex]

Substituting, you get:

[tex]A_{gate}=\frac{5ft}{2}(10ft+7ft)=42.5ft^2[/tex]

Calculate the area of the rectangular glass panel, with the formula:

[tex]A_{panel}=l*w[/tex]

Where the lenght is [tex]l=1.43ft[/tex] and the width is [tex]w=0.71ft[/tex]

Then:

[tex]A_{panel}=(1.43ft)(0.71ft)=1.01ft^2[/tex]

The area he needs to paint is:

[tex]A=A_{gate}-A_{panel}\\A=42.5ft^2-1.01ft^2\\A=41.49ft^2[/tex]

If painting the gate costs $2.50 per ft², for 41.49 ft² he will have to spend:

[tex]=(41.49)(\$2.50)\\=\$103.725[/tex]

Therefore the answer is the third option.

To calculate the cost of painting the gate, find the area of the glass panel by multiplying its length and width. Multiply the area by the cost per square foot to find the total cost.

To calculate the cost of painting the gate, we need to find the area of the glass panel first. Let's say the length of the panel is 'l' feet and the width is 'w' feet. The area of a rectangle is given by the formula A = l × w. Once we have the area, we can multiply it by the cost per square foot ($2.50) to find the total cost. So the formula to calculate the cost of painting the gate is: Cost = Area × Cost per square foot. Substitute the values you know into the formula and solve for the cost.

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Answer: 2.5 or 2 1/2

Step-by-step explanation:

You can convert the mixed fractions to decimal numbers:

- Divide the numerator by the denominator of the fraction.

- Add the result to the whole number.

Thenyou have:

Barbara's time: [tex]3\ 3/10=3+0.3=3.3[/tex]

Donna's time: [tex]2\ 4/5=2+0.8=2.8[/tex]

Cindy's time: [tex]4\ 3/5=4+0.6=4.6[/tex]

Nicole's time: [tex]2\ 1/10=2+0.1=2.1[/tex]

As you can see, the fastest girl is Cindy and the slowest girl is Nicole.

Then, you must make the following subtraction to calculate the difference:

[tex]4.6-2.1=2.5[/tex] or 2 1/2

Answer:

Cindy's correct time is 3 2/5 (for the portfolio assignment that this question goes with).

Step-by-step explanation:

ANSWER

The height of the square pyramid is 4.8m

EXPLANATION

The volume of a square pyramid is calculated using the formula:

[tex]Volume = \frac{1}{3}(base \: area) \times height[/tex]

It was given that;

The volume of the square pyramid is

[tex]25 \frac{3}{5} {m}^{3} [/tex]

The side length of the square base is

[tex]4m[/tex]

We substitute the given values and then solve for the height.

[tex]25 \frac{3}{5} = \frac{1}{3}( {4}^{2} ) \times height[/tex]

We solve for the height to obtain;

[tex]height = \frac{25 \frac{3}{5} }{ \frac{16}{3} } [/tex]

We simplify to get;

[tex]height = 4.8m[/tex]

Hence, the height of the square pyramid is 4.8 meters.

Answer:

The height of the square pyramid is 4.8 meters.

Step-by-step explanation:

I just know

Answer:

Option A. 3.5x + 15 ≥ 55

Step-by-step explanation:

Points Rosh received for becoming a member = 15

Points Rosh received for visiting the moving theater = 3.5

Total points needed for a free movie ticket = 55

For each visit he receives 3.5 points, so for x visits he will receive 3.5x points.

Total points = Points received on becoming a member + Points received on x visits

So,

Total Points = 15 + 3.5x

These points must be at least 55 for a free movie ticket. At least means equal to or greater than. So the total points must be equal to or greater than 55 in order to earn a free movie ticket. This can be expressed as:

3.5x + 15 ≥ 55

So, option A gives the correct answer

Answer:

option. A

Step-by-step explanation:

I had the exacgt same question

Answer:

the answer is 119g

Step-by-step explanation:

x-120/4.3=-0.25

x-120=-1075

x=118.925=119g

Approximately 40% of the tomatoes weigh less than 119 g.

The correct answer is option D.

A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.

It measures the unusual or extreme a particular data point is compared to the rest of the distribution

We have,

To solve this problem, we can use the cumulative distribution function (CDF) of the normal distribution.

The CDF gives the probability that a random variable is less than or equal to a given value.

Given that the mean of tomato weight is 120 grams and the standard deviation is 4.3 grams,

We can use this information to find the probability that a randomly selected tomato weighs less than a certain amount.

Let's calculate the z-score for each option:

A. 111 g:

z-score = (111 - 120) / 4.3 ≈ -2.093

B. 114 g:

z-score = (114 - 120) / 4.3 ≈ -1.395

C. 117 g:

z-score = (117 - 120) / 4.3 ≈ -0.698

D. 119 g:

z-score = (119 - 120) / 4.3 ≈ -0.233

Now, we can use a standard normal distribution table or a calculator that provides the cumulative distribution function (CDF) of the standard normal distribution to find the probability corresponding to each z-score.

The option with the highest probability, or approximately 40%, is the correct answer.

Based on the calculations, it appears that option D. 119 g has the highest probability of approximately 40% for a tomato weighing less than that amount.

Thus,

Approximately 40% of the tomatoes weigh less than 119 g.

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Answer:

Step-by-step explanation:

Left Frame

Consecutive angles (angles that are one after another) add up to 180 degrees. (The are supplementary).

9x + 6x = 180o               Combine like terms

15x = 180o                      Divide by 15

15x/15 =180/15

x = 12

===============

You could do this the way it is done in the more formal proof.

9x + 6x + 9x + 6x = 360     Combine like terms: each quadrilateral = 180o

30x = 360                            Perform Division Property of equality

x = 360/30                           Do the division

x = 12

Right frame

The left side of line 3 is the substitution property.

<A = 9x

<B = 6x

<C = 9x

<D = 6x

The left side of line 4 is 30x. This comes from 9+6 + 9 + 6

The right side of line 5 is the division property of equality

Answer:

the pdf wnt lad gimme dem pons doe

Step-by-step explanation:

Answer:The answer is x=12

Step-by-step explanation: 2*6=12 and 12/6=2

Answer:

x = 12

Step-by-step explanation:

12/6 = 2

Answer:

16.51

Step-by-step explanation:

In a parallelogram, the opposite angles are always equal in measure. So two of the angles in the parallelogram measure 39 degrees each.

The sum of angles of the parallelogram must be 360 degrees. Let the other two angles be x degree each. We can set up the following equation for the angles:

39 + 39 + x + x = 360

78 + 2x = 360

2x = 282

x = 141

This means, the other two angles measure 141 degree each. The shorter diagonal will be opposite to the shorter angle.

Hence, the diagonal opposite to the angle 39 degree will be the shorter one. A diagonal divides the parallelogram in two triangles. So we will have two sides and an included angle and we have to find the third side of the triangle which can be found using the law of cosines. Let the third side be c as shown in image below, using the law of cosines, we can write:

[tex]c^{2} = a^{2}+ b^{2} -2ab cos(\gamma)\\\\c^{2}=18^{2}+26^{2}-2(18)(26)cos(39)\\\\ c^{2}=272.59\\\\ c=16.51[/tex]

Thus the shorter diagonal will be 16.51 feet in measure.

To find the shorter diagonal of a parallelogram with given side lengths and angle, use the formula √(a^2 + b^2 - 2abcosθ).

To find the shorter diagonal of a parallelogram, we need to use the formula:

Shorter diagonal = √(a^2 + b^2 - 2abcosθ)

Where a and b are the sides of the parallelogram and θ is the angle between them.

Using the given information, we have a = 18 ft, b = 26 ft, and θ = 39°.

Substituting these values into the formula, we get:

Shorter diagonal = √(18^2 + 26^2 - 2(18)(26)cos(39°))

Calculating this expression gives us:

Shorter diagonal ≈ 9.15 ft

Answer:

380.13 m

Step-by-step explanation:

You first need to write down the Area formula for a circle which is  A=pi x radius^2 .

So 11^2 x 3.1415...

121 x 3.1415... = 380.13 m

[tex]x - |-20| = |-34|\\x-20=34\\x=54[/tex]

Answer:

4(9x-4)

Step-by-step explanation:

➷ Find the greatest common factor between the two values:

In this case, it is 4

This value will go outside the parenthesis

Divide each of the values by 4:

36x/4 = 9x

-16/4 = -4

The final answer is 4(9x - 4)

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Answer:

The y-coordinate of the y-intercept is [tex]-4[/tex]

Step-by-step explanation:

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

In this problem we have

[tex]F(x)=-3x^2+5x-4[/tex]

Find the y-intercept

For [tex]x=0[/tex]

[tex]F(0)=-3(0)^2+5(0)-4=-4[/tex]

The y-intercept is the point [tex](0,-4)[/tex]

therefore

The y-coordinate of the y-intercept is [tex]-4[/tex]

Answer:

The value would be -4.

Step-by-step explanation:

Answer:

1 1/4

Step-by-step explanation:

rigjt answer

Diagonal = SQRT(8^2 + 12^2 + 30^2)

Diagonal = SQRT(64 + 144 + 900)

Diagonal = SQRT(1108)

Diagonal = 33.3 feet

Answer: step 3

I just took the test and got a 100%

Answer:

Step 3

Step-by-step explanation:

Here, the given expression,

[tex]7b + 3.2b - 5 = 18.92[/tex]

Since, when we solve the given expression the steps of solution are as follows,

Step 1 : 7b + 3.2b - 5 = 18.92

Step 2 : 10.2b - 5 = 18.92      ( Combining like terms in left side )

Step 3 : 10.2b = 23.92           ( Adding 5 on both sides )

Step 4 : b = 4.6                       ( Dividing both sides by 10.2 )

Hence, by the above explanation it is clear that she made her mistake in step 3 ( she did not add 5 on right side )

Answer:

Step-by-step explanation:

(a) when there is a negative in front of the leading coefficient  (- x^2), that is a reflection over the x axis.  a regular parabola opens up.  In this case, the negative in front of the first term makes it open downward.  

-f(x) is a reflection    so -2x^2 would open downward.

(b) the vertex of the parabola is -b/2a

in this problem a x^2 + bx + c = y

                         -2x^2 + 4x + 3 = y

a = -2, b = 4, c = 3

formula for vertex -b/2a  = -4/2(-2)    = -4/-4  = 1    This is the x-value of the vertex.  Plug back into original equation to find the y value.

(1, ?)    -2(1)^2 + 4(1) + 3 = 5

vertex is (1,5) and is above the x axis

[tex]\begin{cases}4x - y = 16 \\2x + 3y = - 2 \end{cases} \\ \Leftrightarrow \begin{cases}4x - y = 16 \\4x + 6y = - 4 \end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{y + 16}{4} \\7y = - 20 \end{cases} \\ \Leftrightarrow \begin{cases}x = \frac{23}{7} \\y = - \frac{20}{7} \end{cases}[/tex]

Maybe you wrote the system wrong somewhere because there is no right answer

Answer:

Angle of 1 part: 40°

Angle of 2 parts: 80°

Step-by-step explanation:

Angles in a circle / Equal parts of a circles = Angle of 1 part

360/9 = 40°

40 x 2 = 80

Answer:

Yes - he is correct

Step-by-step explanation:

If she has 75 pennies, she would have 15 rows with 5 pennies in each row with a 3:5 ratio for the rectangle.

Lata's father is correct.

Rectangle is a type of quadrilateral having two opposite sides that are equal in measurement.All the angles of Rectangle are of 90°.

Area of rectangle = Length * Width

Perimeter of rectangle =2(length + width)

Given,

Total number of pennies Lata have  = 75

If she arranges the pennies in 15 rows with 5 pennies in each row.

i.e; 15 * 5 = 75

Then she will get Rectangle of side of length 15 and width 5

So, her father is correct.

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Answer:

1. B 2. C

Step-by-step explanation:

1. B is the answer because if you add 8 times 1 to 11 you get 19 and if you add 8 times 2 to 11 you get 27 so that is the expression to represent the pattern.

2. C is the answer because if you add -9 times 1 to 80 you get 71 and if you add -9 times 2 to 80 you get 62 so that is the expression to represent the pattern.

Answer:

5/7 or 71%

Step-by-step explanation:

4/7 (blue) + 1/7 (belt) = 5/7

Answer: Probability of event A = 0.57

Probability of event B = 0.14

Step-by-step explanation:

The data is:

2 blue shirts

1 red shirt

1 blue jacket

1 red belt

1 blue pair of pants

1 red pair of pants

the total number of garments is: 2 + 1 + 1 + 1 + 1 + 1 = 7

the number of blue ones is: 2 + 1 + 1 = 4

the number of belts is: 1

then, the probability of selecting at random one blue garment is equal to the number of blue ones divided the total number:

Pa = 4/7 =0.57

the probability of selecting the belt is equal to the number of belts divided the total number of garments, this is:

Pb = 1/7 = 0.14

1 cup = 8 ounces

so you'll have 5 ounces in each cup

5/8+5/8+5/8=15/8 (roughly 15 ounces or just under 2 cups of water)

you got everything right

Answer:

B

Step-by-step explanation:

We can use the logarithm property shown below to evaluate this:

[tex]Log(x*y*z)=logx+logy+logz[/tex]

Now we can write Log 12 as Log (2*2*3).

Using the rule, we can write:

Log (2*2*3) = Log 2 + Log 2 + Log 3

We are given values of Log 2 and Log 3, plugging these we get:

Log (2*2*3) = Log 2 + Log 2 + Log 3

Log (2*2*3) = 0.3010 + 0.3010 + 0.4771 = 1.0791

Answer choice B is right.

We can factor out 12 using 2 and 3.

log(12) = log(2^2 * 3)

Rewrite it using the product rule [ log(xy) = log(x) + log(y) ]

log(2^2 * 3) = 2 log(2) + log(3)

Simplify using the given values.

2(0.3010) + 0.4771

0.602 + 0.4771

1.0791

Therefore, the answer is b. ≈ 1.0791

Best of Luck!