Answer:
x≈ 3.2056
Step-by-step explanation:
Set both sides by log. Then, solve for x.
1. 14^(x + 1) = 36
(x + 1)log(14) = log(36)
x + 1 = log(36)/log(14) . . . Divide both sides by log(14)
x = log(36)/log(14) - 1 . . . . Subtract both sides by 1.
x ≈ 0.3579 . . . . . . . . . . . .Use calculator to simplify the expression.
Note that the second problem is similar to the first.
2. 12^(y - 2) = 20
(y - 2)log(12) = log(20)
y - 2 = log(20)/log(12)
y = log(20)/log(12) + 2
y ≈ 3.2056
Answer:
X=2.5
Step-by-step explanation:
14x +1 =36
14x + 1 =36
- 1 = 36
14x = 35
14x / 2 = 35 / 2
x = 2.5
there’s also D
D: 4m on top and 4m on the side
Answer:
A and B.
Step-by-step explanation:
To find the area, you need to multiply the length and width.
A = L x W
5 x 4 = 20
10 x 2 = 20
A side length of a regular hexagon is 14 inches. What is the perimeter of the hexagon?
Answer:
84 inches
Step-by-step explanation:
A regular hexagon has 6 sides where all 6 sides are congruent meaning that each side is 14 inches.
Hence:
14*6=84
In Conclusion:
The perimeter of the hexagon is 84 inches.
Hope this helps!
Answer:
84
Step-by-step explanation:
14+14+14+14+14+14=84
A hexagon has 6 equal sides and you add all of the sides to find perimeter.
The diameter of the circle is 18 m Eugene incorrectly says that the circumference of the circle is about 113.04 m what is the circumference of the circle? What mistake did Eugene make? Use 3.14 for pie
Hi
formula. for circumference of a circle is. : 2πR. if you have the radius.
As the diameter is twice the radius, then circumference is. diameter π
then : 18*π≈ 56.52
the mistake was to take the diameter as the radius.
Final answer:
The circumference of the circle is 56.52 m. Eugene made the mistake of using the radius instead of the diameter to calculate the circumference.
Explanation:
The circumference of a circle can be found using the formula C = πd, where C represents the circumference and d represents the diameter.
In this case, the diameter of the circle is given as 18 m. If we substitute this value into the formula, we get:
C = 3.14 * 18 = 56.52 m
Eugene's mistake was that he used the value of the radius instead of the diameter to calculate the circumference. The correct circumference is 56.52 m, not 113.04 m.
21. In 4 + In(4x - 15) = In(5x + 19)
Answer:
[tex]x=-30;\quad \:I\ne \:0[/tex]
Step-by-step explanation:
[tex]In\cdot \:4+In\left(4x-15\right)=In\left(5x+19\right)[/tex]
[tex]\:4+In\left(4x-15\right):\quad -11nI+4nxI\\In\cdot \:4+In\left(4x-15\right)\\=4nI+nI\left(4x-15\right)\\\\\:In\left(4x-15\right):\quad 4nxI-15nI\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=In,\:b=4x,\:c=15\\=In\cdot \:4x-In\cdot \:15\\=4nxI-15nI\\=In\cdot \:4+4nxI-15nI\\\mathrm{Simplify}\:In\cdot \:4+4nxI-15nI:\quad -11nI+4nxI\\In\cdot \:4+4nxI-15nI\\\mathrm{Group\:like\:terms}\\=4nI-15nI+4nxI\\\mathrm{Add\:similar\:elements:}\:4nI-15nI=-11nI\\=-11nI+4nxI\\[/tex]
[tex]\mathrm{Expand\:}In\left(5x+19\right):\quad 5nxI+19nI\\In\left(5x+19\right)\\=nI\left(5x+19\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=In,\:b=5x,\:c=19\\=In\cdot \:5x+In\cdot \:19\\=5nxI+19nI\\\\-11nI+4nxI=5nxI+19nI\\\\\mathrm{Add\:}11nI\mathrm{\:to\:both\:sides}\\-11nI+4nxI+11nI=5nxI+19nI+11nI\\Simplify\\4nxI=5nxI+30nI\\\mathrm{Subtract\:}5nxI\mathrm{\:from\:both\:sides}\\4nxI-5nxI=5nxI+30nI-5nxI\\\mathrm{Simplify}\\-nxI=30nI\\[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-nI;\quad \:I\ne \:0\\\frac{-nxI}{-nI}=\frac{30nI}{-nI};\quad \:I\ne \:0\\\mathrm{Simplify}\\\frac{-nxI}{-nI}=\frac{30nI}{-nI}\\\mathrm{Simplify\:}\frac{-nxI}{-nI}:\quad x\\\frac{-nxI}{-nI}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{nxI}{nI}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{xI}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=x\\\mathrm{Simplify\:}\frac{30nI}{-nI}:\quad -30\\\mathrm{Apply\:the\:fraction\:rule}:[/tex]
[tex]\quad \frac{a}{-b}=-\frac{a}{b}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{30I}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=-30\\x=-30;\quad \:I\ne \:0[/tex]
There are 8 flavors of ice cream and
you can have one of 2 kinds of cones
with 4 different kinds of sprinkes on
top. How many combinations are
possible?
Answer:
64
Step-by-step explanation:
you do 8x2x4
Express 8^1/2 in simplest radical form.
Final answer:
To express [tex]8^{1/2[/tex]in simplest radical form, recognize that it's equivalent to the square root of 8, then simplify to 2√2 by breaking down 8 into prime factors and finding pairs of factors.
Explanation:
To express [tex]8^{1/2[/tex] in simplest radical form, we follow these steps:
Recognize that an exponent of 1/2 is equivalent to the square root.
Find the square root of 8, which can also be written as √8.
Since 8 is not a perfect square, we can simplify it by breaking it down into its prime factors: 8 = 2 x 2 x 2.
Group the factors into pairs to determine the square root: 8 has one pair of 2s.
This pair comes out of the radical as a single 2, leaving one 2 inside the radical: 2√2.
Therefore, 8^1/2 simplifies to 2√2, which is the simplest radical form.
What is the area of the rhombus?
square units
Answer:
Area = 80
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
Vertical length-16
Horizontal length- 10
make four separate triangles out of the rectangle
each triangle has an area of of 20 (8×5= 40 40/2=20)
multiply by 4
20×4=80
An actor invests some money at 5% simple interest, and $23,000 more than 3 times the amount at 6% simple interest. The total annual interest earned from the investment is $28,290. How much did he invest at each amount? Use the 6 step method.
Answer:
He invested $117,000 at 5% interests and 3*117,000 + 23000 = $374,000 at 6% interests
Step-by-step explanation:
Let's call x to the some money at 5% simple interest the actor invest. Then, he invested 3x + 23000 dollars at 6% simple interest.
At 5% simple interest, after one year he earned the following interests:
I = P*r*t
I = x*0.05
At 6% simple interest, after one year he earned the following interests:
I = (3x + 23000)*0.06 = 0.18x + 1380
The total annual interest earned from the investment is $28,290, then:
0.05x + 0.18x + 1380 = 28290
x = (28290 - 1380)/0.23
x = $117,000
A triangular prism. The rectangular sides are 6 centimeters by 10 centimeters, 10 centimeters by 5 centimeters, and 10 centimeters by 5 centimeters. The 2 triangular bases have a base of 6 centimeters and height of 4 centimeters. What is the surface area of the triangular prism shown? 32 square centimeters 120 square centimeters 184 square centimeters 1,560 square centimeters
Answer:
184
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
What is equivalent to the expression (x+3)(x-7)+(x+8)(x+3)
Answer:
[tex]2x^2+7x+3[/tex]
Step-by-step explanation:
[tex](x+3)(x-7)+(x+8)(x+3)[/tex]
[tex](x^2-4x-21)+(x^2+11x+24)[/tex]
[tex]x^2-4x-21+x^2+11x+24[/tex]
[tex]2x^2+7x+3[/tex]
Define the Negative Exponent Property
Answer:
Dividing is the inverse (opposite) of Multiplying.
A negative exponent means how many times to divide by the number.
Answer:
There is a power property for negative exponent powers which says that a power with a negative exponent is equal to 1 between the same power, but with a positive exponent. In other words, to convert the exponent from negative to positive, the power is converted to the denominator
Step-by-step explanation:
Sylvie is planning to visit her mother who lives 387 miles away. If
the price of gas ranges from $1.95 to $2.13 per gallon and Sylvie's
car gets 25 miles per gallon, about how much should she plan to
spend on gas for the trip there?
more than $50
$30 to $40
less than $30
$40 to $50
Answer:
$30 to $40
Step-by-step explanation:
387/25= 15.48 (this is how big the tank is)
15.48*2.13= 32.97 (about 33 paying for the highest price)
Sylvie will need approximately 15.48 gallons of gas for her 387-mile trip. With gas prices ranging from $1.95 to $2.13 per gallon, she should plan to spend between $30.20 and $32.96. Therefore, the anticipated cost falls between $30 and $40 that is option B is correct.
To calculate the cost of gas for the trip, we need to follow these steps:
Determine the number of gallons of gas needed for the trip:
Number of Gallons = Total Miles / Miles per Gallon
Number of Gallons = 387 miles / 25 miles per gallon = 15.48 gallons
Calculate the minimum and maximum cost of gas:
Minimum Cost = Number of Gallons * Minimum Price per Gallon
Minimum Cost = 15.48 gallons * $1.95 per gallon ≈ $30.20
Maximum Cost = Number of Gallons * Maximum Price per Gallon
Maximum Cost = 15.48 gallons * $2.13 per gallon ≈ $32.96
Both calculations indicate the cost will fall between $30 and $40. Therefore, the correct answer is: $30 to $40.
13. In a week the prices of a bag of rice were 350,280,340,290,320, 310,300. The range is
A. 60
B. 70
C. 80
D. 100
so the right answer is 70.
Look at the attached picture ⤴
Hope it will help u
Answer:
B
Step-by-step explanation:
The range can be found by subtracting the lowest number from the highest number
First, arrange the numbers in order from least to greatest
350,280,340,290,320, 310,300
280, 290, 300, 310, 320, 340, 350
So, our lowest number is 280, and our highest is 350.
highest number - lowest number
Subtract 280 from 350
350-280
70
So, our range is 70, making B the correct answer
A scaled drawing uses a scale factor of 1:25. Is the drawing a reduction or an enlargement? Support your conclusion with an example.
Answer:
Reduction scale
Step-by-step explanation:
Enlarging scale means that the drawing is larger than the actual object. Hence the representative fraction will be greater than unity. For reducing scale the representative fraction is less than unity.
So now looking at 1:25, we see it's a reduction scaling because it's fraction is less than unity.
And what 1:25 means is that 1 on paper while the actual size of the object is 25
Rectangle A’B’C’D is similar to rectangle ABCD, as shown on the coordinate plane below. Which sequence or transformations maps rectangle ABCD onto rectangle A’B’C’D
The reflection over the [tex]y-axis[/tex] then a dilation by the factor of
[tex]\frac{1}{2}[/tex] with a center of dilation at the origin.
Reflection of the point:Reflecting on the [tex]y-axis[/tex] we get the rectangle A, B, C, D.
A dilation by the factor of [tex]\frac{1}{2}[/tex] with the center of dilation at the origin transforms the rectangle A, B, C, D onto the rectangle A'B'C'D'.
So, the reflection over the [tex]y-axis[/tex] then a dilation by the factor of [tex]\frac{1}{2}[/tex] with a center of dilation at the origin.
The image is attached below.
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The correct sequence of transformations to map rectangle ABCD onto rectangle A'B'C'D' is a dilation by a scale factor of 1/2. This transformation reduces the size of the original rectangle without additional translation, reflection, or rotation.
The correct sequence of transformations that maps rectangle ABCD onto rectangle A'B'C'D' is:
c. a dilation by a scale factor of 1/2
Here's why:
1. A dilation by a scale factor of 1/2 reduces the size of the original rectangle by half. This transformation scales down all the coordinates by a factor of 1/2. Given the coordinates of ABCD and A'B'C'D', this is the only transformation needed to achieve similarity.
Options a and b involve additional transformations (translation and reflection) that are not required to achieve similarity, and option d introduces a rotation which is not a dilation by itself.
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Find the unit rate.
150 mi on 10 gal of gas
A: 15 mi per gal
B: 10 mi per gal
C: 150 mi per gal
The unit rate of miles per gallon is found by dividing the total miles (150 mi) by the total gallons (10 gal), resulting in a unit rate of A) 15 miles per gallon.
To find the unit rate of miles per gallon when given 150 miles on 10 gallons of gas, we divide the total number of miles driven by the number of gallons of gas used. The calculation is as follows:
Write down the given values: 150 miles (mi) and 10 gallons (gal).
Divide the total miles by the total gallons to find the unit rate: 150 mi ÷ 10 gal = 15 mi/gal.
Therefore, the unit rate is 15 miles per gallon, which is option A: 15 mi per gal.
PLEASE HELP!!!
Carl is on the school track team. To prepare for an upcoming race, he plans to run 217 miles total over the next 31 days.
Write an equation to determine how many miles, m, he needs to run per day, assuming he runs the same amount each day.
How many miles does Carl need to run each day?
GIVING BRANLIEST
Which ordered pair is the solution to this system of equations?
y = 4
3x - 2y = 4
Group of answer choices
(0, 6)
(0, 4)
(-4, 4)
(4, 4)
Answer:
(4,4)
Step-by-step explanation:
Answer:
(4,4). You already know the y value is 4, so you just plug that into the second equation. You'd get 3x-8=4, then 3x=12, then x=4. (x,y)=(4,4)
In the right triangle shown, what is the value of x (to the nearest tenth)? (Picture shown above)
a. 9.1
b. 11.0
c. 21.4
d. 23.7
Answer:
i think it is c. good luck!!
Step-by-step explanation:
The value of x is 11.037
The correct option is (B)
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
Using Trigonometry,
cos 25 = B/ H
cos 25 = 10 / x
0.906 = 10/ x
x= 10/ 0.906
x= 11.037
Hence, the value of x is 11.037.
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3 ratios that are equivalent to 3/8
Answer:
30/80 9/24 6/16
Step-by-step explanation:
Answer:
just multiply a fraction equal to 1 for example 2/2
3/8 x 2/2 = 6/16
3/8 x 3/3 = 9/24
3/8 x 4/4 = 12/32
it is equivalent because 2/2 is equal to 1 so it is being multiplied by 1
Step-by-step explanation:
two line are ___ if and only if they lie in the same plane and do not intersect, and two lines are __ if and only if they lie in the same plane and intersect at the right angles
A) partaken, perpendicular
B) perpendicular, bisectors
C) parallel, bisectors
D) perpendicular, parallel
the answer is C, I think because parallel lines never touch
The required answer is two lines are parallel if and only if they lie in the same plane and do not intersect, and two lines are perpendicular if and only if they lie in the same plane and intersect at the right angles. Option A is correct.
Given that,
An incomplete statement is given,
We have to complete the statement using the appropriate options that thinks fit to black space.
The line is a curve showing the shortest distance between 2 points.
Here,
Two lines are ___ if and only if they lie in the same plane and do not intersect.
The above statement is the definition of parallel lines, so the complete statement is,
Two lines are parallel if and only if they lie in the same plane and do not intersect.,
Two lines are __ if and only if they lie in the same plane and intersect at the right angles
The above statement is the definition of perpendicular,
So the complete statement is,
Two lines are perpendicular if and only if they lie in the same plane and intersect at the right angles.
Thus, the required correct option is option A, Parallel and perpendicular.
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Find the area of the parallelogram shown below.
Answer:
The answer is 21
Step-by-step explanation:
The answer is 21 because...
It is hard to explain but for step one you need to take the dotted line and the shape above hat and move it underneath the other shape to make a perfect rectangle.Step two since the dotted line is our new bottom. It has a length of 7. In this step we multiply 3 times 7 Step 3 this is the final step in which 3 times 7 equals 21.Hope this helped :)Simplify
12x^9
————
2x^3
o 6х3
o 6х6
o10х3
o10х6
Answer:
6 * x^6
Step-by-step explanation:
We have (12x^9) / (2x^3)
(12x^9) / (2x^3) = 6 * (x^9/x^3) Divide the constants first
(12x^9) / (2x^3) = 6 * x^ (9-3)
(12x^9) / (2x^3) = 6 * x^6
79.99 - 12% + 8%
please dhow your work
thank you
And be safe
Answer:
79.95
Step-by-step explanation:
The first step is to rewrite the percentages into decimals so they can be added or subtracted easier. To turn a percentage into a decimal, remove the percent sign and move the decimal two spaces to the left (in other words, divide the number by 100).
12% becomes -0.12
8% becomes 0.08
Now, let's solve.
79.99 - 0.12 + 0.08
Evaluating 79.99 - 0.12, the equation becomes 79.87 + 0.08.
Evaluating 79.87 + 0.08, we get the final answer, 79.95.
Joseph is ordering a taxi from an online taxi service. The taxi charges $4 just for the
pickup and then an additional $1 per mile driven. How much would a taxi ride code if
Joseph is riding for 9 miles? How much would a taxi ride cost that is m miles long?
Answer: $13 for the 9 mile ride.
The taxi ride that is m miles long would cost as follows: 4 + m
Step-by-step explanation:
The cost of Joseph's taxi ride is calculated by adding a flat fee of $4 to $1 for each mile driven. Thus, a 9-mile ride would cost $13. For a ride of m miles, the cost would be $4 plus $1 per mile.
Explanation:The cost of a taxi ride can be determined using a function that considers two components: a flat fee, and a rate per mile. In Joseph's case, the online tax service charges a $4 flat fee for pickup, and $1 per each mile driven. Hence, the equation for the cost of a taxi ride (C) for Joseph is as follows: C= 4+1*m.
For a ride of 9 miles, we would substitute m with 9: C = 4+ 1*9, which simplifies to C = $13. Therefore, a 9-mile ride would cost $13.
For a taxi ride that is m miles long, the cost would be C = 4 + 1*m. The 4 represents the flat fee, and the 1*m represents the cost per mile that is driven multiplied by the number of miles in the ride. Therefore, a taxi ride that is m miles long would cost $4 plus $1 per mile.
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Use the divisibility tests to determine whether 900 is divisible by 2, 3, 5, 6, and 10
Answer:3
Step-by-step explanation:
Help looks like i forgot to read a ruler
Answer:
the second one
Step-by-step explanation:
Answer:
2nd one is right
Step-by-step explanation:
Simplify the expression:
-5a – 6a + -9a
Answer:
-20a
Step-by-step explanation:
-5a-6a+-9a
-11a+-9a
-20a
A hat contains four balls. The balls are numbered 3, 6, 6, and 7. One ball is randomly selected and not replaced, and then a second ball is selected. The numbers on the two balls are added together.
A fair decision is to be made about which of three sizes of ice cream cone will be ordered, using the sum of the numbers on the balls. The sizes are small, medium and large.
Which description accurately explains how a fair decision can be made in this situation?
If the sum is 9, a small cone will be ordered.
If the sum is 10 or 13, a medium cone will be ordered.
If the sum is 12, a large cone will be ordered.
If the sum is 9, a small cone will be ordered.
If the sum is 10 or 12, a medium cone will be ordered.
If the sum is 13, a large cone will be ordered.
If the sum is 9 or 10, a small cone will be ordered.
If the sum is 12, a medium cone will be ordered.
If the sum is 13, a large cone will be ordered.
If the sum is 9 or 12, a small cone will be ordered.
If the sum is 10, a medium cone will be ordered.
If the sum is 13, a large cone will be ordered.
Answer:
I believe the answer is B
Step-by-step explanation:
3. What is the relative frequency of a
customer 40 years or older getting
information from the Internet?
A 20%
C 50%
B 40%