Answer:
x = [tex]\frac{ln(16)}{ln(2)}[/tex]
Step-by-step explanation:
[tex]4^{2x-1} =8^{x+2}[/tex]
ln both sides like you would add the same number to both sides to keep the equation equivalent
[tex]ln4^{2x-1} = ln 8^{x+2}[/tex]
using log rules, exponents can be brought down as a constant multiplying ln
[tex](2x-1)ln(4) =(x+2)ln(8)[/tex]
use distributive property to remove parentheses
2xln(4) - ln(4) = xln(8) + 2ln(8)
isolate x
2xln(4) - xln(8) = 2ln(8) + ln(4)
rewrite the logs using log rules: ln(x) - ln(y) = ln([tex]\frac{x}{y}[/tex]) and the exponent rule stated above
xln([tex]4^{2}[/tex])-xln(8) = ln([tex]\frac{8^{2} }{4}[/tex])
factor out x
x(ln[tex]4^{2}[/tex]-ln8) = ln([tex]\frac{8^{2} }{4}[/tex])
again use log rules: ln(x) - ln(y) = ln([tex]\frac{x}{y}[/tex])
x* [tex]ln(\frac{4^{2} }{8}[/tex][tex])[/tex]= ln([tex]\frac{8^{2} }{4}[/tex])
now simplify the stuff inside the ln parentheses
x*ln(2) = ln(16)
x = [tex]\frac{ln(16)}{ln(2)}[/tex]
The atmosphere balances the unequal heating of Earth’s surface by moving _____. cool air toward the east and warm air toward the west cool air toward high latitudes and warm air toward the equator warm air toward the east and cool air toward the west warm air toward high latitudes and cool air toward the equator
Answer:
warm air toward high latitudes
Step-by-step explanation:
Known to sailors around the world as the doldrums, the Inter-Tropical Convergence Zone, (ITCZ, pronounced and sometimes referred to as the “itch”), is a belt around the Earth extending approximately five degrees north and south of the equator. From google
The atmosphere balances the unequal heating of Earth’s surface by moving warm air toward high latitudes and cool air toward the equator.
What is Atmosphere?An atmosphere is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body.
The atmosphere balances the unequal heating of Earth’s surface by moving warm air toward high latitudes and cool air toward the equator.
This is because the Earth's surface is heated unequally due to differences in solar radiation and other factors.
The equator receives more direct sunlight and is therefore warmer, while the poles receive less direct sunlight and are cooler.
As a result, warm air rises at the equator and cool air sinks at the poles, creating a circulation pattern in the atmosphere known as the Hadley cell.
Hence, the atmosphere balances the unequal heating of Earth’s surface by moving warm air toward high latitudes and cool air toward the equator.
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Write the expression 2x2x2x2+7-5x5x5 using exponents
Answer: 2^4+7 -5^3
Step-by-step explanation:
Answer:
(2 to the power of 4 )plus 7 minus( 5 to the power of 3)
Step-by-step explanation:
A store starts the day with 36 packages of juice boxes. Each package contains the
same number of juice boxes. By the end of the day, there are only 8 packages of
juice boxes left.
Part A
Write an expression with two terms to represent the number of juice boxes the
store sold.
Part B
Simplify your expression to create an equivalent expression.
Step-by-step explanation:
Given:
Number of packets at the beginning of the day, Nb = 36 packets
Number of packets at the end of the day, Ne = 8 packets
A.
Number of packets sold, Ns = Nb - Ne
36 - Number of packets sold, Ns = Ne
8 = 36 - Ns
Ns = 28
B.
8 = 36 - Ns
8 = 36 - 28
Final answer:
The expression representing the number of juice boxes sold is 28 multiplied by x, where x is the number of juice boxes per package. Since x is unknown, the expression cannot be simplified further and remains as 28 × x.
Explanation:
Part A: Representing the Number of Juice Boxes Sold
To represent the number of juice boxes sold, let's denote the number of juice boxes in each package as x. The store started with 36 packages and ended with 8. We are looking for the number of juice boxes in the packages that were sold. The expression is:
28 × x (since 36 - 8 = 28, and 28 packages were sold)
Part B: Simplifying the Expression
To simplify the expression, we do not have further information to simplify 28 × x more because x represents an unknown number of juice boxes per package. The simplified expression remains as:
28 × x
What are the solutions of x^2-3x+3=0
The solutions to quadratic equation are:
[tex]x = \frac{3 + i \sqrt{3}}{2}\\\\x = \frac{3 - i \sqrt{3}}{2}[/tex]
Solution:
Given is:
[tex]x^2 - 3x + 3 = 0[/tex]
We have to find the solutions to quadratic equation
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-3,\:c=3:\\\\x=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}[/tex]
[tex]x=\frac{3 \pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}\\\\x = \frac{3 \pm \sqrt{-3}}{2}\\\\x = \frac{3 \pm i \sqrt{3}}{2}[/tex]
We have two solutions :
[tex]x = \frac{3 + i \sqrt{3}}{2}\\\\x = \frac{3 - i \sqrt{3}}{2}[/tex]
The solutions to the quadratic equation x^2 - 3x + 3 = 0 can be found using the Quadratic Formula. The solutions are complex numbers: x = 3/2 ± (i*sqrt(3))/2.
Explanation:The given equation is a quadratic equation of the form ax^2 + bx + c = 0. To find the solutions to this equation, we can use the Quadratic Formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a).
Here a=1, b=-3, c=3.
Plugging these values into the formula,
we get x = [3 ± sqrt((-3)^2 - 4*1*3)] / (2*1).
Simplifying this equation will give us x = [3 ± sqrt((9 - 12)] / 2.
Now, note that the value under the square root is negative, indicating that the solutions will be complex.
Finally, we have the solutions:
x = [3 ± sqrt(-3)] / 2
= 3/2 ± (i*sqrt(3))/2, where 'i' is the imaginary unit.
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The recipe for a dozen muffins call for 4 teaspoons of vanilla. Tyler is making 6 dozen muffins for a bake sale. How many tablespoons of vanilla does he need? Remember 1 tablespoon equals 3 teaspoons
Answer: 8 tablespoons
Step-by-step explanation:
If 1 doz muffins= 4 teapoons = 4/3 tablespoon
6 dozens muffin= 4/3 × 6
24/3 = 8 tablespoon
Answer:
8 tablespoons
Step-by-step explanation:
Add 3/6 + 1/6 what is the sum in lowest terms
9.86 divided by 0.85
Answer:
9.86 / 0.85 = 11.6
Step-by-step explanation:
Gardner want to fence a circular garden of diameter 21 metre find the length of the wire he needs to purchase and cost of it at rupees 4 per metre
The cost of wire to purchase is Rs 264.
Step-by-step explanation:
Given,
The diameter of the circular garden is 21 m
The radius(r) = [tex]\frac{21}{2}[/tex] m
To find, the length of wire of the fence we need to find the circumference.
Formula
The circumference of the circle = 2πr meter
=2×[tex]\frac{22}{7}[/tex] ×[tex]\frac{21}{2}[/tex] m
=66 meter
So, the length of the wire = 66 m
The cost of wire Rs 4 per meter.
The total cost = Rs 4 × 66
= Rs 264
write the equation of a function that passes through these points
Answer:
heine is a former member and the chief of the United nations and th t in my experience with the United states and t the u.s. government of th world and is th American standard bible in a very good country of th I think 8is the most popular among women and the men in a society where the oth was the other one that had the most of t to the world that I would not like you to be in my life and I don't know how much I
Jada earned a 7% commission on a $500 sale of a boat. How much was her commission?
Answer:
$35
Step-by-step explanation:
To solve this problem you need to know how what and how is percentage work.
Percentage(%) is a unit that equals to 1/100 or one hundredths. So, 7% will be equal to 7*1/100= 7/100. The commission is given based on the price of the boat. If the boat sold at $500 the commission will be:
commission= percentage * boat price
commission= 7/100 * $500
commission= $35
Mary needs to ship a cubed shaped box to her aunt Lucy. She needs to find the volume of the box to know if she has enough room for a ring that she is sending. Find the volume of a cube with a side length of \frac{1}{2}1 2 an inch. Use the formula V = s3, where s is the side length of the cube.
Answer:
[tex]0.125 \ in^3[/tex]
Step-by-step explanation:
Given the sides of the cube as 0.5 inch.
#the volume of a cube is calculated as the product of the three sides:
[tex]V=s^3, \ \ \ \ s=0.5in\\\\V=0.5\ in\times 0.5\ in\times 0.5\ in\\\\V=(0.5\ in)^3\\\\V=0.125\ in^3[/tex]
Hence, the volume of Mary's cube is 0.125 cubic inches
Barry was born with 10 fingers . Every year , the numbers of fingers does not change .
Answer:
HE will have 10 fingers
Step-by-step explanation:
Solve for X. -x < -29
Answer:x<29
Step-by-step explanation:
X<29
please help me i need this to pass
x = 7 and x = –7.
Solution:
Given data:
[tex]$f(x)=x^{2}+15[/tex] and [tex]f(x)=64[/tex]
To find the solutions when f(x) = 64.
Both are equations of f(x), so equate the given equations, we get
[tex]x^2+15=64[/tex]
To isolate the constant term subtract 15 from both sides.
[tex]x^2+15-15=64-15[/tex]
[tex]x^2=49[/tex]
49 can be written as 7².
[tex]x^2=7^2[/tex]
Taking square root on both sides of the equation, we get
x = ±7
The solutions to f(x) = 64 is x = 7 and x = –7.
please help with number 4!!
The length of SK = 10 units while the length of BK = 8.6602 units.
Step-by-step explanation:
Step 1:
In the given triangle, there are two right-angles triangles with 60° angles. The central line BK is the opposite side for both the triangles. For triangle RK the hypotenuse's length is 10 m. Assume BK = x units and SK = y units.
Step 2:
So first we calculate the length of BK (x).
As we have the values of the angle of the triangle and the hypotenuse, we can calculate the sine of the angle to determine the value of x.
[tex]sin R = \frac{oppositeside}{hypotenuse}, sin 60 = \frac{x}{10}.[/tex]
[tex]sin 60 = 0.86602, x = 0.86602 (10) = 8.6602 units.[/tex]
So x = BK = 8.6602 units.
Step 3:
So now we calculate the length of SK (y).
As we have the values of the angle of the triangle and the opposite side's length, we can calculate the sine of the angle to determine the value of y.
[tex]sin S = \frac{oppositeside}{hypotenuse}, sin 60 = \frac{86.602}{y}.[/tex]
[tex]sin 60 = 0.86602, y = \frac{8.6602}{0.86602} = 9.999units = 10 units[/tex]
So y = SK = 10 units.
__ grams of sugar will dissolve
in 100 g of solution at 90°C.
80.61
91.76
Answer: A. 80.61
Step-by-step explanation:
Dylan plants grass
in a rectangular
space behind the
clubhouse. The
area of the space
is 70 square feet.
If the length of the
space is 14 feet,
what is the width of
the space?
C and D are complementary. The measure of C is (4x) degrees and the measure of D is 26 degrees. What is the value of x
Answer: x=16
Step-by-step explanation:subtract 26 from 90 then divide 64 by 4 and you get 16
Answer:
X=16
Step-by-step explanation:
The answer is 16. 90-26/4=16
the filing cabinets need a total of 55 square feet of space.the doctor asked in which room the filing cabinets will fit
Square B
Explanation:The complete question is written in a comment above. The doctor's office where you work needs to store eight filing cabinets with patient information in one of three secure storage rooms. We know that the filing cabinets need a total of 55 square feet of space. You need to identify in which room the filing cabinets will fit. So we have three rooms:
FIRST OFFICE:
[tex]Square \ A = 8 \times 5[/tex]
In other words, for this room we have the following area:
[tex]Square \ A =40ft^2[/tex]
SECOND OFFICE:
[tex]Square \ B = 9 \times 7.5[/tex]
In other words, for this room we have the following area:
[tex]Square \ B =67.5ft^2[/tex]
THIRD OFFICE:
[tex]Square \ C = 5 \times 10[/tex]
In other words, for this room we have the following area:
[tex]Square \ C =50ft^2[/tex]
How can we know what is the room we need to choose?
Well, the room we need to choose is the one whose area is greater than the area of the filling cabinets. In other words, let's call square x the unknown room, then:
[tex]Square \ x>55ft^2[/tex]
From the, choices the only room that meets our requirements is square B because:
[tex]Square \ B>55ft^2 \\ \\ 67.5ft^2>55ft^2[/tex]
Measure the length and width of a room in feet to calculate its area. Multiply these dimensions to get the area in square feet. The filing cabinets need a room with at least 55 square feet.
Explanation:To determine whether the filing cabinets will fit into a room, we must calculate the area of the room and see if it is at least 55 square feet, the space required for the filing cabinets.
To calculate the area of a room in square feet, measure the length and width of the room in feet and then multiply these numbers together.
For example, if a room is 10 feet wide and 5.5 feet long, its area would be 10 feet times 5.5 feet, which equals 55 square feet. Therefore, the filing cabinets would fit in a room of this size.
Prince Humperdinck has 17 henchmen. Unfortunately, all but six die. How many henchmen does he have left?
Answer:
6
Step-by-step explanation:
The question might be trying to be tricky. If Prince Humperdinck has 17 henchmen and ALL BUT 6 die. That means that 6 are alive.
John paid $450 for a new mountain bicycle to sell in his shop. He wants to pnce it so that he can offer a 10% discount but still make 20% of the price he paid for it. At what price should the bike be marked?
The bike should be marked for $
(Round to the nearest dollar as needed)
Answer:
$486
Step-by-step explanation:
Step 1: Solve
(450 * 0.9) * 1.2
405 * 1.2
486
Answer: $486
10. An archery arrow is shot with a speed of 45 m/s at an angle of 10°. How for
horizontally can the arrow travel before hitting a target at the same height
from which it was released?
Answer:
The horizontal distance travelled by an arrow is 70.6 m.
Step-by-step explanation:
Given : An archery arrow is shot with a speed of 45 m/s at an angle of 10°.
To find : How for horizontally can the arrow travel before hitting a target at the same height from which it was released?
Solution :
The expression for the range of the projectile motion is
[tex]R=\frac{V^2\sin 2\theta}{g}[/tex]
Where, the velocity of an arrow is V = 45 m / s
The angle of release of an arrow is [tex]\theta=10^\circ[/tex]
The acceleration due to gravity is g =9.81 m/s²
Substitute the values,
[tex]R=\frac{45^2\sin 2(10)}{9.81}[/tex]
[tex]R=\frac{2025\sin (20)}{9.81}[/tex]
[tex]R=70.6\ m[/tex]
Therefore, the horizontal distance travelled by an arrow is 70.6 m.
The arrow travels approximately 70.9 meters.
To determine how far the arrow travels horizontally, we need to break the initial velocity into horizontal and vertical components and use the projectile motion equations.
Step-by-step solution:
Determine the horizontal and vertical components of the initial velocity:The arrow travels approximately 70.9 meters horizontally before hitting a target at the same height from which it was released.
GETS BRAINILIST!!!What statistical question might Mary have asked her classmates to gather the data in the bar graph? 6. A new student is wearing mismatched socks. How might you show that the student has 1 red sock and 1 purple sock on the bar graph? Explain your reasoning. LOADING... Click the icon to view the bar graph. 5. Choose the correct answer below. A. How many students are there in the classroom? B. Which color comes first in the rainbow? C. What color socks is the teacher wearing? D. What color socks are you wearing?
Answer:
A.
Step-by-step explanation:
All of the other questions don't make sense because they are statistical
12t+12=-24 what is t?
Answer:
t=-3
Step-by-step explanation:
12t+12=-24
12t=-36
t=-3
How many cubes are needed to fill in the rectangular prism?
8320 cubes can fit into the prism.
Solution:
Convert mixed fraction into improper fraction.
Length of the prism = 20 in
Width of the prism = 2 in
Height of the prism = [tex]3\frac{1}{4}=\frac{13}{4}[/tex] in
Volume of the prism = length × width × height
[tex]$=20\times2\times\frac{13}{4}[/tex]
= 130 in³
Volume of the prism = 130 in³
Length of the cube = [tex]\frac{1}{4}[/tex] in
Volume of the cube = length × length × length
[tex]$=\frac{1}{4} \times\frac{1}{4} \times\frac{1}{4}[/tex]
[tex]$=\frac{1}{64} \ \text{in}^3[/tex]
Volume of the cube = 0.015625 in³
[tex]$\text{Number of cubes}=\frac{\text{Volume of the prism}}{\text{Volume of cube}}[/tex]
[tex]$=\frac{130}{0.015625}[/tex]
= 8320
Number of cubes = 8320
Hence 8320 cubes can fit into the prism.
If 1 measures 135°, what is the measure of 6? (Lines b and c are parallel.)
135°
65°
90°
45°
The Question is Incomplete, the Complete Question is with figure is below.
Answer:
Therefore,
The Measure of angle 6 is
[tex]\angle 6 =45\°[/tex]
Step-by-step explanation:
Given:
m∠1 = 135°
Lines b and c are parallel.
To Find:
m∠6 = ?
Solution:
Linear Pair:
A linear pair of angles is formed when two lines intersect.
Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.
The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Example
∠ 1 and ∠ 2 ∠ 1 and ∠ 3 ,etc
[tex]\angle 1 + \angle 3 = 180\°[/tex]
Substituting the values we get
[tex]135 + \angle 3 = 180\\\\\angle 3 = 180-135=45\°[/tex]
Now,
Lines b and c are parallel. .Given
When Two lines are Parallel Alternate interior angles are equal
∠ 3 and ∠ 6 are Alternate Interior angles
[tex]\angle 3 = \angle 6[/tex]
But [tex]\angle 3 =45\°[/tex]
[tex]\angle 6 =45\°[/tex] ...Transitive Property
Therefore,
The Measure of angle 6 is
[tex]\angle 6 =45\°[/tex]
The radius of a fishing line is 2.5*10^-4 foot. Write this number in standard form. Then write your answer using inches.
To write the radius of the fishing line in standard form, it is 0.00025 foot. In inches, the length is 0.003 inches.
Explanation:The radius of the fishing line is given as 2.5*10^-4 foot. To write this number in standard form, we first need to convert it into decimal form.
To do this, we move the decimal point four places to the left, since the exponent is negative. This gives us 0.00025.
Therefore, the number in standard form is 0.00025 foot.
To convert this into inches, we know that there are 12 inches in a foot. So, we multiply the length in feet by 12 to get the length in inches.
Therefore, the length of the fishing line in inches is 0.00025 foot * 12 inches/foot = 0.003 inches.
6 - (3t+4) = t solve the equation
Answer:
t = 1/2
Step-by-step explanation:
6 - (3t+4) = t
Distribute the minus sign
6 - 3t -4 = t
Combine like terms
2 -3t = t
Add 3t to each side
2 -3t +3t = t+3t
2 = 4t
Divide each side by 4
2/4 =4t/4
1/2 =t
Answer:
6-(3t+4)=t
6-3t-4=t
6-4=t+3t
2=4t
t=2/4
Solve the equation.x/8+12=16
Answer:
x = 32
Step-by-step explanation:
Step 1: Subtract 12 from both sides
x/8 + 12 - 12 = 16 - 12
x/8 = 4
Step 2: Multiply both sides by 8
x/8 * 8 = 4 * 8
x = 32
Answer: x = 32
Answer:
Step-by-step explanation:
[tex]\frac{x}{8}+12=16\\\\\frac{x}{8}=16-12\\\\\frac{x}{8}=4\\\\x=4*8\\\\x=32[/tex]
Which of the following is best described as the quality a design has if it
maintains all of its characteristics when it is reflected over an axis lying in its
plane?
Answer:
Reflectional Symmetry