5^x=62 Giving 20 points!
Algebra 2, Chapter 6-7. Common Logarithms.
The answer key says its 2.5, but I need some help to understand how to get that answer by showing work.
Answer:
x = 2.564 ( to 3 dec. places )
Step-by-step explanation:
Using the rule of logarithms
log[tex]x^{n}[/tex] ⇔ n logx
Given
[tex]5^{x}[/tex] = 62 ( take the ln of both sides )
ln[tex]5^{x}[/tex] = ln 62, that is
x ln5 = ln 62 ( divide both sides by ln 5 )
x = [tex]\frac{ln62}{ln5}[/tex] ≈ 2.564
Answer:
2.5
Step-by-step explanation:
ln(5^x)=ln(62)
[tex]x=\frac{ln62}{ln5}[/tex]
≈2.56433
Find the value of X.
Answer:
x=110 i think
Step-by-step explanation:
x+20+2x-70+x+x+20+x+90
=6x+60
6x+60=720
6x=(720-60)
6x=660
660/6=110
x=110
hope this helps!
Answer:
Step-by-step explanation:
sum of all angles of polygon = (n-2)*180 {n is no of sides}
= (6-2)*180 = 4*180 = 720
90 + 2x-70 + x+20 +x + x+20 + x = 720
Bring like terms together
90 - 70 + 20 + 20 + 2x + x + x + x + x =720
60 + 6x = 720
6x = 720 - 60
6x = 660
x = 660/6
x = 110
Yesterday, Juana sold 84 hot chocolate during her shift at work. If she worked from 7:00 am to 3:00 pm with an hour break for lunch, what was the average sold per hour?
Juana sold an average of 12 hot chocolates per hour during her 7-hour work shift (excluding her lunch break).
Explanation:The question asks us to calculate the average hot chocolate sold per hour by Juana during her shift. Juana worked an 8-hour day but took a 1-hour lunch break, leaving 7 hours of work time.
To find the average sold per hour, the total amount sold (84 hot chocolates) should be divided by the number of hours worked (7 hours). The calculation is as follows:
84 hot chocolates ÷ 7 hours = 12 hot chocolates per hour
Therefore, Juana sold an average of 12 hot chocolates per hour during her shift.
Is the world flat, or not?
Answer:
its round
Step-by-step explanation:
In ΔMNO NM = 3 cm, NO = 4 cm and MO = 5 cm. List the angles in order from smallest to largest.
By identifying triangle MNO as a right-angled triangle with MO as the hypotenuse, the angles are listed from smallest to largest based on their opposite sides: angle M (smallest), angle O (middle), and angle N (largest at 90 degrees).
The student has asked to list the angles of triangle right -angled MNO in order from smallest to largest, given that NM = 3 cm, NO = 4 cm, and MO = 5 cm. This is a case of a right-angled triangle where the sides satisfy the Pythagorean theorem, with MO being the hypotenuse. The angles of a triangle are inversely proportional to their opposite sides. Therefore, the angle opposite the longest side (MO) is the smallest, and the angle opposite the shortest side (NM) is the largest.
Steps to determine angle size:
Use the Pythagorean theorem to confirm the right angle.
Identify the smallest and largest sides to determine the smallest and largest angles.
Apply the fact that the sum of angles in a triangle is 180 degrees to find the middle angle.
Since 3² + 4² = 5², triangle MNO is a right-angled triangle with the right angle at angle N.
The smallest angle is thus at M, opposite the longest side MO.
The largest angle is at O, opposite the shortest side NM.
As angle N is 90 degrees, the remaining angle at O must be the second-largest angle.
A rectangle has a perimeter of 80 inches. Write an equation to represent the area A in terms of width w.
Do I use the perimeter?
Answer:
[tex]A = 40w-w^2[/tex]
Step-by-step explanation:
We are given the following in the question:
Perimeter of rectangle = 80 inches.
Let l be the length and w be the width of rectangle.
Perimeter of rectangle =
[tex]P= 2(l+w)[/tex]
Putting values, we get,
[tex]80 = 2(l+w)\\40 = l+w\\\Rightarrow l = 40 - w[/tex]
Now, we have to find the area of the rectangle in terms of w.
Area of rectangle =
[tex]A = l\times w[/tex]
Putting values, we get
[tex]A = (40-w)w\\A = 40w-w^2[/tex]
is the required expression of area of rectangle in terms of w.
Yes, the perimeter is used to calculate the length of the rectangle in the term of w.
What is the value of z???
Answer: 33
Step-by-step explanation:
all of the numbers add up to 180 degrees
Answer:
33
Step-by-step explanation:
To find the degree, remember: a triangles angles will always add up to 180°. So, add your degrees, then subtract that from 180:
[tex]114+33=147\\180-147=33[/tex]
z=33°
Complete the steps to find the area of the trapezoid.
Area of rectangle = square units
Area of triangle 1 = square units
Area of triangle 2 = square units
Area of triangle 3 = square units
Area of trapezoid = square units
Answer:
Area of rectangle: 256
Area of triangle 1: 24
Area of triangle 2: 16
Area of triangle 3: 96
Area of trapezoid: 120
Step-by-step explanation:
I just did the question on the thing so Ik I'm right.
-The graph measures by twos. To get the area of the rectangle get the base times height of it. That would be 16x16=256.
-Get base (8) times height (6) of triangle 1 then divide by 2, remember to count the squares by 2 for finding all areas. The formula would be 1/2(b)(h) because dividing by 2 is the same as multiplying times 1/2. Plug it in and (8)(6)=48 then divide by 2 which equals 24.
-Same formula for triangle 2. Plug it in and (8)(4)=32 and divide by 2 and it equals 16.
-Same formula for triangle 3. Plugged in is (12)(16)=192 divide by 2 and it equals 96.
-To find the area of the trapezoid get your rectangle area (256) and subtract all the triangle areas. So 256 - 6 - 16 - 96 = 120.
The area of the given shapes are required.
256 square units
24 square units
16 square units
96 square units
120 square units
Area of the rectangle
[tex]A_r=(20-4)\times(20-4)\\\Rightarrow A_r=256\ \text{square units}[/tex]
The area of a right triangle is given by
[tex]\dfrac{1}{2}bh[/tex]
where
b = Base
h = Height
Every triangle here is a right triangle.
Triangle 1
[tex]b=20-14=6\ \text{units}[/tex]
[tex]h=12-4=8\ \text{units}[/tex]
[tex]A_1=\dfrac{1}{2}\times 6\times 8\\\Rightarrow A_1=24\ \text{square units}[/tex]
Triangle 2
[tex]b=20-16=4\ \text{units}[/tex]
[tex]h=20-12=8\ \text{units}[/tex]
[tex]A_2=\dfrac{1}{2}\times 4\times 8\\\Rightarrow A_2=16\ \text{square units}[/tex]
Triangle 3
[tex]b=20-4=16\ \text{units}[/tex]
[tex]h=16-4=12\ \text{units}[/tex]
[tex]A_3=\dfrac{1}{2}\times 16\times 12\\\Rightarrow A_3=96\ \text{square units}[/tex]
Area of trapezoid is Area of the rectangle minus Area of all the triangles.
[tex]A=A_r-(A_1+A_2+A_3)\\\Rightarrow A=256-(24+16+96)\\\Rightarrow A=120\ \text{square units}[/tex]
Learn more:
https://brainly.com/question/14356835
https://brainly.com/question/16928464
A jar contains three red marbles and five green marbles. A marble is drawn at random and not replaced. A second marble is then drawn from the jar. Find the probability that the first marble is red and the second marble is green.
Answer:
P(red then green) = 5/8 * 3/7 = 15/56
Step-by-step explanation: Since this is a logical "and" case, we have to multiply the separate events' probabilities...thus P(red then green) = 5/8 * 3/7 = 15/56
Answer:
3/28
Step-by-step explanation:
3 red+ 5 green = 8 marbles in the jar
1st marble:
P(red) = number of red/ total = 3/8
We keep the marble
2 red+ 5 green = 7 marbles in the jar
P(green) = number of green/ total = 2/7
P (red,keep,green) = P(red)* P(green) = 3/8*2/7 = 6/56 = 3/28
URGENT ! Need help!!!
Which of the sets of ordered pairs represents a function?
A = {(–4, 5), (1, –1), (2, –2), (2, 3)}
B = {(2, 2), (3, –2), (9, 3), (9, –3)} (4 points)
Only A
Only B
Both A and B
Neither A nor B
Answer:
I believe its only B
Answer: I would say neither A nor B
Step-by-step explanation: each input needs to only have 1 output
Andre says 10x + 6 and 5x + 11 are equivalent because they both equal 16 when x is 1. Do you agree with Andre?
Answer:
No, They are not equivalent
Step-by-step explanation:
The two expressions are only said to be equivalent if they are the same regardless of whatever value the variable(s) is.
The variable in this question is x.
To prove this, we equate both expressions:
[tex]10x + 6 = 5x + 11[/tex]
[tex]10x - 5x = 11 - 6\\\\\\5x = 5\\\\\\x = 1[/tex]
This shows that they have the same value ONLY when x is 1.
This is why Andre says that they are equivalent, but they are not.
No, I do not agree with Andre because the two equations 10x + 6 and 5x + 11 are indeed equivalent.
Explanation:No, I do not agree with Andre. Two equations are considered equivalent if they have the same solution for all values of x.
Let's check if 10x + 6 and 5x + 11 are equivalent by substituting x = 1 into both equations:
For 10x + 6: 10(1) + 6 = 10 + 6 = 16
For 5x + 11: 5(1) + 11 = 5 + 11 = 16
We can see that both equations indeed equal 16 when x is 1, so Andre is correct in this case. 10x + 6 and 5x + 11 are equivalent equations.
The length of a rectangle is 2x - 1cm. The width is 6cm.
Write an expression for the perimeter of the rectangle. Simplify the
expression.
Answer: 4x+10 cm
Step-by-step explanation:
length of rectangle= 2x-1cm
breadth of rectangle= 6 cm
perimeter of rectangle= 2(L+B)
= 2( 2x-1+6) (substituting the values)
=2(2x+5)
=4x+10
Therefore, the perimeter of the rectangle is 4x+10 cm.
Hope it will help you...
Write 4.768 as a common fraction, proper or improper and then reduce. .
The number n = 4.768 as a fraction is A = 596/125
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the number be represented as n
Now , let the fraction be A
where the value of n = 4.768
And , to convert a decimal to a fraction, we can write the decimal as a fraction with the decimal value in the numerator and a power of 10 in the denominator that corresponds to the number of decimal places.
For 4.768, the decimal value is 768, which is three decimal places to the right of the decimal point. Therefore, we can write:
4.768 = 4 + 0.768
= 4 + 768/1000
= 4000/1000 + 768/1000
= 4768/1000
This fraction can be reduced by dividing both the numerator and denominator by their greatest common factor, which is 8:
4768/1000 = (8 × 596)/(8 × 125)
A = 596/125
Hence , the fraction is A = 596/125
To learn more about fractions click :
https://brainly.com/question/29766013
#SPJ3
A truck driver drove his truck at an average speed of 45 miles per hour for 3 hours. A bus driver drove an average speed of 50 miles per hour for 5 hours.
Which explanation correctly tells how to find the difference in the distances they drove?
A.
Step 1 Divide: 45 ÷ 3.
Step 2 Divide: 50 ÷ 5.
Step 3 Add the two quotients.
B.
Step 1 Divide: 45 ÷ 3.
Step 2 Divide: 50 ÷ 5.
Step 3 Subtract the two quotients.
C.
Step 1 Multiply: 45 × 3.
Step 2 Multiply: 50 × 5.
Step 3 Add the two products.
D.
Step 1 Multiply: 45 × 3.
Step 2 Multiply: 50 × 5.
Step 3 Subtract the two products.
Answer:
A
Step-by-step explanation:
The length, width and height of a rectangular box are represented by 2x, 4x+1 and 5x-6 respectively. When the volume is expressed as a polynomial in standard from, what is the coefficient of the 2nd term?
Answer:
the coefficient of the 2nd term: - 38
Step-by-step explanation:
V = 2x (4x + 1) (5x - 6)
=(8x² + 2x) (5x - 6)
= 40x³ - 38 x² - 12x
Can someone plz help
The volume of a cube is 2,460.375 cubic inches, what is the length of each side of the cube?
[tex]V=a^3[/tex]
[tex]2,460.375=a^3\\a=\sqrt[3]{2,460.375} \\a=13.5[/tex]
Answer: length is equal to 13.5
what is the slope indicated in the table below
x 4 6 8 10
y 7 14 21 28
Answer:
3/2
Step-by-step explanation:
So for the x it increases by +2. For the y it increases by +7. We do rise over run which is y over x. So it will be 3/2.
Answer: 3.5 or 7/2
Step-by-step explanation: use the slope formula y2-y1 / x2-x1
I chose 14-7 / 6-4
A field has 7,363 1/8 square feet. The width of the field is 62 1/4 feet. Estimate the length of this field.
HELP!!!!
What is the area of the shaded region?
Answer:
15 cm
Step-by-step explanation:
multiply the two numbers
Area of shaded region = Area of bigger circle - Area of smaller circle
[tex] = \pi( {5}^{2} - {3}^{2} ) \\ = 3.14 \times (25 - 9) \\ = 3.14 \times 16 \\ = 50.24 \: {cm}^{2} \\ [/tex]
.. Megan's aquarium has a volume of 4,320 cubic inches. Which could be
the dimensions of the aquarium? Mark all that apply.
A 16 in. by 16 in. by 18 in.
© 12 in. by 15 in. by 24 in.
B 14 in. by 18 in. by 20 in.
D 8 in. by 20 in. by 27 in.
Answer:
Step-by-step explanation:
Find the product.
-7(- a2 )( -b3 )
Answer:
-7a^2 b^3
Step-by-step explanation:
-7(- a^2 )( -b^3 )
-7 * -a^2
A negative times a negative is a positive
7a^2
7a^2 * -b^3
A positive times a negative is a negative
-7a^2 b^3
I’m having a hard time help me
Answer:
The answer is 2881
Step-by-step explanation:
Look at the attached picture ⤴
I have shown the steps there....
So,Hope it will help u ....:)
✴Have a great day✴
Students measure the length of their feet in inches. The data is shown in the frequency table below. If the data were displayed in a dot plot, which of the measures would not be 11? (Check all that apply.)
Foot Length Tally Frequency
9 || 2
10 ||| 3
11 ||||| 5
12 | 1
range
mode
median
mean
Answer: The correct answer is mean and range.
What is the approximate volume of the tube? Round to the
nearest whole cubic centimeter
A cylindrical cardboard tube with a diameter of 8
centimeters and a height of 20 centimeters is used to
package a gift
20 cm
1,005 cm
1,340 cm?
03.351 cm
4,021 cm
8 cm
Answer:
Cylinder Volume = π • r² • height
radius = 4 cm
Volume = π • 4^2 * 20
Volume = PI * 320
Volume = 1,005.3096491487 which rounds to
1,005 cubic centimeters
Actually ALL those answers should say CUBIC CENTIMETERS.
Step-by-step explanation:
A cylinder has a volume of 140 pi cubic meters and a height of 14 meters. What is the area of the base?
10 pi square meters
12 pi square meters
126 pi square meters
1,960 pi square meters
Answer:
10
Step-by-step explanation:
divide 140 by 14 and you get 10
Which shows the most likely side lengths for a parallelogram? A. 9, 4, 9, 4. B. 9, 9, 9, 4 C. 4, 4, 4, 9 or D. 4, 9, 9, 6
Option A(9,4,9,4) shows the most likely side lengths for a parallelogram because opposite sides of parallelogram are always equal.
Hope it will help u...
hello:) I need help with this. Thanks!
Answer:
Please see the attached pictures for full solution
i need help please PL
THE ANSWER IS A PART BECAUSE WHEN YOU MAKE MIXED FACTION IN FRACTION AND FIND THE DENOMINATORS BY TAKING OUT LCM IT WILL BE 18
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 11 ft?
Which equation gives the volume of the sphere?
Answer:
C
Step-by-step explanation:
credit to the first guy
Answer:
D
Step-by-step explanation:
I took the test