Answer:
[tex]\sf x =15.5[/tex]
Step-by-step explanation:
[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=5[/tex]
[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=log_2 (32)[/tex]
[tex]\sf log_2\left\dfrac{(10x+5)}{5} =log_2 (32)[/tex]
[tex]\sf 2x+1 =32[/tex]
[tex]\sf 2x+1 -1=32-1[/tex]
[tex]\sf 2x =31[/tex]
[tex]\sf x =15.5[/tex]
Answer:
Step-by-step explanation:
[tex]log_{a}[/tex] [tex]x_{1}[/tex] - [tex]log_{a}[/tex] [tex]x_{2}[/tex] = [tex]log_{a}[/tex] [tex]\frac{x_{1} }{x_{2} }[/tex]
[tex]log_{a}[/tex] x = b ⇒ [tex]a^{b}[/tex] = x
~~~~~~~~~~~~~~
[tex]log_{2} (10x+5)[/tex] - [tex]log_{2} 5[/tex] = 5
[tex]log_{2} \frac{10x+5}{5}[/tex] = 5
[tex]\frac{10x+5}{5}[/tex] = [tex]2^{5}[/tex]
10x + 5 = 32 × 5
2x + 1 = 32
x = 15.5
ILL MARK BRAINILEST !! 80 POINTS
Question 1: 11 pts
Find the vertex of the parabola y = x2 - 10x + 16.
A. (-5,91)
B. (-9,5)
C. (5,-9)
D. (8,0) and (2,0)
5 and 1/3 divied by 2 and 2/9
Answer:
Step-by-step explanation:
16/3 / 20/9 = 16/3 x 9/20= 12/5 which is 2 2/5e
please ifs due today!!
Select each correct answer.
f(x) is a polynomial function.
f(x) is an exponential function.
g(x) is a polynomial function.
g(x) is an exponential function.
The output values of f(x) will remain greater than those of g(x) as the input values continue to increase.
The output values of g(x) will surpass those of f(x) as the input values continue to increase.
Answer:
f(x) is a polynomial function.g(x) is an exponential function.The output values of g(x) will surpass those of f(x) as the input values continue to increase.Explanation:
f(x) has a function of x³g(x) has a function of [tex]\sf 3^X[/tex]False statements:
The output values of f(x) will remain greater than those of g(x) as the input values continue to increase.f(x) is an exponential function - as crosses x-axis, exponential never crosses x-axisg(x) is a polynomial function - as has no valid power.Answer:
By examining the table of ordered pairs, notice that the function f(x) is the cube of [tex]x[/tex]. Therefore, [tex]f(x)=x^3[/tex]
By examining the table of ordered pairs, notice that as [tex]x[/tex] increases by a constant value, the value of the function g(x) increases by the common ratio of 3. Therefore, [tex]g(x)=3^x[/tex]
From the table, both functions equal 27 when [tex]x=3[/tex], therefore, the point of intersection of the two functions is (3, 27).
As x increases past [tex]x=3[/tex], g(x) increases quicker than f(x) since g(x) is an exponential function and f(x) is a cubic polynomial.
So the following statements are true:
f(x) is a polynomial functiong(x) is an exponential functionThe output values of g(x) will surpass those of f(x) as the input values continue to increase.Please refer to the attached graph of both functions with plotted ordered pairs.
this polygon has an area of 72 square centimeters what is the height of the parallelogram
What happened to rectangle A to become rectangle B in the diagram below?
dilated and then translated
dilated and then rotated 270°
dilated and then reflected
dilated and then rotated 90°
Answer: Dilated and then translated
Step-by-step explanation:
Answer:
dilated and then translated
Step-by-step explanation:
Rectangle A has been enlarged (dilated) and then translated up and to the right.
Find the volume of the given figure. Round your answer to the nearest tenth. See picture for full problem. Please and thank you so much!(:
Answer:
146.7
Step-by-step explanation:
The equation for finding the volume of a pyramid is [tex]V = \frac{l w h}{3}[/tex].
For this pyramid, the height is 8, the width is 5, and the length is 11.
[tex]\frac{11x5x8}{3}[/tex]=146.67
146.67 rounded to the nearest tenth = 146.7.
given triangle, ABC is congruent to triangle EDC find A
Answer:
m<A = 30 degrees.
Step-by-step explanation:
m < C in triangle ABC = m < C in EDC so
x + 13 + 42 + x + 13 = 180
2x = 180 - 13 - 13 - 42
2x = 112
x = 56.
So m < C = 56+13 = 69.
m < B = m < D = 81
M < A = 180 - 69 - 81
= 180 - 150 = 30.
The length of a rectangle is 12 feet more than twice the width. If the area is 320 square feet, what is the length? What is the width?
Answer:
Length of rectangle is 32 feet and width is 10 feetStep-by-step explanation:
Given,
The length of a rectangle is 12 feet more than twice the width and area is 320 square feetLet's assume, width of rectangle x feet and length of the Rectangle be 12 + 2x respectively. To Calculate the length and width of rectangle we'll use the formula of area of rectangle:
[tex] \\ \star \: { \underline{ \boxed { \pmb{ \sf{ \purple{Area _{(rectangle)}= Length \times width}}}}}} \\ \\ [/tex]
Substituting the required values:
[tex]\dashrightarrow \sf \: \: \: \: (12 +2x) (x) = 320 \\ [/tex]
[tex]\dashrightarrow \sf \: \: \: \: 12x + 2x^2 = 320 \\ [/tex]
[tex]\dashrightarrow \sf \: \: \: \: 12x + 2x^2- 320 = 0 \\ [/tex]
[tex]\dashrightarrow \sf \: \: \: \: 2x^2 + 12 - 320 = 0 \\ [/tex]
[tex]\dashrightarrow \sf \: \: \: \: 2(x^2 + 6x - 160) = 0 \\ [/tex]
[tex] \dashrightarrow \sf \: \: \: \: 2(x^2 + 16x - 10x - 160) = 0 \\ [/tex]
[tex]\dashrightarrow \sf \: \: \: \: 2(x - 10)(x + 16) = 0 \\ [/tex]
[tex]\dashrightarrow \: \: \: \: \underline{ \boxed{ \purple{ \pmb{ \rm{ x = 10 \: or \: -16}}}}} \\ [/tex]
Hence,
Width of rectangle = x = 10 feet Length of rectangle = 12 + 2x = 12 + 2(10) = 32 feet[tex]~[/tex]
[tex] \underline{\therefore{ \pmb { \frak{Length \: and \: width \: of \: rectangle \: is \: 32 \: and \: 10 \:ft}}}}[/tex]
What is the area and perimeter? Show your work
Answer:
area = 6
perimeter = 12
Step-by-step explanation:
area:
1.8+3.2 = 5
5*2.4 = 12
12/2 = 6
perimeter:
3+4+1.8+3.2 = 12
answet please and please show work
Answer:
4, 3, 4
Step-by-step explanation:
The unsimplified ratio of squares to triangles is 6:8, which simplifies to 3:4. That means, for every 3 squares, there are 4 triangles
As stated above, the simplified ratio of squares to triangles is 3:4
I need help but I need the correct answer everyone is giving me the wrong answer !!
Answer:
y - 2 = 6 (x - 1)
Step-by-step explanation:
Slope intercept form equations look like this:
y - y1 = m (x - x1)
***m = [tex]\frac{y2-y1}{x2-x1}[/tex]
Using the point (1,2), we know that x1 = 1 and y1 = 2. Let's sub these values into the slope intercept equation:
y - 2 = m (x - 1)
To complete this equation, we need to find slope. Pick out another point on the graph and plug into the slope equation. We can use point (2,8), where (1,2) = Point 1 and (2,8) = Point 2.
[tex]\frac{y2-y1}{x2-x1}=\frac{8-2}{2-1} =\frac{6}{1} =6[/tex]
Now that we know m = 6, let's plug that back into the original equation to get our final answer:
y - 2 = 6 (x - 1)
I hope this helps!
Factor the expression 20x + 12y - 28
Answer:
[tex]\boxed{\sf{4(5x+3y-7)}}[/tex]
Step-by-step explanation:
It is necessary to find the factors and solve them using their expressions in order to solve this problem.
20x+12y-287*4=28
3*4=12
5*4=20
Rewrite the problem down.
5*4x+3*4y+7*4
Solve.
Common term of 4.
4(5x+3y-7)
Therefore, the final answer is 4(5x+3y-7).I hope this helps you! Let me know if my answer is wrong or not.
[tex]========================================[/tex]
In order to factor this expression, we should factor out the common term (divide all terms in the polynomial by the common term)
In this case, the common term is
4
Note:- Usually, we factor out the G.C.F. (Greatest Common Factor)
So here, the G.C.F. is 4.
Why 4? Because in this trinomial (a polynomial with 3 terms) all 3 terms are divisible by 4.
So divide all the terms
5x
3y
-7
Put 4 outside the parentheses:
4(5x+3y-7)
Is the trinomial in its simplest form? Sure!
Hence, we are done! :)
[tex]================================[/tex]
note:-Hope everything is clear; if you need any more clarification/explanation, kindly let me know, and I will comment and/or edit my answer. :)
A recycling bin is in the shape of a right rectangular prism. The bin is 9 meters long, 5 meters wide, and 313 meters tall.
What is the volume of the recycling bin?
Answer: 14085 m^3.
Step-by-step explanation: To find the volume of a right rectangular prism, you need to multiply the length, width, and height. The equation is below:
l x w x h = V where l is the length, w is the width, h is the height, and V is the volume of the right rectangular prism.
The length of this recycling bin is 9 meters, the width is 5 meters, and the height is 313 meters. Now that we know the length, width, and height, we can substitute the variables with the information we've gathered.
9 x 5 x 313 = 14085.
Therefore, 14085 m^3 is your answer.
Have a great day! :)
Please help i will give brainly :
1) The x-axis represents the energy ([tex]E[/tex]), in joules. The y-axis represents the amplitude ([tex]x[/tex]), in milimeters.
2) The curve depicts an monotonous decrecent rate of change.
3) The amplitude is directly proportional to the root square of the energy.
How to analyze a graph relationship between two variables
In this question we have a relationship between two variables, in which we must apply principles of functional analysis to respond three questions presented in the statement.
Now we proceed to answer the three questions below:
What is on the x-axis? The y-axis? R/ The x-axis represents the energy ([tex]E[/tex]), in joules. The y-axis represents the amplitude ([tex]x[/tex]), in milimeters.How would you describe the rate of change of the line? R/ The curve depicts an monotonous decrecent rate of change, that is, the slope converges to zero when the energy tends to infinite.What does this tell you about the relationship between amplitude and energy? R/ The curve show a strong similarity with a function of the form [tex]x = A\cdot \sqrt{E}[/tex]. Hence, the amplitude is directly proportional to the root square of the energy.To learn more on functions, we kindly invite to check this verified question: https://brainly.com/question/12431044
On a circle of radius 10 feet, what angle would subtend an arc of length 6 feet?
Answer:
34.38 (rounding to the nearest hundredth)
Step-by-step explanation:
I have my work linked below, but I used to arc length formula and plugged in all known numbers. Then solved for x which will be the angle you are looking for. Hope this helps!
On a circle of radius 10 feet, 34.37° angle would subtend an arc of length 6 feet.
How to find the length of an arc?The length of an arc formula is represented as follows
The length of arc = Ф / 360 × 2πr
where
Ф = angle, r = radius
It is given that circle of a radius of 10 feet,
The length of arc = 6 ft
Therefore,
6 = Ф / 360 × 2 × 3.14159 × 10
6 = 62.8318Ф / 360
360 x 6 = 62.8318Ф
Ф = 360 x 6 / 62.8318
Ф = 34.3784
Ф ≈ 34.37°
Learn more about the length of the arc ;
https://brainly.com/question/2899332
#SPJ4
What is 170.6% of 366?
Answer:
624.396
Step-by-step explanation:
I did the math myself XD
Given m \| nm∥n, find the value of x.
Answer:
x=140(corresponding angle)
Corresponding angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal
The 140° angle on line m and the x° angle on line n are corresponding angles.
The value of x is 140°
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
The figure is given,
Line m and Line n are parallel.
t line is the transversal line on the two parallel lines, line m and line n.
We see that,
140° angle on line m is corresponding to the x° angle on line n.
Corresponding angles are equal.
So,
140° = x°
x° = 140°
Thus,
The 140° angle on line m and the x° angle on line n are corresponding angles.
The value of x is 140°
Learn more about corresponding angles here:
https://brainly.com/question/1597341
#SPJ5
Pls help I’ll give you 25 points
Answer:
For the 1st row:
6.38 - 6 19/50 - 638%
Step-by-step explanation:
I would suggest using MathPapa if you are trying to do it quick. MathPapa will only really help with finding fractions and percentages, though. To get the decimal, need to find percentages then move decimal to the left 2 times.
ex. 125% -> 1.25
I hope this helps! Have a blessed rest of your night!
6. Complete a glide translation (x-2, y) and then reflect over x axis. What would be the new ordered pairs for P'and S'?
The glide translation and the reflection over x-axis are illustrations of transformation
The new ordered pairs for P'and S'are (x - 2, -y)
How to determine the new ordered pairs?The given parameters are:
Glide translation (x-2, y)
Reflection over x axis
Assume the coordinates of point P and S are (x,y)
When translated, the new points would be:
(x-2, y)
The rule of reflection over the x-axis is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex](x - 2,y) \to (x - 2,-y)[/tex]
Hence, the new ordered pairs for P'and S'are (x - 2, -y)
Read more about transformation at:
https://brainly.com/question/4289712
What is the measure of angle x?
Enter your answer in the box
Answer:
x = 83°Step-by-step explanation:
There are 6 angles, 3 pairs of vertical angles that sum to 360°.
Set below equation and solve for x:
2(41° + 56° + x) = 360°97° + x = 180°x = 180° - 97°x = 83°Opposite angles are equal and linear pairs are supplementary
x+56+41=180x+97=180x=180-97x=83°PLEASE HURRY!
A bag of tokens contains 5 red, 10 green, and 8 blue tokens. What is the probability that a randomly selected token is red and green? Enter your answer as a fraction.
Answer:
50/529
Step-by-step explanation:
Total: 5 + 10 + 8
= 23
P(A and B) = P(A) x P(B)
P(A and B) = 5/23 x 10/23
P(A and B) = 50/529
[Been stuck on this one for a while, please help if you can]
In order for you to carry a bag on the plane, it must fit inside the carry-on Baggage Check Box.
The carry-on Baggage Check Box has dimensions of approximately 22 inches x 14 inches x 9 inches.
Your black bag has a height of 18 inches, a depth of 12 inches and a width of 8 inches.
Your blue bag has a height of 18 inches, a depth of 15 inches and a width of 10 inches.
What is the volume of the Carry-on Baggage Check Box?
What is the volume of the black bag?
What is the volume of the blue bag?
Which bag will definitely fit in the Check Box? Explain.
-------------------------
You notice these two old suitcases stacked in the closet. The smaller suitcase is 25 inches x 8 inches x 9 inches and the larger suitcase is 75 inches x 20 inches x 18 inches.
The bigger suitcase is how many times larger than the smaller suitcase? HINT: You will need to divide on this one.
You decide to use the larger suitcase to transport rectangular prism watermelons back home. The watermelons are about 720 cubic inches. If one of the watermelons is about 10 inches long and 9 inches wide, about how tall would it be? (Hint: V=LxWxH, so plug h in 720=10x9xH and solve for H).
If the watermelons are about 720 cubic inches, what is the MAXIMUM amount of watermelons you’ll be able to bring home in your larger suitcase, assuming all you have in the suitcase is the watermelons. (Hint: Divide the larger suitcase volume and the volume of the watermelon).
The given dimensions of the, Check Box, bag, suitcase, and watermelons, we have;
First part;
Volume of the Check box is 2,772 in.³
Volume of the black bag is 1728 in.³
Volume of the blue bag is 2700 in.³
The bag that will definitely fit in the Check Box is; The black bagSecond part;
The number of times, the bigger suit case is larger than the smaller suit case is 15 timesThird part;
The height of the watermelon = 8 inchesThe maximum number of watermelon the larger suitcase can carry is 36 watermelonHow can the volume of the suitcases be found?Volume of the Carry-on baggage Check box, V_c can be found as follows;
V_c = 22 × 14 × 9 = 2772
Volume of the Check box, V_c = 2,772 in.³Volume of the black bag, V_b, can be found as follows;
V_b = 18 × 12 × 8 = 1728
Volume of the black bag, V_b = 1728 in.³Volume of the blue bag, V_bl, can be found as follows;
V_bl = 18 × 15 × 10 = 2700
Volume of the blue bag, V_bl = 2700 in.³Given that the height, depth and width of the black bag are smaller than the height, depth and width of the check box
The bag that will definitely fit in the Check Box is; The black bagSecond part;
Volume of the smaller suitcase is found as follows;
V_s = 25×8×9 = 1800
Volume of the bigger suitcase is found as follows;
V_b = 75 × 20 × 18 = 27,000
The number of times, the bigger suitcase is larger than the smaller suitcase is therefore;
n = 27,000 ÷ 1809 = 15
The number of times, the bigger suit case is larger than the smaller suit case is 15 timesThird part
The volume of the watermelon = 720 in.³
Which gives;
10 × 9 × H = 720
H = 720 ÷ (10 × 9) = 8
The height of the watermelon = 8 inchesTo maximize the number of watermelons, we have;
The length, 10, is a factor of 20
The width, 9, is a factor of 18
Therefore, we have;
Two rows of watermelon, and two layers of watermelon
Number of watermelon in a row is therefore;
R = 75 ÷ 8 ≈ 9
Maximum number of watermelon is therefore;
Max_n = 9 × 2 × 2 = 36
The maximum number of watermelon the larger suitcase can carry is 36 watermelonLearn more about finding the volume of a figure here:
https://brainly.com/question/1452651
Jill wants to have ride at least 144 miles on her bike. Her riding speed is 9 miles per hour. Which inequality(s) represents how many h hours she needs to ride?
Hey there!
Let's make an equation
=> 9h = 144
{ Make h the subject of formula}
=> 9h = 144
=> 9h/9 = 144/9
=> h = 144/9
=> h = 16
Chloe has a part-time job at an ice skating rink selling hot cocoa. She decided to plot
the number of hot cocoas she sold relative to the day's high temperature and then
draw the line of best fit. What does the line's y-intercept represent?
Answer: a prediction of the number of hot cocoas sold when the temperature is 0F
Step-by-step explanation: i did it on delta math
The line's y-intercept represent ''Number of hot cocoas sold''.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Chloe has a part-time job at an ice skating rink selling hot cocoa.
She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.
Now,
Since, She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.
Hence, By the graph we have;
The line's x - intercept represent ''Temperature''.
And, The line's y-intercept represent ''Number of hot cocoas sold''.
Thus, The line's y-intercept represent ''Number of hot cocoas sold''.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
What are the prime numbers between 2010 and 2020
Answer: 99%
Step-by-step explanation:
Find the volume of the sphere. Round your answer to the nearest tenth.
Use 3.14 for it.
A sphere has a diameter of 3.8 centimeters.
The volume of the sphere is about
cm3
HELP ME PLS
Answer:
Step-by-step explanation:
Remark
You are given the diameter but the formula uses the radius. So your first job is find the radius. Then you use this value in the formula to find the volume. Substitute
Givens
pi = 3.14
d = 3.8
r = d/2
r = 3.8/2 = 1.9
Formula
V = (4/3) * pi * r^3
Solution
V = (4/3) * 3.14 * 1.9^3
V = 4/3 * 3.14 * 6.859
V = 28.7163
The Sum of the measures of angle X & Y is 90 degrees
The measure of angle X is 6x
The measure of angle Y is 24
what is the value of X?
Step-by-step explanation:
X + Y = 90
Y = 24
X = 6x
X + 24 = 90
X = 66
x = X/6 = 66/6 = 11
how do you do thissss???
The solid above is a triangular prism. Therefore, the surface area of the triangular prism is 157.2 cm².
How to calculate surface areaThe figure above is a triangular prism. The surface area of a triangular prism can be calculated as follows:
Surface area = bh + l(p)
where
p = perimeter of the triangular basel = height of prismb = base of the triangular baseh = height of the triangular baseTherefore,
p = 6 + 6 + 6 = 18 cm
l = 7 cm
b = 6 cm
h = 5.2 cm
Therefore,
Surface area = (6 × 5.2) + 7(18)
Surface area = 31.2 + 126
Surface area = 157.2 cm²
learn more on surface area here: https://brainly.com/question/2835293
Can some please explain and solve how to do these unit rate equations?