Answers
We have the question as
[tex]4^{x+6}=20[/tex]Let us introduce logarithms to base 4 to both sides of the equation:
[tex]\log _44^{x+6}=\log _420[/tex]Applying the law of logarithm that states
[tex]\log A^B=B\log A[/tex]we have
[tex](x+6)\log _44=\log _420[/tex]Applying the law that states
[tex]\log _nn=1[/tex]we have
[tex]\begin{gathered} (x+6)\times1=\log _420 \\ x+6=\log _420 \end{gathered}[/tex]Collecting like terms, we have
[tex]x=-6+\log _420[/tex]Therefore, the answer is OPTION C.
Related Questions
The local newspaper charges $34.80 for an 8-week subscription. Paige buys an 8-week subscription. How much does it cost her each week?
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Answer:
$4.35
Step-by-step explanation:
8 weeks = $34.80
1 week = x
Cross-multiply
$34.80/8
=$4.35
So, for each week, Paige will pay $4.35
$(4.35 × 8 = 34.8)
Please help I only have the first given answer.
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By the property of congruency of triangles, the following conclusions are taken from the figure
[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]
[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]
What is congruency of triangles?
Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same.
There are five axioms of congruency
They are SSS axiom, ASA axiom, AAS axiom, SAS axiom, RHS axiom
Here,
In[tex]\Delta AEB[/tex] and [tex]\Delta DEC[/tex]
[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]
[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]
So,
[tex]\Delta AEB \cong \Delta DEC[/tex] [ASA axiom]
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Can you please solve this equation and please explain to me ^step-by-step^ (this is my homework)
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In the equation
[tex]0.07(6t-4)=0.42(t-1)+0.14[/tex]to solve for t, we first expand both sides of the equation.
[tex]0.42t-0.28=0.42t-0.42+0.14[/tex]We subtract 0.42t from both sides to get
[tex]-0.28=0.42+0.14[/tex]The right side does not equal the left side of the equation; therefore, this equation has no solution and choice C is correct.
im gonna send a photo of the problem
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You have the following interval:
(-∞,-2]
the previous interval can be written as follow:
x ≤ -2 as an inequality
and on the number line you have:
I really sure what to do for this question some help would be greatly appreciated
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Given the Domain and the Range of the relation, you need to remember that the Domain is the set of all input values (x-values), and the Range is the set of all the output values (y-values).
Therefore, knowing the input values and the corresponding output values indicated in the Diagram, you can write the following ordered pairs:
[tex](1,9),(4,10),(10,3)[/tex]Notice that they have this form:
[tex](x,y)[/tex]Where "x" is the x-coordinate of the point, and "y" is the y-coordinate.
Therefore, you need to plot all the points on the Coordinate Plane in order to express the relation as a graph.
Hence, the answer is:
Which of the following transformations are used when transforming the graph of the parent function f(x) = log7x to the graph of g(x) = -log7(3x)+4? Select all that apply.
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In this problem, we have the transformations
option B (shift the graph of f(x) 4 units up
option C reflect the graph of f(x) over the y-axis
I need help with my math
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Given data:
The given points are (-2,-1) and (3, -1).
The slope of the line passing through the given points is,
[tex]\begin{gathered} m=\frac{-1-(-1)}{3-(-2)} \\ =\frac{0}{5} \\ =0 \end{gathered}[/tex]Thus, the slope of the line passing through the given points is 0.
what is the mean? 66, 594, 69, or 74what is the median? 74, 66, 69, or 75what is the mode? 74, 90, 21, or 66what is the range? 69, 66, 74, or 594
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We have the distribution;
74, 90, 21, 68, 62, 84, 34, 87,74.
Let's arrange this from ascending to descending order, we obtain;
[tex]21,34,62,68,74,74,84,87,90[/tex]i. The mean or average of this distribution is
[tex]\begin{gathered} \frac{21+34+62+68+74+74+84+87+90}{9}=\frac{594}{9} \\ \operatorname{mean}=66 \end{gathered}[/tex]ii. The median is the central value, in this distribution, there are 9 values, so the median value is the 5th value.
[tex]\operatorname{median}=74[/tex]iii. The mode is the value with the highest frequency, this is the most occurring value, in this distribution;
[tex]\text{mode}=74[/tex]iv. The range is the difference between the highest and lowest values, this is;
[tex]\begin{gathered} 90-21=69 \\ \text{Range}=69 \end{gathered}[/tex]
Britta is preparing a budget. What does this task MOST likely involve?A. She is looking at her credit card bills to predict her credit score.B. She is not allowing herself to spend any money for 30 days.C. She is allotting a set amount of money for her expenses.D. She is determining which investments are the best fit for her goals.
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From the question we are to determine Britta most likely task in preparing a budget.
First let's know what a budget is.
A budget is an estimation of revenue and expenses over a specified future period of time and is utilized by governments, businesses, and individuals. A budget is basically a financial plan for a defined period, normally a year that is known to greatly enhance the success of any financial undertaking.
So with the above explanation of what a budget is, Britta most likely task is to allot a set amount of money for her expenses.
Therefore the correct option is C, which is She is allotting a set amount of money for her expenses.
g(0) 10 Cabin Rental Cost ($) У 70 60 50 + (0,57] ) 40 30 10 1 (0.15) 0 1 2 3 4 5 6 7 8 9 10 Number of Days
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f(x) = x +57
g(x) =7x+15
The solution is (7,64). To rent the cabin for 7 days cost $64
1) Let's examine the graph. We can see two linear equations.
Picking two points for f(t) = (7,64) and (0,57) and for g(t) (0,15) and (7,64) let's find out their respectives slopes:
2) For f(t) , let's plug into the slope-intercept formula, plugging one point:
(0,57)
y=mx+b
57=0x +b
57= b
So the rule for the function is, in terms of f(x) = x +57
(0,15)
y=mx +b
15=0x +b
15 =b
So the rule for the function g(t) , in terms of g(x) is g(x) =7x+15
Interpreting the solution:
The solution to this Linear System of Equations is the common point (7,64).
So filling in the blanks we have:
The solution is (7,64). To rent the cabin for 7 days cost $64
Can you help me solve this? And step by step please?
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Given the sequence:
1/2, 3/4, 9/8, 27/16, ..........
We are to find the recursive formular
A recursive geometric formular has a pattern:
An = An - 1 * r
Where r is the common ratio. But before we write the formular, we need to look for the value of r.
This r value has to be the same between each consecutive number in the series.
Sinces it's geometric, r is multiplied in. To get from 1/2 to 3/2 we find the r value in this way:
x/2 = 3/4 where x/2 is the same as 1/2 x.
Cross multiply to get 4x = 6 and x = 3/2.
That means that if r is 3/2, then we can multiply every term in that sequence by 3/2 to get the next term in line.
3/4 times 32 is 9/8. So, r = 3/2 and the formulat is:
An = An - 1 * 3/2
Therefore, the crrect optio is B.
Writing an equation of a probably given the vertex and focus
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The equation of the vertical parabola in vertex form is written as
[tex]y=\frac{1}{4p}(x-h)^2+k[/tex]Where (h, k) are the coordinates of the vertex and p is the focal distance.
The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.
[tex]p=1-6=-5[/tex]Using this value for p and (3, 1) as the vertex, we have our equation
[tex]y=-\frac{1}{20}(x-3)^2+1[/tex]5)For positive values of x, which expression isequivalent toSquare root 16x2*x2/3+square root 8x^5/3
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The answer is option B
Given:
/16x^2 + x^2/3 + 3/8x^5
You need to simplfiy the expression given which will give you
6 3/x^5 or the second option
[tex]6\sqrt[3]{x^5}[/tex]Use the given information to determine the lateral and surface areas of thesolid. Round your answer to the nearest unit.
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Here, we want to use the given information to calculate the lateral and the total surface area
To find the lateral area, we have to calculate the perimeter of the base and multiply this by the height of the triangular prism
Now, we will make the shape lie on its side
This mean the triangles will represent the base
Mathematically, the perimeter of a triangle is the sum of its side
We need the last side of the triangle
We can get this by the use of Pythagoras' theorem
As we can see, the side measure 5 is the hypotenuse as it faces the right angle
The square of the hypotenuse equals the sum of the squares of the two other sides
3,4 and 5 are a Pythagorean triple
This means that, the measure 3 is the last side of the triangle
So the perimeter is;
[tex]3+4+5\text{ = 12 in}[/tex]The height is the measure 8 inches
Thus, the lateral area is;
[tex]12\text{ }\times8=96in^2[/tex]Now, we want the total surface area, but firstly, we need the area of the base
The area of the base is the area of the triangle
[tex]\begin{gathered} B\text{ = }\frac{1}{2}\times b\times h \\ \\ B\text{ = }\frac{1}{2}\times4\times3=6in^2 \end{gathered}[/tex]two times this is 12 in^2
The total suface area is thus;
[tex]96in^2+12in^2=108in^2[/tex]F (x) +5 x-2 Someone pls help me I’m crying
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Given the function:
[tex]f(x)=2x^2+5\sqrt[]{x-2}[/tex]to find f(3), we have to make x = 3 and substitute on the function, to get the following:
[tex]\begin{gathered} f(3)=2(3)^2+5\sqrt[]{3-2}=2(9)+5\sqrt[]{1}=18+5=23 \\ \end{gathered}[/tex]therefore, f(3)=23
Question #5The table shows four relations.RelationRelation 2Relation 3Rolation 4-2-5-3Y-4-4-2-1- 11312372Which relations represent functions?ARelation 1 and Relation 3BRelation 2 and Relation 4СRelation 3 and Relation 2DRelation 4 and Relation 1
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The RELATION 1 and 3 represent a function
Rationale
There are no x value with several y values.
For a relation to be a function, there should only one y value fot each x
-7>-10 true or false
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To answer this question we need to see it on an axis.
-7> -10 , it is true. -7 it's more near to 0.
Given the diagram below, whereAB||CD, find the measure of xand y.
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Notice that there are two triangles between the parallel lines.
Also, notice that the angle 160° and y are same-side interior angles, so they sum 180°.
[tex]160+y=180[/tex]We solve for y.
[tex]\begin{gathered} y=180-160 \\ y=20 \end{gathered}[/tex]On the other hand, angles 30 and x are alternate interior angles, which means they are congruent.
[tex]x=30[/tex]Therefore, x = 30° and y = 20°.how do I calculate the area of a partial circle?
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A part of a circle is called an arc and an arc is named according to its angle.
what number do you need to add/subtract/multiply/divide each side by in order to solve the problem below?[tex] \frac{5}{6} = - \frac{2}{3} x[/tex]
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The equation is,
[tex]\frac{5}{6}=-\frac{2}{3}\cdot x[/tex]The equation can be solved if on right side there is only variable with any number in multiplication. So equation can be solved as,
[tex]\begin{gathered} \frac{5}{6}\cdot\frac{-3}{2}=-\frac{2}{3}x\cdot\frac{-3}{2} \\ x=-\frac{5}{4} \end{gathered}[/tex]So to eliminate -2/3
At a New Car Dealership, a particularmodel comes in 4 different trim levels(CX, DX, EX, and Si). The same modelcomes in 5 different colors (Night Black,Pearl White, Evening Blue, Sandy Red,and Forest Green). The model of car alsohas 3 different interior options (GreyCloth, Tan Cloth, Black Leather). Howmany different versions of this model canbe created from these options?
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solution
diferent trim levels = 4
different colors = 5
different interior options = 3
then:
[tex]4\cdot5\cdot3=60[/tex]answer: 60 different versions of this model
In the following table of values, what would be the value of “b” in ax2 + bx + c?
–2
–9
–1
–1
0
9
1
21
2
35
1
9
11
22
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The value of b is 11.
From the question, we have
ax² + bx + c
using (0, 9)
substituting the value we get
9 = a(0)² + b(0) + c
c = 9
Therefore,
-1 = a(-1)² + b(-1) + c
-1 = a - b + 9
-1 - 9 = a - b
a - b = - 10
using (-2, -9)
-9 = a(-2)² + b(-2) + 9
-9 - 9 = 4a - 2b
-18 = 4a - 2b
2a - b = -9
combine the equation
a - b = - 10
2a - b = -9
solving the equations we get
a = 1
Then,
1 - b = -10
b = 1 + 10
b = 11
Hence, the value of b is 11.
Subtraction:
The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.
The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.
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What is the equation of the horizontal asymptote of the graph of y = 1/x+5 – 4?
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We can find the horizontal asymptote of this kind of functions using the limit:
[tex]\begin{gathered} \lim _{x\to\infty}\frac{1}{x+5}-4=\frac{1}{\infty}-4=-4 \\ \lim _{x\to\infty}\frac{1}{x+5}-4=\frac{1}{-\infty}-4=-4 \end{gathered}[/tex]Therefore the equation of the horizontal asymptote is:
[tex]y=-4[/tex]Which of the numbers 12, 13, or 14 is the solution of 106 = 118 - x?
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The given expression is
[tex]106=118-x[/tex]First, we add x on each side
[tex]\begin{gathered} 106+x=118-x+x \\ 106+x=118 \end{gathered}[/tex]Then, we subtract 106 from each side
[tex]\begin{gathered} 106-106+x=118-106 \\ x=12 \end{gathered}[/tex]i need to show work pls
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the center of the circle is at O. determine the measure of angle ABC
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If the center of the circle is at O.then the measure of angle ABC is 28 degree
The measure of angle ABC can be calculated by using central angle theorem
What is central angle theorem
The Central Angle Theorem states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points ie if the angle inscribes at the circumference is x, then the angle at the center is 2x.
The angle ABC = 1/2 angle AOC
the angle ABC = 1/2 x 56
the angle ABC is 28
Therefore, if the center of the circle is at O.then the measure of angle ABC is 28 degree
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The table below shows the thickness of coins. Coin Thickness quarter i millimeters 12 millimeters dime nickel millimeters penny 13 millimeters Hailey stacks a dime on top of a penny. She estimates the thickness of the two coins to be less than 3 millimeters. Write a symbol (, or =) in the box to make the statement true. Then use the statement to tell whether Hailey's estimate is correct. 12 + 12 + 1 Is Hailey's estimate correct?
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A dime has a thickness of 1 7/20 mm and a penny has 1 1/2 mm.
Stacking both coins, we will have :
[tex]1\frac{1}{2}+1\frac{7}{20}[/tex]and we have the inequality :
[tex]1\frac{1}{2}+1\frac{7}{20}\boxed{\text{ }}1\frac{1}{2}+1\frac{1}{2}[/tex]Note that 1 7/20 is less than 1 1/2, so the inequality symbol is "<"
[tex]1\frac{1}{2}+1\frac{7}{20}<1\frac{1}{2}+1\frac{1}{2}[/tex]since 1 1/2 + 1 1/2 is equal to 3mm
Therefore, the thickness of stacking coins is less than 3mm
Hailey's estimate is correct (Yes)
Trapezoid ABCD is shown on the coordinate plane.Trapezoid formed by ordered pairs A at negative 4 comma 1, B at negative 3 comma 2, C at negative 1 comma 2, D at 0 comma 1.If trapezoid ABCD is reflected over the x-axis and then reflected over the y-axis, which final step would carry the trapezoid onto itself?Group of answer choicesRotate 180°Rotate 90° clockwiseReflect over the x-axisReflect over the y-axis
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Given: The coordinates of a trapezoid as below
[tex]\begin{gathered} A(-4,1) \\ B(-3,2) \\ C(-1,2) \\ D(0,1) \end{gathered}[/tex]To Determine: The final step on the trapezoid after it is reflected over the x-axis and then reflected over the axis
Solution
Please note that a reflection over the x-axis and reflection over the y-axis is different from the last step, which is a reflection over the y-axis
The reflection over the y-axis could either be a rotation of 90^0 clockwise or anticlockwise.
So get the trapezid onto itself after a reflection over the y-axis from a reflection over teh x-axis requires two steps
We have step 1: Reflection over the x-axis, then
Step 2: Reflection over the y-axis
Hence, the final step is reflection over the y-axis
Solve using substitution. y = 7x + 3 y = 6x + 4(_ , _)
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We have the following:
[tex]\begin{gathered} y=7x+3 \\ y=6x+4 \end{gathered}[/tex]solving using substitution:
[tex]\begin{gathered} 7x+3=6x+4 \\ 7x-6x=4-3 \\ x=1 \end{gathered}[/tex]for y:
[tex]y=7\cdot1+3=7+3=10[/tex]The answer is (1, 10)
1. 2х^2 * 3x^3y * 3x^3y=1. 2х^2 * 3x^3*y * 3x^3*y=
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Given the expressions
[tex]\begin{gathered} (A).2x^2\cdot3x^3\cdot y\cdot3x^3\cdot y= \\ (B).2x^2\cdot3x^{3y}\cdot3x^{3y}= \end{gathered}[/tex]First: we group and multiply the numbers
[tex]\begin{gathered} (A).2x^2\cdot3x^3\cdot y\cdot3x^3\cdot y=(2\cdot3\cdot3)\cdot x^2\cdot x^3\cdot y\cdot x^3\cdot y=18x^2\cdot x^3\cdot y\cdot x^3\cdot y \\ (B).2x^2\cdot3x^{3y}\cdot3x^{3y}=(2\cdot3\cdot3)x^2\cdot x^{3y}\cdot x^{3y}=18x^2\cdot x^{3y}\cdot x^{3y} \end{gathered}[/tex]Now we have the expressions
[tex]\begin{gathered} (A).18x^2\cdot x^3\cdot y\cdot x^3\cdot y \\ (B).18x^2\cdot x^{3y}\cdot x^{3y} \end{gathered}[/tex]Second: we multiply the expressionswith the same base adding its exponents
[tex]\begin{gathered} (A).18x^{2+3+3}\cdot y^{1+1}=18x^8y^2 \\ (B).18x^{2+3y+3y}=18x^{6y+2} \end{gathered}[/tex]