Answers
ANSWER
[tex]C.\text{ }x=1\text{ and }x=-4[/tex]EXPLANATION
We want to find the solution set to the equation given:
[tex]\log_4(x+3)+\log_4x=1[/tex]According to the laws of logarithm, we have that:
[tex]\begin{gathered} \log_ax+\log_ay=\log_a(x*y) \\ \\ and \\ \\ \log_aa=1 \end{gathered}[/tex]Therefore, we can rewrite the equation as follows:
[tex]\log_4[(x+3)*x]=\log_44[/tex]Since the logarithms on both sides have the same base, it implies that:
[tex](x+3)*x=4[/tex]Simplify and solve for x:
[tex]\begin{gathered} x^2+3x=4 \\ \\ x^2+3x-4=0 \\ \\ x^2+4x-x-4=0 \\ \\ x(x+4)-1(x+4)=0 \\ \\ (x-1)(x+4)=0 \\ \\ x=1\text{ and }x=-4 \end{gathered}[/tex]Hence, the correct answer is option C.
Related Questions
14. (04.06 LC)The first four terms of a sequence are shown below:8, 5, 2, -1Which of the following functions best defines this sequence? (5 points)f(1) = 8, f(n + 1) = f(n) + 5; forn 21f(1) = 8, f(n + 1) = f(n) - 5; for n 2 1f(1) = 8, f(n + 1) = f(n) - 3; for n 2 1f(1) = 8, f(n + 1) = f(n) + 3; forna 1
Answers
Given
The sequence, 8, 5, 2, -1.
To find: Which of the following functions best defines this sequence?
a) f(1) = 8, f(n + 1) = f(n) + 5; for n=1,2,3,4,...
b) f(1) = 8, f(n + 1) = f(n) - 5; for n=1,2,3,4,...
c) f(1) = 8, f(n + 1) = f(n) - 3; for n=1,2,3,4,...
d) f(1) = 8, f(n + 1) = f(n) + 3; for n=1,2,3,4,...
Explanation:
It is given that,
The first four terms of a sequence is, 8, 5, 2, -1.
Since,
[tex]\begin{gathered} 5-8=-3 \\ 2-5=-3 \end{gathered}[/tex]Then, the above sequence is an arithmetic sequence.
That implies,
[tex]\begin{gathered} f(n)=f(1)+(n-1)d \\ =8+(n-1)(-3) \end{gathered}[/tex]Therefore, for n=1,2.
[tex]\begin{gathered} f(1)=8 \\ f(2)=8+(2-1)(-3) \\ =8-3 \\ =f(1)-3 \end{gathered}[/tex]Then,
[tex]f(n+1)=f(n)-3[/tex]Final result: Hence, the answer is option c).
1. Rectangular Prism: a. The measures: 1 =5, w = 7, h = 8 .. b. The measures: h =7, w = 7,1 = 7. C. W = 3.6, I = 4.2, h = 8.3
Answers
Volume of rectangular prism = Length x width x height = lwh
Part a
l=5, w=7, h=8
Volume = 5 x 7 x 8
=280 cm^3
Part b
l=7, w=7, h=7
Volume = 7 x 7 x 7
Volume = 343cm^3
Part c
l=4.2, w=3.6, h=8.3
Volume= 125.496 cm^3
If I can read 1,042 words in 5 minutes. What is my reading rate in words per minute?Round your answer to the nearest whole number.
Answers
Find the first three terms and stated term given the geometric sequence, with a1 as the first term. Given termsan=3^n-1, a5
Answers
Answer:
First three terms: 1, 3 and 9
Stated term = 81
Explanation:
Given the formula;
[tex]a_n=3^{n-1}[/tex]Let's go ahead and determine the first three terms of the geometric sequence.
For the 1st term;
[tex]\begin{gathered} a_1=3^{1-1} \\ =3^0 \\ =1 \end{gathered}[/tex]For the 2nd term;
[tex]\begin{gathered} a_2=3^{2-1} \\ =3^1 \\ =3 \end{gathered}[/tex]For the 3rd term;
[tex]\begin{gathered} a_3=3^{3-1} \\ =3^2 \\ =9 \end{gathered}[/tex]Let's now find the stated term;
[tex]\begin{gathered} a_5=3^{5-1} \\ =3^4 \\ =81 \end{gathered}[/tex](6x 2 +3x 3 +7x)−(x+3× 2 +2x 3
Answers
Given
[tex](6x^2+3x^3+7x)-(x+3x^2+2x^3\text{)}[/tex]To solve this question, let's observe the following steps
Step 1: Remove the parentheses (Brackets). So that we will obtain=>
[tex]6x^2+3x^3+7x-x-3x^2-2x^3[/tex]The next step is to collect like terms
[tex]3x^3\text{ }-2x^3\text{ + }6x^2-3x^2\text{ +}7x\text{ - x}[/tex]Then we will proceed to simplify further
[tex]x^3+3x^2\text{ + 6x}[/tex]A pizza restaurant has found that the probability that a customer will order thin crust is 0.4. In a random sample of 5 customers who order a pizza, find the probability that at least three of them want thin crust.
Answers
In this type of exercises, the probability of x successes on n reapeted trials in an experiment is given by the next formula:
[tex]P=\text{nCx}\cdot p^x\cdot(1-p)^{n-x}[/tex]Here the nCx indicates the number of different combinations of x objects selected from a set of n objects. With the given data we can solve it easily:
p = 0.4
n = 5
x = 3
[tex]\begin{gathered} P=5\text{C3}\cdot0.4^3\cdot(1-0.4)^{5-3} \\ P=10\cdot0.064\cdot0.36 \\ P=0.2304 \end{gathered}[/tex]Ms. Kirkland is baking muffins. Each batch of muffins uses 1 ½ pounds of flour. How many batches of muffins can she bake with 7 ½ pounds of flour? ______________ batches. (Just the number).
Answers
Answer:
5
Step-by-step explanation:
7.5/1.5=5
Answer: The answer is 5
Step-by-step explanation: I have my ways ;>
A number is multiplied by 6 and the product is added to 4 the sum is equal to the product of 2 and 17 find the number
Answers
A number = x
Is multiplied by 6 = 6x
And the product is added to 4 = 6x + 4
The sum is equal to the product of 2 and 17 ; 6x + 4 = 2 * 17
Solve for x
6x + 4 = 2 * 17
Combine like terms
6x = 34 - 4
6x = 30
Divide both sides by 6
6x/6 = 30/6
x = 5
Answer:
5, hope this helped my love have a good rest of your day ^^
Step-by-step explanation:
the product of 2 and 17 is 34
34 - 4 is 30
30 devided by 6 is 5
therefore, by working backwords we can figure out that this math riddle would be equal to 5 ^^
ou are making identical door prizes for a charity event. You want to use all of the following items.
54 packages of peanuts
81 fruit bars
18 CDs
You can make at most
door prizes. Each door prize would have
packages of peanuts
fruit bars, and CDs
Answers
Putting the important informations, we want to use all items and divide them into equal groups in a way that we get the most prizes.
We we want a factor that is common to the three quantities, 54, 81 and 18, and is the greatest of them.
This is a question of Greatest Common Factor or Greatest Common Divisor (different names, same thing).
To calculate it, we have to find all the common factors of theses numbers.
One way to do that is to look for numbers that can divide all of them.
The numbers are 54, 81 and 18. As we can see the three numbers are divisable by 3:
[tex]\begin{gathered} \frac{54}{3}=18 \\ \frac{81}{3}=27 \\ \frac{18}{3}=6 \end{gathered}[/tex]So, we now that 3 is a common factor. Let's note it to use later on.
Now have got 18, 27 and 6. We can see that, again, all of them are divisable by 3:
[tex]\begin{gathered} \frac{18}{3}=6 \\ \frac{27}{3}=9 \\ \frac{6}{3}=2 \end{gathered}[/tex]And let's note the "3" again to use later on.
The numbers now are 6, 9 and 2. 2 is only divisable by 2, but 9 isn't, so we don't have any more common factors.
In the end, we have the factor 3 and 3, which makes 3*3 = 9. Thus, 9 is the Greates Common Factor of 54, 81 and 18 and it divides them into 6, 9 and 2.
These are the answers we are looking for, because now we know that the most groups we can divide the items into is 9 and each group will have 6, 9 and 2 of those items.
So the phrase of the answer is:
"You can make at most 9 door prizes. Each door prize would have 6 packages of peanuts, 9 fruit bars, and 2 CDs."
Drake prepared 50 kilograms of dough in 5 hours. How many hours did Drake work if he prepared 70 kilogramsof dough at the same rate
Answers
We will determine how many hours he took to prepare 70 Kg as follows:
[tex]h=\frac{70\cdot5}{50}\Rightarrow h=7[/tex]It took him 7 hours.
graph the system of inequalties make sure your solution area is clear in your graph. then name a solution point & and a non soultion point
Answers
the red line indicates
[tex]y\ge2x-1[/tex]green line indicates
[tex]y<-x+2[/tex]the blue line indicates
[tex]y\ge-4[/tex]to find the solution point in the graph, we need to find the point at which they intersect and this graph, it doesn't have a solution point because all the three points didn't intersect
Thaddeus models the number of hours of daylight in his townas
Answers
We have the following function
[tex]D(t)=2.5\sin\frac{\pi t}{6}+12[/tex]The maximum and minimum of that function happens when sin(x) = 1 or sin(x) = -1, respectively.
Then let's find the maximum, that happens when the sin value is 1
[tex]\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot1+12 \\ \\ D(t)=2.5+12 \\ \\ D(t)=14.5 \end{gathered}[/tex]And the minimum, when sin value is -1
[tex]\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot(-1)+12 \\ \\ D(t)=-2.5+12 \\ \\ D(t)=9.5 \end{gathered}[/tex]Then the least: 9.5 hours; greatest: 14.5 hours.
Find the values of x, y, and ..m x =30020VOm 4y =m 2 =64°Po
Answers
Here is a linear equation: y=1/4x+5/41. Are (1, 1.5) and (12,4) solutions to the equation?A. Both (1, 1.5) and (12,4) are solutions to the equation.B. Neither (1, 1.5) and (12,4) are solutions to the equation.C. (1, 1.5) is a solution but (12,4) is not.D. (12,4) is a solution to the equation but (1, 1.5) is not.Explain your reasoning.3. Find the x-intercept of the graph of the equationExplain or show your reasoning.
Answers
To find if any given point is a solution for the linear equation, simply plug in the x and y values given and check if the equality stands, as following:
[tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ (1,1.5) \\ \rightarrow1.5=\frac{1}{4}(1)+\frac{5}{4}\rightarrow1.5=\frac{6}{4}\rightarrow1.5=1.5✅ \end{gathered}[/tex][tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ (12,4) \\ \rightarrow4=\frac{1}{4}(12)+\frac{5}{4}\rightarrow4=3+\frac{5}{4}\rightarrow4=4.25✘ \end{gathered}[/tex]Thereby the answer is:
C. (1, 1.5) is a solution but (12, 4) is not
Now, to find the x-intercept just make y = 0 and clear x, as following:
[tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ \rightarrow0=\frac{1}{4}x+\frac{5}{4}\rightarrow0=\frac{x+5}{4}\rightarrow0=x+5\rightarrow-5=x \\ \rightarrow x=-5 \end{gathered}[/tex]Therefore, the x-intercept is -5
A biologist just discovered a new strain of bacteria that helps defend thehuman body against the flu virus. He puts 75 cells in a petri dish, theygrow at rate of 20% per hour. How many hours will it take to create aneffective dosage of 1,750 cells? *O About 17 hoursAbout 14 hoursO About 28 hoursAbout 20 hours
Answers
Given:
Rate = 20%
Here let's use the exponential growth function to find the number of hours.
47 Dominic used the equation below to find d, the amount in dollars he would spend on gasolineto drive a distance of m miles.d =(3.5)Based on this equation, how much would Dominic spend on gasoline to drive a distance of180 miles?A $25.203.628B $21.00 - 2.94C $24.50 -343: 3.02D $28.00
Answers
Answer
Explanation
The equation that
I need help figuring out the answer to the m2
Answers
The area of the composite figure can be solved by separating the figure into 3 portions, which are 2 identical rectangles with one rectangle.
The image of the composite figure will be shown below
Let us sketch out the image of the two identical rectangles
The formula for the area(A) of a rectangle is,
[tex]A=length\times width[/tex]where,
[tex]\begin{gathered} l=length=5m \\ w=width=2m \end{gathered}[/tex]Therefore, the area(A1) of the two identical rectangles are
[tex]\begin{gathered} A_1=2\times(5\times2)=2\times5\times2=20m^2 \\ \therefore A_1=20m^2 \end{gathered}[/tex]Let me sketch the second rectangle
Therefore, the area(A2) will be
[tex]\begin{gathered} A_2=3\times2=6m^2 \\ \therefore A_2=6m^2 \end{gathered}[/tex]Hence, the area(A) of the composite figure is
[tex]\begin{gathered} A=A_1+A_2=20m^2+6m^2=26m^2 \\ \therefore A=26m^2 \end{gathered}[/tex]Therefore, the area is
[tex]26m^2[/tex]
The height of the triangle is 3 feet less than twice its base. The area of the triangle is 52 ft2. What is the height of the triangle?
Answers
Given:
Base of triangle = b
Height of triangle, h, is 3 feet less than twice its base. This is expressed as:
h = 2b - 3
Area of triangle = 52 ft²
To find the height of the triangle, use the Area of a triangle formula below:
[tex]A=\frac{1}{2}bh[/tex]Thus, we have:
[tex]\begin{gathered} 52=\frac{1}{2}\times b\times(2b-3) \\ \\ 52=\frac{b(2b-3)}{2} \end{gathered}[/tex]Let's solve for the base, b:
[tex]\begin{gathered} 52=\frac{2b^2-3b}{2} \\ \\ Multiply\text{ both sides by 2:} \\ 52\times2=\frac{2b^2-3b}{2}\times2 \\ \\ 104=2b^2-3b \end{gathered}[/tex]Subtract 104 from both sides to equate to zero:
[tex]\begin{gathered} 2b^2-3b-104=104-104 \\ \\ 2b^2-3b-104=0 \end{gathered}[/tex]Factor the quadratic equation:
[tex](2b+13)(b-8)[/tex]Thus, we have:
[tex]\begin{gathered} (2b+13)\text{ = 0} \\ 2b\text{ + 13 = 0} \\ 2b=-13 \\ b=-\frac{13}{2} \\ \\ \\ (b-8)=0 \\ b=8 \end{gathered}[/tex]We have the possible values for b as:
b = - 13/2 and 8
Since the base can't be a negative value, let's take the positive value.
Therefore, the base of the triangle, b = 8 feet
To find the height, substitute b for 8 from the height equation, h=2b-3
Thus,
h = 2b - 3
h = 2(8) - 3
h = 16 - 3
h = 13 feet.
Therefore, the height of the triangle, h = 13 feet
ANSWER:
13 feet
The angle of the roof on Makenna's dollhouse is 24°. She built a scale model of the dollhousewith a scale ratio of 1 : 4. What is the measure of the angle of the roof of the model?
Answers
Note that in scaling objects, the lengths will increase or decrease and the angles will be the same.
From the problem, the angle of the roof on Makenna's doll house is 24 degrees, and the scale model will be 1 : 4
The angle is still equal to 24 degrees.
The answer is B. 24 degrees
Evaluate 42+5/9r if r= -1/2 42 + 5/9r=
Answers
Answer:
41 13/18
Explanation:
Given the expression:
[tex]42+\frac{5}{9}r[/tex]When the value of r is given to be:
[tex]r=-\frac{1}{2}[/tex]We substitute to obtain:
[tex]\begin{gathered} 42+\frac{5}{9}r=42+\frac{5}{9}(-\frac{1}{2}) \\ =42-\frac{5}{18} \end{gathered}[/tex]Next, we take the lowest common multiple of the denominators (1 and 18).
[tex]\begin{gathered} =\frac{756-5}{18} \\ =\frac{751}{18} \\ =41\frac{13}{18} \end{gathered}[/tex]Therefore, when r=-1/2, the value of the expression is:
[tex]41\frac{13}{18}[/tex]Find the slope of the line graft below. I found the coordinates but I am unsure of the formula.
Answers
Answer;
[tex]m\text{ = -}\frac{4}{3}[/tex]Explanation;
Here, we want to find the slope of the given line
To do this, we are going to use the slope of a line formula
Mathematically, to use this, we need the coordinates of two points that lie on the given line
We have these already marked in red
Identifying the points, we have them as (0,1) and (3,-3)
Now, we write the formula to use and substitute the coordinates of the points as appropriate
We have this as:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (0,1)} \\ (x_2,y_2)\text{ = (3,-3)} \\ \\ m\text{ = }\frac{-3-1}{3-0}\text{ = }\frac{-4}{3} \end{gathered}[/tex]
Which of the expressions are equivalent to the one below? Check all thatapply.3. (2 + 6) + 4.5A. (6+2): 3+ 4.5B. 3.2 + 3.6+4.5O C.3.2 + (6 + 4): 5D. 5·4+3.(6+2
Answers
We have
[tex]3\cdot(2+6)+4\cdot5=44[/tex]For the other expressions
[tex](6+2)\cdot3+4\cdot5=44[/tex][tex]3\cdot2+3\cdot6+4\cdot5=44[/tex][tex]3\cdot2+(6+4)\cdot5=56[/tex][tex]5\cdot4+3\cdot(6+2)=44[/tex]As we can see the expressions that are equivalent are A, B, and D.
ANSWER
A, B, and D.
Simplity the expression:4b+9b
Answers
Since both variables are equal (b) we can add them:
[tex]4b+9b[/tex][tex]13b[/tex]Perform the indicated operation.1.61 kg -200 g1.61 kg - 200 g-9 (Type [whole number or a decimal.)
Answers
Answer:
Explanation:
We are asked to subtract 200 g from 1.61 kg. To perform this operation, we first convert kg to grams.
Now,
1 kg = 1000g
therefore,
1.61 kg = 1.61 * 1000 g = 1610 g.
The operation now becomes
1610 g - 200 g
which evaluates to
1610 g - 200 g = 1410 g
Which is our answer!
For a craft project you need 182 inches of ribbon, but it is only sold by the meter. Determine the amount of ribbon, in meters, you need to buy for the project. (1 inch = 2.54 centimeters and 1 centimeter = 0.01 meter)
462
47
12
5
Answers
The length of the ribbon used for the craft project is 5 meters.
What is conversion?A conversion factor is a quantity that is multiplied or divided between two different sets of units. In the event that a conversion is necessary, it must be carried out using the proper conversion factor to produce an equivalent value. When translating between inches and feet, 12 inches equals one foot.
To represent the same attribute in a different unit of measurement, employ a unit conversion. Hours can be replaced with minutes, and miles can be replaced with feet, kilometers, or any other unit of measurement when describing distance. Measurements are frequently given in one unit of measurement, like feet, but are required in another, like chains.
Given,
The length of ribbon needed for the craft project = 182 inches
So, the length of the ribbon needs to be in meters.
Thus, we can convert inched to centimeters by
1 inches = 2.54 centimeters
As 1 cm = 0.01 m
So, 1 inch = 2.54 x 0.01 m
1 inch = 0.0254 m
Then for the length of 182 inches,
114 inch = 0.0254 x 182 meters
= 4.6228
≈ 5 meters
Therefore, the length of the ribbon is 5 meters
To learn more about the conversions, visit:
https://brainly.com/question/1560145
#SPJ1
Answer: 5
Step-by-step explanation: i did the test
PLEASE ANSWER QUESTION 2(1.) The members of the gardening group plan to build a walkway through the garden as formed by the hypotenuse of each of the four triangles in the drawing. That way, the gardeners will be able to access all sections of the garden. Calculate the length of the entire walkway to the nearest hundredth of a yard. answer: 10 yards(2.)Is the value you just wrote for the total length of the walkway a rational or irrational number? Explain.
Answers
We need to compute the hypotenuse of 4 right triangles.
The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of the right triangle.
In one of the triangles, the length of the legs are: 6 and 8 yards. Then the length of the hypotenuse is:
[tex]\begin{gathered} c^2_1=6^2+8^2 \\ c^2_1=36+64 \\ c_1=\sqrt[]{100} \\ c_1=10yd_{} \end{gathered}[/tex]In another triangle, the length of the legs are: 12 and 8 yards. Then the length of the hypotenuse is:
[tex]\begin{gathered} c^2_2=12^2+8^2 \\ c^2_2=144+64 \\ c_2=\sqrt[]{208} \\ c_2=4\sqrt[]{13}\text{ yd} \end{gathered}[/tex]In the triangle whose hypotenuse (c3) is 15 yd and one of its legs is 12 yd, the unknown is one of the legs, b, which can be computed as follows:
[tex]\begin{gathered} 15^2=12^2+b^2 \\ 225=144+b^2 \\ 225-144=b^2 \\ \sqrt[]{81}=b \\ 9=b \end{gathered}[/tex]The last triangle has legs of 9 yd and 6 yd. Its hypotenuse is:
[tex]\begin{gathered} c^2_4=9^2+6^2 \\ c^2_4=81+36 \\ c_4=\sqrt[]{117} \\ c_4=3\sqrt[]{13} \end{gathered}[/tex]Finally, the length of the walkway is:
[tex]\begin{gathered} c_1+c_2+c_3+c_4=10+4\sqrt[]{13}+15+3\sqrt[]{13}= \\ =(10+25)+(4\sqrt[]{13}+3\sqrt[]{13})= \\ =35+7\sqrt[]{13} \end{gathered}[/tex]This value is irrational because it includes and square root
Juan's office had already recycled 24 kilograms this year before starting the new recycling
plan, and the new plan will have the office recycling 1 kilogram of paper each week. After
16 weeks, how many kilograms of paper will Juan's office have recycled?
kilograms
Answers
Answer:
40kg
24+16=40kg
Write 62° 21´ 47´´ as a decimal to the nearest thousandth. 62.413°62.366°62.363°62.373°
Answers
The given number is °:
[tex]62\degree21^{\prime}47^{\doubleprime}[/tex]To write it as a decimal, start by placing the integer part the same, now to find the decimal part, let's take the minutes 21' and divide it by 60 (because there are 60 minutes in 1°):
[tex]\frac{21^{\prime}}{60}=0.35[/tex]Now, let's divide the seconds 47" by 3600 (because there are 3600 seconds in 1°):
[tex]\frac{47^{\doubleprime}}{3600}=0.013[/tex]Thus, the number is:
[tex]62\degree+0.35\degree+0.013\degree=62.363\degree[/tex]A mover brings a box up the stairs in 10 seconds. If he applied a force of 20 N over a distance 10 m on the box, calculate the power required for him to complete this action
Answers
Total work done is calculated as
[tex]\begin{gathered} \text{work}=\text{force}\times dis\tan ce \\ \text{ =20N}\times10m \\ \text{ =200 J} \end{gathered}[/tex]The power is calculated as ,
[tex]\begin{gathered} \text{Power}=\frac{work}{\text{time}} \\ \text{ =}\frac{\text{200 J}}{10\text{ sec}} \\ \text{ =20 W} \end{gathered}[/tex]Use the image below to describe at least three different ratios, written In simplest form. Indude at least one part-to-part ratio and one part-to-whole ratio.
Answers
Par
In the figure shown we notice that there are 15 blue squares and 10 white squares. The ratio between them is 15 to 10, this is equivalent to a ratio 3 to 2.
Therefore, there are 3 blue squares for each 2 squares, this can be written as:
[tex]3\colon2[/tex]