Final answer:
The equation 4x + 3 = 7 is solved algebraically by subtracting 3 from both sides and then dividing by 4 to find x = 1. There is no need for logarithms or the change of base formula to solve this linear equation.
Explanation:
The equation 4x + 3 = 7 is a linear equation and can be solved using simple algebraic manipulations rather than the change of base formula for logarithms. However, to show how logarithms could hypothetically be used (even though it's over-complicating this particular problem), we can take the following steps:
Divide both sides by 4: x = 1.
Therefore, the solution to the equation is x = 1. There is no need to round to the nearest thousandth as the solution is a whole number. The change of base formula, logb y = (log y) / (log b), is not necessary for this equation.
The solution to the equation [tex]\(4x + 3 = 7\) is \(x = 1\),[/tex] obtained by isolating [tex]\(x\)[/tex]
Step-by-Step Solution:
1. Write down the equation:
[tex]\[ 4x + 3 = 7 \][/tex]
2. Isolate the term with the variable [tex]\(x\):[/tex]
- To do this, we need to remove the constant term on the left side by subtracting 3 from both sides of the equation.
[tex]\[ 4x + 3 - 3 = 7 - 3 \][/tex]
- Simplify both sides:
[tex]\[ 4x = 4 \][/tex]
3. Solve for [tex]\(x\):[/tex]
- To isolate [tex]\(x\)[/tex], divide both sides of the equation by 4:
[tex]\[ \frac{4x}{4} = \frac{4}{4} \][/tex]
- Simplify both sides:
[tex]\[ x = 1 \][/tex]
Conclusion:
The solution to the equation [tex]\(4x + 3 = 7\)[/tex] is:
[tex]\[x = 1\][/tex]
What function equation is represented by the graph?
A. f(x)=-2^x−3
B. f(x)=-2^x-2
C. f(x)=2^x-2
D. f(x)=2^x-3
Answer:
The correct option would be D, f(x)=2^x-3
Step-by-step explanation:
You can immediatly cross out options A and B because it cannot be negative. If it was negative, the graph would be going the opposite direction, it would curve closer to the negative numbers that the positive. We can cross out C because if it was -2, then it would cross the y-axis at -1 rather than -2.
hope this helps :)
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.
Will Mark Branliest, Please Help ASAP
Answer:
i)
The confidence interval is at 90%
ii)
The margin of error is 5%
iii)
The 90% confidence interval is (70%, 80%)
iv)
We are 90% confident that the average score of seniors in the field test is between 70% and 80%.
Step-by-step explanation:
i)
The confidence interval is at 90%
We are informed that the exam creator claims that on this particular exam, nine times out of ten, seniors will have an average score within 5% of 75%. This implies that we are 9 times out of 10 confident that seniors will have an average score within 5% of 75%.
The level of confidence is thus;
(9/10)*100 = 90%
ii)
The margin of error is 5% or equivalently 0.05
We are informed that the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Since the average score is within 5%, the margin of error is 5%
iii)
A confidence interval is calculated using the formula;
point estimate ± margin of error
Our point estimate is 75%
Our margin of error is 5%
The 90% confidence interval is thus;
75% ± 5% = (70%, 80%)
iv)
The 90% confidence interval is interpreted as;
We are 90% confident that the average score of seniors in the field test is between 70% and 80%.
This is a confidence interval for the mean, the level of confidence is 90% and our confidence interval is (70%, 80%).
Find the values of the variables in the parallelogram. The diagram is not to scale.
Answer:
A
Step-by-step explanation:
Opposite angles of a parallelogram are equal, so z = 96.
Alternate interior angles are congruent, so x = 31.
Angles of a triangle add up to 180, so y = 53.
Based on the parallelogram shown above, the values of the variables are: x = 31°, y = 53°, z = 96°.
What is a parallelogram?In Mathematics, a parallelogram is a type of quadrilateral and two-dimensional geometrical figure that is composed of two equal and parallel opposite sides.
According to the opposite angles theorem, the opposite angles of a parallelogram are always congruent or equal and as such, we have the following:
m∠z = 96°
Based on the alternate interior angles theorem, angles on opposite of a line are congruent;
x = 31°.
Based on angle sum property, we have the following supplementary angles;
x + y + z = 180
31° + y + 96° = 180°
y = 180° - 127°
y = 53°.
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What is the value of x if 5x + 45 = 35?
Answer:
-2
Step-by-step explanation:
5x+45=35
Next step--> subtract 45 from 35 to start to get x by itself
5x= -10
Next divide by 5 on both sides so x is by itself to get
x=. -2
Answer:
x = - 2
Step-by-step explanation:
5x + 45 = 35
5x = 35 - 45
x = - 10
x = - 10 ÷ 5
x = - 2
Factor each expression. Show your work. 11. r2 + 12r + 27 12. g2 – 9 13. 2p3 + 6p2 + 3p + 9
Answer:
11. (r+9)(r+3)
12.(g-3)(g+3)
13.(p+3)(2p^2+3)
A math test has 12 multiplication problems and 24 division problems. What is the ratio value of multiplication problems to division problems? [Type your answer as a fraction in simplest form, and use / for the fraction bar.
Answer:
1/2
To simplify 12/24 you have to find a common multiple. a common multiple is 12. you see how many times 12 goes into each number. 12/12 is 1 and 24/12 is to. therefore 1/2 is the correct answer
The ratio of multiplication problems to division problems on the given math test is 1/2.
Explanation:To answer the question, you need to set up a ratio between the number of multiplication problems and the number of division problems. In this case, you have 12 multiplication problems and 24 division problems.
The ratio would be set up as 12 (multiplication problems) to 24 (division problems), written as 12/24 in fractional form. However, we need to reduce this to its simplest form. Both 12 and 24 can be divided by 12, simplifying the ratio to its simplest form of 1/2.
Therefore, the ratio of multiplication problems to division problems on this math test is 1/2.
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To convert 360 inches to yards you would use the ratio 36 inches over 1 yard True Or False?
Answer:
False
Step-by-step explanation:
we know that
1 yard= 36 inches
To convert 360 inches to yards
Multiply
(360)*(1/36)=10 yards
therefore
You would use the ratio 1 yard over 36 inches
Answer:
false
Step-by-step explanation:
Renee is playing a game with marbles and a spinner. The spinner has four sections: orange, black, purple, and white. The marbles are kept in a bag and come in three colors: orange, black, and purple. Renee first spins the spinner and then picks a marble from the bag without looking. What is the probability that the color of the marble matches the color on which the spinner lands? brainly
Answer:
[tex]\frac{1}{16}[/tex] Is the chance of the colours matching.
Step-by-step explanation:
The possibility of the spinner landing on an orange side is [tex]\frac{1}{4}[/tex]
and the possibility of the marble being orange is [tex]\frac{1}{4}[/tex] in this case you have to remember, in the fraction, you have 4 possibilities and 1 desirable outcome, when you have two dependant possibilities you have to multiply them:
[tex]\frac{1}{4} * \frac{1}{4}[/tex]
And the result of that multipliction is [tex]\frac{1}{16}[/tex] which is the probability of the marble and the spiner colours matching.
Answer:
Step-by-step explanation:
1/4
In which direction does the graph of the function shown below open?
[tex]f(x) = 2x^2+5x-4[/tex]
A. Down
B. Left
C. Right
D. Up
Answer:
D. Up
Step-by-step explanation:
When a parabola has the form [tex]y=ax^2+bx+c[/tex] , It is vertical (opens up or down).
Because the variable "x" is squared.
If "a" is positive, then the parabola opens up, but if it is negative, then the parabola opens down.
In this case you have the quadratic function:
[tex]f(x) = 2x^2+5x-4[/tex]
Which can be rewritten as:
[tex]y = 2x^2+5x-4[/tex]
Therefore, it is vertical, because it has the form: [tex]y=ax^2+bx+c[/tex]
You can observe that the value of "a" is:
[tex]a=2[/tex]
Then, since "a" is positive, the parabola opens up.
Which type of climate is the most common in Australia's Outback?
A) Dry desert climate
B) Tropical climate
C) Humid and rainy climate
D) Mild climate with seasonal monsoons
OOPS i put it as mathematics IM SO SORRY!
Please answer QUICK if can!
i think its letter A. The outback seems very dry and desert like
Answer:
Dry desert
Step-by-step explanation:
did the quiz
There are 500 computers in an office building. The IT manager randomly chose 40 computers to be inspected for viruses. Of those inspected, 6 computers had viruses.
What is the best estimate of the percent of computers in the building that have viruses?
Enter your answer in the box.
___%
Answer:
15%
Step-by-step explanation:
The population proportion can be estimated as the sample proportion.
6 / 40 = 0.15
Approximately 15% of the computers have viruses.
Answer: Hence, there are 15% of computers have viruses.
Step-by-step explanation:
Since we have given that
Total computers in an office = 500
Number of computers to be inspected = 40
Number of computers had viruses = 6
We need to find the percentage of the computers in the building that have viruses.
So, Percentage of computers in the buildings have viruses is given by
[tex]\dfrac{6}{40}\times 100\\\\=\dfrac{600}{40}\\\\=15\%[/tex]
Hence, there are 15% of computers have viruses.
Last one! I just need to know what the slope of the line in this graph is, ty!
The slope is 4/6 because its going up by 4 over by 6 .hope this helps
Answer:
slope = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (6, 0) ← 2 points on the line
m = [tex]\frac{0+4}{6-0}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
Emily wants to hang a painting in a gallery. The painting and frame must have an area of 31 square feet. The painting is 5 feet wide by 6 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (5 points)
Answer:
4x² + 22x − 1 = 0
Step-by-step explanation:
Start off with the standard formula to finding area with polynomials and quadratic functions.
(2x + 5)(2x + 6)
Work out like a normal binomial.
4 + 22x + 30 - 31
(You're subtracting 31 to take out the minimum of what the frame has to be)
4 + 22x - 1 = 0
Answer:
4x² + 22x − 1 = 0
Can someone please check this?
Answer:
Your answers are correct.
Step-by-step explanation:
The equality will be true for odd multiples of π/4, so the last two choices will not show the expression to be not an identity.
Marlye posted a story on her blog. On the first day there were 80 responses and on the second day there were 180 responses. What percent is the increase, 100, of the original number of responses, 80?
55%
80%
100%
125%
Answer:
80 * 80% = 64 So it's not A
80 * 55% = 44 so it's not B
80 * 100% = 80 so it's not C
80 * 125% = 100 so D is your answer
Step-by-step explanation:
Answer:
125%
Step-by-step explanation:
Given,
Responses on first day or original responses = 80
While responses on second day or final responses = 180,
Thus, the percentage increase in the responses
[tex]=\frac{\text{ final responses- original responses}}{\text{original responses}}\times 100[/tex]
[tex]=\frac{180-80}{80}\times 100[/tex]
[tex]=\frac{10000}{80}[/tex]
[tex]=125\%[/tex]
Hence, fourth option is correct.
May someone help me out :)
Answer:
∠FIG = (47/2)° = 23.5° . . . . . rounds to 24°
Step-by-step explanation:
The value of x can be found from ...
72 = 3x+3 . . . . the central angle and the arc measure are the same
24 = x+1 . . . . . divide by 3
23 = x . . . . . . . .subtract 1
The measure of ∠FIG is half the difference of the arc measures FG and RZ, so is ...
m∠FIG = (1/2)(3x+3 - (x+2)) = (1/2)(2x +1) = x +1/2
m∠FIG = 23 1/2 . . . . degrees
_____
Perhaps you're supposed to round this to 24°.
This dot plot shows scores on a recent math assignment.
Find the measures of central tendency and variability.
Mean:
Median:
Mode:
Range:
The mean is 7.7.
The range is 4.
The mode is 8.
The median is 8.
What are the measures of central tendency and variability?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
(5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 9 + 9 + 9 + 9 + 9) / 20
154 / 20 = 7.7
Mode is the number that occurs the most in the data set. The mode is 8.
Range is the difference between the highest number and the lowest number in the data set.
Range = 9 - 5 = 4
Median is the number at the center of the data set. The median is 8.
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Answer: The mean is 7.7.
The range is 4.
The mode is 8.
The median is 8.
Step-by-step explanation: I did the assignment.
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!!
The area of one face would he h^2.
There are 6 faces, so the total surface area would be h^2 x 6
Replace total surface area with 2.16, so you now have:
2.16 = h^2 x 6
Now we can solve for h.
Divide both sides by 6:
h^2 = 2.16/6
Take the square root of both sides:
h = √2.16/6
The answer is A.
Please please help!!!
Answer:
1/2
Step-by-step explanation:
cos(θ) = √(1 -sin(θ)²) = √(1 -3/4) = √(1/4)
cos(θ) = 1/2
Find the slope of the line
Answer:
-4
Explanation:
The slope of the line intersects points that are 4 points below and one point to the right of the previous point. (-4/1) = -4
Answer:
-4
Step-by-step explanation:
The line goes through the points (-1,3) and (0,-1)
We can find the slope by using the formula
m = (y2-y1)/(x2-x1)
= (-1-3)/(0--1)
= (-1-3)/(0+1)
= -4/1
= -4
Divide assume that no denominator equal zero. b^4/ 2a^2 divided by b^3/ a
Answer:
Step-by-step explanation:
Essentially, what you have is a fraction divided by a fraction. The rule there is to bring up the bottom fraction and then flip it to multiply. That would look like this:
[tex]\frac{b^4}{2a^2}[/tex]×[tex]\frac{a}{b^3}[/tex]
Now you can do some canceling out of like terms. There is a b^3 in the denominator and a b^4 in the numerator. You can take 3 b's out of 4, so the b^3 cancels completely out with the b^4, leaving only one b behind. The a in the numerator cancels with one of the a's in the a^2, leaving one behind. So the answer to this is:
[tex]\frac{b}{2a}[/tex]
⊙X≅⊙Y and RQ = 35.6. Identify ED, rounded to the nearest tenth.
Answer:
Your answer is 7.0
Step-by-step explanation:
If the circles are congruent and RQ measures 35.6, then so does CB. That means that half of it (the radius XD which measures 26 cuts the length of CB in half) is 17.8. If the base of that right triangle is 17.8 and the hypotenuse is 26, then Pythagorean's Theorem tells us that the height of the triangle is 18.95151709. Subtract that from the radius length of 26 and you'll have the length of DE
The value of length ED would be, 7.0
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
⊙X≅⊙Y
And, Length of RQ = 35.6
Now, We get;
⇒ CB = RQ = 35.6
Hence, EB = 1/2CB
= 1/2 (35.6)
= 17.8
Applying Pythagoras theorem,
⇒ XE² = XB² - EB²
⇒ XE² = 26² - 17.8²
⇒ XE² = 19
Thus, The length of ED is,
⇒ ED = XD - XE
⇒ ED = 26 - 19
⇒ ED = 7.0
Therefore, The value of length ED would be, 7.0
Learn more about the circle visit:
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Algebra Help Please
Moira buys a new rectangular rug that is 3 inches shorter than her old rectangular rug. The area of the new rug is (x2 + 2x - 15)in2.
Describe the width of Moira’s new rug in terms of the length of her old rug.
Moira’s new rug is (blank) inches (blank) than the length of her old rug.
Choices 7, 5, 0, 15 | Narrower, Wider
Answer:
5 inches wider
Step-by-step explanation:
The given area expression factors as ...
x² +2x -15 = (x -3)(x +5)
Apparently, we're to assume that these factors represent length times width, and the factor x-3 corresponds to a length that is 3 inches shorter than the old length (x). Then the width is (x+5), which is 5 inches wider than the old length.
Answer:
5 in wider is right
Step-by-step explanation:
The diagonals of a parallelogram are 24 meters and 40 meters and intersect at an angle of 60º. find the length of the longer side.
Answer:
The length of the longer side is 28 meters
Step-by-step explanation:
we know that
In a parallelogram, the intersecting diagonals bisect each other;
The supplementary angle of 60° is 120°.
see the attached figure to better understand the problem
Let
a ----> the length of the longer side
b ----> the length of the shorter side.
Apply the Law of Cosines to the lower triangle.
[tex]a^2 = 20^2 + 12^2 - 2(20)(12) cos(120\°)[/tex]
[tex]a^2 = 784[/tex]
[tex]a=28\ m[/tex]
therefore
The length of the longer side is 28 meters
There are 18,076 books in our public library. How should this number be written in expanded form? A) 10,000 + 8,000 + 70 + 6 B) 10,000 + 8000 + 700 + 6 C) 18,000 + 700 + 60+ 0 D) 18,000 + 70 + 60 + 0
Answer:
A) 10,000 + 8,000 + 70 + 6
Step-by-step explanation:
Write one digit at a time, with the others shown as zero. The sum of those numbers is the expanded form.
___
There are other ways to write a number in expanded form. One I like uses exponents to show the place value.
1×10⁴ +8×10³ +0×10² +7×10¹ +6×10⁰
Understanding this form can help you write the number in scientific notation.
PLEASE HELP ASAP 40 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
b
Step-by-step explanation:
(-2x³ - 4x²+ 9x² + 18x - 19x - 38 + 40)
÷ (x + 2)
[-2x²(x+2) + 9x(x+2) - 19(x+2) + 40]
÷ (x+2)
-2x² + 9x - 19 + 40/(x+2)
(GEOMETRY) What are three of the five ways to prove triangles are similar?
Step-by-step explanation:
There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.
SSS (side, side, side) SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. ...
SAS (side, angle, side) ...
ASA (angle, side, angle) ...
AAS (angle, angle, side) ...
HL (hypotenuse, leg)
Answer:
HL, ASA, SAS
Step-by-step explanation:
Hypotenuse Leg
Angle, side, angle
side, angle, side
Given circle P, which of the following options best represents the mACD
a. 60 degrees
b. 120 degrees
c. 180 degrees
d. 240 degrees
منوال 60 is the answer you get ألب
Answer:
180
Step-by-step explanation:
PLEASE HELP ASAP 25 PTS + BRAINLIEST TO RIGHR/BEST ANSWER.
sorry for the screen
Answer:
The answer is A I just looked it up on mathaway and it is never wrong
Step-by-step explanation:
Standard form always has the largest coefficients first
Answer:
A
Step-by-step explanation:
When putting polynomials into standard form, the highest degree goes first.
(for example 5x³ + x² + 8x + 9)
The sum of twice a number and another number is 24. The difference of twice the first number and the other number is 12. Which system would model this situation, and what is the solution?
Answer:
The system that models the situation is:
[tex]\left \{{{2x + y = 24} \atop {2x - y = 12}} \right.[/tex]
The solution is:
(9, 6)
Step-by-step explanation:
We must write the equations as indicated in the problem.
The sum of twice a number and another number is 24
a number: x
other number: y
Then
[tex]2x + y = 24[/tex]
The difference of twice the first number and the other number is 12
first number: x
other number: y
Then:
[tex]2x - y = 12[/tex]
The system that models the situation is:
[tex]\left \{{{2x + y = 24} \atop {2x - y = 12}} \right.[/tex]
To solve the system we add both equations to find the value of x
[tex]2x + y = 24\\\\2x - y = 12[/tex]
---------------------
[tex]4x +0 = 36\\\\x=\frac{36}{4}\\\\x=9[/tex]
[tex]2(9) +y = 24\\\\y=24-18\\\\y=6[/tex]
The solution is:
(9, 6)