[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here's the solution :
[tex]\qquad \sf \dashrightarrow \:(2 {x}^{2} + 5x - 7) + (3 - 4 {x}^{2} + 6x)[/tex]
[tex]\qquad \sf \dashrightarrow \: 2{x}^{2} + 5x - 7 + 3 - 4 {x}^{2} + 6x[/tex]
[tex]\qquad \sf \dashrightarrow \:2 {x}^{2} - 4 {x}^{2} + 5x + 6x - 7 + 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - 2 {x}^{2} + 11x - 4[/tex]
How is the change of base formula used in solving logarithmic equations?
Answer:
See below
Step-by-step explanation:
The change of base formula for logarithms is [tex]\log_a(x)=\frac{\log_b(x)}{\log_b(a)}[/tex]. This formula allows us to rewrite a logarithmic expression so that the new expression contains a different base.
How do I do these problems?
Answer:
12) x= 21
13) x = 1
14) x = 9
15) x = 1
Step-by-step explanation:
Here, we are being asked to solve the given equations and check our work.
To check the work, we need to substitute the found value of x into the equation to check if it makes a true and correct statement.
12) Solve for x:
[tex]\sf 12)\ \dfrac{2}{3}x + 2 = 16\ \textsf{[subtract 2 from both sides]}\\\\\implies \dfrac{2}{3}x + 2 - 2 = 16 - 2\\\\\implies \dfrac{2}{3}x = 14\ \textsf{[multiply both sides by 3]}\\\\\implies 3\left(\dfrac{2}{3}\right)x = 14(3)\\\\\implies 2x = 42\ \textsf{[divide both sides by 2]}\\\\\implies \dfrac{2x}{2}=\dfrac{42}{2}\\\\\implies \boxed{\sf x = 21}[/tex]
Check your work:
[tex]\sf \dfrac{2}{3}x + 2 = 16\ \textsf{[substitute 21 for the value of x]}\\\\\implies \dfrac{2}{3}(21) + 2 = 16\ \textsf{[multiply]}\\\\\implies \dfrac{42}{3} + 2 = 16\ \textsf{[divide]}\\\\\implies 14 + 2 = 16\ \textsf{[add]}\\\\\implies 16 = 16\ \checkmark \textsf{[true statement]}[/tex]
13) Solve for x:
[tex]\sf 13)\ \dfrac{x}{2} + \dfrac{x}{3} = \dfrac{5}{6}\ \textsf{[multiply both sides by 6 - LCM of 2, 3, and 6]}\\\\\implies 6\left(\dfrac{x}{2} + \dfrac{x}{3}\right) = 6\left(\dfrac{5}{6}\right)\ \textsf{[multiply]}\\\\\implies \left(\dfrac{6x}{2} + \dfrac{6x}{3}\right) = \dfrac{30}{6}\ \textsf{[divide]}\\\\\implies 3x+2x=5\ \textsf{[combine like terms]}\\\\\implies 5x = 5\ \textsf{[divide both sides by 5]}\\\\\implies \dfrac{5x}{5}=\dfrac{5}{5}\\\\\implies \boxed{\sf x = 1}[/tex]
Check your work:
[tex]\sf \dfrac{x}{2} + \dfrac{x}{3} = \dfrac{5}{6}\ \textsf{[substitute 1 for the value of x]}\\\\\implies \dfrac{1}{2} + \dfrac{1}{3} = \dfrac{5}{6}\ \textsf{[rewrite the fractions with a common denominator of 6]}\\\\\implies \dfrac{1\times3}{2\times3} + \dfrac{1\times2}{3\times2} = \dfrac{5}{6}\ \textsf{[multiply]}\\\\\implies \dfrac{3}{6} + \dfrac{2}{6} = \dfrac{5}{6}\ \textsf{[add]}\\\\\implies \dfrac{5}{6} = \dfrac{5}{6}\ \checkmark \ \textsf{[true statement]}[/tex]
14) Solve for x:
[tex]\sf 14)\ \dfrac{x-1}{6} - \dfrac{x+1}{8} = \dfrac{1}{12}\ \textsf{[multiply both sides by 24 - LCM of 6, 8, and 24]}\\\\\implies 24\left(\dfrac{x-1}{6} - \dfrac{x+1}{8}\right) = 24\left(\dfrac{1}{12}\right)\ \textsf{[multiply]}\\\\\implies \left(\dfrac{24x-24}{6}\right) - \left(\dfrac{24x+24}{8}\right) = \dfrac{24}{12}\ \textsf{[divide]}\\\\[/tex]
[tex]\sf\\\implies (4x-4)-(3x+3)=2\ \textsf{[distribute the negative sign]}\\\\\implies (4x-4)+(-3x-3)=2\ \textsf{[combine like terms]}\\\\\implies x - 7 = 2\ \textsf{[add 7 to both sides]}\\\\\implies x - 7 + 7 = 2 + 7\\\\\implies \boxed{\sf x = 9}[/tex]
Check your work:
[tex]\sf 14)\ \dfrac{x-1}{6} - \dfrac{x+1}{8} = \dfrac{1}{12}\ \textsf{[substitute 9 for the value of x]}\\\\\implies \dfrac{9-1}{6} - \dfrac{9+1}{8} = \dfrac{1}{12}\ \textsf{[simplify]}\\\\\implies \dfrac{8}{6} - \dfrac{10}{8} = \dfrac{1}{12}\ \textsf{[rewrite the fractions with a common denominator of 24]}\\\\\implies \dfrac{8\times4}{6\times4} - \dfrac{10\times3}{8\times3} = \dfrac{1\times2}{12\times2}\ \textsf{[simplify]}\\\\[/tex]
[tex]\sf\\\implies \dfrac{32}{24}-\dfrac{30}{24}=\dfrac{2}{24}\ \textsf{[subtract]}\\\\\implies \dfrac{2}{24}=\dfrac{2}{24}\ \textsf{[reduce]}\\\\\implies \dfrac{1}{12}=\dfrac{1}{12}\ \checkmark\ \textsf{[true statement]}[/tex]
15) Solve for x:
[tex]\sf \dfrac{1}{4}+\dfrac{x+1}{8}=\dfrac{1}{2}\ \textsf{[multiply both sides by 8 - LCM of 2, 4, and 8]}\\\\\implies 8\left(\dfrac{1}{4}+\dfrac{x+1}{8}\right)=8\left(\dfrac{1}{2}\right)\textsf{[multiply]}\\\\\implies \left(\dfrac{8}{4}+\dfrac{8x+8}{8}\right)=\dfrac{8}{2}\ \textsf{[divide]}\\\\\implies 2 + x + 1 = 4\ \textsf{[add]}\\\\\implies x + 3 = 4\ \textsf{[subtract 3 from both sides]}\\\\\implies x + 3 - 3 = 4 - 3\\\\\implies \boxed{\sf x = 1}[/tex]
Check your work:
[tex]\sf \dfrac{1}{4}+\dfrac{x+1}{8}=\dfrac{1}{2}\ \textsf{[substitute 1 for the value of x]}\\\\\implies \left(\dfrac{1}{4}+\dfrac{1+1}{8}\right)=\dfrac{1}{2}\ \textsf{[simplify]}\\\\\implies \left(\dfrac{1}{4}+\dfrac{2}{8}\right)=\dfrac{1}{2}\ \textsf{[reduce]}\\\\\implies \left(\dfrac{1}{4}+\dfrac{1}{4}\right)=\dfrac{1}{2}\ \textsf{[add]}\\\\\implies \dfrac{2}{4}=\dfrac{1}{2}\ \textsf{[reduce]}\\\\\implies \dfrac{1}{2}=\dfrac{1}{2}\ \checkmark\ \textsf{[true statement]}[/tex]
Lisa brought $5.60 to the bakery. She spent $2.95 on cupcakes. How much money does Lisa have left?
Answer:
2.65
Step-by-step explanation:
5.60-2.95 = the sum of the money left.
A circle has an area of 155 square feet. What is the approximate radius of the approximate radius of the circle?
Answer:
7.02ft
Step-by-step explanation:
What is the result when the number 51 is decreased by 75%?
Answer:
12.75
Step-by-step explanation:
12.75
Answer:
24 percent
Step-by-step explanation:
PLEASE HELP ASAP!!
A savings account starts with $420. After 6 years of continuously compounding at an interest rate, r, the account has a balance of $1,300. What is the interest rate percentage (do not type % it is already there)? Round answer to the nearest hundredth.
Answer:
18.83% (nearest hundredth)
Step-by-step explanation:
Continuous Compounding Formula
[tex]\sf A=P(e)^{rt}[/tex]
where:
A = amountP = principal (initial amount)e = mathematical constant ≈ 2.7183r = interest rate (in decimal form)t = time in yearsGiven:
A = $1,300P = $420t = 6 yearsSubstituting given values into the formula:
[tex]\sf \implies 1300=420(e)^{6r}[/tex]
[tex]\sf \implies \dfrac{1300}{420}=e^{6r}[/tex]
[tex]\sf \implies e^{6r}=\dfrac{65}{21}[/tex]
Taking natural logs of both sides:
[tex]\sf \implies \ln e^{6r}=\ln \dfrac{65}{21}[/tex]
[tex]\sf \implies 6r\ln e=\ln \dfrac{65}{21}[/tex]
[tex]\sf \implies 6r(1)=\ln \dfrac{65}{21}[/tex]
[tex]\sf \implies 6r=\ln \dfrac{65}{21}[/tex]
[tex]\sf \implies r=\dfrac16 \ln \dfrac{65}{21}[/tex]
[tex]\sf \implies r=0.1883108054...[/tex]
Therefore, the interest rate is 18.83% (nearest hundredth)
i’m struggling and my brain won’t work right now help
Answer:
10sr2 or 14.1421356
Step-by-step explanation:
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
if the triangle is an Isosceles triangle, then it's other two angles measure 45° each.
So, let's use Trigonometry here :
[tex]\qquad \sf \dashrightarrow \: \cos(45) = \dfrac{10}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{ \sqrt{2} } = \dfrac{10}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = 10 \sqrt{2} [/tex]
Therefore, the value of x is 10√2 units
Round 15.209 to the nearest hundreth
A. 15.21
B. 15.20
C. 15.2
D. 16
Answer:
A.15.21
Step-by-step explanation:
In rounding of numbers when the next number is greater than 5 u round it on next number by adding one
can someone please help me with this question
Answer:
C. Students in language arts classes.
Step-by-step explanation:
Because out of all of the options, this one seems like it is the best time that they could get the students attention and get an acurate response.
Moesha needs $79 for a class trip.
She alreadv has s22 and she can earn
the rest by babysitting for 8 hours.
If h represents her hourly earnings,
which of the following equations can
be solved to find Moesha's hourly
earnings? Select all that apply. Answer : 79=22+8H
Answer:
79-22=57.
Your answer is correct. You also have to fill in the second one (B)
Answer:
79-22=57
Step-by-step explanation:
I can explain on phone
What is the equation of the line parallel to the line with equation y=2/3x +1 and passing through the point (6,-2)?
Step-by-step explanation:
y= (-2/3) x-6 is parallel to y= (-2/3)x +4 goes through the point (3,-8)
Oscar's spinner has scores from 1 to 4. The table shows the probabilities of scores 1, 2 and 3
1=0.1
2=0.5
3.0.1
4=?
Work out 4
If f(3) = 3^x and g(x) = 7^x then the graph of g(x) will be — the graph of f(x) when x<0.
Using the given exponential functions, it is found that the graph of g(x) will be less than than the graph of f(x) when x < 0.
What are the exponential functions?The given exponential functions, f(x) and g(x), are respectively given by:
[tex]f(x) = 3^x[/tex][tex]g(x) = 7^x[/tex]When x < 0, one possible value is x = -1, hence evaluating the functions at these values:
[tex]f(-1) = 3^{-1} = \frac{1}{3}[/tex]
[tex]g(-1) = 7^{-1} = \frac{1}{7}[/tex]
[tex]\frac{1}{3} > \frac{1}{7}[/tex], hence, the graph of g(x) will be less than than the graph of f(x) when x < 0.
More can be learned about exponential functions at https://brainly.com/question/25537936
Compare by finding the LCM of denominator 3/8 and 3/4
LCM = 8
[tex]\frac{3}{8}[/tex] < [tex]\frac{6}{8}[/tex]
Step-by-step explanation:Finding the LCM is useful to compare the size of 2 different fractions.
LCM
First, let's define LCM. LCM stands for least common multiple. A multiple is a product of 2 numbers. For example, the multiples of 4 include 4, 8, 12, etc. The LCM of 4 and 8 is 8.
Comparing
Using the LCM we can find new fractions with the same denominator. These fractions are [tex]\frac{3}{8}[/tex] and [tex]\frac{6}{8}[/tex]. From this, we can tell that 6/8 is larger than 3/8.
What is the measure of the third angle in a triangle if the sum of the other two angle measures is 110°?
Step-by-step explanation:
the third angle in a triangle= 70
In triangle ABC, the measure of angle A is90, the measure of angle B 45 and measure of angle C 45 what is the combined measure of the three angles?
180.....,...........
Step-by-step explanation:
angle A + angle B + angle C = 90+45+45
= 180
Which of the following is the equation of the circle shown below?
Answer: A
Step-by-step explanation:
The radius of the circle is 7, and the center is at (6,-2), so if we substitute into the formula for the general equation of a circle, we get answer choice A.
Hussain and sam are sharing money in the ratio of 2:5 sam got 70p how much money were they sharing in total
Answer:
if 5=70
2=?
cross multiply=28
add 70+28=98
Step-by-step explanation:
What is the answer elmo wants it
[tex]\bold{Heya!}[/tex]
→ Answer :-[tex]\sf{= 10}[/tex]
→ EXPLANATION :-Convert mixed numbers to imporved fractions: [tex]\sf{3 \frac{3}{4} = \frac{15}{4}[/tex]
[tex]\sf{= \frac{15}{4}[/tex] ÷ [tex]\sf{\frac{3}{8}[/tex]
Apply the fraction rule: [tex]\sf{\frac{a}{b}[/tex] ÷ [tex]\sf{\frac{c}{d} = \frac{a}{b} \: x \: \frac{d}c}[/tex]
[tex]\sf{= \frac{15}{4} \: x \: \frac{8}{3}[/tex]
Multiply fractions: [tex]\sf{\frac{a}{b} \: x \: \frac{c}{d} = \frac{a \: x \: c}{b \: x \: d}[/tex]
[tex]\sf{= \frac{15 \: x \: 8}{4 \: x \: 3}[/tex]
Multiply the numbers: [tex]\sf{ 4 \: x \: 3 = 12}[/tex]
[tex]\sf{= \frac{110}{12}[/tex]
Divide the numbers [tex]\sf{\frac{120}{12} = 10[/tex]
[tex]\sf{= 10}[/tex]
Hopefully This Helps! ~
#LearnWithBrainly
[tex]\underline{Answer :}[/tex]
Jaceysan ~
if a=6, evaluate the following expression:
10+a/4
Answer:
11.5
Step-by-step explanation:
10 + a / 4 if a = 6
10 + 6 / 4
10 + 1.5
11.5
I hope this helps! Have a lovely day!! :)
Answer:
23/2 or 11.5
Step-by-step explanation:
Simplify 6/4 --> 3/2
Convert 10 into a fraction --> 20/2
20/2 + 3/2 = 23/2
help its for calculus
Answer:
the first one
Step-by-step explanation:
Answer:
its 1/sqrt{5}+2
I have no idea what to do, help :’)
Answer:
x = 52
Step-by-step explanation:
I have included a chart to identify which angles are congruent (only alternate exterior/interior and corresponding). Basically if they are not alternate exterior/interior or corresponding, then they add up to = 180 degrees.
So since these angles are same side interior, they add up to = 180 degrees. We can write this as: A + B = 180
A + B = 180
2x + 76 = 180
2x = 104
x = 52
I hope this helps!
Answer: x=52
Step-by-step explanation:
uh i just knew
What is the equation of the blue line?
Answer:
y=2x+3
Step-by-step explanation:
Because the y-intercept starts at 3 and it goes up by 2 and to the side 1 so it would be y = 2x +3
Answer: y = 2x + 3
Step-by-step explanation:
We will write the equation in slope-intercept form.
y = mx + b
The slope can be found with "rise over run" since we have clear points on the graph.
Start at (0, 3), count up 2 units, and count one unit to the right. This gives us a slope of positive 2.
Rise / run = 2 / 1 = 2
The "b" value is where the line hits the y-axis. It hits the y-axis at y-coordinate 3, so our y-intercept is positive 3.
Final equation:
y = 2x + 3
Describe the characteristics of this scatterplot.
The characteristics of this scatter plot
D⇢positive O⇢No outliersF⇢LinearS⇢ModerateHence ,this scatter plot has Moderately postive linear relationship without any outliner
If f(x) = 10x^3-37x^2+15x+18 and x-3 is a factor of f(x), then find all of the zeros of f(x) algebraiclly.
Answer:
x=6/5 and x=-(1/2)
Step-by-step explanation:
[tex]f(x) = 10x^3-37x^2+15x+18\\f(x) = \frac{(5x-6)(2x+1)(x-3)}{(x-3)}\\ f(x) = (5x-6)(2x+1)[/tex]
To find the zeros, we set f(x) = 0 for both factors
[tex]5x-6=0\\5x=6\\x=6/5[/tex]
[tex]2x+1=0\\2x=-1\\x=-1/2[/tex]
Therefore the zero's of f(x) are x = 6/5 and x= -(1/2)
answer asap-30 points
Find the measure of angle R.
A- 45
B- 90
C- 60
D- 30
Examine the following piecewise function.
Which statements are true?
Select all that apply.
1.The function is increasing over the interval 2≤x≤3.
2.The function is increasing over the interval −2≤x≤2.
3.The function is increasing over the interval −8≤x≤−2.
4.The function is decreasing over the interval 3≤x≤7.
5.The function is constant over the interval −2≤x≤2.
A piecewise function is a function that's simply built from pieces of different functions over several intervals.
What is a piecewise function?Your information is incomplete as the function isn't given. Therefore, an overview will be given. It should be noted that a piecewise function simply means a function that's defined by multiple sub functions.
In this case, each sub-function applies to different interval in the domain as it's way of expressing the function.
Learn more about piecewise function on:
https://brainly.com/question/17966003
Select all the expressions that describe the area of this rectangle.
Answer:
a, c, d
Step-by-step explanation:
This is because there share the same answer:
12x + 6
hope this helps =)
At school, Akihiro draws a model of the flag of Japan in the coordinate plane.
What is the perimeter of the flag Akihiro draws?
The perimeter of the flag Akihiro draws is the sum of the flag's side lengths
The perimeter of the flag Akihiro draws is 20 units
How to determine the perimeter of the flag?From the coordinate plane, the side lengths of the flag are:
6 units, 4 units, 6 units and 4 units
Add up the side lengths, to determine the perimeter (P)
P = 6 units + 4 units + 6 units + 4 units
Evaluate the sum
P = 20 units
Hence, the perimeter of the flag Akihiro draws is 20 units
Read more about perimeter at:
https://brainly.com/question/24571594
Answer:
20 units
Step-by-step explanation:
Find the value of x. 69 30.9 38.1
Answer:
x = 30.9
Step-by-step explanation:
[tex]x = \frac{1}{2} (138 - 76.2) = \frac{1}{2} (61.8) = 30.9[/tex]