Answers
First, let's edit the given equations.
In 9:[tex]2(32-x^2)=4x4-2\\\\64-2x^2=14[/tex]
Then, to check if [tex]x=5[/tex] is a solution to this equation, let's put the [tex]5[/tex].
[tex]64-2(5)^2=14\\\\64-50=14[/tex]
That's correct!
In 10:[tex]4^2-x\leq x(6-5)\\\\16-x\leq 6x-5x\\\\16-x\leq x\\\\16\leq 2x\\\\x\geq 8[/tex]
Then, we must put [tex]15[/tex].
[tex]15\geq 8[/tex]
That's correct!
Good luck! If you have any question(s), then feel free to ask in comments!
Hi Student!
Let us first look at what the first question is asking for us to do and what is provided to do that. Looking at the first question we see that they are asking if x = 5 is a solution to the expression that they provided. This type of problem is fairly simple and what we basically do is just plug in the value 5 for the variable x in the expression and the simplify both sides to see if they are the same.
Plug in the values
[tex]2(32 - x^2) = 4 * 4 - 2[/tex][tex]2(32 - (5)^2) = 4 * 4 - 2[/tex]Simplify the square and subtract inside of the parenthesis
[tex]2(32 - 25) = 4 * 4 - 2[/tex][tex]2(7) = 4 * 4 - 2[/tex]Simplify both sides
[tex]2 * 7 = (4 * 4) - 2[/tex][tex]14 = (16) - 2[/tex][tex]14 = 14[/tex]Looking at the final expression that we have, we can see that we have 14 is equal to 14 which is true and therefore x = 5 is a solution of the expression provided.
Moving onto the next question, we can see that it asks for us to do something really similar to the previous question but this time to check if x = 15 is a solution of a different expression. Let's follow the same steps that we did last time.
Plug in the values
[tex]4^2 - x \le x(6 - 5)[/tex][tex]4^2 - (15) \le 15(6 - 5)[/tex]Distribute the x
[tex]4^2 - (15) \le (15 * 6) + (15 * -5)[/tex][tex]4^2 - (15) \le 90 - 75[/tex]Simplify both sides
[tex]16 - 15 \le 90 - 75[/tex][tex]1 \le 15[/tex]Looking at the final expression that we have, we can see that it states that 1 is less than or equal to 15 and that is true. Therefore, x = 15 is a solution of the expression that was provided.
Related Questions
Identify the zeros given the quadratic equation y= -16(x+7)(x-5)
Answers
Answer:
wouldn't it be -7 and 5? I'm pretty sure that you switch the signs around.
Step-by-step explanation:
set y=0 and solve. -7 + 7 = 0 and 5 - 5 = 0. my teacher told me to switch the signs for each factored term. hope this helps.
Answer:
x = -7
x = 5
Step-by-step explanation:
Hello!
We can use the Zero Product Property to solve for the Zeroes.
Zero product PropertyThe zero product property stars by factoring a quadratic. You then set each of the factors to zero, and solve for the variable in the factor.
Factored form: y = a(x - h)(x - k)
0 = a(x - h)(x - k)0 = (x - h)(x - k) Divide by aNow, let's call each factor, A and B. To get to 0, either A, B, or both have to be 0. We prefer to solve for both.
Solvey = -16(x + 7)(x - 5)0 = -16(x + 7)(x - 5)0 = (x + 7)(x - 5) Divide by -16x + 7 = 0, x = -7x - 5 = 0, x = 5The zeroes of the Quadratic is -7 and 5.
Why do we replace it with 0?
Zeroes means the x-intercepts, or the roots of a quadratic. An x-intercet is when y is equal to 0. So we replace y with 0, and solve for x.
interest rate of 2.99% compounded monthly for a 4 year loan, find the regular monthly payments required to repay the loan.
Answers
Using it's formula, considering a loan of $10,000, the regular monthly payments required to pay off the loan will be of $221.3.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, we have that the parameters are given as follows:
P = 10,000, r = 0.0299, n = 4 x 12 = 48.
Then:
r/12 = 0.0299/12 = 0.00249167.
Hence, the monthly payment will be given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 10000\frac{0.00249167(1+0.00249167)^{48}}{(1+0.00249167)^{48} - 1}[/tex]
A = 221.3.
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vertex (3,-2) and y-intercept (0,7).
Write your answer in this form: (X₁,Y1), (X2,2).
If necessary, round to the nearest hundredth.
Enter the correct answer.
Answers
Answer:
3±√2/3 = x
Step-by-step explanation:
As you already have the vertex, the equation for this is y = a(x – h)^2 + k,
so by plugging all this in using the vertex coordinates, you get y = 3(x - 3)^2-2, so, if you divide everything by three you get 2/3 = (x - 3)^2
This means that the two x-intercepts are:
A square has a triangular hole in it. What is the area of the figure?
9 in. 3 in.
76.5 in 2
89 in 2
72 in 2
3 in.
9 in.
Answers
Answer:
76.5in²
Step-by-step explanation:
First we will find the area of the square. This is done by multiplying the side length (9in) by itself.
[tex]9 * 9 = \boxed{81}[/tex]
The area of the square is 81in².
Next we will find the area of the triangular hole. We can use the formula [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle (3) and h is the height of the triangle (3).
[tex]\frac{1}{2}bh\\\frac{1}{2}(3)(3)\\\frac{9}{2}\\\boxed{4.5}[/tex]
The area of the triangle is 4.5in².
Now we can find the area of the figure by subtracting the area of the square and the area of the triangular hole.
[tex]81 - 4.5 = \boxed{76.5}[/tex]
The area of the figure is 76.5in².
That is the answer
- Kan Academy Advance
Aaron solved an inequality and then graphed the solution as shown below.
-8-7
1 0 1 2 3 4 5
Which inequality did Aaron solve?
|x+2| <3
Ox+2| >3
|x+3| <2
|x+31 > 2
Answers
Based on the graph that Aaron made, we can infer that the inequality he solved is | x + 2 | < 3.
What inequality was solved by Aaron?
The value of x in the graphed inequality is:
-5 < x < 1
If 2 was added to both sides, the least value would be - 3 and the highest value would be 3.
The inequality then becomes:
-3 < x < 3
This in line with the first option which is that when 2 is added to any value of x, it will be less than 3.
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PLEASE HELP! ITS DUE SOON IM SO CONFUSED SOMEONE PLEASE HELP ME!
Answers
Answer:
40.6°
Step-by-step explanation:
formula of area of triangle
1) √[(s)(s-a)(s-b)(s-c)] , s= (a+b+c)/2
2) 1/2ab sin c
calculate the area first
s= (9.6+6.3+8.1)/2
=12
area= √[(12)(12-9.6)(12-6.3)(12-8.1)]
= √640.224
= 25.3026
1/2(9.6)(8.1) sin c = 25.3026
sin c = 25.3026(2)/(9.6*8.1)
sin c = 0.6508
c = sin-¹ 0.6508
c = 40.6 (nearest tenth)
Directions: Follow the instructions for the following inequalities. 1. 4<7 Multiply both sides by 7 , then by 6, then by 3, then by 10 2. 11>-2 Add 5 to both sides, then add 3, then add (-4) 3. -4<-2 Subtract 6 from both sides, then 8, and then 2 4. -8<8 Divide both sides by -4, then by -2 5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
Answers
In the given question, we have to perform this experiment and test if the inequality is true or not.
Adding the same value to both sides of the inequality will not change the inequality sign
Inequalitydata;
4 < 711 > - 2-4 < - 2-8 < 8In the first case, we would do follow the process
[tex]6 * 7 * 4 < 7 * 7 * 6\\168 < 294[/tex]
In the second case;
[tex]11 > - 2\\\\5 + 11 > -2 + 5\\3 + 16 > 3 + 3\\4+ 19 > 6 + 4\\23 > 10[/tex]
In all the scenarios, the operations did not affect the inequality sign because we are doing it equally to all side and at the end of the day nullifies each other.
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Pls help me with no26
Answers
Answer:
a) 8
Step-by-step explanation:
The prime factors for 24 are 2, 2, 2, 3 -> The greatest is 3
The prime factors for 35 are 5, 7 -> The smallest is 5
So the sum is 3+5=8
Arun took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4 plus $4.25 per mile. The total fare was $110.25, not including the tip. How many miles was the taxi ride?
Answers
Answer:
Answer = 25 miles
Step-by-step explanation:
We can make an equation based off of this information in the form of 4.25x+4=110.25. When we solve for x we find that it equals 25.
Hope that helps! :)
EASY POINTS Which of the following best describes DG?
Answers
Answer:
A. median
Step-by-step explanation:
the median is the middle of the shape :)
If a hot air balloon pilot inflates the balloon at an average wind speed of about 5 miles per hour with an altitude of 35,000 feet, how fast will the radius of the balloon increase as it goes up higher and higher performing certain tricks? Using the differentiation formula applicable for this situation, estimate the speed of inflation and the speed of landing. Will this be able to help the pilot still perform other tricks before making a colorful landing? Give at least two comprehensible reasons and explain your answer.
Answers
The speed of landing is 15.69 ft/sec.
What is differentiation ?"Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. In contrast to the abstract nature of the theory behind it, the practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions.
The three basic derivatives (D) are: (1) for algebraic functions, D(xn) = nxn − 1, in which n is any real number; (2) for trigonometric functions, D(sin x) = cos x and D(cos x) = −sin x; and (3) for exponential functions, D(ex) = ex."
Let the length of the rope = r
Height of the balloon = h
we are given dr/dt = 15ft/sec
at any time t we know:
[tex]r = 125 + 15*t[/tex]
By the Pythagoras theorem we know:
[tex]h^2 + 125^2 = r^2[/tex]
We have to find dh/dt at time t = 20 sec
[tex]d/dh(h^2 + 125^2) = d/dt(r^2)[/tex]
By chain rule:
[tex]d/dh(h^2 + 125^2)*dh/dt\\ = d/dr(r^2)*dr/dt\\2h*dh/dt = 2r* dr/dt\\h*dh/dt = r*dr/dt\\dh/dt = (r/h)*dr/dt[/tex]
[tex]= [(125 + 15*20)/(425^2 - 125^2)^1/2]*15[/tex]--------------------- at time t = 2
=15.69 ft/sec
Hence dh/dt = 15.69 ft/sec
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what is the answer divided
Answers
Answer:
4m/9
Step-by-step explanation:
A circle has a radius of 7 in. Find the radian measure of the central angle 0 that intercepts an arc of length 15 in. Do not round any intermediate computations, and round your answer to the nearest tenth.
Answers
The measure of the central angle is 2.15 radians if the radius of the circle is 7 in.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
The radius of the circle = 7 in
Arc length = 15 in
We know,
s = rθ
s is the arc length, θ is the central angle, and r is the radius of the circle.
15 = 7θ
θ = 15/7
θ = 2.142 radians ≈ 2.15
Thus, the measure of the central angle is 2.15 radians if the radius of the circle is 7 in.
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Find the amount of money
accumulated after investing a
principle P for years t at interest
rate r, compounded continuously.
t = 6
P = $1,500 r = 7%
Answers
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &6 \end{cases} \\\\\\ A=1500e^{0.07\cdot 6}\implies A=1500e^{0.42}\implies A\approx 2282.94[/tex]
Jessie is painting a cardboard box for a school project and needs to know much paint she needs to cover the box.
6n
10 in.
Answers
Answer:
incomplete question
Step-by-step explanation:
in order to calculate for the surface area of a rectangular box we would need 3 measurements:
length
width
height
you only provided 2
Determine if the following angles are congruent. What theorem proves them to be congruent. Explain your reasoning.
Answers
Answer: AAS
Step-by-step explanation:
We know that [tex]\angle TSN \cong \angle HSU[/tex] because they are vertical angles, meaning the triangles are congruent by AAS.
A picture frame has a perimeter of 40 inches. Its length is 2 inches greater than one-half its width. Let w represent the width in inches of the picture frame, and let l represent the length in inches. Which system of equations can be used to find the dimensions of the picture frame?
Answers
Equations can be used to find the dimensions of the picture frame:
Length = 2 +1/2w
and, 2(l+b)=40
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Perimeter = 40 inches.
let the width be w
length= 1/2w+2
So.
Perimeter of rectangle
40= 2 (l+b)
40= 2(0.5w+2+w)
20=1.5w+2
18=1.5w
w= 12
length= 8
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Which of the following points is not coplanar with points C, D and E?
Answers
The point R is the point which is not coplanar with points C, D and E.
We need to find the point which is not coplanar with points C, D and E.
What are coplanar points?The points that lie on the same plane are called coplanar points.
In the given figure there are five planes which are as follows:
BCUD, BRAE, BRAC, BTDE, ACUDE
Now, points C,D and E lie in plane ACUDE.
In the plane ACUDE points A, C, U, D, E and S lies.
From the options point, R is not lining in the same plane as C, D and E lies.
Therefore, the point R is the point which is not coplanar with points C, D and E.
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PLEASE HELP ME I WILL GIVE BRAINLYEST
Answers
Answer:
your answer will be 85 1/3ins
Step-by-step explanation:
16x 5 1/3 = 85.3333333333
then I took the 85 and the 1/3
and just put em together
b) How many more 18-year
old students than 12-year
old students spent
between 25 and 35 mins
on social media?
Answers
The number if 18-year old 12-year old students that took part in the survey is 320.
The number of more 18-year old students than 12-year old students that spent between 25 and 35 mins on social media is 20.What is the survey about?Looking at the survey chart one can see that the total number of 18year old that partook of the survey are:
30 + 20 + 60 + 70 + 40 + 60 + 40
= 340
From the diagram , 18 year old = 60
12 year old = 40
The differences will be:
= 60 - 40
= 20
Therefore, The number if 18-year old 12-year old students that took part in the survey is 320 and the number of more 18-year old students than 12-year old students that spent between 25 and 35 mins on social media is 20.
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A survey asked people how many siblings they have, and the results were recorded in this line plot.
How many people surveyed have 4 or more siblings?
dot plot
Answers
Answer:
we need a pic of the graph to be able. to work this out.
THANK YOU
Answer:
It's 5.
Step-by-step explanation:
8-3= 5
help what is
thr circumference of a circle is 36π cm
what is the radius of teh circle?
Answers
Let's consider the relationship between the circumference and the radius:
⇒ first, consider the equation for finding the circumference
[tex]Circumference = 2\pi *radius[/tex]
Let's consider the known information
Circumference ⇒ 36πLet's plug the known information to find the radius:
[tex]Circumference = 2\pi *radius\\36\pi =2\pi *radius\\radius = 18[/tex]
Thus the radius is 18 cm
Answer: 18 cm
Hope that helps!
write a rule for the nth term of the arithmetic sequence
-11, -4, 3, 10...
Answers
Answer: aₙ = -11 + 7(n - 1)
Step-by-step explanation: The equation of an arithmetic sequence is
aₙ = a₁ + d(n - 1).
a₁ is the first term.
d is the common difference.
Ali takes a full-time position as a makeup artist in Atlanta. Her starting salary is $29,000. Her taxes are 28%. What is her net monthly income?
a. $2,416
b. $3,840
c. $2,088
d. $1,740
I couldn't find the answer to this question when I really needed it, so I did the work myself and got D as the answer. I ended up getting it right because you divide 29,000 by 12, then multiply the answer (2416) by 28%, which gives you the answer, D, 1740. Hope that helped!
Answers
Answer:
d. $1,740
Step-by-step explanation:
The annual after-tax salary is found by subtracting the tax from the salary. The tax is found by multiplying the tax rate by the salary. The monthly after-tax income is 1/12 of the annual after-tax income.
__
stepsannual tax = 0.28 × $29,000 = $8,120
annual take-home pay = $29,000 -8,120 = $20,880
monthly take-home pay = annual pay / months per year
= $20,880 / 12 = $1,740 . . . . net monthly income
_____
Additional comment
The net pay will be (1 - 0.28) = 0.72 times the nominal salary. The monthly pay will be 1/12 of the annual pay. These combined factors give a monthly net pay of (0.72)(1/12) = 0.06 times the annual pay.
0.06 × $29000 = 6×$290 = $1740
Find the value of x.
6
14
8
0
21
x = [ ? ]
3x-12
Answers
Answer: 7
Step-by-step explanation:
By the angle bisector theorem,
[tex]\frac{21}{14}=\frac{3x-12}{6}\\21(6)=14(3x-12)\\126=14(3x-12)\\9=3x-12\\21=3x\\x=\boxed{7}[/tex]
Select the best definition of repeating decimal.
A. any number that does not repeat, or terminate, that can not be written as a fraction.
B. a decimal that has a recurring sequence of numbers that follow a pattern
C. any number that can be written as a fraction, repeating or terminating decimal
D. a decimal which has digits that do not go on forever.
Answers
The correct option that defines repeating decimals correctly is Option B;
a decimal that has a recurring sequence of numbers that follow a pattern.
What is a Repeating Decimal?A repeating decimal is also called a recurring decimal and it is a decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero.
From the above definition, it means that the correct option that defines repeating decimals correctly is Option B.
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In ΔXYZ, x = 27 cm, y = 79 cm and ∠Z=142°. Find the length of z, to the nearest centimeter.
Answers
The value of side z will be equal to 99.32 cm.
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.
Given that:-
In ΔXYZ, x = 27 cm, y = 79 cm and ∠Z=142°
So by applying the formula given below:-
z² = x² + y² - 2xyCos(142)
z² = 79² + 27² - 2 ( 79 x 27 x Cos142 )
z = 99.32 cm
Hence the value of side z will be equal to 99.32 cm.
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I need help asap!!!!!!!!!
Answers
Find the degree of the polynomial b5 + 2b3 + 7.
Answers
Answer:
5
Step-by-step explanation:
b^5 + 2b^3 + 7
Here,
degrees are 5 and 3.
The degree of the polynomial is the highest / greatest number in the degree.
Out of 3 and 5
5 is the highest / greatest number.
Hence,
the degree of the given polynomial is 5.
1) - 6z+2+3= 15
How do I solve this question
Answers
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to solve the equation [tex]\mathrm{-6z+2+3=15}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
The goal is to isolate x.Notice that we can add 2+3 right off the bat:
[tex]\star~\mathrm{-6z+5=15}[/tex]
Subtract 5 from both sides of the equal sign:
[tex]\star~\mathrm{-6z=10}[/tex]
Divide both sides by -6:
[tex]\star~\mathrm{z=\cfrac{10}{-6}}[/tex]
Simplify!
[tex]\star~\mathrm{z=-\cfrac{5}{3}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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