We have the expression 4x+9-6x+6 and we have to simplify it.
We can group the terms that are alike. We have two groups of terms: the ones that are multiplied by "x" and the ones that are just numbers alone.
Then, the terms 4x and (-6x) are alike and we can add them, getting (-2x). In this terms, x is the common denominator of both terms.
The other terms that are alike are 9 and 6, that can be added to get 15.
[tex]\begin{gathered} 4x+9-6x+6 \\ (4-6)x+(9+6) \\ -2x+15 \end{gathered}[/tex]The answer is -2x+15.
65091/4562Long division This this is to solve how many brownies Joshua has. Help please and thank you.
Given:
[tex]\frac{65091}{4562}[/tex]Number of Brownies= 14.27
Number of Brownies=14 (approximately)
I need help with a question
we must replace the value of D
A.-11
[tex]\begin{gathered} 2(-3(-11)-8)\le98 \\ 2(33-8)\le98 \\ 2(25)\le98 \\ 50\le98 \end{gathered}[/tex]the option is right
B. -36
[tex]\begin{gathered} 2(-3(-36)-8)\le98 \\ 2(108-8)\le98 \\ 2(100)\le98 \\ 200\le98 \end{gathered}[/tex]the option is wrong
C.-19
2()
D.-29
this graph ( below ) shows how thr total number of pieces greta knows how to sing depends on the number of weeks she takes voice lessons . what is the rate of change .
The rate of change of the line is equal to its slope. To calculate the slope, choose two points on the line and write down their coordinates.
Take the points:
[tex]\begin{gathered} (0,4) \\ (5,6) \end{gathered}[/tex]Given two arbitrary points:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]The slope between them is given by the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]Substitute y_2=6, y_1=4, x_2=5 and x_1=0 into the formula for the slope to find the rate of change:
[tex]\begin{gathered} m=\frac{6-4}{5-0} \\ =\frac{2}{5} \end{gathered}[/tex]Therefore, the rate of change of the vocal pieces that Greta can sing over the weeks that she takes voice lessons, is 2/5.
How much should you invest a 4.9% simple interest in order to earn $90 interest in 10 months?$ Round to 2 decimal places
$2212.93 should be invested
Explanations:Let the amount to be invested be the principal, P.
The interest rate, r = 4.9%
r = 4.9/100
r = 0.049
Time, t = 10 months
12 months = 1 year
10 months = 10/12
t = 10/12 years
t = 0.83
The interest in the next 10 months, I = $90
Interest, I, is given by the formula:
I = P x r x t
90 = P x 0.049 x 0.83
90 = P x 0.04067
P = 90 / 0.04067
P = $2212.93
So, if you look at number 17 I need to know how to do the strategy so I can wright it down and study it for my test tomorrow! Will give 5 stars if you do an amazing explanation!
Question:
What is:
[tex]51+5^2.31+18^2-9.7[/tex]Solution:
Consider the following expression:
[tex]51+5^2.31+18^2-9.7[/tex]By precedence in arithmetic operations, we will first perform the powers:
[tex]51\text{ + (25)(31)+(324)-(9)(7)}[/tex]now, by precedence in arithmetic operations, we will perform the multiplications:
[tex]51\text{ +775+324-}63[/tex]now, by precedence in arithmetic operations, we will perform the sums:
[tex](51\text{ +775+324)-}63[/tex]that is:
[tex]1150-63[/tex]Finally, we perform the respective subtraction:
[tex]1083[/tex]so that, we can conclude that the correct answer is:
[tex]1083[/tex]
What is the image of (-4, 8) after a dilation by a scale factor of centered at the
1/4
origin?
The image of the given point (-4, 8) is (1,-2).
The coordinates of the point are (4,-8).
Point is dilated by a scale factor of k centered at the origin.
When an image is subjected to dilation:
Upon dilation, with a scale factor of k centered at the origin, then the rule of dilation is defined as:
(x , y) → (kx , ky)
Using the above rule, we get
(-4 , 8) is dilated by a scale factor of 1/4 centered at the origin
(-4, 8) → (-4 x 1/4, 8 x 1/4)
(-4, 8) → (-1, 2)
Therefore, the image of the given point (-4, 8) is (1,-2).
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The daily dose for a man who weighs 175 pound is
Daily dosage of medicine for every 20 pounds of body weight = 70 mg
Daily dosage of medicine for every 1 pound of body weight = 70/20 mg
Daily dosage of medicine for every 1 pound of body weight = 3.5 mg
Daily dosage of medicine for every 175 pounds of body weight = 175 x 3.5
Daily dosage of medicine for every 175 pounds of body weight = 612.5 mg
Therefore, the daily dose for a man who weighs 175 pounds is 612.5 mg
If the man is to receive 900 mg in 8 hours
Dosage he will receive in 1 hour = 900/8
Dosage he will receivw in 1 hour = 112.5 mg
Dosage he will receive in 24 hours = 112.5 x 24
Dosage he will receive in 24 hours = 2700 mg
This means the man will take 2700 mg instead of the normal 612.5 mg. He is receiving the wrong dosage
Suppose the heights of women at a college are approximately Normally distributed with a mean of 66 inches and a population standard deviation of 1.5 inches. What height is at the 35thpercentile?
Given data:
Mean: 66 in
Standard deviation: 1.5in
Find height is at the 35th percentile
Use the formula to find the z-score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]z is the z-score corresponding to an area of 0.35 in the normal curve (35th percenlite)
μ is 66in
σ is 1.5in
Find the value of x corresponding to the given percentile:
1. Use a z-table to find the z score:
z=-0.39
2. Use the formula of z score and the given data to solve x:
[tex]\begin{gathered} -0.39=\frac{x-66}{1.5} \\ \\ 1.5(-0.39)=x-66 \\ \\ -0.585=x-66 \\ \\ -0.585+66=x \\ \\ x=65.415 \end{gathered}[/tex]Then, the 35th percentile is 64.4 inchesConsider the right triangle with leg lengths of 5 and 12 units shown in the image below. One vertex of the triangle is located at (-6, 4).
Step 1
Define the equation of a circle
[tex]\text{The equation of a circle = (x-h)}^2+(y-k)^2=r^2[/tex]Step 2
Write down the parameters
r = radius = ?
h = -6
k = 4
Step 3
find the radius
Considering the triangle we can find the radius using the Pythagoras theorem
[tex]r^2=5^2+12^2[/tex][tex]\begin{gathered} r\text{ = }\sqrt[\square]{25\text{ + 144}} \\ r\text{ = }\sqrt[]{169} \\ r\text{ = 13} \end{gathered}[/tex]Step 3
Substitute the values into the equation and simplify
[tex]\begin{gathered} (x-(-6))^2+(y-4)^2=13^2 \\ (x+6)^2+(y-4)^2=13^2 \end{gathered}[/tex]Answer is option A
The midpoint of a segment can be found using the formulas for a directed line segment, x =C DaQ+bX2-X1) + X, and46]«y =aa + b-6/2 – Yı) + y1. When using these formulas to find a midpoint, which is true?O a = 1 and b= 2a = 2 and b = 1a = 1 and a + b = 2a = 2 and a + b = 2NextSubmitSave and ExitMark this and return
In general, the formula to find the midpoint of a line segment which ends have the coordinates (x₁,y₁) and (x₂,y₂) is given by
[tex]M=(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})[/tex]Working with the formula we are given, for the x coordinate of the midpoint we have:
[tex]x=(\frac{a}{a+b})(x_2-x_1)+x_1=\frac{a(x_2-x_1)}{a+b}+\frac{(a+b)x_1}{a+b}[/tex]In order for this to be like the previous formula, we have the following equation:
[tex]\frac{a(x_2-x_1)}{a+b}+\frac{(a+b)x_1}{a+b}=\frac{x_2+x_1}{2}[/tex]From here, we see that a+b must be equal to 2, so:
[tex]\frac{a(x_2-x_1)}{2}+\frac{2x_1_{}}{2}=\frac{ax_2-ax_1}{2}+\frac{2x_1}{2}=\frac{ax_2-ax_1+2x_1}{2}=\frac{x_2+x_1}{2}[/tex]In order for this last equation to be true, a must equal 1:
[tex]\frac{x_2-x_1+2x_1}{2}=\frac{x_2+x_1}{2}[/tex]Let's verify this with the formula for the y coordinate of the midpoint:
[tex](\frac{1}{2})(y_2-y_1)+y_1=\frac{y_2-y_1}{2}+y_1=\frac{y_2-y_1}{2}+\frac{2y_1}{2}=\frac{y_2-y_1+2y_1}{2}=\frac{y_2+y_1}{2}[/tex]Since using our previous deduction leads us to the correct formula for the y coordinate of the midpoint as well, we can conclude that a=1 and a+b=2.
Dayna deposited $3,805 into savings account that pays a simple annual interest rateof 1.2%. How much interest will she earn after 3 months? Round answer to thehundredths place. If answer does not have a hundredths place then include zeros soit does.
ANSWER
$11.42
EXPLANATION
The equation for simple interest is,
[tex]i=P\cdot r\cdot t[/tex]Where P is the deposited amount, r is the interest rate, and t is the time in years. In this case, we have to find how much is the interest after 3 months, which is 1/4 of a year, so we have:
• P = 3805
,• r = 1.2% = 0.012
,• t = 1/4 year = 0.25 year
The interest earned is,
[tex]i=3805\cdot0.012\cdot0.25=11.415\approx11.42[/tex]Hence, the interest Dayna will earn in 3 months is $11.42.
Which of the following is more likely to happen?Entering room A and room B simultaneously.Sending an e-card to your friend on Uranus.Your height will be reduced by half.Getting a promotion in the next year.
Most likely = more probability.
ANSWER
Getting a promotion in the next year.
if a plane traveled 2100 miles in 210 minutes how many mph was it going?
First, let's convert 210 minutes to hours:
[tex]210\text{ minutes}=\frac{210}{60}\text{ hours}=3.5\text{ hours}[/tex]Now, to calculate the velocity in mph, let's divide the distance in miles by the time in hours:
[tex]velocity=\frac{2100}{3.5}=600\text{ mph}[/tex]simple interest of finance
The Simple Interest on the loan = $563.5
Explanations:Simple Interest is given by the formula:
[tex]I\text{ = }\frac{P\times R\times T}{100}[/tex]where I is the Simple Interest
P is the principal
R is the rate
T is the time in years
From the question:
P = $10500
R = 9.2%
T = 7 months = 7/12 years
Substituting the values of P, R, and T into the formula:
[tex]\begin{gathered} I\text{ = }\frac{10500\times9.2\times\frac{7}{12}}{100} \\ I\text{ = 105 }\times\text{ 9.2 }\times\text{ }\frac{7}{12} \\ I\text{ = }563.5 \end{gathered}[/tex]The Simple Interest on the loan = $563.5
A person is running a distance rate at a constant rate. What time will they finish the race? What information would i need to be able to dolve this problem?
We know
[tex]D=RT[/tex]Where
D is the distance
R is the rate (or speed)
T is the time
We would need to know ANY 2 variables to solve for the 3rd variable.
Since, we want to know the time (T), we MUST somehow know R (rate/speed) and D (distance).
This way, we will be able to solve the problem.
3. Make Sense and Persevere In the equation 0.755s - 5/8= 44, how do you combine the like terms
The equation given is:
[tex]0.755s-\frac{5}{8}=44[/tex]"Like terms" are terms whose variables are the same. The coefficient (number in front of the variable) can be different. Also, constant (single numbers) are like terms with other constants.
In the equation given,
There is one term with the variable "s" and two "constant terms".
Thus, we combine the two constant terms and leave the "s" term as is because there isn't any other like term to combine it with.
So,
We have:
[tex]\begin{gathered} 0.755s-\frac{5}{8}=44 \\ 0.755s=44+\frac{5}{8} \\ 0.755s=44\frac{5}{8} \end{gathered}[/tex]Note that we added (5/8th) to the right hand side with "44". When we change sides, we change signs.
An angle has a cosine of 4/5. What will its cosecant be?
Recall that the cosine ratio is determined by adjacent side, divided by the hypotenuse of a right triangle.
Given that cosine is 4/5, the opposite side is
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2+(4)^2=(5)^2 \\ a^2+16=25 \\ a^2=25-16 \\ a^2=9 \\ \sqrt{a^2}=\sqrt{9} \\ a=3 \end{gathered}[/tex]Now that we have solved for the opposite side, recall that cosecant is determined by the equation
[tex]\csc\theta=\frac{\text{hypotenuse}}{\text{opposite}}[/tex]Substitute
hypotenuse = 5
opposite = 3
and we get
[tex]\csc\theta=\frac{5}{3}\text{ \lparen final answer\rparen}[/tex]1. Find the equation of the line of best fit. (y=mx+b) 2. Use the graph to predict what the correct mileage for a 7-year-old car should be. 3. Using your equation in 7d, calculate the mileage for a 25-year-old car.
From the graph
The two point ( 0, 35.8514 ) and ( 51.269, 0 )
[tex]\begin{gathered} \text{Slope m = }\frac{0\text{ - 35.8514}}{51.269\text{ - 0}} \\ \\ m\text{ = }\frac{-35.8514}{51.269} \\ m\text{ = -0.69928} \\ \\ \text{Intercept b on the y-a}\xi s\text{ = 35.8514} \\ b\text{ = 35.8514} \end{gathered}[/tex]1) y = mx + b
y = -0.69928x + 35.8514
2) Mileage for 7 years
y = -0.69928 ( 7) + 35.8514
y = -4.89496 + 35.8514
y = 30.9564
Mileage for 7 years = 30.9564
3) Mileage for 25 years
y = -0.69928 ( 25) + 35.8514
y = -17.482 + 35.8514
y = 18.3694
Mileage for 25 years = 18.3694
(G.12, 1 point) Given: Circle P with center at (-6, 4) and a radius of v19. Identify the equation that could represent circle P. O A. (X+6)2 + (y + 4)2 = 19 o B. (X - 6)2 + (-4)2 = 19 C. (x + 6)2 + (y - 4)2 = 19 OD. (X-6)2 + (y + 4)2 = 19
In this case, we'll have to carry out several steps to find the solution.
Step 01:
center (-6, 4)
radius = √19
equation of the circle = ?
Step 02:
equation of a circle
(x - a)² + (y - b)² = r²
(x - (-6)) + (y - (4)) = (√19)²
(x + 6)² + (y - 4)² = 19
The answer is:
(x + 6)² + (y - 4)² = 19
Find the value of x in the picture below using the provided 4 answer choices.
The second choice is the correct answer
which fraction is equivalent to 35/50a) 25/45b 18/20c) 7/9d) 28/40
EXPLANATION:
To know which of all is the equivalent fraction, we must try with the same number, that is, divide the numerator and denominator by the same number;
Also in the opposite case, we must multiply the numerator and denominator by the same number.
So we have the following:
first step, check each fraction:
[tex]\frac{35}{50}\text{ divide }5=\frac{7}{10}[/tex]factor the equation 3x^2 +16x-12
(3x - 2)(x + 6)
Explanation:3x² +16x-12
a = 3, b = 16, c = - 12
a(c) = 3(-12) = -36
The factors of -36 whose sum will give +16 are -2 and 18
3x² + 18x - 2x - 12
3x(x + 6) -2(x + 6)
(3x - 2)(x + 6)
The factorisation: (3x - 2)(x + 6)
The residents of a city voted on whenever to raise property taxes. The ratio of yes votes to no votes was 8 to 5. If there were 8463 total votes, how many no votes were there?
1) Gathering the data
The ratio of yes votes to no votes was 8 to 5.
8/5
8463 votes
2) Let's use the property of proportions, to write an expression to solve that problem:
[tex]\begin{gathered} \frac{8}{5}=\frac{8463-x}{x} \\ 8x\text{ = 5(8463-x)} \\ 8x=42315-5x \\ 13x=42315 \\ x=3255 \end{gathered}[/tex]So there were 3255 no votes.
The time, in years, that it takes an amount of money to double when invested at a simple interest rate can be approximated by dividing 0.72 by the interest rate expressed as a decimal. Approximately how many years would it take an investment of $1000 to be worth $2000 if the money were invested at a simple interest rate of 4%?
11)
The number of years for the investment to double = 0.72/interest
From the information given,
interest = 4% = 4/100 = 0.04
Therefore,
number of years for the investment to double = 0.72/0.04 = 18
Option 5 is correct
ethan buys vidio games for 39.99 sale on 20% how much ethan payed
The amount that Ethan pays for the video game is 47.988.
How to calculate the value?From the information illustrated, it should be noted that it was stated that Ethan buys video games for 39.99 sale on 20% tax.
In this case, the amount that he will pay will be:
= Original amount + Tax
= 39.99 + (20% × 39.99)
= 39.99 + 7.998
= 47.988
The amount is 47.988.
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Complete question
Ethan buys vidio games for 39.99 sale on 20% tax how much ethan payed
6 Find the height of the triangle pictured above, if the area is 12. Round your answer to the nearest tenth
We have that the area of a triangle is given by:
[tex]A=\frac{b\cdot h}{2}[/tex]We replace the values we know:
[tex]12=\frac{6\cdot h}{2}[/tex]Now, we solve for h:
[tex]\Rightarrow h=4[/tex]From this, we have that the height of the triangle is 4 units.
Find the measure of arc BC, the measure of angle A, and the measure of arc AB.
Explanation
If we have the question as
Then, we will have the measure of arc BC as 45 degrees (An arc measure is an angle the arc makes at the center of a circle)
For the measure of angle A
[tex]Measure\text{ of angle A=}\frac{1}{2}\times45^0=22.5^0(Angle\text{ at center is twice that at the center})[/tex]To get the measure of angle AB
we will have
So that
[tex]\begin{gathered} x+x+45=360 \\ 2x=360-45 \\ 2x=315 \\ x=\frac{315}{2} \\ \\ x=157.5^0 \end{gathered}[/tex]Therefore, the measure of the arc AB is 157.5 degree
What is the total amount of the monthly payments for a $5,300, 4-year
loan with an APR of 3% ? (Follow Example 2)
Do not use the $ sign in your answer and round to the nearest Cent
(100th):t
The principal amount given out as loan is 239447.08
Monthly PaymentThe monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.
Monthly payment = $5300Time = 4 yearsrate = 3%Principal = ?n = number of times compoundedThe formula is given as
[tex]m = P[\frac{r(1+r)^n}{(1+r)^n^-^1}[/tex]
Substituting the values and solving for the principal amount, this will cost 239,447.08.
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Consider the graph of f(x) = 5 ^ x + 1 1. Explain how to find the average rate of change between x = 0 and x = 4 . What is the average rate of change ?
1. To determine the average rate of change of a function "f(x)" between the points "x = a" and "x = b" we use the following formula:
[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]2. In this case, we have the following function:
[tex]f(x)=5^x+1[/tex]And we have the points:
[tex]\begin{gathered} x=0 \\ x=4 \end{gathered}[/tex]Now we determine the value of f(b) by replacing x = 4 in the function:
[tex]\begin{gathered} f(4)=5^4+1 \\ f(4)=626 \end{gathered}[/tex]Now we determine f(0):
[tex]\begin{gathered} f(0)=5^0+1 \\ f(0)=1+1=2 \end{gathered}[/tex]Replacing in the formula for the average rate of change we get:
[tex]A=\frac{626-2}{4-0}[/tex]Solving the operations:
[tex]A=\frac{624}{4}=156[/tex]Therefore, the average rate of change is 156.
what is the product of 3/4 and -6/7. see attached
Solution
For this case we can do the following:
[tex]\frac{3}{4}\cdot(-\frac{6}{7})=-\frac{18}{28}=-\frac{9}{14}[/tex]Then the answer is:
-9/14