Question 2:
[tex]9K-2K+5+7=[/tex]Let us simplify the above expression
The terms are already combined so we just need to simplify them
[tex]\begin{gathered} 9K-2K+5+7 \\ 7K+5+7 \\ 7K+12 \end{gathered}[/tex]Question 3:
[tex]3-5y+6=[/tex]Let us simplify the above expression
Combine the like terms together and simplify
[tex]\begin{gathered} 3-5y+6 \\ 3+6-5y \\ 9-5y \end{gathered}[/tex]Question 4:
[tex]7r-r=[/tex]Let us simplify the above expression
Simply subtract r from 7r
[tex]\begin{gathered} 7r-r \\ 6r \end{gathered}[/tex]Therefore, the simplified expressions are
[tex]\begin{gathered} 2.\: \: 9K-2K+5+7=7K+12 \\ 3.\: \: 3-5y+6=9-5y \\ 4.\: \: 7r-r=6r \end{gathered}[/tex]Ira Patton purchased a home and
obtained a 15-year loan of $219,990 at an annual
interest rate of 8.7%. Find the amount of interest paid
on the loan over the 15 years.
Show work
The amount of interest Ira Patton paid on the loan over the 15 years is $174,605.31.
How is the interest amount determined?The interest amount is computed using an online finance calculator with the following set of parameters.
The interest shows the finance costs that Patton bears for taking the mortgage loan over 15 years.
The interest amount includes the time value of money and the financial loss due to inflation.
N (# of periods ) = 180 months (15 years x 12)
I/Y (Interest per year) = 8.7%
PV (Present Value) = $219,990
FV (Future Value) = $0
Results:
PMT = $2,192.20
Sum of all periodic payments = $394,595.31
Total Interest = $174,605.31
Thus, at the end of 15 years, Patton must have paid $174,605.31 interest.
Learn more about interest costs at https://brainly.com/question/16134508
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the point between p and k that is four times as far from p as it is k
Equations
Let's call
x = distance of the required point to the point P
The distance from P to K is 5 - (-2) = 7. This means the distance from the required point to K is (7 - x).
Our point is located 4 times as far from P than from K, thus:
4(7 - x) = x
Operating:
28 - 4x = x
Adding 4x:
28 = 5x
Dividing by 5:
x = 28/5 = 5.6
The required point is located at -2 + 5.6 = 3.6
Checking the distances:
3.6 - (-2) = 5.6
7 - 5.6 = 1.4
It can be verified that 5.6 is four times 1.4, thus
x = 5.6
When a transversal crosses parallel lines, the alternate interior angles are ___?
From the illustration above, two parallel lines are crossed by a transversal. The marked angles are called alternate interior angles.
Alternate interior angles are congruent
58.165 to the 1st significant figure
Answer:
60
Step-by-step explanation:
The first significant figure is 5. Since the second number is 8 (greater than or equal to 5), the 5 rounds up to a 6. Thus the number becomes 60.
A recipe for 1 loaf of bread calls for 3 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt. The recipe can be scaled up to make multiple loaves of bread. Complete the table that shows the numbers to use for multiple loaves of bread.
We have to apply the rule of three to solve this.
We will use the equivalencies of the first row to complete the others.
The cups of flour needed are 3 cups/loaf.
The water needed is 12 tablespoons/loaf.
The salt needed 1 teaspoon/loaf.
With these equivalencies we can calculate the ingredients needed for any number of loaves:
[tex]\begin{gathered} \text{Number of loaves}=2,\text{ then} \\ \text{Cups of flour}=2\text{ loaves}\cdot\frac{3\text{ cups}}{\text{ loaf}}=6\text{ cups} \\ \text{Water}=2\text{ loaves}\cdot\frac{12\text{ tablespoons}}{\text{ loaf}}=24\text{ tablespoons} \\ \text{Salt}=2\text{ loaves}\cdot\frac{1\text{ teaspoon}}{\text{ loaf}}=2\text{ teaspoons} \end{gathered}[/tex]Answer the following.(a) Find an angle between 0° and 360° that is coterminal with 1260°(b) Find an angle between 0 and 2pi that is coterminal with-23pi/12Give exact values for your answers.
Answer:
[tex]\begin{gathered} a)\text{ 180 deg} \\ b)\text{ }\frac{\pi}{12} \end{gathered}[/tex]Explanation:
a) Here, we want to find an angle between 0 and 360 degrees that is coterminal with 1260
To find angles coterminal with an angle, what we have to do is to subtract multiples of 360 degrees from it
Now, let us find the number of times we can have 360 in 1260
By division, we have it that 1260/360 = 3.5
Now, to find the coterminal angle within the range, we have it that:
[tex]1260-3(360)\text{ = 1260-1080 = 180}[/tex]The coterminal angle within the given range is 180 degrees
b) Mathematically, we know that the term "pi" represents 180 degrees
Thus 2 pi is same as 2 * 180 = degrees
For ease of convenience, let us have the angle given in degrees
We have this as:
[tex]\frac{23\times180}{12}\text{ = -345 }[/tex]Now, let us proceed
What we have to do is to add this to 360 degrees so we can get the positive coterminal in degrees
We have this as -345 + 360 = 15
Lastly, we represent this in radians as follows:
[tex]\frac{\pi}{12}[/tex]
Solve the question give your rounded answer to the correct number of significant figures
The formula to calculate the volume of the brick is given to be:
[tex]V=l\times w\times h[/tex]We have the following dimensions, converted to meters, as follows:
[tex]\begin{gathered} l=\frac{110}{100}\text{ }cm=1.1\text{ }m \\ w=\frac{655}{100}\text{ }cm=6.55\text{ }m \\ h=\frac{1330}{100}\text{ }cm=13.3\text{ }m \end{gathered}[/tex]Therefore, the volume is:
[tex]\begin{gathered} V=1.1\times6.55\times13.3 \\ V=95.8\text{ }m^3 \end{gathered}[/tex]What is the volume of a sphere with a radius of 6.891 cm?
Given: A sphere with a radius of 6.891 cm.
Required: To determine the volume of the sphere.
Explanation: The volume of a sphere with radius r is given by the formula-
[tex]V=\frac{4}{3}\pi r^3[/tex]Substituting the value into the formula as-
[tex]V=\frac{4}{3}\times3.14\times(6.891)^3[/tex]Further solving gives the volume as-
[tex]V=1369.9828\text{ }cm^3[/tex]Final Answer: The volume of the sphere is 1369.983 cubic centimeters (approx).
Your neighborhood movie theater has a 25-foot-high screen located 8 feetabove your eye level. If you sit too close to the screen, your viewing angle is toosmall, resulting in a distorted picture. By contrast if you sit too far back, theimage is quite small, diminishing the movie's visual impact. If you sit & feet backfrom the screen, your viewing angle is given by0 = tan-1 33-tan-11) Choose a value for ærepresenting how far back you want to sit in feet and usethe formula above to calculate the viewing angle 8 for that distance. Make sureyour calculator is in radian mode.2) Go to Movie Theater Mewing Angle and compare your choice of distance tothe optimal choice of distance. How close or far are you to the optimal(maximum) viewing angle?3) What is your viewing angle in degrees? (convert your angle to the nearesttenth)
1. We are given that the angle is determined by the formula
[tex]\theta=tan^{\text{ - 1}}(\frac{33}{x})-tan^{\text{ -1 }}(\frac{8}{x})[/tex]lets say we want to sit at x = 25 feet. So if we replace x with 25 and we plug it in our equation, using a calculator in radians we get
[tex]\theta=tan^{\text{ -1}}(\frac{33}{25})-tan^{\text{ -1}}(\frac{8}{25})\text{ = }0.61276\text{ radians}[/tex]3. To transform one angle that is in radians, to degrees, we must mutiply by 180° and divide by pi radians. So, in our case we get
[tex]\theta\text{ = 0. 61276}\cdot\frac{180}{\pi}\text{ = }35.1086\text{ degrees}[/tex]When two coins are tossed at the same time, what is the theoretical probability of an outcome of one head and one tail?1/21/33/41/4
To find the proability we need to remember the product rule of proabbility that states that:
[tex]P(A\cap B)=P(A)P(B)[/tex]in this case event A is "getting head" and event B is "getting tail"; we know that each of this events have a proability of 1/2, then:
[tex]P(A\cap B)=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]Therefore the probability we are looking for is 1/4.
3. Eric has rock and classical mp3 on his computer. The number of rock mp3 is 3 times more than the number of classical mp3. Let c represent the number of classical mp3. Write an expression of the number of rocks mp3s
Let the rock mp3 on Eric's computer be x.
Given the classical mp3 on Eric's computer be c.
Given the number of rocks, mp3 is 3 times more than the number of classical mp3.
[tex]\begin{gathered} x=3c+c \\ x=4c \end{gathered}[/tex]The length of a rectangle is 3 centimeters longer than the width. The perimeter of the rectangle is less than 15cm. Figure out the inequality and solve.
we have the following:
[tex]\begin{gathered} l=3+w \\ 15>2\cdot l+2\cdot w \\ 15>2\cdot(3+w)+2\cdot w \\ 15>6+2w+2w \\ 15-6>4w \\ 4w<9 \\ w<\frac{9}{4} \end{gathered}[/tex]therfore, the answer is:
[tex]\begin{gathered} l=3+\frac{9}{4}=5.25 \\ w<\frac{9}{4}<2.25 \end{gathered}[/tex]Find, in radical form, the distance between (2, 1) and (-1,3).
You have the following two points:
(2,1)
(-1,3)
In order to determine what is the distance between the previous points, you use the following formula:
[tex]d=\sqrt[]{(x_1-x_2)^2-(y_1-y_2_{}^{})^2}[/tex]where (x1,y1) and (x2,y2) are the points with a distance between them of d.
You use the given points to replace them into the formula for d:
[tex]\begin{gathered} d=\sqrt[]{(1-3)^2-(2-(-1))^2} \\ d=\sqrt[]{(-2)^2+(3)^2} \\ d=\sqrt[]{4+9} \\ d=\sqrt[]{13} \end{gathered}[/tex]hence, the distance between the given points is √13
i can’t find the answer, help?
Answer:
-3
Step-by-step explanation:
4a - 2(a + b) + 1 = ?
4(2) - 2(2 + 4) + 1
8 - 2(6) + 1
8 - 12 + 1
-4 + 1 = -3
I hope this helps!
The Phil price of an item is 4/5 the original price of the item is X.Which statement explains why both for 4/5 and 0.8x can find the sale price of the item?1. multiplying by 5/4 os the same as multiplying by 0.82. Multiply by 4/5 is the same as multiplying by 80%3. The fraction 4/5 is the same as a decimal 0.2, therefore, 4/5x can be written is 0.2x4. Expressions are not equivalent
We are given that the price of an item is 4/5 , meaning itis 4/5x , this is the same expression as in 4/5 x = 0.8x
Because 4/5 in decimal form is 0.8
So the correct option would be option 2.
Multiplying 4/5 is the same as multiplying by 0.8
QUICK ANSWERS ONLY! 47. Find the value of x. The diagram is not to scale.4242402323A. 80B. 84C. 40D. 46
The first Option is the correct option
PLEASE HELP ME!! The 7th grade has already saved $60 for a field trip to Hershey Park. They need to raise at least$720 in order to pay for the trip. They decide to sell T-shirts to raise money. They earn $12toward the trip for every T-shirt they sell.Write the inequality that represents this situationHow many T-shirts must they sell to eam at least $720? Show how you determined your answer
We have to calculate how many T-shirts the hay to sell in order to raise $720, including the $60 dollars they already saved.
They earn $12 for every T-shirt, so the amount of money raised is 12x, being x the number of T-shirts.
Then, 12x has to be at least equal to 720-60=660:
[tex]12x\ge660[/tex]Then, if we divide both sides by 12, we get the number of T-shirts they have to sell:
[tex]\begin{gathered} 12x\ge660 \\ \frac{12}{12}x\ge\frac{660}{12} \\ x\ge55 \end{gathered}[/tex]They have to sell at least 55 T-shirts.
Mark simplified the equation 36 – 7x = -7(x -7(x - 5) to36 – 7x = -7x + 35. This means that the equation has:A. only 1 solutionB. no solutionsC. infinitely many solutions
We are to simplify the given equation to determine if it has 1 solution, no solution or infinitely many solutions.
So,
If 36 - 7x = -7(x - 5) to 36 - 7x = -7x + 35.
Let's work on the second equation.
36 - 7x = -7x + 35
First let's collect like terms.
36 - 35 = -7x + 7x
From what we can see the equation, -7x + 7x will cancel out.
Therefore, there are no values of x that makes the equation true.
So, there is No Solution.
The correct option is B, which is No Solution.
Which of the following functions shows the quadratic parent function,F(x) = x?, horizontally stretched?
The parent function is,
[tex]F(x)=x^2[/tex]The graph is stretched horizontally when x is replaced by kx where k is less than 1.
Thus, option (B) is the correct solution as x is replaced by x/2 in the F(x) to get G(x).
The red curve represents F(x) and the blue one represents G(x).
How much thread is left on the spool in meters
Given:
The total 5 yards of thread on the spool.
Convert yard into meters.
[tex]1\text{ yard}\approx0.9144\text{ meters}[/tex]For 5 yards to meters is,
[tex]\begin{gathered} 5\text{ yards}\approx\text{5}\times0.9144\text{ meters} \\ \approx4.572\text{ meters} \end{gathered}[/tex]Allison uses 3.5 meters of the thread, the thread remains is,
[tex]4.572-3.5=1.072[/tex]Answer: The thread left will be approximately 1.072 meters.
write an equation of the line in point slope form that passes through the given points (3,4) and (4,6)An equation of the line is??
re The point-slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]The slope m of the line passing through these two points is the difference between their y coordinates divided by the difference between their x - coordinate.
[tex]m=\frac{6-4}{4-3}[/tex][tex]m=2[/tex]Now we need only find the y-intercept.
Let us use the point (3, 4) which tells us that at x = 3, y = 4; therefore,
[tex]4-y_1=2(3)[/tex][tex]y_1=-2[/tex]Hence, the question of our line in point-slope form is
[tex]\textcolor{#FF7968}{y+2=2x}[/tex]Alternatively, when we have the slope of the line we would just use one of the points to quickly write the point-intercept form.
The y_1 and x_1 in the very first equation are the coordinates of one of the points on the line =. We know that one of the point on our line is (3, 4);
Michaela has $2.05 in dimes and nickels in her change purse. She has seven more dimes than nickels. How many coins of each type does she have?
Answer: Michaela has 16 Dimes, and 9 Nickels.
Simplify the following 4^9x 4^3
Answer:
261144^x and 64
Step-by-step explanation:
4^9x = (4^9)^x = 262144^x
4^3 = 64
But maybe I don't understand the task?
Find anequation for the vertical line through the point (-5, -3).
A line is vertical, then all points lie on it have the same x-coordinates
If line L is a vertical line and passes through the point (a, b), then its equation is
[tex]x=a[/tex]Since the given line is a vertical line and passes through the point (-5, -3)
That means a = -5
Then its equation is
[tex]x=-5[/tex]Question 1 ask the same thing but only they ask if the account is growing or decaying and it was growing so nowQuestion 2 what is the rate of growth or decayA 250B 0.97C 0.03D 1.03
.Explanation
The question gives us an exponential equation and asked that we determine the growth rate
Growth rates refer to the percentage change of a specific variable within a specific time period
From the given expression:
[tex]f\mleft(x\mright)=250\left(1.03\right)^x[/tex]If we are to deduce the growth rate, then we will have to compare it with the general formula
[tex]\begin{gathered} f\lparen x)=A\left(b\right)^x \\ where\text{ b is the growth factor} \end{gathered}[/tex]The growth factor is the factor by which a quantity multiplies itself over time. The growth rate is the addend by which a quantity increases (or decreases) over time
Thus, in our case
[tex]\begin{gathered} Growth\text{ factor=b=1.03} \\ Growth\text{ rate =Growth factor -1} \end{gathered}[/tex]Thus
[tex]Growth\text{rate=Growthfactor-1=1.03-1=0.03}[/tex]Hence, the growth rate is 0.03
Because the account increases by 0.03 overtime
The answer is 0.03
in a random sample of 900 B.Admin students 225 said that they wanted to become Statisticians. Assume the population of B. Admin students are normally distributed. Calculate the expected value of the population proportion estimator.
Answer: 0.25
Explanation:
The formula for calculating the population proportion is expressed as
p' = x/n
where
number of trials
number of success
From the information given,
x = 900
n = 225
Thus,
p' = 225/900
p' = 0.25
the expected value of the population proportion estimator is 0.25
Find the domain and the range help please.
Answer:
Domain: [tex]-5 < x\leq 6[/tex]
Range: [tex]-5 < y\leq 2[/tex] and [tex]y=3[/tex]
Step-by-step explanation:
The domain does not include negative five because it is an open dot at (-5,-5)
The domain includes -2 even though their is an open dot because their is one closed dot at (-2, -2) as well.
The domain includes 3 because there is a closed dot at point (3,2)
The range does not include negative five because it is an open dot at (-5,-5).
Range does not include anything between [tex]2\leq x\leq 3[/tex] because there is nothing there.
Finally we include y=3 because the is a horizontal line where y=3.
the question is asking can the number of mosquito bites be represented as a function of the amount of repellent used? yes or no? I need help
If we have a set of ordered pair (like this table here) we can know if it can represent a function if the numbers on x (the variable that the function depends on) are repeated or not. If they repeat, then is not a function.
In this problem we can see that the amount of cans of repellent used is 0 1 5 4 2 4 3 2. This is our x. You see, of these numbers, 4 and 2 repeat so the answer is no, it cannot be represented as a function of the amount of cans of repellent used.
Two angles in a triangle measures 101° and 29° what is the measure of the third angle?
We are given that two angles in a triangle measure 101° and 29°
What is the measure of the third angle?
Recall that the sum of three interior angles of a triangle must be equal to 180°
Let x be the third angle of the triangle, then we can write
[tex]x+101\degree+29\degree=180\degree[/tex]Let us solve the above equation for x
[tex]\begin{gathered} x+101\degree+29\degree=180\degree \\ x+130\degree=180\degree \\ x=180\degree-130\degree \\ x=50\degree \end{gathered}[/tex]Therefore, the measure of the third angle is 50°
Question Use set-builder notation to describe the set of all odd integers. Select the correct answer below: O {n|2n +1 €Z} O {2n | neZ}O {2n +1 | * € Z} O {2n +1 ne Z}
First let's define how to write the odd intergers:
When you have an odd it menas you have the result of a number multiply by 2 (or a even number) +1, so, if you need to express the odds you have:
2n+1
Now the ingergers are represented by the Z
Then so, the set of all odd integers is:
[tex]2n+1\in Z[/tex]where
∈ means belongs
Z means intergers
n is the n- umpteenth term.