We have the progression
91, 85, 79, ..., -29.
Also we can test:
85 - 91 = -6
79 - 85 = - 6
Hence, the progression is an arithmetic progression with d = -6.
Now, using the general formula of an arithmetic progression, we can find the position of term -29; as follows:
[tex]\begin{gathered} a_n=a_1+(n-1)\times d_{} \\ -29\text{ = 91 + (n - 1)(-6) } \end{gathered}[/tex]So n = 21
Now we know -29 is the term on the 21 position, we can proceed to find the sum of the first 21st terms of the progression:
[tex]S_n\text{ = }\frac{a_1+a_n}{2}n\text{ }[/tex]Solving the formula we have:
[tex]S_{21}\text{ = }\frac{91-29_{}}{2}\text{ x 21 }[/tex]S₂₁ = 651
Given: AQRS = ATRS R Q T S Prove: AQST is isosceles
we know that
If two triangles are congruent, then its corresponding angles and its corresponding sides are congruent
In this problem
triangle QRS and TRS are congruent -------> given
so
that means
by definition of congruence
by definition of congruence
by definition of congruence
QR=TR ---> by definition of congruence
RS=RS ---> by definition of congruence
QS=TS ---> by definition of congruence
Remember that
A triangle isosceles has two equal sides and two equal interior angles
In the triangle QST we have
QS=TS
and that means-----> the triangle has two equal sides and two equal interior angles
therefore
QST is an isosceles triangle
Alex (the contractor) is to build eight homes on a block in a new subdivision, using two different models: standard and deluxe. (All standard homes are the same, and all deluxe models are the
same.)
(a) How many different choices does Alex have in positioning the eight houses if he decides to build three standard and five deluxe models?
(b) If Alex builds two deluxes and six standards, how many different positionings can he use?
The required number of choices for (a) is 112 choices and (b) 56 choices.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
(a)
According to the question,
Choices can be given as,
= 8C3 + 8C5
= (8)(7)(6)/(3)(2)(1) + (8)(7)(6)/(3)(2)(1)
= 2[(8)(7)(6)/(3)(2)(1)]
= 2[56]
= 112 choices,
Similarly,
(b)
Choices can be given as,
= 8C2 + 8C6
= 8C2 + 8C2
= 2(8C2)
= 2 (8×7/2×1)
= 2(28)
= 56 choices.
Thus, the required number of choices for (a) is 112 choices and (b) 56 choices.
Learn more about permutations and combinations here: https://brainly.com/question/2295036
#SPJ1
word problem: Solve I=prt for t
Then
[tex]t=\frac{l}{pr}[/tex]Looking at the Diagram what is the correct theorem,ASA Or AAS
In the given image, you have the following:
- side OP (first triangle) is congruent to side QR
- angle N is congruent to angle S
- angle O is congruent to angle Q
if angles N and S, and O and Q are equal, it is necessary that angles P and R are equal. Do to all interioir angles are equal, it is necessary that all sides of both trangles have the same length (beacuse one of such sides is equal to one side of the other triangle.)
Hence, you can conclude that both triangles are congruent:
ΔOPN ≅ ΔQRS
moreover, the specific theorem to express the congruent of both triangles is:
AAS
Exercises 12.3 Complete the following: 1. Complete the squares for each quadratic, list the center and radius, then graph each labeling its translated center: ra) x² + 2x + y² - 4y=4 (b) x² + y2 - 4x = 0) (c) 2x2 + 2y2 + 3x - 5y = 2 (d) x² + y²– 2x-3y=8 (e) x2 + y2 + 3x = 4 - (1) 4x² + Any? - 16x + 2Any = -2 (g) x2 + y2 + 4x = 0 (h) x2 + y2 – 7y = 0 (i) x2 + y2 + 2mx - 2ny = 0 (j) x2 + y2 - 2ax + 2by =
1) Let's complete the square, and label the Center, and the radius
x² + 2x + y² - 4y=4 Dividing the coefficients of x and y by 2
x² +2x +1 +y²-4y+4=4+5 Adding on both sides the new addends
(x+1)²+(y-2)²=9
How do I get the answer to this? (+7) - (+12)=
The given equation is +7 - (+12)
Now when two opposite signs are multiplied the answer is always negative.
Then,
- x + = -
Hence,
+7 - (+12) = +7 - 12 = -5
Sot he answer is -5.
Solve the quadratic equation by the square root method and write the solutions in radical forms simplify the solutions
Given the following quadratic equation:
[tex](8x+20)^2=50[/tex]We will solve the equation by the square root method.
Taking the square root of both sides:
[tex]\begin{gathered} \sqrt{(8x+20)^2}=\pm\sqrt{50} \\ \\ 8x+20=\pm\sqrt{50} \\ Note:\sqrt{50}=\sqrt{25*2}=5\sqrt{2} \\ \\ 8x+20=\pm5\sqrt{2} \end{gathered}[/tex]Subtract 20 from both sides
[tex]\begin{gathered} 8x+20-20=-20\pm5\sqrt{2} \\ 8x=-20\pm5\sqrt{2} \end{gathered}[/tex]Divide both sides by 8
[tex]x=\frac{-20\pm5\sqrt{2}}{8}[/tex]So, the answer will be:
[tex]x=\frac{-20+5\sqrt{2}}{8};or;\frac{-20-5\sqrt{2}}{8}[/tex]adding and subtracting polynomials find each sum or differenceplease do minimum steps
Solve the sums or differences between similar terms.
[tex]\begin{gathered} 5ax^2+3ax^2+3a^2x-5ax-5x+7x \\ 8ax^2+3a^2x-5ax+2x \end{gathered}[/tex]Evaluate the expression when b=48 and c=7.b+2c3Simplify your answer as much as possible.
You have the following expression:
b + 2c³
where b = 48 and c = 7. By replacing these values into the previous expression you obtain:
b + 2c³ = 48 + 2(7)³ = 48 + 2(343) = 48 + 686 = 734
Hence, the result is 734
If BD= 4x+3, find x. Round your answer to answer to the nearest tenth if necessary BC= 37CD = x-3
ok
BD = 4x + 3
BC = 37
CD = x - 3
37 + x - 3 = 4x + 3
37 - 3 - 3 = 4x - x
37 - 6 = 3x
31 = 3x
x = 31/3
That's all
The sum of the interior angles of an n-gon is 3420°. How many sides does the n-gon have?
In order to solve we remember that the sum of internal angles of a polygon is given by:
[tex]\text{anlge}=(n-2)\cdot180[/tex]Where "n" is the number of sides.
So, we solve now:
[tex]3420=(n-2)\cdot180\Rightarrow n-2=19[/tex][tex]\Rightarrow n=21[/tex]So, the polygon has 21 sides.
Hello :) Can you help me understand this and break it down for me after solving please thanks in advance
The domain of a function is the set of x-values that you can put into any given equation. For the equation:
[tex]g(x)=\sqrt[3]{x+8}[/tex]There are no restrictions, therefore, the domain is all real numbers:
[tex]D\colon(-\infty,\infty)[/tex]---------------------------------------------------
[tex]\begin{gathered} x=16 \\ g(16)=\sqrt[3]{16+8}=\sqrt[3]{24}\approx2.88 \end{gathered}[/tex]I’m having trouble with this problem please help?The second part of the question is at the beginning of the Answer Tab.
To answer this question, we have the following points for the line:
(2018, $3200) and (2020, $2000).
Since we want to find the relationship between the number of years after 2018, x, and the value of the computer, y, we need to have the year 2018 as the starting year, and we can replace it with 0. The rest of the years will be the number of years after 2018. For example, the year 2020 will be 2 years after 2018. The year 2022 will be 4 years after 2018 and so on.
Therefore, we have to find the equation of the line for the following points:
• (0, $3200), (2, $2000)
Then to find the equation line, we have to apply the two-point form of the line equation:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)_{}[/tex]If we label each point first, we have:
[tex]\begin{gathered} x_1=0,y_1=3200 \\ x_2=2,y_2=2000 \end{gathered}[/tex]Now, we can substitute these values into the two-point form of the line equation:
[tex]\begin{gathered} y-3200=\frac{2000-3200}{2-0}(x-0) \\ y-3200=\frac{-1200}{2}x \\ y-3200=-600x \\ y-3200+3200=-600x+3200 \\ y=-600x+3200 \\ f(x)=y=-600x+3200 \end{gathered}[/tex]Therefore, the relationship between years after 2018 (x) and the value of the computer (y) is as follows:
[tex]y=-600x+3200[/tex]Estimating the value of the computer in the year 2022We can see that the year 2022 is four (4) years after the year 2018:
[tex]2022-2018=4[/tex]Therefore, we can estimate the value of the computer in the year 2022 substituting x = 4 into the linear function:
[tex]\begin{gathered} y=-600(4)+3200 \\ y=-2400+3200 \\ y=800 \end{gathered}[/tex]Hence, the value of the computer, following this linear model is in the year 2022 of $800.
Estimating the value of the computer in the year 2024
We need to find the number of years in 2024 after 2018:
[tex]2024-2018=6[/tex]Now, we have to substitute this value into the linear equation as follows:
[tex]\begin{gathered} y=-600x+3200 \\ y=-600(6)+3200 \\ y=-3600+3200 \\ y=-400 \end{gathered}[/tex]We have that the value of the computer is -$400.
In this case, it does not have any sense to calculate this value. The item, in this case, is "creating" losses to the company (we can see it is a negative value), and we can sell the item before its value is zero. In a few words, it does not have any sense to calculate or estimate the value of the computer in 2024 because the item has become totally depreciated before that year.
Solve for s.1/2s=7/2s=1/7s=2/7s=3s=7
Solving a linear equation
Then
1/2s = 7/2
(1/2)s = 7/2
Its important to use correctly parenthesis
In 1/2s, s is dividing
In (1/2)s , s is multiplying
Then
1/2s = 7/2
1/(7/2) = 2s
2/7 = 2 s
1/7 = s
And , using parenthesis if
(1/2)s = 7/2
s = (7/2)/(1/2) = 7
It’s an essay with five point explain how to use an estimation to help find the product of two decimals give an example with both estimated an actual answers it is in math
In mathematics, estimation means approximating a quantity to the required accuracy. This is obtained by rounding off the numbers involved in the calculation and getting a quick and rough answer.
To approximate numbers,
We can give the following examples
Example 1
[tex]8.9\times2.1[/tex]We can approximate the numbers as follow
[tex]\begin{gathered} \text{For 8.9} \\ we\text{ will round 9 up to give 1} \\ \text{This is then added to 8 to give 9} \\ \text{Thus} \\ 8.9\cong9 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 2.1 \\ we\text{ will round down 1 to 0} \\ So\text{ that 2.1}\cong2 \end{gathered}[/tex]Thus, we will have
[tex]8.9\times2.1\cong9\times2=18[/tex]Therefore, the approximated value is 18
The actual answer is
[tex]8.9\times2.1=18.69[/tex]We can look at another example
[tex]11.23\times36.06[/tex]Thus
[tex]\begin{gathered} 11\times36=396 \\ \end{gathered}[/tex]The actual answer is
[tex]11.23\times36.06=404.95[/tex]In both cases, we can see that the approximated values and the actual values are not so far from each other.
A ball is dropped from a height of 10 feet and returns to a height that is one-half of the height from which it fell the Ball continues to bounce half the height of the previous bounce each time. How far how far will the ball have traveled when it hits the ground for the fourth time? It might be helpful to sketch the part of ball.
To solve this problem we can write a general equatio so:
[tex]y=10(1-0.5)^x[/tex]whre y is the high and x are the number of bounces so for 4 will be:
[tex]\begin{gathered} y=10(0.5)^4 \\ y=0.62ft \end{gathered}[/tex]A wildlife sanctuary has two elephants. One has a weight of 11,028 pounds and the other has a weight of 5.2 tons. A platform can hold 22,000 pounds. Can the platform hold both elephants? Explain your reasoning. (1 ton = 2,000 pounds)
Step 1:
Write the weight of both elephant
11028 pounds and 5.2 tons
Total weight of the platform = 22000 pounds
Step 2:
Convert tons to pounds
1 ton = 2000 pounds
5.2 tons = 5.2 x 2000 = 10400 pounds
Step 3:
Add the total weight of both elephants
= 11028 + 10400
= 21428 pounds
Step 4:
Final answer
The platform can hold both elephants because the weight of the platform is 572 pounds heavier than the combined weight of the two elephants.
hhhhhhneed help with math
If your last name starts with P, it is in the range of M-R. So the answer for the first question is the range of 6000 and 6999. So we can choose
[tex]6352[/tex]and if we can choose between 12% and 16%. let us choose
[tex]14\text{ \%}[/tex]and if we want that to be in decimal form, we have to divide 14 by 100
[tex]\frac{14}{100}=0.14[/tex]and those are the answer
I have trouble with system of equations. I always get one right and one wrong
To solve the system of equations above:
1. Rewrite the second equation to be similar to the frist equation:
[tex]\begin{gathered} \text{Add 2 in both sides of the equation:} \\ -x+2y-2+2=0+2 \\ -x+2y=2 \end{gathered}[/tex]2. Multiply the equation you get in step 1 by -1:
[tex]\begin{gathered} -1(-x+2y=2) \\ x-2y=-2 \end{gathered}[/tex]As you get that both equations in the system are the same (x-2y= -2) (the lines are the same) the system has infinitely many solutions (all the values of x and y are solutions for the system)
[tex]\begin{gathered} -2y=-2-x \\ \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]the area of North Carolina is about 5.3 x 10 to the 4th square miles. The area of Rhode Island the smallest state is about 1.3 x 10 to the third square miles. Approximately how many times greater is the area of North Carolina as compared to the area of Rhode Island?
The area of North Carolina is given by:
[tex]NC\text{ = 5}\cdot10^4miles^2[/tex]While the area of Rhode Island is:
[tex]RI\text{ = 1.3}\cdot10^3miles^2[/tex]We need to find how many times the area of North Carolina is bigger than the area of Rhoad Island. To do that we will have to divide the area from North Carolina by the area of Rhode Island. When dividing numbers in scientific notation, we need to divide the numbers and subtract the powers as shown below:
[tex]\begin{gathered} \text{ratio = }\frac{5\cdot10^4}{1.3\cdot10^3}\text{ } \\ \text{ratio = }3.85\cdot10^{4-3} \\ \text{ratio = 3.85}\cdot10 \\ \text{ratio = 38.5} \end{gathered}[/tex]The area of North Carolina is 38.5 times greater than the area of Rhoad Island.
Write the equation of the vertical line, through the point (2,−5).
Answer:
Explanation:
Given:
Point (2,-5)
To find the equation of the vertical line, we use:
x = a
where:
a= the value that x takes
Based on the given point (2,-5), the x value is 2. So,
x=a
x=2
Therefore, the equation of the vertical line is:
x=2
I need help, Solve the system of equations x=-2y and x-y=9
Given
x = -2y
and
x - y = 9
Replace 2nd equation with the 1st:
x - y = 9
(-2y) - y = 9
-2y - y = 9
-3y = 9
y = 9/ -3
y = -3
So, now we know x = -2y, thus
x = -2(-3) = 6
So, the solution is:
(6,-3)
The half life of silicon -32 is 710 years. If 30 grams is present now, how much will be present in 300 years? (Round your answer to three decimal places.)
The half-life exponential decay equation is
[tex]\begin{gathered} N(t)=N_0(\frac{1}{2})^{\lambda} \\ \text{where} \\ \lambda=\frac{t}{t_{\frac{1}{2}}} \end{gathered}[/tex]N_0 is the initial quantity of the substance, t_1/2 is the half-life and t is the time.
In our case,
[tex]\begin{gathered} \lambda=\frac{300}{710}=\frac{30}{71} \\ N_0=30 \end{gathered}[/tex]Therefore,
[tex]N(300)=\frac{30}{2^{\frac{30}{71}}}=22.3833\ldots\approx22.383_{}[/tex]The answer is 22.383 grams.
Select the correct answer from each drop-down menu.y 110+8C46+4+2BАAB-5-448--2AABC goes through a sequence of transformations to form AA'BC. The sequence of transformations involved is afollowed by a
The Solution.
It was a translated 2 units right, and then reflected over the y- axis.
Last week you worked 32 hours, and earned $304. What is your hourly pay rate? per hour Give your answer in dollars and cents (like 5.50)
32 hours worked corresponds to $304 earned. To find how much you earned after 1 hour, we can use the next proportion:
[tex]\frac{32\text{ hours}}{1\text{ hour}}=\frac{304\text{ \$}}{x\text{ \$}}[/tex]Solving for x:
[tex]\begin{gathered} 32\cdot x=1\cdot304 \\ x=\frac{304}{32} \\ x=9.5 \end{gathered}[/tex]Your hourly pay rate is $9.50
I remind you that the answer will be always available in your profile
per hour
16. A hamster drinks cup of water each day. If Melissa pours 6 cups of water into the hamster's drink cylinder, how many days will the water last?
According to the information, the drink cylinder will last 6 days.
Because
1 cup --------------------- 1 day
6 cups -------------------- x
x = (6 x 1) / 1
x = 6/1
x = 6 days
Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor. IN NI -------4-2 LE M 122 HE Figure LMNO is VI congruent to Figure EFGH because rigid motions | be used to map Figure LMNO onto Figure ERGH. can Figure LMNO is dilations can similar to Figure EFGH because rigid motions and/or be used to map Figure LMNO onto Figure EFGH. The scale factor from Figure LMNO to Figure EFGH is 1
Given: the figures LMNO and EFGH
WE will find the length of each side of the figure LMNO
AS shown:
[tex]\begin{gathered} LM=3 \\ MN=\sqrt[]{2^2+4^2}=\sqrt[]{20}=2\sqrt[]{5} \\ NO=\sqrt[]{6^2+2^2}=\sqrt[]{40}=2\sqrt[]{10} \\ OL=\sqrt[]{1^2+2^2}=\sqrt[]{5} \end{gathered}[/tex]Now, we will find the length of each side of the figure EFGH:
[tex]\begin{gathered} FG=4 \\ GH=\sqrt[]{3^2+3^2}=\sqrt[]{18}=3\sqrt[]{2} \\ HE=\sqrt[]{1^2+3^2}=\sqrt[]{10} \\ EF=\sqrt[]{2^2+4^2}=\sqrt[]{20}=2\sqrt[]{5} \end{gathered}[/tex]By comparing the lengths of the corresponding sides
The figures are not congruent and not similar
So, the answer will be neither congruent nor similar
(a) Find h(- 2), h(0), h(2) , and h(3) (b) Find the domain and range of h.(c) Find the values of x for which h(x) = 3 .(d) Find the values of x for which h(x) <= 3 .(e) Find the net change in h between x = - 3 and x = 3 .УА3h-303X
To find values of the function h at different x values, we go straight to that x value and find the corresponding y value of the graph.
From the graph, we have:
[tex]\begin{gathered} h(-2)=1 \\ h(0)=-1 \\ h(2)=3 \\ h(3)=4 \end{gathered}[/tex](b)The domain of a function is the set of x-values for which the graph of the function is defined.
The range of a function is the set of y-values for which the graph of the function is defined.
Looking at the graph, we see that from
x = - 3 to x = 4, the function is defined.
Also, from
y = - 1 to y = 4, the function is defined.
Thus, we can write the domain and range as >>>>>
[tex]\begin{gathered} D=-3\leq x\leq4 \\ R=-1\leq y\leq4 \end{gathered}[/tex](c)h(x) = 3 means y = 3
We will draw a horizontal line at y = 3 and see the points at which that line and curve crosses. Then, we will draw a perpendicular from that point to the x-axis. These are the values of x for which y = 3.
The graph:
We see from the graph drawn that for x = - 3, x = 2, and x = 4, the value of the function h is 3.
So,
[tex]x=-3,2,4[/tex](d)The values of x for which the function is ≤ 3 can be found by again drawing a line y = 3 and finding the places where the graph is BELOW that line.
Graph:
So, we can see that from x = - 3 to x = 2, the function is less than or equal to 3.
Thus,
[tex]-3\leq x\leq2[/tex](e)From x = - 3 to x = 3, the function changes several values. But the net change can be found by finding the respective values of the function at x = - 3 and at x = 3 and finding the difference.
At x = - 3, the function has a value of "3".
At x = 3, the function has a value of "4".
Thus, the net change is 4 - 3 = 1
Net Change = 1
5. Solve the division expression from the problem above (4 + 3). 4 3 A. 12 B. 1 c. 13 D. 14 3
A division as follow:
[tex]\frac{4}{3}[/tex]Can be solve as:
4/3 is equal to sum 1/3 four times:
[tex]\frac{4}{3}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}[/tex]As 3/3 is equal to 1 unit:
[tex]=1+\frac{1}{3}[/tex]Writen as a mixed number:
[tex]1\frac{1}{3}[/tex]A lake is stocked with 20 carp. If the carp population grows at a rate of 7.5% per month, when will the pond contain 500 carp? Round your answer to the nearest hundredth.
We have a lake with 20 carp and a gowth rate of 7.5% per month, so the equation of the population at time t is:
[tex]\begin{gathered} P(t)=P_0\cdot(1+\frac{7.5}{100})^t \\ \text{Where t is the time in months, P}_0\text{ is the initial population (t=0) and P(t) is the population at time t.} \end{gathered}[/tex]So, we need to find the value of t when P(t)=500 and P0 (the initial population) is 20:
[tex]\begin{gathered} P(t)=500=20\cdot(1+\frac{7.5}{100})^t \\ \frac{500}{20}=1.075^t \\ \log (25)=\log (1.075^t) \\ \log (25)=t\cdot\log (1.075) \\ t=\frac{\log(25)}{\log(1.075)}=44.51 \end{gathered}[/tex]The lake contain 500 carp in 44.51 months.