The number of digits in 7000 is 4
The number of digits in w=7000
[tex](w)^{\cdot}=\text{ the number of digits in w+2}[/tex][tex](w)^{\cdot}=\text{7000+2}[/tex][tex](w)^{\cdot}=7002[/tex]Hence the required value is 7002.
Given right triangle ABC, with altitude CD intersecting AB at point D. If AD = 5 and DB = 8, find the length of CD, in simplest radical form. In your video include whether you would use SAAS or HYLLS to solve (and WHY), the proportion you would set up, how you would solve for the missing side, and how you know your answer is in simplest radical form.
First we dra a triangle:
To prove that the triangles are similar we have to do the following:
Considet triangles ABC and ACD, in this case we notice that angles ACB and ADC are equal to 90°, hence they are congruent. Furthermore angles CAD and CAB are also congruent, this means that the remaining angle in both triangles will also be congruent, therefore by the AA postulate for similarity we conclude that:
[tex]\Delta ABC\approx\Delta ACD[/tex]Now consider triangles ABC and BCD, in this case we notice that angles ACB and BDC are congruent since they are both equal to 90°. Furthermore angles ABC and DBC are also congruent, this means that the remaining angle in both triangles will, once again, be congruent. Hence by the AA postulate we conclude that:
[tex]\Delta ABC\approx\Delta BCD[/tex]With this we conclude that traingles BCD and ACD are both similar to triangle ABC, and by the transitivity property of similarity we conclude that:
[tex]\Delta ACD\approx BCD[/tex]Now that we know that both triangles are similar we can use the following proportion:
[tex]\frac{h}{x}=\frac{y}{h}[/tex]this comes from the fact that the ratios should be the same in similar triangles.
From this equation we can find h:
[tex]\begin{gathered} \frac{h}{x}=\frac{y}{h} \\ h^2=xy \\ h=\sqrt[]{xy} \end{gathered}[/tex]Plugging the values we have for x and y we have that h (that is the segment CD) has length:
[tex]\begin{gathered} h=\sqrt[]{8\cdot5} \\ =\sqrt[]{40} \\ =\sqrt[]{4\cdot10} \\ =2\sqrt[]{10} \end{gathered}[/tex]Therefore, the length of segment CD is:
[tex]CD=2\sqrt[]{10}[/tex]21 - 7∆ = 4 - 8∆ 5∆ - 3 + 3∆ = ∆ + 7 + 6∆solve these.
We are given the following equation:
[tex]21-7\Delta=4-8\Delta[/tex]We need to solve for delta, to do that we will first add 8delta on both sides:
[tex]21-7\Delta+8\Delta=4-8\Delta+8\Delta[/tex]Now we add like terms:
[tex]21+\Delta=4[/tex]Now we subtract 21 on both sides:
[tex]21-21+\Delta=4-21[/tex]Adding like terms:
[tex]\Delta=17[/tex]Therefore delta is 17
A bank features a savings account that has an annual percentage rate of 4.8 % with interest compounded monthly. Umbrosia deposits $6,500 into the account.
How much money will Umbrosia have in the account in 1 year?
What is the annual percentage yield (APY) for the savings account?
S(8)=3500(1+(.047/4))^32
S(8)=$5086.40 in the account after 8 years.
a)The relative growth rate is .25, or 25%
b)at t=0, the population is 955e^.25(0)=955
c)at t=5; the population is 955*e^.25(5)=955*3.49=3333.28 bacterium.
which ordered pair is a solution of the equation 7x−5=4y−6?PLEASE HURRY THIS IS DUE NOW A. only (2,4)B. only (3,6)C. both A and BD. neither A or B
To answer this question, we can take the coordinates (2, 4), and (3, 6) and substitute each of them in the given equation. Then, we can determine which of these ordered pairs is a solution of the equation 7x - 5 = 4y - 6. Then, we have:
1. Case: Ordered pair (2, 4):
[tex]7\cdot(2)-5=4\cdot(4)-6\Rightarrow14-5=16-6\Rightarrow9\ne10[/tex]This ordered pair is NOT a solution.
2. Case: Ordered pair (3, 6):
[tex]7\cdot(3)-5=4\cdot(6)-6\Rightarrow21-5=24-6\Rightarrow16\ne18[/tex]This ordered pair is NOT a solution.
Therefore, neither the ordered pair (2, 4) nor (3, 6) are solutions to the given equation (Option D).
A. Side a is 24 inches longand side bis 21 inches longB. Side a is 63 inches long and side bis 54 inches long.C. Side a is 18 inches long and side bis 15 inches long.D. Side a is 7 inches long and side bis 6 inches long.
Since both drawings are similar and have a scale factor, we can say that all sides keep the same scamle factor, if the scale drawing is in a proportion of 3:1 means that all of its sides is 3 times the real objects sides.
write this as equations
[tex]\begin{gathered} 3\cdot a=21in \\ 3\cdot b=18in \end{gathered}[/tex]to find the respetive values for a and b we divide the sides by 3
[tex]\begin{gathered} a=\frac{21in}{3}=7in \\ b=\frac{18in}{3}=6in \end{gathered}[/tex]The correct answer is D.
how many term has G.p whose 2nd term is 1/2 and common ratio and the last term are 1/4and1/128respestively
The geometric progression has the form:
[tex]\mleft\lbrace a,ar,ar^2,ar^3,\ldots,ar^n\mright\rbrace[/tex]We have the information about the second term, a*r:
[tex]ar=\frac{1}{2}[/tex]We know that the common ratio is
[tex]r=\frac{1}{4}[/tex]So from this information we can get the coefficient a:
[tex]\begin{gathered} ar=\frac{1}{2} \\ a\cdot\frac{1}{4}=\frac{1}{2} \\ a=\frac{4}{2}=2 \end{gathered}[/tex]And we also know that the last term is 1/128, that is
[tex]ar^n=\frac{1}{128}[/tex]From this one we can find n:
[tex]\begin{gathered} 2\cdot(\frac{1}{4})^n=\frac{1}{128} \\ (\frac{1}{4})^n=\frac{1}{128\cdot2} \end{gathered}[/tex]We can apply the property of the logarithm of power to get n:
[tex]\begin{gathered} \log ((\frac{1}{4})^n)=\log (\frac{1}{256}) \\ n\cdot\log (\frac{1}{4})^{}=\log (\frac{1}{256}) \\ n=\frac{\log (\frac{1}{256})}{\log (\frac{1}{4})} \\ n=4 \end{gathered}[/tex]Be careful, because n is not the number of terms. The number of terms is n+1, so the G.P. has 5 terms
2(4-2x)-5=-2(x+5)+8x
The equation 2(4-2x)-5=-2(x+5)+8x has a value of 1.3 for x
How to determine the solution to the equation?From the question, the equation to solve is given as
2(4-2x)-5=-2(x+5)+8x
Rewrite the equation properly
This is represented by the following representation
2(4 - 2x) - 5=-2(x + 5) + 8x
Start by opening the brackets in the equation
So, we have the following equation
8 - 4x - 5 =-2x - 10 + 8x
Collect the like terms in the equation
So, we have the following equation
8x - 2x + 4x = 10 +8 - 5
Evaluate the like terms in the equation
So, we have the following equation
10x = 13
Divide both sides of the equation by 10
So, we have the following equation
x = 1.3
Hence, the solution to the equation for x is 1.3
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The following table represents C, an appliance repairman’s charges based on t, the hours it takes to make a repair.Which of the following equations could be used to determine the repairman’s charges for a repair?A: C=27t +3B: C=27tC: C=35tD: C=35t + 2
Given the table below
To find the equation of the values of the table, we will first calculate the rate of change, then use a point and the rate of change calculated fo find the equation for the repairman's charges for the repair
To find the rate of change we have
[tex]\text{ Point 1}\Rightarrow(1,62)\Rightarrow t_1=1,c_1=62[/tex][tex]\text{ Point 2}\Rightarrow(3,116)\Rightarrow t_2=3,c_2=116[/tex]The rate of change formula is
[tex]m=\frac{c_2-c_1}{t_2-t_1}=\frac{116-62}{3-1}=\frac{54}{2}=27[/tex]Having calculated the rate, we can use slope and one point form equation of a line to get the desired equation. This is given below:
[tex]c-c_1=m(t-t_1)[/tex]Substitute the given values of t and c and the rate in the formula above
[tex]\begin{gathered} c-62=27(t-1) \\ c-62=27t-27 \\ c=27t-27+62 \\ c=27t+35 \end{gathered}[/tex]Hence, the repairman's charges for a repair is given as C = 27t + 35
What is the probability that a student does not play on a sports team?
Answer:
P = 0.5
Explanation:
The probability can be calculated as the division of the number of students that does not play on sports team by the total number of students.
Taking into account the table, there is a total of 20 students and from those 10 does not play on a sports team. Therefore, the probability is:
P = 10/20 = 0.5
Kevin went to the nursery and bought a 5 ft tall tree. After planting the tree, Kevin made a table to record theheight, h, of the tree, t years after it was planted. Verbally describe the relationship between h and t.t 0 1 2 3 4h 5 6 7 8 9
As we can see inthe table foe every year that pass the thre grows 1 ft
As we can see inthe table foe every year that pass the thre grows 1 ft
what does frilling mean
Answer:
A ruffled, gathered, or pleated border or projection, such as a fabric edge used to trim clothing.
Step-by-step explanation:
Brainlest, Please!
Describe how the graph of the function g(x)=1/4|x|-2 can be obtained from the basic graph. Then graph the function.Start with the graph of h(x)=|x|. Then [__] it vertically by a factor of [__]. Finally, shift it [___] units.
Start the graph of h(x) = |x|, then stretch it vertically by a factor of 1/4 . Finally, shift it down by 2 units
The original graph can be seen above
what it becomes can be seen below
Hence the final answer is option B
The difference between two numbers is 28. The sum of the two numbers is 56. Let x be the larger number and y be the smaller number. Which system of equations represents this proble O y - x = 28 I + y = 56 O x=y= 28 x + y = 56 Oy - 2 = 56 x + y = 28 - y = 56
Since x is the larger number and y is the smaller number
Since their sum is 56
That means add x and y then equate them by 56
[tex]x+y=56(1)[/tex]Since the difference between them is 28
That means subtract y from x and equate the answer by 28
[tex]x-y=28(2)[/tex]Look at the answer to find the correct answer
It is B
x - y = 28 and x + y = 56
inding Total CostsStore AStore BWhat is the cost of the repair and sales tax combinedat Store B?ComputerRepair$1,200$1,350Sales Tax6%7%Gratuity15%15%ShippingFree2% of totalprice
Store B :
Computer repair : $1,350
Sale tax = 7%
To obtain the sale tax amount, multiply the price by the percentage in decimal form (divided by 100);
$1,350 x (7/100) = 1,350 x 0.07 = $94.5
Add both:
1,350+94.5=$1,444.5
The measure of angle c below is(Hint: Slide 2)95/640
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
In the right triangle of the figure
we have
c+d+64=180
we have that
d=90 degrees (right angle)
substitute
c+90+64=180
c+154=180
c=180-154
c=26 degrees
Find the mean of the set of data. Round to the nearest tenth if necessary 6.4,6,8, 8.1,5.4, 11.1,6.7 The mean is
Given a set of data:
6.4,6,8, 8.1,5.4, 11.1,6.7
The sum of the given data =
[tex]6.4+6.8+8.1+5.4+11.1+6.7=44.5[/tex]The number of the data = 6
so, the mean =
[tex]\frac{44.5}{6}=7.4166667[/tex]Rounding to the nearest tenth, so, the answer will be:
Mean = 7.4
f(x) = 3x² + 9x – 16
Find f(-8)
Answer: 104
Step-by-step explanation:
[tex]f(-8)[/tex] represents [tex]f(x)[/tex] evaluated at [tex]x=-8[/tex].
[tex]f(-8)=3(-8)^2 +9(-8)-16\\\\=192-72-16\\\\=120-16\\\\=104[/tex]
pls help the hw is due today
Answer: the slope for the line is
y= -2x-4
What is the slope of this horizontal line from 10-13 minutes?
We are asked to determien the slope of the line between 10 and 13 minutes. Since this is a horizontal line, it's slope is 0.
Find f.Write your answer in simplest radical form. ___ units
Answer:
The value of f is;
[tex]f=3\sqrt[]{2}\text{ units}[/tex]Explanation:
Given the triangle in the attached image.
Recall that;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]from the given figure;
[tex]\begin{gathered} \theta=30^{\circ} \\ \text{opposite}=f \\ \text{adjacent}=3\sqrt[]{6} \end{gathered}[/tex]substituting the values;
[tex]\begin{gathered} \tan 30=\frac{f}{3\sqrt[]{6}} \\ f=3\sqrt[]{6}\tan 30 \\ f=3\sqrt[]{6}(\frac{\sqrt[]{3}}{3}) \\ f=3\sqrt[]{2} \end{gathered}[/tex]Therefore, the value of f is;
[tex]f=3\sqrt[]{2}\text{ units}[/tex]Assume that a particular professional baseball team has 12 pitchers, 5 infielders, and 8 other players. If 3 players' names are selected at random, determine the probability that 2 are pitchers and 1
is an infielder.
What is the probability of selecting 2 pitchers and 1 infielder?
(Type an integer or a simplified fraction.)
Step-by-step explanation:
Pitchers(p) = 12
Infielders(i) = 5
Others(o) = 8
Total players = 25
Probability(2p and 1i) =
[tex]( \frac{2}{25} ) \times ( \frac{1}{25} ) = ( \frac{2}{625} )[/tex]
The circle graph shows the results of a survey by a bakery on which of their new products 105 customerspreferred most. How many customers preferred cake? Round your answer to the nearest whole number.
If 105 customers were the total, and 35% prefers cake, we must calculate 35% of 105, then we must do 105 multiplied by 35%, we can doit transforming the 35% in the fraction notation:
[tex]35\%=\frac{35}{100}[/tex]And the multiplication
[tex]105\cdot\frac{35}{100}=36.75[/tex]Therefore, if we round it to the nearest whole number, the number of customers that prefer cake is 37.
37 customers prefer cake.
please help me asap, Evaluate 9 exponent 2
81
Explanation
Remember
[tex]a^b=\text{ a multiplied by itself b times}[/tex]Step 1
apply
[tex]\begin{gathered} 9^2=9\cdot9 \\ 9\cdot9=81 \end{gathered}[/tex]giving that -3+20=5x-4 write 3 more equations that you know are true
Answer:
Step-by-step explanation:
ft7654
A math book is 2.5 cm thick.
How many of these books can
be stored on a shelf that is
one meter long?
The number of books that can be stored on one meter-long shelf is (forty) = 40.
Given
a book is 2.5 cm thick
number of books required are
Convert meters into centimeters first 1m = 100 cm now, divide them:
= 100 cm ÷ 2.5 cm to remove the decimal point divide 2.5 by 10 = 2.5/10
= [tex]100 * \frac{10}{25}[/tex]
= 40
thus the total number of books that can be stored on a one-meter bookshelf is 40 books.
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Elijah is snorkeling above a shipwreck. The ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation. What is Elijah's elevation?
Elijah's elevation when Elijah is snorkeling above a shipwreck is -14.
What is elevation?Elevation simply has to do with the height above sea level.
In this case, Elijah is snorkeling above a shipwreck and the ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation.
Elijah's elevation will be:
= Fraction of his snorkeling × Ship's elevation
= 2/15 × (-105)
= -14
This shows the elevation of Elijah.
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use the distributive property to simplify the left side of the equation 2(x/8+3)=7+1/4x
Given data:
The given expression is 2(x/8+3)=7+1/4x.
The given expression can be written as,
2(x/8)+2(3)=7+1/4x
x/4+6=7+1/4x
x/4-1/4x=7-6
x/4-1/4x=1
x^(2)-1=4x
x^(2)-4x-1=0
Thus, the final expression is x^(2)-4x-1=0 after applying distributve property on left side.
x - 5 = 2(4x-3) - 5 = 7x - 6 1/7= xx - 5 = 8x - 6-5 + 6 = 7x-6+6 1 = 7x x-x-5 = 8x - x - 6 1/7 = 7x/7Original equationCombine like terms. Solution Distributive PropertyAddition Property of EqualityCombine like terms.Subtraction Property of EqualityDivision Property of Equality What is the order to do this equation.
We have to solve the equation:
[tex]\begin{gathered} x-5=2(4x-3) \\ x-5=8x-6 \\ x-x-5=8x-x-6 \\ -5+6=7x-6+6 \\ 1=7x \\ \frac{1}{7}=\frac{7}{7}x \\ \frac{1}{7}=x \end{gathered}[/tex]The steps are:
1. Original equation
2. Distributive property
3. Substraction property of equality
4. Addition property of equality
5. Combine all terms
6. Division property of equality
7. Solution
14|x + 14| + 13 =-69
Solve for x
Answer: No real solutions
Step-by-step explanation:
[tex]14|x+14|+13=-69\\\\14|x+14|=-82\\\\|x+14|=-82/14[/tex]
Since absolute value is always non-negative, there are no real solutions.
x-y=3x+y=5unit 7 systems of linear equations
then
[tex]\begin{gathered} x+y=5 \\ 3+y+y=5 \\ 3+2y=5 \\ 3+2y-3=5-3 \\ 2y=2 \\ \frac{2y}{2}=\frac{2}{2} \\ y=1 \end{gathered}[/tex]solve for x
[tex]\begin{gathered} x=3+y \\ x=3+1 \\ x=4 \end{gathered}[/tex]answer: C. (4,1)