[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -5}{2}~~~ ,~~~ \cfrac{ y +2}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(2~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -5}{2}=2\implies x-5=4\implies \boxed{x=9} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +2}{2}=-5\implies y+2=-10\implies \boxed{y=-12}[/tex]
a) Write 1.76 x 10³ as an ordinary number.
b) Write 3.21 x 10 as an ordinary number.
c) Write 850 000 000 in standard form.
d) Write 0.0000509 in standard form.
Answer:
a 1760.
b 32.1
c 8.5 × 10^8
d 5.09×10^-5
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
15 cm
7 cm
22 cm
0
Question 2
The area of the triangle with the given dimensions are 77cm.
According to the statement
We have to find that the area of the triangle.
So, For this purpose, we know that the
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.
From the given information:
15 cm
7 cm
22 cm
Then
The base of the triangle is 7 cm and the height of the triangle is a 22cm.
Then
A = 1/2 × b × h.
A = 1/2 × 7 × 22.
Now solve it then
A = 154/2
A = 77cm.
So, The area of the triangle with the given dimensions are 77cm.
Learn more about area of a triangle here
https://brainly.com/question/8409681
#SPJ9
the function f(x) is an unshifted exponential function which goes through the points (2,5) and (3,4).
A. what is the equation for f(x)
B. Find f(10) and f(100)
[tex]f(x) = ae {}^{bx} \\ f(2) = 5 \: \: \: \: \: f(3) = 4[/tex]
[tex]5 = ae {}^{2b} \: \: \: \: \: \: \: 4 = ae {}^{3b} \\ divide \: both \: systems \\ e {}^{b} = \frac{4}{5} \: \: \: \: so \: \: \: b = ln(0.8) \\ solving \: for \: a \: we \: get \: that \: a = \frac{125}{16} [/tex]
[tex]f(x) = \frac{125}{16} e {}^{ln(0.8)x} [/tex]
[tex]f(10) = \frac{125}{16} e {}^{10ln(0.8)} = \frac{65536}{78125} \approx0.838861 \\ f(100) = \frac{125}{16} e {}^{100ln(0.8)} = \frac{4 {}^{98} }{5 {}^{97} } \approx1.59 \times 10 {}^{ - 9} [/tex]
its on the pic that i put
The value of x in 5 - x < 4/7 based on the information given will be x < 4 3/7.
How to illustrate the expression?It should be noted that based on the information given in the question, the expression will be:
5 - x < 4/7
Therefore, collect like terms
5 - x <4/7
x < 5 - 4/7
x < 4 3/7
Therefore, the value of x is less than 4 3/7.
Learn more about expressions on:
brainly.com/question/25968875
#SPJ1
The basketball team has developed a carnival game at
homecoming to raise money for new uniforms. They are
charging $3 per ticket to play. The expected pay out for each
play is $1.75. What can you conclude from this situation?
C
Answer:
Step-by-step explanation:kfn
Help me asap Geometry!!!
Applying the triangle sum theorem, the value of x is: 4.
How to Apply the Triangle Sum Theorem?When we add the three interior angles of a triangle together, the sum must be equal to 180 degrees according to the triangle sum theorem.
Given the triangle with the following interior angles, 35°, (22x - 3)°, and 60°. Therefore:
35 + (22x - 3) + 60 = 180 [triangle sum theorem]
Solve for x
35 + 22x - 3 + 60 = 180
Combine like terms
92 + 22x = 180
Subtract 92 from each side of the equation
92 + 22x - 92 = 180 - 92
22x = 88
Divide both sides by 22
22x/22 = 88/22
x = 4
Thus, applying the triangle sum theorem, the value of x is: 4.
Learn more about the triangle sum theorem on:
https://brainly.com/question/7696843
#SPJ1
Ten grams is what percent of 1 ounce? Round your answer to the nearest tenth percent.
Answer:
0.4oz
Step-by-step explanation:
conversion factor 1oz = 28.35g
(10g/1)(1oz/28.35g) cross out grams
10/28.35oz = 0.3|527 = 0.4oz
can someone please help?
Approximately 7.4 is 1.9 times larger than 3.9.
[tex]10^{-8}[/tex] is 3 times smaller than [tex]10^{-5}[/tex] .
7.4 x [tex]10^{-8}[/tex] is 1.9 x x [tex]10^{-3}[/tex] smaller than 3.9 x [tex]10^{-5}[/tex].
What is the scientific notation?Scientific notation is used to compress larger numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, when 100 is written in scientific notation it becomes 1 x 10².
For negative numbers, the sign in front of the power would be negative. For example, 0.0012 becomes 1.2 x [tex]10^{-3}[/tex] in scientific notation.
0.000039 becomes 3.9 x [tex]10^{-5}[/tex]
Difference between 7.4 and 3.9 : 7.4 / 3.9 = 1.9
Difference between [tex]10^{-8}[/tex] and x [tex]10^{-5}[/tex]
= [tex]10^{-8 - (-5)}[/tex]
= [tex]10^{-8 + 5}[/tex]
= [tex]10^{-3}[/tex]
[tex]10^{-8}[/tex] is three times smaller than [tex]10^{-5}[/tex]
To learn more about scientific notation, please check: https://brainly.com/question/25334755
#SPJ1
The half life of the isotope dubnium-263 is 29 seconds. A sample of dubnium-263 was first measured to have 1024 atoms. After t seconds, there were only 32 atoms of the isotope remaining.
Write an equation in terms of t that models the situations
Question based on Khan Academy
The radiactive decay equation in terms of t that models the situation is 32 = 1024e^{(-0.0239/s)t}
What is radioactive decay?Radioactive decay is the spontaneous disintegration of atoms with the emission of radiation.
What is half life of a radioactive isotope?The half life of a radioactive isotope is the time it takes for half the number of atoms in a given sample to disintegrate.
How to Write an equation in terms of t that models the situations?To model the situation, we use the equation for radioactive decay which is given below
[tex]N = N_{0}e^{-{\lambda}t}[/tex] where
N = Number of atoms remaining after t seconds, N₀ = initial number of atoms, λ = decay constant = 0.693/T where T = half life of isotope and t = time of decayGiven that the half life of the isotope dubnium-263 is 29 seconds and sample of dubnium-263 was first measured to have 1024 atoms. Then, after t seconds, there were only 32 atoms of the isotope remaining. we have that
N = 1024 atoms, N₀ = 32 atoms, T = 29 sSo, λ = 0.693/29 s = 0.0239 /s
So, susbtituting the values of the variables into the equation, we have
[tex]N = N_{0}e^{-{\lambda}t}[/tex]
[tex]32 = 1024e^{-(0.0239/s)t}[/tex]
So, the radiactive decay equation in terms of t that models the situation is 32 = 1024e^{(-0.0239/s)t}
Learn more about radiactive decay equation here:
https://brainly.com/question/27542728
#SPJ1
After a 25%increase, the price is 300€.how many euros was the increase?
Step-by-step explanation:
the €300 as current price is 125% relative to the original price. in other words : 1.25 times the original price.
to get the amount of the increase we need to get the original price first and then subtract the original price from the current price.
to get the original price we need now to divide the actual price by 1.25 to undo the increase.
the original price
OP = 300/1.25 = €240
the price increase (of 25%) was then
300 - 240 = €60
Determine if the sequence below is arithmetic or geometric and
determine the common difference / ratio in simplest form.
This is
equal to
17, 13, 9, ...
V sequence and the
is
The sequence is an arithmetic sequence due to the presence of a common difference.
Arithmetic and Geometric sequenceAn arithmetic sequence is a sequence that has a common difference while a geometric sequence is a sequence with a common ratio. For instance, given the sequence below:
a, b, c, d...
The sequence is an arithmetic sequence if;
common difference = b - a = c - b = d - c
The sequence is a geometric progression if;
common ratio = b/a = c/b = d/c
Given the sequence 17, 13, 9, ...
d = 13 - 17 = 9 - 13
d = -4
Since the sequence has a common difference, hence the given sequence is an arithmetic progression.
Learn more on arithmetic progression here: https://brainly.com/question/24191546
#SPJ1
Solve for x in the equation 3x2-18x+5=47-
Ox-3+√23
Ox-3± √51
Ox-3+√41
O x-3+√5
Answer:
x = 3 ± √23
Step-by-step explanation:
Simplify the quadratic equation.
[tex]3x^2-18x+5 = 473x^2-18x+5-47 = 0\\3x^2-18x-42 = 0\\\\a = 3\\b = -18\\c = -42\\\\x = (-(-18)\pm\sqrt{ (-18)^2-4(3)(-42) )} \div 2(3)\\x = (18\pm\sqrt{ 324+504)} \div 6\\x = (18\pm\sqrt{ 828}) \div 6[/tex]
Simplify further.
[tex]x = (18\pm\sqrt{ 23\times 36}) \div 6\\x = (18\pm6\sqrt{ 23}) \div 6\\x = 6(3\pm\sqrt{23}) \div 6[/tex]
Thus, the solution is
x = 3 ± √23
Hope this helps.
x = 3 + √23 and x = 3 - √23 are the two solutions of the given quadratic equation.
What is a Quadratic equation?ax²+bx+c=0, with a not equals to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
To solve for x in the equation 3x^2 - 18x + 5 = 47, we can begin by simplifying the equation:
[tex]3x^2 - 18x - 42 = 0[/tex]
Next, we can divide both sides of the equation by 3 to get:
[tex]x^2 - 6x - 14 = 0[/tex]
To solve for x, we can use the quadratic formula:
[tex]x =\frac{ (-b \pm \sqrt{(b^2 - 4ac))} }{ 2a}[/tex]
In this case, a = 1, b = -6, and c = -14, so we have:
[tex]x = \frac{(-(-6) \pm \sqrt{((-6)^2 - 4(1)(-14)))}}{2(1)} \\x = \frac{(6 \pm \sqrt{(36 + 56))}}{ 2} \\x = (6 \pm \sqrt{92}) / 2[/tex]
Simplifying the radical, we get:
x = (6 ± 2√23) / 2
Dividing both the numerator and denominator by 2, we get:
x = 3 ± √23
Therefore, the two solutions to the equation [tex]3x^2 - 18x + 5 = 47[/tex] are x = 3 + √23 and x = 3 - √23.
Learn more about Quadratic equations here:
https://brainly.com/question/22364785
#SPJ5
How many ways can Nick choose 5 pizza toppings from a menu of 8 toppings if each topping can only be chosen once?
In combination, 56 ways can Nick choose topping can only be chosen .
What is permutation and combination?
Subsets of a set can be created in two separate ways: combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.Examples of permutations include arranging persons, digits, numbers, alphabets, letters, and colors. Examples of combinations include choosing the menu, the cuisine, the clothes, the subjects, and the team.given that Nick choose pizza = 5
menu of toppings if each topping =8
chosen once = 8c5
=> 8! / (5!(8−5)!)
=> 56
Learn more about permutation and combination
brainly.com/question/16837159
#SPJ9
Given the function f(x) = −2x2 + 4x − 7, find f(−4).
Answer:
A is the answer of the question
Every rhombus is a parallelogram
Answer: A parallelogram is a quadrilateral with 2 pairs of parallel sides. The opposite sides on every rhombus are parallel, so every rhombus is a parallelogram.
Step-by-step explanation:
Which graph represents a function? A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative 2, negative 2), ( 1, 1), and (2, negative 2). A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative 3, negative 3), (negative 1, 1), and (1, 4). A coordinate plane shows 4 points with the following coordinates: (negative 4, 4), (negative 4, 1), (negative 2, 1), and (2, 1). A coordinate plane shows 4 points with the following coordinates: (negative 3, 3), (negative 3, negative 3), (1, negative 4), and (1, 1).
The ordered pair that represents a function is:
⇒ (-3, -3), (-2, 2), (1, 1), (2, -2)
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
The given points are;
(-3, -3), (-2, 2), (1, 1), (2, -2)
(-3, 3), (-3, -3), (-1, 1), (1, 4)
(-4, 4), (-4, 1), (-2, 1), (2, 1)
(-3, 3), (-3, -3), (1, -4), (1, 1)
Now, For an ordered pair to be a function, either of the following must be true:
Each x-value have exactly one corresponding y-value.
More than one x-values have the same corresponding y-values.
And, If any of the following conditions is true, then the ordered pair is not a function,
One x-value have multiple corresponding y-values.
More than one x-values have the multiple corresponding y-values.
From the given options, only ordered pair (-3, -3), (-2, 2), (1, 1), (2, -2) satisfies the condition to be a function.
Because none of its x-values have multiple corresponding y-values.
And, Other ordered pairs are either one-to-many or many-to-many.
So, The ordered pair that represents a function is:
⇒ (-3, -3), (-2, 2), (1, 1), (2, -2)
Learn more about ordered pairs visit:
https://brainly.com/question/19267542
#SPJ1
Triangle ABC is dilated with a scale factor of 3. Round all your results to the nearest tenths place (one decimal place), if necessary.
The length of the sides AB and B'C' will be 2.7 units and 16.2 units, and the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
Triangle ABC is dilated with a scale factor of 3. Then the scale factor will be 3.
If the side BC is 5.4 units long, then the length of the side B'C' will be
B'C' = 3 x BC
B'C' = 3 x 5.4
B'C' = 16.2 units
If the side A'B' is 8.2 units long, then the length of the side AB will be
AB = A'B' / 3
AB = 8.2 / 3
AB = 2.7 units
If the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.
There is no effect of dilation on the angle. Then the angles will remain the same.
The length of the sides AB and B'C' will be 2.7 units and 16.2 units, and the measure of the angles ∠A, ∠B, and ∠C are 77.5°, 54.2°, and 48.3°, respectively.
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ1
How do i solve 5+2(6+3 ÷ 3)
Answer:
19
Step-by-step explanation:
Arrange into parentheses and start at the innermost parentheses
[tex]5 + (2 \times (6 + (3 \div 3)))[/tex]
Start with 3 ÷ 3
[tex]3 \div 3 = 1[/tex]
Continue with the other parts of the equation in order
[tex]1 + 6 = 7\\7 \times 2 = 14\\14 + 5 = 19\\= 19[/tex]
Hope this helped you understand better, have a great day!
set of even numbers less than 15
Step-by-step explanation:
for positive numbet (2, 4, 6, 8, 10, 12, 14)
2, 4, 6, 8, 10, 12, and 14.
Step-by-step explanation:
even number is 2,4,6,8.....
odd number is 1,3,5,7.......
wish you have a great day
Use sigma notation to represent the sum of a geometric series with a first term of 3 and a common ratio of 10/9
The sum of a geometric series with a first term of 3 and a common ratio of 10/9 is;
∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex] where, K = 1 to n.
What is Geometric series?
A geometric series is a list of numbers having a common ratio. Each term after the first is gotten by multiplying the previous one by the common ratio.
Given that;
The first term is 3 and the common ratio is 10/9.
Now, A geometric sequence has the form:
a, ar , ar², ar³, . . .
Hence, The nth term of a geometric sequence is;
⇒ ∑ [tex](ar^k^-^1)[/tex] where, k = 1 to n.
Therefore, the sum of geometric series with a first term of 3 and a common ratio of 10/9 is:
⇒ ∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex] where, k = 1 to n.
So, The sum of a geometric series with a first term of 3 and a common ratio of 10/9 is;
⇒ ∑ [tex]3 (\frac{10}{9} )^k^-^1[/tex] where, k = 1 to n.
Learn more about the geometric series visit:
https://brainly.com/question/9891309
#SPJ1
The sum of the square of a positive number and the square of 2 more than the number is 20. What is the number?
Answer:
2
Step-by-step explanation:
2^2 is 4 and two more than 2, which is 4, is 16 when squared. 16+4=20
Simplify 5¹⁰ ^ 5²
...........................................
It should be noted that simplifying 5¹⁰ × 5² will be 5^12.
How to calculate the value?It should be noted that these values have to do with powers. In this case, since that have same base and we want to multiply, we will add their powers.
Therefore, 5¹⁰ × 5² will be:
= 5¹⁰ × 5²
= 5^12
In conclusion, the value will be 5 raise to power 12
Therefore, based on the information, it should be noted that the value of 5¹⁰ × 5² will be 5^12.
Learn more about numbers on:
brainly.com/question/24644930
#SPJ1
Simplify 5¹⁰ × 5²
ANSWR ASAP ILL GIVE BRAINLYEST AND 5 STAR
The missing steps of the expression are as follows;
[tex](\frac{9 + 4 }{0.25} ) - 10.4[/tex] ÷452 - 10.4 ÷ 4How to solve an expression?The expression can be solved as follows:
step 1
[tex](\frac{3^{2} + 4 }{|-0.25|} ) - 10.4[/tex] ÷ 4
Step 2
The absolute value will remove the minus sign of the denominator.
[tex](\frac{3^{2} + 4 }{0.25} ) - 10.4[/tex] ÷ 4
Step 3
We have to find the square of the 3 in the numerator. Therefore, the step 3 will be as follows:
[tex](\frac{9 + 4 }{0.25} ) - 10.4[/tex] ÷ 4
Step 4
We have simplify the numerator.
[tex](\frac{13 }{0.25} ) - 10.4[/tex] ÷ 4
Step 5
52 - 10.4 ÷ 4
Step 6
Using PEMDAS rule, we have to solve the division sign. Therefore, the step 6 is as follows;
52 - 2.6
Step 7
49.4
learn more on expression here: https://brainly.com/question/28393820
#SPJ1
Which of the following shows 16 more than a number, written as an algebraic expression?
16n
16 − n
n − 16
16 + n
Answer:
16 + n
Step-by-step explanation:
Whenever something says "more" it typically includes addition.
It says 16 more than a number, meaning that you add 16 to an number (n)
*Please mark brainliest
Answer:
16 + n
Step-by-step explanation:
I got 100% on the test
Stephanie brings a 10% off coupon if the sweater cost 22.00 how much does she pay after she uses the coupon
Answer:
22/10
=2.2
22-2.2=19.8
Stephanie pays £19.8
Aliyah has $94 in 13 bills in her wallet, including ones, fives, and twenties. If she has one less twenty dollar bill than she has one dollar bills, how many of each denomination does Aliyah have in her wallet?
Answer:
$1 x 4
$20 x 3
$5 x 6
Step-by-step explanation:
$94
at least 4 $1 bills
$90
at least 3 $20 ($60)
$30
the remaining $30 can be made up of 6 $5 bills
4 + 3 + 6 = 13 bills total
Someone is 18 1/2 inches long when they are born and their twin is 20 3/4 inches long. What is the difference between how big they are.
8.
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
The measure of the central angle m∠VWU is 69 degrees
How to find central angles?Central angle is the angle formed by two arms and having the vertex at the centre of a circle.
The diameter of a circle runs from the centre of a circle.
The diameter SU and RT intersect each other at point Q.
Therefore,
m∠VWS = m∠TWU (Vertically opposite angles)
m∠VWU = m∠SWT (Vertically opposite angles)
Hence,
m∠TWU = 111 degrees.
Therefore,
m∠VWU = 360 - 111 - 111 /2
m∠VWU = 360 - 222 / 2
m∠VWU = 138 / 2
m∠VWU = 69 degrees
Therefore, the measure of the central angle m∠VWU is 69 degrees
learn more on central angle and diameter here: brainly.com/question/15272508
#SPJ1
a1=3 and a8= -6561
find: ratio r
Answer:
-4920.75 or 18
Step-by-step explanation:
I'm not quite sure if this is correct because I got two diffrent soultions for a.
In a1=3 I got a=3
In a8= -6561 I got a= -820.125
So i plugged my two solutions in to find a6
I got
18
or
-4920.75
That doesn't really seem correct, but I tried!!
6. The question is in the screenshot
Answer:
None of these
Step-by-step explanation:
We can estimate f'(9) by finding the slope of the secant through the two points closest to (9, f(9)).
[tex]\frac{f(10)-f(8)}{10-8}=\frac{16-10}{2}=3[/tex]