Using the figure,
a
c
=
d
a
.
What steps need to be taken to change this to a² = cd?
Example: Multiply by 2; divide by a, etc
Answers
[tex] \frac{a}{c} \times ac = ac \times \frac{d}{a}[/tex]
Because the end result looks like the numerator on the left is multiplied by the denominator on the right, and vice versa, the process is often referred to as "cross multiplying." That is an illusion. The rules of algebra require the same thing be done to both sides of the equation. In this case, that is multiplication of both sides by the product of the denominators.
Related Questions
Using the equation, y=10000(0.97)x predict the purchasing power of $10000 ten years later
Answers
$7374
Answer:
The purchasing power is $7374
Step-by-step explanation:
We are given an equation [tex]y=10000(0.97)^x[/tex]
where,
y represents purchasing power.
x represents the number of years.
We need to find purchasing power of $10000 after 10 years.
Put x=10 into equation and solve for y
[tex]y=10000(0.97)^{10}[/tex]
[tex]y=7374.24\approx 7374[/tex]
After 10 years the purchasing power of $10000 becomes $7374
As we can see the value of the product decrease.
Hence, The purchasing power is $7374
what is the solution of the equation 1.6m - 4.8 = -1.6m
Answers
1.6 m - 4.8 = -1.6 m
Add 1.6 m to both sides:
1.6 m + 1.6 m - 4.8 = 1.6 m - 1.6 m
1.6 m - 1.6 m = 0:
1.6 m + 1.6 m - 4.8 = 0
1.6 m + 1.6 m = 3.2 m:
3.2 m - 4.8 = 0
Add 4.8 to both sides:
3.2 m + (-4.8 + 4.8) = 4.8
4.8 - 4.8 = 0:
3.2 m = 4.8
Divide both sides of 3.2 m = 4.8 by 3.2:
(3.2 m)/3.2 = 4.8/3.2
3.2/3.2 = 1:
m = 4.8/3.2
4.8/3.2 ≈ 1.5:
Answer: m ≈ 1.5
Answer:
m=1.5
Step-by-step explanation:
I took the test.
A class of 32 students shares a class set of 78 colored pencils. On a day with six students absent, which statement is true? A. For each student, there are 4 colored pencils. B. For each student, there are 3 colored pencils. C. For every 3 students, there is 1 colored pencil. D. For every 4 students, there is 1 colored pencil. I need help solving the problem
Answers
Selection B is appropriate.
Math help!! 5 questions!!! A classmate believes that a triangle can have both right angle and an obtuse angle. Which of the following statements would you use to convince him that he is incorrect. A. Its is not possible because the sum of the angles in the triangle can't exceed 180 d. B. It is not possible because if a triangle has an obtuse triangle , that means all the angles are obtuse angles. C. It is not possible because if a triangle has a right triangle, that means all the angles are right angles. Its is possible. The classmate is correct.
Answers
Final answer:
A triangle cannot have both a right angle and an obtuse angle, as the sum of its angles must always equal 180 degrees.
Explanation:
To convince your classmate that a triangle cannot have both a right angle and an obtuse angle, you should explain that according to Euclidean geometry, the sum of the angles in any triangle must equal two right angles, or 180 degrees.
If a triangle has a right angle (90 degrees), then the remaining two angles must sum up to 90 degrees as well. Introducing an obtuse angle, which is any angle greater than 90 degrees, would cause the total sum of the angles to exceed 180 degrees, which is impossible.
Therefore, the correct statement to use would be 'A. It is not possible because the sum of the angles in the triangle can't exceed 180 degrees.'
Abigails mom said she will be home from work in 65 minutes its 4:27 pm and abigail has dance practice at 6:00 pm. How much time will abigail have between the time that her mom gets home from work and the beginning of dance practice
Answers
The time that her mom gets home from work and the beginning of dance practice is 28 minutes.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, It is 4:27 pm and Abigail's mom said she will be home from work in 65 minutes.
Now 60 minutes from 4:27 pm is 5:27 pm and 5 minutes more is 5:32 pm.
Abigail has dance practice at 6:00 pm, So the time that her mom gets home from work and the beginning of dance practice is 28 minutes seems obvious.
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How are exponential functions related to logarithmic functions?
Model that with an example.
Answers
If we use the natural logarithm (ln) as an example, the constant "e" is the base of ln, such that:
ln(x) = y, which is really stating that the base (assumed "e" even though not shown), that:
[tex] {e}^{y} = x[/tex]
if we try to solve for y in this form it's nearly impossible, that's why we stick with ln(x) = y
but to find the inverse of the form:
[tex]{e}^{y} = x[/tex]
switch the x and y, then solve for y:
[tex] {e}^{x} = y[/tex]
So the exponential function is the inverse of the logarithmic one, f(x) = ln x
Exponential and logarithmic functions are related in that they are inverses of each other.
Logarithmic functions and exponential functions are inverses of each other.
For instance, let [tex]log a = b[/tex]
In order to eliminate the logarithmic function, we will apply an exponential function ([tex]e[/tex])to both sides.
[tex]e^{loga} = e^b[/tex]
The exponential function will cancel out the logarithmic function since they are inverses of each other to give:
[tex]a = e^b[/tex]
This example shows the inverse relationship that exists between the logarithmic and exponential functions.
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Choose the correct simplification of (8x4y3)2. (5 points)
Answers
(8x^4y^3)^2 the answer should be
64x^8y^6
Answer:
the person below is correct 64x8y6 is the right answer
Step-by-step explanation:
If sec(x)=13/12 what is cos(x)?
Answers
can u show me common core way this problem how to do 5/9 ×3 1/2
Answers
3x2= 6 6+1=7, then put 7 over your denominator which would be 7/2.
2.) multiply 5/9 times 7/2
5 times 7 is 35
9 times 2 is 18
your answer is 35/18
3.) make it a proper fraction
18 times 2 is 36 so that would't work to have two!
so you only can put 18 into 32 once so subtract 32-18 so you know what is left over after you take a whole out. 32-18=14. 14 is now the numerator and so put your whole number first then put your numerator over your denominator: 1 14/18
4.) simplify
1 14/18= 1 7/9, I divided 14 and 18 by 2 to simplify
The answer is 1 7/9
[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies\cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}\\\\ -------------------------------\\\\ \cfrac{5}{9}\times 3\frac{1}{2}\implies \cfrac{5}{9}\times\cfrac{7}{2}\implies \cfrac{5\times 7}{9\times 2}\implies \cfrac{35}{18}\implies 1\frac{17}{18} \\\\\\ \textit{keep in mind that }1\frac{17}{18}\implies \cfrac{1\cdot 18+17}{18}\implies \cfrac{35}{18}[/tex]
You find that the going rate for a home mortgage with a term of 30 years is 5% APR. The lending agency says that based on your income, your monthly payment can be at most $750 . How much can you borrow?
Answers
A=monthly payment
P=amount borrowed (present value)
i=5%/12 per month (period)
n=30*12 months (months)
Then
[tex]P=\frac{A*((1+i)^n-1)}{i*(1+i)^n}[/tex]
Substitute values
[tex]P=\frac{750*((1+.05/12)^{360}-1)}{.05/12*(1+.05/12)^{360}}[/tex]
[tex]=\frac{750*((1+.05/12)^{360}-1)}{.05/12*(1+.05/12)^{360}}[/tex]
[tex]=139711.21[/tex] to the nearest cent
the hardware store sells sparklers for the 4th of july. they charge 19 cents apiece. the firework stand charges 85 cents for four. which is the better deal? how can you tell
Answers
8.73e16 in simple form
Answers
= 8.73 x 10^16 ..............................scientific form
= 87,300,000,000,000,000 ...........standard form
Solution:
we have been asked to write [tex]8.73e^{16}[/tex] in the simplest form.
This can be alternatively written as [tex]8.73*10^{16}[/tex]
And as we know that a number written in scientific notation can be re-written in the simple form by removing the "10 to the power" term by expanding the given number as below
[tex]8.73*10^{16}=8.73*1000,000,000,000,0000[/tex]
It can be further written by removing the decimal as below
[tex]8.73*10^{16}=87,300,000,000,000,000[/tex]
Hence the required simple form is 87,300,000,000,000,000
Your state's bigbucks lottery prize has reached $100,000,000, and you decide to play. you have to pick ve numbers between 1 and 60, and you'll win if your numbers match those drawn by the state. you decide to pick your "lucky" numbers using a random number table. which numbers do you play, based on these random digits? 43680 98750 13092 76561 58712
Answers
.. 1 + floor(60*N/100000)
The possibilty of collision needs to be considered. One way to deal with that is to add or subtract a constant, using the next higher available number, for example. This would give the choices {8, 27, 36, 46, 60}.
You observe one pine tree. if the probability of not being a foxtail pine is equal to 0.06, what is the probability that this tree is a foxtail pine? (calculate to 2 decimals)
Answers
99.94%
Final answer:
The probability that the observed pine tree is a foxtail pine is 0.94 or 94%, calculated by subtracting the probability of it not being a foxtail pine (0.06) from 1.
Explanation:
If the probability of not being a foxtail pine is 0.06, we can find the probability of a tree being a foxtail pine by subtracting this from 1 (since the sum of all probabilities for an event and its complement must equal 1). Therefore, the calculation to find the probability of the tree being a foxtail pine is 1 - 0.06.
Carrying out this subtraction gives us:
1 - 0.06 = 0.94.
Thus, the probability that the observed pine tree is a foxtail pine is 0.94, or 94%, when calculated to two decimals.
Which of the following are the correct properties of slope A.If two lines have the same slope, then they are the same line. B.The slope of a line that moves up from left to right is positive. C.A steep line has negative slope. D.Some lines have an undefined slope. E.The slope of a line is always positive.
Answers
Answer:
B.The slope of a line that moves up from left to right is positive.
Step-by-step explanation:
Slope is the ratio of vertical change to horizontal change. If a line moves up as x-values increase, then the signs of both changes are positive, and the slope is positive. This observation matches selection B.
_____
Comments on other choices
If a line is vertical, it will exhibit a vertical change with no horizontal change. The denominator of the ratio for slope will be zero. Division by zero is undefined, so we say the slope of a vertical line is "undefined."
Lines with the same slope will be parallel, if they're not the same line.
A line that moves down to the right has a negative change in its vertical coordinate for a positive change in its horizontal coordinate. The ratio of changes will have a negative sign. So, the slope of a line that moves down to the right is negative, not positive.
As per an axiom in Euclidean geometry, if points lie in a plane, the containing those points also lies in the same plane?
A) two/plane
B) three/plane
C)two/line
D)three/line
Answers
Your answer is C.
Answer: two, line
Step-by-step explanation:
we built a fence around the back of his yard he built 7 feet of fence every day in July and was finished how long is the fence explain how you got the answer
Answers
Troy is going to Spain and needs to convert his dollars to euros. He knows that when he goes, $5.00 is equivalent to about 3.45 Euros, How many will he get for $125?
Answers
25*3.45=86.25
86.25 euros
$5/3.45 euros = $125/x euros
then, cross multiply
5x=(3.45)(125)
5x=431.25
x=86.25
The answer is 86.25 euros
When a grizzly bear hibernates, it’s heart rate drops to 10 beats per minute, which is 20% of its normal value. What is a grizzly bear’s normal heart rate when not hibernating?
Answers
Susan been a total of $26 at the State Fair she's mad she spent 9 on food in the rest of the money susan spent on games,g.
Answers
Mr. Lin baked banana bread for a bake sale to raise money for the math team. He said that he added a spoonful of walnuts for each of the students in his three classes, and that he added more than 250 walnuts. He used the inequality
16w + 24w + 10w > 250 to represent this situation, where w represents the number of walnuts in each spoonful. How many walnuts can be in a spoonful?
Answers
expand the equation 1/3(2/5-2/3w)
Answers
= 1/3 * 2/5 - 1/3 *2/3w
= 2/15 - 2/9w
Tom spent 1/3 of his monthly salary for rent and 1/7 of his monthly salary for his credit card bill. If $1320 was left, what was his monthly salary?
Answers
x -1/3x - 1/7x = 1320
11/21x =1320
x = 1320 divides by 11/21
x = $ 2520
his monthly salary was $ 2520
The expression 17n+11 represents the perimeter of the triangle.
A simplified expression that represents the measure of the third side is
Answers
Answer: the answer is 8n
The third side of a triangle whose perimeter is 17n + 11 and the other two sides are (5n + 6) and (4n + 6) is 8n
The perimeter of any shape is total distance around the shape
In the triangle shown:
The perimeter = 17n + 11
The first side = 5n + 6
The second side = 4n + 5
Let the third side be represented by M
The perimeter = (The first side) + (The second side) + (The third side)
Substitute perimeter = 17n + 11, first side = 5n + 6, second side = 4n + 5, and third side = M into the equation above
17n + 11 = (5n + 6) + (4n + 5) + M
M = 17n + 11 - 5n - 6 - 4n - 5
Collect like terms
M = 17n - 5n - 4n + 11 - 6 - 5
M = 8n
Therefore, the third side of a triangle whose perimeter is 17n + 11 and the other two sides are (5n + 6) and (4n + 6) is 8n
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A realtor earns a 0.8% commission on the homes sje sells. Last month, she sold a $380,000 home. How much did the realtor earn as her commission for the sale
Answers
Answer:
Her commission for the sale was $3,040
Step-by-step explanation:
A realtor sold a home costs = $380,000
She earns commission on the home she sells = 0.8%
Commission for the sale she earns = 0.8% of 380,000
[tex]\frac{0.8}{100}[/tex] × 380,000
0.008 × 380,000 = 3,040
Her commission for the sale was $3,040
is the sample valid? what percent of students prefer caramel popcorn?
Answers
First you must see if the number of students in the table corresponds to the number of students surveyed that was 75.
We have then:
33 + 15 + 27 = 75
We have then that:
The sample is valid.
what percent of students prefer caramel popcorn?
We can make the following rule of three to answer this question:
75 ---> 100%
27 ---> x
Clearing x we have:
x = (27/75) * (100)
x = 36%
36% percent of students prefer caramel popcorn
This table shows the weekly rainfall, in inches, for two cities for ten weeks. City A 0.2 0 1.5 1.3 2.5 3 0.4 0.3 0.2 1 City B 0 0 0.4 0.2 0.3 1 1 1 0.1 0.1 Which conclusion can be drawn from the data?
WILL GIVE BRAINLISET
Answers
A. During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.
this is correct. rainfall of 1 inch was recorded on three days so it was the most often recorded rainfall.
B. The range between the maximum and minimum values for City B is greater than the range between the maximum and minimum values for City A.
range for city A - 3 - 0 = 3
range for city B - 1- 0 = 1
this statement is incorrect as the range for city B is lesser than the range for city A.
C. For the ten weeks, City A received less rainfall, on average, than City B
the average rainfalls for;
City A - 1.04
city B - 0.41
city A received more rainfall on average than city B on average therefore this statement is incorrect.
D. The median for City A is less than the median for City B.
city A - 0.7
city B - 0.25
median for city A is greater than median for city B therefore this statement is incorrect.
Therefore the conclusion that can be drawn from the data is During the 10 wk period, the rainfall amount recorded most often for City B was 1 in. - Statement A
Answer:
During the 10 wk period, the rainfall amount recorded most often for City B was 1 in
Step-by-step explanation:
Convert a length of 25.0 m to inches.
express your answer numerically in inches.
Answers
Answer:
98.4 inches
Step-by-step explanation:
You want the length 25.0 meters expressed in inches.
ConversionThere are 0.254 m in an inch, so the distance d can be found from the proportion ...
d/(25 m) = (1 in)/(0.254 m)
Multiplying by 25 m, we find ...
d = 25/0.254 in ≈ 98.4252 in
The length is about 98.4 inches.
__
Additional comment
The value to convert is given to 3 significant figures. The conversion factor is exact. The answer is appropriately expressed using 3 significant figures.
Box contains 4 bolts. two of them, labeled #1 and #2 are 5 mm in diameter, and two of them, labeled #3 and #4, are 7 mm in diameter. bolts are randomly selected until a 5 mm bolt is obtained. the outcomes are the sequences of the bolts that can be selected. so one outcome is 1, and another is 342. let x represent the number of bolts selected.
a.find the probability mass function of x.
Answers
The following is the last method.
1
2
31
32
341
342
41
42
431
432
So there are 10 possible outcomes, out of which 2 have a single pick, 4 have 2 picks, and 4 have 3 picks.
The pmf of x is therefore
x p
1 1/5
2 2/5
3 2/5
In the diagram below QRS=NMP what is length in inches of MP