Step-by-step explanation:
Let x be the smaller than 4 ×[tex]10^{-2}[/tex].
To find, the number of times smaller is 2 × [tex]10^{-3}[/tex] than 4 × [tex]10^{-2}[/tex] = ?
∴ x = [tex]\dfrac{4\times 10^{-2}}{2\times 10^{-3}}[/tex]
= 2 × [tex]10^{-2}[/tex] × [tex]10^{3}[/tex]
Using the identity,
[tex]a^{m}=\dfrac{1}{a^{-m}}[/tex]
= 2 × [tex]10^{-2+3}[/tex]
Using the identity,
[tex]a^{m} \timesa^{n}=a^{m+n}[/tex]
= 2 × [tex]10^{1}[/tex]
= 2 × 10
= 20
Thus, the required "option A) 20" is correct.
(a,1/b) and (b,1/a) find the slope of the line joining the points whose coordinates are
Answer:
[tex]m=\frac{1}{ab}[/tex]
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the points
(a,1/b) and (b,1/a)
substitute
[tex]m=\frac{1/a-1/b}{b-a}[/tex]
[tex]m=\frac{\frac{b-a}{ab}}{b-a}[/tex]
[tex]m=\frac{1}{ab}[/tex]
The slope of the line joining the points (a,1/b) and (b,1/a) is calculated using the slope formula and is found to be 1 divided by the product of a and b, assuming a and b are not equal and neither is zero.
Explanation:To find the slope of the line joining the points with coordinates (a,1/b) and (b,1/a), we use the slope formula, which is the change in y divided by the change in x. We can write the formula as:
slope (m) = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula gives us:
slope (m) = (1/a - 1/b) / (b - a)
If we assume that a does not equal b and neither a nor b is zero, the slope can be calculated by simplifying the numerator and the denominator:
slope (m) = ((b - a) / (ab)) / (b - a)
The (b - a) terms cancel out, leaving us with:
slope (m) = 1 / (ab)
Therefore, the slope of the line is the reciprocal of the product of a and b.
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Round the following
numbers to the nearest 100.
817 →
368 →
1,4 51 →
Answer:
817 ---- 800
368 ---- 400
1,451 ---- 1500
Rationalise: [tex]\frac{\sqrt{48} }{\sqrt{3} }[/tex]
Answer:
4
Step-by-step explanation:
Root(48)/Root(3)
= root(48/3)
= root(16)
=4
6a + 3 in Number of Terms
The expression '6a + 3' consists of two terms: '6a' and '3'. In mathematical expressions, terms are separated by addition or subtraction operations.
Explanation:The expression given, 6a + 3, is a mathematical expression that involves operations of addition and multiplication. In this expression, there are two terms separated by a plus sign. To clarify, a term refers to the separated parts of an expression when it is written as a sum or difference. This expression contains one numerical value (3) and one algebraic term (6a).
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Which equation can be solved by using this system of equations?
[y= 3x2 - 7x2 + 5
Ly = 7x4 + 2x
Question:
Which equation can be solved by using this system of equations?
y = 3x^3 - 7x^2 + 5
y = 7x^4 + 2x
A.) 3x^3 - 7x^2 +5 = 0
B.) 3x^3 - 7x^2 + 5 = 7x^4 +2x
C.) 7x^4 +2x = 0
D.) 7x^4 +3x^3 -7x^2 +2x + 5 = 0
Answer:
Option B: [tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex] is used to solve this system of equations.
Explanation:
The two equations are [tex]y=$3 x^{3}-7 x^{2}+5$[/tex] and [tex]y=$7 x^{4}+2 x$[/tex]
Using substitution method, let us substitute [tex]y=$7 x^{4}+2 x$[/tex] in the equation [tex]y=$3 x^{3}-7 x^{2}+5$[/tex], we get,
[tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex]
Thus, [tex]3x^{3} -7x^{2} +5=7x^{4} +2x[/tex] is used to solve this system of equations.
Hence, Option B is the correct answer.
Answer:
Answer is B. 3x^3-7x^2+5 = 7x^4+2x
Step-by-step explanation:
got it right!
hope this helps
Solve the system of linear equations by substitution.
3x−2y=15
y=2x−11
The solution set is (7,3).
Step-by-step explanation:
Given system of equations is;
3x−2y=15 Eqn 1
y=2x−11 Eqn 2
Substituting value of y from Eqn 2 in Eqn 1
[tex]3x-2(2x-11)=15\\3x-4x+22=15\\-x+22-15=0\\7=x\\x=7[/tex]
Putting x=7 in Eqn 2
[tex]y=2(7)-11\\y=14-11\\y=3[/tex]
The solution set is (7,3).
Keywords: linear equation, substitution method
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candace is at a coffee shop and knows she can spend more than $52 before tax she sees this price list in the coffee shop
[tex]21+7.50p\leq 52[/tex]
Explanation:For inequalities, "a is no more than b" can be written as:
[tex]a\leq b[/tex]
Here we know Candace that can spend no more than $52 before tax. She can spend a certain amount of money in both Dark Roast coffee and Morning Blend coffee. So she spends:
2 pounds of Morning Blend coffee.p pounds of Dark Roast coffeeTherefore:
Amount of money for Morning Blend coffee:
[tex]2\times 10.50=\$21[/tex]
Amount of money for Dark Roast coffee:
[tex]p\times 7.50=\$7.50p[/tex]
So the total amount of money:
[tex]21+7.50p[/tex]
Finally, the inequality becomes:
[tex]21+7.50p\leq 52[/tex]
Besides, in order to know how many pounds she can spend let's solve for p:
[tex]7.50p\leq 52-21 \\ \\ 7.50p\leq 31 \\ \\ p\leq 4.13[/tex]
So she can spend less that 4.13 pounds.
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Final answer:
The correct inequality to determine the possible values for the number of pounds of Dark Roast coffee, p, along with 2 pounds of Morning Blend coffee for $52 or less is 9p + 15.10 ≤ 52. This inequality can be used to solve for p, the number of pounds of Dark Roast coffee Candace can buy which is p ≤ 4.1.
Explanation:
Calculator Candace wants to determine the number of pounds of Dark Roast coffee, represented as p, she can buy if she purchases 2 pounds of Morning Blend coffee for a total of $52 or less. The price of the Morning Blend coffee is $7.55 per pound. To calculate this, we need to create an inequality that represents the scenario:
The cost for 2 pounds of Morning Blend coffee: 2 x $7.55 = $15.10The maximum amount Candace can spend: $52Now, the inequality will consider the total price of the Morning Blend coffee and add the price of the Dark Roast coffee (which is $9.00 per pound). So the inequality should look like this:
9p + 15.10 ≤ 52
This inequality can be used to solve for p, the number of pounds of Dark Roast coffee Candace can buy which is p≤4.1.
the sum of a number z divided by three and the number
Answer:
z ÷ 3 + z
Step-by-step explanation:
What is the area of this figure?
Enter your answer in the box.
m²
Area of the figure is 532 m².
Solution:
In the given image the shape is splitted into 2 shapes.
First shape is the square.
In square 4 sides are equal.
Area of the square = side × side
= 18 m × 18 m
Area of the square = 324 m²
Second shape is the triangle in the bottom.
Base of the triangle = 18 m + 8 m = 26 m
Height of the triangle = 16 m
Area of the triangle = [tex]\frac{1}{2}\times{\text{base}}\times{\text{height}}[/tex]
[tex]$=\frac{1}{2}\times16\times26[/tex]
Area of the triangle = 208 m²
Area of the given shape = area of the square + area of the triangle
= 324 m² + 208 m²
Area of the given shape = 532 m²
Hence area of the figure is 532 m².
Answer: 532 is answer
Hope u get a good grade
(c) Mez bought 9 tubes of paint. She
received $16 change from $70.
How much did each tube of
paint cost?
Answer:
$6
Step-by-step explanation:
9 tubes of paint costs
$70 - $16 = $54
1 tube of paint cost
$54 : 9 = $6
HELP!! PLEASE... ANSWER
5. Determine whether each pair of triangles is similar. Justify your answer.
Answer:
A
Step-by-step explanation:
Consider Δ JKL and Δ GDF
If the ratios of corresponding sides are equal then the triangles are similar.
[tex]\frac{JK}{GD}[/tex] = [tex]\frac{24}{20}[/tex] = [tex]\frac{6}{5}[/tex]
[tex]\frac{xJL}{GF}[/tex] = [tex]\frac{18}{15}[/tex] = [tex]\frac{6}{5}[/tex]
[tex]\frac{KL}{DF}[/tex] = [tex]\frac{12}{10}[/tex] = [tex]\frac{6}{5}[/tex]
Since the ratios are equal then Δ JKL and Δ GDF are similar by SSS postulate.
What the answer is to question number 4
Please help me on this math problem!
Answer:
427 feet.
Step-by-step explanation:
Which algebraic expression is equivalent to the expression below? 9(2x - 6) A. 9x - 3 B. 18x - 54 C. 9x - 8
Answer:
B
Step-by-step explanation
multiply 2 and 6 by 9
Answer:
its b
Step-by-step explanation:
The sum of three numbers is 89 The second number is 6 times the first. The third number is 15 less than the second. What is the first number?
The first number is 8
Solution:
Let the first number be "x"
The second number is 6 times the first
Second number = 6x
The third number is 15 less than the second
Third number = second number - 15
Third number = 6x - 15
The sum of three numbers is 89
Therefore,
First number + second number + third number = 89
[tex]x + 6x + 6x - 15 = 89\\\\13x - 15 = 89\\\\13x = 89+15\\\\13x = 104\\\\Divide\ both\ sides\ by\ 13\\\\x = 8[/tex]
Thus the first number is 8
A small jar of salsa contains 12 1/2 ounces. A large jar of salsa contains 75 ounces. How many small jars of salsa equal the same number of ounces as 1 large jar of salsa?
We can start off by making 12 1/2 to an improper fraction:
12 1/2 = 25/2
Divide the large jar of salsa by the small jar of salsa: 75 / 25/2.
Reciprocal of second and turn divide to multiply:
75 * 2/25.
150/25 = 6.
So 6 jars of small salsa = 1 large jar of salsa.
Solve for x and y
5x + 3y = 7
y = 4
Answer: x= -1 y= 4
Step-by-step explanation:
We are going to solve this using substitution.
Here is the work...
5x+3(4)=7
That is what it woud look like because y is equal to 4.
3 times 4 is 12.
So now we have...
5x+12=7
Now we want to get All the common factors together...
To do this we will subtract 12 from 7 and we get -5.
Here is our equation now...
5x=-5
Now we divide x by 5 to get x alone, but we also divide -5 by 5.
x=-1
Now all we have to do to solve for y is put x in an equation.
In this case here is what we will do...
5(-1)+3y=7
Multiply...
-5+3y=7
Now we need to get the common factors together so lets add 5 to 7.
3y=12
3y/3=y
12/3=y
y=4
But that is already in your problem...OOF.Dont worry its still correct.
To solve the system, substitute y=4 into the first equation, leading to x=-1. Thus, the solution is x=-1 and y=4.
Explanation:To solve the system of equations 5x + 3y = 7 and y = 4, we can start by substituting the value of y from the second equation into the first equation. We are given y directly, so the substitution is straightforward.
Substituting y = 4 into the first equation:
5x + 3(4) = 75x + 12 = 75x = 7 - 125x = -5x = -1So, the solution to the system of equations is x = -1 and y = 4. We can say that x and y are variables, and in this case, y is dependent on x in other linear equations but is given directly here.
Can you find the equation in standard form when given 3 or more orders pairs on a parabola
Answer:
Yes, you can
Step-by-step explanation:
The standard form of the equation of a parabola is [tex]y=ax^2+bx+c[/tex]
When given three points, you substitute each point into the equation to obtain 3 simultaneous linear equations.
You then solve the three equations simultaneously to find the values of the constants a,b, and c.
You then substitute these constants into [tex]y=ax^2+bx+c[/tex]
3x-15=2x+3 Find QR
It says the answer is 39 but I can’t figure out how they got 39. Please help
Answer:
look at the picture shown
Matthew drew a scale drawing of the elementary school. He used the scale
1 centimeter : 3 meters. The actual width of the school yard is 42 meters. How wide is the
school yard in the drawing?
Answer:
Step-by-step explanation:
Find the area of the shape shown below.
Answer: 10
Step-by-step explanation:
2 * 4 = 8
8/2 = 4
2 * 2 = 4
4/2 = 2
4 + 2 = 6
2 * 2 = 4
4 + 6 = 10
a fruit punch recipe requires 12 teaspoons of sugar for every 3 quarts of water. at this rate how much sugar is needed for 9 quarts of water
36 teaspoons. since the number of quarts is multiplied by 3, multiply the number of teaspoons as well. 12 × 3 = 36
A store owner bought hats for 6.50 each and sold them for 12.00 the overhead was 2.50. What was the profit on each hat?
I need help everyone so what is 9x9
The value of 9 × 9 is 81.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
The question is to find the product of 9 × 9.
By the definition of multiplication, 9 × 9 is the addition of the number up to 9 times.
That is, 9 × 9 can also be written as,
9 × 9 = 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9
Adding number 9 to itself 9 times we get 81.
So 9 × 9 = 81
Hence the product after multiplying 9 with 9 is 81.
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Combine 2d + 5d
Answer please ?
Answer:
7D
Step-by-step explanation:
2D + 5D
Add the figures
8 1/5 + (4 2/5 + 3 3/10)
Answer:
15.7
Step-by-step explanation:
8 1/5= 8.2
4 2/5= 4.4
3 3/10= 3.1
4.4 + 3.1 = 7.5
7.5 + 8.2 = 15.7
Answer:
Step-by-step explanation:
Combine fractions with similar denominators
81/5 + 42/5 + 33/10
Add 81 and 42
123/5 + 33/10
To write 123/5 as a fraction with a common denominator, multiply by 2/2
123/5 >2/2 + 33/10
Write each expression witha common denominator of 10
123 . 2/10 + 33/10
Common numerator over denominator
123 . 2 + 33/10
Simplify
279/10
Thus answer = 279/10 0r 27.9
What is 5 divided by 25
Answer:
0.2
Step-by-step explanation:
Answer: .2
Step-by-step explanation:
If the question was 25 divided by 5 it'll be 5 but because it's 5 divided by 25 the answer came out as a deciamal.
.2 can also mean it is 2/10 or maybe 20%
what would a line look like if the equation is y=2
Kira ran three times last week. Here are the distances she ran (in kilometers).
19.16, 13, 8.27
What is the total distance Kira ran on these three days?
Answer:
40.43 Kilometers
Explanation:
19.16, 13, 8.27
19.16 + 13 + 8.27
= 40.43
Final answer:
The total distance Kira ran during the three days is the sum of the individual distances she ran on each day, which is 40.43 kilometers.
Explanation:
The total distance Kira ran on the three days is the sum of the distances she ran on each day. To find the total distance, you simply need to add up the three individual distances.
Add the first distance: 19.16 km
Add the second distance: 13 km
Add the third distance: 8.27 km
Calculate the sum: 19.16 km + 13 km + 8.27 km = 40.43 km
Therefore, the total distance Kira ran during the three days is 40.43 kilometers.
What is the median value of the data set shown on the line plot?
LMK answer fast!!
Answer:
i cant solve it for you but i will tell you how to do it
Step-by-step explanation:
You add them all up from least to greatest on a piece of paper then use your two fingers starting from the least and the greatest and go down the line if you get more than 1 number you must add them both up and divide by 2.