The number of bacteria's in petri dish 'A' are 30 times more than the bacteria's in petri dish 'B'.
What is bacteria?Bacteria are small single-celled organisms. Bacteria are found almost everywhere on Earth and are vital to the planet's ecosystems.
Given is a culture of 2.4 × 10¹¹ bacteria is in petri dish 'A' and a culture of
8 × 10⁹ bacteria is in petri dish B.
Number of bacteria's in petri dish A = n[A] = 2.4 × 10¹¹ bacteria
Number of bacteria's in petri dish B = n[B] = 8 × 10⁹ bacteria
For comparison, lets assume that -
k = n[A]/n[B]
k = 2.4 × 10¹¹ / 8 × 10⁹
k = 240 / 8
k = 30
n[A] = 30 n[B]
Therefore, the number of bacteria's in petri dish 'A' are 30 times more than the bacteria's in petri dish 'B'.
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which would not be a step in solving 5x + 15 + 2x = 24 + 4x?
A. Isolate the variable.
B. Collect variable terms on one side.
C. Collect like terms.
D. Use the distributive property.
The step that would not be necessary in solving 5x + 15 + 2x = 24 + 4x is D. Use the distributive property.
What is an equation?An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.
To solve the equation 5x + 15 + 2x = 24 + 4x, we need to simplify and manipulate the equation to isolate the variable on one side.
First, we can combine like terms:
5x + 2x - 4x = 24 - 15
3x = 9
Then, we can isolate x by dividing both sides by 3:
x = 3
Therefore, the correct steps to solve this equation are:
B. Collect variable terms on one side.
C. Collect like terms.
A. Isolate the variable.
We do not need to use the distributive property in this problem.
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Simplify the expression.
55−4⋅5+12
Expression after the simplification is 62.5.
What is an expression?In mathematics, expression is the combining of variables with the application of operations and prescribed rules. It could take the shape of an equation, some numbers, etc.
Given, expression
55 - 4.5 +12
Simplifying,
first, add the numbers.
55 - 4.5 +12
= 67 - 4.5
= 62.5
Hence, the value of the expression is 62.5.
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10. Find the values of x, y, and z in the diagram below.
which of the following are necessary when proving the opposite sides of a parallelogram are congruent? Check all that apply. A) Opposite sides are perpendicular B) Corresponding parts of similar triangles are similar C) Opposite sides are congruent D) Corresponding parts of congruent triangles are congruent
Answer:
C - Opposite sides are congruent
D - Corresponding parts of congruent triangles are congruent
Step-by-step explanation:
A parallelogram is a quadrilateral whose both pairs of opposite sides are parallel. In a parallelogram, the 2 sets of opposite sides are congruent. Also it has 2 sets of opposite angles congruent.
Therefore, the following are necessary when proving the opposite sides of a parallelogram are congruent.
C - Opposite sides are congruent
D - Corresponding parts of congruent triangles are congruent
Determine the sign of cos pi divided by seven without using a calculator.
Write the first ten terms of a sequence whose first term is -10 and whose common difference is -2.
In the diagram below bd is parallel to xy what is the value of y?
we know that
if the lines bd and xy are parallel. then
[tex]y+70\°=180\°[/tex] --------> by consecutive interior angles
so
Solve for y
Subtract [tex]70\°[/tex] both sides
[tex]y+70\°-70\°=180\°-70\°[/tex]
[tex]y=110\°[/tex]
therefore
the answer is
[tex]y=110\°[/tex]
Answer:
Option C. y = 110°
Step-by-step explanation:
In this question BD and XY are two parallel line and a transverse is intersecting both the lines at A and E.
Now ∠BAE = ∠AEY = 70° [ alternate interior angles ]
and ∠EAD + ∠BAE = 180° [ supplementary angles ]
or y + 70° = 180°
⇒ y + 70 - 70 = 180 - 70
⇒ y = 110°
Therefore Option C. measurement of y = 110° is the answer.
"The perimeter of a swimming pool is 126 feet. The difference between the length (x) and width (y) of the pool is 39 feet. What are the dimensions of the pool?"
I'm supposed to figure this out using substitution but I'm not sure how, and any help at all is appreciated!
The dimensions of the swimming pool are 51 feet (length) and 12 feet (width), determined by setting up equations based on the given information (perimeter and difference between the sides) and solving these equations using substitution.
Explanation:The problem at hand is a classic algebraic word problem. It involves determining the length (x) and width (y) of a swimming pool given the perimeter and the difference between the length and width. The formulas we'll use are for the perimeter of a rectangle (2x + 2y = perimeter) and a given equation based on the description (x - y = difference).
Step-by-step Solution
From the question, we know the perimeter of the swimming pool is 126 feet. We express this using the perimeter formula: 2x + 2y = 126. Likewise, we know the difference between the length and the width is 39 feet. This can be expressed as: x - y = 39. We want to use substitution to solve these equations. This means, we need to isolate one of the variables in the second equation. Let's isolate x by rewriting the second equation as: x = y + 39. Now, we can substitute (y + 39) for x in our perimeter equation: 2(y + 39) + 2y = 126. This simplifies to: 4y + 78 = 126. Solving for y, we get: y = 12 feet. Substitute y = 12 into our isolated equation from step 3, we get x = 12 + 39 = 51 feet.
So the dimensions of the swimming pool are 51 feet (length) and 12 feet (width).
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Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k.
k = ______
Can you explain how to figure this out?
A man standing on a sidewalk looks up at the roof edge of a building. The building is 40 feet tall and the man stands 12 feet from the building.
What is the measure of the man's angle of inclination from where he stands?
Enter your answer, rounded to the nearest degree, in the box.
If its rounded it would be 73 degrees
Which equation shows how to find the product of 100,000 and 1,000,000 using scientific notation?
Answer:
[tex]10^5 * 10^6 = 10^{5+6} = 10^{11}[/tex]
Step-by-step explanation:
find the product of 100,000 and 1,000,000 using scientific notation
All whole numbers have a decimal point at the end
convert each number into scientific notation. To get scientific notation move the decimal point after 1
100000. -----> 1.00000 ----> 1* 10^5 ----> 10^5
1000000. -----> 1.000000 ----> 1* 10^6 ----> 10^6
a^m * a^n = a^m+n
[tex]10^5 * 10^6 = 10^{5+6} = 10^{11}[/tex]
If a parabola’s focus is at (1,1) and directrix is at y = 7, what is the standard form of the equation representing this parabola
The standard form of the equation of the parabola with focus at (1, 1) and directrix 'y = 7' is (x - 1)² = 12(y - 4). The vertex is found by determining the midpoint between the focus and directrix, and the 'a' value is found by calculating half the distance between the focus and directrix.
Explanation:To find the standard form of a parabola given the focus and directrix, we'll use the definition of a parabola itself. A parabola is defined as the set of points that are equidistant from a point, known as the focus, and a line, known as the directrix.
The equation representing a parabola is: (x - h)² = 4a(y - k) where (h, k) is the vertex of the parabola and 'a' denotes the distance between the vertex and the focus or the vertex and the directrix.
The mid-point of the focus (1, 1) and the directrix y=7 gives the coordinates of the vertex. So, h = 1 and k = (1+7)/2 = 4.
Now, 'a' is half the distance between the focus and directrix, a = (7-1)/2 = 3.
So, the standard form of the equation is (x - 1)² = 12(y - 4)
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An angle measuring 22 degrees is bisected what is the measure of the angle that are formed
Which of the following equations is an example of a direct variation?
x + 2y = 6
x = 4
y = 3
y = 3.14 x
Answer:
Step-by-step explanation:
y=3.14x
Solve for the variable: x – 2.8 = 1.6
3.4
-1.2
2.3
4.4
Tickets to friday's football game are $5.50 for adults and $4.50 for students. if the school pre-sold 25 tickets for $124.50, how many adult and student tickets were purchased?
What is true about the functional relationship shown in the graph ?
Answer: C. The amount earned is a function of the number of hours worked.
Explanation:
Since, a function is always the type of y= f(x), where x is independent variable and y is dependent variable which is dependent on the value of x.
Here, a graph of Olivia's earning per hour is given.
Since, it is the obvious thing that the earning will depend on hours she works.
Thus, we can say that earning is dependent variable while hours is independent variable.
Therefore, earning makes the y-axis and number of hours makes the x-axis.
So, option C is correct.
HELP WITH SOLVING SYSTEMS WITH THREE VARIABLES, WILL MEDAL
-2x + 2y +3z = 0
-2x - y + z = -3
2x + 3y + 3z = 5
I'm not sure how to work it out, I have to do it by elimination
Ohhhhh! I have a math Brainliest
Use geometry to evaluate the integral from 0 to 6 of the function f of x, dx for f of x equals 3 for x less than or equal to 3 and equals the quantity 6 minus x for x greater than 3.
27
13.5
12
10.5
Final answer:
To evaluate the given integral, split the function at x = 3 and integrate separately. The integral evaluates to 18, which makes the correct answer 18.
Explanation:
The function we're integrating is 1, which makes this the same integral as the one in example 3 on p. 178. To evaluate this integral, we need to split it at x = 3 and integrate the corresponding functions separately.
For x ≤ 3, the function is f(x) = 3. So, the integral from 0 to 3 of 3 dx equals 9.
For x > 3, the function is f(x) = 6 - x. Integrate this from 3 to 6: ∫(6 - x) dx = 6x - 0.5x^2. Evaluating this from 3 to 6 gives 9.
Which graph represents y – 1 = 2(x – 2)?
Thank You! :)
Answer:
Option A
Step-by-step explanation:
Given : Equation [tex]y-1 = 2(x -2)[/tex]
To find : Which graph represents the given equation
Solution :
First thing we plot the graph of the equation.
We see that graph cuts at point (1.5,0) and (0,-3) to the coordinates.
From the given graph Option A graph cuts to these points.
Therefore, Option A is correct.
Refer the attached graph A.
Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing?(–6, –3)(–3, –1)(–3, 0)(–6, –5)
The interval of x-values over which the function is increasing is (-3 , -1), the correct option is B.
What is a Function?A function is a law that relates two variables namely, a dependent and an independent variable.
A function always has a defined range and domain.
The x values and the corresponding function values are shown in the figure.
The x and y values are:
-6 -34
-5 3
-4 -10
-3 -11
-2 -6
-1 -1
0 -2
1 -15
The interval of x-values over which the function is increasing has to be determined.
The first option is (-6, -3) , the function is not increasing in this interval.
The second option is (-3 , -1) , the function is increasing in this interval.
The third option is(–3, 0), the function is not increasing in this interval.
The fourth option is (–6, –5), the function is not increasing in this interval.
Your question seems incomplete, the complete question is attached with the answer.
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Gustavo and Aiden are walking due west through the forest when they happen upon an angry grizzly bear. Gustavo runs away 2 3 23 ∘ 23, degree north of east for 3 0 0 300m300, space, m, and Aiden runs away 3 3 33 ∘ 33, degree south of east for 2 5 0 250m250, space, m. How far are Gustavo and Aiden away from each other?
We can actually solve this problem using the cosine law. We know that Gustavo ran 23° above the horizontal, while Aiden ran 33° below, hence the total angle between them is 56°. Therefore the distance between them is:
c^2 = a^2 + b^2 – 2 a b cos θ
c^2 = (300)^2 + (250)^2 – 2 (300) (250) cos 56
c^2 = 68,621.06
c = 262 m
They are 262 meters apart.
Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal. So, they are 262 meters apart.
What is a cosine law?Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.
Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal.
The total angle between them = 23 + 33 = 56°.
Let the distance between them be c. by using cosine law we have,
c² = a² + b² – 2ab cos θ
Where a and b are distances traveled by Gustavo and Aiden. θ is the angle between them.
Therefore,
[tex]c^2 = a^2 + b^2 - 2 a b cos \theta[/tex]
[tex]c^2 = (300)^2 + (250)^2 -2 (300) (250) cos 56[/tex]
[tex]c^2 = 68,621.06[/tex]
c = 262 m
Thus, the distance between them is 262 meters.
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Kenya exchanges $150 for British pounds(£). Suppose the conversion rate is £1 = $1.60. How many pounds should she receive?
When it is 11:30
a.m. in dublin, it is 2:30 p.m. in moscow. how far ahead of dublin is moscow?
Dublin is 3 hours ahead of Moscow.
What is Time difference?The difference between how time is measured in different ways; the length of a period of time. the time difference between two or more distinct time zones in terms of clock time.
Given Dublin time = 11:30 am
Moscow time = 2:30
we can military time and subtract.
11:30 a.m. = 11:30
2:30 p.m. = 2:30 + 12:00 = 14:30
14:30 - 11:30 = 3:00
Hence the time difference is 3 hours.
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What is the algebraic description for a transformation that translates the point (x,y) nine units to the right and five units down?
An algebraic description of the transformation that translates a point (x, y) nine units to the right and five units down is written as the new point (x + 9, y - 5).
The algebraic description of a transformation that translates a point (x, y) nine units to the right and five units down can be written as the following ordered pair: (x + 9, y - 5).
In this transformation, the x-coordinate of each point is increased by 9 units, reflecting a horizontal translation to the right, and the y-coordinate is decreased by 5 units, representing a vertical translation downwards. Thus, if you have a point (x, y), after the transformation, it becomes (x + 9, y - 5).
For example, if your initial point is (3, 4), after the transformation it would be at (3 + 9, 4 - 5) = (12, -1).
70/b+5a-2b
Evaluate the expression when a=3 and b=10
Number 16. Solve the problem. Correct answer will get brainliest
The composition is performed on . What are the coordinates of B'' and C''?
Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line x + 2y = 6?
Drag each choice into the boxes to correctly complete the table
y= -1/2x+5
-2x+y=-4
-x+2y=2
x+2y=-2
ANSWER
We need to rewrite [tex]x+2y=6[/tex], in slope intercept form.
[tex]\Rightarrow 2y=-x+6[/tex],
[tex]\Rightarrow y=-\frac{1}{2}x+3[/tex]
The given equation has a slope of [tex]-\frac{1}{2}[/tex].
ANSWER TO QUESTION 1
We now the write given options also in slope intercept form.
For the first one, we have
[tex]y=-\frac{1}{2}x+5[/tex]
This first equation also has a slope of [tex]-\frac{1}{2}[/tex].
Hence [tex]y=-\frac{1}{2}x+5[/tex] is parallel to [tex]x+2y=6[/tex].
ANSWER TO QUESTION 2:
The second equation is;
[tex]-2x+y=-4[/tex].
We need to write this one too in slope intercept form.
[tex]y=2x-4[/tex]
This second equation has a slope of 2
Since [tex]2\times -\frac{1}{2}=-1[/tex], the line [tex]-2x+y=-4[/tex]
is perpendicular to [tex]x+2y=6[/tex].
ANSWER TO QUESTION 3
We rewrite the equation [tex]-x+2y=2[/tex] in slope intercept form.
[tex]\Rightarrow 2y=x+2[/tex]
[tex]\Rightarrow y=\frac{1}{2}x+1[/tex]
This equation also has a slope of [tex]\frac{1}{2}[\tex]
since the slope of [tex]-x+2y=2[/tex] is not equal to the slope of [tex]x+2y=6[/tex], and the product of these two slopes [tex]\frac{1}{2} \times - \frac{1}{2} \ne -1[/tex], the two lines are neither parallel nor perpendicular.
QUESTION 4
The given line has equation [tex]x+2y=-2[/tex]. We rewrite this equation in the slope intercept form.
[tex]\Rightarrow 2y=-x-2[/tex]
[tex]\Rightarrow y=-\frac{1}{2}x-1[/tex]
This line has a slope of [tex]-\frac{1}{2}[/tex].
Since this slope is the same as the slope of the given line,
[tex]y=-\frac{1}{2}x-1[/tex] is parallel to [tex]x+2y=6[/tex].
See graph in attachment.