The expression to represent the number of hours Erica babysits each week is 7x .
In mathematics, an expression that was created using integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number) .
However, since they are not produced from integer constants and algebraic operations, transcendental numbers such as such and e are not algebraic. The production of is often done as a geometric expression, but the definition of e requires an infinite number of algebraic operations.A rational expression is one that can be reduced to a rational fraction using the properties of arithmetic operations ( associative properties and commutative properties of addition and multiplication, distributive property and rules for the various operations on the given fractions).Erica works x hours each day and there are 7 days in a week.
Hence Erica works 7x hours in a week
Therefore the expression to represent the number of hours Erica babysits each week is 7x .
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A scuba diver dove from the surface of the ocean to an elevation of −69 9/10
feet at a rate of −21.5 feet per minute. After spending 12.5 minutes at that elevation, the diver ascended to an elevation of −38 9/10
feet. The total time for the dive so far was 19 1/8
minutes. What was the rate of change in the diver's elevation during the ascent? Round your answer to the nearest hundredth.
The rate of change of the divers elevation = 19.274
Given,
The depth to which the Scuba dove = -69 [tex]\frac{9}{10}[/tex] feet
The rate at which he dove = -21.5 feet per min.
The time which he spent at the elevation = 12.5min.
The elevation the diver then ascended to -38 [tex]\frac{9}{10}[/tex] feet
Thee total time for the dove = 19 [tex]\frac{1}{8}[/tex] minutes.
Therefore, the time [tex]t_{d}[/tex] with which the scuba diver descended to -69 [tex]\frac{9}{10}[/tex] feet
is given as follows:
[tex]t_{d} = \frac{Distance}{speed}[/tex] = [tex]= \frac{-69\frac{9}{10} }{-21.5}= \frac{-681}{-21.5}[/tex] = 3.167 minutes
The time [tex]t_{e}[/tex], it took the scuba diver to elevate to -38 [tex]\frac{9}{10}[/tex] feet is given as follows:
[tex]t_{e}[/tex] = 19 [tex]\frac{1}{8}[/tex]minutes - (3.167 + 10.5) minutes = 5.458 minutes
The rate of change of the divers elevation = (Final elevation - Initial elevation)/(Time taken).
∴ The rate of change of the divers elevation
= (-38 [tex]\frac{9}{10}[/tex] - (-69 [tex]\frac{9}{10}[/tex] )) / 5.458 min
=(37.1 - (-68.1))/ 5.458 min
= 19.274 feet/minutes to the nearest hundredth.
Hence, The rate of change of the divers elevation = 19.274
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Is the picture below a graph for the following inequality? Why or why not?
y<6x+1
Given picture is not a graph of inequality y < 6x + 1
In this question, we have been given a graph.
We need to determine whether the picture is a graph for the inequality y < 6x + 1 or not.
We know that the graph of equation y = 6x + 1 is a straight line and we represent a straight line graph by a solid line.
This graph represents a shaded region below dotted line. This means, this is the graph of inequality.
From this graph we can see that x-intercept of the equation is (2, 0) and y-intercept is (0, - 4)
If we find the x and y-intercept of y = 6x + 1 then it would be,
x - intercept = (-1/6 , 0)
y - intercept = (0, 1)
This means, given picture is not a graph of inequality y < 6x + 1
Therefore, given picture is not a graph of inequality y < 6x + 1
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An egg of a particular bird is very nearly spherical. The radius to the inside of the shell is 4 millimeters and the radius to the outside of the shell is 4.3 millimeters. Use differentials to approximate the volume of the shell. [Remember that V(r) =
#x p3, where r is the radius.]
If the radius to the inside of the shell is 4 millimeters and the radius to the outside of the shell is 4.3 millimeters. the volume of the shell is 19π mm³.
Volume of the shellv = 4 / 3πr³
dv =4 / 3π (3r²) dr
Where:
r= radius = 4 cm
dr = 4.3 -4 = 0.3
Hence,
dv = 4 / 3π (16) 3/10
dv =4 / 3π(16) 0.3
dv = 19.2π mm³
dv = 19π mm³ (Approximately)
Therefore the volume of the shell is 19π mm³.
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7. Consider a line containing the points (0,14) and (2, -8). What is the slope of any line
perpendicular
to it?
Answer:
a= (0,14) (2,-8)
Step-by-step explanation:
You must cut a triangle out of a sheet of paper. The only
requirements you must follow are that one of the angles
must be 60°, the side opposite the 60° angle must be 40
centimeters and one of the other sides must be 15
centimeters. How many different triangles can you make?
1,2,3 or4?
Write an equation that represents the pattern in the table
A mathematical expression known as an algebraic expression includes variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions include terms. Here, y=3x.
What is algebraic expression?The idea behind algebraic expressions is to represent numbers using letters or alphabets rather than giving their exact values. In algebraic basics, we learned how to express an unknown number using letters like x, y, and z. We will refer to these letters as variables from now on. An algebraic expression may have both constants and variables. Any amount that is added to a variable before it is multiplied by another is known as a coefficient.
A mathematical expression known as an algebraic expression includes variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions include terms.
There are 3 main types of the algebraic expressions which include:
Monomial ExpressionBinomial ExpressionPolynomial ExpressionFor the above question:
4x3=12 , 5x3=15 , 6x3=18 ,.....
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The complete question:
"Write an equation that represents the pattern in the table
x 4,5,6,7,8
y 12,15,18,21,24 y = __ x"
Mai biked 6\frac{3}{4} miles today, and Noah biked 4\frac{1}{2} miles.
How many times the length of Noah’s bike ride was Mai’s bike ride?
Mai's bike ride was 1.5 times the length of Noah's bike ride
Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Distance travelled by Mai in miles = 6 3/4 miles
Distance of Mai in improper fraction = 27/4
Distance travelled by Noah in miles = 4 1/2
Distance of Noah in improper fraction = 9/2
Length of Noah's bike ride as compared to Mai's bike ride = (27/4)/(9/2)
= 27/4*2/9
= 3/2 or 1.5 times
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need help asap
please do it
It is to be noted that the information for the completed table is given accordingly to show the perimeters in millimeters and in centimeters.
What is a Perimeter?Perimeter simply refers to the total or sum of all the sides of a geometric shape. Note that the perimeter in units is obtained by counting the number of rectangles.
In the case of A:
Perimeter in Units = 10 Units.
Length is 60mm and width is 40mm
Perimeter = 30 + 20 + 30 + 20 = 100mm; and 10 cm
Recall that I cm = 10mm.
Hence, 100 /10 = 10 cm.
In the case of shape B:
Perimeter in Units = 41 Units.
Length is 400mm (that is 200 + 200)
Breath is 40mm (20 + 20)
Perimeter therefore is:
400 + 40 = 440mm
Perimeter in cm = 44
Recall, 10mm = 1cm
In the case of shape C:
Perimeter in Units = 36 Units.
Length is 10cm (that is 5 + 5)
Breath is 14mm (7 + 7)
Perimeter therefore is:
10+ 14 = 24cm
Perimeter in mm= 240
Recall, 10mm = 1cm
In the case of Shape D:
Perimeter in Units = 51 Units.
Length is 200mm (that is 100 + 100)
Breath is 100mm (50 + 50)
Perimeter therefore is:
200 + 100 = 300mm
Perimeter in cm= 230
Recall, 10mm = 1cm
In the case of Shape D:
Perimeter in Units = 53 Units.
Length is 260mm (that is 130 + 130)
Breath is 80mm (40 + 40)
Perimeter therefore is:
260 + 80 = 340mm
Perimeter in cm= 34
Recall, 10mm = 1cm
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Please help, super behind in the class and still trying to learn and catch up.
Given the equation and table below, determine the following
(Picture below)
Answer: See attached and/or view below.
Step-by-step explanation:
Since we are given the equation, we can plug the values into it and solve for the unknown. We will solve by isolating the variable and using reverse operations.
x = 1, y = 34
2x + y = 36
2(1) + y = 36
2 + y = 36
y = 34
x = -2, y = 40
2x + y = 36
2(-2) + y = 36
-4 + y = 36
y = 40
y = 18, x = 9
2x + y = 36
2x + (18) = 36
2x = 18
x = 9
Fae is following a recipe to make dough. The amount of water (in ounces) she uses depends on the amount of flour she uses (in cups). The amounts for each ingredient are shown in the graph.
The unit rate of ounces of water per cup of flour for this situation is; 3 ounces per cups
What is the unit rate of the graph?
From the given graph, we are expected to find the unit rate of ounces of water per cup of flour for the situation.
Now, to find the unit rate , all we need to do is to pick two coordinates on the line graph and find the slope. Thus;
Slope = (y2 - y1)/(x2 - x1)
Slope of graph = (12 - 9)/(4 - 3)
Slope = 3/1
Slope = 3
Let us pick another two points to verify;
Slope = (6 - 3)/(2 - 1)
Slope = 3/1
Slope = 3
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What is 21.00$ with a 7%
tax
Answer:
22.47
Step-by-step explanation:
7/100 = 0.07 (the tax rate) 21 * 0.07 = 22.47, the tax adds on 1.47
Which classifications of the real number system describe all numbers in the set? (Choose all correct answers.)
{0.4, 10,-√196,1/3)
Answer:
Rational
Step-by-step explanation:
The point (-4,1) is rotated 180 degrees counterclockwise using center (-3,0). What are the coordinates of the image?
By using a rotation rule, the image of point P = (- 4, 1) after rotating 180° counterclockwise using center (- 3, 0) is equal to point P'(x, y) = (- 2, 1).
How to determine the coordinates of the image of a point by using a transformation ruleIn this problem we find the case of a point that must be rotated 180° counterclockwise (+ 180°) about the point (- 3, 0). Rotation is a kind of rigid transformation, that is, a kind of transformation applied on a point such that Euclidean distance is conserved. The rotation formula for a point P(x, y) = (x, y) around the center O(x, y) = (Ox, Oy) is introduced below:
P'(x, y) = (Ox + (x - Ox) · cos θ - (y - Oy) · sin θ, Oy + (x - Ox) · sin θ + (y - Oy) · cos θ)
Where θ is the angle of rotation.
If we know that O(x, y) = (- 3, 0), P(x, y) = (- 4, 1) and θ = 180°, then the coordinates of the image are:
P'(x, y) = (- 3 + [- 4 - (- 3)] · cos 180° - (1 - 0) · sin 180°, 0 + [- 4 - (- 3)] · sin 180° + (1 - 0) · cos 180°)
P'(x, y) = (- 3 - [- 4 - (- 3)], - 1)
P'(x, y) = (- 3 - (- 1), - 1)
P'(x, y) = (- 2, - 1)
The coordinates of the image are P'(x, y) = (- 2, 1).
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When Sam launched a potato from their potato cannon the potato traveled a horizontal distance of 150 feet and, at its highest, reached 90 feet.
Part A. Create a graph to represent the scenario. The graph should include at least the x- and y-intercepts and the vertex. (A complete graph consists of axis labels and appropriate scales, ordered pairs for each identified point, the function, and appropriate domain/range.)
Part B. Write a function to model the scenario.
Part C. Create a table of values to represent the scenario. Be sure to include at least five
values. Values should include at least the x- and y-intercepts and the vertex.
Part D. Identify how you see the x- and y-intercepts and vertex in the table, graph, and equation.
(PLEASE HELP)
This statement about distance is proved.
What is distance ?
It is length of space between two points.
Okay, so the first three components of this issue involve more physics and math. So, part A received the formula Ds = R. D. Data. We have to track down S. Therefore, we simply integrate both sides equally using R. D. Data. Our data are provided. Therefore, the upon integration over our data is just R 0 Santa plus 12 beta zeta squared for part B. We'll make sure S = V T. We combine these two by using the above equation as an equal. In order to allow it to reach its roots once positive, we can see that this is Justin's equation for data. The other negative, which is naturally a positive one because it has the proper physical meaning, would indicate that the rotation is occurring in the opposite direction.
Standard units, uh, are zero point 24/7 times, so switch to the nature radio's negative six setting. Additionally, we are given the time, which is 74 minutes, or 4440 seconds. Thus, plugging everything. Injecting R 0 and data mm hmm into the expression for data. Therefore, we enter better Data. V also appears. Everything is therefore known. We can confidently conclude that the data is, um, 1.337 x 10-5 brilliant. or 2.13 x 10 to 4 revolutions, in terms of turns. Okay. We simply re-insert the numbers for beta and tr zero V into the previous expressions for omega and alpha in the final section of the problem.
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The points ( – 5,j) and (5, – 6) fall on a line with a slope of – 7/10 . What is the value of j?
Answer:
j = 1
Step-by-step explanation:
calculate the slope m between the 2 points and equate to - [tex]\frac{7}{10}[/tex]
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, j ) and (x₂, y₂ ) = (5, - 6 )
m = [tex]\frac{-6-j}{5-(-5)}[/tex] = [tex]\frac{-6-j}{5+5}[/tex] = [tex]\frac{-6-j}{10}[/tex]
then equating gives
[tex]\frac{-6-j}{10}[/tex] = - [tex]\frac{7}{10}[/tex] ( cross- multiply )
10(- 6 - j) = - 70 ( divide both sides by 10 )
- 6 - j = - 7 ( add 6 to both sides )
- j = - 1 ( multiply both sides by - 1 )
j = 1
what makes this statement true?
-1/8 ? -3/8
Answer:
-1/8>-3/8
Step-by-step explanation:
You can write it as a decimal.
-0.125 ? -0.375
The longest worm is ? times as long as the shortest worm.
The two lines at right represent the growing profits of Companies A and B. Homework Help ✎ Sketch this graph on your paper. If Company A started out with more profit than Company B, determine which line represents A and which represents B. Label the lines appropriately. In how many years will both companies have the same profit? Approximately what will that profit be? Which company’s profits are growing more quickly? How can you tell?
Using concepts of linear functions, it is found that:
They will have the same profit after 3 years.This profit will be of $65,000.Due to the higher slope, Company B profit is growing more quickly.What do the slope and the intercept of a linear function represent?The slope-intercept representation of a linear function is:
y = mx + b.
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).Two linear functions have the same value when they intersect each other, hence, from the graph given at the end of the answer, they intersect around point (3,65), meaning that they will have the same profit after 3 years, and this profit will be of $65,000.
From the Graph, as it assumes higher values as n goes to infinity, company B has the higher slope, hence it's profit is growing more quickly.
What is the missing information?The graph is missing, and is given by the image at the end of the answer.
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Sergio has two similar cylindrical pots, Pot A and Pot B. The radius of Pot A is 15 inches, and the radius of Pot B is 3 inches. What is the ratio of the volume of Pot A to the volume of Pot B?
15:3
45:9
125:1
5:1
Answer:
125 : 1
Step-by-step explanation:
given 2 similar objects with ratio of sides a : b , then
ratio of volumes = a³ : b³
here
ratio of pot A : pot B = 15 : 3 = 5 : 1
ratio of volumes = 5³ : 1³ = 125 : 1
Solve for x.
E
G
×
11
C
7
J
D
(3x - 11)°
(2x+16)
H
Answer:
35
Step-by-step explanation:
The consecutive interior angles are supplementary, so:
[tex]3x-11+2x+16=180 \\ \\ 5x+5=180 \\ \\ x+1=36 \\ \\ x=35[/tex]
Trigonometry please help!
Answer:
the first one
Step-by-step explanation:
Factorise
y²-2y-48
Answer: y²-2y-48=(y-8)(y+6)
Step-by-step explanation:
[tex]y^2-2y-48=\\\\y^2-8y+6y-48=\\\\y(y-8)+6(y-8)=\\\\(y-8)(y+6)[/tex]
Answer:
y²-2y-48=(y-8)(y+6)
Step-by-step explanation:by factorization
y2-2y-48= y2-8y+6y48= y(y-8)+6(y-8)= (y-8)(y+6)
c. What is -3-6? What does that tell you about how many points Soledad has after the next round?
Step-by-step explanation:
i.)add 3 in 6 which = 9
ii.) follow the negative sign of the larger value which now ur finally answer is -9
what property is 3x+2x+1-7=x+22
11) Convert 3 miles to feet
Answer: 15840[tex]covert 3 miles to feet[/tex]
Step-by-step explanation:
3 miles equals 15840 feet
Answer: 15840
Step-by-step explanation:
3 miles have 15840 feet
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Solve for X.
x² =50
x³ = 37
Answer:
x^2= 50 ------ (equation 1)
x^3= 37 ------- (equation 2)
dividing (equation 2) by (equation 1)
=> x^3/x^2 = 37/50
=> x = 37/50
Answer: x= 37/50
20 points. Someone please help
Step-by-step explanation:
[tex](4(2) \: - 6(7) \: 5(1)) \\( 2( - 1) \: 4(5) \: - 1(2) ) \\ (8 \: - 42 \: \: 5 \\ - 2 \: \: \: 20 \: \: - 2)[/tex]
Could anybody help me? Math!!!!
The products of the fractions given are:
1. (-3/4)(7/8) → -21/32
2. (2/3)(-4)(9) → -24
3. (5/16)(-2)(-4)(-4/5) → -2
4. (2 3/5)(7/9) → 91/45
How to Multiply Fractions?To multiply two or more fractions, multiply the denominators of both fractions together, and their numerators together.
1. (-3/4)(7/8)
Multiply the denominators of the fractions together, and also multiply their numerators:
= (-3 × 7) / (4 × 8)
= (-21) / (32)
(-3/4)(7/8) → -21/32
2. (2/3)(-4)(9)
Multiply the denominators of the fractions together, and also multiply their numerators:
= (2 × -4 × 9) / (3)
= -72/3 = -24
(2/3)(-4)(9) → -24
3. (5/16)(-2)(-4)(-4/5)
= (5 × -2 × -4 × -4) / (16 × 5)
= -160/80 = -2
(5/16)(-2)(-4)(-4/5) → -2
4. (2 3/5)(7/9)
= (13/5)(7/9)
= (13 × 7)/(5 × 9) = 91/45
(2 3/5)(7/9) → 91/45
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A teacher is buying markers. Each set of markers includes 5 markers and cost $3.00. The teacher uses a $3-off coupon toward the total cost of all the markers bought. If there is no tax added to the final cost of the markers after the coupon and the teacher paid a total of $15, how many markers did she buy?
A. 6
B. 25
C. 30
D. 35
Answer:
30 markers
Step-by-step explanation:
(15 what she spent)+(3 the 3 dollors off)=
18/(3 the price of markers)=
(6 sets)*(5 how many is in a set)=
(30 final anwser)
I need help with this question
he Solution:
iven:
The y-intercept of function 1 is:
[tex]y-\text{intercept}=5\text{ }[/tex]The y-intercept of function 2 is:
[tex]y=1[/tex](a) So, the farthest y-intercept from 0 is function 1.
he slope of function 1 is
[tex]\text{Slope}=\frac{2-5}{1-0}=-\frac{3}{1}=-3[/tex]The slope of function 2 is
[tex]\text{slope=}\frac{3-1}{1-0}=\frac{2}{1}=2[/tex]he solope of function 3 is -1
The slope of function 4 is 5
(b) hus, the steepest graph is the function with the highest slope.
So, the steepest graph is the graph of function 4 since it has the greatest slope.
(c)
Functions with y-intercept greater than -3 are:
unction 1, function 2, amnd function 4.
[tex]\text{ function 3 has y-intercept=-4}<-3[/tex]