well, the subtotal cost will be 48.30 + 17.75 = 66.05, now let's add the tax to that
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 66.05}}{\left( \cfrac{6}{100} \right)66.05} ~~ \approx ~~ 3.96~\hfill \underset{total~cost}{\stackrel{66.05~~ + ~~3.96}{\approx \text{\LARGE 70.01}}}[/tex]
The total cost of the purchase is $70.013.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Set of baseball cleats = $48.30
Baseball gloves = $17.75.
Sales tax = 6%.
This means,
6% of (48.30 + 17.75)
= 6/100 x 66.05
= $3.963
Now,
Total cost.
= 48.30 + 17.75 + 3.963
= $70.013
Thus,
The total cost is $70.013.
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construct a right-angled isosceles triangle whose equal side measure 2 cm
A construction of a right-angled isosceles triangle whose equal side measure 2 cm is shown in the image attached below.
What is an isosceles right triangle?In Mathematics, an isosceles right triangle can be defined as a type of right-angled triangle in which two (2) of its side lengths are equal and one of its angle is a right angle.
What are the steps for the construction of a right-angled isosceles triangle?Generally speaking, the steps that are required for the construction of a right-angled isosceles triangle include the following:
You should draw a line segment, with line AB equal to 2 cm (AB = 2cm).At point A, draw an angle with a measure of 90 degrees (90°).You should draw an arc of radius from point A in order to intersect the perpendicular drawn at point A at the point C.You should join point A and point B.In conclusion, triangle ABC (ΔABC) is the required right-angled isosceles triangle as shown in the image attached below.
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Solve the equation
4sinxcosx^2 - 1 = 2cos(sin x - 1)
Answer:
Step-by-step explanation:
To solve this equation, we can start by using the identity cos(A-B) = cosAcosB + sinAsinB. Substituting A=sin x and B=1, we have:
2cos(sin x - 1) = cos(sin x)cos(1) + sin(sin x)sin(1)
We can then substitute this expression on the left-hand side of the original equation and simplify:
4sinxcosx^2 - 1 = cos(sin x)cos(1) + sin(sin x)sin(1)
Rearranging terms, we have:
4sinxcosx^2 - cos(sin x)cos(1) - sin(sin x)sin(1) = 1
We can now use the identity sin^2x+cos^2x=1 to simplify the left-hand side further:
4sinxcosx^2 - (sin^2x + cos^2x)cos(1) = 1
Simplifying further:
4sinxcosx^2 - (cosx)cos(1) = 1
Now we can divide both sides by cos(1):
4sinxcosx^2/cos(1) - cosx = 1/cos(1)
Rearranging terms:
cosx(4sinxcosx^2/cos(1) - 1) = 1/cos(1)
Finally, we can use the identity cos2x = 2cos^2x - 1 to simplify the left-hand side further:
(2cos^2x - 1)(4sinxcosx^2/cos(1) - 1) = 1/cos(1)
We can then divide both sides by (4sinxcosx^2/cos(1) - 1):
2cos^2x - 1 = 1/cos(1) (4sinxcosx^2/cos(1) - 1)
And finally, we can solve for cosx:
cosx = 1/2 + 1/2cos(1) (4sinxcosx^2/cos(1) - 1)
This is the solution to the equation.
What is the slope of the line shown below?
10
(-5, -1)
10
-10
y
10
5
(5, 11)
10
15
O
A.
B.
O C.
O D.
96
The slope of the line is C) [tex]\frac{6}{5}[/tex].
What is slope?
Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line. Any two distinct places along the line can be used to determine the slope of any line.
Here the given point is [tex](x_1,y_1)=(-5,-1)[/tex] and [tex](x_2,y_2)=(5,11)[/tex]
Now using slope formula then,
=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> Slope m = [tex]\frac{11-(-1)}{5-(-5)}[/tex]
=> slope m = [tex]\frac{11+1}{5+5}[/tex]
=> slope m = [tex]\frac{12}{10}[/tex]
=> slope m = [tex]\frac{6}{5}[/tex]
Hence the slope of the line is C) [tex]\frac{6}{5}[/tex].
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When making homemade ice cream in a hand-cranked freezer, the tub containing the ice cream mix is surrounded by a brine (water/salt) solution. To freeze the ice cream mix rapidly so that smooth and creamy ice cream results, the brine solution should combine crushed ice and rock salt in a ratio of 5 to 1. A small ice cream freezer requires cups of crushed ice. How much rock salt should be mixed with the ice to create the necessary brine solution?
If the ratio of crushed ice to rock salt is 5 to 1, for every 5 cups of crushed ice, 1 cup of rock salt is needed.
To find out how much rock salt is needed for the small ice cream freezer, you can use this formula:
Rock Salt = (Crushed Ice / 5) * 1
If the small ice cream freezer requires cups of crushed ice, then:
Rock Salt = (5 cups / 5) * 1 cup
Rock Salt = 1 cup
So, you will need 1 cup of rock salt to mix with the 5 cups of crushed ice to create the necessary brine solution.
Suppose f(x) = x² − 2x³ + ax²+x+3, where a is a constant. If f(3) = 2, then
what is a?
Answer:
a = [tex]\frac{41}{9}[/tex]
Step-by-step explanation:
Evaluate f(3):
f(3) = (3)² -2(3)³ + a(3)² +3 +3
9a - 39 = 2
9a = 41
a = [tex]\frac{41}{9}[/tex]
Which of the following fractions have the same value as 16 ÷ (–3)? Check all that apply.
StartFraction 16 over negative 3 EndFraction
StartFraction negative 16 over negative 3 EndFraction
StartFraction negative 16 over 3 EndFraction
StartFraction 16 over 3 EndFraction
Negative (StartFraction 16 over 3 EndFraction)
Negative (StartFraction 16 over negative 3 EndFraction)
Find the quotient:
–20 ÷ 5 =
The fractions that have the same value as 16 ÷ (–3), include:
16 over negative 3negative 16 over 3Negative (StartFraction 16 over 3 EndFraction)The quotient of the problem given is - 4.
How to find the equivalent fractions ?To find the equivalent fractions to ,16 ÷ (–3), first solve for the quotient:
= 16 ÷ (–3)
= - 5. 33
Then, solve the fractions in the options to see if they give the same result as when you solved 16 ÷ (–3).
Fraction : 16 over negative 3
= 16 / -3
= - 5.333
This has the same value
Fraction : negative 16 over negative 3
= -16 / -3
= 5. 333
This does not have the same value
Fraction : negative 16 over 3
= - 16 / 3
= - 5. 333
This has the same value
Fraction : 16 over 3
= 16 / 3
= 5. 333
This is not the same value
Fraction: Negative (StartFraction 16 over 3 EndFraction)
= - ( 16 / 3 )
= - 5. 33
This is the same
The quotient of - 20 / 5 :
= - 20 / 5
= - 4
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Find an equation for the line with the given properties . Express your answer using either the general form or the slope- intercept form of the equation of a line. Slope = - 5; y - intercept = 4
Answer:
y = -5x + 4
Step-by-step explanation:
The general form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.
Given that the slope of the line is -5 and the y-intercept is 4, we can substitute these values into the general form of the equation of a line to get:
y = -5x + 4
This equation represents a line with a slope of -5 and a y-intercept of 4.
What is the inverse of the function? f(x)= 1/3 x −5
Answer:
The inverse of a function, denoted as f^-1 (x), is a new function that "undoes" the original function. To find the inverse of a function, you need to switch the x and y variables and then solve for y. To find the inverse of f(x) = 1/3 x - 5, you need to switch the x and y variables and then solve for y:
Step-by-step explanation:
To solve for y, you need to get x alone on one side of the equation:
x + 5 = 1/3 y
3x + 15 = y
The inverse of f(x) = 1/3 x - 5 is f^-1 (x) = 3x + 15
It is important to note that not all functions have an inverse, only functions that are one-to-one or "injective" functions have inverses.
Answer: 3x + 15 = the inverse function of f(x)
Explanation:
First of all, arrange the equation and leave the "x" alone.
x/3 - 5 = y (Multiply both sides by 3)
x - 15 = 3y (Then, leave "x" alone)
x = 3y + 15 (As the final step, change x and y variables.)
y = 3x + 15 (This is the inverse function of f(x).)
Write an equation for a line perpendicular to y= -5x-1 and passing through the point (10,3)
Answer: A line is perpendicular to another line if the slope of the first line is the negative reciprocal of the second line. The equation of the line y = -5x-1 has a slope of -5. The negative reciprocal of -5 is 1/5.
A line passing through a point (x1, y1) has an equation in slope-intercept form of y = m(x-x1) + y1, where m is the slope of the line.
So, we can use the point (10,3) and the slope of the line which is 1/5 to write the equation of the line:
y = 1/5(x-10) + 3
Therefore, the equation of the line perpendicular to y = -5x-1 and passing through the point (10,3) is y = 1/5x + 1/5
Step-by-step explanation:
What is the value of y that makes T Parallel to U
The required value of y for the angle is 18.
What is corresponding angles?The angles created when a transversal intersects two parallel lines are known as corresponding angles. Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks.
According to question:By Corresponding angles
7x = 3x + 36
4x = 36
x = 9
And
Angle in straight line
(6y + 9)+(3x+36) = 180
(6y + 9)+(27+36)
6y + 72 = 180
6y = 108
y = 18
Thus, required value of y is 18.
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Use elimination to solve
-3x+12y = 9
x-4y=-3
Answer:
Step-by-step explanation:
Elimination is a method of solving a system of equations by adding or subtracting the equations from each other to eliminate one of the variables.
In this case, we will be using elimination to solve the system of equations:
-3x + 12y = 9
x - 4y = -3
Step 1: Multiply the first equation by -1.
(Multiplying by -1 switches the sign of every number in the equation)
3x - 12y = -9
Step 2: Add the two equations together.
3x - 12y = -9
+x - 4y = -3
______________
4x - 16y = -12
Step 3: Isolate the y-variable by adding 16y to both sides of the equation.
4x - 16y = -12
+16y +16y
______________
4x = -12 + 16y
Step 4: Divide both sides of the equation by 4 to isolate the y-variable.
4x = -12 + 16y
4/4 4/4
______________
x = -3 + 4y
Therefore, the solution to the system of equations is x = -3 + 4y.
Let A and B be sets, where:
A = {3, 6, 8}
B = {0, 2, 4, 5, 9}
Greg washes cars on Saturdays at his dad’s car dealership. His dad pays him $50 plus $5 for each car that he washes. Greg washed 11 cars last Saturday. Use function notation to write an equation that gives the total amount Greg earns as a function of the number of cars he washes. Use the equation to find how much he earned last Saturday.
(SHOW WORK)
Answer:
605
Step-by-step explanation:
11x55=605
The age of a father is three times that of his son, but six years ago, the sum of their ages was 45. What is the present age of the son?
Answer: Let's call the present age of the son x and the present age of the father y.
We know that y = 3x and that six years ago, the sum of their ages was 45.
So, we can write the equation:
x + (y-6) = 45
x + (3x-6) = 45
4x = 51
x = 12.75
The present age of the son is 12.75 years.
Step-by-step explanation:
It's raining, and Vince and his friends are stuck inside. They decide to play a marble game called Revenge. To start, Vince divides a bag of m marbles evenly among the 3 players. Each player gets 10 marbles.
The total number of marbles are 30.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, to start, Vince divides a bag of m marbles evenly among the 3 players. Each player gets 10 marbles.
Here, m/3 =10
m=30
Therefore, the total number of marbles are 30.
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Classify the system of equations
Answer:
The correct answer is: parallel
The two equations are in the form of y = mx + b and y = mx + b, which are the standard forms of linear equations.
and the slope of the two equations are different, so they are not coincident and not intersecting. They are parallel lines that never meet, so the system of equations is parallel.
a cylinder container 12 inches tall with a radius of 6 inches is completely filled with vanilla, chocolate, and strawberry ice cream in the ratio 3:2:1. Which statement(s) are correct?
A.) The volume of vanilla ice cream is V = 216π in^3
B.) The total volume of ice cream is V = 1728π in^3
C.) The total volume of ice cream is V = 432π in^3
D.) The volume of strawberry ice cream is V = 288π in^3
E.) The volume of chocolate ice cream is V = 576π in^3
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2 (12)\implies \stackrel{\textit{total volume of ice-cream}}{V=432\pi ~in^3}[/tex]
An isosceles triangular prism can be unfolded into the net shown
below. Find the lateral surface area of the triangular prism.
8.3 in
9 in
7 in
17 in
The latera surface area of the triangular prism is 425 inches².
How to find the lateral surface area of a triangular prism?The isosceles triangular prism is unfolded into the net shown below. Therefore, the lateral surface area of the triangular prism can be found as follows:
The lateral surface area of the triangular prism is the product of the perimeter of the triangle and the height of the prism.
Hence,
lateral surface area of the triangular prism = ph
where,
p = perimeter of the triangleh = height of the prismTherefore,
lateral surface area of the triangular prism = (9 + 9 + 7)17
lateral surface area of the triangular prism = 25 × 17
lateral surface area of the triangular prism = 425 inches²
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Which choice correctly expresses the number below in scientific notation? 0.000611
D. 6.11 * 10 ^ - 5
C. 6.11 * 10 ^ - 3
OE. 6.11 * 10 ^ - 4
OF. 611 * 10 ^ - 6
B. 611 * 10 ^ - 4
A. 61.1 * 10 ^ - 5
0.000611
The scientific notation of the given number is 6.11×10⁻⁴. Therefore, option E is the correct answer.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
The given decimal number is 0.000611.
0.000611 in scientific notation, we get
6.11×10⁻⁴
Therefore, option E is the correct answer.
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Which of the following are square roots to the number below? Check all that apply.  625
A. 625^1/2
B.-625^1/2
C.-25
D.15
E.125
F.25
The square root of 625 is 25 and the square root of 25 is 5. Therefore, option A and F are the correct answers.
What is the square root?The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.
A) [tex]625^{\frac{1}{2}[/tex]
= [tex](25^2)^{\frac{1}{2}[/tex]
= 25
F) 25
= 5
Therefore, option A and F are the correct answers.
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hey can anuyone please help with this question
answer is 25
use the formula to get the rest of the a's
6. Using any method(s), solve △KHP when h=16.1, p=24.9 and k=12.8
The angles of the triangle KHP are P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°, respectively.
How to determine the measures of missing angles in a triangle
In this question we have the case of a triangle where the lengths of three sides are known and measures of angles must be determined. The missing angles can be found by means of law of cosine, whose equations related to the triangle are introduced below:
p² = h² + k² - 2 · h · k · cos P
h² = p² + k² - 2 · p · k · cos H
k² = h² + p² - 2 · h · p · cos K
Where:
h, k, p - SidesH, K, P - AnglesIf we know that h = 16.1, p = 24.9 and k = 12.8, then the measures of the angles are:
cos P = (p² - h² - k²) / (- 2 · h · k)
cos P = (24.9² - 16.1² - 12.8²) / (- 2 · 16.1 · 12.8)
cos P = - 0.478
P ≈ 118.555°
cos H = (h² - p² - k²) / (- 2 · p · k)
cos H = (16.1² - 24.9² - 12.8²) / (- 2 · 24.9 · 12.8)
cos H = 0.823
H ≈ 34.614°
cos K = (k² - h² - p²) / (- 2 · h · p)
cos K = (12.8² - 16.1² - 24.9²) / (- 2 · 16.1 · 24.9)
cos K = 0.892
K ≈ 26.844°
Triangle KHP has the following missing angles: P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°.
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The Empty Number Line
Consider the list of six variable expressions:
1. With your partner, think about where you would place each
expression and sketch your conjecture.
2. Compare your number line with another group's number line.
What is the same? What is different?
An empty number line is a visual tool used to represent numbers and their relative positions. It can be used to compare, order, and perform operations on numbers.
How to learn and understand comparison of numbers?A number with more digits is always greater than a number with fewer digits, according to Rule I.
Rule II states that when two numbers have the same number of digits, we compare the digits starting from the leftmost position until we find an unequal number of digits. Greater numbers are those with more digits.
As far as we are aware, a number with more digits is always greater than one with fewer digits.
The sum of the first two digits is bigger than the sum of the first one.The number with three digits is larger than the number with two or one.A four-digit number has more digits than a three-, two-, or one-digit number.A five-digit number over a four-digit number. Three-digit number, etc.Six digits > Five digits > Four-digit number, etc..To learn more about number line visit:
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Rewrite 15 + (72 + 19) using the Associative Law of Addition.
Answer: (15 + 72) + 19
Explanation: "Associative Law = (a + b) + c = a + (b + c)"
The cost of 2 bottles of water and 3 bags of pretzels is $7.05. The cost of a bag of pretzels is $1.35. Write a system of equations to represent this situation. Solve and explain what the answer means.
(SHOW WORK)
Answer:
The cost of the water is $5.70.
Step-by-step explanation:
7.05-1.35=5.70 You just have to - 7.05 by 1.35
PLEASE HELP ILL GIVE YOU 25 POINTS
The length of side x for the triangle is 5√3.
What is an equilateral triangle?An equilateral triangle is one with equally long sides on both sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. It is also known as an equiangular triangle since each angle is 60 degrees.
Given an equilateral triangle,
length of the side is 10 units,
and a perpendicular is drawn with length x,
so a perpendicular drawn from one of the vertices to the opposite side of an equilateral triangle bisects that side.
we know the angle of the equilateral triangle is 60°,
by the sine function, we can calculate the value of x
sinФ = p/h
p = perpendicular = x
h = hypotenuse = 10
Ф = 60°
sin60 = x/10
x = 10*sin60
x = 10(√3/2)
x = 5√3
Hence the value of x is 5√3.
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Janice drives to the grocery store and
back every Tuesday. The drive home
takes twice as long because of traffic.
If her total travel time is forty-eight
minutes, how long does it take Janice
to drive to the grocery store?
Method 1 Table of Values
Please help, I’ll mark brainlest
The graph of the quadratic function g(x) = - (x - 2)² + 4 on Cartesian plane is shown in the image attached below.
How to analyze and graph a quadratic equation
In this question we find the case of a quadratic equation in vertex form, whose definition is shown below:
y - k = a · (x - h)²
Where:
(h, k) - Coordinates of the vertex.a - Vertex constantThe equation of the axis of symmetry is shown below:
x = h
We can graph by using the coordinates of the vertex and two other points and understanding the vertex constant. Please notice that the parabola has an absolute minimum when vertex constant is positive, otherwise it is an absolute maximum.
First, find the coordinates of the vertex of the parabola:
(h, k) = (2, 4)
Second, determine the nature of the absolute extreme by interpretating the sign of vertex constant:
a = - 1 (The vertex is an absolute maximum)
Third, evaluate the function at two distinct points:
x = 0
g(0) = - (0 - 2)² + 4
g(0) = - (- 2)² + 4
g(0) = 0
x = 4
g(4) = - (4 - 2)² + 4
g(4) = - 2² + 4
g(4) = - 4 + 4
g(4) = 0
Fourth, graph the parabola on Cartesian plane. (Image is done with the help of a graphing tool)
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(Look at picture) thanks! <3
Answer:
Here are the true statements:
Initially, the gas tank has 10 gallons of gasoline. (This is the y-intercept of the equation G(t) = 10 - 2t)It takes 10 hours for the vehicle to run out of gas. (This is the x-intercept of the equation G(t) = 10 - 2t)The rate of gas consumption of the vehicle is 2 gallons per hour. The slope of G(t) represents the rate of fuel consumption of the vehicle.The false statement is:
The G-intercept of G(t) represents the total distance the vehicle traveled. The t-intercept of G(t) represents the time it takes the vehicle to run out of gas. (This is not the case, the y-intercept represents the initial amount of gas and the x-intercept represents the time it takes the vehicle to run out of gas)
Graphing Lines How would you graph 10x-3y=15
Answer:
Step-by-step explanation:
To graph 10x-3y=15, start by rearranging the equation to the slope-intercept form of y = mx + b, where m = the slope and b = the y-intercept. 10x-3y=15 becomes 3y = 10x - 15. Solve for y by dividing both sides by 3 to get y = (10/3)x - 5.
Now that the equation is in the slope-intercept form, draw a graph on a coordinate plane. Start by plotting the y-intercept at (0, -5). Next, use the slope of 10/3 to determine the rise and run of the line. The rise is +10 and the run is +3. Starting at the y-intercept, draw a line that moves up 10 and to the right 3, and continue doing this until you reach the end of the graph. This line is the graph of 10x-3y=15.
Answer:
y=10/3x+5
(0,5), (3,15)
Step-by-step explanation:
First, put the graph in slope-intercept form. We can do this by subtracting 10x from both sides.
-3y=-10x-15
Next, we divide by -3.
y=10/3x+5
If you don't know how to graph an equation with slope-intercept form,
it is in the format of y=mx+b, where m is the slope (in this case, 10/3) and b is the y-intercept (in this case 5, or (0,5)). First graph the y-intercept.
(0,5).
Then implement the slope. Here we would go up by 10 and then go right by 3. This makes our second point (3,15).
Now that we have two points (0,5) and (3,15), just construct your line.
