The percentage discount on the item will be equal to 8%.
What is the percentage?
The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
Price of the item before tax and discount = $17After discount and before tax price is = $15.64The percentage of the discount will be calculated as:-
Percentage discount = ( 17 - 16.64 ) / ( 17 )
Percentage discount= ( 1.36 ) / ( 17 )
Percentage discount = 0.08 x 100 = 8%
Therefore the percentage discount on the item will be equal to 8%.
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If ADAB
ACBA,
ZDAB = 35° and ZCBA = 8x + 3
A
D
x = [?]
X
C
B
Answer:
x=4
Step-by-step explanation:
We are given that the triangles are congruent.
Specifically, the order of the letters gives that the angles ∠DAB and ∠CBA are corresponding parts of the two congruent triangles. Since corresponding parts of congruent triangles are themselves congruent, ∠DAB ≅ ∠CBA. Thus, m∠DAB = m∠CBA.
Given the expressions for the two angles, we can substitute into the equation, and solve for the requested variable.
[tex]m\angle DAB=m\angle CBA\\(35)=(8x+3)\\(35)-3=(8x+3\!\!\!\!\!\!\!\!\!\!{--})-3 \!\!\!\!\!\!\!\!\!\! {--}\\32=8x\\\dfrac {32}{8}=\dfrac {8x\!\!\!\!\!\!\! {-}}{8\!\!\!\! {-}}\\4=x[/tex]
A coin toss is used to determine which team will receive the ball at the beginning of a football game. The Cougars always choose tails in the toss. What are the odds in favor of the Cougars losing the toss in exactly two of three games?
3:5
3:8
5:3
8:3
The odds in favor of the Cougars losing the toss in exactly two of three games is 3:8 option second is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
A coin toss is used to determine which team will receive the ball at the beginning of a football game.
The Cougars always choose tails in the toss.
There will total of 8 cases and in 8 cases there will be three cases in which exactly two heads will come so,
3:8
The cases = {TTT, TTH, THT, HTT, HHT, HTH, HHT, HHH}
Thus, the odds in favor of the Cougars losing the toss in exactly two of three games is 3:8 option second is correct.
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What is the inverse of the function f(x) = 2x +1?
Answer:
y=0.5(x−1)
Step-by-step explanation:
Explanation: To find the inverse of a function, you have to substitute y for x in the equation and simplify to get a normal equation again. In this case, f(x) is y.
y=2x+1
x=2y+1
2y+1=x
2y=x−1
y=0.5(x−1)
Answer
[tex]y=\frac{x-1}{2}[/tex]
Step-by-step explanation:
To find the inverse of a function [tex]f(x)=2x+1[/tex] , we substitute x and y for each other and then solve for y to get a new function.
We rewrite the original function as:
[tex]x=2y+1[/tex]
And then we solve for y:
[tex]x-1=2y[/tex]
[tex]y=\frac{x-1}{2}[/tex]
This is our answer.
The price of one kilograms of apple at a fruit mart is $4.00. If there is a special price this week with a
15% discount, how much do I need to pay if I buy 3 Kg of apple?
Write as an algebraic expression and then simplify if possible :
the sum of x and x+3
Answer:
2x + 3.
Step-by-step explanation:
x + x + 3
= 2x + 3.
Answer:
2x+3
Step-by-step explanation:
x+x+3=2x+3
sum means to add both expression together and we can see there are 2 x's so we can add them and get 2x+3
Simplify the expression.
Answer:
D
Step-by-step explanation:
The first part is How many halves are in 8
2nd part is 16
Thank me later:)
The first part is half of the second part. The first part is 16 and the second part is 8.
What exactly is simplification?Simplifying means making something easier to do or comprehend, as well as making something less difficult.
Let the first part is x, y os the second part, and the no of half times is z then the equation is;
x × y = z
16×(1/2) = 8
Hence,the first part is half of the second part. The first part is 16 and the second part is 8.
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Given triangle ABC, A=105°, a=10cm, b=7cm, find B,C and c.
The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.
What is law of cosine?Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
a² + b² – 2ab cos C = c²
Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.
Then we have
7² + c² – (2 · 7 · c) cos 105° = 10²
c² + 3.62c – 51 = 0
On solving, we have
c = 5.56
Then the angle C will be
10² + 7² – 2 · 7 · 10 · cos C = 5.56²
149 – 140 cos C = 30.91
cos C = 0.8435
C = 32.49°
We know that
∠A + ∠B + ∠C = 180°
105° + ∠B + 32.49° = 180°
∠B = 42.51°
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A car manufacturer has parked some new cars in 2 car parks.In the first car park there are 60 cars in the ratio 1 red car for every 2 blue cars and 3 silver cars.In the second car park there are 80 cars in the ratio 2 blue cars for every 3 red cars and 5 silver cars.
11. How many red cars are there altogether?
12.How many blue cars are there altogether?
13.How many silver cars are there together?
(PLS BE FAST!!)
The number of red car altogether is 34
The number of blue cars altogether is 36
The number of silver car altogether 70
How to use the ratio to find the number of cars?The car manufacturer has parked some cars in 2 car parks .
The first car park has 60 cars.
In the ratio 1 :2:3
Therefore,
red car = 1 / 6 × 60 = 10 cars
blue car = 2 / 6 × 60 = 20 cars
Silver car = 60 - 30 = 30 cars
The second car park has 80 cars.
The ratio are
In the ratio 3:2 5
Therefore,
red cars = 3 / 10 ×80 = 24
blue cars = 2 / 10 × 80 = 16
silver cars = 5 / 10 × 80 = 40
Therefore,
The number of red car altogether is 24 + 10 = 34 red car
The number of blue cars altogether is 20 + 16 = 36 blue cars
The number of silver car altogether is 30 + 40 = 70 silver cars
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Is 50.2 a rational or an irrational number, why?
Answer:
Rational.
Step-by-step explanation:
[tex]\textbf{A rational number is a real number that can be expressed as}~ \dfrac{p}{q},\\\\\textbf{where}~ p~ \textbf{and}~ q~ \textbf{are integers.}\\\\ \boxed{50.2 = \dfrac{502}{10}}\\\\ \textbf{50.2 can be expressed as a ratio of two integers,}~ \textbf{so it is a rational number.}[/tex]
What is y + 1 = -2x - 3 in standard form
[tex]y+1=-2x-3\\y=-2x-4\\y+2x=4[/tex]
Which statement regarding the diagram is true?
m∠WXY = m∠YXZ
m∠WXY < m∠YZX
m∠WXY + m∠YXZ = 180°
m∠WXY + m∠XYZ = 180°
The statement m∠WXY + m∠YXZ = 180° is true.
ExplanationFrom the diagram, m∠WXY > m∠YXZ ⇒ m∠WXY ≠ m∠YXZ. So, option (a) is not true.
From the diagram, m∠WXY > 90° and m∠YZX < 90° ⇒ m∠WXY ≠ m∠YXZ. So, option (b) is not true.
The line WXZ is a straight line so ∠WXY and ∠YXZ are Linear pair. The sum of collinear angles is 180°. So, option (c) is correct.
From the diagram, m∠YXZ ≠ m∠XYZ but since m∠WXY + m∠YXZ = 180° ⇒ m∠WXY + m∠XYZ ≠ 180°. So, option (d) is not correct.
Option (c) is, thus, the correct option.
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Disclaimer: The question was incomplete. Please find the dull content below.
QuestionWhich statement regarding the attached diagram is true?
m∠WXY = m∠YXZ
m∠WXY < m∠YZX
m∠WXY + m∠YXZ = 180°
m∠WXY + m∠XYZ = 180°
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its math please help me
Answer:
460
Step-by-step explanation:
if you look at the values you'll notice the next month is just half their value
7360 / 2 = 3680
3680 / 2 = 1840
1840 / 2 = 920
so
920 / 2 = 460 which should be month 5
Question 4(Multiple Choice Worth 4 points)
(06.06)
A rectangle with width of 5. There is a vertical line that splits rectangle into two sections with different lengths. One length is x the other is 3.
5(x + 3) represents the area of the rectangle above. Which expression below is equivalent by the Distributive Property?
By the distributive property, 5(x+3) is equal to 5x + 15.
5.)(2x + 8) - (4y + 1)
6.)-5x * (3x^2 - 2x - 1)
5) 2x + 8 - 4y - 1 = 2x - 4y + 7
6) -5x(3x² - 2x - 1) = -15x³ + 10x² + 5x
The volume of the cube is given as V= x³, where x is the side length of the cube. Find the domain of the volume of
the cube.
Answer: None of the choices
Step-by-step explanation:
1. It couldn't be integers (whole numbers positive or negative), because a cube couldn't have a negative volume.
2. It could be natural numbers, but the problem is, that a volume could have decimal values, for example, 3.62 meters cubed which a natural number doesn't support.
3. Set of whole numbers is the same as integers, so it can't be that.
4. None of the choices, which in my opinion is the correct one.
I'm not sure it is correct, but I hope I helped you!
Point p has coordinates (-4,-2) and point q has coordinates (4,3) calculate the shortest distance between P and Q. Give your answer to 1 decimal place
Answer:
distance = 9.4 units
Step-by-step explanation:
* using the distance formula *
d =
[tex] \sqrt{(x2 - x1 )^{2} + (y2 - y1)^{2} } [/tex]
[tex] \sqrt{( - 4 - 4) ^{2} + ( - 2 - 3) ^{2} } [/tex]
= 9.4 units
Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?
What needs to be corrected in this construction of a line parallel to line AB passing through C?
A and B endpoints of line segment is intersected at point D with a transversal. D as center, arc 1 is drawn above intersecting transversal at point E, and at point F on the segment. E as center, arc 2 is drawn intersecting the transversal at point C.
A.
The first arc should pass through C.
B.
The first arc should be centered at C.
C.
The second arc should be centered at C.
D.
The second arc should cross the first arc.
E.
The second arc should be centered at F.
The option that needs to be corrected in this construction of a line parallel to line AB passing through C is C: the second arc should be centered at C.
Why should the second arc be centered at C?The second arc should be centered at C because as it crosses passing through Line C, it is seen that it was not touching or intersecting AB and so one can say that it is parallel to it.
Looking at the other lines, we will see that they are all touching AB and are not running parallel to it.
Hence, The option that needs to be corrected in this construction of a line parallel to line AB passing through C is C: the second arc should be centered at C.
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in a test out of 40,the marks of 15 students were 31,18,6,26,36,24,23,14,28,28,32,9,11,22,21.
a.calculate the mean mark for the test
b.express the mean mark as a percentage
Answer:
a. The mean mark for the test was 20.667.
b. The mean mark as a percentage is 51.6%.
Step-by-step explanation:
a. Calculate the mean mark for the test.
Add all of the scores from each student. [tex]31+18+6+26+36+24+23+14+28+28+32+9+11+22+2=310[/tex]Divide the sum by the amount of students who took the test.[tex]310/15=20.667[/tex]Therefore, the mean mark for the test was 20.667.b. Express the mean mark as a percentage.
Put mean mark and total possible marks in fraction form.[tex]\frac{20.667}{40}[/tex]Divide the numerator by the denominator (essentially changing the fraction into the decimal form). [tex]20.667/40=0.516[/tex]Multiply the quotient by 100. [tex]0.516*100=51.6[/tex]Therefore, the mean mark as a percentage is 51.6%Work out the equation of line B. Give your answer in the form y = mx + c, where m and care integers or fractions in their simplest forms. Work out the equation of line B. Give your answer in the form y = mx + c , where m and care integers or fractions in their simplest forms .
Answer:
y = -3x + 1
Step-by-step explanation:
the line crosses the y-axis at (0,1) then c = 1
The points (0,1) and (1,-2) lie on the line then
m = slope = [(-2)-1]÷(1-0) = [-3]÷(1) = -3÷1 = -3
Therefore,
The equation of the line is : y = -3x + 1
Find the surface area for the rectangular prism below.
Please answer with steps! :)
how do you solve this pls
Step-by-step explanation:
The equation of a exponential function is
[tex]a \times (b) {}^{x} [/tex]
where a is the y value of the y intercept, b is the constant rate of change.
Here the y intercept is (0,4), the y value of the y intercept is 4.
So a=4
The graph passes through point (1,2) so
[tex]h(x) = 4 \times b {}^{x} [/tex]
Plug in 1 for x, 2 for h(x)
[tex]2 = 4 \times {b}^{1} [/tex]
Anything to the first power is itself so
[tex]2 = 4 \times b[/tex]
Isolate b.
[tex] \frac{1}{2} = b[/tex]
So our function is
[tex]4 \times ( \frac{1}{2} ) {}^{x} [/tex]
Answer:
[tex]h(x)=4\left(\dfrac{1}{2}\right)^x[/tex]
Step-by-step explanation:
Exponential Function
General form of an exponential function:
[tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form.x is the independent variable.y is the dependent variable.From inspection of the given diagram, the defined points on the curve are:
(0, 4)(1, 2)As one of the defined points is the y-intercept (0, 4) then:
[tex]\implies a=4[/tex]
Substitute the found value of a and the point (1, 2) into the general form of an exponential function and solve for b:
[tex]\begin{aligned}h(x)=ab^x & \\\implies h(1)=4b^1 & = 2\\4b & = 2\\b & = \dfrac{2}{4}\\b & =\dfrac{1}{2} \end{aligned}[/tex]
Finally, substitute the found values of a and b into the general formula to complete the equation for the function h(x):
[tex]\implies h(x)=4\left(\dfrac{1}{2}\right)^x[/tex]
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Which expression is equivalent to
i need help asap
Expressions - Part 1
16÷(2+1/2)² ?
From the given expression, the equivalent expression would be 64/25.
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
Given;
16÷(2+1/2)²
16÷(5/2)²
16÷(25/4)
16 x (4/25)
= 64 / 25
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Give your answer in the form y = mx + c , where m and care integers or fractions in their simplest forms.
Find the general term for the sequence 6, 9, 12, 15, .... n + 5 3 n + 3 4 n + 2 6 n + 3
The general term for the arithmetic sequence is aₙ = 3 + 3n
How to find the general term of an arithmetic sequence?The general term of an arithmetic sequence is as follows:
aₙ = a + (n - 1)d
where
a = first termd = common differencen = number of termsTherefore,
a = 6
d = 9 - 6 = 3
aₙ = 6 + (n - 1)3
aₙ = 6 + 3n - 3
aₙ = 3 + 3n
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(a) The average velocity of 25 taxies is 40 km/hr and the average velocity of 35 trucks is 30 km/hr. Find the combined average velocity of both types of vehicles. ( a ) The average velocity of 25 taxies is 40 km / hr and the average velocity of 35 trucks is 30 km / hr . Find the combined average velocity of both types of vehicles.
Answer:
10hr/m because the average velocity is divided by number
Find the coordinates of the intersection of the diagonals of parallelogram HJKL with the given vertices: H(-1, 4), J(3, 3), K(3, -2), L(-1, -1). (Drawing a picture helps!)
thank you!
Answer:
(1, 1)
Step-by-step explanation:
Given vertices of the parallelogram:
H = (-1, 4)J = (3, 3)K = (3, -2)L = (-1, -1)Therefore the parallel sides are:
[tex]\sf \overline{HJ} \parallel \overline{LK}\:\: \textsf{ and }\:\: \overline{LK} \parallel \overline{HL}[/tex]
Therefore, the diagonals of the parallelogram are:
[tex]\sf \overline{LJ} \:\: \textsf{ and }\:\:\overline{HK}[/tex]
To find the coordinates of the intersection of the diagonals, either:
draw a diagram (see attached) and determine the point of intersection of the diagonals from the diagram, ordetermine the midpoint of either diagonal (as the diagonals of a parallelogram bisect each other, i.e. divide into 2 equal parts).Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
To find the midpoint of diagonal LJ, define the endpoints:
[tex](x_1,y_1)=L=(-1, -1)[/tex][tex](x_2,y_2)=J=(3,3)[/tex]Substitute the defined endpoints into the formula and solve:
[tex]\begin{aligned} \implies \textsf{Midpoint of LJ} & =\left(\dfrac{3-1}{2},\dfrac{3-1}{2}\right)\\ & =\left(\dfrac{2}{2},\dfrac{2}{2}\right)\\ & =\left(1,1\right) \end{aligned}[/tex]
Therefore, the coordinates off the intersection of the diagonals of parallelogram HJKL are (1, 1).
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Check the order
HJKLMeans H,J and K,L are adjacent coordinates
Hence HK and JL are diagonals
We know diagonals of a parallelogram bisect each other so midpoint of any diagonal would be the intersection point
Midpoint of HK
(x1+x2/2,y1+y2/2)(-1+3/2,4-2/2)(2/2,2/2)(1,1)Which pair of functions are inverses of each other?
The pair of functions are inverse of each other is, [tex]\rm f(x)=5x-9 \ and \ g(x) = \rm \frac{x-9}{5}[/tex].Option C is correct.
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
On checking the function one by one we get that option c satisfies the conditions;
[tex]\rm f(x)=5x-9[/tex]
Change the coefficient;
y=f(x) as x=f(y)
The function is written as;
y=5x-9
x=5y-9
Simply the function;
[tex]\rm y = \frac{x+9}{5} \\\\ y=g(x) \\\\\ g(x) = \frac{x+9}{5}[/tex]
The pair of functions are inverses of each other is,[tex]\rm f(x)=5x-9 \ and \ g(x) = \rm \frac{x-9}{5}[/tex]
Hence option C is correct.
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