Answer:
1. [tex]\bold{S=f(P) = 0.07P}[/tex]
2. x = 16
3. Part 1: P is the independent variable and S is the dependent variable.
Part 2: x is the independent variable and y is the dependent variable.
Step-by-step explanation:
1. To write the function notation for:
Sales tax is 7% of the total price.
Let the total price be [tex]P[/tex].
And sales tax be [tex]S[/tex].
As per the given statement:
[tex]S = 7\% \ of\ P\\\Rightarrow S =\dfrac{7}{100}P\\\Rightarrow S=0.07P[/tex]
Writing it in the function notation:
[tex]\bold{S=f(P) = 0.07P}[/tex]
2. To find the value of x such that [tex]f(x) = 14[/tex] and
[tex]f(x) = \dfrac{1}4x + 10[/tex]
Putting the value of [tex]f(x) = 14[/tex]
[tex]14 = \dfrac{1}4x + 10\\\Rightarrow \dfrac{1}4x =14-10\\\Rightarrow \dfrac{1}4x =4\\\Rightarrow x =4\times 4\\\Rightarrow \bold{x =16}[/tex]
3. To find the dependent and independent variable.
Independent variables are those whose value is not dependent on the other variable's values.
Dependent variables are dependent on the value of other variables.
In question 1:
[tex]\bold{S=f(P) = 0.07P}[/tex]
P is the independent variable.
S is the dependent variable.
In question 2:
If we write it as follows:
[tex]y=f(x) = \dfrac{1}4x + 10[/tex]
x is the independent variable and y is the dependent variable.
HELLLPPPP I need a explication on whether or not these angle relationships are possible
Answer:
Step-by-step explanation:
5x+30 is a corresponding angle with 4x-9 so set them equal to each other. 4x-9+2x+3 will equal 180
Answer:
no, the values would be above 180º
Step-by-step explanation:
if...
(4x - 9) + (2x + 3) + y = 180
(5x + 30) + y = 180
then...
(4x - 9) + (2x + 3) = 5x + 30
so...
6x - 6 = 5x + 30
x = 36
plug it in.
4(36) - 9 = 135
2(36) + 3 = 75
already you can see the sum of these two angles surpasses 180 which is not possible for a triangle.
Please answer this question now
Answer:
If it's not too late by now, the answer is 19.9 [tex]mm^{2}[/tex]
What is the volume in cubic inches of the solid figure, rounded to the nearest cubic inch? Do not use units or commas in your answer.
Answer:
1131 cubic inches.
Step-by-step explanation:
The front side of the figure contains a rectangle and a semicircle.
Area of rectangle is
[tex]A_1=length\times breadth[/tex]
[tex]A_1=11\times 12[/tex]
[tex]A_1=132\text{ in}^2[/tex]
Radius of semicircle is
[tex]r=17-11=6\text{ in}[/tex]
Area of semicircle is
[tex]A_2=\dfrac{1}{2}\pi r^2[/tex]
[tex]A_2=\dfrac{1}{2}\pi (6)^2[/tex]
[tex]A_2\approx 56.55[/tex]
Area of front side is
[tex]A=A_1+A_2=132+56.55=188.55\text{ in}^2[/tex]
Let front side is the base of prism and height is 6 in. So, volume of given figure is
[tex]V=\text{Base area}\times height[/tex]
[tex]V=188.55\times 6[/tex]
[tex]V=1131.3[/tex]
[tex]V\approx 1131\text{ in}^3[/tex]
Therefore, the required volume is 1131 cubic inches.
The image shows a geometric representation of the function f(x) = x2 + 2x + 3 written in standard form.What is this function written in vertex form?
Answer:
[tex]f(x) = (x+1)^2 +2[/tex]
Step-by-step explanation:
Well you complete the square and get,
[tex]x^2 + 2x + 1 ^2 - 1^2 +3[/tex]
Then you use the binomial formula to get,
(x + 1)^2 + 2
Thus,
f(x) = x^2 + 2x + 3 is f(x) = (x + 1)^2 + 2.
Hope this helps :)
Carter bought a bear and paid for a football uniform. The total cost was $38.50. Write and solve an equation to find the cost, x, of buying a bear.
Answer:
Equation:- [tex]x + y = 38.50[/tex]
Solution of x:- [tex]x = 38.50 - y[/tex]
Step-by-step explanation:
Given
Total Purchase = $38.50
Required
Determine the equation for finding the cost of a bear
From the question; we understand that the cost of 1 bear is represented with x
Solving further; by representing the cost of 1 football uniform with y
So;
[tex]1\ bear + 1\ uniform = 38.50[/tex]
Substitute x for 1 bear and y for 1 uniform to give us an equation
[tex]x + y = 38.50[/tex]
Solving for x (Subtract y from both sides)
[tex]x +y - y = 38.50 - y[/tex]
[tex]x = 38.50 - y[/tex]
The equation can't be solved further
How do you solve -6(4d+5)+7d=-2d
Answer:
d = -2Step-by-step explanation:
-6(4d + 5) + 7d = -2d -24d - 30 + 7d = - 2d -17d - 30 = -2d+2d+30 +2d+30
-15d = 30÷(-15) ÷(-15)
d = -2my mistake it's actually d= -30/19 sometimes I forget you put them in fractions
Find the value of X and Y in the following parallelogram.AD =X+8 D=2y +13 C=16-x CB=5y+4 AB=o
Answer:
The answer is below
Step-by-step explanation:
AD = X + 8 ∠D = 2y +13 ∠C = 16 - x CB = 5y+4
In a parallelogram, consecutive angles are supplementary and opposite sides are equal.
Therefore for parallelogram ABCD, AB = CD, CB = AD
Since AD = CB (opposite sides of a parallelogram are equal):
x + 8 = 5y + 4
5y - x = 8 - 4
5y - x = 4 (1)
∠C + ∠D= 180° (consecutive angles of a parallelogram are supplementary). Therefore:
16 - x + 2y + 13 = 180
2y - x + 29 = 180
2y - x = 180 -29
2y - x = 151 (2)
To find x and y, subtract equation 1 from equation 2:
3y = -147
y = -49
Put y = -49 in equation 2
2(-49) - x = 151
x = -98 - 151
x = -249
Which of the following is a rational number?
Answer:
The answer is B
Answer: B
Step-by-step explanation:
In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.
All you need to do is find which of following is a whole number or integer.
Given that
7
x
−
2
y
=
35
Find
y
when
x
=
−
9
Answer:
y = - 49
Step-by-step explanation:
Given
7x - 2y = 35 ← substitute x = - 9 into the equation
7(- 9) - 2y = 35, that is
- 63 - 2y = 35 ( add 63 to both sides )
- 2y = 98 ( divide both sides by - 2 )
y = - 49
Answer:
[tex]\boxed{y = -49}[/tex]
Step-by-step explanation:
=> [tex]7x-2y = 25[/tex]
Given that x = -9
=> [tex]7(-9)-2y = 35[/tex]
=> [tex]-63 -2y = 35[/tex]
Adding 63 to both sides
=> [tex]-2y = 35+63[/tex]
=> [tex]-2y = 98[/tex]
Dividing both sides by -2
=> [tex]y = 98/-2[/tex]
=> [tex]y = -49[/tex]
The area of a circle is 49\pi square units. What is the radius of the circle, in units?
Answer:
7
Step-by-step explanation:
The formula to find the area of a circle is pi*r^2.
We were given 49pi. This means that 49=r^2.
The square root of 49 is 7.
So our radius is 7.
Hope this helps! <3
Select steps that could be used to solve the equation 1 + 3x = -x + 4.
A. add x, subtract 1, divide by 4
B. add x, subtract 4, divide by 4
C. subtract 3x, subtract 4, divide by 4
D. subtract 3x, subtract 4, divide by -4
E. subtract 1, add x, divide by 4
Answer :
A. add x, subtract 1, divide by 4
D. subtract 3x, subtract 4, divide by -4
Step-by-step-explanation : Further explanation
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\1+3x-1=-x+4-1\\Simplify\\3x=-x+3\\\mathrm{Add\:}x\mathrm{\:to\:both\:sides}\\3x+x=-x+3+x\\Simplify\\4x=3\\\mathrm{Divide\:both\:sides\:by\:}4\\\frac{4x}{4}=\frac{3}{4}\\x=\frac{3}{4}[/tex]
I hope it helps:)
4^3/4 x 2^x = 16^2/5
work out the exact value of x
Answer:
x = 1/10Step-by-step explanation:
[tex] {4}^{ \frac{3}{4} } \times {2}^{x} = {16}^{ \frac{2}{5} } [/tex]
In order to solve the equation express each of the terms in the same base .
in this case we express each of the terms in base 2
That's
[tex] {4}^{ \frac{3}{4} } = {2}^{2 \times \frac{3}{4} } = {2}^{ \frac{3}{2} } [/tex]
And
[tex] {16}^{ \frac{2}{5} } = {2}^{4 \times \frac{2}{5} } = {2}^{ \frac{8}{5} } [/tex]
So we have
[tex] {2}^{ \frac{3}{2} } \times {2}^{x} = {2}^{ \frac{8}{5} } [/tex]
Since the left side are in the same base and are multiplying, we add the exponents
[tex] {2}^{ \frac{3}{2} + x } = {2}^{ \frac{8}{5} } [/tex]
Since they have the same base we can equate them
That's
[tex] \frac{3}{2} + x = \frac{8}{5} [/tex]
[tex]x = \frac{8}{5} - \frac{3}{2} [/tex]
[tex]x = \frac{1}{10} [/tex]
Hope this helps you
I SHALL NAME THEE BRAINLIEST! (: Use Associative and Commutative Properties to combine like terms. Simplify the expression. Plz help me. -5X + 8X - 4 -5Y + 3 - 6Y + 2Y + 4 6 + X - 5 + 3X + 8 3B - B + 7 + 4B
Answer
6B+7X-9Y+19
Step-by-step explanation:
greatly appreciate help :) picture below
Answer:
The answer is None.
Step-by-step explanation:
I took the test on FLVS and I got the answer right.
I hope this helps. I am sorry if you get this wrong.
Answer:
None. Say the obtuse angle is 100 degrees. Since the sum of all angles in a triangle cannot be bigger than 180, it's not possible because 195 (100+95) is greater than 180 degrees.
Step-by-step explanation:
HIJ has coordinates H(-4,3), I7(-2, 0), and J (-4,1). Graph the triangle and its
translation 3 units to the right and 2 units down. What are the coordinates of J'?
Answer:
J'(-1; -1)Step-by-step explanation:
Look at the picture.
x - horizontal
y - vertical
left, right - horizontal
n units to the right: x + n
n units to the left: x - n
up, down - vertical
n units up: y + n
n units down: y - n
J(-4; 1)
3 units to the right: -4 + 3 = -1
2 units down: 1 - 2 = -1
J'(-1; -1)
What is x, if the volume of the cylinder is 768 pi cm3? Do not use units or commas in your answer.
Answer:
48
Step-by-step explanation:
We have that the volume of a cylinder is given by:
V = pi * (r ^ 2) * h
In this case we know the diameter, we know that the radius is half the diameter like this:
r = d / 2
r = 8/2
r = 4
Now we know that the V equals 768 pi
we replace and we have:
768 * pi = pi * (4 ^ 2) * h
768 = 16 * h
h = 768/16
h = 48
Therefore the value of x would be 48 cm
can someone please help me?
Answer:
-1Option C is the correct option.
Step-by-step explanation:
Let the points be A and B
A ( -2 , 7 ) -----> ( x1 , y1 )
B ( 2 , 3 )-------> ( x2 , y2)
Now, let's find the slope:
Slope = [tex] \frac{y2 - y1}{x2 - x1} [/tex]
plug the values
[tex] = \frac{3 - 7}{2 - ( - 2)} [/tex]
Calculate the difference
[tex] = \frac{ - 4}{2 - (2)} [/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
[tex] = \frac{ - 4}{2 + 2} [/tex]
Add the numbers
[tex] = \frac{ - 4}{4} [/tex]
Any expression divided by its opposite equals -1
[tex] = - 1[/tex]
Hope this helps..
Best regards!!
How much material would you need to fill the following cylinder? Radius 13 in. and Height 9 in.
39π in3
117π in3
1053π in3
1521π in3
Answer:
Volume of the cylinder is 1521π in³
Step-by-step explanation:
Hello,
To find the volume of a cylinder, we need the know the formula used for calculating it.
Volume of cylinder = πr²h
r = radius
h = height
Data,
Radius = 13in
Height = 9in
Volume of a cylinder = πr²h
Now we need to substitute the values into the formula
Volume of a cylinder = π × 13² × 9
Volume of a cylinder = 169 × 9π
Volume of a cylinder = 1521π in³
Therefore the volume of the cylinder is 1521π in³
Answer:
1521
Step-by-step explanation:
What is the range of the function represented by this graph?
Answer: The range is real numbers less than 1
[1, -∞)
Step-by-step explanation: The range is all the y-values. The top of the parabola (vertex) is at 1 above the x-axis. You have to look at the scale and notice that the scale is in increments of 2, The vertex is between 0 and 2. The parabola extends down to negative infinity.
Answer:
y < 1
(the < has a line underneath it)
Step-by-step explanation:
Given: AB ∥ DC , m CB =62°, m∠DAB=104° Find: m∠DEA, m∠ADB
Answer:
m∠DEA = 62°
m∠ADB (arc) = 194°
Angle ∠ADB = 21°.
Step-by-step explanation:
The given information are;
[tex]AB\left | \right |DC[/tex], m CB (arc) = 62°, m∠DAB (arc) = 104°
arc∠BCD = 360° - 104° = 256°
m DC (arc) = arc∠BCD - arc CB = 256° - 62° (Sum of angles)
Therefore DC (arc) = 194°
m DA ≅ m CB = 62° (Parallel lines congruent arc theorem. Arc between two parallel lines)
m∠DEA = 1/2×(arc DA + arc CB) = 1/2×(62° + 62°) =62°
m∠DEA = 62°
Arc AB = m∠DAB (arc) - m DA = 104° - 62° = 42°
m∠ADB (arc) = 360 - m∠DAB (arc) - m CB (arc) (Sum of angles around a circle or point)
∴ m∠ADB (arc) = 360 - 104 - 62 = 194°
m∠ADB (arc) = 194°
Angle ADB = subtended by arc AB = ∴1/2×arc AB
Angle ∠ADB = 42/2 = 21°.
Angle = 21°
Two trains 150 miles apart are traveling toward each other along the same track. The first train goes 60 miles per hour; the second train rushes along at 90 miles per hour. A fly is hovering just above the nose of the first train. It buzzes from the first train to the second train, turns around immediately, flies back to the first train, and turns around again. It goes on flying back and forth between the two trains until they collide. If the fly's speed is 120 miles per hour, how far will it travel?
Answer:
120 miles
Step-by-step explanation:
Distance = 150 miles
train 1 = 60 mph
train 2 = 90 mph
directions of trains = towards each other
Time to meet = 150/(60+90) = 150 miles / 150 mph = 1 hour
Speed of fly = 120 mph
Since fly has been flying for one hour, it travelled 120 miles.
The length of the room is 2½ times the breadth. The perimeter of the room is 70 m. What are the length and breadth of the room.
Answer:
Length = 25 cmBreadth = 10 cmStep-by-step explanation:
Let breadth of the room be 'x'
Let length of the room be '[tex]2 \frac{1}{2} x = \frac{5}{2} = 2.5 \: x[/tex]'
Perimeter ( P ) = 70 cm
Now, let's find the breadth of the room 'x '
Perimeter of rectangle = [tex]2(l + b)[/tex]
plug the values
[tex]70 = 2(2.5x + x)[/tex]
Collect the like terms
[tex]70 = 2 \times 3.5x[/tex]
Calculate the product
[tex]70 = 7x[/tex]
Swap the sides of the equation
[tex]7x = 70[/tex]
Divide both sides of the equation by 7
[tex] \frac{7x}{7} = \frac{70}{7} [/tex]
Calculate
[tex]x = 10 \: cm[/tex]
Breadth = 10 cm
Now, Let's find the length of the room ' 2.5x '
Length of the room = [tex]2.5x[/tex]
Plug the value of X
[tex] = 2.5 \times 10[/tex]
Calculate the product
[tex] = 25 \: cm[/tex]
Thus , The length and breadth of the room is 25 cm and 10 cm respectively.
Hope this helps..
Best regards!!
Amanda rides her bike due east for 10 km. Angela rides her bike 20 degrees south of east 12 km. How far apart are Amanda and Angela? (Round to the nearest tenth).
Answer:
Distance between Amanda and Angela (c) = 4.30 km (Approx)
Step-by-step explanation:
Given:
Amanda rides (a) = 10 km
Angela rides (b) = 12 km
Angel between them = 20°
Find:
Distance between Amanda and Angela (c)
Computation:
Using law of cosines:
c² = a² + b² - 2abCosФ
c² = 10² + 12² - 2(10)(12)Cos20°
c² = 100 + 144 - 2(10)(12)(0.9397)
c² = 244 - 225.528
c² = 18.472
c = 4.2979
Distance between Amanda and Angela (c) = 4.30 km (Approx)
I need the answer and maybe someone can tell me how to do it? Please and Thanks!! :))
Answer:
83
Step-by-step explanation:
The 126 angle is an exterior angle of the triangle.
The 43 and x angles are the two remote interior angles of the 126 angle.
Theorem:
The measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles.
x + 43 = 126
x = 83
Answer:
x = 83
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
126 = x+43
Subtract 43 from each side
126-43 = x+43-43
83 = x
There were 56 females and 84 males present at the high school pep rally. Find the ratio of males to the total number of people present. Express as a simplified ratio.
Answer:
3:5 or 3/5
Step-by-step explanation:
We know that there are -->
56 Females
84 Males
We need to find the total amt. of ppl
56 + 84 = 140
Males/140 --> Plug 84 in => 84/140
Since it wants simplified, divide both by 7 as 7 is a factor of both -->
12/20 --> Divide by 4
3/5 => This is the most simplified we can get and -->
thus, our answer is 3:5 or 3/5
Hope this helps!
i don't get division at all i did but i moved a lot of places and i forget things
Answer:
What is the question
Step-by-step explanation:
____________________________________________________________________
Bennett brings 3 gallons of water to his football game. His teammate, Jordan, brings 3 times as many gallons of water as Bennett. If one gallon of water contains 128 fluid ounces, how many ounces of water did Bennett and Jordan bring to their football game?
Answer:
It could be 768 fl. oz I think?
Step-by-step explanation:
Bennett has 3 gallons of water and Jordan has 3 times as many gallons as bennett
Let's calculate how many gallons do Jordan has
3*3 = 9Jordan has 9 gallons of water
every gallon of water contains 128 fluid ounces
BenettBenett has 3 gallons
so the fluid ounces are given by : 3*128=384
Benett has 384 ounces
JordanJordan has 9 gallons so 9*128 = 1152
so Jordan has 1152 fluid ounces
here are some facts about units of length 18 ft=____yd and 3 ft= ___in
Answer:
18 ft = 6 yds
3 ft = 36 inches
Step-by-step explanation:
We know that 3 ft = 1 yd
Divide 18 ft by 3
18 ft /3 ft = 6 yds
We know that 1 ft = 12 inches
3 ft * 12 inches /ft = 36 inches
Answer:
[tex]\large \boxed{18 feet = 6 yards}[/tex]
[tex]\large \boxed{3 feet = 36 inches}[/tex]
Step-by-step explanation:
1 foot = 1/3 of a yard
Multiply both sides of this equation by 18
[tex]\large \boxed{18 feet = 6 yards}[/tex]
1 foot = 12 inches
Multiply both sides of the equation by 3
[tex]\large \boxed{3 feet = 36 inches}[/tex]
Hope this helps!
Find the value of each trigonometric ratio.
Answer:
12 / 37 (or:=0.324324324...)
Step-by-step explanation:
Sinθ = opposite / hypotenuse
Hence
sinA = 12 / 37
(=0.324324324...)
Answer:
A = 19
Step-by-step explanation:
sin A = opp/hyp
sin A = 12/37
A = sin- ¹ 12/37
A= 18.92 or 19
What is the actual distance, in miles, between two cities that are 3 inches apart on the map?
Answer:
Step-by-step explanation: to answer this question I need to know what 1 inch to a mile is. like every one inch= 12 miles