Final answer:
The equation that shows the value on the gift card over time is: Value on gift card = Initial value - Total amount spent.
Explanation:
The equation that shows the value on the gift card over time is: Value on gift card = Initial value - Total amount spent.
Since the initial value of the gift card is $50 and each day a drink costs $3, the equation can be written as: Value on gift card = 50 - 3x, where x represents the number of days.
This equation will give you the value remaining on the gift card after x days of buying a $3 drink.
The length of a rectangle is 1 ft more than twice the width, and the area of the rectangle is 66ft. Find the dimensions of the rectangle
Answer:
12 ft long by 5½ ft wide
Step-by-step explanation:
1. Set up an expression for the area.
Let l = the length of the rectangle
and w = the width. Then
2w = twice the width and
2w + 1 = 1 more than twice the width. Then
l = 2w + 1
The formula for the area of a rectangle is
A = length × width
A = lw
66 = (2w +1)w
66 = 2w² + w
2w² + w - 66 = 0
2. Solve the quadratic for w
2w² + w - 66 = 0
(a) Multiply the first and last terms
2 × (-66) = -132
(b) List all the factors of 132
1 132
2 66
3 42
4 33
6 22
11 12
(c) Find a pair of factors whose product is -132 and whose sum is 1.
After some trial and error, you will choose -11 and +12,
-11 × 12 = -132 and -11 + 12 = 1.
(d) Rewrite w as -11w + 12w
2w² - 11w + 12w - 66 = 0
(e) Factor by grouping
w(2w - 11) + 6(2w - 11) = 0
(w + 6)(2w - 11) = 0
(f) Use the zero product theorem
w + 6 = 0 2w - 11 = 0
w = -6 2w = 11
w = 5½
We reject the negative answer, so w = 5½ ft
3. Calculate l
l = 2w + 1 = 2 × 5½ + 1 = 11 + 1 = 12 ft
The rectangle is 12 ft long and 5½ ft wide.
The dimensions of the rectangle are length = 12 ft and wide = 5½ ft
What is an area of a rectangle?
The area of the triangle is the product f length and breath.
Calculation:-
Let l = the length of the rectangle
w = the width.
According to the question: length l = 2w + 1
The area of a rectangle is
⇒ 66 = (2w +1)w
⇒ 66 = 2w² + w
⇒ 2w² + w - 66 = 0
wide=5.5 ft = 5½ ft
lenght =12 ft
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Solve the equation.1/8+c=4/5
Answer:
27/40
Step-by-step explanation:
We want to isolate the variable c. In order to do so, we have to subtract 1/8 from both sides. Then, on the left side, we have c, and on the right side we have 4/5-1/8. The fractions 4/5 and 1/8 do not have a common denominator, so we need to multiply 4/5 by 8/8 and 1/8 by 5/5 in order to reach a common denominator of 40 (5 and 8's least common multiple). Then, we get 32/40-5/40, or 27/40.
Side note: we are able to multiply by 8/8 and 5/5 because both of those fractions equal 1.
1. Identify the vertex and the y-intercept of the graph of the function y=-2(x+ 2)+2.
Answer:
Please let me know if your quadratic is [tex]y=-2(x+2)^2+2[/tex].
And if so your vertex is (-2,2) and your y-intercept is (0,-6)
Step-by-step explanation:
It says vertex so I'm thinking you meant [tex]y=-2(x+2)^2+2[/tex]. Please correct me if I'm wrong.
The vertex form of a quadratic is [tex]y=a(x-h)^2+k[/tex]. It is called that because it tells you the vertex (h,k).
So if you compare the two forms you should see -h=2 while k=2.
-h=2 implies h=-2.
So the vertex is (h,k)=(-2,2).
To find the y-intercept, set x=0 and find y.
[tex]y=-2(0+2)^2+2[/tex]
[tex]y=-2(2)^2+2[/tex]
[tex]y=-2(4)+2[/tex]
[tex]y=-8+2[/tex]
[tex]y=-6[/tex]
So the y-intercept is (0,-6).
Solve the equation 5x + (−2) = 6x + 4 using the algebra tiles. What tiles need to be added to both sides to remove the smaller x-coefficient? What tiles need to be added to both sides to remove the constant from the right side of the equation?
Answer:
a) Adding -5x on both sides of the equation to remove the smaller x-coefficient
b) Adding -4 on both sides will remove the constant from the right side of the equation
Step-by-step explanation:
Given equation:
5x + (−2) = 6x + 4
a) What tiles need to be added to both sides to remove the smaller x-coefficient?
Smaller x-coefficient is 5x to remove the smaller x-coefficient
So, Adding -5x on both sides of the equation to remove the smaller x-coefficient
b) What tiles need to be added to both sides to remove the constant from the right side of the equation?
the constant on right side is 4
Adding -4 on both sides will remove the constant from the right side of the equation
Answer:
What tiles need to be added to both sides to remove the smaller x-coefficient?
✔ 5 negative x-tiles
What tiles need to be added to both sides to remove the constant from the right side of the equation?
✔ 4 negative unit tiles
What is the solution?
✔ x = –6
(0201 LC)
Melissa made some chocolate pudding For every 3 cups of chocolate, she added 7 cups of milk. The ratio of chocolate to milk in Melissa's chocolate pudding is
Answer:
its c
3 : 7
3/7
Step-by-step explanation:
Answer:
3/7
Ratio is explained in sentence: For every 3 cups of chocolate, she added 7 cups of milk.
This is another way to say/show a ratio. It is also said as: 3:7, 3/7, and 3 to 7
which point is the image P
Answer:
(-5,2)
Step-by-step explanation:
It alogns with negative 5 on the X axis, and positive 2 on the Y axis, meaning its written as (-5,2)
erika raked 5% more leaves than adam raked. erika raked 357liters of leaves. how many liters of leaves did adam rake?
Erica raked 5% more, so she racked 1.05 times as much.
Divide the amount she racked by the 1.05:
357 / 1.05 = 340
Adam racked 340 liters.
Write an equation of the line with the given slope and y-ntercept -5,b-4
Answer:
y = - 5x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
here m = - 5 and b = - 4, hence
y = - 5x - 4 ← equation of line
In circle A, ∠BAE ≅ ∠DAE.
What is the value of x?
14
17
27
34
Answer:
x=17
Step-by-step explanation:
In circle A, ∠BAE ≅ ∠DAE.
∠BAE = 3x-24
∠DAE = x+10
According to the given condition:
∠BAE ≅ ∠DAE.
3x-24 = x+10
Combine the like terms:
3x-x=10+24
2x=34
Divide both the sides by 2
2x/2 = 34/2
x=17
Therefore the value of x = 17
The correct option is 17....
Answer:
The answer is 17 units on edg
Step-by-step explanation:
9 cu yd 113 cu in - 4 cu ft 129 cu in
Answer:
=8 yd³ 22 ft³ 1712 in³
Step-by-step explanation:
To perform the indicated operation we need to convert the given measurements of volume to common units.
1 yd = 3 ft
1 yd³=27ft³
1 ft³=1728 in³
Thus 9 yd³=(27×9)ft³
=243 ft³
113 in³ into ft= 113/1728
9 yd³ 113 in³= 243 113/1728 ft³
4 ft³ 129 in³= 4 129/1728 ft³ = 4 43/576 ft³
Performing the operation given in the equation:
243 113/1728 ft³ - 4 43/576 ft³ = 238 1712/1728 ft³
238 ft³= 8 yd³ 22 ft³ + (1712/1728) × 1728
=8 yd³ 22 ft³ 1712 in³
How do you express 140 degrees in radians? Round to nearest tenth
Answer:
2.4 rad
Step-by-step explanation:
To convert degree measure to radian measure
radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]
Thus for 140°
radian = 140 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{7\pi }{9}[/tex] ≈ 2.4
Answer:
7π/9
Step-by-step explanation:
Degrees To Radians : × · π/180
Radians To Degrees : × · 180/π
Plug into Equation And Solve: 140π/180
Simplify: 7π/9
Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <3, 0>, v = <0, -6>
Answer:
They are orthogonal.
Step-by-step explanation:
u = <3, 0> v = <0, -6>
u.v =|u| |v|cosθ
if u.v is 0 this means that cos θ is 0 so θ = 90°
[tex]\theta=cos^{-1}\frac{u.v}{|u|\ |v|}[/tex]
If u.v = 0 then they are orthogonal.
If u.v ≠ 0 then they are neither parallel nor orthogonal
If u.v ≠ 0 and u = kv where k is constant then they are parallel
u.v = 3×0+0×-6
⇒u.v = 0
They are orthogonal.
Which relation describes a function?
A) {(0, 0), (0, 2), (2, 0), (2, 2)}
B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}
C) {(2, −1), (2, 1), (3, −1), (3, 1)}
D) {(2, 2), (2, 3), (3, 2), (3, 3)}
Explaine Why you chose your answer.
Answer:
B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}
Step-by-step explanation:
For a relation to be a function, every x value must have only one y value. For a, c, and d, some of the x values have multiple different y values
Answer:
B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}
Step-by-step explanation:
For a function to be valid, each value within the domain of the function must give exactly one value in the range of the function.
That is to say, for a function to be valid, every value of x must give only 1 unique value for y.
So basically if you have one value of x which gives a value for y, and if the same value for x gives you another value of y which is different than the first time, then you do NOT have a function.
With this in mind, we can see that for option B, every unique value for x, gives an equally unique value for y. Hence this is a function.
Lets compare this with option A (for example)
For A, we can see that for (0,0), an input of x=0, gave y=0. But then notice that the next set of coordinates (0,2), an input of x=0 gave y=2!!!! (this contradicts the first set (0,0), hence this is not a function.
you'll see similar contradictions for
option C (2,-1) vs (2,1)
option D (2,2) vs (2,3)
A large college wishes to determine the average SAT scores for students who apply from New York. They surveyed 105 students from New York and discovered a mean SAT score of 1519. Which of the statements below represent the parameter and the statistic, respectively, of the survey?
I. The mean SAT score of all students from New York
II. The mean SAT score of 105 students from New York
III. The 105 students who apply to the college from New York
IV. All students who apply to the college from New York
Statements I and IV
Statements II and III
Statements I and II
Statements II and IV
Answer:
Statements I and II
Step-by-step explanation:
In Statistics, parameter is any numerical value that characterizes a population while statistics are numerical values that characterizes a sample from a given population.
Statistics are most often used to estimate the population parameters
For example the sample mean is a statistic and the population mean is a paranmeter
The mean SAT score of all students from New York is the parameter.
The mean SAT score of 105 students from New York is called the statistic.
The correct choice is the third option.
What is the distance between (8, -3), (4,-7)?
A.- 6
B. 9
C.[tex]\sqrt{35}[/tex]
D.[tex]\sqrt{42}[/tex]
Thank You!
Answer:
[tex]4\sqrt{2}[/tex] which is none of your choices....
Did you mean (8,-3) and (4,-7)?
Step-by-step explanation:
We need to first find the distance between the x's.
Then the distance between the y's.
The distance between the x's is 8-4=4.
The distance between the y's is -3-(-7)=4.
So the distance between two points [tex](x_1,y1)\text{ and }(x_2,y_2)[/tex] is [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex].
So we already found x1-x2 and y1-y2 so now we have:
[tex]\sqrt{(4)^2+(4)^2}[/tex]
[tex]\sqrt{16+16}[/tex]
[tex]\sqrt{2(16)[/tex]
[tex]\sqrt{16}\sqrt{2}[/tex]
[tex]4\sqrt{2}[/tex]
Which point on the y-axis lies on the line that passes through
point C and is perpendicular to line AB?
O(-6,0)
O (0, -6)
O (0, 2)
O (2,0)
Answer:
0(0,2)
Step-by-step explanation:
0(0,2)
0(0,-6)
0(2,0)
0(-6,0)
The line perpendicular to the line AB passes through the point (0, 2)
What are perpendicular line?Two geometric objects are perpendicular if their intersection forms right angles at the point of intersection called a foot.
The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.
Given is a graph of a line, we need to find the which point on the y-axis lies on the line that passes through point C and is perpendicular to line AB,
From the given figure in the question it is observed that the line AB passes through the points (-2, 4) and (2, -8)
The coordinate of point C is, (6, 4)
Obtain the slope of the line AB.
-8-4 / 2+2 = -3
Consider the slope of AB as, m1
m1 = -3
Consider a line which is perpendicular to the line AB passing through the point C.
Assume the slope of the perpendicular line as m2,
The product of the slope of two mutually perpendicular lines is always equal to -1
The equation formed for the slope is as follows: 1/3
Finding the equation of the line,
y-y₁ = m(x-x₁)
3y - x = 6
Therefore, the equation of the perpendicular line is 3y - x = 6
In option 3 it is given that the line perpendicular to AB passes through the point (0, 2)
The equation of the line which is perpendicular to AB is 3y - x = 6
Substitute for in the above equation
3y - (0) = 6
3y = 6
y = 2
From the above calculation it is concluded that the line passes through the point (0, 2).
This implies that option 3 is correct.
Hence, the line perpendicular to the line AB passes through the point (0, 2)
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A soda bottle holds 1.5 liters of soda. How many milliliters does the bottle hold?
Answer:
1.5 = 1,500
Step-by-step explanation:
I actually converted 1.5 to milliliters.
That is how I got 1,500.
The bottle holds 1500 milliliters soda.
How to convert liter to milliliter ?We know that, 1 liter = 1000 milliliters
So, to convert something from liter to milliliter, we have to multiply the given value by 1000.
What is the required value ?Given, the bottle of soda holds 1.5 liters of soda.
So, we have to multiply 1000 with that to get the required value.
∴ 1.5 liters = (1.5 × 1000) milliliters
= 1500 milliliters
The required quantity of soda is 1500 milliliters.
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If sin x = -1/2, and 270° < x < 360°, what is cos(x - 30°)?
Answer:
x = -30
cos(x - 30) = ½
Step-by-step explanation:
Look at the picture
Select the correct answer.
Which expression is equivalent to x + y + x + y + 3(y + 5)?
Answer:
Step-by-step explanation:
Remove the brackets.
x + y + x + y + 3y + 15
Collect the like terms
2x + 5y + 15
This should be your answer.
Answer: 2x + 5y + 15
Write an equation:
The product of a number and 12 is 78
Answer: 12 x X=78
Step-by-step explanation: An equation of this would be 12 x X =78.
the perimeter and area of each figure:
a. A square with a side length of 3.5 inches.
[tex]3.5 \times 3.5 = 12.25 \: for \: are \\ 3.5 \times 4 = 14 \: for \: perimeter[/tex]
need the answer asap !! #34 !!
Answer:
A) 46 mph
Step-by-step explanation:
Step 1: To find the speed, you need to find the distance and time to travel between Chicago and Cleveland.
Distance = 354 miles
Time = 9: 50 am to 5: 30 pm
Time = 7 hours 40 minutes
Step 2: Convert time to hours
1 hour = 60 minutes
40 minutes = 60/40 = 2/3 hours
Step 3: Find the speed
Speed = Distance/Time
Speed = 354/7 + 2/3
Speed = 1062/23
Speed = 46.17 miles per hour rounded off to 46 mph
Therefore, A is the correct answer.
!!
The probability of spinning a 7 on a spinner is 0.083. If you spun 250 times, approximately how many times would the spinner land on 7
Answer:
21 times
Step-by-step explanation:
To find out how many times the spinner would land on the 7, take the probability times the number of times spun
250 * .083
20.75
It would land on 7 approximately 21 times
Answer:
The spinner will land on 7 approximately 21 times
Step-by-step explanation:
According to your question. The probability of spinning a 7 on the spinner is 0.083 (8.3%). You spin the spinner 250 times and you would like to know how many times the spinner would land on 7 based on the previous probability. To do this we will need to multiply the probability of the spinner landing on 7 in one spin with the amount of total spins.
[tex]250*0.083 = 20.75[/tex]
As shown above we can see that with a probability of 8.3% on 250 spins, the spinner will land on 7 approximately 21 times.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Square ABCD has side length 4. Determine the
area of the shaded region (use pi as 3).
Answer:
The area of the shaded region is [tex]8\ units^{2}[/tex]
Step-by-step explanation:
step 1
Find the curved area ACD (formed by segment AD, segment DC and the curved segment AC)
we know that
The curved area ACD is equal to the curved area ACB
The curved area ACD is equal to the area of the square minus the area of a quarter of circle
[tex]ACD=b^{2} -\frac{1}{4}\pi b^{2}[/tex]
we have that
[tex]b=4\ units[/tex]
substitute
[tex]ACD=4^{2} -\frac{1}{4}(3)(4)^{2}[/tex]
[tex]ACD=16 -12=4\ units^{2}[/tex]
step 2
Find the area of the shaded region
The area of the shaded region is equal to the area of the square minus two times the curved area ACD
so
[tex]4^{2} -2(4)=16-8=8\ units^{2}[/tex]
If y= x+1/2-x , evaluate y given x= 5i .
By substituting x = 5i in to the equation y = x+1/2-x, we find that y = 1/2.
Explanation:To solve for y in the equation y= x+1/2-x given that x= 5i, we simply substitute x with 5i.
So, y = 5i + 1/2 - 5i
The term 5i in the numerator and the denominator cancels out so we are left with: y = 1/2
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3x + 7y + 6 = 0 what is the y intercept
Answer:
The y-intercept is located at (0, -6/7)
Step-by-step explanation:
First, we should convert this equation from Standard Form(ax+by+c=0) into Slope-Intercept Form(y = mx+b), with b being the y-value of the y-intercept.
Work:
3x+7y+6=0
First, isolate the variables by subtracting 6 from both sides to keep the equation equal
3x+7y = -6
Next, isolate the y-variable by subtracting 3x from both sides to keep the equation equal
7y = -3x - 6
Then, divide by +7 on both sides to keep the equation equal and to simplify the left side even more, to completely isolate the variable
y = -3x/7 -6/7
The y-intercept is located at (0, -6/7)
rationalize the denomintaors 3square root of 3 - 3 square root of 3
Answer:
Please see attached image
Step-by-step explanation:
An analysis of the expression can be seen in the image below
See attached figure
How many meters are in .02 kilometers?
Answer:
the answer is 20 meters
Answer:
20
Step-by-step explanation:
What is the domain for the following function?
Y= (x+1)/(x^2+x-6)
A) {x does not equal -1}
B) {x does not equal -3; x does not equal 2}
C) {x does not equal -3}
D) {x does not equal 0}
Answer:
it's B
Step-by-step explanation:
the set of numbers for which a function is defined is called a domain of a function
if a number is not in the domain of a function, then the function is undefined for that number
denominator must not be zero
if we plug -3 then the y
=(-3+1)/(9+-3-6)
=(-2)/9-9
=-2/0
which is undefined for x=-3
now
if we plug 2 we have
(2+1)/(4+2-6)
=3/0
the function is undefined for x=2
so
x≠3, x≠2
The domain of the given function is {x does not equal -3; x does not equal 2}.
Explanation:The domain of a function is the set of all allowable input values. In this case, we need to find the values of x that make the denominator of the function equal to zero, because division by zero is undefined.
To find the domain, we set the denominator equal to zero and solve for x. The denominator is x^2 + x - 6, so we set it equal to zero and factor it: (x+3)(x-2) = 0. Now, we set each factor equal to zero and solve for x: x+3=0, x=-3; x-2=0, x=2.
The domain is the set of all values of x that make the function defined, so the answer is: (B) {x does not equal -3; x does not equal 2}.
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5. Regal Reflective signs make speed limit signs for the state department of transportation. By low these signs must be displayed every 5/8 of a mile. How many signs will be required on a new highway that is 34 3/8 miles long?