The x-coordinates of the x-intercepts of the parabola are 1/2 and -7
What are parabola equations?Parabola equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the x-coordinates of the x-intercepts?The parabola is given as
y = 2x^2 + 13x - 7
It should be noted that the x-intercept of the function is the point or points where the graph of the function crosses the x-axis
i.e. the point where the function equals 0
So, we have
y = 2x^2 + 13x - 7
Expand
y = 2x^2 + 14x - x - 7
Factorize the equation
So, we have
y = 2x(x + 7) - 1(x + 7)
Set the equation to 0
So, we have
2x(x + 7) - 1(x + 7) = 0
Factor out x + 7
So, we have
(2x - 1)(x + 7) = 0
Expand
2x - 1 and x + 7 = 0
Solve for x
x = 1/2 and x = -7
Hence, the x-coordinates of the x-intercepts are 1/2 and -7
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write an equation for there consevite integers whose sum id 306
The equation for three consecutive integers whose sum is 36 is n + (n+1) + (n+2) = 306.
What is an equation?A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.
What are consecutive numbers?Whole numbers that follow one another without a gap are known as consecutive integers.
Given the sum of three consecutive integers = 306
Let the integers be n, n+1, n+2
Then, n + (n+1) + (n+2) = 306
⇒3n + 3 = 306
⇒n = 303/3
⇒n = 101
Hence, n+1 = 102 and n+2 = 103
Therefore, the equation for three consecutive integers whose sum is 36 is n + (n+1) + (n+2) = 306.
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At a book fair, a tote bag costs $5 and books cost $3.50 each. you spend a total of $19.00 before taxes. how many books did you buy in addition to the tote bag?
Answer:
4 books
Step-by-step explanation:
Let b equal the number of books.
[tex]5 + 3.50b = 19[/tex]
[tex]3.50b = 14[/tex]
[tex]b = 4[/tex]
if a tv has a 30 inch screen and a height of 18 inches what is the width of the tv
Answer:
24 inches
Step-by-step explanation:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]18^{2}[/tex] + [tex]b^{2}[/tex] = [tex]30^{2}[/tex]
324 + [tex]b^{2}[/tex] = 900
[tex]b^{2}[/tex] = 576
[tex]\sqrt{b^{2} }[/tex] = [tex]\sqrt{576}[/tex]
b = 24
Answer:
24 inches
Step-by-step explanation:
Since the size of the screen is measured from the lower corner to the opposite upper corner.
therefore it forms a right angled triangle.
given hypotenuse is 30inch
the height is 18 inches
using the Pythagorean theorem
[tex] {hypotense}^{2} = {width}^{2} + {height}^{2} [/tex]
then
[tex] {30}^{2} = {width}^{2} + {18}^{2} \\ 900 = {width}^{2} +324[/tex]
Subtract 324 from both sides
[tex]576 = {width}^{2} \\ width = \sqrt{576} = 24 \: \: inches[/tex]
What is the value of x in the triangle?
Find y' if arctan (xy) = 4 + xy².
Answer:
y=2x
Step-by-step explanation:
hope this helps
:) :3
Pls help
Step by step
Solve the x and y
1.5x-4.5y=9
Answer:
1.5x=9+4.5y
x= [tex]\frac{9+4.5y}{1.5}[/tex]
x = 6 + 3y
3y= x - 6
y = x/3-2
What do you add to
[tex]3 \frac{3}{8} [/tex]
to make 7?
Answer:
[tex]\frac{29}{8}[/tex]
Step-by-step explanation:
3[tex]\frac{3}{8}[/tex] equals to [tex]\frac{27}{8}[/tex], then we can write out the equation:
[tex]\frac{27}{8} + x = 7[/tex]
then subtract [tex]\frac{27}{8}[/tex]on both sides of the equal sign,
[tex]x = 7 - \frac{27}{8}[/tex]
and then we calculate x
[tex]x=\frac{56-27}{8}[/tex]
[tex]x=\frac{29}{8}[/tex]
Thus the answer is [tex]\frac{29}{8}[/tex]
Please help!!!!!!!!!
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Neil bought a house for £235 000
In the first year the value of the house depreciated by 4%
In each of years 2 and 3 the value of the house increased by 6%
Work out the value of the house at the end of year 3
Answer:
Based on the given conditions, formulate: 235000×(1+1-4%)
Calculate the sum or difference:235000×(2-0.04)
Calculate the sum or difference:235000×1.96
Calculate the product or quotient:460600
get the result:460600
So the answer is 460600
Answer:
£ 253,484.16
Step-by-step explanation:
Cost of house for first year = £235,000
Year 1
Depreciation for first year is 4% = 4/100
Depreciation in £ = 235,000 x 4/100 = £9,400
Effective value of house at end of first year
= 235000 - 9400 = £225,600
Year 2
In the second year the house value increased by 6% = 6/100
So total increase in £ at the end of year 2 with an initial value of £225,600 = £225,600 x 6/100 = £13,536
So actual value of house at end of year 2
= £225,600 + £13,536
= £239,136
Year 3
The value increased by 6% for year 3.
Value at beginning of year 3 = £239,136
Increase in value at 6% = £239,136 x 6/100 = £14,348.16
Total Value at end of year 3
= £239,136 + £14,348.16
= £253,484.16
Answer: £253,484.16
Note
Another way of quickly calculating this is noting that 4% depreciation means the new value is (1 - 4%) of initial value = 1 - 4/100 = 0.96
An increase of 6% means the new value will be 1.06 times the initial value
So the value of the house after 4% depreciation for the first year and 6% appreciation for the next 2 years
= 235000 x (0.96)(1.06)(1.06) = 253,484.16
If you know the names of the remaining students in the spelling bee, what is the probability of randomly selecting an order and getting the order that is used in the spelling bee?.
The probability of randomly selecting an order and getting the order that is used in the spelling bee is 0.001388888
Given we have the following:
Number of students in the spelling bee = 6
Number of ways selecting a student in the spelling bee = 6!
The probability of randomly selecting an order and getting the order that is used in the spelling bee :
P(selecting the correct spelling bee order) = 1/6!
= 1/6*5*4*3*2*1
= 1/720
= 0.001388888
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At a garage sale, Liyah priced
her scooter for $15.50. She
ended up selling it for $10.75.
Find the percent of decrease
in the price of the scooter.
Round to the nearest tenth if
necessary
If she priced scooter for $15.50 and ended up selling it for $10.75, then the percentage of decrease in the price of the scooter is 30.64%
The initial price of the scooter = $15.50
The selling price of the scooter = $10.75
The amount decrease in the price of the scooter = Initial price of the scooter - The selling price of the scooter
= 15.50-10.75
= $4.75
The percent of decrease in the price of the scooter = (The amount decrease in the price of the scooter ÷ The initial price of the scooter)×100
= (4.75/15.50)×100
= 30.64%
Hence, if she priced scooter for $15.50 and ended up selling it for $10.75. then the percentage of decrease in the price of the scooter is 30.64%
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3862 × 874 pls write step by step
надеюсь что объяснила точно и нормально
1. A grocery store sells salmon for $7.84 per pound. What would be the cost of 2 1/4
pounds of salmon?
Answer:
$17.64
Step-by-step explanation:
Multiply 7.84 by 2.25
7.84 x 2.25 = 17.64
Answer:
$17.64
Step-by-step explanation:
1 pound salmon = 7.84
2.25 (2 1/4) pound salmon = 17.64
Directions: Rewrite each list of numbers in order from least to greatest 2%, 4¹ , 7/25, 2×10¹, √2, 0.2 repeating
Order from least to greatest is 2% ,0.2,[tex]\frac{7}{25}[/tex] ,[tex]\sqrt{2}[/tex],2×10¹
What is basic algebra ?The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including trigonometry, calculus, and coordinate geometry. 2x + 4 = 8 is a straightforward algebraic expression. In algebra, symbols are used, and operators are used to connect the symbols to one another. It is more than just a mathematical idea; it is a skill that we all utilize on a regular basis without even being aware of it.
Order from least to greatest is 2% ,0.2,[tex]\frac{7}{25}[/tex] ,[tex]\sqrt{2}[/tex],2×10¹
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pls pls help whoever gets it right gets marked brainliest
Answer: a
Step-by-step explanation:
i think the answer is a
There are 11 cups. Six of the cups contain milk. One of them contains soda. Four of them contains water. What fraction of the cups contain water and milk
Answer:
10/11
Step-by-step explanation:
count how many cups and then what ones have water and milk
what is the mean of 21,23,19,23,and 21
Answer:
21.4 (or 107/5)Step-by-step explanation:
what is the mean of 21,23,19,23,and 21?
Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.
(21+23+19+23+21) : 5 =
107 : 5 =
21.4 (or 107/5)
How can you write the expression using rational exponents?
5 square root n4
By using exponent properties, we can see that the equivalent expressions are:
[tex]5*\sqrt{n^4} = 5*n^2[/tex]
How to rewrite the expression?Here we need to use some rules for exponents and roots. Remember that:
[tex]\sqrt[n]{x} = x^{1/n}[/tex]
We also will use that:
[tex](a^n)^m = a^{n*m}[/tex]
Now we have the following expression:
[tex]5*\sqrt{n^4}[/tex]
Particularly, the square root is equivalent to an exponent of 1/2, then we can write:
[tex]5*\sqrt{n^4} = 5*(n^4)^{1/2}[/tex]
Using the second property we can rewrite:
[tex]5*(n^4)^{1/2} = 5*n^{4*1/2} = 5*n^2[/tex]
So the equivalent expressions are:
[tex]5*\sqrt{n^4} = 5*n^2[/tex]
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Which equation shows a line perpendicular to y = 3x + 2
a) y-1=1/3 (x-2)
b) y-1=3(x-2)
c) y-1=-1/3(x-2)
d) y-1=-3(x-2)
The straight line y-1=-1/3(x-2) is perpendicular to y = 3x + 2 .
The common form for two-variable linear equations is Ax + By = C which is also the general form of a straight line.
For instance, the linear equation 6x+5y=11 uses standard form. Finding an equation's two intercepts (x and y) is fairly straightforward with this procedure.
The cartesian equation for a straight line is Y = mx + c, where m stands for the gradient or slope of the line and c for the point at which it intersects the y-axis.
If two geometrical objects cross at a right angle, they are perpendicular.
We know that when two line are perpendicular the product of their respective slopes equal to -1.
Now in the given options let us find the slope of each line.
a) y-1=1/3 (x-2)
slope = 1/3
b) y-1=3(x-2)
slope = 3
c) y-1=-1/3(x-2)
slope = -1/3
d) y-1=-3(x-2)
slope = -3
Therefore the slope of the third equation is the negative reciprocal of the slope of the given line.
Hence y-1=-1/3(x-2) is perpendicular to y = 3x + 2 .
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solve the system of equations
Janet picked a number, added 7 to the number, multipled the sum by 2,
and then subtracted 4. If the final result was 28, what number did Janet pick?
HELP PLEASE!!!!!
the number chosen by Janet was 9 .
What is linear / non-linear equation ?An equation is a statement in which the values of two mathematical expressions are equal. These statements consist of constants and variables. Constants are values that never change. Variables like y or x represent unknown numerical values. Nonlinear equations are equations that appear as curved lines when you graph them. After plotting pairs of values that make the equation true on a coordinate grid, you can't draw a straight line between the points.
Calculationfrom the question given we can come to an equation that is
2( x+7) - 4 = 28
if the number chosen by Janet is x
lets find x
2x + 14 - 4 = 28
2x = 18
x = 9
therefore the number chosen by Janet was 9 .
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CAN SOMEONE PLEASE HELP ME
Answer:
^2¤{{●○|<♤7◇○◇○◇7~♡6°<♤~{¡\ ~announced unbeknownst.fi
30 POINTS!
Select ALL the correct answers
Which figures show that ST || QR?
The figure that shows that ST || QR is the first figure
How to find the figure that show that ST is parallel to QR
For lines ST and QR to be parallel they have equal distance form the base of the triangle.
Taking the ratio of the distances from the apex we have
PS / SQ = PT /TR
The figure that has it's ratio equal is the figure that the lines ST and QR are parallel
Checking the first figure gives
= PS / SQ
= 7.5 / 17.5
= 0.428571
Also
= PT /TR
= 8.7 / 20.3
= 0.428571
since the ratio is equal the two lines are parallel in the
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Answer:I’m not sure what the second one is
Step-by-step explanation:
Which function is odd? Check all that apply.
A. y = sin x
B. y = csc x
C. y = tan x
D. y = cos x
The odd function is
y = sin x
y = cos x
A function f is deemed weird if f(-x) Equals -f for any value of x. (x). A function is said to be an even function if f(-x) = f for any value of x. (x).
What do odd functions entail?
The meaning of odd function
T function where the absolute value does not change if the independent variable's sign is reversed but the sign of the function itself does.
If f(-x) = -f for any number x, a function f is considered strange (x). When f(-x) = f for any number x, a function is referred to as an even function (x). Even while most functions are neither odd nor even, some of the most significant functions are.
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Answer:
A. y = sin x
B. y = csc x
C. y = tan x
Step-by-step explanation:
K
An investor has $75,000 to invest in a CD and a mutual fund. The CD yields 7% and the mutual fund yields 6%
The mutual fund requires a minimum investment of $9,000, and the investor requires that at least twice as much
should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the
mutual fund to maximize the return? What is the maximum return?
DO
To maximize income, the investor should place $ in CDs and $
dollar as needed.)
The maximum return is $ (Round to the nearest dollar as needed.)
H
min
CH
point(s) possible
MA
√i Vi
P
in the mutual fund. (Round to the nearest
X
(,)
More
Next
x
25000 in mutual funds
50000 in CD
Pool of money managed by a professional Fund Manager is termed mutual fund. It is a trust that collects money from other investors who have a common investment objective and invests the same in equities and bonds.
Let X be the amount in Mutual Funds
Y be the amount in CDs
the constraints:
Y = 2x
x>9000
Y = 75000 - x
There has to be at least 2x + x = 75000
3x = 75000
x = 25000
Objective function for the return of investment is R(x,y) = 0.06X + 0.07Y
After graphing linear equations and inequalities, the vertices of the critical region are as:
(9000,18000) --> 1710
(25000,50000) ---> 4750
(75000,0) --> 3750
25000 in mutual funds
50000 in CD
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Simplify: (8c3+c2d)−(9cd2−5d3)+(−3c2d−8cd2)
What is the circumference of a circular park with a radius of 100 meters?
(Round your answer to the nearest tenth.)
OA. 628.3 m
OB. 157.1 m
OC. 314.1 m
OD. 1256.6 m ?
Writing to Explain Timothy is solving the problem 50+ 108x ÷ 4.
What order of operations should he follow?
Answer:
27x+50
Step-by-step explanation:
How to solve your problem
50 + 108x/4
Simplify
Cancel terms that are in both the numerator and denominator
50+ 108x/4
50+ 27x
Rearrange terms
50 + 27x
27x +50
=27x+50
The speed of a car from point A to D is m/s however the velocity is 10 m/s due West. Calculate the speed of vehicle in m/s if it covers a distance of 1.5 km in 5 minutes.
Speed of car is 5 m/sec
What is speed?
In ordinary language and kinematics, an object's speed is defined as the magnitude of its position change over time or the magnitude of its position change per unit of time; it is therefore a scalar number. The distance traveled by an item in a time interval is divided by the duration of the period; the instantaneous speed is the limitation of the average speed as the length of time period tends to zero. Velocity is not the same as speed. Distance divided by time is the dimension of speed. The metre per second (m/s) is the SI unit of speed, while the kilometre per hour (km/h) is the usual unit.
The speed of the car = 1.5/5 km/min = 0.3 km/min
Speed in m/sec = 0.3x1000/60 = 5m/sec
Hence, speed of car = 5 m/sec
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