Answer:
Inequality
Step-by-step explanation:
An expression is a mathematical phrase that contains numbers, variables, or both. Expressions never have an equal sign. An equation is a mathematical sentence that says two expressions are equal.
f{x) = a (x − a}² + 1]
In the function f defined above, a > 1. Which of the
following best represents the graph of f in the
xy-plane?
Step-by-step explanation:
1 f(x) = ax (x − a)² + 1
Take the derivative
f'(x) = d/dx ( a x( x -a) ²+1
Use differentiation rules
f' x = ax2 x-a +0
Simplify
= f'(x)=2ax-2a²
answer
Solve.
−2/5x −9 < 9/10
Answer: x> -99/4
Step-by-step explanation:
−2/5x −9 < 9/10
Multiply Both Sides
-4x-90<9
Move the constant to the right
-4x < 9 + 90
Calculate
-4x < 90
Divide both sides
Answer x> -99/4
a road is inclined at angle of 6 degrees after driving 4900 feet
A road is 6 degrees inclined after 4900 feet of travel. The driver's increasing in altitude is 509.6
Given that,
A road is 6 degrees inclined after 4900 feet of travel.
We have to find the driver's increasing in altitude.
In a right angle triangle,
According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of the angles is a right angle (90°). Triangle ABC is a right triangle in the illustration, consisting of the base, altitude, and hypotenuse. The significant side of a right triangle is the hypotenuse, which is the longest side and sits in opposition to the triangle's right angle.
Sinθ=Altitude/Hypotenuse
Sinθ×Hypotenuse=Altitude
Altitude=Sin6°×4900
Altitude=0.104×4900
Altitude=509.6
Therefore, The driver's increasing in altitude is 509.6
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HELLO HELP PLEASE
y = x^2 - 10
heres a picture if it helps you understand it more i guess- Thank you!
Find the slope……….—-
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{ -4 }{ 5 } \implies - \cfrac{ 4 }{ 5 }[/tex]
Find the equation of the line that:
Passes through ( 1, 7 ) and is parallel to y= -3x +4
PLEASE HELP ME ILL GIVE BRAINLIEST!!! I need an explanation on how to do this.
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient so equation of line is y = -3x + c.
Substitute (1,7) into the equation to find c.
7 = -3(1) + c
c = 10
Hence equation of line is y = -3x + 10
I NEED ANSWERS ASAP!!
Fill in the blanks to explain what needs to be done in the current step to get to the next step.
3x +4 2x +9=17-x
Step 1: 3x +4- 2x +9 = 17-x
Step 2: x +13= 17 -x
Step 3: x + x +13= 17-x+ x
Step 4: 2x +13= 17
Step 5: 2x + 13 - 13 = 17-13
Step 6: 2x = 4
Step 7: x = 2
b = ____ ( look at photo )
Answer:
b = 64°
Step-by-step explanation:
The sum of interior angles of a polygon is 180°(n - 2), where "n" is number of sides.
~~~~~~~~~~
180°(6 - 2) = 720°
114° + (b + 49°) + (2b - 25°) + 142° + (b + 39°) + (3b - 47°) = 720°
7b + (114° + 49° - 25° + 142° + 39° - 47°) = 720°
7b + 272° = 720°
7b = 448°
b = 64°
in instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this does not prove that the null hypothesis is true.
You must explicitly state that the null hypothesis is demonstrated to be true in cases where there is insufficient evidence to disprove it.
A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory's veracity. It is sometimes referred to as just "the null," and its symbol is H₀
Even though we are unable to rule out the null hypothesis, this does not always imply that it is accurate. The reason for this is that a hypothesis test cannot tell which hypothesis is true or even which is more likely. It just evaluates whether there is sufficient evidence to disprove the null hypothesis.
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Two APs have the same first and last terms. Tye first AP has 21 terms with a common difference of 9. How many terms has the other AP if it's common difference is 4
The number of terms of the second arithmetic progression is 46.
How to find the number of terms of an arithmetic progression?The two arithmetic progression have the same first and last terms.
The first arithmetic progression has 21 terms with a common difference of 9.
The second arithmetic progression have common difference of 4.
Therefore,
using the first arithmetic progression,
a + (n - 1)d = nth term
a + 20(9) = last term
last term = a + 180
using the second arithmetic progression,
a + (n - 1)d = nth term
They have the same last and first term,
Hence,
a + 180 = a + (n - 1)4
a + 180 = a + 4n - 4
180 + 4 = 4n
184 = 4n
n = 184 / 4
n = 46
Therefore, the number of terms is 46
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Isabelle is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $9, and her grandmother has pledged $1 per mile. If Isabelle walks a certain distance, the two donors will end up owing the same amount. How much will each donor owe?
In this case, we're given the following information:
Mother = $9Grandmother = $1 per mileIsabelle walks x miles, mother pledge = grandmother pledgeThe mother's donation of $9 will not change no matter how many miles Isabelle has walked, so if both the mother's and grandmother's donations are equal, they must each owe 9$.
AnswerEach donor owes $9.
Given that the line 3y - mx + 3 = 0 is parallel to the line y = x + 5, find the value of m..
Answer:
m= 3
Step-by-step explanation:
In the slope-intercept form (y= mx +c), the coefficient of x (when the coefficient of y is 1) is the slope.
y= x +5
Slope of line= 1
Parallel lines have the same slope, hence the slope of 3y -mx +3= 0 is also equal to 1.
Let's rewrite the equation into slope-intercept form.
Keep the y term on the left-hand side, bring the others to the right.
3y= mx -3
Divide both sides by 3:
[tex]y = \frac{m}{3} x - 1[/tex]
Given that the slope is 1,
[tex] \frac{m}{3} = 1[/tex]
Multiply both sides by 3:
m= 1(3)
m= 3
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A coordinate plane with a line passing through points (1, 2) and (4, 4) The slope of the graphed line is . Which formulas represent the line that is graphed? Check all that apply. y – 1 = (x – 2) y – 2 = (x – 1) y – 4 = (x – 4) f(x) = x + f(x) = x +
Answer:
A straight line is represented by a linear equation.
The possible equations are:
\mathbf{3y = 2x + 4}3y=2x+4 .
\mathbf{y = \frac 23x + \frac{4}{3}}y=
3
2
x+
3
4
.
\mathbf{y = \frac 23(x - 1) + 2}y=
3
2
(x−1)+2 .
\mathbf{y = \frac 23(x - 4) + 4}y=
3
2
(x−4)+4
The points are given as:
\mathbf{(x,y) = \{(1,2),(4,4)\}}(x,y)={(1,2),(4,4)}
Start by calculating the slope (m)
\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}m=
x
2
−x
1
y
2
−y
1
So, we have:
\mathbf{m = \frac{4-2}{4-1}}m=
4−1
4−2
\mathbf{m = \frac{2}{3}}m=
3
2
The equation in slope intercept form is then calculated as:
\mathbf{y = m(x - x_1) + y_1}y=m(x−x
1
)+y
1
So, we have:
\mathbf{y = \frac 23(x - 1) + 2}y=
3
2
(x−1)+2
or
\mathbf{y = \frac 23(x - 4) + 4}y=
3
2
(x−4)+4
Expand \mathbf{y = \frac 23(x - 1) + 2}y=
3
2
(x−1)+2
\mathbf{y = \frac 23x - \frac 23 + 2}y=
3
2
x−
3
2
+2
Take LCM
\mathbf{y = \frac 23x + \frac{-2 + 6}{3}}y=
3
2
x+
3
−2+6
\mathbf{y = \frac 23x + \frac{4}{3}}y=
3
2
x+
3
4
Multiply through by 3
\mathbf{3y = 2x + 4}3y=2x+4
So, the possible equations are:
\mathbf{3y = 2x + 4}3y=2x+4 .
\mathbf{y = \frac 23x + \frac{4}{3}}y=
3
2
x+
3
4
.
\mathbf{y = \frac 23(x - 1) + 2}y=
3
2
(x−1)+2 .
\mathbf{y = \frac 23(x - 4) + 4}y=
3
2
(x−4)+4
if a 1.3 vv battery stores 6.4 kjkj of energy (a reasonable value for an inexpensive c cell), for how many minutes could it sustain a current of 1.5 aa ?
A Energy t = 54.70 min could it sustain a current.
What does energy mean according to science?
Energy is referred to by scientists as the capacity for work. People have figured out how to transform energy from one form to another and then use it to accomplish tasks, making modern civilization possible.Energy can take on a variety of shapes. Examples of these include: electrical energy, sound energy, chemical energy, nuclear or atomic energy, light energy, heat energy, mechanical energy, gravitational energy, and so on. Each form has the ability to shift or transform into the others.apply power = energy/time = Vi
so energy E = vit
time t = E/vi
t = 6400/(1.3* 1.5)
t = 6400/1.95 sec
t = 3282.05 sec
t = 54.70 min
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If someone could help me with these two problems please.
( will mark brainliest if correct )
Answer: 7. 140° 8. 60°
Step-by-step explanation:
7.
A internal angle of a convex poligon is:
[tex]\displaystyle\\x=\frac{(n-2)180^0}{n} \\\\n=9\\\\So,\\\\x=\frac{(9-2)180^0}{9} \\\\x=7*20^0\\\\x=140^0[/tex]
8.
[tex]\displaystyle\\x=\frac{(n-2)180^0}{n} \\\\n=3\\\\So,\\\\x=\frac{(3-2)180^0}{3} \\\\x=1*60^0\\\\x=60^0[/tex]
NEED HELP FAST PLEASE!!! The perimeter of a geometric figure is the sum of the lengths of its sides. The perimeter of the pentagon (five-sided figure) on the right is 42 centimeters.
A. Write an equation for the perimeter
B. Solve the equation in part (a)
C. Find the length of each side
a. The equation of the perimeter is x + x + x + 2x + 2x = 42. Option A
b. x = 6 centimeters
c. The lengths are 6 centimeters , 6 centimeters , 6 centimeters , 12 centimeters and 12 centimeters respectively.
How to determine the perimeterIt is important to note that the formula for calculating the perimeter of a pentagon is expressed as;
Perimeter = 5a
Where: 'a' represents the length of one of its side
From the information given, we have that the perimeter of the geometrical figure is the sum of its sides.
Given the sides;
x , x , x, 2x , 2x
Now, substitute the values into the formula for perimeter
x + x + x + 2x + 2x = 42
collect like terms and add them
7x = 42
Now, make 'x' the subject of formula by dividing both sides by the coefficient of the variable 'x'
We have;
7x/7 == 42/7
x = 6 centimeters
But the length of the sides is determined by substituting the value of x as 6
x = 6 centimeters
x = 6 centimeters
x = 6 centimeters
2x = 2(6) = 12 centimeters
2x = 2(6) = 12 centimeters
Hence, the lengths are 6, 6, 6 , 12 and 12 centimeters respectively.
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Find the inequality represented by the graph
The inequality representing the shaded region is given by 2y - x < 4.
What is meant by the term inequality?A statement of an order relationship between two numbers or algebraic expressions (greater than > , greater than or equal to ≥, less than < , or less than or equal to ≤). Inequalities can be expressed as questions, similar to equations, and solved using similar methods, or as factual statements in the type of theorems.For the given question, the graph is shown,
Consider two coordinates from the graph and find the slope using them.
(x₁, y₁) = (0, 2)
(x₂, y₂) = (4, 4)
slope m = (y₂ - y₁)/(x₂ - x₁)
Put the values.
m = (4 - 2)/(4 - 0)
m = 1/2
Put the value of slope in the equation of line in slope intercept form.
y - y₁ = m(x - x₁)
Put the values;
y - 2 = 1/2(x - 0)
Simplifying;
2y - 4 = x
2y - x = 4
Now, from the graph, as the origin of the coordinate axis and the shaded region region of the graph lies on the same side, the inequality is less than.
2y - x < 4, only less than as the graph is made with dotted lines.
Thus, the inequality representing the shaded region is given by 2y - x < 4.
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Which of the following statements best describes the value of the expression 18x – 35, when x = 2?
A. The result is not a whole number.
B. The result is a prime number.
C. The result is a composite number.
D. The result is a whole number that is neither prime nor composite.
7TH Grade Math!
The statements which best describes the value of the expression 18x – 35, when x = 2 is that the result is a whole number that is neither prime nor composite and is denoted as option D.
What is a Prime number?This is referred to as the number which is divided by one and itself and there must be exactly two numbers involved.
18x – 35 = 18(2) – 35
= 36 - 35 = 1
In the case of 1, the numbers involved is just one which 1 which is why it isn't regarded as a prime number. A composite number can be formed with two small integers and the formation of 1 is 1 × 1 which is why 1 isn't.
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Answer:
The Answer Is: D.! The Results is A Whole Number That is Neither Prime nor Composite
Step-by-step explanation:
Hope This Helped! You Have a Great Day!
someone pls help i need this
if a researcher uses u.s. census data to examine changes in the number of individuals in each racial group across states over time, she is using .
If a researcher uses u.s. census data to examine changes in the number of individuals in each racial group across states over time, she is using stratified sampling.
How are samples classified?Samples may be classified as:
A convenient sample is drawn from a conveniently available pool.In a random, all the options into a hat and drawn some of them.In a systematic, every kth element of the sample is taken. Cluster sampling divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified sampling also divides the population into groups. Then, a equal proportion of each group is surveyed.For this problem, we have that the population is divided into groups, according to their racial group, and then parts of the sample are surveyed, hence stratified sampling is used.
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-(2x + 5.9) +8.3 = 4+3(-x+ 2.8)
Answer:
x =10
Step-by-step explanation:
Equation
-(2x + 5.9) +8.3 = 4+3(-x+ 2.8) Carefully remove both sets of brackets
Solution
-2x - 5.9 + 8.3 = 4 + -3x + 8.4 Combine like terms on both sides
-2x + 2.4 = -3x + 12.4 Add 3x to both sides
-2x+3x + 2.4 = -3x+3x + 12.4 Combine
x + 2.4 = 12.4 Subtract 2.4 from both sides
x + 2.4 - 2.4 = 12.4 - 2.4 Combine
x = 10
Pls help this is due tonight
Graph is plotted below.
Define co ordinates.A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x, y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To get the y-coordinate, repeat the previous step while adhering to a horizontal line. A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
Coordinates are:
(-6,-8)
(1,--8)
(10,-8)
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Billy had a balance of -$21.46 in his bank account. As soon as he saw this * 1 point
balance, he deposited $35.50 into the account. What was the account
balance after the deposit?
O-$14.04
O $14.04
$35.50
O $56.96
Answer:
$14.04
Step-by-step explanation:
-21.46 + 35.50 is the same as
35.50 - 21.46 = $14.04
Answer: 14.04
Step-by-step explanation: -21.46 + 35.50 = 14.04
In the formula: c = πd
c represents the circumference of a circle (distance around)
is a number that is approximately equal to 3.14
d represents the diameter of a circle (distance across)
Solve the formula for d when c = 25.12 inches
d = ?
The value of d i.e. the diameter will be 8 inches when the circumference is 25.12 inches.
What is diameter and circumference of a circle?The distance a circle's circumference extends from one end to the other is known as the diameter.
The circumference of a circle is the distance of its outer length.
According to the formula, c = πd, c is the circumference of the circle and d is the diameter of the circle.
Value of π is 3.14
When c = 25.12 inches, the value of d will be
d = c/π
d = 25.12/3.14
d = 8 inches
The diameter will be 8 inches when circumference is 25.12 inches.
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Help please. geometry.
Answer:
Area - 532 in²Volume - 576 in³==========================
GivenRight rectangular prism with dimensions 6 in, 8 in, 12 in.To findSurface area,VolumeSolutionEquation of surface area:
S = 2(lw + lh + wh)Substitute and calculate:
S = 2(8*12 + 8*6 + 12*6) = 2(216) = 532 in²Equation of volume:
V = lwhSubstitute and calculate:
V = 12*8*6 = 576 in³Solve for x .-.
[tex] \tt {x}^{2} + 9 = 298[/tex]
Answer:
x = 17
Step-by-step explanation:
Solving for 'x':x² + 9 = 298
Subtract 9 from both sides,
x² + 9 - 9 = 298 - 9
x² = 289
Prime factorize 289,
x² = 17*17
Take square root,
[tex]\sf \sqrt{x^2}= \sqrt{17*17}[/tex]
x = 17
Write 5x−4y=10 in slope-intercept form.
Answer:
y = 1.25x - 2.5
Step-by-step explanation:
To write the equation of a line in line in slope intercept form,
we can use y = mx + c
According to the question, writing the given equation in slope intercept form makes y the subject.
5x - 4y = 10
First, subtract 5x from both sides.
- 4y = 10 - 5x
Now, divide both sides by -4.
[tex]\frac{-4y}{-4}=\frac{10-5x}{-4} \\\\y = \frac{-5x}{-4}+\frac{10}{-4}\\\\y= 1.25x-2.5[/tex]
Write an absolute value equation representing all numbers x whose distance from 8 is 6 units.
The absolute value equation representing all numbers x whose distance from 8 is 6 units will be x = {2, 14).
How to illustrate the information?Based on the information given, it should be noted that the distance of x, positive or negative from 8 can be expressed as |x - 8|.
Since the distance is equal to 6, our equation will be:
|x - 8| = 6
x = 8 + 6 = 14
or
- |x - 8| = 6
-x + 8 = 6
-x = 6 - 8
-x = -2
x = 2
Therefore, the appropriate equation is x = {2, 14).
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The standard form of a parabola is y=ax² +bx+c. Find the equation to the parabola that
passes through the points (0,4), (2,4) and (-2,8).
The equation to the parabola that passes through the points (0,4), (2,4) and (-2,8) is y = 6x+8.
What is a parabola?A parabola is a mirror-symmetrical, nearly U-shaped planar curve in mathematics. It correlates to a multitude different statistical equations that appears to be superficially distinct and yet all define the exact same arcs. A point and a line are used in one definition of a parabola. the intersection of a right circular cone with a plane parallel to an element of the cone; a plane curve produced by a point moving so that its distance from a fixed point is equivalent to its length from a dedicated line. Anything resembling a bowl (such as an antenna or microphone reflector). A parabola graph shows a quadratic function as a U-shaped curve. A parabola is one of the conic sections in mathematics and is created by the intersection of a right circle .
y= ax²+ bx +c
Always begin with the coordinates which has 0 in it
(0,4)
4=a(0)² + b(0) + c
4=c
y = ax²+ bx + 4
The next set of coordinates (2,4)
4 = a(2)² + b(2) + 8
4 = 4a + 2b + 8
-4 = 4a + 2b
The other set of coordinates(-2,8)
8 = a(-2) + 2-2b + 8
0 = 4a-2b
Add the two above equations together...
0 = 8a
0 = a
Subtract the two equations from each other...
= 0 + 4b
24 = 4b
6 = b
y = 6x+8
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Solve the inequality for x and identify the graph of its solution.
|x + 3| < 2
Answer:
B.
X>-5 and X<-1
Step-by-step explanation:
|x+3|<2
The absolute value is already isolated for, so now you make two different equations.
x+3>-2
and
x+3<2
you get x>-5 and x<-1