Answer:
6x + 9 = 4
Step-by-step explanation:
Solve for x in the diagram below.
(2x+45)
Answer:
Step-by-step explanation:
you can't really solve for x because there is no equal sign to determine how much x needs to be in order to get the sum.
Determine whether each equation represents a proportional relationship. If it does, identify the constant of proportionality
The proportional relationship of the given statement is a between x and y and the constant of proportionality is 0.5.
According to the statement
We have to find that the constant of proportionality.
So, For this purpose, we know that the
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
From the given information:
each equation represents a proportional relationship.
Then
We know that the A proportional relationship is one in which two quantities vary directly with each other
That's why
An equation has a proportional relationship if it can be written in the form y=kx where k is the constant of proportionality.
A linear function of x is given as y = 0.5x - 2.
Yes, this function of x represents a proportional relationship between x and y.
The constant of proportionality is given to be 0.5 provided that the dependent variable y has an initial value of - 2 at x = 0.
The graph of this equation will be a straight line and that means that the equation consists of a proportional relationship.
So, The proportional relationship of the given statement is a between x and y and the constant of proportionality is 0.5.
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Question:
Determine whether each equation represents a proportional relationship. if it does identify the constant of proportionality. y = 0.5 x -2
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See the attached screenshot.
The Area of the given composite shape is; 40 square units
What is the Area of the Composite Shape?
We can breakdown the shape into triangle and rectangle and as such we know that;
Formula for area of triangle is;
Area = ¹/₂ * base * height
Formula for area of rectangle is;
Area = Length * Width
Thus;
Area of composite shape = (10 * 3) + (¹/₂ * 10 * 2)
Area of composite shape = 30 + 10
Area of composite shape = 40 square units
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where RS=8y+5, ST=3y+4, and RT=97.
a. What is the value of y?
b. Find RS and ST
The answer of part a is y = 8
The answer of part b is RS = 69, ST = 28
Step-by-step explanation:
a. Since RT = RS + RT, subsitute values of RS and RT in the equation
97 = (8y + 5) + (3y + 4)
97 = 11y + 9
97 - 9 = 11y
88 = 11y
y = 8
b. Subsitute the value of y in RS and ST just like done in part a
NO LINKS!! Please help me with these problems. Part 11a1
y = 3x^2
Domain: (−∞,∞) , {x|x ∈ R}
Range: [0,∞) , {y|y ≥ 0}
Continuity: y=3x^2 is a parabola opening upwards, the vertex is at (0,0) and the focus is (0,1/12)
Max's and Min's: the minimum and maximum x value goes to infinity while for the y value the minimum is 0 and goes up to infinity.
Intervals: both x and y start to increase from the origin
Symmetry: the axis of symmetry is x=0 so therefore there the parabola is symmetrical
Answer:
Domain: (-∞, ∞)Range: [0, ∞)Continuity: Function is continuous on its domain (-∞, ∞). Minimum stationary point (turning point) at (0, 0).Increasing function: (0, ∞)Decreasing function: (-∞, 0)Symmetry: Even (symmetry about the y-axis).Step-by-step explanation:
Given function:
[tex]y=3x^2[/tex]
DomainThe domain is the set of all possible input values (x-values).
The domain of the given function is unrestricted.
Therefore, the domain is (-∞, ∞).
RangeThe range is the set of all possible output values (y-values).
As x² ≥ 0, the range of the given function is [0, ∞).
ContinuityA function f(x) is continuous when, for every value [tex]c[/tex] in its domain:
[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]
Therefore, the function is continuous on its domain (-∞, ∞).
Maximums and MinimumsStationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
[tex]\begin{aligned}y & = 3x^2\\\implies \dfrac{\text{d}y}{\text{d}x} & = 6x\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies 6x & = 0\\x & = 0\end{aligned}[/tex]
[tex]\textsf{When} \:x = 0 \implies y=3(0)^2=0[/tex]
Therefore, the stationary point of the given function is (0, 0).
To determine if a stationary point is minimum or maximum, differentiate the function again and substitute the x-value of the stationary point:
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 6x\\\implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6 \end{aligned}[/tex]
As the second derivative is positive regardless of the x-value of the stationary point, the stationary point is a minimum.
Increasing/Decreasing Function[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]
Increasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies 6x & > 0 \\ x & > 0\end{aligned}[/tex]
Decreasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies 6x & < 0 \\ x & < 0\end{aligned}[/tex]
Therefore:
The function is increasing in the interval (0, ∞).The function is decreasing in the interval (-∞, 0).Symmetry[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]
[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]
As x² ≥ 0 and there is symmetry about the y-axis,
[tex]\textsf{then $f(x)=f-x)$ for all $x$,}[/tex]
so the function is even.
Arianys wants to ride her bicycle 55.5 miles this week. She has already ridden 19 miles. If she rides for 5 more days, which equation could be used to determine, m, the average number of miles she would have to ride to meet her goal?
19m=55.5 − 5
5m=19−55.5
m=55.5−19/5
55.5=19m+5
The equation that could be used to determine, m, is 5m = 55.5 - 19. The correct option is C.
m = (55.5 - 19)/5
How do we come up with the Equation?We are to deduce from the question the equation that may be used to calculate, m, the average number of miles she would have to ride to reach her objective.
Given:
"Arianys wants to ride her bicycle 55.5 miles"
and
"She has already ridden 19 miles"
Hence,
The number of miles she needs to ride more is
55.5 miles - 19 miles
= 36.5 miles
'
If m is the average number of miles she must cycle in 5 days to reach her objective,
Then, we can write that
m = 36.5/5
OR
m = (55.5 - 19)/5
As a result, the equation that may be used to get m is 5m = 55.5 - 19.
C. m = (55.5 - 19)/5 is the right answer.
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The sum of 4 consecutive even integers is the same as the least of the integers find the integers
The four numbers are: -4, -2 ,0, 2 Answer.
How do you solve this: the sum of four consecutive even integers is equal to least of the integer
Solution: Let the numbers be n, n+2, n+4 and n+6.
Their sum = 4n+12 = n or
3n+12 = , or
3n = -12,
n= -4
therefore we get -4, -2, 0, 2
The four numbers are: -4, -2 ,0, 2 . Answer.
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A car is traveling at a speed of 45 kilometers per hour. What is the car's speed in meters per second? How many meters will the car travel in 2 seconds?
Answer:
12.50m/s
in 2 seconds: 25
im not really good at math but i tried
Which polynomial represents the sum below?
+
2x² + 5x+4
5x2+
Answer:
????
Step-by-step explanation:
I don't get this
at all
A rectangle is 59.63 m2. If the length of the rectangle is 6.7 meters, shat is the width in meters?
Answer:
8.9
Step-by-step explanation:
When given the area of the rectangle to be 59.63m2.....AND the length to be 6.7m
To calculate the area of a rectangle = L×B
Width = Area ÷ Length
= 59.63m2 ÷ 6.7m
Width = 8.9m
Answer:
width = 8.9 meters
Step-by-step explanation:
Area of a rectangle = length * width
In this case:
Width = Area of a rectangle / length
Width = 59.63m² / 6.7m
Width = 8.9 m
The table below models a particular physical situation.
x −9 −3 4 10
y 9 1 −7 10
Find the piecewise linear equation that models the data above. Round to three decimal places if needed.
y={
___ x + ___. −9 ≤ x ≤ −3
___ x + ___. −3 < x ≤ 4
___ x + ___. 4 < x ≤ 10
The piecewise linear function that models the situation is given as follows:
y = -4/3x + b, −9 ≤ x ≤ −3,y = -8/7x - 17/7, −3 < x ≤ 4,y = 17/6x - 110/6, 4 < x ≤ 10.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.A piecewise function is a function that has different definitions based on the input.
For x between -9 and -3, the function decreases by 8 when x increases by 6, hence the slope is given by:
m = -8/6 = -4/3, hence:
y = -4/3x + b.
When x = -9, y = 9, hence we use it to find b as follows:
9 = -4/3(-9) + b
9 = 12 + b
b = -3.
Thus the first definition is:
y = -4/3x + b, −9 ≤ x ≤ −3
For x between -3 and 4, the function decreases by 8 when x increases by 7, hence the slope is given by:
m = -8/7
y = -8/7x + b.
When x = -3, y = 1, hence we use it to find b as follows:
1 = -8/7(-3) + b
1 = 24/7 + b
b = -17/7
Thus the second definition is:
y = -8/7x - 17/7, −3 < x ≤ 4.
For x between 4 and 10, the function increases by 17 when x increases by 6, hence the slope is given by:
m = 17/6
y = 17/6x + b.
When x = 10, y = 10, hence we use it to find b as follows:
10 = 17/6(10) + b
b = 10 - 170/6
b = -110/6
Thus the third definition is:
y = 17/6x - 110/6, 4 < x ≤ 10
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Find the slope of the line if it exists.
Answer:
The slope would be [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
The mass of an oxygen molecule is about 0.000000000000000000000053 g. What is it’s scientific notation?
Answer:
5.3 x 10^-23 g
At what coordinate would you place point e so that is partitions df in a ratio of 5:3
In general, a
person is 1% shorter in the evening than in the
morning. Use your height to write a conditional
that uses this fact.
The conditional statement is that; If generally a person is 1% shorter in the evening than in the morning, then my height is about 1.62326 m in the evening.
How to write conditional statements?
First, we will calculate how much is one percent of your height and then subtract that percentage from the total height to get your" height in the evening".
For example:
If my height is 1.64 m, then;
0.01 * 1.64 m = 0.0164 m
Step 2 is;
1.64m - 0.0164m = 1.62326 m
Now, using these height, let's write a conditional that uses the described fact:
Conditional:
If generally a person is 1% shorter in the evening than in the morning, then my height is about 1.62326 m in the evening.
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if x² = √16 = x
true or false?
Step-by-step explanation:
it is true
the square root of 16 is 4
Grady's father is building a 15-meter fence with the start of the fence at coordinates(8, 5) and the midpoint of the fence at coordinates(3.5, -1) . What are the coordinates of the other end of the fence?
Based on the calculations, the coordinates of the other end of the fence are equal to (-1, -7).
What is a line segment?A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.
How to determine the coordinates of the other end of the fence?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint on x-coordinate is given by:
xm = (x₁ + x₂)/2
3.5 = (8 + x₂)/2
Cross-multiplying, we have:
7 = 8 + x₂
x₂ = 7 - 8
x₂ = -1.
Midpoint on y-coordinate is given by:
ym = (y₁ + y₂)/2
-1 = (5 + y₂)/2
Cross-multiplying, we have:
-2 = 5 + y₂
y₂ = -2 - 5
y₂ = -7.
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PLEASE HELP I DONT UNDERSTAND
According to the image, the figure moved four times to return to its initial position.
What is the initial position of the figure?The starting position of the figure is in the lower left corner of the frame.
How does it move from position 1 to position 2?The movement made by the figure from position 1 to position 2 is that it moves from the lower left corner to the lower right corner.
How do you move from position 2 to position 3?The movement made by the figure from position 2 to position 3 is that it moves from the lower right corner to the upper right corner. Additionally, the figure rotates to the left 180°.
How does it move from position 3 to position 4?The movement that the figure performs from position 3 to position 4 is that it moves from the upper right corner to the upper left corner.
How does it move from position 4 to position 5?The movement made by the figure from position 4 to position 5 is that it moves from the upper left corner to the lower left corner. Additionally, the figure is rotated 180° to the left again.
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please help reflictions
Answer:
A would be reflected on the y-axis first then translated up 6 units
Step-by-step explanation:
A 20-year U.S. Treasury bond has a 3.50 percent interest rate, while a same maturity corporate bond has a 5.25 percent interest rate. Real interest rates and inflation rate expectations would be the same for the two bonds. If a default risk premium of 1.50 percentage points is estimated for the corporate bond, determine the liquidity premium for the corporate bond.
The liquidity premium for the corporate bond is 0.25%.
What is liquidity?Any additional compensation needed to stimulate investment in assets that cannot be quickly and effectively converted into cash at fair market value is known as a liquidity premium. For instance, due to its relative illiquidity, a long-term bond will have a higher interest rate than a short-term bond.
Liquidity premium for corporate bond will be:
= 5.25 - 3.5 - 1.5
= Interest - Treasury - Default risk
= 0.25%.
Therefore, the liquidity is 1.25%.
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solve the quadratic formula simpliest set for y^2-7y-9=0
Please help me yall!! This is due tomorrow… I would really appreciate it if y’all could give me some feedback!! Please and thank you!!
Answer:
[tex]\sf (A' \cap B) \cup (A' \cap C') =\{1,6,7\}[/tex]
Step-by-step explanation:
[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]
Given sets:
Universal = {1, 2, 3, 4, 5, 6, 7, 8}A = {2, 4, 5, 8}B = {1, 4, 6}C = {1, 2, 3, 4, 5}Therefore, the complement sets are:
[tex]\begin{aligned}\sf A' & = \text{U}-\sf A\\& = \{1,2,3,4,5,6,7,8 \}- \{2,4,5,8 \}\\& = \{1,3,6,7 \}\end{aligned}[/tex]
[tex]\begin{aligned}\sf B' & = \text{U}-\sf B\\& = \{1,2,3,4,5,6,7,8 \}- \{1,4,6 \}\\& = \{2,3,5,7,8 \}\end{aligned}[/tex]
[tex]\begin{aligned}\sf C' & = \text{U}-\sf C\\& = \{1,2,3,4,5,6,7,8 \}- \{1,2,3,4,5 \}\\& = \{6,7,8 \}\end{aligned}[/tex]
Solution
[tex]\begin{aligned}\sf (A' \cap B) \cup (A' \cap C') & = \sf \left(\{1,3,6,7 \} \cap \{1,4,6\} \right) \cup \left(\{1,3,6,7 \} \cap \{6, 7, 8 \} \right)\\\\& = \sf \{1,6\} \cup \{6,7 \} \\\\& = \sf \{1,6,7\} \end{aligned}[/tex]
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To two decimal places,
√70
must lie between ____
and _____.
To two decimal places,
√70
must lie between 8.3
and 8.4
Write the standard form of the equation of the circle with the given characteristics.
Center: (-3, 4); Radius: 3
4. [-/6 Points]
DETAILS
LARPCALC11 1.3.027.
Find the slope of the line passing through the pair of points. (If an answer does not exist, enter DNE.)
(-8, -12), (1, 24)
The standard form of the equation of the circle is (x+3)²+(y-4)²=9 .
The slope of the line is
A circle is defined as the locus of a moving point which is always equidistant from a given point.
This given point is called the center of the circle.The distance between the center and the circumference of the circle is the radius if the circle.The standard form of a circle is given by the equation : (x-x₁)²+(y-y₁)²=r² , where (x₁,y₁) is a point on the circle and r is the radius.The given point on the circle is (-3, 4) and the radius is 3 units.
Hence the standard form of the equation of the circle is :
(x-{-3})²+(y-4)²=3²
or, (x+3)²+(y-4)²=9
Let the two given two points as A(-8, -12) and B(1, 24).
Now the slope of the line AB can be calculated by the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}.[/tex]
Now let us put the given values in the equation to calculate slope:
[tex]m_{AB}=\frac{24-(-12)}{1-(-8)}\\\\or, m_{AB}=\frac{36}{9} \\\\or, m_{AB}=4[/tex]
Hence the slope of the line is 4.
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Side KN of figure KLMN is parallel to side LM. Figure KLMN is rotated 90 degress clockwise about Point P to produce Figure RSTU. Based on this information, select all statement that are true.
The figure KLMN is being rotated by 90°, which is a rigid transformation, the true statements are therefore;
(D) Figure RSTU is congruent to figure KLMN
(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
How can the similarities between the two figures following the rotation be found?The given parameters are;
In KLMN, KN||LM
The transformation applied to figure KLMN = A 90° clockwise rotation about point P.
The image of KLMN following the rotation transformation is Figure RSTU.
Please find attached a drawing of the possible diagram in the question obtained from a similar question online.
The options from the question are;
(A) [tex] \overline{ST}[/tex] is parallel to [tex] \overline{RU}[/tex]
(B) [tex] \angle R[/tex] is the same measure as [tex] \angle N[/tex]
(C) [tex] \overline{RS} [/tex] is the same length as \overline{MN}
(D) Figure RSTU is congruent to figure KLMN
(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
A rotation transformation is a rigid transformation, therefore;
The distances between any two points on the pre–image is the same as the distance between corresponding points on the image, which gives;
Figure KLMN [tex] is congruent to [/tex] Figure RSTU
Figure KLMN [tex] \cong [/tex] Figure RSTU
According to the postulate, Corresponding Angles of Congruent Figures are Congruent, we have;
[tex] \angle T \cong \angle M[/tex]
Which gives;
[tex] \angle T[/tex] = [tex] \angle M[/tex]
[tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
The correct options are therefore;
(D) Figure RSTU is congruent to figure KLMN
(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]
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Why was his velocity 0? Explain.
Which numbers are between 5 & 6 not including 5 & 6
Answer:5.1,5.2,5.3,5.4,5.6,5.7,5.8,5.9,
Step-by-step explanation:
Select the approximate value of 9 - √7 on a number line.
The value of 9 - √7 is between 6 and 7:
4 < 7 < 9
⇒ √4 < √7 < √9
⇒ 2 < √7 < 3
⇒ -3 < -√7 < -2
⇒ 9 - 3 < 9 - √7 < 9 - 2
⇒ 6 < 9 - √7 < 7
which of the following statements is true about the function f in the equation f(10)=5
The cordinates of the turning point of the graph of y=f(x) occurs at (1.1) and (5/3, 23/27)
2
(x−2)+1
Now, differentiating w.r.t. x, we get
f
′
(x)=2(x−1)(x−2)+(x−1)
2
=(x−1)[2(x−2)+x−1]
=(x−1)[3x−5]
Hence,
f
′
(x)=0 implies x=1 and x=
3
5
Corresponding values of y are y=1 and y=
27
23
respectively.
∴ Co-ordinates of turning point of the graph of f(x) occurs at (1,1) and (
3
5
,
27
23
)
Now,
f(x)=(x−1)
2
(x−2)+1
=(x
2
−2x+1)(x−2)+1
=x
3
−2x
2
−2x
2
+4x+x−2+1
=x
3
−4x
2
+5x−1
The value of p for which the equation f(x)=p has 3 distinct solutions lies in interval (
27
23
,1)
Area enclosed by f(x),x=0,y=1 and x=1 is
A=∫
0
1
(1−f(x))dx
⇒∫
0
1
(4x
2
−x
3
−5x+2) dx
⇒A=
12
7\
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find the value of k if it is known that the line y=kx goes through the point B(-30,3)
Answer:
k = -0.1
Step-by-step explanation:
An ordered pair is in the form (x,y) We can use the x and y from the point (-30,3) to find k
y = kx We will replace x with -30 and y with 3
3 = (-30)k divide both sides by -30
-0.1 = k or [tex]\frac{-1}{10}[/tex] in the fraction form