Neither 2 nor 7 have inverses mod 6 or 7, respectively, so the expressions in (a) and (b) cannot really evaluated... At least we can evaluate (c) :
[tex]5\times3 \equiv 15 \equiv 1 \pmod 7 \\\\ \implies 3\times2\div5 \equiv 3\times2\times3 \equiv18 \equiv \boxed{4 \pmod{7}}[/tex]
Daredevil Danny hoop jump Step 4: b) Using your values of a, b, and c, did Daredevil Danny successfully pass through the Flaming Hoop Jump of Awesome? If not, describe what happened. Then, go back to critique your work and revise it. Write about your revision. (5 points) d) Once you have determined the correct values of a, b, and c, verify algebraically that Daredevil Danny will successfully pass through the Flaming Hoop Jump of Awesome. (5 points)
Pleasee Helppp I can't figure it out and I'm running out of time to get it turned in.
The equation of Daredevil Danny's jump in vertex form is y = -0.32(x - 25)^2 + 32
The values of the coefficients a, b and cThe graph of Daredevil Danny's jump is added as an attachment
A quadratic function is represented as:
y = a(x - h)^2 + k
From the graph, we have:
Vertex, (h, k) = (25,32)x-intercepts = 15 and 35So, we have:
y = a(x - 25)^2 + 32
Substitute the value of the x-intercept
0 = a(15 - 25)^2 + 32
Subtract 32 from both sides
a(15 - 25)^2 = -32
Solve for a
a = -0.32
Substitute a = -0.32 in y = a(x - 25)^2 + 32
y = -0.32(x - 25)^2 + 32
Expand the exponent
y = -0.32(x^2 -50x + 625) + 32
Expand the bracket
y = -0.32x^2 + 16x - 200 + 32
This gives
y = -0.32x^2 + 16x - 168
Hence, the values of the coefficients a, b and c are -0.32, 16 and -168
Did he jump successfully?Yes, he jumped successfully
This is so because his maximum height (i.e. the vertex of his jump) is higher than the vertex of the hoop
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You can work a total of no more than 40 hours each week at your two jobs. Housecleaning pays $8 per hour and your sales job pays $119 per hour. You need to earn at least $323 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job.
A) h+ s ≥ 40 and 8h + 11s ≥ 323
B) h+ s < 40 and 8h + 11s ≤ 323
C) h + s ≤ 40 and 8h + 11s ≥ 323
D) h + s ≤ 40 and 8h + 11s < 323
Answer:
C
Step-by-step explanation:
you can only work 40 or less hours per week but you must earn greater then or equal to $323.
To pay for a fishing boat, mai made a down payment of and took out a loan for the rest. on the loan, she paid monthly payments of for years. (a) what was the total amount mai ended up paying for the fishing boat (including the down payment and monthly payments)? (b) how much interest did mai pay on the loan?
Write the equation given the following polynomial graph.
Answer: Option (2)
Step-by-step explanation:
There is a double root at x=-1, so there is a factor of [tex](x+1)^2[/tex].
Eliminate options (1) and (3).Also, as x approaches both positive and negative infinity, the graph approaches negative infinity, so the leading coefficient is negative.
Eliminate (4).Reduce to simplest form
- 9/15 + 5/15
Answer: -4/15
Step-by-step explanation: Since the base denominator is the same, all we have to do is add the numerators (the denominators stay the same.)
-9 + 5 = -4 which is -4/15.
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Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
555. 0 .041
Answer:
Hence, 0.041 can be expressed as [tex]$4.1 \times 10^{-2}$[/tex].
Step-by-step explanation:
- Given 0.041
- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .
- Then count n and write in scientific notation.
Step 1 of 1
Consider 0.041
[tex]$$\Rightarrow 4.1$$[/tex]
Decimal has moved to 2 places at right.
The power will be negative as original no. is less than 1 .
So, [tex]$4.1 \times 10^{-2}$[/tex]
[tex]$$0.041=4.1 \times 10^{-2} \text {. }$$[/tex]
Triangles L M N and L K N are connected at side L N. A line is drawn from point M to point K and intersects side L N at point P.
Examine this figure. Which two pieces of information, if true, would help to prove that ΔLMP ≅ ΔNMP by HL? Select two options.
Point P is the midpoint of MK.
Line MK is the perpendicular bisector of LN.
ML ≅ MP
ML ≅ MN
PK ≅ PK
The true statement is Line MK is the perpendicular bisector of LN and ML is ≅ MN.
What is perpendicular?Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Given:
Δ LMN and Δ LKN are connected at side LN.
As per the information,
Line MK is the perpendicular bisector of LN. and ML ≅ MN.
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Answer: b and d
Step-by-step explanation:
Look at the number line below.
←
-2
-1
0
1
What point is marked on the number
line?
Distinguish arithmetic vs geometric sequences
Answer:
Arithmetic sequence
Step-by-step explanation:
The given sequence is arithmetic because it is increases gradually by 5
so the answer is "an arithmetic" and "difference" is equal to "5"
7. Find an equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4.
The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5
How to find the equation of a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4
Hence,
perpendicular lines follows the rule below:
m₁m₂ = -1
Hence,
5x - 3y = 4
5x - 4 = 3y
y = 5/ 3 x - 4 / 3
m₁ = 5 / 3
5/3 m₂ = -1
m₂ = - 3 / 5
Hence,
using (-4, 5)
5 = - 3 / 5 (-4) + b
5 = 12 / 5 + b
b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5
Therefore,
y = -3 / 5 x + 13 / 5
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Answer:
3x +5y = 13
Step-by-step explanation:
The equation of a perpendicular line through a given point can be obtained by swapping the x- and y-coefficients of the original line's equation, and negating one of them. The constant in the equation needs to be chosen so the equation will be true at the given point.
Form of perpendicular lineSwapping the coefficients of the given equation, we have ...
3x -5y = c . . . . . for some constant c
Negating the y-coefficient gives a perpendicular line:
3x +5y = c
Particular solutionWe want the equation to be true for (x, y) = (-4, 5), so the constant needs to be ...
3x +5y = 3(-4) +5(5) = -12 +25 = 13
The equation of the perpendicular line is ...
3x +5y = 13
__
Additional comment
This process works for equations given in any form. If you start with point-slope form or slope-intercept form, some manipulation of the result may be required to get to the form you want. Standard-form or general-form equations are the easiest to apply this method to.
Note that equations in standard form want to have a positive leading coefficient. That is why we chose to change the sign of the y-coefficient, rather than the x-coefficient.
what is the side view ? the rest are right like i've tried loads of combinations but they're not right
Answer:
a view from the side.
"the parts are shown in the sectioned side view"
Please assist me with this question
Answer:
x+25=180 [Being sum of angle of triangles]x=180 - 25
x=155
NowX+ 144+25=180[ Being sum of angle of a triangles ]x+ 169=180
x=180-169
x=11
I need help with this geometry question.
1st transformation: A vertical translation of the figure down by 8 units
2nd transformation: Shows a reflection on both axis and vertical translation up the plane by 8 units
Transformation of coordinatesTransformation is a way of changing the position of an object on an xy-plane.
For the translation
(x, y)-> (x, y-8)
It shows a vertical translation of the figure down by 8 units while the translation;
(x, y - 8) -> (-x, -y)
shows a reflection on both axis and vertical translation up the plane by 8 units
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Find and interpret the slope of the line ca
(10,4) and (2,44)
Answer: -5
Step-by-step explanation:
Slope can be found with change in y over change in x.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Let (10, 4) be point 1 and (2, 44) be point 2.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{44-4}{2-10}[/tex]
[tex]\displaystyle \frac{40}{-8}[/tex]
[tex]\displaystyle \frac{40}{-8}[/tex]
-5
With out calculation the answer, is 1/3 x 7/15 greater or less than 1/3?
Answer:
it might be greater i think
Triangle sqt is isosceles. the measure of angle stq is 48°. what is the measure of angle s t r? 24° 38° 48° 76°
The measure of ∠STR in the isosceles triangle is 24°
What is an isosceles triangle?
A triangle having two sides of equal length is termed as an isosceles triangle. The base angles of an isosceles triangle are also equal in measure. The fact that the perpendicular bisector of the base and the angle bisector of the vertex angle are the same is another crucial characteristic of an isosceles triangle. We refer this as Isosceles Triangle Theorem.
What is the value of angle STR?
It is given that in isosceles triangle SQT,
∠STQ = 48°
Since, the line TR is the angle bisector of angle STQ, we have,
∠STR = ∠RTQ
And, ∠STR + ∠RTQ = ∠STQ
Let ∠STR be x, the, we get,
x + x = ∠STQ
⇒ 2x = 48°
⇒ x = 24°
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Triangle J K L is shown. Point N is the midpoint of side J L and point M is the midpoint of side K L. The length of J K is 19.6 meters. The lengths of J N and N L are 7.4 meters. The lengths of K M and M L are 10.7 meters.
What is the distance between points M and N?
meters
The distance between points M and N according to the task content is; 9.8 meters.
What is the distance between points M and N?From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints of KL and JL respectively.
Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;
NM/19.6 = 7.4/(2×7.4)
NM = 19.6/2 = 9.8 meters.
This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.
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Answer: 9.8 meters
Step-by-step explanation: Trust Me!! I got the answer correct on Edge.
Q: What is the distance between points M and N?
A: 9.8 meters
Help
x =x=x, equals
^\circ
∘
degrees
The value of x in the straight line shown in the attached diagram is 64°
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
From the image:
x + 26 + 90 = 180° (sum of angles in a straight line)
hence:
x + 116 = 180
x = 64°
The value of x in the straight line shown in the attached diagram is 64°
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The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?
a)0 = –4.9t2 + 19.6t + 24.5
b)0 = –4.9t2 + 24.5t + 19.6
c)19.6 = –4.9t2 + 24.5t
d)24.5 = –4.9t2 + 19.6t
Answer:
s(t) = -4.9t² + 39.2t
Step-by-step explanation:
Given the projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s²
Given
g = -4.9m/s²
v0 = 39.2m/s
s0 = 0m (the initial height)
On substituting into the formula;
s(t) = gt² + v0t + s0
s(t) = -4.9t² + 39.2t + 0
s(t) = -4.9t² + 39.2t
This gives the equation that models the height
The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10). On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8). On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10). On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).
Using translation concepts, the graph of g(x) is given as follows:
It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent and translated functions are given, respectively, by:
f(x) = x².g(x) = (x - 5)² + 1.The transformations are as follows:
x -> x - 5, hence the function was shifted right 5 units.y -> y + 1, hence the function was shifted up 1 unit.f(x) has vertex at (0,0), hence g(x) will have the vertex at (5,1). When x = 2, g(x) = (2-5)^2 + 1 = 10, hence the correct statement is:
It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
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Describe fully the single transformation which takes shape A to shape B.
You have the correct answer. Apply a 180 degree rotation around the point (0,2)
Reason:
We'll connect corners between figures A and B.
Draw a line from the upper right corner of figure A to the lower left corner of figure B. This line is in red (see diagram below).
Draw another line from the lower right corner to the upper left corner. This line is in blue.
The red and blue lines intersect at the center of rotation (0,2)
The line segments constructed consist of endpoints of "before" and "after". For instance, the upper right corner in figure A rotates to the lower left corner of figure B. This happens because of the 180 degree rotation.
Note: You can do this rotation either clockwise or counterclockwise, and you would get the same result.
help meee please
20 points
Answer:
16 sq. yds
Step-by-step explanation:
1. Split the shape into 2
The small square is 2(2) = 4
The bigger rectangle is 3(4) = 12
4 + 12 = 16 sq. yds
Already tried simplifying and dividing, but i didn't get the correct answer. Could a step by step explanation be provided so i know how to do this in the future?
Answer:
[tex]\sf \dfrac{x+2}{x}[/tex]
Step-by-step explanation:
Simplifying the expression:
1. Factorize each expression.
x² + 8x + 15
Sum = 8
Product = 15
Factors = 3 , 5 {When we add 3 & 5 we get 8 and when we multiply 3*5, we get 15}
x² + 8x + 15 = x² + 3x + 5x + 15
= x(x + 3) + 5(x + 3)
= (x + 3)(x + 5)
x² - 2x - 15
Sum = -2
Product = -15
Factors = 3 , (-5) {When we add 3 + (-5) =2 and when we multiply, 3*(-5) = -15}
x² - 2x - 15 = x² + 3x - 5x - 15
=x(x + 3) -5(x + 3)
= (x + 3)(x - 5)
x² + 5x = x( x + 5)
x² - 3x - 10
Sum = -3
Product = -10
Factors = 2 , (-5) {When we add 2 +(-5) = -3 and when we multiply 2 *(-5) = -10}
x² - 3x - 10 = x² + 2x - 5x - 10
=x(x + 2) - 5(x + 2)
= (x + 2)(x - 5)
2. Use KCF method and simplify.
K - keep the first fraction
C - change division to multiplication
F - Flip the second fraction.
[tex]\sf \dfrac{x^2 + 8x + 15}{x^2 - 2x - 15} \ \div \ \dfrac{x^2 + 5x}{x^2 - 3x - 10}=\dfrac{x^2 + 8x + 15}{x^2-2x - 12}*\dfrac{x^2 - 3x - 10}{x^2 + 5x}[/tex]
[tex]\sf = \dfrac{(x +3)*(x +5)}{(x+3)(x - 5)}*\dfrac{(x + 2)(x - 5)}{x(x+5)} \\\\= \dfrac{x + 2}{x}[/tex]
11. A rectangle is graphed on a coordinate plane. The coordinates for two of the
vertices of the rectangle are (-5,8) and (-5, -6). What is the distance between the
two vertices?
A
2 units
B
C
4 units
10 units
D 14 units
Answer:
D. 14 units
Step-by-step explanation:
d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-x_{1})^{2} }[/tex]
= [tex]\sqrt{(-5 - (-5))^{2} + (-6 - 8)^{2} }[/tex]
= [tex]\sqrt{0^{2} + -14^{2} }[/tex]
= [tex]\sqrt{0 +196 }[/tex]
= [tex]\sqrt{196}[/tex]
= 14
Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
With the help of trigonometric function, the above problems have been calculated. See explanation below.
What are Trigonometric functions?The term "trigonometric function" refers to functions that are periodic in nature and that shed light on how a right-angled triangle's angles and sides relate to one another.
The solutions to x in the respective problems is given as follows:
1) x = 5 /Sin(30°)
x = 10
!) Sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°)
= (3√3) / x
x = (3√3) / 3
W) In trigonometry, every right-triangle that is isosceles in nature, the angle made by the legs and the hypotenuse will always equal 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3
= 4√3 / 3
S) Sin(60°) = x / (10/3)
x = (5√3) / 3
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PLEASE HELP (ASAP)
In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal.
Angle x of the triangle PQR is 53 degrees.
Angle x is gotten by alternate angle relationship.
How to find an angle in a triangle?Line AB is parallel to line CD
Therefore,
AB║CD
Hence,
62 + x = 115(alternate angles)
62 - 62 + x = 115 - 62
x = 53°
We got the angle x degrees from alternate angle relationship.
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Answer:
x = 50
Step-by-step explanation:
Angle <BPR and angle <PRD are supplementary angles so their sum is equal to 180
m<BPR + 115 = 180 subtract 115 from both sides
m<BPR = 65
angles:
<APQ, x, and <BPR form a straight line and so their sum is equal to 180
65 + x + 65 = 180 add like terms
130 + x = 180 subtract 130 from both sides
x = 50
From the diagram below, we can say that ___.
Select one:
a.
Δ CED is similar to Δ BEA by AA.
b.
Δ CED is similar to Δ BEA by ASA
c.
the two triangles are not similar
Answer: The correct answer is choice A.
Step-by-step explanation:
This is because the triangles have the same angles, but are scaled differently. Thus because of the scale, there can be no correlation between the sides. Because the triangles share point E you can see that both triangles share the same angle but also notice how lines CD and AB are parallel. This makes all angles identical proving the triangles are the same but different sizes. Concluding that choice A is correct.
What’s the length of three pieces of pipe if they all equal 72m
Answer:
72 × 3 = 216m
216 m is the combined length
what is x over 4 equal to -7
Answer:
-28
Step-by-step explanation:
x/4= -7
4* x/4= -7*4
x= -28
Simplify the following expression.
Answer:
0y^2 + 2z^3 + 3y^3
Step-by-step explanation:
The simplified form of the expression is 0y²+2z³ + 3y³
The given expression is -1/3y² + 2/3 z³ +1/3y² +3y³+4/3z³.
In the expression y, z are the variables.
Combine the like terms:
(-1/3+1/3)y²+(2/3+4/3)z³ + 3y³
Simplify each term:
0y²+2z³ + 3y³
Hence, the simplified form of the expression is 0y²+2z³ + 3y³
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