Answer:
factor polynomial is x+q so x=-q
putting the value of x in both equations
eqn 1)a^2+p(-a)+q=0
a^2 -ap+q=0
eqn 2)a^2+m(-a)+n=0
a^2-am+n=0
Since both are equal to zero,we can write:
a^2-ap+q=a^2-am+n
-ap+am=n-q
a(-p+m)=n-q
a=(n-q)/(m-p)
Explanation:
Since (x + a) is a factor of the two polynomials, when x = -a, the polynomials should both equal 0 (this is known as the factor theorem).
• First equation:
[tex]x^{2} + px + q[/tex]
When x = -a:
[tex](-a)^{2} + p(-a) + q = 0\\\\a^{2} -pa + q = 0[/tex]
• Second equation:
[tex]x^{2} + mx + n[/tex]
When x = -a:
[tex](-a)^{2} + m(-a) + n = 0\\\\a^{2} -ma + n = 0[/tex]
• As both equations equal 0, we can equate them:
[tex]a^{2} -pa + q = a^{2} -ma + n \\\\-pa + ma = n - q\\\\a(m - p) =n -q\\\\a = (n - q)/ (m - n)[/tex][proven]
The lighthouse and the boat shown below
are 24.6 km apart.
The boat is 13.5 km east of the lighthouse.
Work out the bearing of the lighthouse from
the boat.
Give your answer to the nearest degree.
|FFFFLD
Lighthouse
N
Boat
Not drawn accurately
Answer:
213°
Step-by-step explanation:
Consider the angle measured at the lighthouse between North and the Boat. The lengths given in the problem statement are the lengths of the side opposite that angle, and the length of the hypotenuse of the right triangle shown. The trig function that relates the angle and those sides is ...
Sin = Opposite/Hypotenuse
ApplicationThe sine of the angle at the lighthouse is ...
sin(bearing to boat) = (13.5 km)/(24.6 km) = 45/82
The value of the angle is found using the inverse sine function, called the arcsine function:
bearing to boat = arcsin(45/82) ≈ 33°
Reverse bearingThe bearing from the boat to the lighthouse is in the opposite direction. It can be found by adding 180° to this angle:
bearing to lighthouse = 33° +180° = 213°
__
Additional comment
The attached image shows a calculator making this calculation. Note that the angle mode is set to DEG (lower left corner). The arcsine function is usually found as the 2nd function of the Sin key.
Mackenzie is a waitress at a restaurant. Each day she works, Mackenzie will make a guaranteed wage of $25, however the additional amount that Mackenzie earns from tips depends on the number of tables she waits on that day. From past experience, Mackenzie noticed that she will get about $15 in tips for each table she waits on. How much would Mackenzie expect to earn in a day on which she waits on 13 tables? How much would Mackenzie expect to make in a day when waiting on tt tables?
Answer: If she waits on 13 tables than she should expect to earn $220
Step-by-step explanation:
15*13=195
195+25=220
Consider the given solids with the dimensions shown. Which solids are similar? three cubes. Figure 1 has side lengths of 5 ft, figure 2 has side lengths of 7 feet, figure 3 has side lengths of 10 feet. Figures not drawn to scale A. only figure 1 and figure 2 B. only figure 1 and figure 3 C. only figure 2 and figure 3 D. all three figures
Answer:
D. all three figures
Step-by-step explanation:
A cube is a rectangular prism that has every edge equal in length to every other edge. This ratio of edge lengths holds for all cubes. Every cube is similar to every other cube.
ApplicationCubes with edge lengths of 5 ft, 7 ft, and 10 ft will all be similar. Any pair of corresponding edges of different cubes will have the same ratio.
What is the equation of a line passing through (-3, 7) and having a slope of 5 ?
Answer:
B
Step-by-step explanation:
since the slope is 5, 1/5x or -1/5x cannot be the slope. since the slope isn't negative it also cancels out -5x. 5x can be your only slope and that is in answer B.
in the rectangle abcd, AC= -6x-2, BP= -4x-3, DP+ -6y-19 find the value of y
is that 2.11 I think so
Step-by-step explanation:
I don't know explain it to you and
Simplify using order of P
operations.
3² - (2 + 1)²
E
MD
AS
Answer:
o
Step-by-step explanation:
Order of operations. Left-to-Right prevails
P = parenthesis first
E = exponentiation
MD multiplication/division leftmost has higher priority
AS addition/subtraction leftmost first
1st computation: (2 + 2) because of P ==> 3
2nd Computation: 3² = 9
3rd computation (1+2)² = 3² = 9
Answer 9 - 9 = 0
Perpendicular bisector: put the following steps in order using what you know about constructing a perpendicular bisector.
In order to draw a perpendicular bisector you must have ruler , compass and a pencil.
Given nothing and we have to show the steps to draw a perpendicular bisector.
Perpendicular bisector is the line which divides the line into two equal parts and makes 90° angle on other line.
If we want to make a perpendicular bisector on a line then we have to follow the following steps:
1) First draw a line with the help of ruler on which we want to make perpendicular bisector.
2) Now take a compass and a pencil.
3) Put the pencil in the compass and strech the compass equal to half or little more of the length of the line.
4) Now put the compass on one end of the line and draw an arc on the line or may be just upward.
5) Now repeat the step 4 from other end.
6) Now draw a line from the point where two arcs intersects on the line.
7) It is the perpendicular bisector of the line.
Hence to draw a perpendicular bisector we require compass, ruler and a pencil.
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2. Match each transformation with the correct description
A. (x,y) → (3x, y)
B. (x,y) → (x + 3, y)
C. (x,y) → (x, 3y)
D. (x,y) →
(x, y + 3)
E. (x,y) → (3x, 3y) d
—
—▬▬▬▬▬
dilation with scale factor 3
translation 3 units up
translation 3 units right
horizontal stretch by a factor of 3
vertical stretch by a factor of 3
PLS IF YOU CAN HELP WITH THE TWO QUESTION THAT WOULD BE GREAT
Answer:
Step-by-step explanation:
The Matching for each transformation is
1. (x,y) → (3x, y)
horizontal stretch by factor 3.
2. (x,y) → (x + 3, y)
translation 3 unit right
3. (x,y) → (x, 3y)
Vertical stretch by factor 3.
4. (x,y) → (x, y + 3)
translation 3 unit up.
5. (x,y) → (3x, 3y)
dilation with Scale factor 3.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
1. (x,y) → (3x, y)
It is horizontal stretch by factor 3.
2. (x,y) → (x + 3, y)
It is translation 3 unit right because the rule for translation for 3 unit right is x - > x + a
3. (x,y) → (x, 3y)
It is Vertical stretch by factor 3.
4. (x,y) → (x, y + 3)
It is translation 3 unit up.
5. (x,y) → (3x, 3y)
It is dilation with Scale factor 3.
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find the mean of factors of 16
Answer:
The answer is 6.2
Step-by-step explanation:
The factors of 16 are 1,2,4,8, and 16.
get the sum of the factors which is 31, then divide it to number of the addends which is 5.
31/5 = 6.2
please help
PART A
(length of the foot) = 0.860 • (length of the forearm) + 3.302
17= 0.860 x 17 + 3.302= 17.922
If you let y = length of the foot and x = length of the forearm, this equation can be simplified to y = 0.860x + 3.302.
y = 0.860 (17) + 3.302= 17.922
PART B
Could the equation in Part A represent a function? Would this be a linear function? Why or why not? Explain your answer.
Answer:
PART A
length of foot = y
length of forearm = x = 17
Equation: y = 0.860x + 3.302
Plug in 17 for x in the equation, and simplify. Remember to follow PEMDAS, first multiply, then combine like terms:
y = (0.860)(17) + 3.302
y = 14.62 + 3.302
y = 17.922
length of foot = y = 17.922 inches long
What is the value of the expression below?
32^3/5
O A. 6/5
B. 6
O c. 96/5
O D. 8
Answer:
D. 8
Step-by-step explanation:
32^(3/5) is the same as [tex]\sqrt[5]{32}[/tex]^3.
[tex]\sqrt[5]{32}[/tex] = 2 because 2^5=32
2^3 = 8
Simplify the expression.
Rewrite 32 as 2⁵.
[tex]\bf{\left(2^{5}\right)^{\frac{3}{5} } }[/tex]
Apply the power rule and multiply exponents, (αᵐ)ⁿ=αᵐⁿ.
[tex]\bf{2^{5}^{(\frac{3}{5} )} }[/tex]
Cancel the common factor of 5.
Cancel the common factor.
[tex]\bf{2^{\not{5}}^{(\frac{3}{5} )} }[/tex]
Substitute the expression.
[tex]\bf{2^{3} \ \ \to \ Calculate \ power. }[/tex]
Raise 2 to the power of 3.
8 ===> AnswerWe conclude that the correct option is "D".
{ Pisces04 }Please help meee! im confused!
f(x)=y=√x looks something like this:
(4,2)
(9,3)
(16,4)
Whilst your graph is much higher slope, for lack of better term
Rules of transformation
f(x)+b - function is shifted b units upward (up y-axis)
f(x)-b - function is shifted b units downward (down y-axis)
f(x+b) - function is shifted b units to the left (negative x-axis)
f(x-b) - function is shifted b units to the right (positive x-axis)
-f(x) - function is reflected over x-axis
f(-x) - function is reflected over y-axis
bf(x) - vertical stretch for |b| > 1, vertical shrink for 0< |b| <1
f(bx) - horizontal shrink for |b| > 1, horizontal stretch for 0< |b| <1
**INVALIDATE my answer, as statements were given 10 mins after posted**
Answer:
The graph is translated to the left by 3
Step-by-step explanation:
the equation would be y= sqrt(x)+3
In Mr. Romano's class, the ratio of the number of girls to the number of boys is 3:2. A student is selected at random from
the class. The probability that the selected student is a boy is
F. 1/6
G. 1/3
H. 2/5
J. 3/5
K. 2/3
Please help ill give whoever answers the best the brainliest answer :)
Answer: The first answer choice
Step-by-step explanation:
In the first answer choice, the distance increases for two units, then decreases for three units. The distance then increased for 4 units, stayed level for 3 units, and then decrease slowly for 6 units. The graph exactly follows this trend.
The second answer is immediately wrong because it relates the distance between the car and the concert venue. It never mentioned that the car moved, and the venue obviously can't move.
The third answer says that after the first increase/decrease, Tyler went to go text his friends. However, the graph does not show a flat area after the first increase/decrease.
The fourth answer, like the second answer is immediately wrong because homes and schools can't move.
This is my first response, so I hope it was helpful. :D
Guys help me with this problem, please. I really need help right now.
Answer:
A
Step-by-step explanation:
So whenever you're finding the difference between two numbers you generally use the equation: |a-b| since a-b may or may not be negative, but |a-b| will always equal |b-a|. Since the only thing that differs is the sign. So when you have: [tex]|-\frac{2}{3}-\frac{5}{3}|[/tex], in this case a=-2/3 and b=5/3 (b is positive since you're subtracting b, so if b appeared positive in the equation, it's actually negative, since the negative sign in |a-b|, which would make the two negatives cancel out). This means A is the correct answer. You could also calculate what the value is. Calculating gives you: [tex]|-\frac{7}{3}| = \frac{7}{3}[/tex]. And as you can see the top one, has two numbers separated by 7 one thirds.
Answer:
A
Step-by-step explanation:
It is absolute value and when it is absolute value, it is positive.
the sum of perimeter of two similar polygons is 48cm,and the ratio of their corresponding sides is 1:3, find the perimeter of the larger polygon
Answer:
Step-by-step explanation:
Perimeter is the sum of lengths of triangles. Hence it's unit in
c
m
. Area has unit
c
m
2
i.e., length squared. So if measurements are in the ratio
3
:
4
, areas are in the ratio
3
2
:
4
2
or
9
:
16
. This is because the two triangles are similar.
A total area is
75
square centimeters, we need to divide it by the ratio
9
:
16
Of which first will be the area of the smaller triangle.
Hence the area of the smaller triangle is
75
×
9
9
+
16
=
75
×
9
25
=
75
3
×
9
25
1
=
27
square centimeters
The area of larger triangle would be
75
×
16
9
+
16
=
3
×
16
=
48
square centimeters
Two cell phone companies charge a flat fee plus an added cost for each minute or part of a minute used. The cost is represented by C and the number of minutes is represented by t.
Call-More: C = 0.40t + 25
Talk-Now: C = 0.15t + 40
a) Which company is cheaper if a customer talks for 50 minutes?
b) Under what conditions do the two companies charge the same?
Answer:
a) Call-more is cheaper
b) 60 minutes
Step-by-step explanation:
Call-More: C = 0.40t + 25
Talk-Now: C = 0.15t + 40
a) Substitute t = 50 minutes in the above equations.
Call-More:
C = 0.40*50 + 25
= 20 + 25
C = 45
Talk-Now:
C = 0.15*50 + 40
= 7.5 + 40
C = 47.40
Company Call-more is cheaper than Talk-now.
b) We have to find the conditions under what condition the two companies charge the same.
Charge of company Call-more = charge of company Talk-now.
0.40t + 25 = 0.15t + 40
0.40t = 0.15t + 40 -25
0.40t = 0.15t + 15
0.40t - 0.15t = 15
0.25t = 15
[tex]\sf t = \dfrac{15}{0.25}\\\\ t = \dfrac{15*100}{25}\\\\[/tex]
t = 15*4
t = 60 minutes
Two companies charge the same for 60 minutes.
In general, the greater the between group variance compared to the within group variance, the more likely you are to:
In general, the greater the between-group variance compared to the within-group variance, the more likely you are to find statistical significance.
Unlike the inside group version, where the focus is on the differences among a population and its implication, the between-organization variant is concerned with finding how the method of corporations differ from each other.
Inside-organization version (on occasion referred to as mistakes organization or error variance) is a time period used in ANOVA tests. It refers to variations because of variations within individual businesses (or ranges). In other words, no longer all of the values within every group (e.g. method) are equal.
With the purpose to examine multiple groups right away, we can study the ANOVA, or analysis of Variance. not like the t-test, it compares the variance within every sample relative to the variance between the samples.
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please can someone help me
Answer: A=48 squared centimeters
Step-by-step explanation: First you need to find the area of the whole rectangle. Area equals length times width (9*8), which is 72. Next you find the area of the white region: 4*6=24. Finally, you subtract the smaller region from the whole: 72-24=48. BOOM: you got the exact right answer :)
Determine the vertex of the quadratic relation y=2(x+2)(x-6).
Answer:
vertex = (2, - 32 )
Step-by-step explanation:
given a quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
given
y = 2(x + 2)(x - 6) ← expand factors using FOIL
= 2(x² - 4x - 12 ) ← distribute parenthesis
y = 2x² - 8x - 24 ← in standard form
with a = 2, b = - 8 , then
x = - [tex]\frac{-8}{4}[/tex] = 2
substitute x = 2 into the function for corresponding y- coordinate
y = 2(2 + 2)(2 - 6) = 2(4)(- 4) = 8 × - 4 = - 32
vertex = (2, - 32 )
Solve the system of equations using elimination: -x+3y=-24− and -4x+2y=4
Answer:
[tex]\begin{cases}x=-6\\y=-10\end[/tex]
Step-by-step explanation:
[tex]\begin{cases}-x+3y=-24 \left(1)\right\\-4x+2y=4 \left(2)\right\end[/tex]
Make x the subject in (1)
[tex]x=3y+24 \left(3)\right[/tex]
Sub into (2)
[tex]-4(3y+24)+2y=4\\\\\implies-12y-96+2y=4\\\\\implies10y=-100\\\\y=-10[/tex]
Sub into (3)
[tex]x=-30+24\\\\x=-6[/tex]
Hence
[tex]\begin{cases}x=-6\\y=-10\end[/tex]
Answer:
[tex]\left \{ {{x=-6} \atop {y=-10}} \right. .[/tex]
Step-by-step explanation:
[tex]\left \{ {{-x+3y=-24\ \ (1)} \atop {-4x+2y=4\ \ \ (2)}} \right. \ \ \ \ \\[/tex]
We multiply equation (1) by -4:
-x+3y=-24 |*(-4)
-x*(-4)+3y*(-4)=-24*-(-4)
4x-12y=96. (3) ⇒
[tex]\left \{ {{4x-12y=96\ \ (3)} \atop {-4x+2y=4\ \ \ (2)}} \right.[/tex]
We summarize equations (2) and (3):
[tex]-10y=100\ |:(-10)\\y=-10.\\Make\ y \ the\ subject\ in\ (1):\\-x+3*(-10)=-24\\-x-30=-24\\-x=-24+30\\-x=6\ |*(-1)\\x=-6.[/tex]
Question 8 c
A bag of tokens contains 7 red, 9 green, and 6 blue tokens. What is the probability that
a randomly selected token is not red? Enter your answer as a fraction.
Below is the graph of y=b^x. Find b.
b=
Answer: 1
Step-by-step explanation:
When [tex]x=0[/tex], [tex]y=\boxed{1}[/tex]
1. The following diagram shows a slide at a park. a. Find the vertical distance from the ground to the top of the slide. b. Find the length of the slide. c. What is the area of the space under the slide. Steps 2 m /70* Slide 40° H
The area of the space under the slide is 2.10 square meters
The vertical distanceThe diagram in the question is added as an attachment
The vertical distance is represented by h.
So, we have:
sin(70) = h/2
Solve for h
h = 2 * sin(70)
Evaluate
h = 1.88 m
Hence, the vertical distance is 1.88 m
The length of the slideThis is calculated using
sin(40) = h/Slide
This gives
sin(40) = 1.88/Slide
Solve for Slide
Slide = 1.88/sin(40)
Evaluate
Slide = 2.92
Hence, the length of the slide is 2.92 m
The area of the space under the slideThis is calculated using:
A = 0.5 * h * slide * sin(∅)
Where
∅ = 90 - 40 = 50
So, we have:
A = 0.5 * 1.88 * 2.92 * sin(50)
Evaluate
A = 2.10
Hence, the area of the space under the slide is 2.10 square meters
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PLEASE HELP ME ASAP!!!!!
what is m(angle) DCE
Applying the inscribed angle theorem, m∠CED = 34°.
What is the Inscribed Angle Theorem?According to the inscribed angle theorem, measure of inscribed angle DCE = 1/2(measure of intercepted arc ED).
m(ED) = 180 - 112 [semicircle]
m(ED) = 68°
m∠CED = 1/2(68°) [inscribed angle theorem]
m∠CED = 34°
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A baseball player makes 4 hits every 7 times at bat. At this rate, how many times did you hit if you hit 24 hits? 42 times 96 times 168 times 24 times
Answer:
42 times
Step-by-step explanation:
Here,
4 hits = 7 times
1 hits= 7/4 times
24 hits = 7/4 × 24
= 42 times.
The number of times that the baseball player makes the hit if he hit 24 hits is 42 times, which is an option (a).
Given that:
A baseball player makes 4 hits every 7 times at bat.
It is required to find the number of times that the player hits if he hit 24 hits.
Number of times that 4 hits are made = 7
Number of times that 1 hit is made = 7/4
So, the number of times that 24 hits are made can be found by the following formula.
Using the proportional concept, the number of times, N, is:
[tex]N=\frac{7}{4} \times 24[/tex]
[tex]=7\times6[/tex]
[tex]=42[/tex]
Hence, the correct option is (a).
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Simplify the expression write the answer using scientific notation (8x10^7)(2x10^6)
Answer:
Second option 1.6x10^14
Step-by-step explanation:
Area=
Please help, thanks so much
The area of LMNP is 6. 25 π^2
How to determine the areaArea of a rectangle = length × width
Circumference = 2 (length + width)
If circumference = 10 π
Let's find the length and width
10π = 2( L+ W)
10 π = 2(L + W)
10π = 2(L+ W)
L + W = 10π ÷ 2
L + W = 5π
Length = 2. 5π
Width = 2. 5π
Area = 2. 5π× 2. 5π
Area = 6. 25 π^2
Thus, the area of LMNP is 6. 25 π^2
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A bowl holds three green and three black marbles. Three marbles are selected randomly. What is the probability that all three are green
The formula for Classical Probability.
The probability of a simple event happening is the number of times the event can happen, divided by the number of possible events. The “math” way of writing the formula is P(A) = f / N.
Without replacing drawn marbles:
Probability of drawing 3 green:
3/10*2/9*1/8=1/120
Probability of drawing 3 black:
4/10*3/9*2/8=1/30
Probability of drawing 3 green:
3/10*2/9*1/8=1/120
Adding these three: 6/120 =5%
If replacing marbles after each draw
Probability of drawing 3 black:
(3/10)^3=9/1000
Probability of drawing 3 green:
(4/10)^3=16/10000
Probability of drawing 3 black:
(3/10)^3=9/1000
Adding these three: 34/1000= 3.4%.
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