Therefore, the solution to this problem is (x - 2)(x + 3) are the factors of p(x) (2x - 5).
Examine the equation.An equation is a mathematical statement that is created by connecting two expressions using the equivalent sign. An example of an equation is 2x - 5 = 15. By resolving this equation, we may ascertain that the variable x has a value of 5.
Here,
Given, the polynomial in this case is 2x3 - 3x2 - 17x + 30.
It is necessary to factor the polynomial.
Let p(x) equal 2x3, 3x2, 17x, and 30.
P(xconstant )'s term is 30.
Factors of 30 are equal to 1, 2, 3, 5, 6, 10, 15, and 30.
Consider x = 2.
Replace x = 2 in p. (x),
2(2)³ - 3(2)² - 17(2) + 30 =p(2)
=> 2(8) - 34 - 3(4) + 30
= >16 - 16
= 0
So, x - 2 is a factor of 2x³ - 3x² - 17x + 30.
Now splitting the x² and x terms,
2x³ - 4x² + x² - 2x - 15x + 30= 2x³ - 3x² - 17x + 30
=> x(x - 2) - 15(x - 2) + 2x²(x - 2)
= > (x - 2) * (2x² + x - 15)
factoring 2[tex]x^{2}[/tex] + x - 15
= 2[tex]x^{2}[/tex] + 6x - 5x - 15
= - 5(x + 3) + 2x(x + 3)
= (x + 3)(2x - 5)
Therefore, the solution to this problem is (x - 2)(x + 3) are the factors of p(x) (2x - 5).
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Please help me I am having a hard time with this activity
Answer:
Step-by-step explanation:
b.
[tex]\frac{a^2+6a+9}{a^2-9} *\frac{3a-9}{a+3} \\=\frac{a^2+2*a*3+3^2}{a^2-3^2} *\frac{3(a-3)}{a+3} \\=\frac{(a+3)^2}{(a+3)(a-3)} *\frac{3(a-3)}{a+3} \\=\frac{3(a+3)^2}{(a+3)^2} \\=3[/tex]
d.
[tex]\frac{3x^2-6x}{3x+1} *\frac{x+3x^2}{x^2-4x+4} \\=\frac{3x(x-2)}{3x+1} *\frac{x(1+3x)}{x^2-2x-2x+4} \\=\frac{3x(x-2)}{3x+1} *\frac{x(1+3x)}{x(x-2)-2(x-2)} \\=\frac{3x(x-2)}{3x+1} *\frac{x(1+3x)}{(x-2)(x-2) } \\=\frac{3x^2}{x-2)}[/tex]
e.
[tex]\frac{2x^2-10x+12}{x^2-4} *\frac{2+x}{3-x} \\=\frac{2[x^2-5x+6]}{x^2-2^2} *\frac{2+x}{-(-3+x)} \\=\frac{2[x^2-2x-3x+6]}{(x+2)(x-2)} *\frac{x+2}{-(x-3)} \\=\frac{2[x(x-2)-3(x-2)]}{(x+2)(x-2)} *\frac{x+2}{-(x-3)} \\=\frac{2(x-2)(x-3)}{(x+2)(x-2)} *\frac{x+2}{-(x-3)} \\=\frac{2}{-1} \\=-2[/tex]
k.
[tex]\frac{6x^2-11x-10}{6x^2-5x-6} *\frac{6-4x}{25-20x+4x^2} \\=\frac{6x^2-15x+4x-10}{6x^2-9x+4x-6} *\frac{-4x+6}{4x^2-10x-10x+25} \\=\frac{3x(2x-5)+2(2x-5)}{3x(2x-3)+2(2x-3) } *\frac{-2(2x-3)}{2x(2x-5)-5(2x-5)} \\=\frac{(2x-5)(3x+2)}{(2x-3)(3x+2)} *\frac{-2(2x-3)}{(2x-5)(2x-5)} \\=\frac{-2}{2x-5}[/tex]
Kosey needs to get 80% of his
questions correct on his math test
to get a B for the quarter. If his
test has 60 questions, how many
questions will he need to get right?
Answer:
48 questions
Step-by-step explanation:
There are 60 questions on the test
to see how many questions he needs to solve to get 80% we multiply 60 with 80 and divide it by 100
60 x 80 ÷ 100 = 48
Given Triangle ABC if sides AB is congruent to side AC, and angle B = 5x +9 , C = 8x-30 Then, find the value of X
Answer:
x = 13
Step-by-step explanation:
When we say side AB is congruent to Side AC it means both side are the same.
This is written Mathematically as:
AB = AC
We are asked to find x
angle B = 5x +9 , angle C = 8x-30
5x + 9 = 8x - 30
Collect like terms
9 + 30 = 8x - 5x
8x - 5x = 30 + 9
3x = 39
Divide both sides by 3
x = 39/3
x = 13
Calculate the radian measure of a 30 degree angle. Use any method you like, including sketching in the circle diagram provided. Explain or show your reasoning.
Answer:
The radian measure of 30° is [tex]\frac{\pi}{6}[/tex] radians.
Step-by-step explanation:
A complete revolution equals 360°, that is, 2π radians. If the given angle is 30°, then the value of the radian measure is calculated by the following simple rule of three:
[tex]x = \frac{30^{\circ}}{360^{\circ}}\times 2\pi[/tex]
[tex]x = \frac{\pi}{6}\,rad[/tex]
The radian measure of 30° is [tex]\frac{\pi}{6}[/tex] radians.
Write the equation of this graph.
what fraction has the greatest value?
Answer:
5/6
Step-by-step explanation:
Answer: 5/6
Step-by-step explanation: 1 whole would be 6/6 and 5/6 is very close to 1 whole
Plzzz help me asappp I’m begging you
I don’t know I need help
Answer:
[B] 9.8 Cubic FeetExplanation:
Formula: πr²ʰ⁄₃Radius: 1.9
Height: 2.6
π: 3.14
Formula: V = 1.9²ʰ⁄₃ = 3.14 · 1.9² · 2.6 / 3 = 9.829Round: 9.8
Rewrite the expression with a rational (fraction) exponent:
7Vz
PLEASE HELP ASAP
Answer:
z^1/7
Step-by-step explanation:
trust me
Amiera has 3/4 of a bag of cat food. Her cat eats 1/10 of a bag per week. How many weeks will the food last?
Answer:
Step-by-step explanation: lets say the fod is chicken 3/4 is 75 out of 100 1/10 out of 100 is 10 lets see how many times we can take 10 out of 75 .
you can do it 7 time because 7 rimes 10 is 70 meaning that you have 7 weeks
and half a week hope this helps B)
Help me please , will mark
Included picture
Question is not hard so please answer correctly
Answer:
SometimesStep-by-step explanation:
The product of two irrational numbers is sometimes rational.Answer:
sometimes
Step-by-step explanation:
The following examples to illustrate
[tex]\sqrt{2}[/tex] is irrational
[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 2 ← which is rational
[tex]\sqrt{3}[/tex] is irrational and
[tex]\sqrt{2}[/tex] × [tex]\sqrt{3}[/tex] = [tex]\sqrt{6}[/tex] ← which is irrational
Result is therefore sometimes
 Find sin2x, cos2x, and tan2x if sinx=-15/17 and x terminates in quadrant III
Given:
[tex]\sin x=-\dfrac{15}{17}[/tex]
x lies in the III quadrant.
To find:
The values of [tex]\sin 2x, \cos 2x, \tan 2x [/tex].
Solution:
It is given that x lies in the III quadrant. It means only tan and cot are positive and others are negative.
We know that,
[tex]\sin^2 x+\cos^2 x=1[/tex]
[tex](-\dfrac{15}{17})^2+\cos^2 x=1[/tex]
[tex]\cos^2 x=1-\dfrac{225}{289}[/tex]
[tex]\cos x=\pm\sqrt{\dfrac{289-225}{289}}[/tex]
x lies in the III quadrant. So,
[tex]\cos x=-\sqrt{\dfrac{64}{289}}[/tex]
[tex]\cos x=-\dfrac{8}{17}[/tex]
Now,
[tex]\sin 2x=2\sin x\cos x[/tex]
[tex]\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})[/tex]
[tex]\sin 2x=-\dfrac{240}{289}[/tex]
We know that,
[tex]\cos 2x=1-2\sin^2x[/tex]
[tex]\cos 2x=1-2(-\dfrac{15}{17})^2[/tex]
[tex]\cos 2x=1-2(\dfrac{225}{289})[/tex]
[tex]\cos 2x=\dfrac{289-450}{289}[/tex]
[tex]\cos 2x=-\dfrac{161}{289}[/tex]
Using the trigonometric ratios, we get
[tex]\tan 2x=\dfrac{\sin 2x}{\cos 2x}[/tex]
[tex]\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}[/tex]
[tex]\tan 2x=\dfrac{240}{161}[/tex]
Hence, the required values are [tex]\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}[/tex].
f(x) = -2x^2 + 8x -1 Evaluate f(6)
Step-by-step explanation:
f(x) = 2x²+ 8x -1
f(6) = 2(6) + 8(6)-1
= 13 + 48 - 1
= 61-1
= 60.
Mihn invested $1,479.81 last year. What is the place value of the 8 in 1,479.81?
thousands
tens
tenths
thousandths
The simple interest on a certain sum for 5years at 8% per annum is Rs200 less than the simple interest on the same sum for 3years and 4months at 18% per annum.Find the sum
Answer:
Step-by-step explanation:
The simple interest on a certain sum for 5years at 8% per annum is Rs200 less than the simple interest on the same sum for 3years and 4months at 18% per annum.Find the sum
The formula for Simple Interest = PRT
From above question, we have to find the Principal
The simple interest on a certain sum for 5years at 8% per annum is Rs200
Hence,
R = 8%
T = 5 years
Rs 200 = P × 8% × 5
P = 200/8% × 5
P = Rs500
The principal = Rs 500
The simple interest on the same sum for 3years and 4months at 18% per annum.
Simple Interest = PRT
R = 18%
T = 3 years and 4 months
Converted to years
T = 3 + (4 months/12 months)
T = 3.33 years
Hence,
Simple Interest = Rs 500 × 18% × 3.33 years
= Rs 299.7
If y varies directly with x. and y=10 when x=5.6, find the value of y when
X=3
Answer: 5.3571
Step-by-step explanation:
The formula used to calculate direct proportion is: y = kx
We will find the constant of proportionality when y=10 and x=5.6. This will be:
y = kx
10 = 5.6k
k = 10/5.6
k = 1.7857143
The value of y when X=3 will be:
y = kx
y = 1.7857143 × 3
y = 5.3571
The measure of angle 1 is 65 degrees. What are the measures of the other seven angles? (Enter the
number only)
Help I need big brains for it and I need it fast please help please
Answer:
See solution below
Step-by-step explanation:
According to the diagram shown
m<1 = m<5 = 5=65 degrees (corresponding angle)
m<5 = m<4 - 65 degrees (alternate interior angle)
m<9 = m<8 = 65degrees (corresponding angle)
m<5 = m<8 = 65dgrees (vertically opposite angles)
m<6+m<8 = 180
m<6 + 65 = 180
m<6 = 180 - 65
m<6 = 115degrees
m<2 = m<6 = 115degrees (corresponding angles)
m<6 = m<7 = 115degrees (vertically opposite angles)
m<3 = m<7 = 115degrees(corresponding angle)
)
The measures of the other seven angles are evaluated as:
[tex]m\angle 1 = 65^\circ = m\angle 5\\m\angle 2 =115^\circ = m\angle 6\\m\angle 3 =65^\circ = m\angle 7\\m\angle 4 = 115^\circ =m\angle 8[/tex]
What are supplementary angles?Two angels whose sum is 180° are called supplementary angles.
When they are added together graphically, they form a straight line.
What are vertical angles?Each of the pairs of the opposite angles made by two intersecting lines are called vertical angles. They are of same measurement.
What are corresponding angles?In literal sense, corresponding means pair wise angles. Like the right corner angles of two triangles etc. But usually we take them as:
For two similar figures, the pair by pair similar angles of those two similar figures are called corresponding angles. They are of same measurement.
For this case, we have:
Angle 1,2,3 and 4 corresponding to 5,6,7 and 8 angle respectively. It is because the two lines A and B are parallel and the traversing line intersects both of them. When single line intersect two parallel lines, it makes same corresponding angles on both of the sides. That means
[tex]m\angle 1 = m\angle 5\\m\angle 2 = m\angle 6\\m\angle 3 = m\angle 7\\m\angle 4 = m\angle 8[/tex]
where that small 'm' denotes that we're taking about their measurements.
Thus, we will only find 1,2,3,and angle 4's measurements and rest four would be found.
Since angle 1 and angle 4 are vertical angles, they are same measurement. Since angle 1 is of 65 degrees, thus:
[tex]m\angle 1 = 65^\circ = m\angle 4[/tex]
Now, since angle angle 3 is supplementary to angle 1 and so as angle 2 to angle 4, thus:
[tex]m\angle 2 + m\angle 4 = 180^\circ\\m\angle 2 = 180-m\angle 4= 115^\circ\\\\m\angle 3 + m\angle 1 = 180^\circ\\m\angle 3 = 180-m\angle 1= 115^\circ[/tex]
Thus, we get the measurement of all angles as:
[tex]m\angle 1 = 65^\circ = m\angle 5\\m\angle 2 =115^\circ = m\angle 6\\m\angle 3 =65^\circ = m\angle 7\\m\angle 4 = 115^\circ =m\angle 8[/tex]
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3 (x - 6) + 5 (a + 1) - 2 (4x + 2)
someone pleasr help!!
Answer:
I think the answer is 7x+ 6a
Step-by-step explanation:
3 (x - 6) + 5 (a + 1) - 2 (4x + 2)
3 (-6x) + 5 (1a) -2 (6x)
3x + 6a + 4x
= 7x+ 6a answer!
please answer asap!
which inequality matches this graph?
Answer:
D
Step-by-step explanation:
The point on the Number line is a closed( shaded circle) So it will include a greater than or equal sign. Since the arrow is pointing right it will be B is greater than/ equal to 135. if the arrow was pointing the opposite way it would be less than or equal to symbol.
SOMEONE HELPP PLSS QUICK
In what direction is the line containing the point (3, 3) and (1,3) going?
Answer:
Horizontal (Braniest pls)
Step-by-step explanation:
Since (3,3) and (1,3) is on the same line, it is moving horizaontally (Braniest pls)
Do you know the answer toPart A: 25% of 50 = Part B: 25% of 60 = Part C: 50% of 60 = Part D: 75% of 60 = Part E: 75% of 30 = Part F: 100% of 22.5 = Part G: 10% of 22.5 = Part H: 50% of 45.7 =
Answer:
Part A: 25% of 50 = 12.5
Part B: 25% of 60 = 15
Part C: 50% of 60 = 30
Part D: 75% of 60 = 45
Part E: 75% of 30 = 22.5
Part F: 100% of 22.5 = 22.5
Part G: 10% of 22.5 = 2.25
Part H: 50% of 45.7 = 22.85
Step-by-step explanation:
To find - Do you know the answer to
Part A: 25% of 50 =
Part B: 25% of 60 =
Part C: 50% of 60 =
Part D: 75% of 60 =
Part E: 75% of 30 =
Part F: 100% of 22.5 =
Part G: 10% of 22.5 =
Part H: 50% of 45.7 =
Proof -
Part A :
25% of 50 = [tex]\frac{25}{100} *50[/tex] = [tex]\frac{1}{4}*50[/tex] = 12.5
⇒25% of 50 = 12.5
Part B :
25% of 60 = [tex]\frac{25}{100} *60[/tex] = [tex]\frac{1}{4}*60[/tex] = 15
⇒25% of 60 = 15
Part C :
50% of 60 = [tex]\frac{50}{100} *60[/tex] = [tex]\frac{1}{2}*60[/tex] = 30
⇒50% of 60 = 30
Part D :
75% of 60 = [tex]\frac{75}{100} *60[/tex] = [tex]\frac{75}{10}*6[/tex] = 45
⇒75% of 60 = 45
Part E :
75% of 30 = [tex]\frac{75}{100} *30[/tex] = [tex]\frac{75}{10}*3[/tex] = 22.5
⇒75% of 30 = 22.5
Part F :
100% of 22.5 = [tex]\frac{100}{100} *22.5[/tex] = 22.5
⇒ 100% of 22.5 = 22.5
Part G :
10% of 22.5 = [tex]\frac{10}{100} *22.5[/tex] = 2.25
⇒ 10% of 22.5 = 2.25
Part H :
50% of 45.7 = [tex]\frac{50}{100} *45.7[/tex] = [tex]\frac{1}{2}*45.7[/tex] = 22.85
⇒50% of 45.7 = 22.85
Complete both and will give brainliest
Answer:
1)12 people voted
2)60mph
Step-by-step explanation:
Round to the nearest tenth.
7.61577310586
Answer:
7.6
Step-by-step explanation:
1is less than 5 so let it rest
Fill in the table using this function rule.
Y = -5x + 1
Answer:
55 or 53.
Step-by-step explanation:
STOP SCROLLING HELP ME PLSSSSSS!
Answer:
use proportions??
Step-by-step explanation:
i
d
k
h
o
w
t
o
do
this i am only in 5th grade yikes
In this figure, triangle GHJ is similar to triangle POR.
Based on this information, which ratio represents tan H?
Answer:8/15
Step-by-step explanation:
Tanθ in a right angle triangle is the ratio of its perpendicular to its base. The ratio that represents the Tan(∠H) is [tex]\dfrac{8}{15}[/tex].
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
Base is the adjacent smaller side of the angle θ.
As it is given that the two of the given triangles are similar triangles, therefore, their corresponding sides will be in the same ratio.
[tex]\dfrac{QR}{HJ} = \dfrac{RP}{JG} = \dfrac{PQ}{GH}[/tex]
Further, the sides can be written as,
[tex]\dfrac{QR}{HJ} = \dfrac{RP}{JG}\\\\\dfrac{QR}{RP} = \dfrac{HJ}{JG}=\dfrac{15}{8}[/tex]
Now, the Tan(∠H) can be written as,
[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
Substituting the value for the ∠H in ΔHJG,
[tex]\rm Tangent(\angle H) = \dfrac{JG}{HJ}[/tex]
As the ratio is already known, therefore,
[tex]\rm Tangent(\angle H) = \dfrac{8}{15} = 0.5\bar3[/tex]
Hence, the ratio that represents the Tan(∠H) is [tex]\dfrac{8}{15}[/tex].
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The radius of a circle is 5 m. Find its circumference in terms of \piπ.
Answer: C≈ 31.42m
C=2πr=2·π·5≈31.41593m
Step-by-step explanation: hope this helps
7y+5y-3y= How would I simplify this?
Answer:
9y
Step-by-step explanation:
Add 7y and 5y which equals 12y. Then subtract 3y from 12y and u get 9y. It might be wrong
help me please aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
v=-16
Step-by-step explanation:
-2=2+v/4
(we know that 2+-4=-2 so we can see if that works)
(4*-4=-16)
2+-16/4=-2
(-16/4=-4)
2+-4=-2
Find the coordinates of the point for the reflection.
(-8,5) across the x-axis
Answer:
(-8, -5)
Step-by-step explanation:
If (-8, 5) is reflected across the x-axis, the x-coordinate stays the same (-8), but the y coordinate becomes -5. Hence the coordinates of the reflection are (-8, -5).
If point (-8, 5) is reflected across the x axis, the new point is (-8, -5)
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
If point (-8, 5) is reflected across the x axis, the new point is (-8, -5)
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