How many x intercepts does the polynomial function y=(x-8)(x+3)^2
Answer:
The answer is 2 x-intercepts
Step-by-step explanation:
To determine the x-intercepts we set y to zero and solve for x:
y=0
(x-8)(x+3)^2=0
The product of 2 factors is 0 means that one of them must be 0:
x-8=0 ⇒ x=8 →first x-intercept
or (x+3)^2=0 ⇒ x+3=0 ⇒ x=-3 →second x-intercept
Therefore the polynomial function two roots, so it has two x-intercepts x=8 and x=-3
Hope this helps :)
Consider the line 2x-7y=-7. Find the equation of the line that is perpendicular to this line and passes through the point (-8,-6). Find the equation of the line that is parallel to this line and passes through the point(-8,-6).
Step-by-step explanation:
2x - 7y = -7
2x + 7 = 7y
y = (2/7)x + 1
the slope of the line is the factor of x : 2/7
FYI that is the ratio y/x and means, when x changes by 7 points to the plus (right) side, then y changes 2 points to the plus (up) side.
the parallel line will have the same slope, of course. just a different y-axis-interception point. that means, the "+" term at the end changes. changes to what ?
well, we use the given point coordinates
-6 = (2/7)×-8 + c
-6 = -16/7 + c
-42/7 = -16/7 + c
-26/7 = c
so, the equation of the parallel line is
y = (2/7)x - 26/7
y = (2/7)×(x - 13)
the perpendicular line is a line that intercepts our original line with a 90 degree angle.
that means its slope will switch x and y of the original line slope and also flips the sign (from + to - or vice versa).
=> the slope of the perpendicular line is -7/2.
the line equation looks like
y = (-7/2)x + c
and again, we use the given point coordinates to find the missing c (y-intercept).
-6 = (-7/2)×-8 + c
-6 = -7×-4 +c
-6 = 28 + c
-34 = c
so, the full equation of the perpendicular line is
y = (-7/2)x - 34
If the orientation of two shapes is not the same, which transformation(s) should you use to show they are congruent? Why?
Answer:
The answer is below
Step-by-step explanation:
Transformation s the movement of a point from its initial location to a new location. If an object is transformed, the all its points are also transformed. Types of transformation are rotation, reflection, translation and dilation.
Two shapes are congruet if they have the same shape and size, two objects are congruent if they can be moved without changing their shape or size. Congruent transformations are transformation that create congruent objects. The three types are:
Translation: sliding an object either up, down, left or right.Reflection: Flipping an object over a lineRotation: turning an object about a pointAnswer:
Reflection and Rotation
Step-by-step explanation:
If the orientation of two shapes is not the same, first check which directions they point. Changing the orientation of a shape to map it onto another is only possible through either reflection or rotation. So, choose a suitable transformation—either reflection or rotation—to map one shape onto the other. Translations alone would not show the congruence of shapes with different orientations.
What are the rules of trichotomy???
Answer:
Step-by-step explanation:
The answer is in the attachment.
Besides this, there are more rules of trichotomy.
Answer:
Let us consider any two numbers 6 and 9 then we have the relation.
\( \gray{ \frak{9 > 6 \: \: \: or \: \: \: 6 < 9}}\)
Rule 1.
Adding 2 on both sides then;
\( \frak{ \gray{9 + 2 > 6 + 2 \: \: \: or \: \: \: 6 + 2 < 9 + 2}}\)
\(\frak{ \gray{ \therefore \: 11 > 8 \: \: \: or \: \: \: 8 < 11}}\)
Both are true for addition.
Thus,when equal number is added to both sides of trichotomy symbol,the symbol remains the same.
Rule 2.
Subtracting 2 on the both sides then,
\(\frak{ \gray{9 - 2 > 6 - 2 \: \: \: or \: \: \: 6 - 2 < 9 - 2}}\)
\(\frak{ \gray{\therefore \: 7 > 4 \: \: \: or \: \: \: 4 < 7}}\)
Both are true for subtraction.
Thus,when equal number is subtracted to both sides of trichotomy symbol,the symbol remains the same.
Rule 3.
Multiplying both sides by 2 then,
\(\frak{ \gray{9 \times 2 > 6 \times 2 \: \: \: or \: \: \: 6 \times 2 < 9 \times 2}}\)
\(\frak{ \gray{ \therefore \: 18 > 12 \: \: \: or \: \: \: 12 < 18}}\)
Both are true for multiplication by positive numbers.
But if we multiplied by -2 then there will be,
\(\frak{ \gray{ - 18 > - 12 \: \: \: or \: \: \: - 12 < - 18}}\)
These are not true.
To be true,there must be:
\(\frak{ \gray{ - 18 < - 12 \: \: \: and \: \: \: - 12 > - 18}}\)
Thus,when both sides of trichotomy symbol are multiplied by equal positive number then the symbol remains the same.When both sides of trichotomy symbols are multiplied by equal negative numbers then the symbol changes as follows:
'<' Changes to'>' and '>' Changes to'<'.
Similarly check for division then get the same result as in multiplication.
Thus,when both sides of trichotomy symbol are divided by an equal positive number, the symbol remains the same.When both sides of trichotomy symbol are divided by an equal negative number,the symbol '<' is changed to'>' or '>' is changed to'<'.
\(\boxed{\frak{\gray{BrainlyFairy}}}\)
Use a half angle formula to find the exact value of the expression tan 22.5 degree
Answer:
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPP
complete the synthetic division below
The quotient in polynomial form is C. x² - x ₊ 1.
What is synthetic division?In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less calculation than long division.
The given problem is-
-3 | 1 2 -2 3
Using synthetic division method,
-3 | 1 2 -2 3
| -3 3 3
|1 -1 1 6
So, the remainder from the calculation is 6 .
And the quotient polynomial is x² - x ₊ 1.
Hence, the correct answer for the given question is C. x² - x ₊ 1
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Perform the arithmetic operation
(5/3)^0*2^-1
Answer:
0.5
Step-by-step explanation:
Answer:
0.5
Step-by-step explanation:
3.1 Which basic property of operations was used in each of the following
calculations?
3.1.1 25 x 4 = 4 x 25 = 100
3.1.2 412 412 412 + (-412) = 0
3.1.3 25 +37
-
=
= 20 + 5+ 30+7
= 20 +30 +5+7
= 50+ 12 = 62
3.1.1 The basic property of operations used is the commutative property of multiplication.
3.1.2 The basic property of operations used is the additive inverse property.
3.1.3 The basic property of operations used is the associative property of addition.
3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.
3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.
3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.
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(URGENT)An engineer has a 40:1 scale drawing of a bridge. The dimensions of the scaled bridge deck are 24 inches by four and four fifths inches. What is the area of the actual bridge deck in square feet?
460 square feet
640 square feet
960 square feet
1,280 square feet
The area οf the actual bridge deck in square feet is 1,280 square feet.
What is Area?Area refers tο the measurement οf the size οf a twο-dimensiοnal surface, usually measured in square units such as square inches, square feet, οr square meters. It represents the amοunt οf space that is inside the bοundary οf a flat οbject οr shape.
The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).
The dimensiοns οf the scaled bridge deck in feet are:
24 inches = 2 feet
4 and 4/5 inches = 0.4 feet
Sο, the area οf the scaled bridge deck in square feet is:
2 feet x 0.4 feet = 0.8 square feet
Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:
Area οf actual bridge deck = 0.8 square feet x (40²) = 1280 square feet
Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.
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Answer:
Step-by-step explanation:
The scale factor indicates the actual bridge is 40 times larger than the drawing.
Increase the scale dimensions by the factor of 40.
24 times 40 = 960"
4.8 times 40 = 192" (I changed 4 4/5 to 4.8)
Area = length times width
960 times 192 = 184320 sq inches actual bridge deck in square inches
Divide 183320 by 144 (sq inches in a square foot) = 1280 sq feet
I really need help with this ?
Answer:
j
Step-by-step explanation:
128 less than a number is 452
Answer:
580
Step-by-step explanation:
"128 less than a number is 452" is represented by:
n - 128 = 452
Solve for 'n':
n - 128 + 128 = 452 + 128 (Addition Property of Equality)
n = 580
An isosceles triangle whose sides are 5cm, 5cm and 6cm is inscribed in a circle. Find the radius of the circle.
Answer:
To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:
r = (a/2) * cot(π/n)
where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.
In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:
6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)
36 = 50 - 50cos(x)
cos(x) = (50 - 36)/50
cos(x) = 0.28
x = cos^-1(0.28) ≈ 73.7°
Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:
(5/2)^2 + h^2 = 5^2
25/4 + h^2 = 25
h^2 = 75/4
h = sqrt(75)/2 = (5/2)sqrt(3)
Now we can find the radius of the inscribed circle using the formula:
r = (a/2) * cot(π/n)
where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:
r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm
Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.
Prove that 25^9+5^17is divisible by 30
Answer:
proof is below
Step-by-step explanation:
Answer:
25^9 + 5^17=
=2^18 + 5^17
=5^17(5+1)
=5^17×6
=5^16×30 is divisible by 30
Anymore can solve this?
Answer:
c
Step-by-step explanation:
they are not right triangles, so you can't use HL. All the other postulates require 3 things to be congruent, and there are only two. Therefore, the triangles are not congruent.
Put the events in order of increasing probability.
P = 0
P = 1
You pull a yellow ball from a box of all yellow balls.
You roll a 6-sided die and it lands on 3, 4, 5, or 6.
You pull a gray ball from a box of all pink balls.
You roll a 6-sided die and it lands on a multiple of 4.
You flip a dime and it lands on tails.
Representation of the events probability in increasing order that from P =0 to P =1are as follow:
a. Pulling of grey ball from a box of all pink balls.
b. After rolling a six sided die and the outcomes lands on multiple of 4.
c. Flipping a dime and outcome land on tails.
d. After rolling a six sided die and the outcomes lands on 3, 4, 5, or 6.
e. Pulling of a yellow ball from a box of all yellow balls.
As given in the question,
Representation of the given events probability in increasing order that from P =0 to P =1are as follow with explanation:
Let P represents the probability of the given events.
a. Pulling of grey ball from a box of all pink balls.
Number of grey balls in a box of pink balls = 0
P(pulling a grey ball) = 0
b. After rolling a six sided die and the outcomes lands on multiple of 4.
Total outcomes = {1,2,3,4,5,6}
Favourable outcomes ={4}
P(multiple of 4) = 1/6
c. Flipping a dime and outcome land on tails.
Total outcomes = 2
Favourable outcomes =1
P(tails) = 1/2
d. After rolling a six sided die and the outcomes lands on 3, 4, 5, or 6.
Total outcomes = {1,2,3,4,5,6}
Favourable outcomes ={3,4,5,6}
P(3,4,5,or 6) = 4/6
e. Pulling of a yellow ball from a box of all yellow balls.
Every time pulling a yellow balls probability is :
P(pulling a yellow ball) =1
Increasing order is:
0 <1/6 < 1/2< 4/6<1
Therefore, representation of the events probability in increasing order that from P =0 to P =1are as follow:
a. Pulling of grey ball from a box of all pink balls.
b. After rolling a six sided die and the outcomes lands on multiple of 4.
c. Flipping a dime and outcome land on tails.
d. After rolling a six sided die and the outcomes lands on 3, 4, 5, or 6.
e. Pulling of a yellow ball from a box of all yellow balls.
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Robert's book bag is weighing him down. His bag alone weighs 4 pounds. His library book
weighs 2 pounds. The math book is 4 times the weight of the library book, and his science
book is 2 times the weight of the math book. How much does his book bag weigh with all
these books? What is the heaviest book in his book bag?
Answer:
1) 30 pounds is the weight of the bag all together
2) science book is the heaviest book
Step-by-step explanation:
bag=4 pounds
library book=2 pounds
maths book=2×4=8 pounds
science book=8×2=16 pounds
4+2+8+16=30 pounds all together
heaviest book= science book (16 pounds)
plz plz plz plz help
Answer:
1 milimeter
Step-by-step explanation:
the rest you can see easily by naked eye
Answer:
D
Step-by-step explanation:
1 millimeter cuz its a microscope u use it to see deep into stuff.
Give brainliest
will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest
Area of the given figure is 27.852 in².
What is Area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
In the given figure there is a square.
First let us find the area of square, which has length of side 3 in
Area of square=3²=9
Now there are two semicircles with diameter 3 in.
Radius of semicircle = 3/2=1.5 in
Area of semicircle=2πr
=2×3.142×1.5
=9.426
As there are two semicircles
2×9.426
18.852
Area of figure is 9+18.852
27.852 in²
Hence, area of the given figure is 27.852 in².
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Write the equation of the line that is parallel to the line 5x- 4y = 4 and passes through one point (-8, 2).
Answer:
y = 5/4x - 8
Step-by-step explanation:
first you convert the equation to y = mx + b
then you add the the -8 into the x and the 2 into the y and solve for b
b = -8 and since it is parallel same slope.
hope this helps :)
Wilma goes to a college that is 106 miles away. Wilma drives a Honda Civic and gets 35 mpg. If Wilma plans on making 8 round trips to and from her college this year, how much will she spend on gas over the course of the year? (Assume that gas remains constant at $3.59/gal).
Answer: $173.96
Step-by-step explanation: If I'm not mistaken first you have to take 106 and multiply it by 2 to count for the round trips so that makes 212 miles for one trip, then you have to multiple by 8 to figure out how many miles in total which equals 1696, then you divide by the 35 to figure out how many gallons she use, which is 48.457(rounded) then you multiple that by the rate of gas which is 3.59 which means she spent 173.96(rounded to the nearest tenth)
How many milliliters is 719.01 liters?
Answer:
719010
Step-by-step explanation:
how many ways can this be done. if a committee of 5 people from 7 men and 8 women?
Answer:
3003 ways
Step-by-step explanation:
(7+8)C5
= 15C5
= 15!/(5!10!)
= 3003
Rationalize the denominators.
Step-by-step explanation:
that probably should be your answer
How many three-letter "words" can be made from 10 letters "FGHIJKLMNO" if repetition of letters (a) is allowed? Your answer is (b) is not allowed? Your answer is
a. The number of permutations of three letter words that can be formed with repetition is 1000 words
b. The number of permutations of three letter words that can be formed without repetiton is 720 words
What are permutations?Permutations are the number of ways in which x objects can be arranged out of n objects.
The number of permutations is given by ⁿPₓ = n(n - 1)(n -2)...(n - x + 1)
a. How to find the number of ways in which the 10 letters can be arranged if repetition is allowed?Since we require the number of three-letter "words" can be made from 10 letters "FGHIJKLMNO" with repetition, we note that there are 10 letters.
Since repetition is allowed, for the first slot, we have 10 letters, for the second position, we have 10 letters and for the third position, we have 10 letters.
So, the total number of permutations is n = 10 × 10 × 10
= 1000 words
So, the number of three letter words that can be formed is 1000 words
b. How to find the number of ways in which the 10 letters can be arranged if repetition is not allowed?Since we require the number of three-letter "words" can be made from 10 letters "FGHIJKLMNO" without repetition, we note that there are 10 letters.
Since repetition is not allowed, for the first slot, we have 10 letters, for the second position, we have 9 letters and for the third position, we have 8 letters.
So, the total number of permutations is ¹⁰P₃ = 10 × 9 × 8
= 720 words
So, the number of three letter words that can be formed is 720 words
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The following probabilities are based on data collected from U.S. adults. Individuals are placed into a weight category based on weight, height, gender and age.
Underweight Healthy Weight Overweight (not Obese) Obese
Probability 0.017 0.377 0.343 0.263
Based on this data, what is the probability that a randomly selected U.S. adult weighs less than the overweight(but not obese) range?
Answer:
the probability that a randomly selected U.S. adult weighs less than the overweight(but not obese) is 0.394
Step-by-step explanation:
Given the data in the question;
Underweight Healthy Weight Overweight (not Obese) Obese
Probability 0.017 0.377 0.343 0.263
so
P( underweight) = 0.017
P( Healthy Weight) = 0.377
P( Overweight (not Obese) ) = 0.343
P( Obese ) = 0.263
now, the probability that a randomly selected U.S. adult weighs less than the overweight(but not obese) range will be;
P( weigh less than overweight(but not obese) = P( underweight) + P( Healthy Weight)
P( weigh less than overweight(but not obese) = 0.017 + 0.377
P( weigh less than overweight(but not obese) = 0.394
Therefore, the probability that a randomly selected U.S. adult weighs less than the overweight(but not obese) is 0.394
Annette has 3 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 9mph and walks back at a speed of 3mph , how long should she plan to spend walking back?
Answer:
Annette should plan to spend 2.25 hours walking back.
Step-by-step explanation:
To solve this problem, we can use the formula:
Time = Distance / Speed
Let's assume the distance of the race is D miles.
Annette spends her time running the distance of the race, which takes:
Time running = D / 9 hours
She then walks back the same distance, which we need to find the time for:
Time walking = D / 3 hours
Since Annette has a total of 3 hours for her training, the sum of the running time and walking time should equal 3 hours:
D / 9 + D / 3 = 3
To simplify the equation, we can multiply all terms by 9 to eliminate the denominators:
D + 3D = 27
Combining like terms:
4D = 27
Dividing both sides of the equation by 4:
D = 6.75
So, the distance of the race is 6.75 miles.
To find the time Annette should spend walking back, we substitute the distance into the time-walking formula:
Time walking = D / 3 = 6.75 / 3 = 2.25 hours
Therefore, Annette should plan to spend 2.25 hours walking back.
please help me asap
Answer:A, C, C
Step-by-step explanation:
Answer:
rueiwiejr rjrjrjrjrjrrjriirjrjrjrrj
Write the equation for the horizontal line passing through (3, 4).
Answer:
equation for a straight horizontal line passing through the coordinates (3,4):
y=4
Step-by-step explanation:
Solve for the portion. Round to hundredths when necessary.
14.5% of 1,800 is
The value of 14.5% of 1,800 is 261 by using the concept of percentage.
What is meant by percentage?In mathematics, a percentage is a value or ratio expressed as a fraction of 100.
The term percent is derived from the Latin per centum, which means "hundred" or "by the hundred." The sign for "percent" comes from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and finally disappeared entirely. The "cento" was reduced to two circles divided by a horizontal line, from which the present "%" symbol was derived.
A % is a relative figure that indicates one-tenth of a quantity. One percent (symbolized 1%) is the one-hundredth part; consequently, 100 percent denotes the complete amount, and 200 percent specifies twice the supplied amount.
Given,
14.5% of 1,800
=(14.5/100)×1800
=261
Therefore, the answer is 261.
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Help solve these problems
Answer:
Step-by-step explanation:
Expression; coefficient, variable; constant; substitute, though I think it should be substitute 7 for x, not 3 for x; and simplify