We can not write the polynomial g(x) as a product of linear factors.
What is polynomial?
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents (No division operation by a variable).
Given:
g(x)=x³ + 3x² - 7x − 3 and x = -1 is a zero of g(x).
Since, if x = a is a zero of the polynomial then (x - a) is a factor of polynomial.
Here (x - (-1)) = (x + 1) is a factor of g(x).
First to check x = -1 is a zero of polynomial or not.
Plug x = -1 in g(x).
g(-1) = (-1)^3 + 3(-1)^2 - 7(-1) - 3
g(-1) = -1 + 3+ 7 - 3
g(-1) = 6
g(-1) ≠ 0
Hence, we can not write the polynomial g(x) as a product of linear factors.
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Find the discriminant for the following guodutie function. Describe the number and Apes of roots it will have. Then find the roots. Write your answer in simplest radical form. Sketch a graph of the parabola using 5 points, including the vertex. f(x)= 1/2x^2-2x+10
Answer:
discriminant: -16, two complex conjugate rootsroots: 2±4igraph: see attachedStep-by-step explanation:
You want the discriminant, roots, and graph of the quadratic function ...
f(x) = 1/2x² -2x +10
DiscriminantThe discriminant of the quadratic function
y = ax² +bx +c
is ...
d = b² -4ac
The given function has a=1/2, b=-2, c=10, so the discriminant is ...
d = (-2)² -4(1/2)(10) = 4 -20 = -16
The discriminant of -16 means there will be two distinct complex conjugate roots.
RootsThe roots are ...
x = (-b ±√d)/(2a)
x = (-(-2) ±√(-16))/(2(1/2)) = 2 ±4i
Graph
A graph of the function is attached.
Does the given information represent a function?
Find a33 first term in the sequence is 3 and the common difference is -1
A. -29
B. 36
C. -36
D. -30
Answer:
Step-by-step explanation:
After the antibiotic Streptomycin is given to a patient, the population (in million) of Mycobacterium in the body is given by the function f(t) = -0.02(t)2 + 3, where t is in hours. Find the rate at which the population of the bacteria is changing after 4 hours.
Dangerous, antibiotic resistant bacteria have been observed with increasing frequency over the past several decades.
In this review the factors that have been linked to this phenomenon are addressed. Profiles of bacterial species that are deemed to be particularly concerning at the present time are illustrated. Factors including economic impact, intrinsic and acquired drug resistance, morbidity and mortality rates, and means of infection are taken into account. Synchronously with the waxing of bacterial resistance there has been waning antibiotic development. The approaches that scientists are employing in the pursuit of new antibacterial agents are briefly described. The standings of established antibiotic classes as well as potentially emerging classes are assessed with an emphasis on molecules that have been clinically approved or are in advanced stages of development. Historical perspectives, mechanisms of action and resistance, spectrum of activity, and preeminent members of each class are discussed.
What antibiotic Streptomycin ?
Streptomycin injection is used to treat moderate to severe bacterial infections in many different parts of the body.
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Patricia run a mall event-organizing company baed in Nairobi. She ha jut received
an order to organize an SME development eminar at the Sarova Stanley Hotel hoted by
the World Bank. She i billing World Bank Kh 10,000 per participant while the hotel
charge her Kh 2,500 per participant for meal in addition to a charge of Kh 225,000
for the hall and other amenitie. Aume there i linear relationhip between the cot and
the number of participant. Required:
i. Obtain the minimum number of participant required to attend the forum for Patricia
to break even
Assuming that costs increase linearly with the number of attendees, Patricia needs at least 30 people to attend the forum in order to break even.
Patricia needs 75 attendees to attend the forum in order to make a profit of 337,500.
By dividing the fixed costs by the contribution margin per unit, we are able to determine the break-even threshold in units. Divide the fixed costs by the contribution margin ratio to get the break-even threshold in dollars.
The percentage of the contribution margin to the sales revenue is known as the contribution margin ratio. Prior to the division operation, we add
the profit to the fixed cost in order to reach the goal profit.
Billing rate per participant = 10,000
Hotel charges per participant = 2,500
Contribution per participant = 7,500 (10,000 - 2,500)
225,000 is the fixed fee for the hotel room and amenities.
Break-even point in units = Contribution per unit – Fixed cost
= 30 individuals (225,000 -7,500)
Fixed cost plus profit minus contribution per unit equals break-even point in units with target profit.
Target profit = 337,500
= (225,000 + 337,500) ÷ 7,500
= 75 participants
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Find the sum of the terms.
The numerator of the simplified sum is
Answer:
numerator = 4x + 6
Step-by-step explanation:
x²+3x + 2
(x+2)(x+1)
x/(x+2)(x+1) + 3(x+2)/(x+2)(x+1)
(x+3x+6)/(x+2)(x+1)
(4x+6)/(x+2)(x+1)
true or false? about 60% of u.s. women older than 16 years are either currently employed or looking for work.
Answer: True
Step-by-step explanation:
Simple.
the measure of the base angels in an isoceles triangle is 8 less than 3 times the measuee of a vertex angle.find the
The measure of base angles and vertex angle are 133° and 47° respectively.
What is an isosceles triangle ?
A triangle with two equal-length sides is known as an isosceles triangle (/assliz/). The term "equilateral triangle" can refer to a shape with either exactly two sides that are the same length or at least two sides that are the same length, with the latter definition containing the equilateral triangle as an exception.
Let the vertex angle to be 'x'
So, according to the question, the measure of the base angels in an isosceles triangle is 8 less than 3 times the measure of a vertex angle
So, Base angles = (3 × vertex angle) - 8
We know that sum of all angles of a triangle is 180° and the base angles of an isosceles triangle are equal.
∴ Base angles + vertex angle = 180°
(3 × vertex angle) - 8 + x = 180°
3x - 8 + x = 180°
4x = 188°
x = 47°
∴ The vertex angle is 47° and,
Base angles = (3 × vertex angle) - 8
= 3 × 47 - 8
= 141 - 8
= 133°
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what does x equal????
Answer:
x=15.56
Step-by-step explanation:
You need to use pythagoras for this question.
Formula for pythagoras: a^2 + b^ =c^2
a= 11
b=11
c=?
11^2+11^2=c^2
121+121=c^2
242=c^2
[tex] \sqrt{242} [/tex]
=c
c=15.56
Use the quadratic formula to solve. Express your answer in simplest form.
22d²- 35d + 12 = -3d²
Answer:
x= -22d/44 x = -48d/44 is your answer
where d =2x
Step-by-step explanation:
22d²- 35d + 12 = -3d²
22d²- 35d + 12 +3d²
25d²- 35d + 12 = a b c formula= - b-/+ / b^2 - 4 ac / 2a
= -35d -+/ 35^2 - 4 *22d *12 / 2*22d
= -35d -+/1225d-4 (22) (12) /44d
= -35d -+/1225d- (88) (12) /44d
= -35d -+/1225d- (1056) /44d
= -35d -+/169d- /44d
=-35d -/+ 13d /44 x= -22d/44 x = -48d/44
The discriminant b2−4ac>0
so, there are two real roots.
The cell phone plan from Company C costs $10 per month, plus $15 per gigabyte for data used. The plan from Company D costs $80 per month, with unlimited data.
Rule C gives the monthly cost, in dollars, of using g gigabytes of data on Company C's plan. Rule D gives the monthly cost, in dollars, of using g gigabytes of data on Company D's plan.
Which is less, C(4) or D(4)? What does this mean for the two phone plans?
The solution: is C(g) = 10 + 15g, C'(g) = 80.
Monthly pricing for utilizing 2 Gigabytes of data at Company C.
Detailed explanation:
Company C's cell phone plan is $10 per month + $15 for every gigabyte of data utilized. Company D's monthly fee is $80 and includes unlimited data.
The monthly cost for using g gigabytes of data at Company C is now: C(g) = 10 + 15g.... (1)
Again, the monthly cost for using g gigabytes of data at Company D will be as follows: C'(g) = 80......... (2) (2)
Statement C(2) = 10 + 15 2 = 40 represents Company C's monthly charges for utilizing 2 Gigabytes of data use, according to equation (1).
Thanks for your question. I had an interesting time solving this.
Let O , P , and Q be distinct collinear points with PQ=3 . Let P′ and Q′ be the images of points P and Q under dilation from point O with scale factor 4 .
What is the length of the image segment P′Q′ ?
Responses
1. 1
2. 7
3. 9
4. 12
Answer If O, P, and Q are collinear points with PQ = 3, and P' and Q' are the images of P and Q under dilation from O with a scale factor of 4, then the length of the segment P'Q' will be 4 times the length of the segment PQ. Since PQ = 3, the length of P'Q' will be 4 * 3 = $\boxed{12}$.
To see why this is the case, recall that a dilation with a scale factor of 4 expands or contracts a figure by a factor of 4 in each direction. In this case, the dilation from O with a scale factor of 4 expands the segment PQ by a factor of 4, resulting in the segment P'Q' with a length of 4 times the length of PQ. Since PQ = 3, the length of P'Q' will be 4 * 3 = 12.
A garden contains secral diffrent types of flowers in the garden 2/3 of the flowers are roses of the roses 1/5 of the flowes are white and 3/5 of the flowers are pink. What fractin of the total flowers in the garden are white or pink?
The total flowers in the garden white or pink is 8/15.
What is fraction?The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.
In our garden, there are 2/3 total roses, making the total number of blooms that aren't roses 1/3
4/5 = 2/3 +1/3.
Since 3 is a division of 6, we must multiply by 6 to arrive at the solution.
4 x 6 =24
5 x 6 =30
24/30
Next, we calculate half of 30 and add it to get 3/3.
Then we find 1/2 of 30 and add this to make 3/3
Just like 1/2 of 2 = 1 and 2+1 = 3
30 / 2 = 15
15 + 30 =45
The answer is 24/45
We then reduce this fraction by 3 as 6 + 8 do not divide into 45
24/45 = 8/15
The total flower in the garden is 8/15
The proportion of white or pink flowers in the entire garden is 8/15.
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Square ABCD has an area of 64 units^2
2
. It is rotated 270^{\circ}
∘
clockwise around vertex C resulting in square A'B'C'D'.
What is the side length of C'D'?
On solving the provided question, we got to know that side length of the square is 8 units.
What is a square?Four sides that are equally spaced apart make up a square. Around us, a lot of things are rectangular. Equal sides and a 90° interior angle serve as a visual cue to identify a square. A closed square has four sides and exists in two dimensions (2D). A square has an equal number and parallel alignment of its four sides.
What to identify a square?A four-sided shape known as a square has sides that are all the same length and angles that are all right angles with a 90 degree angle.
Here,
Area of square = [tex](side)^2[/tex]
64 = [tex](side)^2[/tex]
[tex]Side = \sqrt{64}[/tex]
Side = 8 units
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question is in the image, i need the method answer for part b.
the question says: "the diagram shows the position of two ships, A and B, and the coastguard station, C."
Step-by-step explanation:
it seems like you understood the law of cosine (extended Pythagoras for non-right-angled triangles) and applied it mostly correctly for a).
but you made a little typo : suddenly, in the second half of the formula you changed the side length BC from 83.1 to 81.3. but it is 83.1.
so, the correct calculation is
a² = 83.1² + 95.5² - 2×95.5×83.1×cos(101) =
= 16,025.86 - 15,872.1×cos(101) =
= 16,025.86 - -3,028.539456... =
= 19,054.39946...
a = sqrt(19,054.39946) = 138.037674...
the rounded result is the same (138 km), but just for your information, and also, I want to use the correct numbers for b)
for b) we need to know :
bearings are angles, measured clockwise from north (north would be 0°).
when ship A looks to station C, the bearing is 146°.
when ship A looks to ship B, the corresponding bearing is 146 - the triangle angle at A (because that is how far we have to turn from looking at C to looking at B).
so, now, we need to apply the law of cosine again. this time to get angle A, as we have now side a.
c² = a² + b² - 2ab×cos(C)
and we want to get C, means now (since you called the baseline "a" in the first part)
83.1² = 95.5² + a² - 2×a×95.5×cos(angle A)
6,905.61 = 9,120.25 + 19,054.39946... - 2×138.037674...×95.5×cos(angle A)
6,905.61 = 28,174.64946... - 26,365.19574...×cos(angle A)
-21,269.03946... = -26,365.19574...×cos(angle A)
cos(angle A) = -21,269.03946.../-26,365.19574...
= 0.806708953...
angle A = 36.22437773...°
therefore, the bearing from A to B is
146 - 36.22437773... = 109.7756223...°
3.3. A triangle has sides of lengths (7x + 1) cm, (4x - 1) cm and (14- x) cm. If the
perimeter is 84 cm, find the dimensions of the triangle.
Answer:
7 cm.
The triangle dimensions are: 50, 27, and 7 cm
Step-by-step explanation:
The three sides of the triangle make up the entire perimeter. Add each side and set the result equal to 84cm, the perimeter.
(7x+1) + (4x-1) + (14-x) = 84 cm
10x + 14 = 84
10x = 70
x = 7 cm
Use x=7 to find the three dimensions:
1) (7x+1) = 50 cm
2) (4x-1) = 27 cm
3) (14-x) = 7 cm
Do these add to 84 cm?
(50+27+7) = 84 cm YES
Which graph represents the function f(x) = 5 ^ x
What is the slope of the line shown?
Answer:
Below
Step-by-step explanation:
Find two convenient integer coordinates ( 0,7) and (5,-3)
slope = (y1-y2) / (x1-x2)
it does not matter which point your assign as '1' or '2'
slope = ( 7 - - 3 ) / (0-5) = 10 /-5 = -2
what are the intercepts of the line - 4x + 7y=3
Answer:
The intercepts are: (0, 3/7) and (-3/4, 0)
Step-by-step explanation:
If X=0
-4(0) + 7y = 3
7y = 3
Y = 3/7
If Y=0
-4x + 7(0) = 3
-4x = 3
X = -3/4
Help with ixl please
The most horizontal line is straight so it equal 180°. You know that one side (lower left section) is 67° meaning the other side is 180° - 67° = 113° (lower right side).
The most vertical line is straight so it equal 180°. You know that one side (lower right side) is 113°. The entire right side you have: 113°, 42°, and f.
f = 180° - (113° + 42°)
f = 25°
Answer:25 deegrees
Step-by-step explanation:
Konrad buys a skateboard that costs c dollars. After 7.5% sales tax is added, the total cost can be expressed by the expression c+0.075c . What is this expression written in simplest form?
When the skateboard's price, c, and the 7.5% sales tax are included, the simplified expression for the provided expression, c+0.075c, becomes 1.075c.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.
Here,
Given expression,
=c+0.075c
total cost=1.075c
The simplified expression for the given expression c+0.075c will be 1.075c when the skateboard cost c and the sales tax of 7.5% is added.
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if anna divides the ingredients equally into 4 pots and she has 2/3 onions how many cups of onions will she need in each pot
Anna will need 1/2 cup of onions in each pot. This is because 2/3 of a cup is equal to 4/6 of a cup, and when divided by 4 pots, the result is 1/2 cup of onions in each pot.
What is ingredient?An ingredient is a substance that is used as part of a recipe or product formulation. Ingredients are the components of a mixture that are used to produce a food, beverage, cosmetic, pharmaceutical, or other product. Ingredients can be natural, such as water, spices, and herbs, or man-made, such as preservatives, colorings, and flavorings. The amount and type of each ingredient used in the formulation of a product determines its properties and characteristics.
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what are some features that make highway roads safer for drivers who are driving at higher rates of speed? (select 5 correct answers)
There are the some features that make highway roads safer for drivers who are driving at higher rates of speed is :(5 correct answers)
1.Median barriers
2.Guard rails
3.Brake away signs
4.Rumble strips
5.Controlled access
Given,
In the question:
What are some features that make highway roads safer for drivers who are driving at higher rates of speed?
Now, According to the question:
There are the some features that make highway roads safer for drivers who are driving at higher rates of speed is :(5 correct answers)
1.Median barriers
2.Guard rails
3.Brake away signs
4.Rumble strips
5.Controlled access
Hence, There are above 5 highway roads safer for drivers.
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Find the value of the expression 2xy(8x - 3y), when x = 2 and y = 4
A 48
B 72
C 64
D 24
Line L is the perpendicular bisector of segment WY, Z is a point on L.
NIcholas noticed that WXZ and YXZ are congruent based on side-angle-side congruency postulate.
What theorem can we prove using these congruent triangles?
Choose 1 answer:
A. Vertical angles are congruent.
B. Measures of interior angles of a triangle sum to 180\degree180°180, degree.
C. A point on the perpendicular bisector of a line segment is equidistant from the segment’s endpoints.
D. Any line segment is congruent to itself because every point on the segment maps to itself.
Given that WXZ and YXZ are congruent based on side-angle-side congruency, we can prove the theorem that states "A point on the perpendicular bisector of a line segment is equidistant from the segment’s endpoints." This theorem is often referred to as the "Perpendicular Bisector Theorem."
The required details for "Perpendicular Bisector Theorem" in given paragraph
The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a line segment, then it is equidistant from the segment's endpoints. This means that if we draw a line through a point that is perpendicular to a line segment, and that line passes through the midpoint of the segment, then the point is equidistant from the endpoints of the segment. In this case, we are given that line L is the perpendicular bisector of segment WY, and that Z is a point on L. We are also told that WXZ and YXZ are congruent based on side-angle-side congruency. Since WXZ and YXZ are congruent, it follows that WX and YX are congruent and that WZ and YZ are congruent. This means that the distances from Z to W and Y are equal, so Z is equidistant from W and Y.
Therefore, we can conclude that Z is a point on the perpendicular bisector of segment WY, and the Perpendicular Bisector Theorem is proved. The answer is C. "A point on the perpendicular bisector of a line segment is equidistant from the segment’s endpoints."
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Felix invested $2,800 at a rate of 3.4%, compounded quarterly. [HINT: Use the
formula A = P(1 + 5 )nt]
26 aleged to 19dmun si of bas
a) What exponential growth function would model this situation?
b) What is the value of the investment after 5 years? (Round your response to the nearest
dollar).
23.02
The value of the investment after 5 years will be $3309.48.
What is compound interest?Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.
In finance and economics, interest is the payment of an amount above the repayment of the principal sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.
The value of the investment after 5 years will be,
[tex]A = P[(1 + \dfrac{r}{100} )^{nt}]\\A = 2800[(1+0.034)^{5}[/tex]
A = $3309.48
Therefore, the value of the investment after 5 years will be $3309.48.
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For the month of April, a checking account has a balance of $501 for 23 days, $2428 for 3 days, and $241 for 4 days. What is the account’s mean daily balance for April?
The account’s mean daily balance for April will be $105.7.
What is a mean?Mean is the total added values of all the data in a set divided by the number of data in the set.
The account had the following balances;
$501 for 23 days
$2428 for 3 days
$241 for 4 days.
To find the mean; add the total amount and divide by the total number of days
[tex]mean = \frac{501 + 2428 + 241}{23 + 3 + 4}[/tex]
[tex]mean = \frac{3170}{30}[/tex]
mean = $105.7
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Two water tank are hown. Tank A i a rectangular prim and Tank B i a triangular prim Tank A i filled with water to the 6-meter mark ome of the water from tank A i being tranferred to Tank B o that the water in tank a i at 2 meter. Shade the amount of water in tank B to indicate the approximate height of the water in tank bafter the tranfer alo write the height, to the nearet whole number of meter, in the pace provided
The water tank's illustrated prism will stand 8 meters tall.
What is a Prism?Prisms are significant polyhedron family members with congruent polygons at the base and top.
A prism's other faces are referred to as its lateral faces. It denotes that a prism's face is not curved.
The cross-section of a prism is constant along its length. The names of the prisms are determined by their cross-sections. The best example of a prism that best represents a real-world object is a metallic nut.
A rectangular prism that best represents a real-world object is a fish aquarium.
According to our question-
The following formula will be used to determine the triangle prism's base's area:
= 1/2 × 4 × 9
= 18m²
The rectangular tank's water will be drained of the following volume:
= (6 × 6) × 4
= 144m³
As a result, the height will be determined as follows:
18 × h = 144
18h = 144
h = 144/18
h = 8m
Hence, The water tank's illustrated prism will stand 8 meters tall.
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Given the following information, calculate the product cot per unit. Direct material = $28,000 Direct labor = $42,000. Overhead application rate = $15 per direct labor hour. Direct labor hour = 5,200. Unit product = 7,400. Product cot per unit = $
The product cost per unit is $53.30 along the rims and $28.29 along the posts.
What does the mean cost mean in math?The average cost price is the quantity as an arithmetic average of the average amount. Average or mean is defined as the product of the total number of data given and the total number of data given. We have the cost of the goods and the overall quantity of goods or products provided when determining average cost pricing.
How do you find the cost in math?Cost price, for instance, equals selling price plus profit. Cost is equal to Selling price plus Loss. Cost price = 100 Selling Price + 100 + Profit (when the Selling Price and Profit Percentage are given)
According to the above questions :-
Direct Materials rims $20
Direct Labour rims $12
Overhead $21.30
Total cost is $53.30
Direct Materials posts $18
Direct Labour posts $6
Overhead $4.29
Total cost is $28.29
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9
Are the following equations the same line? *
y - 3 = 4(x - 2)
2)
and
and y + 2 = 4(x + 7)
no, because they are not the same in slope - intercept form
it would be impossible to tell
yes, because both equations are the same in slope - intercept form
(5 Points)
Answer: No, because they are not the same in slope - intercept form
Step-by-step explanation:
First, we will distribute and simplify into slope-intercept form.
Equation 1:
y - 3 = 4(x - 2)
y = 4(x - 2) + 3
y = 4x - 8 + 3
y = 4x - 5
Equation 2:
y + 2 = 4(x + 7)
y = 4(x + 7) - 2
y = 4x + 28 - 2
y = 4x + 26
We see that the answer to this question is "No, because they are not the same in slope - intercept form" as they have different y-intercepts, one being -5 and one being 26.