Write an expression to represent the product of 6 and the square of a number plus 15. In your expression what is the value of the coefficient? A. 1 B. 6 C. 15 D. 2
Answer:
B) 6
Step-by-step explanation:
Let the number be x
Product of 6 and square of number plue 15 : (6x²) + 15
Coefficient of x² = 6
please show the steps
Answer:
x = -3, 0, or 7
Step-by-step explanation:
After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.
__
Step 1Write the equation in standard form.
4x³ -16x² -84x = 0
Step 2Factor out the common factor from all terms.
= 4x(x² -4x -21) = 0
Step 3Compare to the factored form of a quadratic:
(x +a)(x +b) = x² +(a+b)x +ab
This tells you the constants 'a' and 'b' in the factors can be found by considering ...
(a+b) = -4 . . . . the coefficient of the x term of the quadratic
ab = -21 . . . . . the constant term of the quadratic
It is often helpful to list factor pairs of the constant:
-21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum
The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...
a = -7, b = 3
Step 4Put it all together.
4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation
Step 5Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:
4x = 0 ⇒ x = 0
x -7 = 0 ⇒ x = 7
x +3 = 0 ⇒ x = -3
Solutions to the equation are x ∈ {-3, 0, 7}.
_____
Additional comment
What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.
A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.
Consider the following expression.
4x4y+4y3
Identify the degree.
Answer:
Consider the following expression: 3x. 2. +7x−2−4x. It can also come as 16xy+4y
=3.
Solve to determine the solution set of the inequality |x +3] <5.
1. Rewrite for two solutions: (x + 3) <5,-(x + 3) <5
2. Solve first inequality:
x<2
3. Solve second inequality: -X-3 < 5
-X < 8
X > -8
4. Write the inequality of the solution set: 2
Answer:
-8<x<2
Step-by-step explanation:
Let g(x) be the indicated transformation of f(x) = −|3x| − 4. Stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3 and reflect it across the x-axis. Identify the rule and graph of g(x).
The final rule for g(x) is g(x) = 3|3x| + 12.
To stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3, we multiply the function by 3. This will result in a vertical stretching of the graph.
So, the rule for g(x) is g(x) = 3f(x).
Now, let's find the expression for g(x) using the given function f(x) = −|3x| − 4:
g(x) = 3f(x)
g(x) = 3(-|3x| - 4)
g(x) = -3|3x| - 12
This is the expression for g(x), which represents the transformed graph.
To reflect the graph of g(x) across the x-axis, we change the sign of the function. This means that the negative sign in front of the absolute value will become positive, and the positive sign in front of the constant term will become negative.
Therefore, the final rule for g(x) is g(x) = 3|3x| + 12.
Now, let's consider the graph of g(x). The graph will have the same shape as f(x), but it will be stretched vertically by a factor of 3 and reflected across the x-axis.
The original graph of f(x) = −|3x| − 4 is a V-shaped graph that opens downward and passes through the point (0, -4). The transformed graph of g(x) will have a steeper V-shape, opening downward, and passing through the point (0, 12) instead of (0, -4).
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HELP!!!!!
find the slope of (7,7) and (4,19)
Answer:
-4
Step-by-step explanation:
y2-y1/x2-x1
solve for slope
Answer:
-4
Step-by-step explanation:
At Tim Hortons, mike bought three coffees and 1 doughnut for $19. Bob bought one coffee and one doughnut for $9. Using the price of one coffee=c and the price of one doughnut=d . Answer the following questions 14,15,16 and 17
So first of all we need to write an algebraic equation for Mike. We know that he bought 3 coffees and 1 doughnut. Then the total price of these things is:
\(3c+1d=3c+d\)And we know that he had to pay $19 so this expression is equal to 19:
\(3c+d=19\)Then the answer to question 14 is the second option.
Bob bought one coffee and one doughnut so the total cost of his purchase is:
\(c+d\)We know that this cost is equal to $9 so we get:
\(c+d=9\)And the answer to question 15 is the third option.
In question2 16 and 17 we need to find c and d. For this purpose we need to use the algebraic equations for Mike and Bob:
\(\begin{gathered} 3c+d=19 \\ c+d=9 \end{gathered}\)Let's take the second equation and substract c from both sides:
\(\begin{gathered} c+d-c=9-c \\ d=9-c \end{gathered}\)Now we substitute this expression in place of d in the first equation:
\(\begin{gathered} 3c+d=3c+(9-c)=19 \\ 3c+9-c=19 \\ 2c+9=19 \end{gathered}\)Now we substract 9 from both sides:
\(\begin{gathered} 2c+9-9=19-9 \\ 2c=10 \end{gathered}\)And we divide both sides by 2:
\(\begin{gathered} \frac{2c}{2}=\frac{10}{2} \\ c=5 \end{gathered}\)Then the price of one coffee is $5 so the answer to question 16 is the third option.
Now we are going to take the equation for Bob and take c=5:
\(c+d=5+d=9\)If we substract 5 from both sides we get:
\(\begin{gathered} 5+d-5=9-5 \\ d=4 \end{gathered}\)Then the price of one doughnut is $4 and the answer to question 17 is the second option.
What 12x12 I need help please help me
Answer:
144
Step-by-step explanation:
-0- Easy :D
Suppose corn chips cost 32.5 cents per ounce. What would a bag of chips cost if it contained 19 oz? Round your answer to the nearest cent, if
necessary
Answer:
$6.18 :)
Step-by-step explanation:
617.5 cents would a bag of chips cost if it contained \(19\) oz.
What is unitary method?Unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
According to question,
Corn chips costs = \(32.5\) cents per ounce.
A bag of chips of \(19\) oz costs = 32.5 * 19
= 617.5 cents
Hence, 617.5 cents would a bag of chips cost if it contained \(19\) oz.
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Area of composite shapes, There is a pair of parallel sides in the following shape.
What is the area of the shape?
The following form has two parallel sides, and, in accordance with the provided assertion, its area is 21 cm².
What does mathematicians mean by area?Area is the entire amount of space occupied by a flattened (2-D) surface or form of an item. The area of a planar figure is the space that its perimeter encloses. The quantity of unit rectangles that completely encircle a closed figure's surface is its area. Square units such as cm² and m² are used to measure area.
The ratio will also be 1/2 * (bases 1 + base 2) * length since it is a trapezium.
So, 1/2 * ( 9+5) * 3
= 1/2 * 14 * 3
= 1/2 * 42
= 21 cm²
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The ratio of boys to girls is 7 : 5. There are 63 boys. Choose a ratio tool and determine the number of girls.
Answer:
63:45 =7:5
Step-by-step explanation:
7 goes into 63 9 times. Since you got 9 you multiply that by the ratio of girls.
9x5=45
Have a wonderful day!
Which value for x makes the sentence true? 1/35 + x = 1/7
A. 6/35
B. 1/28
C. 4/35
D. 1/21
WHATS THE ANSWER :(
PLS HELP ME !!!!!!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
All sides make a cube
Answer:
D
Step-by-step explanation:
What are the two possible measures of the angle below
Answer:
Option 1
Step-by-step explanation:
The angle is a right angle, and Option 1 is the only option with two angles coterminal to positive or negative 90°.
What is f(-2)?
-3
-1
1
3
ESAY MATH PLS HELP
is this sss,sa,aa,or none
Answer:
SAS
Step-by-step explanation:
If b = -2, what is 3b-7 ?
Add and Subtract Decimals to
1. (02.01 LC)
Round 0.39 to the nearest tenth. (1 point)
0.3
0.35
0.4
2. Blake interviewed 24 students to see whether they collected sports cards and whether they participated in sports. The table below shows his data Sports-Card Collecting and Sports Participation Collects Sports Cards Does Not Collect Sports Cards Participates in Sports 6 Does Not Participate in Sports 3 7 How many total students Blake interviewed, participate in sports?
Therefore, out of the 24 students that Blake interviewed, 9 of them participate in sports.
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value.
Here,
According to the table, Blake interviewed a total of 24 students. To find out how many of these students participate in sports, we need to add up the number of students who collect sports cards and participate in sports, as well as the number of students who do not collect sports cards and participate in sports. So:
Total students who participate in sports = Number of students who collect sports cards and participate in sports + Number of students who do not collect sports cards and participate in sports
Total students who participate in sports = 6 + 3
Total students who participate in sports = 9
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A student keeps track of how many minutes they play video games in the course of a week as part of a class project. The counts were: 345 min, 223 min, 117 min, 154 min, 96 min, 412 min and 521 minutes. How many total minutes did the student spend watching video games?
The total minutes did the student spend watching video games is 1868 minutes.
Total
When we need to find the total of two or more numbers, the result or the answer we get can be defined as the SUM. The numbers that are added are called addends.
Given,
A student keeps track of how many minutes they play video games in the course of a week as part of a class project. The counts were: 345 min, 223 min, 117 min, 154 min, 96 min, 412 min and 521 minutes.
Here we need to find how many total minutes did the student spend watching video games.
To find the total number of minutes we need to add all the given values,
Then we get,
=> 345 + 223 + 117 + 154 + 96 + 412 + 521 minutes.
=> 1868 minutes.
So, he watched almost 1868 minutes in a week.
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Use the line segments below to create a triangle with vertices at the following points. (-9,4), (-4,9), (-9,7) y 8 6 Click to add vertices 2 -8 - 6 - 4 2 4 6 8 -4 -6- -8 just send me a picture back please thank you
Answer:
Step-by-step explanation:
Este. DVD ex xxx xxx
received the new experimental drua. 23 subiects were assigned to the control group and received a standard, well-known treatment. after a suitable period. the reduction in blood pressure for each subiect was recorded. thev are going to conduct a test at a 5% sianificance level to see if the mean reduction in blood pressure is different between the arouos. the resultina statistics are as follows:
To determine if the mean reduction in blood pressure is different between the two groups, you can use a statistical test such as a two-sample t-test. This test compares the means of two groups and determines whether the difference between the means is statistically significant.
To conduct the t-test, you will need the following information:
The sample size of each group (number of subjects in each group)The mean reduction in blood pressure for each groupThe standard deviation of the reduction in blood pressure for each groupThe level of significance (in this case, 5%)Once you have this information, you can use a statistical software or calculator to perform the t-test and determine the p-value. The p-value is a measure of the probability that the difference between the means is due to chance.
If the p-value is less than the level of significance (5% in this case), then the difference between the means is statistically significant and you can conclude that there is a significant difference in the mean reduction in blood pressure between the two groups.
If the p-value is greater than the level of significance, then the difference between the means is not statistically significant and you cannot conclude that there is a difference in the mean reduction in blood pressure between the two groups.
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12) 36 gallons is equal to how many quarts? 4 qt=1 gallon*
Answer:
144
Step-by-step explanation:
36 x 4
Answer:
144
Step-by-step explanation:
1 gallon 4
36 gallon 4*36 =144
State if the triangles in each pair are similar. If so, state how you know they are similar.
Answer:
A) similar; SAS similarity.
Step-by-step explanation:
SAS Triangle Similarity
The SAS criterion for triangle similarity states that if two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.
We are given two triangles BCD and JKL. Sides DB and JL have a ratio of 90/20 = 4.5
Sides JK and BC have a ratio of 81/18 = 4.5
Since both sides are proportional and their included angle of 43° are congruent, then both triangles are similar, SAS similarity.
A) similar; SAS similarity.
Find the perimeter of the triangle. Perimeter is the distance around the outside. *
Answer:
s=
\( \frac{1}{2} \)
Answer:
To find the perimeter of an equilateral triangle, the formula is Side X 3
If it's a Scalene or an Isosceles triangle , add all sides.
Hope it helps ;)
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Can anybody please help me out with this question I would really appreciate it so much . Please and thank you .
Answer:
x=3 MT=36 MH=18
Step-by-step explanation:
The two triangles are the same, so 7x+8=10x-1
3x=9
x=3
MT=12x3=36
MH=36/2=18
A river flows due south at 1.4 mi/h. In what direction should the swimmer head, at a velocity of 3 mi/h, in order to arrive at a landing point due east of his starting point? (Round your answer to one decimal place.)
Solution:
It is that a river is flowing in the south direction with a speed of \($v_r$\)1.4 mi/h.
A swimmer wishes to cross the river in a horizontal direction so that he lands at a point which is due east of his starting point.
The speed of the swimmer is \($v_s$\) = 3 mi/h
Therefore he has to swim in such a direction that his resultant is in the direction east to his starting point.
Let this angle be θ.
Therefore, from the figure,
\($\sin \theta = \frac{v_r}{v_s}$\)
\($\sin \theta = \frac{1.4}{3}$\)
\($\theta = \sin^{-1}(0.46)$\)
\($=27.4^\circ\)
Therefore, the swimmer has to swim in the northeast direction making an angle of (90+27.4) = 117.4° with the direction of flow of river (i.e. south).
A rectangle has an area of
72 square centimeters. The width of the rectangle is 8 centimeters.
Answer:
\(\boxed{\bf length=9\; cm}\)Step-by-step explanation:
Given:-
Area = 72
width = 8
Area = length × width
\(\bf 72=length \times 8\)
Divide 72 / 8:-
\(\bf length=9\; cm\)
If you're asking to find the length, this's your answer.
____________________________
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Miles is 33 year old and single in 2020 his only income consisted of $10500 in wages what is the maximum amount he can contribute to a traditional ira for 2020
Answer:
$6,000
Step-by-step explanation:
$6,000 Because miles younger than 50
Which expression represents a cube root of 1 + i?
OVE (cos()+ i sin (24))
OVE (cos (37) + i sin (3))
/
O & (cos (4) + i sin (24))
V2 (cos (37) + 1 sin (37))
Answer:c
Step-by-step explanation is va cuz when your multiply:
Answer:
\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)
Step-by-step explanation:
The analysis is as attached below.