In the given expression, the number of terms is 5, the constants are 8, -5 6, -10 and 2. The fourth term is j and the coefficient of the third term is 6
What are Mathematical ExpressionsIn mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An algebraic expression consists of unknown variables, numbers and arithmetic operators. It does not contain any equality or inequality symbols. An expression in math is a statement involving at least two different numbers (known or unknown) and at least one operation.
In the given expression, we have to answer some questions here;
a) The number of terms in the expression is 5
b) The constant of the expression are 8, -5, 6, -10 and 2
c) The fourth term in the expression is j
d) The coefficient of the third term is 6
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The oxygen saturation level of a river is found by
dividing the amount of dissolved oxygen the river
water currently has per liter by the dissolved oxygen
capacity per liter of the water and then converting to a
percent. If the river currently has 7.3 milligrams of dis-
solved oxygen per liter of water and the dissolved
oxygen capacity is 9.8 milligrams per liter, what is the
oxygen saturation level, to the nearest percent?
Answer:
sub
gghhhhhhhhgtyyuuiiiiii
Find a polynomial function of degree 3 with the given numbers as zeros. Assume that the leading coefficient is 1.
1+7i, 1−7i, −4
x³ + 2x² + 49x² - 54 = 0 is the required polynomial equation of degree .
What does the word "polynomial" mean?
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).
The given roots are let α = -2, β = 7i and γ = - 7i
the leading coefficient is 1
The required polynomial is
x³ - ( α + β + γ)x² + ( αβ + βγ + αγ )x - αβγ = 0
x³ - ( -2 + 7i - 7i )x² + (( -2.7i + 7i ( -7i) + ( -2 ( -7i ))x - (-2.7i. ( -7i)) = 0
x³ - ( -2)x²+ ( -14i - 49i² + 14i )x + 54i² = 0
x³ + 2x² + 49x² - 54 = 0
is the required polynomial equation of degree .
We have used the polynomial equation whose are x^3-(sum of the roots)x^2+(sum of the product of the two roots)x-product of the roots =0
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Write the equation of the line that is parallel to line m and passes through the point (4, - 5).
The slope of the line parallel to the given line will be same as that of the given line.
Let 'm' be the slope of the line,
[tex]y-b=m(x-a)[/tex]Substitute a=4 and b=-5 in the above expression.
[tex]\begin{gathered} y-(-5)=m\times(x-4) \\ y+5=mx-4m \\ y=mx-4m-5 \end{gathered}[/tex]Thus, the expression of the parallel line is y=mx-4m-5.
The following table shows the distances each of four students jumped at a long jump competition:
Student Distance (in feet)
Aleena 9.46
Susan 9.068
Molina 9.601
Anna 9.04
Which student jumped the greatest distance? (1 point)
Aleena
Susan
Molina
Anna
Molina jumped the greatest distance at a long jump competition which is 9.601 feet
What is meant by Decimal?Decimal: A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.
Given in the question that, the distance each of four students jumped a long jump competition
Student Distance
Aleena 9.46 feet
Susan 9.068 feet
Molina 9.601 feet
Anna 9.04 feet
let us compare the feet jumped by the students
write them in ascending order to get the highest feet based on decimal values
9.04, 9.068, 9.46, 9.601
by checking the order we can confirm that 9.601 feet is the highest
9.601 feet long jump was done by Molina
so we can conclude that Molina jumped the greatest distance
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Which values are solutions to the inequality below?Check all that apply.√x ≤ 11choices: 121, 120, 111, -10, 122, no solution
Consider the given inequality,
[tex]\sqrt[]{x}\leq11[/tex]Note that a square root inequality is defined only if the 'x' is non-negative.
[tex]x\ge0[/tex]Now, squaring both sides will not affect the inequality as both sides are positive terms,
[tex]\begin{gathered} (\sqrt[]{x})^2\leq11^2 \\ x\leq121 \end{gathered}[/tex]Combining the two results,
[tex]0\leq x\leq121[/tex]Thus, the solution set to the inequality is the set of all real numbers from 0 to 121 .
find the surface area of the prism choose the correct units
We have a rectangular prism, with dimensions 7 ft tall, 1 ft wide and 4 ft deep.
The surface area of the prism is the sum of the area of all their faces.
We can start by listing the faces. We will have 3 pair of faces:
- One pair of 7 ft * 1 ft
- One pair of 1 ft * 4 ft
- One pair of 4 ft * 7 ft
Then, we can write and solve the expression for the surface area as:
[tex]\begin{gathered} A=2\cdot A_1+2\cdot A_2+2\cdot A_3 \\ A=2\cdot(7\cdot1)+2\cdot(1\cdot4)+2\cdot(4\cdot7) \\ A=2\cdot7+2\cdot4+2\cdot28 \\ A=14+8+56 \\ A=78\text{ ft}^2 \end{gathered}[/tex]Answer: the surface area is 78 square feet.
write a quadratic equation in the form x^2 + bx + c =0 that has the following rootsroots {10,5}
If the roots are 10 and 5, then the equation can be expressed as:
(x - 10)(x - 5)
Distributing,
x*x - x*5 - 10*x + 10*5 =
= x² - 15x + 50
Identify the vertical and horizontal asymptotes of the following rational function…..The rest of option D was cut off, but it says:Vertical asymptotes: x = -3 , x = 6.Horizontal asymptote at y = 0
The function is given to be:
[tex]h\mleft(x\mright)=\frac{\left(x-2\right)\left(x+3\right)\left(x-6\right)}{\left(x-4\right)\left(x+3\right)^{2}\left(x+2\right)}[/tex]Vertical Asymptotes:
The vertical asymptote of a function is the x value gotten when the denominator is equated to 0.
The denominator of the function given can be equated to 0 as shown below:
[tex](x-4)(x+3)^2(x+2)=0[/tex]Therefore, we can get the values for x using the Zero Factor Principle given to be:
[tex]\begin{gathered} If \\ ab=0, \\ \text{then} \\ a=0,b=0 \end{gathered}[/tex]Therefore, we have
[tex]\begin{gathered} x-4=0,\therefore x=4 \\ x+3=0,\therefore x=-3 \\ x+2=0,\therefore x=-2 \end{gathered}[/tex]Hence, the horizontal asymptotes are at:
[tex]x=4,x=-3,x=-2[/tex]Horizontal Asymptotes:
The horizontal asymptotes can be gotten by checking the degree of the functions that make up the numerator and denominator of the whole function. If the degree of the numerator is less than that of the denominator, then the asymptote is at y = 0.
Degree of Numerator: 3
Degree of Denominator: 4
Therefore, the horizontal asymptote is at:
[tex]y=0[/tex]ANSWER:
The correct option is OPTION B.
Find the area of a rectangle whose length and breadth are 3x²y² and 5xy2 respectively.
Answer:
A = 15x³[tex]y^{4}[/tex]
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × breadth
= 3x²y² × 5xy²
= 3 × 5 × x² × x ×y² × y²
= 15 × x³ × [tex]y^{4}[/tex]
= 15x³[tex]y^{4}[/tex]
What is the solution for g in this equation 4/3g+7/3g+9=-1/3g-3
Given:
[tex]\frac{4}{3g}+\frac{7}{3g}+9=\frac{-1}{3g}-3[/tex]Multiply through the equation by 3g
This gives
[tex]3g\times\frac{4}{3g}+3g\times\frac{7}{3g}+3g\times9=3g\times\frac{-1}{3g}-3g\times3[/tex]This gives
[tex]\begin{gathered} 4+7+27g=-1-9g \\ 11+27g=-1-9g \end{gathered}[/tex]Collect like terms
[tex]27g+9g=-1-11[/tex]Simplify and solve for g
[tex]\begin{gathered} 36g=-12 \\ g=\frac{-12}{36} \\ g=-\frac{1}{3} \end{gathered}[/tex]Hence, the value of g is
[tex]-\frac{1}{3}[/tex]Keisha is planning an event for her company. It will take place the 3rd Saturday of May, and will be four hours long. There will be 35 employees at the event, and each can bring one guest She must make arrangements for venue, décor, food, beverages and entertainment She has a budget of $3,000. After researching available options, she has developed the following list of possible vendors. Décor A: $300, Décor B. $500, Décor C. $750 Food A: $15 per person, Food B: $18 per person, Food C. 5800 Beverage A: 53 per person, Beverage B: 55 per person, Beverage C: $500 Entertainment A: 516 per person; Entertainment B: $1,000; Entertainment C: $1,500 She now needs to decide what to buy and who to hire in order to stay under budget. In order to further guard against going over budget, she has decided to leave herself 10 percent of the budget for a contingency fund. Assuming all vendors listed above are of similar quality, how should she decide among vendors? If her boss is not pleased by her initial choice, is there another under-budget combination of vendors she can suggest?
Keisha has a budget of $3,000 to set up an event for her company. She decided to guard against going over budget, she left 10% of the budget for a contingency fund. This leaves a budget of $3,000 - 10*3000/100 = $2,700.
Now analyze the possible vendors, considering it's expected to have 70 people attending the event (35 employees + 35 guests).
Vendor A has the following cost scheme:
Décor: $300
Food: $15 per person * 70 = $1,050
Beverage: $53 per person * 70 = $3,710
Entertainment: $516 per person * 70 = $36,120
---------------------
Vendor B has the following cost scheme:
Décor: $500
Food: $18 per person * 70 = $1,260
Beverage: $55 per person * 70 = $3,850
Entertainment: $1,000
---------------------
Vendor C has the following cost scheme:
Décor: $750
Food: $5,800
Beverage: $500
Entertainment: $1,500
Since all vendors are of the same quality, Keisha should pick the cheapest choice for each item, that is:
Decor (From vendor A): $300
Food (From vendor A): $1,050
Beverage (From vendor C): $500
Entertainment (From vendor B): $1,000
Total budget: $300+$1,050+$500+$1000=$2,850
This is a valid option. She goes over her safe budget, but she can use part of that funds.
If her boss is not pleased by her choice above, we could try to replace some of the options with a more expensive item such that the total budges is not exceeded.
I cannot find any other combination of items that does not exceed the $3,000 limit, thus the presented combination is the only one that fulfills the conditions.
Triangle XYZ is translated by the rule (x + 1, y − 1) and then dilated by a scale factor of 4 centered at the origin. Which statement describes the properties of triangles XYZ and X''Y''Z'' after the transformations?
Using the given transformations, namely translation and dilation, the correct statement is given as follows:
Segments YZ and Y''Z'' are proportional after the dilation and congruent after the translation.
TranslationThe translation rule in this problem is given as follows:
(x, y) -> (x + 1, y - 1).
Meaning that the triangle was shifted:
One unit right, due to x -> x + 1.One unit down, due to y -> y - 1.The only change with the dilation was in the position of the triangle, hence the translated triangle is congruent to the original triangle.
DilationThe triangle was dilated by a scale factor of 4, meaning that the coordinates of each vertex of the triangle is multiplied by 4, changing the side lengths of the triangle, thus the dilated triangle is not congruent to the original triangle.
The angles keep the same measure for both cases, translation and dilation, hence the first two statements are incorrect.
The change in the side lengths is proportional, due to the scale factor of 4, hence the correct statement is:
Segments YZ and Y''Z'' are proportional after the dilation and congruent after the translation.
What is the missing information?The correct options are missing and are given by the image at the end of the answer.
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Owners of a recreational area are filling a small pond with water. They are adding water at a rate of 31 L per minute. There are 600 liters in the pond to start. Let W represent the total amount of water in the pond in liters, and let T represent the total number of minutes that water has been added. Write an equation relating to W to T then use this equation to find the total amount of water after 11 minutes.
we have that
the linear equation that represents this situation is
W=31T+600so
For T=11 min
substitute
W=31(11)+600
W=941 litersClassify the following variables as quantitative or qualitative variables. If the variable is quantitative, identify whether it is discrete or continuous.1. The type of payment used by customers.
A quantitative variable is the one who has a numerical significance such as number of items, time spent on playing a video game while a qualitative variable is the one who has not a numerical significance attached to it such as Gender , Eye color
So, the type of payment used by customers can be cash, card, etc.
Thus, the variable is qualitative.
Based on the information in the diagram, which trigonometric ratio would help determine the measure of side X? What is the measure of side x to the nearest tenth 0.0 of a centimeter?
A)
[tex]undefined[/tex]To find the quotient of 4 ÷ 18, count the number of in four whole circles.A faster way to add eight parts, four times, is to multiply 4 by .The quotient of 4 ÷ 18is
The quotient
[tex]\frac{4}{\frac{1}{8}}[/tex]Represent the total number of slices. Let's solve it.
[tex]\frac{4\cdot8}{1}=32[/tex]The total number of slices is 32.
On the other hand, a faster way to add the eight parts of each circle is to multiply 4 times 8 since there are 8 divisions inside each circle. This gives 32 also.
The table shows a proportional relationship.
Workout (hours) 1 2 3
Calories Burned 240 480 720
Create a description in words for the table.
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 240 calories burned, and for a two-hour workout, there are 480 calories burned.
The number of calories burned is dependent on the number of hours working out. For every 240-hour workout, there is 1 calorie burned, and for every 480-hour workout, there are 2 calories burned.
The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 240 calories burned, and for a two-hour workout, there are 480 calories burned.
The number of hours working out is dependent on the number of calories burned. For every 240-hour workout, there is 1 calorie burned, and for every 480-hour workout, there are 2 calories burned.
Workout hours are 1 2 3
Calories Burned are 240 480 720
Option B is correct.
Given that,
The table is a proportional relationship.
Workout hours are 1 2 3
Calories Burned are 240 480 720
We can conclude from the form of the question that the quantity of calories we burn is determined by the length of time we spend practicing, making the activity (hours) the independent variable and the calories burned the dependent one. The responses C and D are automatically canceled out by this.
The table's information is all we can then depend on. The assigned hours were 1, 2, and 3, and the corresponding calories were 240, 480, and 720. Just make sure that's reflected in the response.
Therefore, Option B is correct.
The number of hours spent exercising determines the quantity of calories expended. 240 calories are expended during a one-hour workout, and 480 calories are burned after a two-hour workout.
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Rearrange the equation
a = 1/4 b
to make b the subject
Answer:
b = 4a
Step-by-step explanation:
a = [tex]\frac{1}{4}[/tex] b ( multiply both sides by 4 to clear the fraction )
4a = b
one city reported that the number of fires caused by arson had dropped 17% in one year to 185. find the number of fires caused by arson in the previous year. (round ur answer to the nearest whole number as needed)
Let x represent the number of fires caused by arson in the previous year.
We were told that it dropped by 17%
Percentage is expressed in terms of 100.
Thus, the amount by which it dropped would be
17/100 * x = 0.17x
Due to this drop, the number of fires caused by arson had dropped to 185. Thus,
x - 0.17x = 185
0.83x = 185
x = 185/0.83
x = 222.892
Rouding to the nearest whole number, the number of fires caused by arson in the previous year is 223
Brenda drove to her friend's house and back. On the trip there she drove 30 kmh and on the return trip she went 20 km/h. How long did the trip there take if the return trip took three hours?
Answer: 2 hours
Step-by-step explanation:
If the return trip took 3 hours and she went 20 km/hr she would be going 60 miles because you can use the formula [tex]v*t=d[/tex] to figure it out. Now you have to figure out how much time it took for her to drive 60 miles going 30 miles an hour. Use the formula [tex]\frac{d}{v} =t[/tex] and you will figure out that she is driving for 2 hours.
dilate the figure about the given point a scale factor of 2.
1) The first thing to dilate a figure, is to know the scale factor and if it's about the origin or not.
We have k=2, as our scale factor. So the image will be twice larger (scaled) than the pre-image.
2) Since it is not about the origin but about the point, We need to count from the center of dilation (that point).
2.1) Let's locate each point of the vertex, and call them by ABCD for that pre-image, and call E the point which is going to be the center of dilation.
Counting the distances from figure ABCD to point E
Pre-image
A (7,6) ------------------ > A' ( 5 units to the left , 5 down)
B (9,6) ---------------> B' (7 to the left, 5 down)
C (6,3) -----------------> C' (4 to the left, and 2 down)
D (10,3) --------------> D' ( 8 to the left, and 2 down)
The new figure will be at
A ' ( 10 units to the left, 10 units down
B' (14 to the left, 4 down)
C' ( 8 to the left, and 4 down)
D' ( 16 to the left, and 4 down)
L
A' =(-3,-4) B' (-5,2) C' (-2, -1) D' (-6,-1)
Figure 12.14 shows the floor plan for a long one story house. Calculate the area of the floor of the house, explain your reasoning
We have the following:
Now we are going to calculate the area of each square and then we add each block and thus we calculate the total area:
[tex]\begin{gathered} S_1=40\cdot40=1600 \\ S_2=16\cdot24=384 \\ S_3=16\cdot40=640 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} S_T=S_1+S_2+S_3=1600+384+640 \\ S_T=2624 \end{gathered}[/tex]The answer is 2624 square foot
Change the equation to standard form the state from x and y intercepts
We will have the following:
[tex]y=\frac{3}{2}x-\frac{1}{2}\Rightarrow(2)y=(\frac{3}{2}x-\frac{1}{2})(2)[/tex][tex]\Rightarrow2y=3x-1\Rightarrow3x-2y=1[/tex]So, the equation in standard form is:
[tex]3x-2y=1[/tex]And now, we determine the x & y intercepts:
x-intercept:
[tex]3x-2(0)=1\Rightarrow3x=1[/tex][tex]\Rightarrow x=\frac{1}{3}[/tex]So, the x-intercept is located at:
[tex](\frac{1}{3},0)[/tex]y-intercept:
[tex]3(0)+2y=1\Rightarrow2y=1[/tex][tex]\Rightarrow y=\frac{1}{2}[/tex]So, the y-intercept is located at:
[tex](0,\frac{1}{2})[/tex]PLEASE HELP ME I DONT UNDERSTAND AND I WAS SICK TODAY ITS DUE IN 1 HOUR PLEASE HELP
Answer:
x = 3
Step-by-step explanation:
(19x + 3) + (24x - 2) = 130 (exterior angle: angle CBG = angle c + angle d)
43x + 1 = 130
43x = 129
x = 3
Find the sum of the geometric series given a₁ = 2, r = -3, and n = 8.A. 1/2B.-3107OC.-3280D. -3780Reset Selection
The formula to calculate the sum of a geometric sequence is given to be:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]The question has the following parameters:
[tex]\begin{gathered} a_1=2 \\ r=-3 \\ n=8 \end{gathered}[/tex]Therefore, the sum will be:
[tex]\begin{gathered} S_8=\frac{2(1-(-3)^8)}{1-(-3)} \\ S_8=-3280 \end{gathered}[/tex]The correct option is OPTION C.
Nicole runs 7 miles in 60 minutes. At the same rate, how many miles would she run in 24 minutes?
In 24 minutes, Nicole runs the distance of 2.8 miles.
What is miles?
In mathematics, The term 'miles' is a unit of distance. It is used for the calculation of displacement measurement. It is defined as the starting point and endpoints on the graph.
According to the question, Nicole runs 7 miles in 60 minutes. Therefore, the parameters are:
Distance = 7 miles; Time = 60 minutes
Therefore, Speed = Distance/Time = 7/60 miles/minutes
Now, the time is 24 minutes and speed is 7/60 miles/minutes.
The required distance can be calculated as:
Distance = (Speed)(Time) = (7x24/60) = 28/10 = 2.8 miles
Hence, In 24 minutes, Nicole runs 2.8 miles.
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Ryan is going to make a sculpture from a rectangular block of clay. Thevolume of the block is (x + 8) (x - 3)(2x- 5).
Given:
The volume of the block is (x + 8) (x - 3)(2x- 5).
Required:
Select the correct option.
Explanation:
We know volume
[tex]=\text{ Base area}\times\text{ Height}[/tex]So, option D satidfying this condition.
Answer:
Option D is correct.
A group of six friends ordered a pizza I wanted to arrive. There were 12 pieces of equal size 4 hours later 3/8 of pizza still remained and was going to be split evenly amongst six friends so they could finish the pizza.
Using the mathematical operations, the quantity that each of the six friends got from the 3/8 of pizza remaining after 4 hours is 0.75.
What are the mathematical operations?The mathematical operations that are used to perform basic number operations are division, multiplication, subtraction, and addition.
These basic mathematical operations can be used to compute the quantity of pizza that each friend got from the remainder.
For instance, after determining that 4.5 of the pizza is remaining, this value can be shared by 6 to get 3/4 or 0.75 for each friend.
The number of friends in the group = 6
The number of equal pieces of pizza = 12
The quantity of pizza remaining after 4 hours = 3/8 or 4.5 (12 x 3/8)
The quantity received by each friend after the equal splitting of the remainder = 0.75 (4.5/6) or 3/4 (3/8 ÷ 6).
Thus, basic mathematical operations show that each friend will get 3/4 more pizza.
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Question Completion:How much did each of the six friends get from the 3/8 remaining pizza?
What is an equation of the line that passes through the point (-3,-5) and isparallel to the line 25 + 3y = 15?
We have to find the equation of a line that pass through the point (-3,5) and is parallel to the line 25x+3y=15.
All parallel lines to 25x+3y=15 can be written as:
[tex]25x+3y=C[/tex]where C is a constant that allows us to change the position of the line to fit any point.
As the point (-3,5) belongs to the line we are looking for, it has to satisfy the equation. So we can write:
[tex]\begin{gathered} 25x+3y=C \\ 25(-3)+3(5)=C \\ -75+15=C \\ C=-60 \end{gathered}[/tex]With the value of C defined, we can write the equation of the line as:
[tex]25x+3y=-60[/tex]Answer: 25x+3y=-60
5x^2+9x+4=0 can someone help me please
Answer:
x = -4/5 or x = -1
hope this helps
