A binomial square have the following form:
[tex](x+a)^2=x^2+2ax+a^2[/tex]So, from the coefficient of the second term, we can get the value a and with the value a we can calculate a² for the value of the third term, that is, the value we need to add to make it a perfect square.
We have the expression:
[tex]x^2+14x[/tex]By comparing the second terms, we see that:
[tex]\begin{gathered} 14=2a \\ 2a=14 \\ a=\frac{14}{2} \\ a=7 \end{gathered}[/tex]Since we have a, we can calculate a²:
[tex]a^2=7^2=49[/tex]So, this means the number we need to add is 49 and, since a is 7, the trinomial can be rewritten as:
[tex]x^2+14x+49=(x+7)^2[/tex]So, add 49 and the square binomial is:
[tex](x+7)^2[/tex]Hi can you give me the basic answer for 12 please
Given the equation of the line:
[tex]y=-5x-\frac{1}{2}[/tex]• You can identify that it is written in Slope-Intercept Form:
[tex]y=mx+b[/tex]Where "m" is the slope of the line, and "b" is the y-intercept.
Notice that:
[tex]\begin{gathered} m_1=-5 \\ b_1=-\frac{1}{2} \end{gathered}[/tex]• By definition, parallel lines have the same slope, but their y-intercepts are different.
Therefore, you can determine that the slope of the line parallel to the first line is:
[tex]m_2=-5[/tex]You know that this line passes through this point:
[tex](-4,2)[/tex]Therefore, substituting the slope and the coordinates of that point into this equation:
[tex]y=m_2x+b_2[/tex]And solving for the y-intercept, you get:
[tex]\begin{gathered} 2=(-5)(-4)+b_2 \\ \\ 2-20=b_2 \\ \\ b_2=-18\frac{}{} \end{gathered}[/tex]Then, the equation of the line parallel to the first line is:
[tex]y=-5x-18[/tex]• By definition, the slopes of perpendicular lines are opposite reciprocal, therefore, the slope of this line is:
[tex]m_3=\frac{1}{5}[/tex]Using the same procedure used before to find the y-intercept, you get:
[tex]\begin{gathered} 2=(\frac{1}{5})(-4)+b_3 \\ \\ 2+\frac{2}{5}=b_3 \\ \\ b_3=\frac{14}{5} \end{gathered}[/tex]Therefore, its equation is:
[tex]y=\frac{1}{5}x+\frac{14}{5}[/tex]Hence, the answer is:
- Equation for the parallel line:
[tex]y=-5x-18[/tex]- Equation for the perpendicular line:
[tex]y=\frac{1}{5}x+\frac{14}{5}[/tex]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
Solve each system of the equation by elimination method. 2x+3y=258x+5y=37
Answer:
x = -1 and y = 9
Explanation:
Given the below system of equations;
[tex]\begin{gathered} 2x+3y=25 \\ 8x+5y=37 \end{gathered}[/tex]To solve by using the elimination method, the 1st step is to multiply the 1st equation by 8 and the 2nd equation by 2, we'll have;
[tex]\begin{gathered} 16x+24y=200 \\ 16x+10y=74 \end{gathered}[/tex]The 2nd will be to subtract the 4th equation from the 3rd equation and solve for y;
[tex]\begin{gathered} 0+14y=126 \\ y=\frac{126}{14} \\ y=9 \end{gathered}[/tex]The 3rd step is to substitute y = 9 into the 1st equation and solve for x;
[tex]\begin{gathered} 2x+3(9)=25 \\ 2x+27=25 \\ 2x=-2 \\ x=\frac{-2}{2}=-1 \end{gathered}[/tex]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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y=-2/3 3 what is the slope of the equation entered as a fraction
The equation:
[tex]y=-\frac{2}{3}x-1[/tex]has the form:
y = mx + b
with
[tex]\begin{gathered} m=-\frac{2}{3} \\ b=-1 \end{gathered}[/tex]m is known as the slope of the line, then the slope is -2/3
La suma de tres numeros consecutivos impares es 63
Answer:
19, 21, 23
Step-by-step explanation:
A health inspector from the Food and Drug Administration was tasked with oversight of a pharmaceutical company in their development of a new medication. He used a 99% confidence interval to estimate the true mean amount of propionic acid in each 800 mg pill. Propionic acid is an important ingredient in several medications, including ibuprofen. His confidence interval was (3.2 mg, 6.5 mg). Which one of the following is the best interpretation of this confidence interval?
The best interpretation of the confidence interval is given by:
We are 99% sure that the true mean amount of propionic acid in all 800 mg pills of the new medication is between 3.2 mg and 6.5 mg.
What is the interpretation of a x% confidence interval?The x% confidence interval means that it is x% likely that the population parameter(mean/proportion/standard deviation) is between the bounds a and b of the confidence interval
The bounds of the confidence interval are given by the estimate plus/minus the margin of error.
In this problem, the bounds of the problem are already given, as follows:
3.2 mg.6.5 mg.The variable of interest is given by:
Mean amount of propionic acid in all 800 mg pills of the new medication
The level of confidence is of 99%, hence, considering the variable and the bounds, the interpretation of the interval is:
We are 99% sure that the true mean amount of propionic acid in all 800 mg pills of the new medication is between 3.2 mg and 6.5 mg.
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14x^2y^4-7x^5y^3 Factor with GCF method
[tex]14x^2y^4-7x^5y^3[/tex]
The GCF is
[tex]7x^2y^3[/tex]Factoring out using the GCF, we have
[tex]\begin{gathered} 7x^2y^3(\frac{14x^2y^4}{7x^2y^3}-\frac{7x^5y^3}{7x^2y^3}) \\ \\ 7x^2y^3(2y-x^3) \end{gathered}[/tex]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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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
What is the slope intercept equation for this line?
the slope for this line is 2
what is slope?The slope or gradient of a line is a number that describe both the direction and the steepness of the line. the steepness of a line is defined as the slope (or gradient). The slope is the ratio of vertical distance to the horizontal distance between any two points on a line. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).The greater the value of the slope, the "steeper" the slope is, and vice versa. So the smallest value of the absolute value of these slopes is 1/2.
So, A.T.Q:-
The formula of slopet intercept is Y2 -Y1 /X2-X1
From the question:
slope = -1-1/0-1
slope = 2
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The circumference of a circle is 25.2 cm. Find the area of the circle correct to 1 decimal place. Area = cm²
The area of the circle is 12.56 [tex]cm^{2}[/tex].
What is area of circle?
The space occupied by a circle in a two-dimensional plane is defined as its area. A circle is a critical geometric figure found in many fields, including construction, engineering, and many others. Geometry problems involving circles necessitate the ability to calculate the area of a circle. The area of a circle is calculated as A = πr2, where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, in2, and so on.
Here the circumference of the circle is,
=> C = 25.2 cm
=> 2πr = 25.2
=> 2×3.14×r=25.2
=> r = [tex]\frac{25.2}{2*3.14}[/tex]
=> r= 4cm
Now area of the circle A= π[tex]r^2[/tex] [tex]unit^{2}[/tex]
=> A= 3.14*4 = 12.56 [tex]cm^{2}[/tex]
Hence area of the circle is 12.56 [tex]cm^{2}[/tex].
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If a woman making $33,000 a year receives a cost-ofliving increase of 2.8%, what will her new salary be?
Answer:
$33,924
Step-by-step explanation:
The amou8nt of the raise is 2.8% of $33,000.
2.8% of $33,000 =
= 2.8% × $33,000
= 0.028 × $33,000
= $924
The amount of the raise is $924.
The new salary is the amount of the raise added to the original salary.
$33,000 + $924 =
= $33,924
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
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.
Line segment LN has endpoints L-2, -3) and N(3, 7).Which of the following determine the coordinates of point M located at the midpoint of LN?M= - (³2/2/², 2/³) 3-2 7-3M= =(3+2, 7+³)M = (-2-³, -3-7)M = (¹+³, 32)
The line segment LN has coordinates as follows;
[tex]\begin{gathered} L=(-2,-3) \\ N=(3,7) \end{gathered}[/tex]The midpoint of a line is derived with the following coordinates;
[tex]M=\frac{(x_1+x_2)}{2},\frac{y_1+y_2}{2}[/tex]The coordinates are thus;
[tex]\begin{gathered} (x_1,y_1)=(-2,-3) \\ (x_2,y_2)=(3,7) \end{gathered}[/tex]The midpoint, which is M, now becomes;
[tex]\begin{gathered} M=\frac{-2+3}{2},\frac{-3+7}{2} \\ \text{Also, re-written as;} \\ M=\frac{3-2}{2},\frac{7-3}{2} \end{gathered}[/tex]ANSWER:
The first option is the correct answer.
Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
The product of 2 and the difference of a number and 5.
Answer:
Submit Answer
attempt 1 out of 2
Answer:
2(x-5).
Step-by-step explanation:
The difference of a number and 5 is x-5.
The product means to multiply, so the answer is 2(x-5).
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.
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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John has a $200 gift card for laser tag. Every time he goes to the laser tag, $25.00
is removed from the gift card. Which of the following functions have the same end behavior as the function that models the money left on John’s gift card?
John can use the gift card for 9 times till his balance becomes zero dollars from $200 using the concept of arithmetic progression.
As per the question statement, John has a $200 gift card for laser tag. So every time he goes to the laser tag, $25.00 is removed from the gift card.
We are supposed to find out the number of times John can use the card till his balance becomes zero dollars from $200 and we will use the concept of arithmetic progression.
We know the formula, a(n) = a + (n-1)*d
where "a" is the first value, "a(n)" is the total value, "d" is the common difference and "n" is the number of times
The AP : 200, 175, 150,......0
Here a = 200, a(n) is 0, n is supposed to be find out and d = 25
Hence using the AP formula,
0 = 200 + (n-1) * 25
n-1 = 8
n = 9
Hence, John can use the gift card for 9 times till his balance becomes zero dollars from $200 using the concept of arithmetic progression.
Arithmetic Progression: A string of figures that fluctuate in value by the same amount throughout time.
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Please reference attached image for the problem that requires solving. Thank you so much for taking the time to help.
Explanation:
The number of times the 6-sided number cube will be rolled will is
[tex]750[/tex]Let the numbers greater than 4 be represented below as
[tex]E_1[/tex][tex]\begin{gathered} E_1=\lbrace5,6\rbrace \\ n(E_1)=2 \end{gathered}[/tex]The number of sample space will be
[tex]n(S)=6[/tex]The probability of rolling a number greater than 4 will be calculated below as
[tex]\begin{gathered} Pr(E_1)=\frac{n(E_1)}{n(S)} \\ Pr(E_1)=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Hence,
To calculate the number of times a number greater than 4 will be rolled will be calculated below as
[tex]\begin{gathered} =Pr(E_1)\times750 \\ =\frac{1}{3}\times750 \\ =250times \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow250\text{ }times[/tex]Determine the CPI for a suit that costs $235 now and cost $90 in 1967.a. 261b. 203c. 219d. 275
Answer:
[tex]A\text{ :261}[/tex]
Explanation:
Here, we want to calculate the CPI for the cost of the suit
To do this,we use the weighted average method
What we will do here is to divide the past price by the current price and convert the value to a percentage
Mathematically, we have this as:
[tex]\frac{\text{Present cost}}{\text{Cost in 1967}}\text{ }\times\text{ 100 \%}[/tex]Substituting the values, we have:
[tex]\frac{235}{90}\text{ }\times\text{ 100 = 261}[/tex]A boy sold $88.50 worth of stationery. If he received a 33 1/3% commission, what was the amount of his commission?
A) $29.50
B) $40
C) $50
D) $62.50
Work Shown:
33 & 1/3% = 0.3333... the '3's go on forever
0.3333*88.50 = 29.49705 which rounds to 29.50
Answer: A. $29.50 is the correct answer.
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 litersif we subtract 2/4 from 3/4, what isthe difference?
Answer:
-[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Ans:
In Fractional/Exact Form:
1/4
In Decimal Form:
Ans=0.25
Steps to Simplify the expression.
Step 1:Find the least common denominator
Step 2:Multiply the least common denominator
Step 3:Simplify the equation
Step 4:Solve
(3/4)-(2/4)= (3-2)/4
Exact Form:
1/4
Decimal Form:
Ans=0.25
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A rectangle is placed around a semicircle as shown below. The width of the rectangle is 6 mm. Find the area of the shaded region.Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Q) In the picture we have a semi-circle inscribed in a rectangle. We see that the diameter is equal to the width of the rectangle (the horizontal side) of the rectangle (w), so we have:
[tex]d=w=6\operatorname{mm}[/tex]From the fact that the diameter is always two times the radius for every circle, we have:
[tex]r=\frac{d}{2}=\frac{6}{2}\operatorname{mm}=3\operatorname{mm}[/tex]Now, we also see from the picture:
[tex]h=r=3\operatorname{mm}[/tex]The question asks us about the area of the shaded region.
A) The shaded region can be computed in the following way:
1) First, we compute the area of the rectangle (Ar).
[tex]A_r=w\cdot h=6\operatorname{mm}\cdot3\operatorname{mm}=18mm^2[/tex]2) Secondly, we compute the area of the semi-circle (Asc), which is half of the area of the entire circle.
[tex]A_{sc}=\frac{1}{2}\cdot A_c=\frac{1}{2}\cdot\pi\cdot r^2=\frac{1}{2}\cdot3.14\cdot(3\operatorname{mm})^2=14.13mm^2[/tex]3) Finally, we compute the area of the shaded region taking the difference between the area of the rectangle and the area of the semi-circle.
[tex]A_s=A_r-A_{sc}=18mm^2-14.13mm^2=3.87mm^2[/tex]Is a triangle whose sides measure 1.25 in ,0.75 in and 1 in, a right triangle?
In a right triangle, the largest side is called the hypotenuse. Furthermore, from the Pythagorean Theorem, the following relation is satisfied:
[tex]c^2=a^2+b^2[/tex]To find if those measures correspond to a right triangle, verify if it satisfies the Pythagorean Theorem:
[tex]\begin{gathered} 1.25^2=1.5625 \\ 1^2+0.75^2=1.5625 \end{gathered}[/tex]Then:
[tex]1.25^2=1^2+0.75^2[/tex]Therefore, the sides of lengths 1.25 in, 1 in and 0.75 in are indeed the sides of a right triangle.
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]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.
