Answer:
Step-by-step explanation:
I think you're supposed to use the quadratic formula Samanth
Know it?
-b ± [tex]\sqrt{b^{2}-4ac }[/tex] / (2a)
so for starters, let me mention, that if 4ac happens to be greater than [tex]b^{2}[/tex] contrary to what all math teacher say, about not being able to taking the square of a negative number, you can, but you just end up with a complex number in the form of A + Bi , where 'i' represents [tex]\sqrt{-1}[/tex] anyway,
for the given equation
A = 1
B = -17
C = 70
{ -(-17) ± [tex]\sqrt{(-17)^{2}-4*1*70 }[/tex] } / (2*1)
{ 17 ± [tex]\sqrt{289-280}[/tex] } / 2
wow, now i'm glad I mentioned about the 4ac being greater :P
it was close, huh
{ 17 ± [tex]\sqrt{9}[/tex] } / 2
{ 17 ± 3 } /2
let's take each case now, the plus and then the minus
{ 17+3 } /2
20 /2
10
now the minus
{17 - 3 } / 2
14 /2
7
now that i've done all that work, I think we could have just done this by inspection :P
(e-7)(e-10)
anyway, hope that helps, ask if you have any questions :)
Hi, im in college and I need help with this here please. Thanks
The solution of given equations are -4 and 1. The solution of an equation is plotted on the graph.
The given equations are M(d)=2x²+8x-4 and R(d)=2x+4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given, the revenue of each item is same.
That is, M(d)=R(d)
⇒ 2x²+8x-4=2x+4
⇒ 2x²+8x-4-2x-4=0
⇒ 2x²+6x-8=0
⇒ 2x²+8x-2x-8=0
⇒ 2x(x+4)-2(x+4)=0
⇒ (x+4)(2x-2)=0
⇒ x=-4 and x=1
Therefore, the solution of given equations are -4 and 1. The solution of an equation is plotted on the graph.
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Write a variation equation for the following situation. Use k as the constant of variation.R varies inversely as the square of h.The variation equation is ______
Given
R varies inversely as the square of h
Find
Equation for the given statement
Explanation
[tex]\begin{gathered} R\propto\frac{1}{h^2} \\ \\ R=\frac{k}{h^2} \end{gathered}[/tex]Final Answer
The equation for given statement is
[tex]R=\frac{k}{h^2}[/tex]Evaluate the expression, writing the result as a simplified complex number.My answer 3iI know is wrong but I don’t know why.
The first thing we can do is solve the i cubed:
[tex]undefined[/tex]Which expression is equivalent to 20 — 3(x + 2)?A 3X+ 14B —3x + 14 C -9x + 21 D 17x— 34
We have to simplify the expression:
[tex]20-3(x+2)[/tex]and see which expression is equivalent.
We can do it like this:
[tex]\begin{gathered} 20-3(x+2) \\ 20-3\cdot x-3\cdot2 \\ 20-3x-6 \\ 20-6-3x \\ 14-3x \\ -3x+14 \end{gathered}[/tex]This expression is equivalent to -3x+14.
Answer: -3x+14 [Option B]
Answer:
first option
Step-by-step explanation:
[tex]\frac{\frac{-2}{x}+\frac{5}{y} }{\frac{3}{y}-\frac{2}{x} }[/tex] ← combine fractions on numerator and denominator
= [tex]\frac{\frac{-2y+5x}{xy} }{\frac{3x-2y}{xy} }[/tex]
leave numerator, change division to multiplication and turn denominator 'upside down'
= [tex]\frac{-2y+5x}{xy}[/tex] × [tex]\frac{xy}{3x-2y}[/tex] ← cancel xy on numerator/ denominator
= [tex]\frac{-2y+5x}{1}[/tex] × [tex]\frac{1}{3x-2y}[/tex]
= [tex]\frac{-2y+5x}{3x-2y}[/tex]
At a cost of s stickers for c cents, how many stickers can be bought for d dollars
First, we need to express the amount of dollars d as cents, we can do this as we know that one dollar equals 100 cents, then d in cents would be:
[tex]d(\text{cents)}=d\times100cents[/tex]And from the statement of the question, we know that s stickers cost c cents, we can express that cost per sticker like this:
[tex]\frac{s\text{ stickers}}{c\text{ cents}}[/tex]And if we want to find the amount of stickers that we can buy, we just have to multiply d in cents by the cost per sticker, like this:
[tex]\text{number of sticker we can buy}=\frac{s\times d\times100}{c}[/tex]Last year, Lisa opened an investment account with $8400. At the end of the year, the amount in the account had decreased by 24.5%. How much is this decrease in dollars? How much money was in her account at the end of last year?
Answer:
The dec
Explanation:
Given that Lisa opened an investment account with $8400, at the end of the year, the amount in the account had decreased by 24.5%. We want to know how much the decrease is, and how much was in her account at the end of last year.
All we are required to find is what value is 24.5% of $8400
24.5% is the same as:
[tex]\frac{24.5}{100}[/tex]24.5% of $8400 is now:
[tex]\begin{gathered} \frac{24.5}{100}\times8400 \\ \\ =24.5\times84 \\ =2058 \end{gathered}[/tex]Therefore 24.5% of $8400 is $2058
This amount is the decrease.
Finally, at the end of last year, the amount in her account is:
$8400 - $2058 = $6342
Answer: If you do 8400 - 24.5% you get 6342. Then if you do 8400 - 6342 you get 2058. So her account decreased by $2,058 and she had $6342 left in her account at the end of the year.
Maybeline is the teacher's assistant today and is correcting homework examples. Help her by selecting correct or incorrect after evaluating each problem.
Here, we need to remember the signs rules
[tex]\begin{gathered} (+)(+\text{ )=+} \\ (+\text{ )(- )=-} \\ (-\text{ )(+ )=-} \\ (-\text{ )(- )=+} \end{gathered}[/tex]Then
[tex](-4)+(-8)=-4-8=-12[/tex]incorrect.
[tex](-9)-(-8)=-9+8=-1[/tex]correct
[tex](+7)\times(-8)=-56[/tex]correct
[tex](-5)(-2.5)=12.5[/tex]correct
[tex]+\frac{1}{2}\times(+6)=3[/tex]incorrect
Find the value of the expression. 07-2 . (131 alw The value is I I
A section of a quilt is shaped like a parallelogram.What is the minimum amount of fabric that is needed to cover this section completely? A 13 Square InchesB 17 Square InchesC 21 Square InchesD 26 Square Inches
The area of a parallelogram is computed as follows:
A = b*h
where b is the base and h is the height.
From the picture, the base is: 2 + 4.5 = 6.5 inches, and the height is 4 inches. Then its area is:
A = 6.5*4 = 26 square inches
Determine the length of the longest side of the triangle ABC. Showyour work and round answers to the nearest tenth. *15 in.CB78°10 in.A
We would make use of the cosine rule,
[tex]\begin{gathered} C^2=A^2+B^2-2AB\cos C \\ C^2=15^2+10^2-2\times10\times15\times\cos 78 \end{gathered}[/tex][tex]\begin{gathered} C^2=325-62.374\text{ =262.626} \\ C=\text{ 16.206 }\approx\text{ 16.2 in} \end{gathered}[/tex]One more question please ?
Find the equation of the line that is parallel to Y = x -3 and contains the point (3,-2)
Given:
The equation of the line is
[tex]y=x-3[/tex]Required:
Find the equation of the line that is parallel to the given line and contains the point (3,-2).
Explanation:
The given equation of the line is
[tex]y=x-3[/tex]Compare the equation with the equation
[tex]y=mx+c[/tex]The slope of the line m = 1.
Since the slope of the parallel lines is equal.
The equation of the line that is parallel to the given line is:
[tex]y=x+b[/tex]This line contains the point (3,-2).
[tex]\begin{gathered} -2=3+b \\ b=-5 \end{gathered}[/tex]Thus the equation of the parallel line is:
[tex]y=x-5[/tex]Final Answer:
[tex][/tex]Determine the slope (m) and y-intercept (b) of the line:y = 2x - 3A) m = 3, b = 2B) m = 2, b = -3C) m = -3, b = 2D) m = 2, b = 3
slope of line(m) = 2 and intercept on y axis is -2 that is 2 unit in negative y axis.
Equation of line in slope intercept form:
Slope:
Slope is known as tangent of an angle made by positive X-axis.
We know equation of line in slope and intercept form is,
y = mx + b
where,
m is slope of line
b is intercept on y axis
hence for the given equation,
y =2x - 3
slope (m) will be = 2
intercept on y axis (b) = -3
thus,
option (B) will be correct.
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Find each value or measure. Assume that all segments that appear to be tangentare tangent. Find JLK
Answer
Angle JLK = 31°
Explanation
To answer this, we will use the tangent-chord theorem.
So, the intercepted arc JNL has an angle 298°
Then, we can solve for the tangent chord angle next to it, Angle JLM first by saying
Angle JLM = (Intercepted arc JNL)/2
Angle JLM = (298°/2)
Angle JLM = 149°
Then, we can see that Angle JLM and Angle JLK lie on the same straight line, KLM.
Sum of angles on a straight line is 180°.
Angle JLK + Angle JLM = 180°
Angle JLK + 149° = 180°
Angle JLK = 180° - 149°
Angle JLK = 31°
Hope this Helps!!!
2. At the gas station, three small drinks and two large drinks contain 108 ounces ofcola. A small drink contains a third as much cola as a large drink. How much coladoes each size drink contain?
Let x = small drinks
Let y = large drinks
3 small drinks and 2 large drinks contain 108 ounces of cola, this is:
3x + 2y = 108
A small drink contains a third as much cola as a large drink, this is:
x = 1/3y
Then, we solve the system of equations:
[tex]\begin{gathered} 3x+2y=108 \\ x=\frac{1}{3}y \end{gathered}[/tex]First, substitute x in equation 1:
[tex]3(\frac{1}{3}y)+2y=108[/tex]And solve for y:
[tex]\begin{gathered} y+2y=108 \\ 3y=108 \\ \frac{3y}{3}=\frac{108}{3} \\ y=36 \end{gathered}[/tex]Next, substitute y = 36 in x:
[tex]x=\frac{1}{3}y=\frac{1}{3}(36)=12[/tex]Answer:
Small drinks: 12 ounces of cola
Large drinks: 36 ounces of cola
For the given functions f and g, find theindicated value.F(x) = x2+ 3x, g(x) =× + 2(f . g) (4)
Given:
[tex]\begin{gathered} f(x)=\text{ x}^2\text{ + 3x} \\ g(x)\text{ = x + 2} \end{gathered}[/tex]Required:
[tex](f\text{ .g\rparen\lparen4\rparen}[/tex]Recall that:
[tex](f.g)(x)\text{ = f\lparen x\rparen. g\lparen x\rparen}[/tex]Substituting we have:
[tex]\begin{gathered} (f.g)(x)=\text{ \lparen x}^2\text{ + 3x\rparen\lparen x+2\rparen} \\ (f.g)(4)\text{ = \lparen4}^2\text{ + 3\lparen4\rparen\rparen\lparen4 + 2\rparen} \\ =\text{ 28 }\times6\text{ } \\ =\text{ 168} \end{gathered}[/tex]Answer: 168
Solve f(x)= x^4 - 3x^2 + 2 using the radical root theorem and synthetic division.
The Census Bureau reports that 82% of Americans over the age of 25 are high school graduates. A survey of randomly selected residents of certain county included 1400 who were over the age of 25, and 1120 of them were high school graduates.(a) Find the mean and standard deviation for the number of high school graduates in groups of 1400 Americans over the age of 25. Mean = Standard deviation =(b) Is that county result of 1120 unusually high, or low, or neither?
Is that county result of 1120 unusually high, low, or neither?
1148 - 2(14.37) = 1119.26
It is neither as it is within 2 standard deviation from the mean 1148.
Given this super-sized board (16x16), what integer lengths are possible for slanted segments? Use the line tool to sketch them (using a different color for each one). Label each length. Then describe how you found them.
A way to find integer line segments is using Pythagorean triples, that is, positive integers that are consistent with the Pythagorean theorem, for example, (3,4,5) because we have
[tex]3^{2^{}}+4^2=5^{2^{}}[/tex]therefore, they can be put in a triangle like this
Therefore, the slanted segment would have a length of 5. That can be done with other Pythagorian triples like (5,12,13) or (8,15,17).
I don’t really know if the lines are parallel an explanation would be helpful thanks
ANSWER
Line K is not parallel to line L.
EXPLANATION
The two angles given are alternate exterior angles. When a line crosses two parallel lines, the alternate exterior angles always sum up to 180 degrees.
So, to confirm if line L is parallel to line K, we check to see if the two given angles sum up to 180 degrees:
[tex]\begin{gathered} 122+68 \\ \Rightarrow190\degree \end{gathered}[/tex]Since they don't sum up to 180 degrees, Line K is not parallel to line L.
A project on Kickstarter for an iPad stylus raised 1,130% of their goal, raising a total of $322,507 from 7,457 supporters. What was their original goal?
Let:
x = Original goal
y = Final goal = $322507
a = Percentage raised = 1.130% = 0.0113
so:
[tex]\begin{gathered} y=x+ax \\ so\colon \\ y=x(1+a) \\ _{\text{ }}solve_{\text{ }}for_{\text{ }}x\colon \\ x=\frac{y}{1+a} \\ x=\frac{322507}{0.0113+1} \\ x=\frac{322507}{1.0113} \\ x=318903.3917 \\ x\approx318903.39 \end{gathered}[/tex]Answer:
The original goal was approximately $318903.39
20. A fast food restaurant estimates the cost of making hamburgers to be $2.05 per hamburger plus an additional cost of $2,000 for facility expenses. If $13,025 represents the total cost of making x hamburgers, which equation can be used to find the number of hamburgers produced?A. 13,025=2.05+2,000 xB. 13,025=2.05 x+2,000C. 13,025 x=2.05+2,000D. 13,025=2.05+2000 x
Answer:
(B)13,025=2.05x+2,000
Explanation:
The cost of making one hamburger = $2.05
The cost of making two hamburgers = $2.05 x 2
Therefore:
The cost of making x hamburgers = $2.05x
Since there is an additional cost of $2,000 for facility expenses.
The total cost will be:
[tex]2.05x+2000[/tex]If $13,025 represents the total cost of making x hamburgers, then:
[tex]13,025=2.05x+2000[/tex]This is the equation that can be used to find the number of hamburgers produced.
The correct choice is B.
Savannah invested $5,300 in an account paying an interest rate of 3 5/8 % compounded daily.
The amount that will be in Savannah's account after 3 years is $6042.
What is compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
To calculate the amount that will be in Savannah's account after 3 years, we use the formula below.
Fromula:
A = P(1+R/365)³⁶⁵ⁿ........... Equation 1Where:
A = Amount P = PrincipleR = Raten = time/yearsFrom the question,
Given:
P = %5300R = 35/8% = 4.375% = 0.04375n = 3 yearsSubstitute these values into equation 1
A = 5300(1+0.04375/365)³ˣ³⁶⁵A = 5300(1.00012)¹⁰⁹⁵A = 5300×1.14A = $6042Hence, there would be $6042 in the account.
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Compelete question: Savannah invested $5,300 in an account paying an interest rate of 3 5/8 % compounded daily, Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 3 years?
12. Given that a || b, what is the value of x? (The fiş290ToI41°5
Ok, so
Here we have the following figure:
We know that both segments are parallel and we want to find the value of x.
For this, remember that the value of x will be the sum of the other two angles:
[tex]\begin{gathered} x=29+41 \\ x=70 \end{gathered}[/tex]This is:
Given the following figure:
The value of x can be find using the following equation:
[tex]x=a+b[/tex]Convert the following: 253 mm to m. ANS. _______ m
253mm is read 253 Millimeter.
'Milli" is a sub-multiple that has a value of:
[tex]10^{-3}[/tex]Thus, 253mm is
[tex]253\times10^{-3}m[/tex]Expressing this in standard form, it becomes:
[tex]2.53\times10^{-1}m[/tex]To Decimal places, it is;
[tex]0.253[/tex]Find the missing length of the triangle. 14 cm 8.4 cm b The missing length is centimeters.
Answer:
11.2cm
Explanation:
To be able to determine the missing length, we have to apply the Pythagorean Theorem which states that, in a right-angled triangle, the square of the hypotenuse(the longest side) is equal to the sum of squares of the other two sides.
Let's go ahead and find b as follows;
[tex]\begin{gathered} 14^2=8.4^2+b^2 \\ 196=70.56+b^2 \\ 196-70.56=b^2 \\ 125.44=b^2 \\ b=\sqrt[]{125.44}=11.2\operatorname{cm} \end{gathered}[/tex]The total bill for repairing Mark’s TV was $211. The repair shop charges $25 an hour for labor plus $16 for parts. How many hours of labor did it take to repair Mark’s TV? Write it in an equation.25/16x = 21125 - 16x = 21125x – 16 =21125x + 16 = 211
Solution:
Given the total, T is $211;
One hour of labor is $25. So, x hours is $25x
Then, the cost of parts is $16.
Thus;
[tex]25x+16=211[/tex]A circular garden with a radius of 4 ft is planted in the center of a 10 ft square. The part of the square that is NOT the garden is covered with small white rocks. what is the area of the region covered with white rocks?
First, draw a diagram to visualize the situation:
The area of the region covered with small rocks can be found by subtracting the area of the circle from the area of the square.
The area A_s of a square with side L is given by:
[tex]A_s=L^2[/tex]And the area A_c of a circle with radius r is given by:
[tex]A_c=\pi r^2[/tex]Replace r=4ft and L=10ft into the equations to find the area of the circle and the square:
[tex]\begin{gathered} A_s=(10ft)^2=100ft^2 \\ A_c=\pi(4ft)^2=16\pi ft^2\approx50.265ft^2 \end{gathered}[/tex]Finally, subtract the area of the circle from the area of the square to find the area of the region covered with rocks:
[tex]A=A_s-A_c=100ft^2-16\pi ft^2\approx49.7ft^2[/tex]Therefore, the area of the region covered with rocks is exactly 100-16π square feet, which is approximately equal to 49.7 square feet.
14. Sarah draws the following array to solve 49 X 56. What values can be 50 6 determined by this array? 40 9 A 2,000; 240; 450; 54 T B. 2,000; 240; 45; 54 c. 200; 240; 450; 54 ; D. 200; 240; 45; 54
From the given figure we have 4 different tills
First till has dimensions 50 x 40, then
First till = 50 x 40 = 2000
Second, till has dimensions 6 x 40, then
Second till = 6 x 40 = 240
Third, till has dimensions 9 x 50, then
Third till = 9 x 50 = 450
Fourth till has dimensions 6 x 9, then
Fourth ti;; = 6 x 9 = 54
Then the values that can be determined by the array are
2000, 240, 450, 54
The answer is A
Based on the graph, what are the solutions of theequationx^3 - 6x^2 + 9x = 0?x = 3x= -3,0 x = 0,3 x = -3, 0,3
SOLUTION
The image of the graph is giving below
Based on the graph above, the solutions of the equation is at the point where the curve touches the x-axis
Hence the solution to the equation
[tex]x^3-6x^2+9x=0[/tex]is
[tex]undefined[/tex]Therefore the third option is correct