We can use the quadratic formula to solve this question. The quadratic formula is given below.
[tex]\begin{gathered} ax^2+bx+c=0 \\ \Rightarrow x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} a=2,b=-2,c=-1 \\ \Rightarrow x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\cdot2\cdot-1}}{2\cdot2}=\frac{2\pm\sqrt[]{4+8}}{4}=\frac{2\pm\sqrt[]{12}}{4}=\frac{2\pm2\sqrt[]{3}}{4} \\ \Rightarrow x=\frac{1}{2}\pm\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Then, the solutions are
[tex]x_1=\frac{1}{2}+\frac{\sqrt[]{3}}{2},x_2=\frac{1}{2}-\frac{\sqrt[]{3}}{2}[/tex]The solutions are 1/2+sqrt(3)/2 and 1/2-sqrt(3)/2
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Answer:
5
Step-by-step explanation:
((12*3)-(3*1/3))/((4*3-5))=
((36)-(1))/((12-5))=
(35)/(7)=5
Answer: it is going to be 35/7 = 5
Find the radian measure of θ if θ is a central angle in a circle of radius r=14in and θ cuts off an arc length s=7π in
The formula for determining the length of an arc is experessed as
arc length = θ x r
where
θ is the central angle
r is the radius of the circle
From the information given,
arc length = 7π in
r = 14 in
By substituting these values into the formula,
7π in = θ x 14 in
We would divide both sides of the equation by 14 in. We have
7π in/14 in = θ x 14 in/14 in
θ = π/2
Points A and C are two opposite
vertices of the ABCD square. Find the
area of this square.
A(3,2), C(7,2)
The area of the square is 8 square units.
According to the question,
We have the following information:
Points A and C are two opposite vertices of the ABCD square.
The coordinates of these points are A(3,2), C(7,2).
Now, we will use the distance formula to find AC:
d = [tex]\sqrt{(y2-y1)^{2}+ (x2-x1)^{2} }[/tex]
d = [tex]\sqrt{(2-2)^{2}+ (7-3)^{2} }[/tex]
d = [tex]\sqrt{4^{2} }[/tex]
d = 4 units
Now, when A and C are opposite vertices then AC is a diagonal.
Side of the square = diagonal/[tex]\sqrt{2}[/tex]
Side = 4/√2 units or 2√2 units
Formula to find the area of square:
Side*side
2√2*2√2
4*2
8 square units
Hence, the area of the square is 8 square units.
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Find g(x), where g(x) is the translation 5 units left of f(x) =3(x+5)^2 -7
The rule for the translated function is:
g(x) = 3*(x + 10)^2 - 7
How to find the rule for g(x)?
First, we know that for a function f(x) a horizontal translation of N units is written as:
g(x) = f(x + N)
If N > 0, the translation is to the left.
if N < 0, the translation is to the right.
A translation of 5 units to the left is written as:
g(x) = f(x + 5)
Replacing f(x) we get:
g(x) = 3*(x + 5 + 5)^2 - 7
g(x) = 3*(x + 10)^2 - 7
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Games at the carnival costs $7 each. The prizes awarded to the winners costs the owner $177.35. How many games must be played for the owner to make at least $75.
Use g as your variable. Round your inital answer to the nearest hundredth.
At least 36.05 games should be played for the owner to make at least $75.
Let the number of games played = g
According to question,
Cost of each game = $7
Cost of g games = 7g
Prizes awarded to the winner costs the owner = $177.35
To make at least $75, the equation is
7g - 177.35 ≥ 75
7g ≥ 75 + 177.35
7g ≥ 252.35
g ≥ 252.35 / 7
g ≥ 36.05
Hence, at least 36.05 games should be played.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 5.3 \text{ } (t > 0)[/tex]
In the equation (x + 4)^2 = 49, if x equals 3 what is another solution for x?
Please answer quickly.
The bull in Ms. Garcia's pasture weighs 0.95 tons. What is the weight of the bull in pounds?
Answer:
The bull weighs 1,900 pounds.
Step-by-step explanation:
2,000 pounds = 1 ton
0.95 x 2,000 = 1,900 pounds
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 6 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer: 1,900 pounds
Step-by-step explanation:
There are 2,000 pounds in a ton, so we will multiply 0.95 tons by 2,000 to figure out the weight of the bull in pounds.
0.95 * 2,000 = 1,900 pounds
The product of eight and a number b
Write a variable expression for the word phrase
How do I get the answers to thisQuestion 1 - 4
Answer:
Lines d and e are parallel and lines s and t are also parallel
1. Alternate Exterior Angles Theorem
2. Corresponding Angles Postulate
3. Alternate Angles Postulate
4. Co-interior Angles Theorem
Explanation:
Given the below;
1. Given that;
[tex]\angle1\cong\angle4[/tex]The theorem that justifies the above is the Alternate Exterior Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
2. Given that;
[tex]\angle2\cong\angle3[/tex]The theorem that justifies the above is the Corresponding Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the corresponding angles are congruent.
3. Given that;
[tex]\angle6\cong\angle7[/tex]The theorem that justifies the above is the Alternate Angles Theorem which states that if a pair of parallel lines are cut by a transversal, then the alternate angles are congruent.
4. Given that;
[tex]m\angle5+m\angle8=180[/tex]The theorem that justifies the above is the Co-interior Angles Theorem which states that if a pair of parallel lines are cut by a transversal, angles that are in the same similar position are supplementary, that is, they add up to 180 degrees.
What is an equation of the line that passes through the points (2, 2) and
(1, -2)
Answer: y = 4x + -6
Step-by-step explanation:
Horatios haunted house
The ratio of screamers to runners are 4:6 and 10:15.
Given,
the ratio of customers who screams and customers who run away is 2:3
Let
number of screamers be 'x'
number of runners be 'y'
To find number of screamers we can solve the ratio in proportion,
[tex]2:3::x:6\\\frac{2}{3}=\frac{x}{6}\\ \frac{2*6}{3}=x\\ 4=x[/tex]
Verify: [tex]4:6=2:3[/tex]
To find number of runners we can solve the ratio in proportion,
[tex]2:3::10:y\\\frac{2}{3}=\frac{10}{y}\\ {y}=\frac{3*10}{2}\\ y=15[/tex]
verify:[tex]10:15=2:3[/tex]
Hence, the ratio of screamers to runners are 4:6 and 10:15.
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I need some help with this problems please Number 10
Explanation:
We can see that this is an isosceles triangle, because there are two sides that are 4 units long and the third side is 3 units long.
For isosceles triangles we have the following congruences:
Therefore angle x is congruent to the one that's 66º.
Then we have that the measures of the interior angles of any triangle add up 180º:
[tex]\begin{gathered} yº+xº+66º=180º \\ y+66º+66º=180º \\ y+132º=180º \\ y=180º-132 \\ y=48º \end{gathered}[/tex]Answers:
• x = 66º
,• y = 48º
EUREKA M
3. Give an example of a scale factor that produces an enlargement. Explain why you chose this
scale factor.
on. Explain why you chose this
scale factor.
We will take an example of a rectangle with a scale factor of enlargement by 2.
For example, consider a rectangle with dimensions of 6 cm and 3 cm.
If we increase the scale factor for the initial rectangle by 2, both sides of the rectangle will be doubled. By raising the scale factor, we mean multiplying the present rectangle measurement by the supplied scale factor. We have multiplied the original rectangle measurement by 2 here.
The rectangle's length was originally 6 cm and its width was 3 cm.
After multiplying by two, the length is 12 cm and the width is 6 cm.
Thus, we took an example of a rectangle with a scale factor of enlargement by 2. We consider this for a better understanding.
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A square pyramid and a square prism have the same length, width, and height. If the volume of the square prism is 900in3 , what is the volume of the square pyramid?
A square pyramid and a square prism have the same length, width, and height. If the volume of the square prism is 900in3 , what is the volume of the square pyramid?
we know that
The volume of the square prism is equal to
[tex]V=b^2\cdot h[/tex]where b is the length side of the square base and h is the height of the prism
The volume of the square pyramid is
[tex]V=\frac{1}{3}\cdot b^2\cdot h[/tex]Remember that
the volume of the square prism is 900in3
so
[tex]900=b^2\cdot h[/tex]substitute in the formula of volume of the pyramid
[tex]\begin{gathered} V=\frac{1}{3}\cdot b^2\cdot h \\ \\ V=\frac{1}{3}\cdot900 \\ V=300\text{ in\textasciicircum{}3} \end{gathered}[/tex]the volume of the pyramid is 300 cubic inches–5 = –3(h − 10) + –8
Answer:
h = 9
Step-by-step explanation:
-5 = -3(h - 10) + (-8)
−5 = −3h + 22
−3h + 22 = −5
−3h = −27
h = 9
--------------
check
-5 = -3(9-10)+(-8)
-5 = -27 + 30 - 8
- 5 = -5
the answer is good
What is the third term of the recursive sequence below
Given the sequence:
[tex]\begin{gathered} a_1=-6 \\ a_n=\frac{1}{2}a_{n-1}-n \end{gathered}[/tex]Let's find the third term of the sequence.
To find the third term, a3, we have:
First find the second term, a2:
[tex]\begin{gathered} a_2=\frac{1}{2}a_{2-1}-2 \\ \\ a_2=\frac{1}{2}a_1-2 \\ \\ a_2=\frac{1}{2}(-6)-2 \\ \\ a_2=-3-2 \\ \\ a_2=-5 \end{gathered}[/tex]The second term is -5.
To find the third term, we have:
[tex]\begin{gathered} a_3=\frac{1}{2}a_{3-1}-3 \\ \\ a_3=\frac{1}{2}a_2-3 \\ \\ a_3=\frac{1}{2}(-5)-3 \\ \\ a_3=-2.5-3 \\ \\ a_3=-5.5 \end{gathered}[/tex]Therefore, the third term of the
if gh=53 and hi=7 then gi=
In the given line, the length of the line gi is 60 units.
What is a line?A line is an indefinitely long, straight object that is drawn with a minimum width in geometry but is said to have no specific width in mathematics since it lacks depth.An angle is created when two straight lines or rays intersect at a single terminal. The vertex of an angle is the location where the two rays meet.So, the length of gi will be:
We know that,
gh = 53hi = 7Now, we can easily see that the given line is:
gi = gh + higi = 53 + 7gi = 60Therefore, in the given line, the length of the line gi is 60 units.
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A graden plot 4m by 12m has one side along the fence.The area of the garden is to be doubled by digging a border of uniform width on the other three sides.What should the width of the border be?
The width of the border is 6 m after digging a border of uniform width on the other three sides.
Step 1:
Original garden plot is 4 m by 12 m. The 12 m side is against the wall.
A border of length D is along three sides of the plot (the 4th side is the wall).
Step 2
area of original garden plot is 12 x 4 = 48 [tex]m^{2}[/tex]
area of new plot = 96 [tex]m^{2}[/tex] (twice the original plot)
96 = (4 + D) (12 + 2D)
Set up equation for the area of the new area of the new plot (double the area of the old garden plot).
Step 3
96 = (4 + D) (12 + 2D)
[tex]96 = 2d^{2}+12d+4(2d+12)[/tex]
[tex]96 = 2d^{2}+12d+8d+48[/tex]
[tex]96 = 2d^{2}+20d+48[/tex]
[tex]96 -2d^2-20d-48 = 0[/tex]
[tex]48-2d^2-20d = 0[/tex]
[tex]-2(d^2+10d-24) = 0[/tex]
d = -12
Now solve for D
Step 4
D = 6 meters
Ignore negative answer because border must be a positive number. So Border is -12 [tex]m^{2}[/tex] (6 m).
Hence the answer is the width of the border is 6 m after digging a border of uniform width on the other three sides.
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Given the end points of A(-8,-2) and B(6,19). The segment AB is divided into the ratio atAR:RB in a 2:5 ratio. Find the coordinates of point R.R=
The given coordinates in the question are
[tex]\begin{gathered} A=(-8,-2)\text{ = x1=-8, y1=-2} \\ B=(6,19)\text{ = x}2=6,y2=19 \end{gathered}[/tex]Let the coordinate at R be
[tex]R=(x,y)[/tex]The ratio of the line segment given is
[tex]AR\colon RB=2\colon5\text{ (m=2,n=5)}[/tex]The formula to calculate the coordinate of a line segment in a given ratio is given below as
[tex](x,y)=(\frac{mx_2+nx_1}{m+n}),(\frac{my_2+ny_1}{m+n})[/tex][tex]undefined[/tex]Jerome and Tara played in a golf
tournament with four rounds. Their
scores for the rounds are given below.
If their final score is the sum of their
four rounds, which statement is true?
Round 1 Round 2 Round 3 Round 4
-4
5
-6
-2
2
-5
-4
-1
Jerome
Tara
Answer:JEROME
Step-by-step explanation:
a ferris wheel casts a 42 m shadow. a man two meters tall casts a 3 m shadow. how tall is the first wheel (in meters)?
The ferris wheel cast a shadow of 42 meters Tall.
A man of height 2 meters cast a shadow of 3 meters . The height of the ferris wheel can be computed below
[tex]\begin{gathered} 2\text{ meters = 3 meters} \\ x\text{ meters=42 meters} \\ \text{cross multiply} \\ 3x=84 \\ x=\frac{84}{3} \\ x=28\text{ meters} \end{gathered}[/tex]height of the ferris wheel = 28 meters
How to find the GCF of 65,39,and 13
Answer:
13
Step-by-step explanation:
65 ÷ 13 = 5
39 ÷ 13 = 3
13 ÷ 13 = 1
(All can be divided by 13 so the GCF is 13)
Tic, Tac and Toe are siblings. Toe is Tic and Tac's brother
but Tic is not Toe's brother. How is Tic related to Toe?
Answer: Tic is either Toe's brother or sister.
Step-by-step explanation: There's really no explanation. It's just outside the box thinking.
Select all of the scenarios below that correctly identify the independent variable. A. Charlie gets paid by the hour. The number of hours he works is the independent variable. B. Oscar likes to go for drives in the car. The cost of the trip increases as the distance he travels increases. The distance is the independent variable. C. How much Caleb weighs is relative to the amount he eats. The amount he weighs is the independent variable. D. The more Mark practices his golf swing, the better he becomes at hitting the ball. The amount of time he practices is the independent variable.
Independent varible are variable that dosent depend on any factor that afftect the scenarios.
the scenarios that identify the independent variable.
A. Charlie gets paid by the hour. The number of hours he works is the independent variable.
B. Oscar likes to go for drives in the car. The cost of the trip increases as the distance he travels increases. The distance is the independent variable.
D. The more Mark practices his golf swing, the better he becomes at hitting the ball. The amount of time he practices is the independent variable.
Only 1 and 2 pls helppp
Answer:
See the attached image for work.
1) The slope is 4.
2) The slope is 2.
Answer:
on the first one the rise is 20 and the run is 5. 5 divided by 20 is 4 so the slope is 4. I haven't answered the second one yet, sorry.
How many one and one-sixths are in five and five-sixths?
Using operations of fractions, the answer obtained is
There are 5 [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
What is fraction?
Suppose there is a collection of objects and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is the denominator,
Let there are x [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
[tex]1\frac{1}{6} x = 5\frac{5}{6}\\\frac{7}{6}x = \frac{35}{6}\\x = \frac{35}{6} \times \frac{6}{7}\\x = 5[/tex]
There are 5 [tex]1\frac{1}{6}[/tex] in [tex]5\frac{5}{6}[/tex]
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estimated sales volume =47.81+0.47(Advertising Expenditures)If the company has a target sales volume of $175,000,how much should the sales manager allocate for the advertising in the budget ? round your answer to the nearest dollar
We are given an estimate equation.
Let the estimate sales volume be "s" and advertising expenditure be "a".
The given equation is:
[tex]s=47.81+0.47a[/tex]The company has a target sales of 175,000, which is a value for "s".
To get how much they need to allocate for advertising, we can solve for "a" in the equation and substitute the "s" value with 175,000:
[tex]\begin{gathered} s=47.81+0.47a \\ 47.81+0.47a=s \\ 0.47a=s-47.81 \\ a=\frac{s-47.81}{0.47} \end{gathered}[/tex]Now we substitute 175,000 into "s":
[tex]a=\frac{175,000-47.81}{0.47}=\frac{174,952.19}{0.47}=372,238.7021\ldots\approx372,239[/tex]So, by the equation estimate, the sales manager should allocate $327,239 for advertising.
Find a pair of adjacent angles:4 and 14Find a pair of vertical angles:233 and 21)
SOLUTION
By definition, adjacent angles are (of a pair of angles) formed on the same side of a straight line when intersected by another line.
Vertical Angles are the angles opposite each other when two lines cross.
Going by this above definition, a pair of adjacent angles in the figure in Q1 are:
4 and 2.
Going by this above definition, a pair of vertical angles in the figure in Q1 are:
3 and 2.
What is the annual percentage yield (APY) for money invested at an annual rate of(A) 4.09% compounded monthly?(B) 4.1% compounded quarterly?
The annual percentage yield is given by the following formula:
[tex]\text{APY}=(1+\frac{r}{n})^n-1[/tex]Where r is the stated annual interest rate (in decimal form) and n is the number of times compounded.
A) APY for money invested at an annual rate of 4.09% compounded monthly.
Thus, the annual interest rate in decimal form is:
[tex]r=\frac{4.09\%}{100\%}=0.0409[/tex]And as it is compounded monthly then n=12.
Replace these values and solve:
[tex]\begin{gathered} \text{APY}=(1+\frac{0.0409}{12})^{12}-1 \\ \text{APY}=(1+0.0034)^{12}-1 \\ \text{APY}=(1.0034)^{12}-1 \\ \text{APY}=1.0417-1 \\ \text{APY}=0.0417 \end{gathered}[/tex]The APY is 0.0417=4.17%.
B) 4.1% compounded quarterly:
The annual interest rate is:
[tex]r=\frac{4.1\%}{100\%}=0.041[/tex]As it is compounded quarterly then n=4.
Replace and solve:
[tex]\begin{gathered} \text{APY}=(1+\frac{0.041}{4})^4-1 \\ \text{APY}=(1+0.0103)^{12}-1 \\ \text{APY}=(1.0103)^{12}-1 \\ \text{APY}=1.1302-1 \\ \text{APY}=0.1302 \end{gathered}[/tex]The APY is 0.1302=13.02%