Answer:
-86
Step-by-step explanation:
8(-10)-6=x
-80-6=x
x=-86
The roots of f(x) = 2x^2
+ 8x + 13 are
and
The vertex of the parabola is
at
Answer:
( 2 , − 5 )
Step-by-step explanation:
Consider the following problem: a box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volume of each configuration. Does it appear that there is a maximum volume
Answer:
) See annex
b) See annex
x = 0,5 ft
y = 2 ft and
V = 2 ft³
Step-by-step explanation: See annex
c) V = y*y*x
d-1) y = 3 - 2x
d-2) V = (3-2x)* ( 3-2x)* x ⇒ V = (3-2x)²*x
V(x) =( 9 + 4x² - 12x )*x ⇒ V(x) = 9x + 4x³ - 12x²
Taking derivatives
V¨(x) = 9 + 12x² - 24x
V¨(x) = 0 ⇒ 12x² -24x +9 = 0 ⇒ 4x² - 8x + 3 = 0
Solving for x (second degree equation)
x =[ -b ± √b²- 4ac ] / 2a
we get x₁ = 1,5 and x₂ = 0,5
We look at y = 3 - 2x and see that the value x₂ is the only valid root
then
x = 0,5 ft
y = 2 ft and
V = 0,5*2*2
V = 2 ft³
Is figure B a scale copy of Figure A ?? Yes Or No
Answer:
No
Step-by-step explanation:
Figure A has an horizontal length of 2 units and a vertical length of 2 units.
Figure B has an horizontal length of 9 units and a vertical length of 7 units
Thus:
Horizontal length of Figure B / Horizontal length of figure A = 9/2
Horizontal length of Figure B / Horizontal Length of Figure A = 7/2
Thus,
9/2 ≠ 7/2
This implies that their corresponding lengths are not corresponding to each other. Therefore, Figure B is not a scale copy of Figure A.
Mary takes out a loan for $ 5 , 000 at a simple interest rate of 3.5 % to be paid back in 36 monthly installments. What is the amount of her monthly payments?
Solve the equation 4(c-3) = 8
What are the two ways to start solving this equation? Choose BOTH ways.
1. Use the distributive property to get 4c- 12 = 8
2. Use the distributive property to get 4c - 3 = 8
3. Add 3 to both sides to get 4c = 11
4. Divide both sides by 4 to get c - 3 = 2
5. Subtract 4 from both sides to get c - 3 = 4
Answer:
Use the distributive property to get 4c-12=8
Divide both sides by 4 to get c-3=2
Step-by-step explanation:
Please help this is super confusing
it's 26 because u count the squares in the poygon
A single die is rolled. Find the odds in favor of rolling a number greater than 3.
Answer:
6:3
Step-by-step explanation:
Answer and Step-by-step explanation:
3 of the options are not to be chosen, and 3 are wanted.
That means that anything above 3 (so, 4, 5, or 6) are the numbers that are wanted, while the numbers 1, 2, and 3 are not wanted.
We have 6 total options.
The ration would be:
3:6, or 3 to 6. This reduces down to 1:2, or 1 to 2.
That means that there is a 50% chance of getting 4, 5, or 6.
#teamtrees #PAW (Plant And Water)
Cooper weights 20 pounds. When he is an adult dog, he will weigh about 315% of his current weight. Write 315% as a fraction and a decimal.
Answer:
3.15 and 3 3/20
Step-by-step explanation:
315 ÷ 100 = 3.15
3.15 = 3 3/20
Please mark me brainlest
Write the equation in slope-intercept form. Y+5= -6(x+7)
y + 5 = -6x - 42
y = -6x -47
What is the cost of a shirt? What is the cost of a soda?
Answer:
Soda = $4 Shirt = $18
Step-by-step explanation:
s- soda
h - shirt
2s+2h = 44 → 2
h + 3h = 30 → 1
1 * 2
2h + 6h = 60 →3
3 - 2
4h = 16
h = $4
s = $18
In the 2009 NFL regular season, quarterback Drew Brees of the New Orleans Saints had an average of 293 passing yards per game with a
standard deviation of 74 yards. Between which two values do you expect the middle 95% of his performances to be?
Your answer:
0 0 and 515
219 and 367
O 0 and 415
145 and 441
Clear answer
Answer:
Drew Christopher Brees (/briːz/;[1] born January 15, 1979) is a former American football quarterback who played in the National Football League (NFL) for 20 seasons.[2] A member of the New Orleans Saints for most of his career, Brees is the NFL leader in career pass completions, career completion percentage, and regular season passing yards, along with being second in career touchdown passes and career pass attempts. He also holds the record of consecutive games with a touchdown pass, breaking the feat held by Johnny Unitas for 52 years.
The scatter plot shows the average price of a major-league baseball ticket from 1997
to 2006.
Use the points (2001, 17.60) and (2002, 18.75) to write the slope-intercept form of equation for the line of fit Baseball Ticket Prices shown in the scatter plot.
Line of Fit:_________
b. Use your equation to tell the price of a ticket in 2009. Is this extrapolation or interpolation?
Answer:
a) y = [tex]\frac{23}{20}[/tex] x + 13
b) ticket price in 2009 would be $23.35 by extrapolation
Step-by-step explanation:
Using your own words, explain direct and inverse proportionality. (Be sure to use complete sentences.)
Direct and Inverse proportionality was discussed with examples.
Direct proportionality: Direct proportionality means the change of a similar kind.
For example, as pressure increases, density also increases, which means both the parameters (pressure and density) are experiencing a similar kind of change i.e. increment in their magnitude.
What is the constant of proportionality?The constant of proportionality is the ratio that relates two given values.
For example, Density ∝ pressure
Density = k(Pressure)
Here k is the constant of proportionality
Inverse proportionality: Inverse proportionality means the change of the opposite kind.
For example, as the population increases, natural resources decrease, which means parameters(population and natural resources) are experiencing the opposite kind of change i.e one is increasing other is decreasing.
Thus, Direct and Inverse proportionality were discussed with examples.
To get more about proportionality visit:
https://brainly.com/question/24868934
How many solutions does the system of linear equations represented in the graph below have?
A
No Solution
B
One Solution
C
Infinitely many solutions
D
None of the above
Answer:
No solution
Step-by-step explanation:
They must intersect to have one solution. For infinite many solutions, the lines would be on top of each other.
A carpenter is creating two new templates for his designs. One template will be in the shape of a right triangle, where the longer leg is 4 inches more than six times the shorter leg.
The second template will be in the shape of a rectangle, where the width is 5 inches more than the triangle’s shorter leg, and the length is 3 inches.
The carpenter needs the areas of the two templates to be the same. Write a system of equations to represent this situation, where y is the area, and x is the length of the shorter leg of the triangle. Which statement describes the number and viability of the system’s solutions?
A.
The system has two solutions, but only one is viable because the other results in negative side lengths.
B.
The system has two solutions, and both are viable because they result in positive side lengths.
C.
The system has only one solution, but it is not viable because it results in negative side lengths.
D.
The system has only one solution, and it is viable because it results in positive side lengths.
Answer:
this is correct on plato/edmentum
Step-by-step explanation:
For an equation to be viable, the result of the equation must be positive (i.e. greater than 1).
The 2 templates, the farmer created have two solutions, but only one of the solutions are viable.
For the first template, we have:
[tex]x \to[/tex] length of the shorter leg of the triangle
[tex]z \to[/tex] length of the longer leg of the triangle
From the question, we have:
[tex]z = 4 + 6x[/tex]
The area (y) of the first template is:
[tex]y = \frac{1}{2}xz[/tex] --- area of a triangle
So, we have:
[tex]y = \frac{1}{2}x(4 + 6x)[/tex]
Open bracket
[tex]y = 2x + 3x^2[/tex]
For the second template, we have:
[tex]Width = 5 + x[/tex]
[tex]Length = 3[/tex]
So, the area (y) of the second template is:
[tex]y = Length \times Width[/tex] --- area of a rectangle
This gives:
[tex]y = 3 \times (5 + x)[/tex]
[tex]y = 3(5 + x)[/tex]
[tex]y = 15 + 3x[/tex]
So, the expression for both areas are:
[tex]y = 2x + 3x^2[/tex] --- template 1
[tex]y = 15 + 3x[/tex] --- template 2
Both areas must be equal. This is represented as:
[tex]2x + 3x^2 = 15 + 3x[/tex]
Collect like terms
[tex]3x^2 +2x - 3x - 15 = 0[/tex]
[tex]3x^2 - x - 15 = 0[/tex]
Solve for x using quadratic formula, we have:
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where:
[tex]a = 3; b =-1; c=-15[/tex]
So, we have:
[tex]x = \frac{-(-1) \± \sqrt{(-1)^2 - 4\times 3 \times -15}}{2 \times 3}[/tex]
[tex]x = \frac{1 \± \sqrt{181}}{6}[/tex]
[tex]x = \frac{1 \± 13.5}{6}[/tex]
Split
[tex]x = \frac{1 + 13.5}{6} \ or \ x = \frac{1 + 13.5}{6}[/tex]
[tex]x = \frac{-12.5}{6} \ or \ x = \frac{14.5}{6}[/tex]
[tex]x = -2.08 \ or \ x = 2.42[/tex]
We can see that x has 2 solutions, but only 1 of the solutions is viable because the other is negative.
Hence, option (a) is correct
Read more about viable and non-viable solutions at:
https://brainly.com/question/10558256
If each quadrilateral below is a rectangle, find the missing measure.
please help :(
Answer:
m<JMK = 54
m<JKH = 63
m<HLK = 90
m<HJL = 27
m<LHK = 63
m<JLK = 27
Step-by-step explanation:
1. Solve for m<JMK
It is given that (<HMJ) and (<JMK) form line (HK), meaning that they are supplementary angles. Thus, their degree measures add up to (180), using this one can form the following equation,
(<HMJ) + (<JMK) = 180
126 + (<JMK) = 180
(<JMK) = 54
2. Solve for m<JKH
It is given that the figure is a rectangle, one of the properties of a rectangle is that diagonals are congruent, and the diagonals bisect each other. This means that segments (JM) and (MK) are congruent. Hence, the triangle (JMK) is an isoceles triangle. Therefore, one can use the base-angles theorem, which states that (<MJK) is congruent to (<JKH). Since the sum of angle measures in any triangle is (180), one can form the following equation,
(<JMK) + (<MJK) + (<JKH) = 180
54 + 2(<JKH) = 180
<JKH = 63
3. Solve for m<HLK
As per its definition, the corner angles in a rectangle are always (90) degrees, this property is applicable for the given rectangle. Thus, (<HLK) = 90 degrees.
4. Solve for m<HJL
To solve for this angle, one can use similar logic as they did to solve for (<JKH). Form the following equation and solve,
(<HMJ) + (<HJL) + (<JHK) = 180
126 + 2(<HJL) = 180
(<HJL) = 27
5. Solve for m<LHK
The vertical angles theorem states that when two lines intersect, the opposite angles are congruent. One can apply this theorem here and say (<JMK) = (<HML). Then, to solve for this angle, one can use the same logic that they used to solve for (<JKH) and (<HJL). Form the equation and solve,
(<HML) +(<LHK) + (<HLJ) = 180
54 + 2(<LHK) = 180
<LHK = 63
6.Solve for m<JLK
To solve for this angle, one can use the same logic that they used to solve for (<LHK). Form the equation and solve,
(<LMK) + (<JLK) + (HKL) = 180
126 + 2(<JLK) = 180
<JLK = 27
WILL GIVE BRAINLIST PLS HELP Find x. Round your answer to the nearest tenth.
Answer:
9. x=13.5
10. x=11.5
Step-by-step explanation:
find the root of 51 and 21
Answer: the root of 51 is 7.141 and the root of 21 is 4.583
Step-by-step explanation:
Hellpppp!! Ik it’s so easy but I have a literal peanut brain
Answer:3 1/3
Step-by-step explanation:
It’s 3 1/3
2. Jim has $57 in her bank account. He wants to buy a video game that costs $69. Should
Jim buy the video: Yes or No. Explain your reasoning using complete sentences.
Answer:
Well I would say John shouldn’t buy any vidoe games becuase first he can’t afford it and no one’s gonna borrow 12 dollars for a video gamer. Plus he can buy it when he has enough.
Need help on this please
9514 1404 393
Answer:
8π miles
Step-by-step explanation:
The circumference of a circle is given by the formula ...
C = 2πr
For a radius of 4 miles, the circumference is ...
C = 2π(4 miles) = 8π miles
Ella has a part-time job selling cupcakes at a cart in the park. She is paid $25 for a shift plus a fee of $0.25 for each cupcake she sells. A) Write and equation that can be used to solve for the total amount, t, Ella earns for working a shift in the park and selling c cupcakes. Ella works a shift and earns $38. B. Use the equation you wrote for part A to solve for the number of cupcakes Ella sold during her shift. Show your work. In the summer, the average number of cupcakes sold during a weekday shift is 36 and the average number of cupcakes sold during a weekend shift is 62. Ella has been given the choice to work a regular schedule of 3 weekday shifts each week or 2 weekend shifts each week. C. Explain which schedule will allow Ella to earn $300 more quickly. Support your answer with mathematical evidence, and state which shift Ella should choose.
9514 1404 393
Answer:
A) t = 0.25c +25
B) c = 52
C) 3 weekday shifts
Step-by-step explanation:
A. The amount Ella earns is $0.25 per cupcake, so for c cupcakes, that is ...
0.25c
In addition, she is paid $25, so her total amount she is paid is ...
t = 0.25c +25
__
B. In order to earn $38, the number of cupcakes sold must be ...
38 = 0.25c +25
13 = 0.25c . . . . . . subtract 25
52 = c . . . . . . . . . multiply by 4
Ella sold 52 cupcakes to earn $38.
__
C. On one of the average weekdays, Ella could be expected to earn ...
t = 0.25(36) +25 = 34
Then for 3 weekday shifts, her earnings would be 3($34) = $102. (It would take Ella 3 weeks to earn $300.)
On one of the average weekend shifts, Ella could be expected to earn ...
t = 0.25(62) +25 = 40.50
Then for 2 weekend shifts, her earnings would be 2($40.50) = $81. (It would take Ella 4 weekends to earn $300.)
Ella would earn $300 more quickly by working weekday shifts.
The perimeter of a rectangle is 58. The length is 4 more than
4 times the width. Find the width and length.
Answer:
Step-by-step explanation:
Simplify (10^-2/
10^3)^-1
0 -100,000
1
10
1
1
10
100,000
DONE
Answer:
huh?
Step-by-step explanation:
Answer:
the answer is D. 100,000.
Step-by-step explanation:
I'm a very big brain specimen.
Given the coordinates (6, 3) and (-8, 1), the midpoint is:
0 (1, -2).
0 (-1,2).
O (-2, 4).
O (2,-4).
Write a system of linear equations for the graph below.
Answer:
[tex]\left \{ {{y=-2x+2} \atop {y=-\frac{1}{4}x-5 }} \right.[/tex]
Step-by-step explanation:
1. the equation for the first line (its poits are (0;2) and (4;-6)):
y= -2x+2;
2. the equation for the seconde line (its points are (0;-5) and (4;-6)):
y= -1/4 x -5;
3. the required system of linear equations is:
[tex]\left \{ {{y=-2x+2} \atop {y=-\frac{1}{4}x-5 }} \right.[/tex]
what is the common denominator for 3/5 and
what is the common dneominter for 5/8
Answer:
The common denominator would be 40
Step-by-step explanation:
Hanna wants to estimate the number of eels in a lake
Find the distance between the given points. Round to the nearest tenth. 5,-2 and 1,2.
Answer:
[tex]4\sqrt{2}[/tex]
Step-by-step explanation:
Use the distance equation
[tex]\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex]
insert values (5,-2)=(x1,y1) and (1,2)=(x2,y2)
[tex]\sqrt{(5-1)^2+((-2)-2)^2}[/tex]
[tex]\sqrt{16+16}[/tex]
[tex]4\sqrt{2}[/tex]
Hope that helps :)
The diameter of a circle is 4 m. Find the circumference to the nearest tenth.
Answer :
[tex] \bf \large 10 \: m[/tex]
Step by step explanation :
Given that :The diameter of a circle is 4 m.to find :Find the circumference to the nearest tenth.formulas used :circumference = π × Diameterwhere,
π = 22/7Diameter = 4 mexplanation :⟼ c = πd
⟼ c = 22/7 × 4 m
⟼ c = 88/7 m
⟼ c = 12•57 m.
Round to the nearest tenth :⟼ c = 12•57 m
⟼ c = 10 m.
∴ circle circumference is 10 m.