For given equation x^2+6x-15=0, value of x is [tex]-3\pm 2 \sqrt{6}[/tex]
The "solutions" of an equation are referred to as the roots of the equation. Solutions are the numbers that, once the variable has been solved, are equal to it. We can use the discriminant formula to obtain the roots of quadratic equations.
The given equation [tex]x^2+6x-15=0\\[/tex] can be solved using discriminant method.
[tex]d=b^2 -4ac\\[/tex].......................1
[tex]x=-b\pm\sqrt{d}/2a[/tex].....................2
To calculate d,
Substitute a=1,b=6,c=-15 in eq 1.
[tex]d=6^2-4\times 1\times -15\\ d=96[/tex]
[tex]x=-6\pm \sqrt{96}/2\\x=-3\pm 2\sqrt6[/tex]
Thus, value of x is [tex]-3\pm 2 \sqrt{6}[/tex]
Learn more about roots, here:
https://brainly.com/question/28123261
#SPJ6
Final answer:
x = -3 ±√24.
Explanation:
To solve the quadratic equation x²+6x-15=0 by completing the square, follow these steps:
First, move the constant term to the other side of the equation:
x² + 6x = 15.
Add the square of half the coefficient of x to both sides to complete the square: (6/2)² = 9, so add 9 to both sides resulting in x² + 6x + 9 = 24.
Now the equation is a perfect square on the left side:
(x+3)² = 24.
Take the square root of both sides to solve for x:
x+3 = ±√24.
Subtract 3 from both sides to find the values of x:
x = -3 ±√24.
Which is bigger? 3kg or 40000mg
Answer:
3kg
Step-by-step explanation
kg is heavier
I NEED HELP WITH ANGLES!!
Which is the simplified form of the expression (StartFraction (x Superscript negative 3 Baseline) (y squared) Over (x Superscript 4 Baseline) (y superscript 6 Baseline) EndFraction) cubed?
To simplify the expression (x⁻³ × y² / x⁴ × y⁶) cubed, you need to cube each term in the fraction individually.
To simplify (StartFraction (x⁻³) (y²) Over (x⁴) (y⁶) EndFraction) cubed, you need to cube each term in the fraction individually.
Here is the step-by-step breakdown:
Cube the numerator: x⁻⁹y⁶
Cube the denominator: x¹²y¹⁸
Combine the cubed terms: (x⁻⁹y⁶) / (x¹²y¹⁸)
The area of the shaded circle below is 78.5 square inches. The area of the large circle is 314 square inches.A shaded circle is inside of a larger unshaded circle.What is the probability that a point chosen at random will be in the shaded region
Answer:
The probability that a point chosen at random will be in the shaded region is 0.25
Step-by-step explanation:
We have been given a small shaded circle inside a larger un-shaded circle. This is shown in the image attached below.
The area of smaller circle is 78.5 squares inches and the area of larger circle is 314 square inches. We have to find the probability that a point chosen at random will be in the shaded region.
Probability is defined as the ratio of Favorable outcome to the Total outcomes. In this case the favorable outcome is that the point should be inside the shaded region i.e. in an Area of 78.5 square inches. And the total outcome is that the point can be anywhere inside the larger circle i.e. within an Area of 314 square inches. Thus the probability that a point chosen at random will be inside the shaded region will be:
[tex]Probability = \frac{\text{Favorable Outcome}}{\text{Total Outcome}} \\\\ = \frac{78.5}{314}\\\\=0.25[/tex]
Thus, the the probability that a point chosen at random will be in the shaded region is 0.25. This means there is a 25% chance that a randomly chosen point will be inside the shaded region.
What is the equation of the line?
Answer:
y= -4/3x
Step-by-step explanation:
rise over run
up 4, left 3
or
down 4, right 3
(03.01 LC)
The leg of a right triangle is 2 units and the hypotenuse is 5 units. What is the length, in units,
of the other leg of the triangle? (1 point)
C3
C /21
Answer:
The length of the other leg is 4.58 units.
Step-by-step explanation:
A² + B² = C² Use Pythagorean Theorem
2² + B² = 5² Simplify
4 + B² = 25
-4 -4 Subtract 4 from both sides
B² = 21 Take the square root of both sides
B = 4.58 units
If this answer is correct, please make me Brainliest!
Answer:
4.58 units is your answer
Step-by-step explanation:
Si Ana diese 10 libros a Alicia, ambas tendrían la misma cantidad de libros. Si Ana tuviera 10 libros más, tendría el doble que Alicia. Calcula cuantos libros tiene cada una.
Answer:
Ana tiene 50 libros y Alicia 30.
Paul withdrew $17.25 from his savings account every week for 3 weeks. Which expression is the best choice to help him determine the total amount of money he withdrew
(3)(−17.25) = −51.75; he withdrew $51.75
(−3)(17.25) = −51.75; he withdrew $51.75
(3)(17.25) = 51.75; he withdrew $51.75
(−3)(−17.25) = 51.75; he withdrew $51.75
(3)(-17.25)= -51.75
I think thats the right one
Answer:
A
Step-by-step explanation:
I hape that works
HELP PLEASE :(
Three-Dimensional Geometry
Geometric Design
1. Kathrine, Giana, and Jackson are designing jewelry boxes to sell at the art fair. The
dimensions of their boxes are:
Kathrine: 5in x 5in x 5in
Giana: 10in X 12in X 2in
Jackson: 10in X 5in x 4in
If a customer at the art fair is wants to buy the jewelry box that will hold the most amount
of jewelry, whose jewelry box should they purchase?
Answer: The customer should buy Giana’s jewelry box.
Step-by-step explanation:
The jewelry boxes are rectangular prisms, in order to find the box that would hold the most amount of jewelry we need to find the volumes of each box.
V= l.w.h
Katherine’s box: 5x5x5= 125
Giana’s box: 10x12x2= 240
Jackson’s box: 10x5x4= 200
Melanie sold half of her comic books and then bought 9 more. She now has 17. How many did she begin with?
Answer:
16
Step-by-step explanation:
You need to work backwards and do the opposite
So, first do subtraction since Melanie added to her collection. SO do the opposite of addition.
17-9=8
Then, since she sold half of her comics, and she is dividing her collect, you multiply 8 with 2.
8 x 2=16
Final answer
16 comics
I just need help with this table
Answer:
from the looks of it, all you have to do is, for f(x), is plug it in as an exponent. in order (top to bottom), it should be: 64, 2048, 4096, 8192.
g(x) is being squared and then multiplied, so it should be (from top to bottom): 720, 2420, 2880, 3380
Step-by-step explanation:
Help me please please help
Answer:
80
Step-by-step explanation:
The sides of a triangle always add up to 180. 80+20+?=180
Answer:
C, 80 degrees
Step-by-step explanation:
Together, all of the interior angles in a triangle add up to 180 degrees. Therefore, the missing angle is the two other angles subtracted from 180 degrees. 180-20-80=80 degrees, or answer choice C. Hope this helps!
Vera is an ecologist who studies the change in the bear population of Siberia over time. The relationship between the elapsed time, t, in years, since Vera began studying the population, and the total number of bears, N(t), is modeled by the function:
Answer:
Every year, the bear population shrinks by a factor of 2/3 .Explanation:
The concrete question and the function or data were omitted.
I found the complete question on the internet. Please, find attached the picture with the complete question
You must complete the sentence about the yearly rate of change of the bear population, telling whether it grows or shrinks and by what factor.
Thus, the goal is to interpret the rate of change in an exponential model.
The exponential model is:
[tex]N(t)=2187\cdot \bigg(\dfrac{2}{3}\bigg)^t[/tex]
Let's analyze that function.
When t = 0, (2/3)⁰ = 1 and N(0) = 2,187 × 1 = 2,187
Thus, the population of bears starts with 2,187 individuals.
For t = 1, the population will be N(1) = 2,187 × (2/3).
For t = 2, the population will be N(2) = 2,187 × (2/3)²
And so on, every year the population of bears is multiplied by a factor of 2/3.
Since, 2/3 is less than 1, every year the population will be decreasing (decaying), by a factor of 2/3.
Thus, the answer, i.e. the complete sentence, is:
Every year, the bear population shrinks by a factor of 2/3 .
Answer:
shrinks/ 2/3
Step-by-step explanation:
(1)=−10
h(2)=−2
h(n)=h(n−2)⋅h(n−1)
h(3)=
Answer:
6
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
h(3)=h(1)*h(2)=
(-10)*(-2)=
20
To help with packing, Ana needs to find the volume of her suitcase to determine how much she could pack. Her suitcase is a rectangular prism, with dimensions of 19 inches tall, 13 inches wide, and 7
1
2 inches deep. What is the total volume of her suitcase? Explain how you found the volume.
Answer:
1,852.5 in³
Step-by-step explanation:
Volume of a rectangular prism:
Length × width × height (depth)
19 × 13 × 7½
1852.5 inches³
At the beginning of an environmental study, a forest covered an area of 1500 km2 . Since then, this area has decreased by 9.8% each year.Let t be the number of years since the start of the study. Let y be the area that the forest covers in km2.
Write an exponential function showing the relationship between y and t.
Answer:
[tex]A(t)=(0.902)^t \cdot 1500[/tex] [tex][km^2][/tex]
Step-by-step explanation:
In this problem, the initial area of the forest at time t = 0 is
[tex]A_0 = 1500 km^2[/tex]
After every year, the area of the forest decreases by 9.8%: this means that the area of the forest every year is (100%-9.8%=90.2%) of the area of the previous year.
So for instance, after 1 year, the area is
[tex]A_1 = A_0 \cdot \frac{90.2}{100}=0.902 A_0[/tex]
After 2 years,
[tex]A_2=0.902 A_1 = 0.902(0.902A_0)=(0.902)^2 A_0[/tex]
And so on. So, after t years, the area of the forest will be
[tex]A(t)=(0.902)^t A_0[/tex]
And by substituting the value of A0, we can find an explicit expression:
[tex]A(t)=(0.902)^t \cdot 1500[/tex] [tex][km^2][/tex]
The adjusted multiple coefficient of determination is adjusted for
The lengths of a certain species of beetles are normally distributed with a mean of 1.9 centimeters and a standard deviation of 0.2 centimeters.
What is the z-score of a beetle of this species with a length of 2.38 centimeters?
Answer: the z score is 2.4
Step-by-step explanation:
Since the lengths of the certain species of beetles are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = length of the beetle species.
µ = mean length
σ = standard deviation
From the information given,
µ = 1.9 centimeters
σ = 0.2 centimeters
For a species with a length of 2.38 centimeters, the z score is
z = (2.38 - 1.9)/0.2
z = 0.48/0.2
z = 2.4
Joey is trying to prove that CATS is an isosceles trapezoid. He starts by providing that line segment AT is parallel to line segment CS and that line segment AS is about the same as line segment CT. Based on that information, is this enough to prove that CATS is an isosceles trapezoid
Answer:
Yes the information i.e. AT ║ CS and diagonals AS = CT are sufficient to prove that CATS is an isosceles trapezoid.
CATS is an isosceles trapezoid. (Proved)
Step-by-step explanation:
Yes the information i.e. AT ║ CS and diagonals AS = CT are sufficient to prove that CATS is an isosceles trapezoid.
Proof :
Taking Δ CAT and Δ STA,
(i) CT = AS (Given)
(ii) AT is the common side and
(iii) ∠ ACT = ∠ TSA
{Since AT ║ CS and the angles are obtained from the same base AT}
Therefore, by the criteria Side-Side-Angle i.e. SSA, we can say Δ CAT ≅ Δ STA.
Hence, AC = ST {Corresponding sides}
Therefore, CATS is an isosceles trapezoid. (Proved)
When Sanchez left his house this morning, his cell phone was 30% charged and it then started to lose 3% charge for each hour thereafter. Write an equation for the function B(t), representing the charge remaining in Sanchez's battery, as a percentage, t hours after he left his house.
Answer:
The equation that represents the battery charge in Sanchez's phone as a percentage t hours after he left his house is B(t) = 30 - 3*t.
Step-by-step explanation:
The initial state of the battery on Sanchez's phone is 30% so in time t equals zero the battery should be at that value and as time progresses the battery should lose battery charge at a rate of 3% for each hour. We can write this in an equation form by taking the initial state and subtract it by the rate multiplied by the value of time. We have:
B(t) = 30 - 3*t
The equation that represents the battery charge in Sanchez's phone as a percentage t hours after he left his house is B(t) = 30 - 3*t.
in class 30 students,13of them are boys what parcentage of the class are girl give your answer to 1 decimal place
Answer:
56.7%
Step-by-step explanation:
First determine the number of girls
30-13 = 17
The fraction of girls is 17/30
Changing this to a decimal is
.566666666
Changing to a percent
56.666666%
To one decimal place
56.7%
Emma took a taxi from the airport to her house.
She paid a flat fee of $5 plus $3.70 per mile.
The fare came to $42.
For Emma's taxi ride, which equation gives the correct distance (d) in miles
a circle with area 36 pi has a sector with central angle of f 11/6 pi radians
Answer:
33 π
Step-by-step explanation:
Given,
Area of circle = 36 π
Central angle of sector,θ = 11/6 rad
Area of the sector = ?
we know,
A = π r²
36 π = π r²
r = 6
Area of sector
[tex]A = \frac{1}{2} r^2 \theta [/tex]
[tex]A = \frac{1}{2} \times 6^2 \times (\frac{11}{6}\pi)[/tex]
[tex]A = 33\pi \ sqr. units[/tex]
A restaurant offers 5 appetizers and 10 main courses. In how many ways can a person order a two-course meal? Use the Fundamental Counting Principle with two groups of items.
Answer:
5x10=50
Step-by-step explanation:
baba booey
1. Identifique a abscissa e a ordenada dos pontos abaixo.
A(3,-5) abscissa__________ ordenada______________
B(-1,0) abscissa__________ ordenada______________
C(-3,5;-2) abscissa__________ ordenada______________
D(0,-1) abscissa__________ ordenada______________
Answer:
A(3,-5) abscissa:3 ordenada: -5
B(-1,0) abscissa: -1 ordenada: 0
C(-3,5;-2) abscissa: -3.5 ordenada -2
D(0,-1) abscisa: 0 ordenada:- 1
Step-by-step explanation:
What we must take into account is that the abscissa is the value of x and the ordinate is the value of y. There is always a number of the (x,y), that is, the abscissa is the first value and the ordinate is the second value, therefore:
Answer:
We need to identify abscissa and ordenada in each of the pairs given.
For a pair (x, y), x is the abscissa and y is the ordenada.
A (3,-5) abscissa_____3____ ordenada______-5_______
B (-1,0) abscissa____-1____ ordenada_______0_____
C (-3,5;-2) abscissa_____-3.5____ ordenada_____-2______
D (0,-1) abscissa_____0___ ordenada___-1_______
A farmer has determined that a crop of strwberries yields a yearly profit of $1.50 per square yard. If strawberries are planted on a triangul;ar piece of land whose sides are 50 yards, 75 yards, and 100 yards, how much profit to the nearest hundred dollars, would the farmer expect to make from this piece of land during the next harvest.
Answer:
$2700
Step-by-step explanation:
Using Heron's formula, we can find the area of the triangle to be ...
A = √(s(s -a)(s -b)(s -c)) . . . . where s=(a+b+c)/2 and a, b, c are the sides
Here, we have ...
s = (50 +75 +100)/2 = 225/2 = 112.5
A = √(112.5 · 62.5 · 37.5 · 12.5) ≈ 1815.461 . . . square yards
Then the profit is expected to be ...
(1815.451 yd²)($1.50/yd²) = $2723.19 ≈ $2700
The farmer expects a profit of about $2700 from that crop.
The sum is two numbers is 65. The difference of the two numbers is 17. Write systems of equations and find two numbers
Answer:
41 and 24
Step-by-step explanation:
x+y=65 -------(A)
x-y=17 -------- (B)
(A)+(B)
(x+y)+(x-y)=65+17
2x=82
x=41
(B)===>
41-y=17
y=41-17
y=24
Product of 3x - 1 and 4x²-3x+ 8
Answer:
8x squared- 6x+16 is the answer
The product of a number and 5. The answer is 15. What’s the equation and solution
Answer:
3 * 5 = 15
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
[tex]5a = 15\\\frac{5a}{5} = \frac{15}{5} \\a = 3[/tex]
5 * 3 = 15
if the diameter of a nickel is 0.835 in and the width of each nickel is 0.077 in what is the approximate surface area of the 2$ roll of nickels round your answer to the nearest hundredth
Answer:
Step-by-step explanation:
The roll of nickels forms a cylinder
cylinder area includes the sides and the round areas
round areas = pi r^2 there is two so 2 pi r^2
= 2 pi (.835/2)^2
and the side area pi x d x h
pi x .835 ( .077 x 40) (there are 40 nickels in $ 2
Add the areas to get the total ......
To find the total surface area of a $2 roll of nickels, we calculate the surface area of one nickel and then multiply by 40 (the number of nickels in a $2 roll), resulting in an approximate surface area of 47.84 in² when rounded to the nearest hundredth.
To calculate the approximate surface area of a $2 roll of nickels, we must first determine how many nickels are in a $2 roll. Knowing that each nickel is worth 5 cents, a $2 roll would contain 40 nickels ($2.00 / $0.05 = 40). The surface area of a nickel includes the area of the circles on both sides and the area of the edge. The formula for the area of a circle is πr² (where r is the radius) and the formula for the area of the side (cylinder height) is 2πrh (where h is the width).
The diameter of a nickel is 0.835 inches, so the radius is half of that or 0.4175 inches. Using these measurements:
Area of one side = π(0.4175²) = 0.5477 in² (approx).Area of both sides = 2 * 0.5477 in² = 1.0954 in².Surface area of the edge = 2π(0.4175)(0.077) = 0.1006 in² (approx).Total surface area of one nickel = 1.0954 in² + 0.1006 in² = 1.196 in².Therefore, the total approximate surface area for a $2 roll of 40 nickels = 40 * 1.196 in² = 47.84 in².
Rounded to the nearest hundredth, the surface area is 47.84 in².