Step-by-step explanation:
[tex]x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \left(-16\right)}}{2\cdot \:1}\\\sqrt{6^2-4\cdot \:1\cdot \left(-16\right)}\\\sqrt{6^2+64}\\\sqrt{36+64}\\\sqrt{100}\\\sqrt{10^2}\\=10\\x_1=\frac{-6+10}{2\cdot \:1},\:x_2=\frac{-6-10}{2\cdot \:1}\\\\\bold{x_1:2}\\\frac{-6+10}{2\cdot \:1}\\\frac{4}{2\cdot \:1}\\\frac{4}{2}\\=2\\\\\bold{x_2:-8}\\\frac{-6-10}{2\cdot \:1}\\\frac{-16}{2\cdot \:1}\\\frac{-16}{2}\\-\frac{16}{2}\\=-8[/tex]
Answer:
x₁ = 2
x₂ = -8
Please Answer Quickly. Got question from Khan Academy
g is a trigonometric function of the form g(x) = acos(bx+c)+d. Below is the graph of g(x). The function has a maximum point at (3pi/4, "-2)" and a minimum point at (2pi, "-14)." Find a formula for g(x). Give an exact expression.
The formula for the given cosine function is:
g(x) = 6cos(0.8(x - 0.75π)) - 8
Hence the coefficients are:
a = 6, b = 0.8, c = -0.75π, d = -8.
What is the cosine function?The cosine function is defined as follows:
g(x) = acos(bx+c)+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2pi/B.c: phase shift.d: vertical shift.In this problem, we have that the maximum value is of -2 and the minimum value is of -14(difference of 12), hence the amplitude is given as follows:
2a = 12.
a = 6.
A standard cosine function with amplitude would vary the between -6 and 6, while this one varies between -14 and -2, hence the vertical shift is of d = -8.
The minimum and maximum values form half the period, hence:
[tex]\frac{2\pi}{B} = 2\pi - \frac{3\pi}{4}[/tex]
[tex]\frac{\pi}{B} = \frac{5\pi}{4}[/tex]
B = 4π/5
b = 0.8π.
The minimum value in the standard function is at x = 0, while at this function is at x = 3π/4, hence the phase shift is of 3π/4 = 0.75π units to the right, that is, c = -0.75π.
Hence the formula for the given cosine function is:
g(x) = 6cos(0.8(x - 0.75π)) - 8
The graph of the function is given at the end of the answer.
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What is the equation?
Answer:
Slope-intercept form: y=3x-5
Step-by-step explanation:
The slope is 3 and the y-intercept is -5. We plug those in for m and b, respectively.
Factor each expression that can be factored. For an expression that cannot be factored into a product of two binomials, explain why. x²+2 x+1 .
The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The expression is given below.
⇒ x² + 2x + 1
Factorize the expression, then the factor of the expression will be
⇒ x² + x + x + 1
⇒ x(x + 1)x + 1(x + 1)
⇒ (x + 1)(x + 1)
⇒ (x + 1)²
The product of two binomials will be (x + 1) and (x + 1).
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b. Measures greater than m ∠ 8
The exterior angle (∠ 5) is larger than either remote interior angle
( ∠ 7 and ∠ 8) then m ∠ 2 > m ∠ 8 and m ∠ 5 > m ∠ 8.
What is meant by Exterior Angle Inequality Theorem?According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles.
The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.
A triangle's exterior angle is always greater than its two remote interior angles.
By the Exterior Angle Inequality Theorem, the exterior angle (∠ 2) is larger than either remote interior angle (∠ 6 and ∠ 8).
Similarly, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).
m ∠ 2 > m ∠ 8 and m ∠ 5 > m ∠ 8 .
Therefore, the correct answer is ∠ 2 and ∠ 5.
The complete question is:
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition
Measures greater than m ∠ 8
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Points that are on the same line are collinear. Use the definition of slope to determine whether the given points are collinear.
(-2,6),(0,2),(1,0)
Using the definition of slope, the points (-2 , 6), (0 , 2), and (1 , 0) are collinear.
Three or more points are said to be collinear if they lie on a single straight line.
To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.
m = (y2 - y1)/(x2 - x1)
Getting the slope of each pair of points:
(-2 , 6) and (0 , 2)
m = (y2 - y1)/(x2 - x1)
m = (2 - 6)/(0 - -2)
m = -4/2
m = -2
(0 , 2), and (1 , 0)
m = (y2 - y1)/(x2 - x1)
m = (0 - 2)/(1 - 0)
m = -2/1
m = -2
(-2 , 6) and (1 , 0)
m = (y2 - y1)/(x2 - x1)
m = (0 - 6)/(1 - -2)
m = -6/3
m = -2
Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is equal with each other, then they are collinear.
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Choose the true statement.
-2/3 = -3/4
-2/3 > -3/4
-2/3 < -3/4
Out of these equations and inequalities, -2/3 > -3/4 is the true statement.
What is an mathematical statement?Briefly, A mathematical statement is a sentence that is either true or false. It may include words and symbols. "The square root of 4 is 5" is an example of a mathematical statement (which is, of course, false).
We use language in mathematics in a very precise way that is sometimes slightly different from everyday use. We'll start by talking about some common disagreements.
In everyday language, we say "either A or B" to mean that one of the two options is correct but not both.
And therefore out of these equations and inequalities
-2/3 = -3/4
-2/3 > -3/4
-2/3 < -3/4
The true statement is -2/3 > -3/4
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-2= 6/7x please help me
Here are two similar pentagons which make up a badge.
width - 3x cm & length - 27cm - large badge
width - x cm & length - (x+3)cm - small badge
Work out the width of the badge.
Answer: 6
Step-by-step explanation:
3x ÷ x = 3
27 ÷ 3 = 9
9 = x + 3
x = 6
I don't which one is the width so I just assume the smaller badge side x cm is the width
Round 3387 to the nearest hundred
Answer:
Step-by-step explanation:
This number would be between 3,300 and 3,400. Which number would 3387 be closer to? 3350 would be right in the middle and 3387would be larger than 3350 so 3387 is closer to 3400.
Find the circumference of circle described. Round to the nearest hundredth.
b. diameter =16 feet
The circumference is the perimeter of a circle or ellipse in geometry.
If the diameter of the circle be 16 feet then the circumference of circle is 50.24
What is meant by circumference of circle?A circle's circumference is defined as the straight line distance around it. In other words, if you open a circle and draw a straight line through it, the length of that line is the circumference of the circle.
The circumference is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were opened up and straightened out to a line segment.
Let the diameter of the circle, d = 16 feet
Circumference of circle, c = πd
Circumference of circle = 2 (3.14)(16)
Circumference of circle = 9.42 × 16
Circumference of circle = 50.24
Therefore, the Circumference of circle be 50.24
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From the grocery store you need to purchase 1/4 lb cheese, 2.5 lbs sliced ham, 4 loaves of bread, 5 bags of potato chips, and 3 containers of salsa. Prices are listed below.
Item
Cost
Cheese
$2.49/ lb
Sliced Ham
$3.29/ lb
Bread
$2.89/ loaf
Potato Chips
$1.95/ ea OR 2 for $3.00
Salsa
$4.15/ container
Use the space below to calculate the initial cost of your purchases.
The initial cost of the purchases is $40.81.
What is the initial cost?The initial cost of the purchases is the sum of the total cost of each items bought. The total cost of each item bought is the product of the size of the items bought and their price.
The mathematical operations that would be used to determine the initial cost are addition and multiplication. Addition is the process of determining the product of two or more numbers. Multiplication is the process of determining the product of two or more numbers.
Total cost of cheese = 1/4 x 2.49 = $0.62
Total cost of Slice ham = 2.5 x 3.29 = $8.23
Total cost of 4 loaves of bread = 4 x 2.89 = $11.56
Total cost of 5 bags of potato chips = (2 x 3) + $1.95 = $7.95
Total cost of Salsa = 3 x 4.15 = $12.45
The initial cost of the purchase : $12.45+ $7.95 + $11.56 + $8.23 + $0.62 = $40.81
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5
ZOOM
16. Mr. Kitchen is purchasing 1.75 pounds of meat that costs $2.80 per
pound. How much change should Mr. Kitchen receive if he gives
the cashier $20.00
PLS!!!! Read the following excerpt.
The poison arrow frog, which resides in the tropical forests of South America, has enough toxicity on its skin that a dart rubbed across the surface of the body can kill a small mammal.
Which of the following sentences uses an ellipsis correctly?
1 "The poison arrow frog … has enough toxicity on its skin … "
2 "The poison arrow frog … has enough toxicity on its skin that a dart rubbed across the surface can kill a small mammal."
3 "The poison arrow frog, which resides in the tropical forests of South America … has enough toxicity on its skin that a dart rubbed across the surface of the body can kill a small mammal."
4 "The poison arrow frog, which resides in the tropic forests of South America, … that a dart rubbed across the surface of the body can kill a small mammal."
Answer:
"The poison arrow frog... has enough toxicity in its skin that a dart rubbed on the surface can kill a small mammal.
Step-by-step explanation:
An ellipsis is a punctuation mark that indicates the interruption of thought and has great power of suggestion. They are also used, for example, in interrupting a character's speech.
The sentence which uses ellipsis correctly is: "The poison arrow frog ... has enough toxicity on its skin ... ".
As per the passage, which defines the ellipsis, that the poison arrow frog who resides in the tropical forest of the South America has enough toxicity on its skin that a dart rubbed across the surface of the body which can kill a small mammals.
The given passage is a missing punctuation marks which defines the ellipsis. In this the thoughts are in the interruption face as well as in the power of suggestion. In this, the suggestions are very important because it is killing the mammals which are resided at the surface.
What is ellipsis?
Ellipsis has number of dots in a sentences or a phrase which define the intention of a passage as well as author. It is also called as punctuation marks with three dots.
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A zebra can run at a constant speed of 0.6 miles per minute. How far can a zebra run in 30 minutes? Choose the equation that could be used to answer this question.
A
d = (0.6)(0.5)
B
30 = 0.6t
C
d = (0.6)(30)
D
0.6 = 30r
Answer:
C
Step-by-step explanation:
hope this works for you :)
Can someone help me!?
Byron agrega una cantidad de 17 / 80 kilogramos por cada pimentero. (Opción correcta: D)
¿Cuánta pimienta pone Byron en cada pimentero?
En este problema debemos interpretar y emplear fracciones para encontrar una cantidad determinada, así como saber utilizar operaciones para obtener el resultado deseado y elegir la opción correcta entre las cuatro disponibles.
Byron tiene 17 / 10 kilogramos de pimienta negra y distribuye equitativamente siete octavas partes de esa pimienta en siete pimenteros. En consecuencia, la cantidad por pimentero es igual a siete octavas partes de la cantidad dispuesta por Byron y dividida a su vez por la cantidad de pimenteros:
x = [(7 / 8) × (17 / 10 kg)] / 7
x = (119 / 80 kg) / 7
x = 17 / 80 kg
Byron agrega una cantidad de 17 / 80 kilogramos por cada pimentero. (Opción correcta: D)
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Write an equation of each line in standard form with integer coefficients.
the line through (-4,2) with slope 3
The equation of the line in standard form passing through the point (-4 , 2) with slope equal to 3 is 3x - y = -14.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values of the slope and the point to set up the equation.
(y - y1) = m(x - x1)
where m = 3 and (x1 , y1) = (-4 , 2)
(y - 2) = 3(x - -4)
y - 2 = 3(x + 4)
y - 2 = 3x + 12
To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.
y - 2 = 3x + 12
3x - y = -2 -12
3x - y = -14
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Jaron received a bonus check for $2,500. He is going to deposit the money into his bank account that receives 5.5% compounded annually. What is Jaron's account balance after 15 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2500\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases} \\\\\\ A=2500\left(1+\frac{0.055}{1}\right)^{1\cdot 15} \implies A=2500(1.055)^{15}\implies A \approx 5581.19[/tex]
Find each sum.
-8+6
Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. 5,8,11,14,17, ........
The next two terms of the given sequence are 20 and 23. And the the formula for finding the nth term of the given sequence is [tex]T_{n+1} = T_{n} + 3[/tex].
According to the given question.
We have a sequence 5, 8, 11, 14, 17...
Since, the first term of the given sequence is 5.
The second term of the given sequence is 8.
The third term of the given sequence is 11.
Here, we can see that each term is 3 more tahn the previous term.
So, the next two terms i.e.
Fifth term = 17 + 3 = 20
Sixth term = 20 + 3 = 23
Therefore, the formula for finding the nth term of the given sequence is given by
[tex]T_{n+1} = T_{n} + 3[/tex]
Hence, the next two terms of the given sequence are 20 and 23. And the the formula for finding the nth term of the given sequence is [tex]T_{n+1} = T_{n} + 3[/tex].
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A circular dwelling has a diameter of 24 feet. What is the area inside of the home? Use 3.14 for TT (pi).
The area inside of the home is [tex]452.16 ft^2[/tex]
Circle closed geometric shape. Technically, a circle is a locus of points moving a fixed distance around a fixed point. A circle is basically a closed curve whose outline is equidistant from the center. The fixed distance from the point is the radius of the circleThe area of a circle is the area occupied by the circle in the two-dimensional plane. This is easily determined using the formula [tex]A=\pi r^2[/tex] . where "r" is the radius of the circle.It is given that circular dwelling has a diameter of 24 feet then , radius will be [tex]r=\frac{24}{2} =12 \ feet[/tex]
Putting r = 12 feet in equation (1) , we get
[tex]A=3.14\times( 12) ^2\\A=3.14\times144\\A= 452.16 ft^2[/tex]
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need help in factorization
Hence , on factorization given equation 2x² + 5xy/3 - 2y² gives ( 2x + 3y)(3x -2y) .
Factorisation of AN algebraical expression means that writing the given expression as a product of its factors.We have given an equation 2x² + 5xy/3 - 2y² .
On simplification , we get
2x² + 5xy/3 - 2y² = 0
6x² + 5xy - 6y² = 0
By splitting in the middle term , we can write 5xy as ( 9 - 4 ) xy
6x² + (9xy - 4xy ) - 6y² = 0
( 6x² + 9xy ) - (4xy + 6y²) = 0
3x ( 2x + 3y) - 2y (2x + 3y ) = 0
( 2x + 3y)(3x -2y) = 0
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Cadence went to the amusement park and paid $14.25 for a souvenir refill cup. Refills cost $1.25 each. If Cadence spent a total of $23, how many refills did she get?
Answer:
Cadence had gotten 7 refills.
Step-by-step explanation:
$14.25 + $1.25r = 23$
23 - 14.25 = 8.75
8.75/1.25 = 7
r = 7
What is a simpler form of 2/x -5 / 6/x - 3} ?
(A) 2-5 x / 6-3 x
(B) 2+5 x / 6-3 x
(C) 2x - 5 / 6 x+3
(D) 6 + 3x / 2 - 5 x
The simpler form of given fraction 2/x -5 / 6/x - 3 is (2 - 5x)/(6 - 3x)
The correct answer is an option (A)
In this question,
we have been given a rational function 2/x -5 / 6/x - 3
We need to simplify given fraction.
2/x -5 / 6/x - 3
= [(2/x) - 5] / [(6/x) - 3]
= [(2 - 5x) / x] / [(6 - 3x) / x]
= (2 - 5x) / (6 - 3x)
Therefore, the simpler form of given fraction 2/x -5 / 6/x - 3 is: (2 - 5x) / (6 - 3x)
The correct answer is an option (A)
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An angle is measured 9 more than two times the measure of its supplement. find the measure of both angles.
Answer:
Step-by-step explanation:
Givens
Let the angle = x
Let it's supplement = 180 - x
Equation
x + 9 = 2*(180 - x) Remove the brackets
Solution
x + 9 = 360 - 2x Add 2x to both sides
x + 2x + 9 = 360 - 2x + 2x Combine
3x + 9 = 360 Subtract 9 from both sides
3x + 9-9 = 360-9 Combine
3x = 351 Divide both sides by 3
3x/3=351/3
x = 117
Answer
Given angle = 117
Supplement = 180 - 117 = 63
5. (a) A surveyor found that a rectangular playground is 20 m long and 13 m wide, corrected to the nearest metre. Suppose the actual length of the playground is x m and the breadth is y m. Write down an inequality for the range of the values of
(i)x
(ii) y
Apply the order of operations to simplify each
expression
4.24-8×2÷4=
A0
B12
C16
D4
The diagram shows a triangle. What is the value of z?
Answer:
z = 53
Step-by-step explanation:
Comment
The three angles of any triangle add up to 180o. There are no exceptions to this rule.
Formula
2z + z - 15 + 36 = 180 Combine like terms on the left.
Solution
3z + 21 = 180 Subtract 21 from both sides
3z + 21 - 21 = 180 - 21 Combine
3z = 159 Divide both sides by 3
z = 53
At a school recess, there needs to be a ratio of 2 adults for every 24 children on the playground. how many adults are needed if there are 72 children? *
Answer: 6
Step-by-step explanation: 2=24 4=48 6=72
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In the first half football season, Marco ran 4 plays for a gain of 60 yards. During the second half of the season, Marco was responsible for 6 penalties resulting in a loss of 80 yards. What was his total yardage for his football season?
Marco ran 4 plays for a total of 60 yards throughout the first half of the football season. Marco committed 6 penalties that cost his team 80 yards in the second half of the season. His total 160 yardage for his football season.
Given that,
Marco ran 4 plays for a total of 60 yards throughout the first half of the football season.
Marco committed 6 penalties that cost his team 80 yards in the second half of the season.
We have to calculate his total season yardage in football.
In the 1st half of the football season, Marco ran 4 plays for a total of 60 yards.
4[tex]\times[/tex]60=240
In the 2nd half of football season, Marco committed 6 penalties that cost his team 80 yards.
That is.
240-80=160
Therefore, his total 160 yardage for his football season.
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Mark had been watching the calories he consumes each day. On the first day, he consumed 1500 calories, then 1450 calories the next day, and 1400 calories the day after that .
Answer:
His calories go down 50 calories every day. Hope it helps!
Step-by-step explanation:
