2y^2- 14y+ 20
By splitting the middle term:
2y^2 -10y -4y +20
By taking the common outside:
2y(y-5) -4(y-5)
=(2y-4)(y-5)
=2(y-2)(y-5)
Therefore D is the right answer
Answer:
D
Step-by-step explanation:
Given
2y² - 14y + 20 ← factor out 2 from each term
= 2(y² - 7y + 10)
To factor the quadratic
Consider the factors of the constant term (+ 10) which sum to give the coefficient of the y- term (- 7)
The factors are - 2 and - 5, since
- 2 × - 5 = 10 and - 2 - 5 = - 7, so
y² - 7y + 10 = (y - 2)(y - 5) and
2y² - 14y + 20 = 2(y - 2)(y - 5) → D
Quadrilateral ABCD is inscribed in a circle with m<A = (x2)°, m<B = (7x - 10)°,
and
m<C = (3x)°.
What is m<D?
Answer:
106°
Step-by-step explanation:
A quadrilateral inside a circle is a cyclic quadrilateral.
It means that the angles opposite are supplementary (add up to 180).
If we draw the quadrilateral ABCD, the angles A and C are supplementary and the angles B and D are supplementary.
Since we know A and C, we can write:
A + C = 180
x^2 + 3x = 180
x^2 +3x - 180 = 0
(x+15)(x-12) = 0
x= -15, or x = 12
Now, if we put x = -15, some angles become negative, so we disregard it and take x = 12.
Now finding B:
B = 7x - 10
B = 7(12) - 10
B = 74
We also know that B + D = 180, so:
B + D = 180
74 + D = 180
D = 180 - 74 = 106
Plz help me with this
Answer: D) at least 6mm
Step-by-step explanation:
95% confidence is 2 standard deviations.
5mm + 2(0.5) = 5 + 1 = 6
The oysters must be at least 6 mm
what is x in -2-3x=19
Answer:
x=-7
Step-by-step explanation:
Since you are solving for x, you need to work backwards. Add 2 to both sides: -2 and 2 cancel out, and 19 plus 2 is 21. Isolate the x by dividing both sides by -3. -3 cancels out, and 21 divided by -3 is -7.
Answer:
-7
Step-by-step explanation
−2−3x=19
−2+−3x=19
−3x−2=19
Step 2: Add 2 to both sides.
−3x−2+2=19+2
−3x=21
Step 3: Divide both sides by -3.
−3x
−3
=
21
−3
x=−7
What is the standard deviation of the data set?
7,3,4, 2, 5, 6,9
Answer:
2.4103
Step-by-step explanation:
The first step in evaluating the sample standard deviation of a data set involves the determination of the sample mean.
The sample mean is simply the average value of the data set;
sample mean = [tex]\frac{7+3+4+2+5+6+9}{7}=5.1429[/tex]
The next step is to evaluate the sum of the squares of deviations from the mean;
sum of squares of deviation = [tex](7-5.1429)^{2}+(3-5.1429)^{2}+(4-5.1429)^{2}+(2-5.1429)^{2}+(5-5.1429)^{2}+(6-5.1429)^{2}+(9-5.1429)^{2}=34.8571[/tex]
We then divide the sum of squares of deviation by (n-1) where n is the sample size to obtain the sample variance;
variance = [tex]\frac{34.8571}{7-1}=5.8095[/tex]
The standard deviation is simply the square-root of variance;
[tex]\sqrt{5.8095}=2.4103[/tex]
find the equations of the tangents to the curve y= x(x-1)(x+2) at the points where the curve cuts the x axis
First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have
[tex]x(x-1)(x+2) = 0 \iff x=0\ \lor\ x-1=0\ \lor\ x+2=0[/tex]
Which means that the roots are
[tex]x=0\ \lor\ x=1\ \lor\ x=-2[/tex]
Next, we can expand the function definition:
[tex]y = x(x-1)(x+2) = x^3 + x^2 - 2x[/tex]
In this form, it is much easier to compute the derivative:
[tex]y' = 3x^2+2x-2[/tex]
If we evaluate the derivative in the points of interest, we have
[tex]y'(-2) = 6,\quad y'(0)=-2,\quad y'(1)=3[/tex]
This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation
[tex]y-y_0=m(x-x_0)[/tex]
is what we need. The three lines are:
[tex]y-0=6(x+2) \iff y = 6x+12[/tex] This is the tangent at x = -2
[tex]y-0=-2(x-0) \iff y = -2x[/tex] This is the tangent at x = 0
[tex]y-0=3(x-1) \iff y = 3x-3[/tex] This is the tangent at x = 1
Given the following diagram, find the missing measure.
Answer:
∠4 = a + b
Step-by-step explanation:
Given ∠2 = a and ∠3 = b
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for ∠1
∠1 = 180 - (a + b) = 180 - a - b
Now
∠1 and ∠4 form a straight angle and are supplementary, hence
∠4 = 180 - (180 - a - b) = 180 - 180 + a + b = a + b
Francis teaches the piano. He charges each student an enrollment fee of $100 plus $15 per hour of piano lessons. The average cost of lessons for a student per hour is $25.
If h represents the number of hours a student spends in lessons, which equation can be used to find the value of h?
Answer:
y=15x+100
Step-by-step explanation:
increases by 15, 100 is starting free
Karoline has 16 marbles oneeight of them are blue how many of coroliens marbles are blue
Answer:
2
Step-by-step explanation:
Total Marbles = 16
Fractional amount blue marbles = 1/8
Number of blue marbles = fractional amount * Total marbles
Number of blue marbles = 1/8 * 16
Number of blue marbles = 2
Answer: 2
Step-by-step explanation:
16 divided by 1/8 = 2
The formula gives the height of an object in free fall at time t and acceleration g.
[tex]h = \frac{1}{2}gt^{2} [/tex]
Solve for t.
[tex]t = (2gh)^{2} [/tex]
[tex]t = 2 \sqrt{gh} [/tex]
[tex]t = \frac{ \sqrt{gh} }{2} [/tex]
[tex]t = \frac{ \sqrt{2hg} }{g} [/tex]
t must equal √2h/g but I don't see that in the choices above
Answer:
t=2hg√g
Step-by-step explanation:
took the test!
Given the line 2x - 3y - 5 = 0, find the slope of a line that is perpendicular to this line.
wlw.
ооо
win
wiw
Answer:
The slope of a line that is perpendicular to the given line is [tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Solve for "y" from the equation of the line [tex]2x - 3y - 5 = 0[/tex]:
[tex]2x - 3y - 5 = 0\\\\-3y=-2x+5\\\\y=\frac{-2}{-3}x+\frac{5}{-3}\\\\y=\frac{2}{3}x-\frac{5}{3}[/tex]
You can observe that the slope of this line is:
[tex]m=\frac{2}{3}[/tex]
By definition, the slopes of perpendicular lines are negative reciprocal, then, the slope of a line that is perpendicular to the give line, is
[tex]m=-\frac{3}{2}[/tex]
which equation can you use to solve for x
As for a specific equation, I could not say. However, I can tell you how to find x!
The first thing to remember is that a straight line has a 180 degree angle.
You see on the bottom side that we have a 146 degree angle. Now look at the top side. Look closely, and you will see that the two sides are actually identical!
Don't see it? Look at the line on top between x and 56, and imagine it is not there. You see that we actually have the same 146 degree angle, just flipped right side up!
However, this angle does not say 146, but makes an extra line between them with x and 56. This means that x + 56 equals 146!
So we can find x by subtracting 56, from 146, which is... 90!
There is a mound of g pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel are added to the mound. Two orders of 900 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,500 pounds of gravel. Write the equation that best describes the situation.
Answer:
The equation that best describes the situation is:
[tex]g +400 -1800 = 1,500[/tex]
Step-by-step explanation:
The initial amount of gravel is g.
[tex]g[/tex]
Then we know that 400 pounds are added
[tex]g +400[/tex]
Two orders of 900 pounds are sold and the gravel is removed from the mound. This is:
[tex]g +400 -2 * 900[/tex]
[tex]g +400 -1800[/tex]
At the end of the day, the mound has 1,500 pounds of serious. This is:
[tex]g +400 -1800 = 1,500[/tex]
The equation that best describes the situation is:
[tex]g +400 -1800 = 1,500[/tex]
And
[tex]g= 1500 +1800 - 400\\\\g=2900[/tex]
The equation that best describes the given situation is[tex]\rm g + 400 - (2\times 900) = 1500[/tex] and this can be determined by forming the linear equation with the help of given data.
Given :
Throughout the day, 400 pounds of gravel are added to the mound.Two orders of 900 pounds are sold and the gravel is removed from the mound.At the end of the day, the mound has 1,500 pounds of gravel.Let the initial amount of gravel be 'g'. Then after the addition of 400 pounds of gravel, the total gravel becomes:
= g + 400
Given that two orders of 900 pounds are sold and the gravel is removed from the mound so, the total gravel now becomes:
[tex]\rm = g + 400 - (2\times 900)[/tex]
= g + 400 - 1800
= g - 1400
At the end of the day, the mound has 1,500 pounds of gravel, that is:
g - 1400 = 1500
g = 1500 + 1400
g = 2900
Therefore, the equation that best describe the given situation is:
g + 400 - 1800 = 1500
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Given right triangle XYZ, which correctly describes the locations of the sides in relation to ∠Y?
Answer:
Step-by-step explanation: a is adjacent, b is opposite, c is the hypotenuse
Answer:
D
Step-by-step explanation:
What is the volume of the pyramid 7x7x8
Answer:
The volume of the pyramid is [tex]130\frac{2}{3}\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the base
H is the height of the pyramid
Find the area of the base B
In this problem we have a square base
[tex]B=7^{2} =49\ units^{2}[/tex]
we have
[tex]H=8\ units[/tex]
substitute
[tex]V=\frac{1}{3}(49)(8)=\frac{392}{3}\ units^{3}[/tex]
Convert to mixed number
[tex]\frac{392}{3}=\frac{390}{3}+\frac{2}{3}=130\frac{2}{3}\ units^{3}[/tex]
you do length x width x be aight divided by 3 to get 392/3
Please help and thank you
Answer:
A
Step-by-step explanation:
Define each of the terms.
f(x) is the total level of radioactivity.
x is the total number of weeks.
[tex]\frac{1}{2}[/tex] is the weekly decay factor.
30 is the initial level of radioactivity.
Express 0.6239 as a fraction.
The value of 0.6239 as a fraction or proportion is
A fraction is a mathematical expression that represents a part or a division of a whole. It is used to represent numbers that are not whole numbers or integers. A fraction consists of two components:
1. Numerator: The numerator is the number on the top of the fraction. It represents the quantity or part of the whole being considered.
2. Denominator: The denominator is the number at the bottom of the fraction. It represents the total number of equal parts into which the whole is divided.
Multiply and divide 0.6239 by 10000,
0.6239 = [tex]\frac{0.6239}{10000} \times[/tex] 10000
= [tex]\frac{6239}{10000}[/tex].
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A dog on intravenous fluids has received 40% of the 1000 mL initially in the i.v. bag. How many mL has it received?
Answer:
The dog should receive 400 mL of the i.v. bag.
Step-by-step explanation:
40% x 1000 = 400
Answer:
The dog received 400mLStep-by-step explanation:
Givens
A dog received 40% of 100 mL of intravenous fluids.To know how many mL the dog received, we just need to find the 40% of 100 mL.
We know that 40% equals 0.40, then we multiply it
[tex]0.40(1000mL)=400mL[/tex]
Therefore, the dog received 400mL
Can 2.5, the square root of 18 and 5 form a right triangle?
Answer:
Step-by-step explanation:
if 2.5, sqrt(18), and 5 make up the sides of a right triangle, then they must satisfy A^2+B^2=C^2, where C is the longer side (hypotenuse).
In this case, 5 is the greater of the 3, so let's see if it satisfies our equation:
2.5^2+sqrt(18)^2=5^2
-> 6.25+18 = 24.25 =/= 25
-> Therefore the answer is a resounding no.
The numbers 2.5, the square root of 18, and 5 cannot form a right triangle. This is determined via the Pythagorean Theorem, which these numbers do not satisfy when squared and added together.
Explanation:In the context of mathematics, specifically geometry, a set of numbers can form a right triangle if they adhere to the Pythagorean Theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a² + b² = c².
Here, let's test the three numbers you've given: 2.5, √18, and 5. First, square each of the values: 2.5² = 6.25, (√18)² = 18, and 5² = 25.
If we consider 2.5 and √18 as sides a and b, and 5 as side c (the hypotenuse), the Pythagorean theorem would look like this: 6.25 + 18 = 24.25 ≠ 25. Thus, these numbers cannot form a right triangle because they do not satisfy the Pythagorean Theorem.
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solve for b. -1/3b = 9
Answer:
B=-27
Step-by-step explanation:
Answer:
-27
-1/3b=9
Divide both sides by -1/3 to get b by itself
-1/3b=9
/-1/3 /-1/3
b=-27
Really need help with this!!!
Answer:
Principal Amount= $500
Formula for compound interest:
[tex]A = p (1 + \frac{r}{n} )^{nt}[/tex]
Formula for simple interest:
A = p(1 + r(t) )
Shelly invested $1,000 at a rate of 5% interest per year. Which equation models the value of the investment, V, after t years?
Answer:
Step-by-step explanation:
You don't say whether this is compound interest or simple interest.
I will assume it's compounding that interests you.
The appropriate formula is
A = P(1 + r)^t, where r is the interest rate as a decimal fraction, t is the time in years, and P is the original amount. Thus:
A = $1000·(1 + 0.05)^t, or A = $1000·(1.05)^t
Please note: There were apparently possible answer choices. Next time, please be sure to list such choices. Thank you.
Final answer:
The equation modeling the value of an investment, V, after t years, for an initial investment of $1,000 at a 5% annual interest rate is V = 1000(1 + 0.05)^t, incorporating the principles of compounding interest.
Explanation:
The question asks about the equation modeling the value of an investment, V, after t years, given an initial investment of $1,000 at a 5% annual interest rate. Using the formula for the future value of a single sum, V = P(1 + r)^t, where P is the principal amount ($1,000), r is the annual interest rate (5% or 0.05), and t is the number of years, we can determine that the equation modeling the value of the investment is V = 1000(1 + 0.05)^t. This formula is applied to calculate the future value of the investment, taking into account the compounding interest over a period t years.
A principal of $3300 is invested at 8.5% interest, compounded anually. How much will the investment be worth after 11 years? Round your answer to the nearest dollar. Please help..
Answer:
[tex]\boxed{\$8378}[/tex]
Step-by-step explanation:
The formula for compound interest is:
A = P(1 + r)ⁿ
Data:
P = 3300
APR = 8.5 %
t = 11 yr
Calculations:
n = 11 × 12 = 132
r = 0.085/12 = 0.007 083
A = 3300(1 + 0.007 083)¹³²
= 3300 × 1.007 083¹³²
= 3300 × 2.5539
= 8378
[tex]\text{The investment will be worth }\boxed{\mathbf{\$8378}}[/tex]
Starting at the top of a square pyramid and make a vertical slice cutting pyramid in half what is the shape of the newly-exposed section
I really appreciate it if you can check my answer. I I think it’s a triangle.
Answer: Triangle
Step-by-step explanation: If you cut it vertically, the base is changed into a triangle.
Hope this helps!
which linear function has the same y -intercept as the one that is represented by the graph ?
Answer:
The answer is C: y = 2x + 3
Step-by-step explanation:
I took the test
Linear function is, y = 2 x + 3.
What does the y-intercept of this relationship represent?The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x. The y-intercept indicates the y-value when the x-value is 0.Which is a y-intercept of the graphed function?The y -intercept of a graph is the point where the graph crosses the y -axis. (Because a function must pass the vertical line test , a function can have at most one y -intercept . ) The y -intercept is often referred to with just the y -value.How do you find the y-intercept of a graph?On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.According to the question:
From the points we can see the y-intercept of the line is 3 as it passes through point (0, 3).
y = 2 x - 4
y-intercept is -4 ≠ 3, incorrect.
y = 2 x - 3
y- intercept is -3 ≠ 3, incorrect.
y = 2 x + 3
y- intercept is 3 = 3, correct.
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Apply the distributive property to factor out the greatest common factor.
30+42=
Answer:
[tex]30+42=6(5+7)[/tex]
Step-by-step explanation:
Let [tex]a,b,c\in \mathbb R[/tex], according to the distributive property:
[tex]a(b+c)=ab+ac[/tex]
The prime factorization of 30 is
[tex]30=2\cdot 3\cdot 5[/tex]
The prime factorization of 42 is
[tex]42=2\cdot 3\cdot 7[/tex]
The Greatest common factor is [tex]2\times 3=6[/tex]
[tex]\implies 30+42=6\times5+6\times7[/tex]
[tex]\implies 30+42=6(5+7)[/tex]
Answer:
Step-by-step explanation:
6(5+7
(a + b - c )(a + b + c )
If you are looking for the expanded version, this is it. It is also possible to group either an a from (a^2 + 2b) or a b from (2ab + b^2). Hope this helps!
Answer:
[tex](a+b-c)(a+b+c)=a^2+2ab+b^2-c^2[/tex].
Step-by-step explanation:
We want to expand: [tex](a+b-c)(a+b+c)[/tex].
We use the distributive property to obtain:
[tex](a+b-c)(a+b+c)=a(a+b+c)+b(a+b+c)-c(a+b+c)[/tex].
We now expand to get:
[tex](a+b-c)(a+b+c)=a^2+ab+ac+ab+b^2+bc-ac-bc-c^2[/tex].
This finally simplifies to
[tex](a+b-c)(a+b+c)=a^2+2ab+b^2-c^2[/tex].
What is the amplitude, period, and phase shift of f(x) = −4 sin(2x + π) − 5?
Amplitude = −4; period = 2π; phase shift: x = -pie/2
Amplitude = −4; period = π; phase shift: x = pie/2
Amplitude = 4; period = π; phase shift: x = -pie/2
Amplitude = 4; period = 2π; phase shift: x = pie/2
Answer:
Amplitude = -4; period = π; phase shift: x = π/2
Step-by-step explanation:
* Lets revise the trigonometry translation
- If the equation is y = A sin (B(x + C)) + D
* A is the amplitude
- The amplitude is the height from highest to lowest points and
divide the answer by 2
* The period is 2π/B
- The period is the distance from one peak to the next peak
* C is the horizontal shift (phase shift)
- The horizontal shift is how far the function is shifted to left
(C is positive) or to right (C is negative) from the original position.
* D is the vertical shift
- The vertical shift is how far the function is shifted vertically up
(D is positive) or down (D is negative) from the original position.
* Now lets solve the problem
∵ f(x) = A sin (B(x + C)) + D
∵ f(x) = -4 sin (2x + π) - 5 ⇒ take 2 from the bract (2x + π) common factor
∴ f(x) = -4 sin 2(x + π/2) - 5
∴ A = 4 , B = 2 , C = π/2 , D = -5
∵ A is the amplitude
∴ The amplitude is -4
∵ The period is 2π/B
∴ The period = 2π/2 = π
∵ C is the horizontal shift (phase shift)
∴ The phase shift π/2 (to the left)
* Amplitude = -4; period = π; phase shift: x = π/2
The amplitude of the function f(x) = −4 sin(2x + π) − 5 is 4, its period is π, and it has a phase shift of x = -π/2.
Explanation:The amplitude of a trigonometric function like f(x) = −4 sin(2x + π) − 5 is the coefficient in front of the sine function which determines the maximum and minimum value of the function's graph. In this case, the amplitude is the absolute value of -4, which is 4.
The period of the function is found by taking 2π divided by the coefficient of x inside the sine function, which is 2 in this case, yielding a period of π.
The phase shift of the function is determined by solving the equation 2x + π = 0 for x, which gives us a phase shift of x = -π/2. Therefore, the correct description is amplitude of 4, a period of π, and a phase shift of x = -π/2.
Find all solutions of the equation in the interval [0, 2 pi) 2 cos0-1=0
Answer:
θ = π/3, 5π/3
Step-by-step explanation:
2 cos θ - 1 = 0
2 cos θ = 1
cos θ = 1/2
θ = π/3, 5π/3
ANSWER
EXPLANATION
The given trigonometric equation is:
[tex]2 \cos( \theta) - 1 = 0[/tex]
[tex] \implies \: 2 \cos( \theta) = 1[/tex]
[tex]\implies \: \cos( \theta) = \frac{1}{2} [/tex]
The cosine ratio is positive in the first and fourth quadrants.
In the first quadrant,
[tex]\theta = \cos ^{ - 1} ( \frac{1}{2}) [/tex]
[tex]\theta = \frac{\pi}{3} [/tex]
In the fourth quadrant,
[tex]\theta =2 \pi - \cos ^{ - 1} ( \frac{1}{2}) [/tex]
[tex]\theta =2 \pi - \frac{\pi}{3} [/tex]
[tex]\theta = \frac{5\pi}{3} [/tex]
Therefore on the interval, [0,2π] the solution to the given trigonometric equation is:
[tex]\theta = \frac{\pi}{3} \: and \: \frac{5\pi}{3} [/tex]
M(4, 2) is the midpoint of RS. The coordinates of S are (6, 1). What are the coordinates of R?
Answer:
(2, 3)
Step-by-step explanation:
There is an easy way to solve this.
Set it up like this, where one end point is on top of the midpoint.
To get from 6 to 4, you subtract 2. So subtract 2 from 4 (that's where the x coordinate comes from). To get from 1 to 2, you add 1. So add 1 to 2 (that's where the y coordinate comes from)
If this sounds confusing, please comment and I'll help ASAP.
Sarah got 16 out of 20 questions correct on a math quiz is each question was worth the same number of pints and the test was worth 50 points total, what was sarah’s score
The total points could be 50.
It has 20 questions, so each question is worth: 50/20 = 2.5 points each.
She got 16 correct, so her score was: 16 x 2.5 = 40