Answer:
1) [tex]x=\dfrac{5}{2}[/tex]
2) [tex]t_1=-1[/tex] and [tex]t_2=6[/tex]
3) (0,12)
4) [tex]\left(\dfrac{5}{2},\dfrac{49}{2}\right)[/tex]
Step-by-step explanation:
The function [tex]h(t) =-2t^2 + 10t + 12[/tex] represents the height (h) of the ball after t seconds.
Find the vertex of the parabola:
[tex]t_v=-\dfrac{b}{2a}=-\dfrac{10}{2\cdot (-2)}=\dfrac{5}{2}\\ \\h_v=h\left(\dfrac{5}{2}\right)=-2\cdot\left(\dfrac{5}{2}\right)^2+10\cdot \dfrac{5}{2}+12=-2\cdot \dfrac{25}{4}+25+12=-\dfrac{25}{2}+37=\dfrac{49}{2}[/tex]
Hence, the vertex of the function is at point [tex]\left(\dfrac{5}{2},\dfrac{49}{2}\right).[/tex]
The axis of symmetry of the function is vertical line which passes through the vertex, so its equation is
[tex]x=\dfrac{5}{2}[/tex]
To find y-intercept, equat t to 0 and find h:
[tex]h=-2\cdot 0^2+10\cdot 0+12=12[/tex]
Hence, y-intercept is at point (0,12)
To find the roots of the quadratic finction, equate h to 0 and solve the equation for t:
[tex]h=0\Rightarrow -2t^2+10t+12=0\\ \\t^2-5t-6=0\ [\text{Divided by -2}]\\ \\D=(-5)^2-4\cdot 1\cdot (-6)=25+24=49\\ \\t_{1,2}=\dfrac{-(-5)\pm \sqrt{49}}{2\cdot 1}=\dfrac{5\pm 7}{2}=6,\ -1[/tex]
Therefore, two roots are [tex]t_1=-1[/tex] and [tex]t_2=6[/tex]
Given the two similar triangles, find y.
A= y = 4
B= y = 5
C= y = 6
D= y = 8
giving brainlist to whoever answers with work.
Answer:
The correct answer is B. y = 5
Step-by-step explanation:
Let's recall that two are triangles are similar when its side lengths are proportional. That is in our case, if Δ ABC is similar to Δ DEF , then the following equation holds:
EF/BC = DF/AC
Replacing with the real values:
6/12 = y/10
Cross multiplication:
12 * y = 10 * 6
12y = 60
y = 60/12
y = 5
The correct answer is B. y = 5
Need help with number 6
Answer:
Step-by-step explanation:
Use substitution to solve the system of equations.
y + x = 3
y = 1.5x + 1
Answer:
x=0.8, y=2.2 (0.8, 2.2).
Step-by-step explanation:
y+x=3
y=1.5x+1
-------------
1.5x+1+x=3
2.5x=3-1
2.5x=2
x=2/2.5
x=0.8
y+0.8=3
y=3-0.8
y=2.2
To solve the given system of equations by substitution, we substitute the second equation into the first, solve for x, and then substitute x back into the second equation to solve for y, which yields x=0.8 and y=2.2 as the solution.
Explanation:To solve the system of equations using substitution, we start by isolating one variable in one of the equations. Here, the second equation already gives us y in terms of x: y = 1.5x + 1.
Next, we substitute this expression for y into the first equation y + x = 3. This gives us:
(1.5x + 1) + x = 3Combine like terms to solve for x:
2.5x + 1 = 32.5x = 2x = 0.8Now that we have the value of x, we can find the value of y by substituting x back into the equation y = 1.5x + 1:
y = 1.5(0.8) + 1y = 2.2Hence, the solution to the system of equations is x = 0.8 and y = 2.2.
As a final step, you may want to check your solution by plugging the values back into the original equations to confirm that they satisfy both equations.
Find the value of y for the following system of equations. x + y = 7 x + y = 7 7 2
The value of y is 28
y = 28
Erik has $50 in a savings account that earns
5% annually. The interest is not compounded. How much will he have in 1 year?
Answer:
[tex]\$52.50[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=1\ year\\ P=\$50\\ A=?\\r=5\%=5/100=0.05[/tex]
substitute in the formula above
[tex]A=50(1+0.05*1)[/tex]
[tex]A=50(1.05)[/tex]
[tex]A=\$52.50[/tex]
Write a polynomial equation with roots 5 and -9i. X^3-?x^2+?X-?=0
Answer:
x³ - 5x² + 81x - 405 = 0
Step-by-step explanation:
Complex roots occur in conjugate pairs.
Thus given x = - 9i is a root then x = 9i is also a root
The factors are then (x - 5), (x - 9i) and (x + 9i)
The polynomial is the the product of the roots, that is
f(x) = (x - 5)(x - 9i)(x + 9i) ← expand the complex factors
= (x - 5)(x² - 81i²) → note i² = - 1
= (x - 5)(x² + 81) ← distribute
= x³ + 81x - 5x² - 405, thus
x³ - 5x² + 81x - 405 = 0 ← is the polynomial equation
The required polynomial equation is x³ - 5x² + 81x - 405 = 0 with roots 5 and -9i.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
As we know that complex roots occur in conjugate pairs.
Thus given x = - 9i is a root then x = 9i is also a root
The factors are then (x - 5), (x - 9i) and (x + 9i)
The polynomial is the product of the roots, that is
f(x) = (x - 5)(x - 9i)(x + 9i)
Expand the complex factors in the above equation
f(x) = (x - 5)(x² - 81i²) [∵ i² = - 1]
f(x) = (x - 5)(x² + 81)
f(x) = x³ + 81x - 5x² - 405
This is equating to zero.
f(x) = 0
Thus, the required polynomial is x³ - 5x² + 81x - 405 = 0
Learn more about the polynomial here:
brainly.com/question/11536910
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What is the largest source of water on earth?
Answer:
Seawater
Step-by-step explanation:
I just took a quiz on this and it said the correct answer is sea water
What is the following product? (Square root 14 - square root 3) (square root 12 + square root 7)
Answer:
Step-by-step explanation:
The product of this expression is option (A) (2√42 + 7√2 - 6 - √21) is the correct answer.
What is simplification of an expression?Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. It involves, multiply out the brackets and then simplify the resulting expression by collecting the like terms.
For the given situation,
The expression is [tex](\sqrt{14} -\sqrt{3})( \sqrt{12} +\sqrt{7} )[/tex]
⇒ [tex]\sqrt{14}\sqrt{12} +\sqrt{14} \sqrt{7} -\sqrt{3} \sqrt{12} -\sqrt{3} \sqrt{7}[/tex]
⇒ [tex]\sqrt{168}+\sqrt{98}-\sqrt{36}-\sqrt{21}[/tex]
⇒ [tex]\sqrt{2^{2}(42) } +\sqrt{7^{2}(2) } -\sqrt{6^{2} }-\sqrt{21}[/tex]
⇒ [tex]2\sqrt{42 } +7\sqrt{2 } -6-\sqrt{21}[/tex]
Hence we conclude that the product of this expression is option (A) (2√42 + 7√2 - 6 - √21) is the correct answer.
Learn more about simplification of an expression here
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. A friend opens a savings account by depositing $1000. He deposits an
additional $75 into the account each month.
a. What is a rule that represents the amount of money in the account as an
arithmetic sequence?
b. How much money is in the account after 18 months? Show your work.
Answer:
the rule is:
75x + 1000
Step-by-step explanation:
after 18 months
plug 18 in for x.
75(18) + 1000
= 1350
1350 + 1000
= 2350
$2350 after 18 months
Answer:
Part (A) 1000+(n-1)75
Part (B) 2,275
subtract the 1 it's not 2350
Step-by-step explanation:
7x-7(x+6)=10
B=infinite
C=no solution
D=x=2/7
A=3/5/7
Answer:
No solution
Step-by-step explanation:
we have
[tex]7x-7(x+6)=10[/tex]
Solve for x
Apply distributive property left side
[tex]7x-7x-42=10[/tex]
Combine like terms left side
[tex]-42=10[/tex] ----> is not true
therefore
The equation has no solution
Select the four choices below that are equal to 2 × 3 × 4.
Final answer:
2 × 3 × 4, which equals 24.
Explanation:
To find equivalent expressions, we need to think about numbers that can multiply together to reach 24, while also keeping in mind the properties of operations and exponents.
One way is to use exponents. For instance, since 2 × 2 × 2 equals 23 or 8, and 3 × 4 equals 12, multiplying these two results gives us 8 × 12 which is also 24.We could also factor the number differently. Considering 2 × 2 × 2 × 3 can be rearranged to get (22 × 2) × 3 which simplifies to 4 × 2 × 3 and again equals 24.Another expression is taking multiples of 4 such as 4 × 6 which is the same as (2 × 2) × (2 × 3), resulting in the original 24.Last but not least, we can use the distributive property to create 2(3+9) since 3 + 9 equals 12, and 2 × 12 is 24.PLZ HELP!!! Katrina is solving the equation x-2(x+3)=4(2x+3)-x(x-4) . Which equivalent equations might Katrina use? Check all that apply.
Answer:
X2-13X-18=0
Step-by-step explanation:
x-2(x+3)=4(2x+3)-x(x-4)
Multiply through the equations
x-2x-6=8x+12-x2+4x
Equate all to zero
x-2x-6-8x-12+x2-4x=0
x2-4x+x-2x-8x-6-12
x2-13x-18=0
Answer:
A. x minus 2 x minus 6 = 8 x + 12 minus x minus 4
E. Negative x minus 6 = 7 x + 8
Step-by-step explanation:
i took the unit test review on edg
Alexis wants to figure out the price to charge friends for the blu-rays. She doesn’t want to make money at this point since it is a brand new business, but does want to cover her costs. Suppose Alexis created 50 blu-rays. What is the cost of producing those 50 blu-rays? How much is it for each blu-ray?
B(x) = 1250 +1.75x
Answer:
The cost of producing 50 blu-rays will be $1337.5
Each blu-rays must be sold of $26.75
Step-by-step explanation:
The cost of producing x number of blu-rays is given by the relation
B(x) = 1250 + 1.75x ........... (1)
Therefore, the total cost for producing 50 blu-rays will be
B(50) = 1250 + 1.75 × 50 = $1337.5 (Answer)
Now, Alexis does not want to make a profit by selling the blu-rays to her friends and wants just to cover her costs.
Therefore, the selling price of 50 blu-rays will be $1337.5.
Hence, each blu-rays must be sold of [tex]\frac{1337.5}{50} = 26.75[/tex] dollars. (Answer)
4/7 - -4/7
It’s confusing I calculated it but there’s no answer so I really need help
Answer:
Step-by-step explanation:
4/7 - (-4/7) = 4/7 + 4/7 = 8/7 or 1 1/7......a negative times a negative is a positive...so those two negatives turn into a positive...so ur basically just adding them
Solve 3x + 6 = 34. need anwser asap
A.-2
B.4
C.6
D.10
The correct solution for the equation 3x + 6 = 34 is x = 9.33 (repeating). The provided options do not match this solution, indicating an error in the given choices.
Explanation:To solve the equation 3x + 6 = 34, start by subtracting 6 from both sides to isolate the term with the variable x on one side. You get 3x = 28. Next, divide both sides by 3 to solve for x, which gives you x = 28 / 3 or 9.33 (repeating). None of the provided options A, B, C, or D matches the solution, indicating a potential error in the question or the options provided.
Which of the following expressions are equivalent to 8 3/2
Answer:
19/2
Step-by-step explanation:
8 3/2=19/2
Answer:
19/2
Step-by-step explanation:
Mason has an offer to buy an item with a sticker price of $14,800 by paying
8530 a month for 36 months. What interest rate is Mason being offered?
A 12.8%
B. 25.7%
C6.4%
d8,5%
Answer:
8.83%
Step-by-step explanation:
Using compound interest formula
A = P ( 1+ r) ^t where A = amount = 530 × 36 = $ 19080, P = the amount of the loan = $ 14800, t = 36 / 12 = 3 years
substitute the values into the equation
19080 = 14800 (1 + r) ^3
19080 / 14800 = (1 + r) ^3
1.2892 = (1 + r) ^3
∛(1.2892) = 1 + r
1.0884 = 1 + r
r = 1.0884 - 1 = 0.0884 × 100 = 8.83%
Answer:
d 8,5%, the most probable, provided the error in the question is confirmed!!!
Step-by-step explanation:
Mason has an offer to buy an item with a sticker price of P= $14,800.
He is to pay $8530 a month for 36 months.
Total amount paid by Mason will be
$8530*36= $307,080
This will be very outrageous compared to the sticker price!!!
If we presume he is paying yearly 8530 for 36 months or 3 years.
Then total amount paid will be 8530*3 = $25590
Also very high in my opinion.
Perhaps the dollar sign was wrongly typed as '8' in the question and he pays only $530 monthly,
Then the total amount paid will be $19,080
This is quite reasonable.
If the interest rate is compounded for n (n=3, 36 months = 3 years)
years, thus
19080= ((P*(1+i)^n) , meaning
19080 =((14800(1+i)^3), which when evaluated yields
i=8.8%
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2), and (1, negative 1). Everything to the right of the line is shaded. The solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution? (0, 2) (2, 0) (1, −2) (−2, 1)
Answer:
(2,0)
Step-by-step explanation:
we know that
If a ordered pair is a solution of the inequality, then the ordered pair must satisfy the inequality
we have
[tex]y > -3x+2[/tex]
Substitute the value of x and the value of y of each point in the inequality and then compare the results
case a) (0, 2)
[tex]2 > -3(0)+2[/tex]
[tex]2 > 2[/tex] ----> is not true
so
the point not satisfy the inequality
therefore
The point is not a solution of the inequality
case b) (2,0)
[tex]0 > -3(2)+2[/tex]
[tex]0 > -4[/tex] ----> is true
so
the point satisfy the inequality
therefore
The point is a solution of the inequality
case c) (1, -2)
[tex]-2 > -3(1)+2[/tex]
[tex]-2 > -1[/tex] ----> is not true
so
the point not satisfy the inequality
therefore
The point is not a solution of the inequality
case d) (-2, 1)
[tex]1 > -3(-2)+2[/tex]
[tex]1 > 8[/tex] ----> is not true
so
the point not satisfy the inequality
therefore
The point is not a solution of the inequality
see the attached figure to better understand the problem
Answer:
(2,0)
Step-by-step explanation:
Mike bought 20 stamps for 0.40 $5 each and 15 Century 0.32 each how much money did Mike spend on stamp
Answer:
$8
Step-by-step explanation:
Here is the correct question: Mike bought 20 stamps for 0.40 each and 15 Century 0.32 each how much money did Mike spend on stamp.
Given: cost of each stamp is 0.40
Total stamp bought is 20.
Using unitary method
Cost of 1 stamp is 0.40.
∴ cost of 20 stamp is =[tex]20\ stamp \times 0.40= 8[/tex]
Cost of 20 stamp is $8
∴ Total money spent by Mike on buying 20 stamp is $8.
The graph of g(x) = (x-h) + k is shown on the coordinate
grid. What must be true about the signs of h and K?
Both hand k must be positive
Answer:
The sign of h must be negative, and the sign of k must be positive.
-3(v - 3) - 6 is greater than or equal to 12
Answer:
v<=-3
Step-by-step explanation:
-3(v-3)-6>=12
-3v+9-6>=12
-3v+3>=12
-3v>=12-3
-3v>=9
v>=9/-3
v>=-3
Draw a picture to show the division. Express your answer as a fraction. 3÷5=
Answer:
your answer is down below
Step-by-step explanation:
Check the picture below.
write an equation for a line parallel to 3x-6y=18
A1.0 kg cart moving right at 5.0 -- on a frictionless track
collides with a second cart moving left at 2.0 m/s.
The 1.0 kg cart has a final speed of 4.0 m/s to the left, and the
second cart has a final speed of 1.0 m/s
to the right.
What is the mass of the second cart?
Consider rightward as the positive direction.
Answer:
3.0 kg
Step-by-step explanation:
Momentum before collision = momentum after collision
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
(1.0 kg) (5.0 m/s) + m (-2.0 m/s) = (1.0 kg) (-4.0 m/s) + m (1.0 m/s)
5.0 kg m/s + m (-2.0 m/s) = -4.0 kg m/s + m (1.0 m/s)
9.0 kg m/s = m (3.0 m/s)
m = 3.0 kg
plzzz help rn i need it
Answer:
Therefore the slope of the line shown on the graph is option D)
[tex]-\dfrac{2}{3}[/tex]
Step-by-step explanation:
Given:
Let the Two points on the line be
point A( x₁ , y₁) ≡ ( 0 , 0) one as a Origin
point B( x₂ , y₂) ≡ (-3, 2)
To Find:
Slope AB = ?
Solution:
For a slope we require two points i.e
[tex]Slope=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Substituting the given values we get
[tex]Slope(AB)=\frac{2-0}{-3-0}\\\\Slope(AB)=-\dfrac{2}{3}[/tex]
Therefore the slope of the line shown on the graph is option D)
[tex]-\dfrac{2}{3}[/tex]
1. You have a 20 foot long ladder that you want to lean against a vertical wall. You want the top of the ladder to touch the wall 19 feet off the ground. What angle will the ladder form with the ground?
2. Using the same 20 foot ladder against the same vertical wall, you decide that it would be better if the ladder formed a 70 degree angle with the ground. How far up the wall will the top of the ladder reach?
3. You want to find the area of triangle BCD but all you have is the information provided in the image below. Then you realize you can use the special right triangle (30-60-90) to find the height of the triangle. Once you know the height and provided base measurement calculate the area.
What is the area of the triangle? Show all steps.
Answer:
1. The ladder forms 71.8° with the ground.
2. The top of the ladder will reach 18.79 feet up the wall.
3. Height = 8.66 cm and area = 21.65 sq. cm.
Step-by-step explanation:
1. If the angle of elevation of the ladder is [tex]\theta[/tex] then we can write
[tex]\sin \theta = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{19}{20}[/tex]
⇒ [tex]\theta = \sin ^{-1}(\frac{19}{20}) = 71.8[/tex] Degrees.
Therefore, the ladder forms 71.8° with the ground. (Answer)
2. Now, if the ladder formed a 70 degree angle with the ground and the length of the ladder remains the same as 20 feet, then we can write
[tex]\sin 70 = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{x}{20}[/tex]
⇒ x = 20 sin 70 = 18.79 feet.
Therefore, the top of the ladder will reach 18.79 feet up the wall.
3. See the attached figure.
We have, [tex]\tan 60 = \frac{BC}{CD} = \frac{BC}{5}[/tex]
⇒ Height = BC = 5 tan 60 = 8.66 cm.
Therefore, the area of the triangle BCD will be = [tex]\frac{1}{2} \times CD \times BC = \frac{1}{2} \times 5 \times 8.66 = 21.65[/tex] sq. cm. (Answer)
what is 85% written as a decimal and as a fraction
Answer:
.85 or 85/100
Step-by-step explanation:
Answer:
0.85 is your decimal. 85 / 100 - not simplified.
17 / 20 - simplified.
Step-by-step explanation:
For the decimal, all you gotta do is move your decimal to the left 2 times.
-Hope this helps.
For the fraction, 85% is per 100, so it's 85 / 100. To simplify, the answer is 17 / 20.
The recursive function for a sequence is given below.
f(1) = 200
f(n) = 2 · f(n − 1), for n = 2, 3, 4, ...
What is the 5th term of this sequence?
Answer:
f(5) = 3200
Step-by-step explanation:
Using the recursive formula to generate the terms, that is
f(2) = 2 × f(1) = 2 × 200 = 400
f(3) = 2 × f(2) = 2 × 400 = 800
f(4) = 2 × f(3) = 2 × 800 = 1600
f(5) = 2 × f(4) = 2 × 1600 = 3200
Answer: 6400
Step-by-step explanation:
Given :
f(1) = 200
f(n) = 2.f(n-1) , for n = 2 ,3 , 4 , ...
To find the 5th term
when n = 2 , the sequence becomes
f(2) = 2 .f(2-1)
f(2) = 2 f(1)
since f(1) = 200
therefore:
f(2) = 2 x 200
f(2) = 400
When n = 3
f(3) = 2f(2)
f(3) = 2 x 400
f(3) = 800
When n = 4
f(4) = 2 f(3)
f(4) = 1600
When n =5
f(5) = 2f(4)
f(5) = 3200
When n = 6
f(6) = 2f(5)
f(6) = 6400
Since n = 2 , 3 , 4 ... this means that the 5th term if f(6) , therefore ,the 5th term is 6400
Find the x and y intercepts of the equation: 2x - 3y = 18 (0, 2) and (-3, 0) (0, 9) and (0, -6) (9, 0) and (0, -6) (2, 0) and (0, -3)
The x - intercept is (9, 0) and y - intercept is (0, -6)
Solution:
Given that the equation is: 2x - 3y = 18
We have to find the x and y intercepts of the equation
The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.
The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero.
Finding x - intercept:
Substitute y = 0 in given equation
2x - 3y = 18
2x - 3(0) = 18
2x = 18
x = 9
Thus the x - intercept is (9, 0)
Finding y - intercept:
Substitute x = 0 in given equation
2(0) - 3y = 18
-3y = 18
y = -6
Thus the y-intercept is (0, -6)
Is Y=-3x-2 linear or no?
Yes!
This would be in-fact a linear equation!
How?This equation is set up in y=mx+b form, therefore we know it is a linear equation.
Example of a linear equation:y=12x+2
The 12 is the mx in the equation.
And the 2 is the B in the equation! :)
That is how we solve that.
Any questions?
Have a great day!