Answer:
[tex]a_{n}[/tex] = 7[tex]a_{n-1}[/tex]
Step-by-step explanation:
A recursive formula allows a rem in the sequence to be found by multiplying the previous term by the common ratio r
For this sequence
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-21}{-3}[/tex] = 7 , then recursive formula is
[tex]a_{n}[/tex] = 7[tex]a_{n-1}[/tex]
Use the given graph to determine the limit, if it exists. (4 points)
A coordinate graph is shown with a horizontal line crossing the y axis at three that ends at the open point 2, 3, a closed point at 2, 1, and another horizontal line starting at the open point 2, -2.
Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x. .
Does not exist; does not exist
1; 1
-2; 3
3; -2
Limit of x approaches two from the left of f of x: 3. Limit of x approaches two from the right of f of x: - 1 (negative 1)
How to find the value of the function as x approaches infinity (+ve or -ve)?If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.
In order to find the limit as x approaches two from the left of f of x:
Lim x→2- f(x) = ?
According to the graph, when x approaches two from the left (x<2), the function approaches 3:
Lim x→2- f(x) = 3
IN order to find the limit as x approaches two from the right of f of x:
Lim x→2+ f(x) = ?
According to the graph, when x approaches two from the right (x>3), the function approaches -1:
Lim x→2+ f(x) = - 1
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if you can solve, i will give brainliest!
What is the sum of StartRoot 3 EndRoot – i and 2 – StartRoot 3 EndRooti?
(2 + StartRoot 3 EndRoot) – (1 –StartRoot 3 EndRoot )i
(2 + StartRoot 3 EndRoot) – (1 + StartRoot 3 EndRoot)i
(2 + StartRoot 3 EndRoot) + (1 + StartRoot 3 EndRoot)i
(2 + StartRoot 3 EndRoot) + (1 – StartRoot 3 EndRoot)i
Answer:
(2 + StartRoot 3 EndRoot) – (1 + StartRoot 3 EndRoot)i
Step-by-step explanation:
I'm 100% sure! ^^
Answer:
B: (2 + StartRoot 3 EndRoot) – (1 + StartRoot 3 EndRoot)i
Step-by-step explanation:
Took the quiz
You are able to walk uphill at a speed of 2 miles per hour and downhill at a speed of 3 miles per hour. What does the graph represent?
Using a piece-wise function, the representation of the graph is given as follows:
Walking uphill for 3 hours and downhill for 1 hour.
What is a piece-wise function?A piece-wise function is a function that has multiple definitions, depending on the input.
In this problem, we have that:
For the first 3 hours, the slope is of 2 miles per hour, equivalent to walking uphill.For the final hour, the slope is of 3 miles per hour, equivalent to walking downhill.Hence the meaning of the graph is:
Walking uphill for 3 hours and downhill for 1 hour.
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Alice is able to produce 3 dozen cupcakes in 90 minutes. How many cupcakes can she produce in 8 hours
Answer:
[tex]\boxed{192~cupcakes}[/tex]
Step-by-step explanation:
dozen = 12
3 × 12 = 36 cupcakes
I.
36 cupcakes ---------------- 90 minutes
x ---------------- 60 minutes
[tex]x=\dfrac{36\cdot 60}{90 } ~ cupcakes\\\\x=24~cupcakes[/tex]
II.
24 cupcakes ---------------------- 60 minutes = 1 hour
y ---------------------- 8 hours
[tex]y=\dfrac{8\cdot 24 }{1} ~cupcakes\\\\\boxed{y=192~cupcakes}[/tex]
They will produce 192 cupcakes in 8 hours.
hellp help
x =x=x, equals
^\circ
∘
degrees
The sum of the unknown angle and 33 degrees are supplementary. The measure of x is 147 degrees
Supplementary anglesThe sum of the unknown angle and 33 degrees are supplementary to have:
x + 33 = 180
Subtract 33 from both sides
x + 33 - 33 = 180 - 33
x = 180 - 33
x = 147degrees
Hence the measure of x is 147 degrees
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Answer:
Step-by-step explanation:
x + 33° = 180°
reason :( they are cointerior angle )
x = 180° - 33°
x = 147°
4. In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
A team of 3 boys and 3 girls be selected from 5 boys and 4 girls in 40 ways
How to determine the number of ways?The selections are given as:
3 boys from 5 boys
3 girls from 4 girls
Each selection is calculated using:
[tex]^nC_r = \frac{n!}{(n- r)!r!}[/tex]
So, we have:
[tex]Ways = ^5C_3 * ^4C_3[/tex]
Apply the combination formula
[tex]Ways = \frac{5!}{2!3!} * \frac{4!}{1!3!}[/tex]
Expand
[tex]Ways = \frac{5 * 4 * 3!}{2 * 3!} * \frac{4 * 3!}{1 * 3!}[/tex]
Simplify
Ways = 5 * 2 * 4
Evaluate
Ways =40
Hence, the number of ways is 40
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Through how many degrees does the hour hand of a clock travel between 3:00pm and 3:15pm?
Answer:
90 degrees
Step-by-step explanation:
the clock is a circle so the entire # of degrees is 360.
there are 12 sections on the clock so 360 /12 =30
so each section is 30 degrees.
if you go from 3:00 to 3:15, that is 3 sections.
so 3 times 30 is 90
How many solutions exist for the system of equations graphed below?
Answer: one
Step-by-step explanation:
When a system of equations is graphed the solutions are the point of intersections. Here, we only have one point of intersection since these are both linear equations. That means there is only one solution.
100 POINTS!!!
PLEASE HELP ITS EZ :)
In 2.44 seconds lindsey be 30 feet in the air.
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .
Given:
y= -16x²+33x+45
If the height is 30 feet.
30= -16x²+33x+45
-16x²+33x+45-30=0
-16x²+33x+15=0
16x²-33x-15=0
Solving the quadratic equation
x=-b±√b²-4ac/ 2a
x= 33 ± √2049/32
x= (33+ √2049)/32 and x=33-√2049/32
x=2.44 and -0.3833
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A projectile is fired from the ground with an upward speed of 245 m/s. What is the maximum height of the projectile?
The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The maximum height (H) of a projectile is given as:
H = u²/2g
Where u is the initial speed = 145 m/s, g is the acceleration due to gravity = 10 m/s²
H = 245²/ 2(10) = 3001.25 m
The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m
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hep me out with this question i will give you brainly!
Answer:
c because have great day
Find x and y.
x - y = 2
3x - y = 12
the answer is
X=5
y=3
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Based on a poll, 867 of 1050 randomly selected adult said that they always wear seat belts. Construct and interpret a 97% confidence interval for the proportion of adults who always wear seat belts.
The 97% confidence interval for the proportion of adults is 0.801<P<0.851.
Given that 867 adults are randomly selected from 1050 who always wear seat belts.
A confidence interval refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.
Let's assume n=1050 and x=867
Find the sample proportion by dividing the given proportion with sample size as,
[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\\hat{p}&=\frac{867}{1050}\\ \hat{p}&=0.826 \end[/tex]
Find the α by subtracting the given confidence interval that is 97% from 1 as
α=1-(97÷100)
α=1-0.97
α=0.03
To find the critical value that is [tex]Z_{\frac{\alpha}{2}}[/tex] by dividing alpha with 2,
[tex]\begin{aligned}Z_{\frac{\alpha}{2}}&=Z_{\frac{0.03}{2}}\\ Z_{\frac{\alpha}{2}}&=Z_{0.015}\end[/tex]
From this table which is shown in the figure it says that the critical value is
[tex]Z_{crit}=\pm 2.17[/tex]
Use this formula to find the confidence interval [tex]P=\hat{p}\pm Z_{Crit}\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Substitute the values in the formula,
[tex]\begin{aligned}P&=0.826\pm 2.17\times \sqrt{\frac{0.826(1-0.826)}{1050}}\\ P&=0.826\pm 2.17\times \sqrt{\frac{0.826\times 0.174}{1050}}\\ P&=0.826\pm 2.17\times 0.0116995\\ P&=0.826\pm 0.025\end{aligned}[/tex]
Hence, a 97% confidence interval for the proportion of adults who always wear seat belts is 0.801<P<0.851.
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11. (21x² - 6x +14) + (x²-3x+18)
Answer:
22x^2-9x+32
Step-by-step explanation:
(21x² - 6x +14) + (x²-3x+18)
To add, we need to combine like terms
21x^2+x^2 -6x-3x +14+18
22x^2-9x+32
Answer:
22x² - 9x + 32
Step-by-step explanation:
(21x² - 6x +14) + (x²-3x+18)
Get rid of the parenthesis:
21x² - 6x + 14 + x² - 3x + 18
Group like terms:
22x² - 9x + 32
Natalie is ordering a burrito. For the main protein, she is given the option of veggie, chicken, carnitas, or carne asada. For the beans, she is given the option of no beans, black beans, or pinto beans. How many possible order combinations are there?
Answer: 12
Step-by-step explanation:
For this counting question, we need to figure out the possible choices for each selection.
For main protein, there are four options, so we can make four slots
_ _ _ _
For beans, there's three options, so we can make three slots
_ _ _
Doing some casework, we know that 4*3 = 12, which is the answer.
The 8. is just the number of the question.
The value of (1+tanx)(1-tanx)+sec²x is 0 and the value of [tex]\frac{sec^{2}-4 }{sec+2}[/tex] is [tex]sec\theta \ -2[/tex].
Given that, (1+tanx)(1-tanx)+sec²x.
Now, (1-tan²x)+sec²x
=1-tan²x+sec²x
=1+sec²x-tan²x
=1-1=0
Now, evaluate [tex]\frac{sec^{2}-4 }{sec+2}[/tex]
[tex]=\frac{sec^{2} \theta \ -2^{2} }{sec\theta \ +2} =\frac{(sec \theta \ +2)(sec \theta \ -2)}{sec \theta \ +2}[/tex] (∵a²-b²=(a+b)(a-b))
[tex]=sec \theta \ -2[/tex]
Hence, the value of (1+tanx)(1-tanx)+sec²x is 0 and the value of [tex]\frac{sec^{2}-4 }{sec+2}[/tex] is [tex]sec\theta \ -2[/tex].
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Which is an equation of the line through (0,0) and (2,-3)?
Answer:
y = -1.5x
How to build equation?
Given points: (0, 0), (2, -3)
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) = \dfrac{-3-0}{2-0} = -1.5[/tex]
Then find equation:
[tex]y-y_1 = m(x - x_1)[/tex]
[tex]y - 0 = -1.5(x -0)[/tex]
[tex]y = -1.5x[/tex]
Answer:
y = (-3/2)x
Step-by-step explanation:
I am going to answer this question in slope-intercept form, which is y = mx + b (m is the slope, b is the y-intercept). The question already gives us the y-intercept, or the point at which the graph crosses the y-axis. It is (0, 0). Now, all we have to do is find the slope, which we can do using the following formula:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
In this formula, (x1, y1) and (x2, y2) are two points that are given to us [the first point is (0,0) and the second point is (2,-3). We can solve for the slope by plugging in:
[tex]m=\frac{-3-0}{2-0}=\frac{-3}{2}[/tex]
Now that we have m and b, we can plug into slope-intercept form to get our equation: y = (-3/2)x + 0 or y = (-3/2)x
Determine the equation of the parabola shown in the diagram in vertex form.
By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².
How to determine the equation of the parabola in vertex form
Parabolae are represented mathematically by second order polynomials, which can be described either in standard form or in vertex form. In accordance to the picture, we have a parabola with a vertical axis of symmetry. The formula in vertex form is described by this expression:
y - k = C · (x - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constantPlease notice that vertices represent the absolute extreme of the parabola. We can determine the equation by knowing the vertex and another point. Let be (h, k) = (3, 1) and (x, y) = (0, 7), then we find that the vertex constant is:
7 - 1 = C · (0 - 3)²
6 = 9 · C
C = 2/3
By the vertex form of the parabola, the equation of the parabola shown in the diagram is equal to the quadratic equation y - 1 = (2/3) · (x - 3)².
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the question is on the image
Answer:
nth term: 0.5n² + 2.5n + 3
Explanation:
pattern 1 = 6 bowls
pattern 2 = 10 bowls
pattern 3 = 15 bowls
pattern 4 = 21 bowls
First difference:
10 - 6 = 415 - 10 = 521 - 15 = 6Second difference:
5 - 4 = 16 - 5 = 1This is not an arithmetic nor a geometric sequence.
Solve:
2a = 2nd difference
2a = 1
a = 1/2 or 0.5
===================
3a + b = 1st difference
3a + b = 4
b = 4 - 3(1/2)
b = 2.5
====================
a + b + c = first term
1/2 + 2.5 + c = 6
c = 3
Quadratic nth term:
0.5n² + 2.5n + 3
true or false: prostulates are accepted as true without proof
Answer:
true
Step-by-step explanation:
Since their wise or intelligent guess
Find the midpoint of a A(3, -1) and B(x, y) is P(4, - 5). Find the coordinates of B. pls answer it is urgent i will mark him or her brainlest
Answer:
is this tye required answer
what is inversion transformation
Answer:
Inversión en una circunferencia es una transformación que conserva la magnitud de los ángulos pero cada ángulo se transforma en un ángulo de signo opuesto . El sentido o dirección de cada ángulo se invierte. La inversión en una circunferencia es una transformación anti-conforme(como la reflexión en una recta).
Step-by-step explanation:
El sentido o dirección de cada ángulo se invierte. La inversión en una circunferencia es una transformación anti-conforme(como la reflexión en una recta).
Answer:
inversion transformations are a natural extension of Poincaré transformations to include all conformal one-to-one transformations on coordinate space-time.
What is the product of the...
Step-by-step explanation:
the answer is C) 8x^5y - 6x^4y^2
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If 1/2 is the fraction representing the ratio of corresponding sides of two similar
triangles, the ratio of the areas of the triangles would be:
Answer:
1/4
Step-by-step explanation:
The ratio of the areas is the square of the ratio of the lengths of sides.
(1/2)² = 1/4
Answer: 1/4
Select the correct answer.
Serena's financial goal is to reduce debt. Which statement could make Serena's financial goal specific and timely?
Serena should focus on a certain credit card and give herself a deadline.
Serena should focus on a certain amount and track her spending.
Serena should track the amount of debt reduced over a period of six months.
Serena should track her purchases at gas stations for one year.
O A.
O B.
O C.
O D.
Serena should focus on a certain amount and track her spending. Option B
What Serena should doFrom the information given, Serena wants to reduce debt and to do this she needs to pay attention on how she borrows and the possible way to pay her debts.
Some possible ways to reduce debts include;
Develop a budgetTrack your expensesDo not take more debtPay bills in timeCheck bills carefullyThus, Serena should focus on a certain amount and track her spending. Option B
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Triangles F G H and F J H share common side F H. Sides F G and G H are congruent. Sides F J and J H are congruent.
Which explains whether ΔFGH is congruent to ΔFJH?
They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.
They are congruent because opposite sides of a parallelogram are congruent.
They are not congruent because only one pair of corresponding sides is congruent.
They are not congruent because only two pairs of corresponding sides are congruent.
ΔFGH is congruent to ΔFJH They are not congruent because only one pair of corresponding sides is congruent.
The correct option is (C)
What is Congruency?Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.
Given:
ΔFGH and ΔFJH share common side FH. Sides FG and GH are congruent.
As, per the information, it can be seen that the triangles are not congruent as one pair of corresponding side is not congruent.
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Answer: C
Step-by-step explanation: edge
Here is a list of ages (years) of children in a room: 9 , 9 , 9 , 4 , 9 , 1 , 10 State the median.
Answer:
the median is 9
Explanation
Finding the median is easy, all you need to do is put the numbers in numeric order and the one that's in the middle of the numbers is the median
9 , 9 , 9 , 4 , 9 , 1 , 10 = 1, 4, 9, (9), 9, 9, 10
(median)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Given the Ages of students: 9,9,9,4,9,1,10. State the median
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\boxed{\begin{minipage}{7cm} Before finding the median, we\\ need to arrange \\ our data from least to greatest. \end{minipage}}[/tex]
Thus,
[tex]\bf{1,4,9,9,9,9,10}[/tex].
[tex]\fbox{The median is the number in the middle.}[/tex]
Thus,
[tex]\bf{9}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=9}[/tex]
Extra information [tex]\curvearrowright[/tex][tex]\begin{tabular}{c | 1} Data Parameter & What to Do \\ \cline{1-2} \\ Mean & Add all the numbers and divide by how many there are \\ Median & Arrange the numbers from least to greatest and take the number \\ & in the middle. Take the mean of the 2 numbers in the middle \\ & if there's an even amount of numbers \\ Mode & The number that occurs the most \\ Range & The largest number minus the smallest number \\ Minimum & The smallest value \\ Maximum & The largest value \end{tabular}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.
Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto’s proof that was not included in Nessa’s proof?
Given: AngleB ≅ AngleN; BC ≅ NM; AngleC is right; AngleM is right
Prove: TriangleABC ≅ TriangleQNM
AngleA ≅ AngleQ because of the third angle theorem.
AB ≅ QN because they are both opposite a right angle.
BC ≅ NM because it is given.
AngleC ≅ AngleM because right angles are congruent.
What would be included to prove both triangles are congruent by the AAS theorem is: B. AB ≅ QN because they are both opposite a right angle.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangle are congruent if both have two pairs of corresponding congruent angles and a pair of non-included corresponding congruent sides.
In the image given, since AB and QN both lie opposite a right triangle, then they are congruent to each other.
Therefore, to prove both triangles are congruent by AAS theorem, what would be included is: B. AB ≅ QN because they are both opposite a right angle.
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Answer:
AngleA ≅ AngleQ because of the third angle theorem
Step-by-step explanation:
right on edge
How can you quickly determine the number of roots a polynomial will have by looking at the equation?
One can determine the number of roots by seeing the degree of the given polynomial.
The number of roots can be determined by just seeing the highest power of the given equation.
1) for the equation x-4=0
here, the highest power of the equation is one. So, it will have one root.
What is the polynomial?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtract multiplication, on, and non-negative integer exponentiation of variables.
Let's check it by simplifying x-4=0 which implies x=4
Hence, the equation has only one root namely x = 4.
2) Consider a quadratic equation,
10t^2-t-3=0
here, the highest power of the equation is two. So, it will have two roots.
Let's check it by simplifying using the middle term splitting method,
10t^2+5t-6t-3=0
5t(2t+1)-3(2t+1)=0
(5t-3)(2t+1)=0
t=-3/5 or t=-1/2
Thus, the equation has two roots.
Hence, one can determine the number of roots by seeing the degree of the given polynomial.
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A pet supply store lets you donate your change to the local animal shelter. Denise buys a bag of dog food for $15.74 and a squeaky toy for $3.98. She gives the cashier $20. If she gives all of her change, how much will Denise donate to the animal shelter?
Considering her change, it is found that she will donate $0.28 to the animal shelter.
How to find the amount of change in a purchase?The amount of change is given by the subtraction of the total paid and the price of the products.
In this problem, the price of the products bought is given by:
$15.74 + $3.98 = $19.72
She paid $20, hence the change is given by:
$20 - $19.72 = $0.28.
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