PLEASE HELP! Solve each of the following by using the general quadratic formula.
Answers
Using the quadratic formula, the solutions are:
a) [tex]x = \frac{3 \pm \sqrt{41}}{4}[/tex]
b) [tex]x = 1 \pm 2i[/tex]
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
Item a:
The coefficients are a = 2, b = -3, c = -4, hence:
[tex]\Delta = (-3)^2 - 4(2)(-4) = 41[/tex][tex]x_1 = \frac{3 + \sqrt{41}}{4}[/tex][tex]x_2 = \frac{3 - \sqrt{41}}{4}[/tex]Item b:
The coefficients are a = 1, b = 2, c = 2, hence:
[tex]\Delta = (2)^2 - 4(1)(2) = -4[/tex][tex]x_1 = \frac{2 + \sqrt{-4}}{2} = 1 + 2i[/tex][tex]x_2 = \frac{2 - \sqrt{-4}}{2} = 1 - 2i[/tex]More can be learned about quadratic equations at https://brainly.com/question/24737967
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Related Questions
The ages of all employees at a small convenience store are 36, 32, 38, and 28. What is standard deviation of ages for this population
Answers
The standard deviation is approximately 3.84
Step 1: Find the mean
Find the sum of the values, and divide by number of terms.
Mean (average) = (36+32+38+28)/4 = 134/4 = 33.5
We must use Standard Deviation formula which is attached as an image below.
X is the mean here, so lets plug in 33.5
Step 2. Distance from the mean squared |x-mean∣²
For each data point, we will plug in the numbers.
|36-33.5|²=2.5²=6.25
|32-33.5|²=1.5²=2.25
|38-33.5|²=4.5²=20.25
|28-33.5|²=5.5²=30.25
Step 3: Find the sum (∑)
We find the sum here by adding all the distances from the mean squared
∑|x-mean|²=59
Step 4: Divide the sum by the amount of points, 4
59/4=14.75
Step 5: Take the square root of step 4
[tex]\sqrt{14.75}[/tex] is about 3.84
The standard deviation is approximately 3.84
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Answers
The vertex form of the function is f(x) = -2(x-4)^2 + 2
Vertex form of a functionThe standard vertex form of a function is expressed according to the expression;
f(x) = a(x-h)^2+k
where
a is a constant = -2
(h, k) is the vertex = (4, 2)
Substitute
f(x) = -2(x-4))^2+2
f(x) = -2(x-4)^2 + 2
Hence the vertex form of the function is f(x) = -2(x-4)^2 + 2
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Suppose that a rectangular piece of glass has a perimeter of 20 meters. if we multiply both its length and its width by 4, what will be the perimeter of the new rectangular piece of glass?
Answers
The perimeter of the new rectangular piece of glass is 80m.
What is the perimeter of a rectangle?The sum of all sides of a rectangle is the perimeter of the rectangle.A rectangle has two equal lengths and two equal widths.Therefore, the perimeter 'P' of a rectangle is the sum of two equal lengths and two equal widths. That is, 'P=2l+2w' where 'l' is the length and 'w' is the width of the rectangle.
Here, a rectangular piece of glass has a perimeter of 20 meters.
As we know the perimeter P of a rectangle is given by the formula,
P = 2l+2w...(1)
Therefore,
20 = 2l + 2w
20 = 2(l + w)
20/2 = l + w
10 = l + w ....(2)
Now, both the length and width of the rectangle are multiplied by 4,
That is,
The new length of the rectangle is, l = 4l
The new width of the rectangle is, w = 4w
Therefore by substituting this in the equation(1) we get,
P = 2(4l) + 2(4w)
P = 8l + 8w
P = 8(l+w)....(3)
Substitute equation (2) in (3),
That is,
P = 8*10
P = 80m
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design a statistical process for finding how satisfied the students are in the cafeteria of the school with the quality of food
Answers
The design of the experiment above will center around:
The administration of questionnaire based on subject's gender, the place of eating, type of school and level satisfaction of meal service. The questionnaires to be used will have 5 point of Likert type scale (where 5 stands for very much agree and 1 is totally disagreed) in regards to the level of satisfaction on the quality of food in school cafeteria.Statistical tests will be done and data analyzed by using SPSS (ver.12.0).What will be the aim of the experiment?The aim of this study is to know and compare student's level of satisfaction with school cafeteria food services so as to improve the quality of food served at school meal service.
Hence The design of the experiment above will center around:
The administration of questionnaire based on subject's gender, the place of eating, type of school and level satisfaction of meal service. The questionnaires to be used will have 5 point of Likert type scale (where 5 stands for very much agree and 1 is totally disagreed) in regards to the level of satisfaction on the quality of food in school cafeteria.Statistical tests will be done and data analyzed by using SPSS (ver.12.0).Learn more about statistical test from
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The sum of three numbers $a, b$ and $c$ is 60. If we decrease $a$ by 7, we get the value $N$. If we increase $b$ by 7, we get the value $N$. If we multiply $c$ by 7, we also get the value $N$. What is the value of $N$
Answers
The value of N is 28.
What is the solution of the equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
According to the question,
a+b+c=60
a-7=N
b+7=N
7c=N
From the above three equations,
a=N+7
b=N-7
c=N/7
So, N+7+N-7+N/7=60
2N+N/7=60
14N+N=420
15N=420
N=28
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I have trouble understanding how stuff is worded so please help me I need to know by 4 o’clock today.
Answers
Answer:
Hector makes a tent shaped like a rectangular pyramid the volume is 56 cubic feet and the area is 24 square feet how tall is the tent
Step-by-step explanation:
The equation t^3=a^2 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?
Answers
Answer:
2√2
Step-by-step explanation:
We can find the relationship of interest by solving the given equation for A, the mean distance.
Solve for A[tex]T^3=A^2\\\\A=\sqrt{T^3}=T\sqrt{T}\qquad\text{take the square root}[/tex]
Substitute valuesThe mean distance of planet X is found in terms of its period to be ...
[tex]D_x=T_x\sqrt{T_x}[/tex]
The mean distance of planet Y can be found using the given relation ...
[tex]T_y=2T_x\\\\D_y=T_y\sqrt{T_y}=2T_x\sqrt{2T_x}=(2\sqrt{2})T_x\sqrt{T_x}\\\\D_y=2\sqrt{2}\cdot D_x[/tex]
The mean distance of planet Y is increased from that of planet X by the factor ...
2√2
suppose cos(a)=4/5. use the trig identity sin^2(a)+cos^2(a)=1 to find sin(a) in quadrant IV.
Answers
Answer:
sin a = -3/5
Step-by-step explanation:
sin^2(a)+cos^2(a)=1
sin^2(a)+ (4/5)^2 = 1
sin^2(a) = 1 - 16/25 = 9/25
sin a = 3/5 ( in Quadrant 1)
In quadrat IV the sine is negative
so sin a = -3/5
A researcher conducts an experiment to determine whether the type of car (sports vs. utility vehicle) and color of the car (red vs. blue) impact how fast people drive. The researcher decides that the best way to conduct the study is to assign each participant to all four conditions of the experiment. The researcher is using a:
Answers
The researcher is using a within-subjects factorial design.
According to statement
A researcher conducts an experiment to determine whether the type of car and color of the car impact how fast people drive.
This can be done by within-subjects factorial design.
In a within-subjects factorial design, all of the independent variables are manipulated within subjects. This would mean that each participant was tested in all conditions.
Another common example of a within-subjects design is medical testing.
So, The researcher is using a within-subjects factorial design.
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Solve the inequality. 14 + 10y ≥ 3(y + 14)
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{14+10y\geq 3(y+14) } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Simplify \ both \ sides \ of \ the \ inequality. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{10y+14\geq 3y+14 } \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Subtract \ 3y \ from \ both \ sides. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{10y+14-3y\geq 3y+42-3y } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{7y+14\geq 41 } \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{ Subtract \ 14 \ from \ both \ sides. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7y+14-14\geq 42-14 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{7y\geq 28 } \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{Divide \ both \ sides \ by \ 7. }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{7y}{7}\geq \frac{28}{7} } \end{gathered}$}\\\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{y\geq 4} \end{gathered}$} }[/tex]re arranging equations
please help choose answer
Answers
Answer:
D. d = √(V/5)
E. A = √(b/c).
Step-by-step explanation:
V = 5d^2
Divide both sides by 5:
V/5 = d^2
Now take the square root of both sides:
d = √(V/5)
Note - it's the square root of the whole term (V/5).
b = cA^2
A^2 = b/c
A = √(b/c).
If a pet store has 15 puppies 12 kittens and 6 rabbits
Answers
I have no clue how to do this
Answers
The length and the width of the rectangle are 10 inches and 6 inches respectively.
In the question, we are given that the length of a rectangle exceeds its width by 4 inches, and the area is 60 square inches.
We are asked for the length and the width of the rectangle.
We assume the width (w) of the rectangle to be x inches.
Its length (l), exceeds its width (w) by 4 inches.
Thus, its length (l) = x + 4 inches.
Now, the area can be calculated using the formula, A = l*w, where A is its area, l is its length, and w is its width.
Thus, the area = (x + 4)x = x² + 4x.
But, we are given that the area is 60 square inches.
Putting the value, we get a quadratic equation:
x² + 4x = 60.
or, x² + 4x - 60 = 0,
or, x² + 10x - 6x - 60 = 0,
or, x(x + 10) - 6(x + 10) = 0,
or, (x - 6)(x + 10) = 0.
By the zero-product rule, we get:
Either, x - 6 = 0, or, x = 6,
or, x + 10 = 0, or, x = -10, but this is not possible as the width of a rectangle cannot be negative.
Thus, the width = x = 6 inches.
The length = x + 4 = 10 inches.
Thus, the length and the width of the rectangle are 10 inches and 6 inches respectively.
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A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Answers
The variation given in the first question is not a direct variation and there is no constant of variation.
Direct variationy = k × x
when
y = -40 and x = -0.5
y = k × x
-40 = k × -0.5
-40 = -0.5k
k = -40/-0.5
k = 80
When y = 8 and x = 2.5
y = k × x
8 = k × 2.5
8 = 2.5k
k = 8 / 2.5
k = 3.2
When y = 4 and x = -3
y = k × x
4 = k × -3
4 = -3k
k = -4/3
when y = 8 and x = -6
y = k × x
8 = k × -6
8 = -6k
k = 8/-6
k = -4/3
This is a direct variation and the constant of proportionality is -4/3
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The difference between two number is 3.take the numbers as x and y form a equation?
Answers
The difference between two numbers are [tex]3[/tex] and numbers are [tex]x[/tex] and [tex]y[/tex] so the equation is [tex]x-y=3[/tex]
How to find the equation and what is the equation ?
equation, statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of mathematics has been driven by attempts to find answers to those questions in a systematic way.
if the difference of two numbers are [tex]3[/tex]
And one number is [tex]x[/tex] and another is [tex]y[/tex]
So we write the equation with operation of subtraction
[tex]x-y=3[/tex]
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If the base angles of a trapezoid are congruent, what can be said about the diagonals of the trapezoid?
They intersect at the median.
They split the trapezoid into 4 congruent parts.
They are congruent.
They bisect each other.
Answers
If the base angles of a trapezoid are congruent, the diagonals are congruent.
Properties of a trapezium?A trapezium is a quadrilateral and the sum of the interior angles is 360 degrees. Therefore, the properties of a trapezium includes the following:
The bases are parallel by definition.Each lower base angle is supplementary to the upper base angle on the same side.If the base angles are congruent, therefore, the trapezium is an isosceles trapezium. This means the diagonals are also congruent.learn more on trapezium here: https://brainly.com/question/9422487
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PLs answer fast i need this questions answer
Answers
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
Given equation:
[tex]x-\left(2x-\dfrac{3x-4}{7}\right)=\dfrac{4x-27}{3}-3[/tex]
Expand the left side:
[tex]\implies x-2x+\dfrac{3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]
Let all terms on the left side have the same denominator of 7:
[tex]\implies \dfrac{7x}{7}-\dfrac{14x}{7}+\dfrac{3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]
Join the terms on the left side:
[tex]\implies \dfrac{7x-14x+3x-4}{7}=\dfrac{4x-27}{3}-3[/tex]
[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27}{3}-3[/tex]
Let all the terms on the right side have the same denominator of 3:
[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27}{3}-\dfrac{9}{3}[/tex]
Join the terms on the right side:
[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-27-9}{3}[/tex]
[tex]\implies \dfrac{-4x-4}{7}=\dfrac{4x-36}{3}[/tex]
Cross multiply:
[tex]\implies 3(-4x-4)=7(4x-36)[/tex]
Expand:
[tex]\implies -12x-12=28x-252[/tex]
Add 12x to both sides:
[tex]\implies -12=40x-252[/tex]
Add 252 to both sides:
[tex]\implies 240=40x[/tex]
Divide both sides by 40:
[tex]\implies 6=x[/tex]
[tex]\implies x=6[/tex]
Help me with this question please
Answers
Answer:
[tex]\dfrac{991}{40\sqrt{2}}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{72}-\dfrac{48}{\sqrt{50}}-\dfrac{45}{\sqrt{128}}+2\sqrt{98}[/tex]
Rewrite 72 as 36·2, 50 as 25·2, 128 as 64·2 and 98 as 49·2:
[tex]\implies \sqrt{36 \cdot 2}-\dfrac{48}{\sqrt{25 \cdot 2}}-\dfrac{45}{\sqrt{64 \cdot 2}}+2\sqrt{49 \cdot 2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sqrt{36}\sqrt{2}-\dfrac{48}{\sqrt{25}\sqrt{2}}-\dfrac{45}{\sqrt{64}\sqrt{ 2}}+2\sqrt{49}\sqrt{2}[/tex]
Rewrite 36 as 6², 25 as 5², 64 as 8² and 49 as 7²:
[tex]\implies \sqrt{6^2}\sqrt{2}-\dfrac{48}{\sqrt{5^2}\sqrt{2}}-\dfrac{45}{\sqrt{8^2}\sqrt{ 2}}+2\sqrt{7^2}\sqrt{2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+2\cdot 7\sqrt{2}[/tex]
Simplify:
[tex]\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+14\sqrt{2}[/tex]
Combine like terms:
[tex]\implies 20\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}[/tex]
Make the denominators of the two fractions the same:
[tex]\implies 20\sqrt{2}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]
Rewrite 20√2 as a fraction with denominator 40√2:
[tex]\implies 20\sqrt{2}\cdot\dfrac{40\sqrt{2}}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]
[tex]\implies \dfrac{1600}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]
Combine fractions:
[tex]\implies \dfrac{991}{40\sqrt{2}}[/tex]
Three consecutive positive prime numbers have a sum that is a multiple of . What is the least possible sum
Answers
Answer:
3, 7, 14
Step-by-step explanation:
small brain
Which statement is true about solutions to 11 -x<7
Answers
Answer:
A. x=5 is a solution, but x=3 is not
Step-by-step explanation:
When x=5, 11-5<7, 6<7, this is a solution
When x=3, 11-3<3l, 8<7, this is not a solution
A school cafeteria uses 10
8 bowls of chocolate pudding.
How many cups of milk are in each bowl of chocolate pudding?
cups
Answers
Using proportions, it is found that there are 5 cups of milk in each bowl of chocolate pudding.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The cafeteria used 10 quarts for 8 bowls, hence the number of quarts per bowl is:
10/8 = 1.25
Each quart has 4 cups, hence the number of cups is:
4 x 1.25 = 5 cups.
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a solution of the equation 3x + y = 15?
Answers
Step-by-step explanation:
Since there is 2 unknown variable ,
so we need 2 equation to find their values.
Mr.david gave ross a number and asked him to divide it by 15. The quotient and remainder obtained by ross are 341 and 12 respectively. Find the number that teacher gave ross.
Answers
The number the teacher gave Ross is 5127
Word problems on linear equationsFrom the question, we are to determine the number that the teacher gave Ross
From the given information,
Mr. David gave Ross a number and asked him to divide it by 15.
Let the number be x
That is,
x/15
The quotient and remainder obtained by ross are 341 and 12 respectively
That is,
x/15 = 341 + 12/15
Now, we will solve the equation for x
x/15 = 341 + 12/15
Multiply through by 15
x = 15×341 + 12
x = 5115 + 12
x = 5127
Hence, the number the teacher gave Ross is 5127
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Alan will be traveling out of town for business. during his travel, he is scheduled to have 4 dinners, 5 lunches, and 3 breakfasts. his employer will pay him for these meals at the following rate: $20.20 for dinner, $10.70 for lunch, and $6.93 for dinner. what is the total amount alan will be paid for these meals?
Answers
money paid by employer to Alan is $ 155.09
word problemA word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.
money paid for dinner by employer=$20.20
money paid for lunch by employer =$10.70
money paid for breakfast by employer =$6.93
according to question,
in this problem we will simply multiply quantity of dinners with amount
to get our answer.
so as given in problem Alan scheduled 4 dinners , 5 lunches and 3 breakfast
(4×$20.20)+(5×$10.70)+(3×$6.93)
80.8+53.5+20.79
=$ 155.09
hence money paid by employer to Alan is $ 155.09
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A Ferris wheel is boarding platform is 2 meters above the ground, has a diameter of 68 meters, and rotates once every 9 minutes. How many minutes of the ride are spent higher than 37 meters above the ground
Answers
4.440 minutes of the ride is spent higher than 37 meters above the ground.
How to find the time spent on the ride?We have to find the amount of time spent by the ride 37 meters above the ground.
We know that 37 meters above the ground is actually one meter above the center.
We can find the angle above the center as shown below:
arcsin(1/34) = 0.0294 radians
Now we have to find the angle of rotation:
The angle of rotation of the Ferris wheel above 37 meters = π - (2*0.0294)
= 3.1 radians
The angular velocity of the Ferris wheel = Angle covered/Time
= 2π/9 rad/min.
Therefore time spent above 37 meters = 3.1*9/2π
= 3.1*9/6.28319
= 4.440 minutes
Therefore, we have found that 4.440 minutes of the ride is spent higher than 37 meters above the ground.
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30. Isla swims 4 laps in 2 minutes, and 1
lap = 25 meters. Which of the following
calculations would give her average
speed in meters per second?
Answers
The average speed is 50 meters per second
How to determine the average speed?The given parameters are:
Laps = 4
Time = 2 minutes
1 lap = 25 meters
Start by calculating the total distance
Distance = Laps * Meters
Distance = 4 * 25 meters
Distance = 100 meters
The average speed is then calculated as:
Speed = Distance/Time
This gives
Speed = 100 meters/2 minutes
Evaluate
Speed = 50 meters per second
Hence, the average speed is 50 meters per second
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Himari gave birth to twins and named them Adrian and Chang. When they were first born, Adrian massed 2.872.872, point, 87 kilograms and was 54.554.554, point, 5 centimeters tall, and Chang massed 4.544.544, point, 54 kilograms and was 515151 centimeters tall.
How much did the babies mass in total?
Answers
The total mass of Adrian and Chang at birth is 7.41 kilograms
MassAdrian weight = 2.87 kilograms and Adrian height = 54.5 centimetersChang weight = 4.54 kilogramsChang height = 51.5 centimetersTotal mass of the babies = Adrian weight + Chang weight
= 2.87 kilograms + 4.54 kilograms
= 7.41 kilograms
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describe how the graph is transformed from its parent function?
Answers
Answer:
It is stretched taller by a factor of 2.
Find the missing side. Round your answer to the nearest tenth.
Answers
Answer:
26.1 to the nearest tenth.
Step-by-step explanation:
tan 43 = x / 28
x = 28 tan 43
= 26.1102
Solve for x.
A. 3
B. 10
C. 6
D. 1
Answers
The values of x is 1 and 6.
According to the statement
we have two tangents which are represented by x+5 and x+1 then
we have to find the value of x to get the perfect value of tangent
so, due to interior values of tangent they are equal to each other but in opposite sign.
But here we have to find the value of x one by one.
It means
Here we take interior value of tangent and exterior value of tangent equal to each other
So, the equations become are written below
X+5= 6 then x = 1
X+1= 7 then x = 6
So, The values of x is 1 and 6.
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