The slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.
First, let us understand the slope intercept form;
The slope intercept form is simply a way of writing a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are obvious.
We know that the slope intercept form of a line is y = mx + c where m is the slope of the line and b is the y-intercept of the line.
We are given:
y = 2 + 34x
y = 34x + 2
Compare with y = mx + c, we will get;
m = 34
b = 2
So, the slope is 34 and the y-intercept is 2.
Thus, the slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.
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Find a formula for the quadratic
function whose graph has its vertex
at (−1, 2) and its y-intercept at
y = 3.
Quadratic function whose graph has its vertex
at (−1, 2) and its y-intercept at y = 3 is f(x) = [tex](x+1)^{2}[/tex] + 2
What do you mean by quadratic equation?
A quadratic equation in algebra is any equation that can be transformed in standard form like the following:
[tex]ax^{2} +bx+c[/tex]
Where x stands for an unknown and a, b, and c are known numbers. The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient
It is given that graph of the quadratic funcion has vertex(-1,2) and y-intercept at y=3
Now, using formula, f(x) = a[tex](x-h)^{2}[/tex] + k, where (h,k) is the vertex of the parabola.
Here, vertex of the quadratic function is (-1,2)
So, f(x) = a[tex](x+1)^2[/tex] + 2
Now, we need to solve for a.
y-intercept is given as y=3, which means f(x)= 3 when x=0
Using this we get ,
f(0) = 3
a(1) + 2 = 3
a + 2 = 3
a = 3 - 2
a = 1
Quadratic function become:
f(x) = [tex](x+1)^{2}[/tex] + 2
Therefore, quadratic function whose graph has its vertex
at (−1, 2) and its y-intercept at y = 3 is f(x) = [tex](x+1)^{2}[/tex] + 2
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Simplify the expression (4/3)(3/7)
The simplification form of the expression (4/3)(3/7) is 4/7 after canceling 3 from the numerator and denominator.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The expression is:
= (4/3)(3/7)
= (4x3)/(3x7)
Cancel 3 from the numerator and denominator
= 4/7
Thus, the simplification form of the expression (4/3)(3/7) is 4/7 after canceling 3 from the numerator and denominator.
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Hi, would be really thankful for an answer
Considering the Central Limit Theorem, it is found that:
a)
The mean is the mean of the sample means.The standard deviation is [tex]\frac{\sigma}{7}[/tex], in which [tex]\sigma[/tex] is the population standard deviation.b) The shape of the distribution is approximately normal.
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample means with size n of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex].
For the sampling distribution of sample means, the mean and the standard deviation are given as follows:
Mean: [tex]\mu[/tex], that is, the same as the population mean.Standard deviation: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], which is the population standard deviation divided by the square root of the sample size.For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
In this problem, the sample size is greater than 30, hence the shape of the distribution is guaranteed to be approximately normal.
The standard deviation is given as follows:
[tex]s = \frac{\sigma}{\sqrt{49}} = \frac{\sigma}{7}[/tex]
As for the mean, it is the same as the mean of the sample means, you have to calculate all the sample means and then divide by 20.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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NO LINKS!! Please help me with this sequence Part 1x
Answer:
2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784 2,490,930 neither 121,800Step-by-step explanation:
1. Recursively-defined sequenceYou want the first 9 terms of the recursive sequence defined by ...
[tex]\begin{cases}s_1=2\\s_2=3\\s_n=s_{n-2}(s_{n-1}-1)\end{cases}[/tex]
The attached spreadsheet uses the given formula for the next term. It shows the terms to be ...
2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784
2. Sequence sumThe attached spreadsheet sum function has been used to find the sum of the first 8 terms. That sum is ...
2490930
3. Sequence typeThe sequence of problem 1 has neither a common difference nor a common ratio between successive terms. It is neither arithmetic nor geometric.
4. Sum of arithmetic sequenceThe sum of the first n terms of an arithmetic sequence with first term a1 and common difference d is given by ...
Sn = (2a1 +d(n -1))(n/2)
You have a sequence with a1 = 12 and d = (18-12) = 6. You want the sum of the first 200 terms.
S200 = (2·12 +6(200 -1))(200/2) = 121,800
The sum is 121,800.
__
Additional comment
A spreadsheet is a nice tool for finding terms of a recursively-defined sequence. The formula can include as many terms as necessary, and it can be replicated thousands of times, if necessary. The limitation is that arithmetic is generally limited to 16 significant figures, or so.
Answer:
1.
s₁ = 2
s₂ = 3
s₃ = 4
s₄ = 9
s₅ = 32
s₆ = 279
s₇ = 8,896
s₈ = 2,481,705
s₉ = 22,077,238,784
2. 2,490,930
3. Neither.
4. 121,800
Step-by-step explanation:
Question 1A recursive rule for a sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.
Given recursive rule:
[tex]\begin{cases}s_n=s_{n-2} \cdot (s_{n-1}-1)\\s_1=2\\s_2=3\end{cases}[/tex]
Therefore, the first 9 terms of the sequence are:
[tex]s_1=2[/tex]
[tex]s_2=3[/tex]
[tex]\begin{aligned}s_3&=s_{3-2} \cdot (s_{3-1}-1)\\&=s_{1} \cdot (s_{2}-1)\\&=2 \cdot (3-1)\\&=2 \cdot 2\\&=4 \end{aligned}[/tex]
[tex]\begin{aligned}s_4&=s_{4-2} \cdot (s_{4-1}-1)\\&=s_{2} \cdot (s_{3}-1)\\&=3 \cdot (4-1)\\&=3 \cdot 3\\&=9 \end{aligned}[/tex]
[tex]\begin{aligned}s_5&=s_{5-2} \cdot (s_{5-1}-1)\\&=s_{3} \cdot (s_{4}-1)\\&=4 \cdot (9-1)\\&=4 \cdot 8\\&=32 \end{aligned}[/tex]
[tex]\begin{aligned}s_6&=s_{6-2} \cdot (s_{6-1}-1)\\&=s_{4} \cdot (s_{5}-1)\\&=9 \cdot (32-1)\\&=9 \cdot 31\\&=279\end{aligned}[/tex]
[tex]\begin{aligned}s_7&=s_{7-2} \cdot (s_{7-1}-1)\\&=s_{5} \cdot (s_{6}-1)\\&=32 \cdot (279-1)\\&=32 \cdot 278\\&=8896\end{aligned}[/tex]
[tex]\begin{aligned}s_8&=s_{8-2} \cdot (s_{8-1}-1)\\&=s_{6} \cdot (s_{5}-1)\\&=279 \cdot (8896-1)\\&=279\cdot 8895\\&=2481705\end{aligned}[/tex]
[tex]\begin{aligned}s_9&=s_{9-2} \cdot (s_{9-1}-1)\\&=s_{7} \cdot (s_{8}-1)\\&=8896\cdot (2481705-1)\\&=8896\cdot 2481704\\&=22077238784\end{aligned}[/tex]
Question 2Given series:
[tex]\displaystyle \sum^8_{k=1} s_k[/tex]
The sum notation asks to find the sum of the first 8 terms of the sequence from question 1.
Therefore:
[tex]\begin{aligned}\displaystyle \sum^8_{k=1} s_k&=s_1+s_2+s_3+s_4+s_5+s_6+s_7+s_8\\&=2+3+4+9+32+279+8896+2481705\\&=2490930\end{aligned}[/tex]
Question 3If a sequence is arithmetic, the difference between consecutive terms is the same (this is called the common difference).
If a sequence is geometric, the ratio between consecutive terms is the same (this is called the common ratio).
As the difference between consecutive terms it not the same, the sequence is not arithmetic.
As the ratio between consecutive terms is not the same, the sequence is not geometric.
Therefore, the sequence is neither arithmetic nor geometric.
Question 4[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given arithmetic sequence:
12, 18, 24, ...Therefore:
a = 12d = 18 - 12 = 6To find the sum of the first 200 terms, substitute the found values of a and d into the formula along with n = 200:
[tex]\begin{aligned}S_{200}&=\dfrac{1}{2}(200)[2(12)+(200-1)(6)]\\&=100[24+(199)(6)]\\&=100[24+1194]\\&=100[1218]\\&=121800\end{aligned}[/tex]
PLEASE HELP
Given: (GH) is a midsegment of ∆DEF. Show all work.
Find the value of x and y.
What is the length of (DF) ?
Using Midsegment theorem, the value of x, y and DE in the triangle are 17, 2, and 20 respectively.
How to find the length of triangle using midsegment theorem?The Midsegment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.
Therefore, DH is midsegment of triangle DEF.
Let's find the value of x.
1 / 2 (28) = x - 3
14 = x - 3
x = 14 + 3
x = 17
Let's find y
x - 7 = y + 8
17 - 7 = y + 8
10 = y + 8
y = 10 - 8
y = 2
Let's find DE
DE = y + 8 + x - 7
DE = 2 + 8 + 17 - 7
DE = 20
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PLEASE HELP!! QUICK!
Answer:
(0,-3)
Step-by-step explanation:
What is the slope of the line through (-2,2) and (3,9)
Answer: The slope is 7/5
Step-by-step explanation:
(-2,2) and (3,9)
The slope formula is [tex]m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]
Lets insert our numbers into there!
[tex]m=\frac{9-2}{3- -2}[/tex]
m= 7/5
Hope this helps! <33
Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The linear equation that could be used to find the price of a tire patch is of:
4x + 1.9 = 22.2.22.2 - 4x = 1.9.What is a linear equation?The slope-intercept representation of a linear equation is shown by the rule presented as follows:
y = mx + b.
In the context of this problem, the meaning of the variables are given as follows:
Slope m: cost of a single tyre.Intercept b: Amount of Ryan's gift card.The values of these intercept is given as follows:
b = 22.2.
Hence the function is:
y = -mx + 22.2.
He bought four tires, hence x = 4, and had y = 1.9, hence the cost of a tire is found as follows:
-4m + 22.2 = 1.9.
Hence the options are:
4x + 1.9 = 22.2 -> first equation, considering the slope as x.22.2 - 4x = 1.9.Missing InformationThe problem is given by the image shown at the end of the answer.
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Rectangle A measures 12 inches by 8 inches. Rectangle B is a scaled copy of Rectangle A. Select all of the
measurement pairs that could be the dimensions of Rectangle B.
6 inches by 2 inches
8 inches by 6 inches
120 inches by 80 inches
60 inches by 36 inches
3 inches by 2 inches
Answer:
120 inches by 80 inches
3 inches by 2 inches
Step-by-step explanation:
So the ratio of 12/8 is 1.5 so we divide all of the numbers to find ratios that equal that
120/80=1.5
3/2=1.5
but we dont put say 6 by 2 because 6/2 is 3
which lines are parallel if m < 4 = m < 5? justify your answer
Answer:
Lines r and s are parallelStep-by-step explanation:
Angles 4 and 5 are congruent and are on the inner side of lines r and s, and opposite side from line l.
If two angles are on the inner sides of two lines and opposite sides of the line intersecting the two lines are equal, then these angles are alternate interior angles.
The two lines are parallel and the intersecting line is the transversal.
Lines r and s are parallel and line l is transversal.
Answer the question below
By just expanding the products, we can see that the expression can be written as:
(x - 1)*(x + 2)*(x + 3) = x³ + 4x² + x - 6
How to rewrite the expression?Here we want to expand the expression:
(x - 1)*(x + 2)*(x + 3)
We can start to expand the first two parts, writing:
(x - 1)*(x + 2)*(x + 3) = [(x - 1)*(x + 2)]*(x + 3)
[x² + (-1)*x + x*2 + (-1)*2]*(x + 3)
[x² - x + 2x - 2]*(x + 3)
[x² + x - 2]*(x + 3)
Now we can finish the expansion:
[x² + x - 2]*(x + 3) = (x²)*x + (x²)*3 + x*x + x*3 + (-2)*x + (-2)*3
= x³ + 3x² + x² + 3x - 2x - 6
= x³ + 4x² + x - 6
That is the polynomial written in standard form.
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Find the two possible values ofX in the GP 72,x,18.
The possible values of X in the GP 72,x,18 is 36.
What is a geometric progression?A geometric progression simply means a sequence that has a common ratio.
From the information, the first term is 72 and the third term is 18
First term a = 72
Third term ar² = 18
Therefore, 72r² = 18
r² = 18/72
r² = 1/4
r = ✓1/4
r = 1/2
Therefore second term will be:
= 72 × 1/2
= 36
Therefore, x is 36.
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A rectangular sheet of metal measures 8 inches by 10 inches. The metal is worth $2.00 per square inch. How much is the sheet of metal worth?
The cost of the 80 square inches metal sheet is $160
The length of the rectangular sheet = 8 inches
The width of the rectangular sheet = 10 inches
The area of the rectangular sheet = The length of the rectangular sheet × The width of the rectangular sheet
Substitute the values in the equation
= 8 × 10
= 80 square inches
The cost of metal per square inch = $2
Then the cost of metal sheet = The area of the rectangular sheet × The cost of metal per square inch
Substitute the values in the equation
= 80 × 2
= $160
Hence, the cost of the 80 square inches metal sheet is $160
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2) Business Zoom Corporation makes model cars. Each sells for $29.99. The unit cos
is $14.25. If the company's fixed costs are $314,800, find the number of units they
need to sell to break even.
Answer: Break-even point in units= 20,000
Step-by-step explanation:
Break-even point in units= 20,000
Step-by-step explanation:
Giving the following information:
Selling price per unit= $29.99
Unitary variable cost= $14.25
Fixed costs= $314,800
To calculate the break-even point in units, we need to use the following formula:
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 314,800 / (29.99 - 14.25)
Break-even point in units= 20,000
Answer:
20,000
Step-by-step explanation:
29.99-14.25 (15.74) it the money that they make per unit without accounting for the fixed cost.
314800 = 15.74x Divide both sides by 15.74
20000 = x
Can you solve these two problems please
Answer:
Step-by-step explanation:
Hi Debbie, the tricky part about these types of problem is recognizing that you know the total angle. 180° for the ABCD question and the angles are equal to each other for the TUWXY question , this tip lets you find X for each.
just add the two angle and set equal to 180 in each problem. I'll do the problems below, but , now that you know how, maybe you could try them and check your answer against mine.
The ABCD question
4x+7 + 2x -1 = 180
6x +6 = 180
6x = 174
x = 29
4(29)+7 = 123°
2(29)-1 = 57°
The TUWXY question
6x+13 = 10x-7
20 = 4x
5=x
then
6(5)+13 = 43°
and the next one should be the same
10(5) -7 =43°
check. so there are your answers. :) get it?
3, 12, 27, 64, 75, 108
a) give the next number in this pattern
b) what is the rule to find the nth term?
c) what is the 20th term?
Please help + explain!
The third term from the sequence should be 48 so that (a) the next term is 147 (b) the rule to find the nth term is 3×n² and (c) the 20th term is 1200.
How to find the next term of the sequenceFrom the question, 3, 12, 27, 64, 75, 108 the third term 64 is supposed to be 48. hence the terms are derived as follows:
1st term; 3 × 1² = 3
2nd term;3 × 2² = 12
3rd term; 3 × 3² = 27
4th term; 3 × 4² = 48
5th term; 3 × 5² = 75
6th term; 3 × 6² = 108
Therefore, the next term which the 7th term is 3 × 7² = 147, the rule for the sequence is 3×n² and the 20th term is 3 × 20² = 1200.
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F(x)=4x+11; f(c+7) solve the equation
We have a translation of 7 units to the left, and it is:
F(c + 7) = 4c + 39
How to evaluate the function?
Here we have the linear function:
F(x) = 4x + 11
And we want to find:
F(c + 7)
So we just need to evaluate the function in x = c + 7, we will get:
F(c + 7) = 4*(c + 7) + 11
F(c + 7) = 4c + 28 + 11
F(c + 7) = 4c + 39
So basically we had a translation of 28 units up of our linear function (or 7 units to the left)
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NO LINKS!! Describe the set of all points P(x, y) in a coordinate plane that satisfy the given condition
Answer:
a) A or first option,b) E or 5th option,c) E or 5th option.Step-by-step explanation:
a) x = - 8Simply check for x-coordinate of - 8, we see only the first option has it, all the others have x = 0 or x = 8 which is impossible to have on the line x = - 8.
It is parallel to the y-axis and x = - 8 for any value of y.
Correct choice is A or 1.
b) y = 8Similar to above, we exclude all the options with a different value of y other than 8.
There are two possible options left:
B or 2- incorrect as y = 0 is parallel to the x-axis, not perpendicular.E or 5 - correct optionc) x ≥ 0Consider line x = 0, this is overlapping with the y-axis.
x ≥ 0 gives us the y-axis (because of equal sign) and all the points to the right from it.
This is matching the description of option E or 5.
Answer:
(a) The line parallel to the y-axis that intersects the x-axis at (-8, 0).
(b) The line parallel to the x-axis that intersects the y-axis at (0, 8).
(c) The set of all points to the right of and on the y-axis.
Step-by-step explanation:
Part (a)
Given condition: x = -8
The equation of a vertical line is x = a.
This line is parallel to the y-axis (since it is vertical) and intersects the x-axis at (a, 0).
Therefore, the description that satisfies the given condition is:
The line parallel to the y-axis that intersects the x-axis at (-8, 0).Part (b)
Given condition: y = 8
The equation of a horizontal line is y = a.
This line is parallel to the x-axis (since it is horizontal) and intersects the y-axis at (0, a).
Therefore, the description that satisfies the given condition is:
The line parallel to the x-axis that intersects the y-axis at (0, 8).Part (c)
Given condition: x ≥ 0
The "≥" symbol means greater than or equal to.
x is greater than zero for all points to the right of the y-axis.
x is equal to zero for all points on the y-axis.
Therefore, the description that satisfies the given condition is:
The set of all points to the right of and on the y-axis.which expressions are equivalent to 3^4/9/3^2/9? select all that apply
Answer:
Two correct answers: subtracting exponents and
3^ 2/9
Step-by-step explanation:
To divide, subtract exponents. To subtract fractions keep the bottom number the same and subtract the top number. See image.
Solve 4 + 2 sinx= 14-8 sinx for 0° ≤ x ≤ 180
x= 90°.
Step-by-step explanation:1. Write the expression.[tex]4 + 2 sin(x)= 14-8 sin(x)[/tex]
2. Subtract "4" from both sides of the equation.[tex]-4+4 + 2 sin(x)= 14-8 sin(x)-4\\ \\2 sin(x)= 10-8 sin(x)[/tex]
3. Add "8sin(x)" to both sides of the equation.[tex]2 sin(x)+8 sin(x)= 10-8 sin(x)+8 sin(x)\\ \\10 sin(x)= 10[/tex]
4. Divide both sides by 10.[tex]\frac{10 sin(x)}{10} = \frac{10}{10} \\ \\sin(x)=1[/tex]
5. Apply the arcsin of sin^-1 to both sides of the equation.[tex]arcsin(sin(x))=arcsin(1)\\ \\x=90[/tex]
6. Conclude.x= 90°.
There are 1-1/2 pizzas to be shared between 4 friends. What fraction of 1 pizza will each get
The fraction of 1 pizza to be shared with 4 friends are 3/8
What is division?Division is breaking a number up into an equal number of parts.
Given that, there are pizzas 1[tex]\frac{1}{2}[/tex] to be shared between 4 friends,
1[tex]\frac{1}{2}[/tex] = 3/2
For sharing = 3/2÷4 = 3/8
Hence, The fraction of 1 pizza to be shared with 4 friends are 3/8
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The graph of y = f(x) is graphed below. What is the end behavior of f(x)?
The end behavior of a graph is defined as what is going on at the ends of each graph when the function approaches positive or negative infinity.
End behaviour of given graph is, x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞
Since, here a graph is attached.
From graph it is observed that, when x tends to negative side, graph is going to upward direction. and when x tends to positive side then graph is going to downward direction.
So, when x tends negative infinity then y tends to positive infinity.
when x tends to positive infinity then y tends to negative infinity.
Therefore, end behaviour of given graph are,
x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞
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Find −3 4/9÷(−2 1/3) . Write your answer as a mixed number in simplest form.
The value of the fraction −3 4/9÷(−2 1/3) is 1 10/21.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, the fraction will be illustrated as:
= −3 4/9÷(−2 1/3)
Change to improper fraction
= -31 / 9 ÷ - 7/3
= 31/9 × 3/7
= 31 / 21
= 1 10/21
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A giant tortoise moves at a slow but steady
pace. It takes the giant tortoise 1 hour to travel
2 miles. ¿How many miles (mi) a tortoise
travels in ¼ hour? Use the bar diagram to help
you.
According to the information, it can be inferred that the turtle travels 0.5 miles in a quarter of an hour (1/4 hours).
How to find the distance that the tortoise travels in a quarter of an hour (1/4 hours)?To find the distance that the tortoise travels in a quarter of an hour we must perform the following operations and take into account the information provided.
1 hour = 2 miles1/2 hour = 1 mile1/4 hour = 0.5 miles1/8 hour = 0.25 milesTo verify that the turtle takes 1/4 of an hour to travel 0.5 miles, we must divide the total number of miles it travels in one hour by 4, because we want to identify how much distance it travels in a quarter of the time, as shown below:
2 miles / 4 = 0.5 miles
Based on the above, we can infer that the tortoise travels 0.5 miles in 1/4 hour.
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Name the line and plane shown in the diagram.
Considering the figure, the line and the plane are
Line PQ and plane PQSWhat is a line and a plane?A plane extends infinitely in two dimensions, but a line is defined as anything that extends infinitely in one direction
The extension of the line and plane in the diagram are defined hence discrete
PQ represents the line on the plane PQS
While Plane covers more space and in two dimension, plane can say to be covering area or measured as area. Line measures just the length
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The entire graph of the function f is shown in the figure below.
Write the domain and range of f using interval notation.
The domain of function f using interval notation is (-3, 3).
The range of function f using interval notation is (-5, 4).
What is a domain?In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
Additionally, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of a graph to the top.
By critically observing the graph of this function shown, we can reasonably infer and logically deduce the following:
Domain = (-3, 3).
Range = (-5, 4).
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In triangle ABC, the measure of angle X is eight times the sum of the measures of angles Y and Z. The measure of angle Y is three times the measure of angle Z. What are the measures of the angles?
x=
y=
z=
The measures of Angle X, Y and Z are 160°, 15°, 5° respectively.
What are Angles?a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
The sum of the three angles X, Y, Z is 180°
X + Y + Z = 180---------------1
if X is 8 times the sum of Y and Z, it means,
X = 8( Y + Z)--------------------2
Also
Y is three times Z, which means
Y = 3Z---------------------3
Substitute equation 3 and 2 in equation 1
8( 3Z + Z) + 3Z + Z = 180
32Z +4Z = 180
36Z = 180
Z = 180/36
Z = 5°
substitute the value of z in equations 1 and 3 to find X and Y
Y = 3Z,
at Z = 5
Y = 3 x 5
Y = 15°
X = 8(Y +Z)
X = 8( 15 + 5)
X = 8 x 20
X = 160°
In conclusion, the Value of the angles X, Y and Z are 160°, 15° and 5° respectively.
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a gymnast practices 6 days each week.She practices the same number of ours each day.If she practices 120 hours in a 4 week period how many hours each day does she practice?
Answer: She practices 5 hours a day
Step-by-step explanation: 6 days a week x 4 weeks = 24 days
120 hours of practice / 24 days = 5 hours of practice a day
Answer:
5hrs
Step-by-step explanation:
120 ÷ 4 = 30. 30 ÷ 6 = 5. She practices for 5hrs a week.
Find the total of the areas under the standard normal curve to the left of z1=−2.575 and to the right of z2=2.575 Round your answer to four decimal places, if necessary.
The total of the areas under the standard normal curve to the left of (z₁ = -2.575) and to the right of (z₂ = 2.575) is equal to 0.0098.
How to determine the total of the areas under the standard normal curve?In Statistics, the standard normal distribution table is designed and developed to provide only the area to the left of a specified z-score. Additionally, since z-score (z₁) and z-score (z₂) are generally symmetric about z = 0 and are negatives of one another, then, by symmetry, the area to the right of z-score (z₂) is always equal to the area to the left of z-score (z₁).
This ultimately implies that, the total areas under a standard normal curve in two tails can be determined by calculating the area to the left of z-score (z₁) and multiplying the value by two (2).
From the z-score table, the area to the left of z-score (z₁ = -2.575) is given by:
The area to the left of z-score (z₁ = -2.575) = 0.0049
For the total areas, we have:
Total areas under a standard normal curve = 2 × 0.0049
Total areas under a standard normal curve = 0.0098.
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A communications satellite is directly above the extension of a line between receiving towers A and B. It is determined
from radio signals that the angle of elevation from tower A is 88.9° and the angle of elevation from tower B is 85.8°. If
A and B are 658 km apart, how far is the satellite from A?
(Ignore the curvature of the earth.)
The distance of the satellite from tower A, using the law of sines, is given by:
11987.216 km.
What is the law of sines?Suppose we have a triangle in which the sides and angles can be seen as follows:
Side with a length of a is opposite to the angle A.Side with a length of b is opposite to the angle B.Side with a length of c is opposite to the angle C.The lengths and the sine of the angles are related by the equality shown as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The internal angles of the triangle in this problem are given as follows:
85.8º -> given.91.1º -> as an angle is supplementary with it's exterior angle, that is, the sum of their measures is of 180º.3.1º -> as the sum of the internal angles of a triangle is of 180º.The distance of the satellite from the tower A is opposite to the angle of 85.8º, while the distance between the towers of 658 km is opposite from the angle of 3.1º, hence the following relation is established:
sin(85.8º)/d = sin(3.1º)/658.
Applying cross multiplication, the distance is obtained as follows:
d = 658 x sin(85.8º)/sin(3.1º)
d = 11987.216 km.
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