Answer:
If you want to round to the nearest hundredths, the answer is 1.73 seconds.
Step-by-step explanation:
So we want to solve h(t)=5 for t because this will give us the time,t, that the diver was 5 m above the water.
[tex]-4.9t^2+1.5t+17=5[/tex]
My goal here in solving this equation is to get it into [tex]at^2+bt+c=0[/tex] so I can use the quadratic formula to solve it.
The quadratic formula is [tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].
So let's begin that process here:
[tex]-4.9t^2+1.5t+17=5[/tex]
Subtract 5 on both sides:
[tex]-4.9t^2+1.5t+12=0[/tex]
So let's compare the following equations:
[tex]-4.9t^2+1.5t+12=0[/tex]
[tex]at^2+bt+c=0[/tex].
[tex]a=-4.9[/tex]
[tex]b=1.5[/tex]
[tex]c=12[/tex]
Now we are ready to insert in the quadratic formula:
[tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]t=\frac{-1.5 \pm \sqrt{(1.5)^2-4(-4.9)(12)}}{2(-4.9)}[/tex]
I know this can look daunting when putting into a calculator.
But this is the process I used on those little calculators back in the day:
Put the thing inside the square root into your calculator first. I'm talking about the [tex](1.5)^2-4(-4.9)(12)[/tex].
This gives you: 237.45
Let's show what we have so far now:
[tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]t=\frac{-1.5 \pm \sqrt{(1.5)^2-4(-4.9)(12)}}{2(-4.9)}[/tex]
[tex]t=\frac{-1.5 \pm \sqrt{237.45}}{2(-4.9)}[/tex]
I'm going to put the denominator, 2(-4.9), into my calculator now.
[tex]t=\frac{-1.5 \pm \sqrt{237.45}}{-9.8}[/tex]
So this gives us two numbers to compute:
[tex]t=\frac{-1.5 - \sqrt{237.45}}{-9.8} \text{ and } t=\frac{-1.5+\sqrt{237.45}}{-9.8}[/tex]
I'm actually going to type in -1.5-sqrt(237.45) into my calculator, as well as, -1.5+sqrt(237.45).
[tex]t=\frac{-16.90941271}{-9.8} \text{ and } t=\frac{13.90941271}{-9.8}[/tex]
We are going to use the positive number only for our solution.
So we have the answer is whatever that first fraction is approximately:
[tex]t=\frac{-16.90941271}{-9.8}=1.725450277[/tex].
The answer is approximately 1.73 seconds.
Final answer:
To determine when the diver was 5 m above the water, we need to solve the equation h(t) = 5. Using the given equation h(t) = -4.9t² + 1.5t + 17, we substitute 5 for h(t) and solve the resulting quadratic equation. The solution is t ≈ 1.82 seconds.
Explanation:
To determine when the diver was 5 m above the water, we need to solve the equation h(t) = 5. We can substitute 5 for h(t) in the given equation and solve for t:
5 = -4.9t² + 1.5t + 17
-4.9t² + 1.5t + 12 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac))/2a
Plugging in the values a = -4.9, b = 1.5, and c = 12, we get:
t = (-1.5 ± √(1.5^2 - 4(-4.9)(12)))/(2(-4.9))
Simplifying further, we find two solutions: t ≈ 1.82 seconds and t ≈ -0.44 seconds. Since time cannot be negative in this context, the diver was 5 m above the water at approximately 1.82 seconds.
Find the equation of the line passing through 2,11
Answer:
Step-by-step explanation:
There is an infinite number of lines that pass through the point (2, 11). Therefore, there is an infinite number of equations. To define a single line, you must have at least two points. One point is not enough.
(WILL MARK BRAINIEST PLEASE ASSIST) Define the inverse secant function by restricting the domain of the secant function to the intervals: 0,π2 and π2,π and sketch the inverse function’s graph.
Answer:
see the attachment
Step-by-step explanation:
The graph attached shows the secant function in red. The restriction to the interval [0, π/2] is highlighted by green dots, and the corresponding inverse function is shown by a green curve.
The restriction to the interval [π/2, π] is highlighted by purple dots, and the corresponding inverse function is shown in purple.
The dashed orange line at y=x is the line over which a function and its inverse are mirror images of each other.
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of each should he use?
Answer:
3lbs of Cashews
Step-by-step explanation:
lbs of Cashews, and 7 lbs of Peanuts
$4.00P + 6.50C = ($4.75/lbs)(10lbs)
$4.00(7) + $6.50(3) = $47.50
$28.00 + $19.50 = $47.50
$47.50 = $47.50
Therefore it's 3lbs of Cashews
Answer:
3lbs of Cashews
hope it helps! x
Which statements about the diagram are true? Select three options.
x = 63
y = 47
z = 117
x + y = 180
x + z = 180
Answer:
x = 63z = 117x + z = 180Step-by-step explanation:
x is a "corresponding" angle for the one marked 63°. Here, corresponding angles are congruent, so x = 63°.
__
x and z are "same-side interior angles," so are supplementary. Their sum is 180°. x + z = 180°.
__
Because x and z are supplementary and z and 63° are supplementary, you know that ...
z = 180° -63°
z = 117°
_____
Comments on the other answer choices
The value of y can be computed using the fact that the sum of angles interior to the triangle is 180°. The unmarked triangle interior angle is a vertical angle to the one labeled 63°, so it is 63°. Then the value of y is ...
y° = 180° -47° -63° = 70° . . . . . . . not 47°
__
We already know that 63° + y + 47° = 180° and x = 63°. That means ...
x + y + 47° = 180°
so it cannot be true that x+y = 180.
Answers are 1,3, and 5
What is the sum of the geometric series?
4
E (-2)(-3)^n-1
n=1
A. –122
B. –2
C. 40
D. 54
[tex]
\Sigma_{n=1}^{4}-2\cdot(-3)^{n-1} \\
(-2)(-3)^{1-1}+(-2)(-3)^{2-1}+(-2)(-3)^{3-1}+(-2)(-3)^{4-1} \\
-2+6-18+54 \\
\boxed{40}
[/tex]
So the answer is C,
[tex]\Sigma_{n=1}^{4}-2\cdot(-3)^{n-1}=40[/tex]
Hope this helps.
r3t40
The sum of the finite geometric series (-2)(-3)ⁿ⁻¹ for n=1 to n=4 is 40, calculated using the geometric series sum formula.So,option C is correct.
The sum of a finite geometric series with a general term given as (-2)(-3)ⁿ⁻¹ where 'n' ranges from 1 to 4. To find the sum of a geometric series, we need to identify the first term (a) and the common ratio (r), and then use the formula Sₙ = a(1 - rⁿ) / (1 - r), where n is the number of terms.
The first term of the series can be found by substituting n = 1 into the general expression, yielding a = (-2)(-3)¹⁻¹ = -2. The second term, with n = 2, is (-2)(-3)²⁻¹ = -6(-3) = 18, indicating a common ratio of -3.
Thus, the sum of the series for the first four terms can be calculated as:
S₄ = (-2)(1 - (-3)⁴) / (1 - (-3))
S₄= (-2)(1 - 81) / (1 + 3)
S₄= (-2)(-80) / 4
S₄ = 160 / 4
S₄ = 40
Therefore, the sum of the given geometric series is 40.
An employee who earned $550 a week working 35 hours had her pay increased by 5 percent. Later, her hours were reduced to 30 per week, but the new hourly rate of pay was retained. What was her new amount of weekly pay?
Answer:
$495
Step-by-step explanation:
After the 5% raise, her weekly pay was ...
$550 × 1.05 = $577.50
If she works 35 hours for that pay, her hourly rate is
$577.50/35 = $16.50
Then, working 30 hours, her weekly pay will be ...
30 × $16.50 = $495.00
To find the new amount of weekly pay, multiply the increase in pay by the new number of hours. The new amount is $577.50.
Explanation:To find the new amount of weekly pay, we need to calculate the increase in pay and then multiply it by the new number of hours.
The employee's pay increased by 5 percent. This means the pay increased by 5% of $550, which is equal to 0.05 imes 550 = $27.50.
Her new hourly rate of pay is the same, so it remains at $550 + $27.50 = $577.50.
Finally, we need to calculate the new amount of weekly pay, taking into account the reduced number of hours. The new pay per hour is $577.50 / 30 = $19.25. Multiply this by the new number of hours to get the new amount of weekly pay: $19.25 imes 30 = $577.50.
Consider the function f(x) = 2X and the function g(x).
How will the graph of g(x) differ from the graph of f(x)?
Answer:
(A)
Step-by-step explanation:
Answer:
Option A is correct.
Step-by-step explanation:
Given : [tex]f(x) =2^{x}[/tex] and [tex]g(x) =2^{x+4}[/tex].
To find : How will the graph of g(x) differ from the graph of f(x).
Solution : We have given that
[tex]f(x) =2^{x}[/tex] and g(x) [tex]g(x) =2^{x+4}[/tex]
By the transformation Rule : If f(x) →→ f(x +h) if mean graph of function shifted to left by h units .
Then graph of [tex]g(x) =2^{x+4}[/tex] is the graph of [tex]f(x) =2^{x}[/tex] is shifted by 4 unt left.
Therefore, Option A is correct.
NEED HELP WITH MATH QUESTION ITS ABOUT FINDING AREA OF A TRIANGLE !! I WOULD BE REALLY GRATEFUL IS SOMEONE HELPED ME WITH A FEW QUESTIONS AFTER THIS
Answer:
65.8 in²
Step-by-step explanation:
Given a triangle with 2 sides and the included angle then the area (A) is
A = 0.5 × a × b × sinΘ
where a, b are the 2 sides and Θ the included angle
here a = 18, b = 12 and Θ = 147°, hence
A = 0. 5 × 18 × 12 × sin147°
= 108 × sin147° ≈ 65.8 ( to the nearest tenth )
Answer:
The area of triangle is 59.2 in².
Step-by-step explanation:
If a, b and c are three sides of a triangle then the area of triangle by heron's formula is
[tex]A=\sqrt{s(s-a)(s-b)(s-c)[/tex] .... (1)
where,
[tex]s=\frac{a+b+c}{2}[/tex]
From the given figure it is clear that the length of sides are 12 in, 18 in and 28.8 in. The value of s is
[tex]s=\frac{12+18+28.8}{2}=29.4[/tex]
Substitute s=29.4, a=12, b=18 and c=28.8 in equation (1).
[tex]A=\sqrt{29.4(29.4-12)(29.4-18)(29.4-28.8)}[/tex]
[tex]A=\sqrt{3499.0704}[/tex]
[tex]A=59.15294[/tex]
[tex]A\approx 59.2[/tex]
Therefore the area of triangle is 59.2 in².
What is the product?
Answer:
=20s³+50s²+32s+6
Step-by-step explanation:
We multiply each of the term in the initial expression by the the second expression as follows:
4s(5s²+10s+3)+2(5s²+10s+3)
=20s³+40s²+12s+10s²+20s+6
Collect like terms together.
=20s³+50s²+32s+6
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
C'(4, 4)
Step-by-step explanation:
We assume dilation is about the origin, so all coordinates are multiplied by the scale factor:
C' = 2C = 2(2, 2) = (4, 4)
Find the value of Y [Inscribed Angle]
Check the picture below.
Answer:
x = 60°
Step-by-step explanation:
From ΔOPQ,
∠OPQ = 120° [ angle at the center inscribed by arc PQ ]
PQ ≅ OQ
so opposite angles to PQ and OQ will be equal
∠OPQ ≅ ∠OQP
∠OPQ + ∠OQP + ∠POQ = 180°
∠OPQ + ∠OPQ + 120 = 180°
2∠OPQ = 180 - 120 = 60°
∠OPQ = 30°
Since radius OP is perpendicular to tangent.
so ∠OPQ + Y = 90°
y + 30° = 90°
y = 90 - 30 = 60°
Answer x = 60°
Select the correct answers in the table.
Answer:
see below
Step-by-step explanation:
To find miles per hour, divide miles by hours:
(5 2/3 mi)/(2 2/3 h) = (17/3 mi)/(8/3 h) = (17/8) mi/h = 2 1/8 mi/h
Hours per mile is the reciprocal of that:
1/(17/8 mi/h) = 8/17 h/mi
If f(x) = -7x + 1 and g(x) = Square root of x-5,
what is (fºg)(41)?
This is similar to the other question you posted. Follow the same steps as before.
First find g(41).
g(41) = sqrt{x - 5}
g(41) = sqrt{41 - 5}
g(41) = sqrt{36}
g(41) = 6
We now find f(6).
f(6) = -7(6) + 1
f(6) = -42 + 1
f(6) = -41
Answer:
(fºg)(41) = -41
Did you follow?
I would like some help with this question plz
Answer:
Step-by-step explanation:
As the value of a increases, the radical function sweeps out higher, increasing the range of the function. The k value moves it up or down. A "+k" moves up (for example, +3 moves the function up 3 from the origin). The h value moves it side to side. A positive h value moves to the right and a negative h value moves to the left. For example, √x-3 moves 3 to the right and √x+3 moves 3 to the left.
In summary, a and k affect the range of the function, k being the "starting point" and a being the "ending point"; h affects the domain of the function.
Which type of transformation of the parent function is shown by the graph
Answer:
horizontal stretch
Step-by-step explanation:
yeye
Parent functions are the simplest form of a given function. Parent function have x as the term with the highest degree and a general form,
[tex]Y=ax+b[/tex]
Transformation of the function takes basic and changes it slightly with predetermined methods. This change will cause the graph of the function to be shifted or moved from the original position.
Given-
We have given the graphs and we have to identify the transformation of the parent function which is shown in the graph. For this we have an idea about the parent function and transformation of the function.
What is parent function?Parent functions are the simplest form of a given function. Parent function have x as the term with the highest degree and a general form,
[tex]Y=ax+b[/tex]
TransformationTransformation of the function takes basic and changes it slightly with predetermined methods. This change will cause the graph of the function to be shifted or moved from the original position.
Transformation of function is of different types.
Horizontal stretch, when graph is shifted towards right or left it is called the horizontal stretch transformation of the function. Vertical stretch, when graph is shifted towards up or down it is called the horizontal stretch transformation of the function.In the given graph the graph is shifted right and hence the transformation of the parent function is horizontal stretch.
Learn more about the transformation of the function here;
https://brainly.com/question/4135838
i rlly h8 math so pwease help me asap!!!! i'll give u brainliest if ur correct!
Answer:
see below
Step-by-step explanation:
sqrt(2) * sqrt(2) = sqrt(4) = 2
sqrt(5) * sqrt(7) = sqrt(35)
sqrt(2) * sqrt(18) = sqrt(36) = 6
sqrt(2)*sqrt (6) = sqrt(12) = sqrt(4 *3) = sqrt(4) sqrt(3) = 2 sqrt(3)
4/3 * 12/3 = 48/9 This is rational because it is written as a fraction with no square roots
32/4 * 15/4 = 480/16 =30 This can be rewritten as 30/1. This is rational because it is written as a fraction with no square roots
sqrt(3)/2 * 22/7 = 11 sqrt(3)/7 This is not rational because there is a square root in the numerator
sqrt(11) *2/3 = 2sqrt(11)/3 This is not rational because there is a square root in the numerator
Washing his dad's car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take Levi's dad to wash the car by himself
Answer:
1 hour and 40 minutes
Step-by-step explanation:
Levi's dad takes time to wash the car by himself is 1.667 hours which is 1 hour and 40 minutes.
What are ratio and proportion?A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Washing his dad's car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour.
Levi's dad take time to wash the car by himself will be
We know that the time is inversely proportional to the work.
Let t₁ is the time taken by Levi and t₂ is the time taken by Levi's dad.
We know that the formula
[tex]\begin{aligned} \dfrac{1}{t_1} + \dfrac{1}{t_2} &= 1\\\\\dfrac{1}{2.5} +\dfrac{1}{t_2} &= 1\\\\\dfrac{1}{t_2} &= 1 - \dfrac{1}{2.5}\\\\\dfrac{1}{t_2} &= \dfrac{3}{5}\\\\t_2 &= \dfrac{5}{3}\\\\t_2 &= 1.667 \end{aligned}[/tex]
Levi's dad takes time to wash the car by himself is 1.667 hours which is 1 hour and 40 minutes.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
The area of rectangle ABCD is 72 square inches. A diagonal of rectangle ABCD is 12 inches and the diagonal of rectangle EFGH is 22 inches. Find the area of rectangle EFGH. Round to the nearest square inch if necessary.
Answer:
The area of rectangle EFGH is [tex]242\ in^{2}[/tex]
Step-by-step explanation:
For this problem I assume that rectangle ABCD and rectangle EFGH are similar
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
Let
z ------> the scale factor
The scale factor is the ratio between the diagonals of rectangles
so
[tex]z=\frac{22}{12}=\frac{11}{6}[/tex]
step 2
Find the area of rectangle EFGH
we know that
If two figures are similar, then the ratio of its areas is the scale factor squared
Let
z------> the scale factor
x -----> area of rectangle EFGH
y ----> area of rectangle ABCD
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{11}{6}[/tex]
[tex]y=72\ in^{2}[/tex]
substitute and solve for x
[tex](\frac{11}{6})^{2}=\frac{x}{72}[/tex]
[tex]\frac{121}{36}=\frac{x}{72}[/tex]
[tex]x=\frac{121}{36}(72)[/tex]
[tex]x=242\ in^{2}[/tex]
The area of rectangle EFGH is approximately 242 square inches.
To find the area of rectangle EFGH given the diagonal lengths of both rectangles and the area of rectangle ABCD, we need to use the properties of rectangles and their diagonals.
Step 1: Analyze Rectangle ABCD
For rectangle ABCD:
- Area [tex]\(A_{ABCD} = 72\)[/tex] square inches
- Diagonal [tex]\(d_{ABCD} = 12\)[/tex] inches
We know the area of a rectangle is given by:
[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]
Let the length be l and the width be w. So,
[tex]\[ l \times w = 72 \][/tex]
Also, for the diagonal of a rectangle, we use the Pythagorean theorem:
[tex]\[ d = \sqrt{l^2 + w^2} \]\\Given \(d_{ABCD} = 12\),\[ 12 = \sqrt{l^2 + w^2} \]\[ 144 = l^2 + w^2 \][/tex]
Step 2: Solve for l and w
We have two equations:
[tex]1. \( l \times w = 72 \)\\2. \( l^2 + w^2 = 144 \)[/tex]
We can solve these equations simultaneously. First, express \(w\) in terms of \(l\):
[tex]\[ w = \frac{72}{l} \]\\Substitute this into the second equation:\[ l^2 + \left(\frac{72}{l}\right)^2 = 144 \]\[ l^2 + \frac{5184}{l^2} = 144 \][/tex]
Multiply every term by [tex]\(l^2\)[/tex] to clear the fraction:
[tex]\[ l^4 + 5184 = 144l^2 \]\[ l^4 - 144l^2 + 5184 = 0 \]Let \(x = l^2\). Then the equation becomes:\[ x^2 - 144x + 5184 = 0 \][/tex]
Solve this quadratic equation using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\[ x = \frac{144 \pm \sqrt{144^2 - 4 \cdot 1 \cdot 5184}}{2 \cdot 1} \]\[ x = \frac{144 \pm \sqrt{20736 - 20736}}{2} \]\[ x = \frac{144 \pm 0}{2} \]\[ x = 72 \][/tex]
So, [tex]\( l^2 = 72 \) and \( w^2 = 72 \)[/tex]. Therefore:
[tex]\[ l = \sqrt{72} = 6\sqrt{2} \]\[ w = \sqrt{72} = 6\sqrt{2} \][/tex]
Step 3: Analyze Rectangle EFGH
For rectangle EFGH:
- Diagonal [tex]\(d_{EFGH} = 22\)[/tex] inches
Let the length be L and the width be W. The relationship for the diagonal is:
[tex]\[ d_{EFGH} = \sqrt{L^2 + W^2} \]Given \(d_{EFGH} = 22\),\[ 22 = \sqrt{L^2 + W^2} \]\[ 484 = L^2 + W^2 \][/tex]
Step 4: Determine Area of Rectangle EFGH
Since the diagonals scale, we assume the rectangles are similar. Thus, the ratios of the corresponding sides (lengths and widths) are the same, and their areas scale with the square of the ratio of the diagonals:
[tex]\[ \text{Area ratio} = \left(\frac{d_{EFGH}}{d_{ABCD}}\right)^2 = \left(\frac{22}{12}\right)^2 = \left(\frac{11}{6}\right)^2 = \frac{121}{36} \][/tex]
So, the area of EFGH is:
[tex]\[ A_{EFGH} = A_{ABCD} \times \frac{121}{36} = 72 \times \frac{121}{36} = 72 \times 3.3611 \approx 242 \text{ square inches} \][/tex]
Thus, the area of rectangle EFGH is approximately 242 square inches.
PLEASE HELP ME!! D:
Use the graph of the line to answer the questions.
What is an equation of the line in point-slope form?
How can the point-slope form be written in function notation?
Answer:
Point-slope form:
[tex]y-0=\frac{1}{3} (x-1)\\f(x)-0=\frac{1}{3}(x-1)[/tex]
Slope-intercept form:
[tex]y=\frac{1}{3}x-\frac{1}{3} \\f(x)=\frac{1}{3} x-\frac{1}{3}[/tex]
Step-by-step explanation:
You have points on that line at (-2, -1) and (1, 0). To find your slope using those points, use the slope formula.
[tex]\frac{y2-y1}{x2-x1} \\\\\frac{0-(-1)}{1-(-2)} \\\\\frac{0+1}{1+2} \\\\\frac{1}{3}[/tex]
Now that we have your slope, you can use your slope and one of your points to write an equation in point-slope form.
[tex]y-y1=m(x-x1)\\y-0=\frac{1}{3} (x-1)\\y=\frac{1}{3} x-\frac{1}{3}[/tex]
To put it in function notation, substitute y for f(x).
[tex]f(x)-0=\frac{1}{3} (x-1)\\f(x)=\frac{1}{3} x-\frac{1}{3}[/tex]
First answer is y+1=(1/3) (x+2)
Second answer is f(x) =(1/3) x-(1/3)
In the circle , mBC =38 and mAD =146
What is m
Answer:
m<AED = 92°
Step-by-step explanation:
It is given that,
measure of arc BC = 38° therefore m<BDC = 38/2 = 19°
measure of arc AD = 146° therefore m<ACD = 146/2 = 73°
To find the measure of <CED
Consider the ΔCDE
m<D = m<BDC = 19° and
m<C = m<ACD = 73°
By using angle sum property m<CED can be written as,
m<CED = 180 -( m<D + m<C )
= 180 - (19 + 73)
= 180 - 92
= 88°
To find the measure of <AED
<AED and <CED are linear pair
m<AED + m<CED = 180
m<AED = 180 - m<CED
= 180 - 88
= 92°
Therefore m<AED = 92°
Scott had an average of 83 on his first three exams. He later scored an average of 92 on the next six exams. What is his average for all nine exams. Round to the nearest tenth if necessary.
Answer:89
Step-by-step explanation:
Given scott had an average of 83 on his first three exams
i.e. the sum of first three exams [tex]\sum S_1=83\times 3[/tex]
later he scored an average on the next six exams
i.e. the sum of later 6 exams is [tex]\sum S_2=92\times 6[/tex]
[tex]\sum S_1+\sum S_2=83\times 3+92\times 6=801[/tex]
therefore his average score is =[tex]\frac{801}{9}=89[/tex]
Thus his average score is 89
To find Scott's average for all nine exams, add up the scores from the first three and next six exams, then divide by the total number of exams.
Explanation:To find Scott's average for all nine exams, we need to calculate the overall average using the given averages for the first three and next six exams.
The average of the first three exams is 83, and the average of the next six exams is 92. To find the average for all nine exams, we can use the formula:Total sum of scores / Number of exams
So, Scott's average for all nine exams is:(83*3 + 92*6) / 9 = 89.1111...
Rounding to the nearest tenth, Scott's average for all nine exams is 89.1.
Learn more about Calculating averages here:
https://brainly.com/question/18554478
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In the system below, use equation (1) with equation (2) to eliminate x. Then use equation (1) with equation (3) to eliminate x. x-y-2z=4 (1) -x+3y-z=8 (2) -2x-y-4z=-1 (3) What is the new 2 × 2 system?
Answer:
2y -3z = 12-3y -8z = 7Step-by-step explanation:
(1) +(2) ⇒ (x -y -2z) +(-x +3y -z) = (4) +(8)
2y -3z = 12
__
2(1) +(3) ⇒ 2(x -y -2z) +(-2x -y -4z) = 2(4) +(-1)
-3y -8z = 7
___
The reduced system of equations is ...
2y -3z = 12-3y -8z = 7Answer:
2y - 3z = 12.
-3y - 8z = 7.
Step-by-step explanation:
x - y - 2z = 4 (1)
-x + 3y - z = 8 (2)
-2x - y - 4z = -1 (3)
Adding (1) + (2):
2y - 3z = 12.
2 * (1) + (3) gives:
-3y - 8z = 7.
What is the slope of the line passing through the points (2,-5) and(4,1)
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-5)}{4-2}\implies \cfrac{1+5}{2}\implies \cfrac{6}{2}\implies 3[/tex]
In the figure below, if angle T measures 130 degrees, what is the measure of angle Q?
Circle theorem:
The angle at the centre (T) is double the angle at the circumference (Q)
---> That also means that:
The angle at the circumference (Q) is half the angle at the centre (T)
Since T = 130 degrees;
Q = 130 divided by 2
= 65°
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Answer:
∠Q = 65°
Answer:
m<Q = 65°
Step-by-step explanation:
It is given that <T = 130°
To find the <Q
From the figure we can see that <T is the central angle made by the arc RS
And <Q is the angle made by the arc RS on minor arc.
We know that m<Q = (1/2)m<T
We have m<T = 130°
Therefore m<Q = 130/2 = 65°
HELLPPPPP!!!!
Which two of the functions shown here have identical graphs and why?
Answer:
Answer C
Step-by-step explanation:
Logs work that way. When you subtract one log from another, you can rewrite it as a fraction.
f and h, because the log of a quotient is the difference of the log.
The answer is option C.
Logs work that way. When you subtract one log from another, you can rewrite it as a fraction.
What do logs mean?A logarithm is a power to which a range of should be raised for you to get a few different wide varieties (see segment 3 of this Math evaluate for extra approximately exponents). As an example, the bottom ten logarithms of a hundred is two because ten raised to the electricity of is one hundred: log a hundred = 2.
Learn more about logarithm here: https://brainly.com/question/25710806
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Please help with this question
Answer:
15/17
Step-by-step explanation:
You can use what is called the Pythagorean identity:
sin(θ)² + cos(θ)² = 1
(-8/17)² + cos(θ)² = 1
cos(θ)² = 1 - 64/289 = 225/289
cos(θ) = √(225/289)
cos(θ) = 15/17 . . . . . . . cosine is positive in the 4th quadrant
There are 527 pencils,646 erasers and 748 sharpeners. These are to be put in separate packets containing the same number of items.find the maximum number of items possible in each packet.
Answer:
31 pencils38 erasers44 sharpenersStep-by-step explanation:
The number of packets is the greatest common divisor of the given numbers of pencils, erasers, and sharpeners.
It can be helpful to look at the differences between these numbers:
748 -646 = 102
646 -527 = 119
The difference of these differences is 17, suggesting that will be the number of packets possible.
527 = 17 × 31
646 = 17 × 38
748 = 17 × 44
The numbers 31, 38, and 44 are relatively prime (31 is actually prime), so there can be no greater number of packets than 17.
There will be 31 pencils, 38 erasers, and 44 sharpeners in each of the 17 packets.
_____
We may have worked the wrong problem. The way it is worded, the maximum number of items in each packet will be 527 pencils, 646 erasers, and 748 sharpeners in one (1) packet. The minimum number of items in each packet will be the number that corresponds to the maximum number of packets. Since 17 is the maximum number of packets, each packet's contents are as described above.
17 is the only common factor of the given numbers, so will be the number of groups (plural) into which the items can be arranged.
Rewrite the equation for x, and express its value in terms of a.
3/a x-4=20
Answer:
x=8a
Step-by-step explanation:
3/a x-4=20
We need to solve for x
Add 4 to each side
3/a x-4+4=20+4
3/a x = 24
Multiply each side by a/3 so we can get x alone
a/3 *3/a x = 24 * a/3
x = 8a
Answer:
x=8a
Step-by-step explanation:
We have to solve for x.
Steps:Add 4 to each side
Multiply each side by a/3 so we can get x
HELP!!
Type the correct answer in each box. Round the vector’s magnitude to the nearest tenth.
Vector u has its initial point at (14, -6) and its terminal point at (-4, 7). Write the component form of u and find its magnitude.
Answer:
Component form of u is (-18,13)
The magnitude of u is 22.2
Step-by-step explanation:
The component form of a vector is an ordered pair that describe the change is x and y values
This is mathematically expressed as (Δx,Δy) where Δx=x₂-x₁ and Δy=y₂-y₁
Given ;
Initial points of the vector as (14,-6)
Terminal point of the vector as (-4,7)
Here x₁=14,x₂=-4, y₁=-6 ,y₂=7
The component form of the vector u is (-4-14,7--6) =(-18,13)
Finding Magnitude of the vector
║u=√(x₂-x₁)²+(y₂-y₁)²
║u=√-18²+13²
║u=√324+169
║u=√493
║u=22.2
Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was 35 the size of the brand name. If the generic television set is 16 inches by 40 inches, what are the dimensions of the brand name television?
List the dimensions of the brand name television.
Show your work.
Answer:
The dimensions of the brand name television are [tex]26\frac{2}{3}\ in[/tex] by [tex]66\frac{2}{3}\ in[/tex]
Step-by-step explanation:
we know that
The generic version was based on the brand name and was 3/5 the size of the brand name
Let
x----> the length of the size of the brand name
y----> the width of the size of the brand name
Find the length of the size of the brand name
we know that
[tex]40=\frac{3}{5}x[/tex] -----> equation A
Solve for x
Multiply by 5 both sides
[tex]5*40=3x[/tex]
Rewrite and divide by 3 both sides
[tex]x=200/3\ in[/tex]
Convert to mixed number
[tex]200/3=(198/3)+(2/3)=66\frac{2}{3}\ in[/tex]
Find the width of the size of the brand name
we know that
[tex]16=\frac{3}{5}y[/tex] -----> equation B
Solve for y
Multiply by 5 both sides
[tex]5*16=3y[/tex]
Rewrite and divide by 3 both sides
[tex]x=80/3\ in[/tex]
Convert to mixed number
[tex]80/3=(78/3)+(2/3)=26\frac{2}{3}\ in[/tex]