It is given that speech can be 15 minutes, or within that time by 4 minutes.
This means that the speech time can vary around 15 minutes by 4 more or less minutes.
So the limits of speech times are:
Upper limit = 15 + 4 = 19 minutes
Lower limit = 15 - 4 = 11 minutes
So, to find out which absolute value equation represents these limits, we have to solve each absolute value equation.
1st equation:
\(\begin{gathered} |t+15|=4 \\ t+15=\pm4 \\ t+15=4,t+15=-4 \\ t=4-15,t=-4-15 \\ t=-11,t=-19 \end{gathered}\)As you can see, these are not the limits we want since they are negative.
So 1st equation is incorrect.
2nd equation:
\(\begin{gathered} |t-4|=15 \\ t-4=\pm15 \\ t-4=15,t-4=-15 \\ t=15+4,t=-15+4 \\ t=19,t=-11 \end{gathered}\)As you can see, these are not limits we want since 11 is negative.
So 2nd equation is also incorrect.
3rd equation:
\(\begin{gathered} |t-15|=4 \\ t-15=\pm4 \\ t-15=4,t-15=-4 \\ t=4+15,t=-4+15 \\ t=19,t=11 \end{gathered}\)Finally, we got the exact same limits that we wanted t = 19 minutes and t = 11 minutes
Therefore, the correct absolute value equation is the 3rd equation.
How much of the circle is shaded? Write your answer as a fraction in simplest form.
Answer:
11/24
Step-by-step explanation:
1/3 =8/24
1/8= 3/24
8/24+3/24=11/24
Evaluate the function /(x) = 5x²+2x for the given value of x. Simplify your answer.
h(-4)
Answer:
h(-4) = 72
Step-by-step explanation:
Given:
h(x) = 5x² +2x
Evaluate the function h(x) = 5x²+2x for x=-4 means to
find h(-4) by substituting x with -4:
h(-4) = 5·(-4)² +2·(-4)
h(-4) = 5·16 -2·4
h(-4) = 5·16 -2·4
h(-4) = 80 -8
h(-4) = 72
Find the surface area
Answer: 120 yds
Step-by-step explanation:
48+30+24+18+120 yds
Rewrite 0,88 as a common fraction
Answer: 22 / 25
Step-by-step explanation:
I know this because I know everything.
Answer:
\( \frac{22}{25} \)
What is the sum of 3 of the interior angles of a regular pentagon?
5 stars and like
Answer: 540°.
Step-by-step explanation:
by
Question 4 What is the z score in the following data set, for the value of x = 14? Consider this data set to represent the entire population. Round to two decimal places, if necessary. 6, 12, 9, 8, 15, 5, 7, 10, 11, 13 n't know One attempt 1.45 1.42 1.43 You answered 3 out of 3 correctly. Asking up to 7
The value of the z-score for the value x = 14 is 1.45
To get the z-score, we need the value of the mean and the standard deviation
We can get the mean by adding up all the numbers and dividing by the count of values
We have this as follows;
\(\begin{gathered} \frac{6+12+9+8+15+5+7+10+11+13}{10} \\ =\text{ }\frac{96}{10}\text{ = 9.6} \end{gathered}\)We also need the value of the standard deviation
We have the value of this as 3.04
The formula for the z-score is;
\(\frac{x-\operatorname{mean}}{SD}\)x in this case is the value 14
So, we have that;
\(\frac{14-9.6}{3.04}\text{ =1.45}\)A rectangular poster is 50 centimeters long and 25 centimeters wide. If 1 centimeter is approximately 0.4 inches, which of the following best represents the area of the poster in inches?
The area of the poster in inches is,
⇒ A = 4 inches²
We have to given that;
A rectangular poster is 50 centimeters long and 25 centimeters wide.
Here, 1 centimeter is approximately 0.4 inches
Hence, Lenght = 50 cm
Lenght = 50 x 0.4
= 2 inches
Width = 25 cm
= 25 x 0.4
= 1 inches
Thus, The area of the poster in inches is,
⇒ A = 1 x 4
⇒ A = 4 inches²
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A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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) Emily baked a cake in 42.5 minutes. She finished making dinner 9 1/10 minutes sooner than the cake. How long did it take her to make dinner? Hint: Change the 9 1/10 to a decimal
It took Emily 33.4 minutes to make dinner.
Define a mixed number?A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.
To solve the problem, we have to convert the mixed number \(9 \frac{1}{10}\) to a decimal number:
⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)
⇒ \(\frac{91}{10}\) = 9.1
This means that Emily finished making dinner 9.1 minutes sooner than the cake.
To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:
⇒ 42.5 - 9.1 = 33.4 minutes
Therefore, it took Emily 33.4 minutes to make dinner.
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The area of a square carpet is 5476 sq.cm. Find the length of its side.
Answer:
Area of square = (side)^2 = 5476 sq.cm
side = √5476 sq.cm
side = √(74 cm)^2
side = 74 cm
Step-by-step explanation:
Answer:
74
Step-by-step explanation:
Since it's a square, all the sides are the same. Just square root 5476.
m∠1=57°, m∠4=85°, m∠6=12°. Find m∠EAN.
Answer:
m∠EAN =154°
Step-by-step explanation:
m∠EAN = m∠1 + m∠4 + m∠6
as given in figure we can see that m∠EAN constitute three angles angle 1, 4 and 6
hence m∠EAN will be sum of these three angles.
Given
m∠1=57°, m∠4=85°, m∠6=12°.
m∠EAN = 57° + 85° + 12° = 154° (answer)
Estimate 6,976 + 3,983 + 13,560 by first rounding each number to the nearest thousand.
Answer:
Step-by-step explanation:
The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000, 3,983 rounded to the nearest thousand is 4,000, 13,560 rounded is 14,000.
7,000 + 4,000+ 14,000 = 25,000
Solve using law of sines, find the area of wxy.
Answer:
area = 828.27 cm²
Step-by-step explanation:
add a line from X, perpendicular to WY, call this point A.
angle Y = 180 - 33 - 121 = 26 degrees
sin 26 = XA/49
0.4384 = XA/49
XA = 21.48 which is the height of the triangle
cos 26 = YA/49
0.8988 = YA/49
YA = 44.04
tan 33 = 21.48/WA
0.6494 = 21.48/WA
WA = 33.08
YW = 77.12
(YW)(XA)(0.5) = area
(77.12)(21.48)(0.5) = area = 828.27 cm²
(x + 1) (x+8) multiply binomials and put in standard form.
Answer:
x² + 9x + 8
Step-by-step explanation:
Step 1: FOIL
x² + 8x + x + 8
Step 2: Combine like terms
x² + 9x + 8
Answer:
x^2 + 9x + 8
Step-by-step explanation:
(x + 1)(x + 8)
x(x + 1) +8(x + 1)
x^2 + x + 8x +8
x^2 + 9x + 8
Out of numbers: 5, 7, 21, 25, 28, 35, 42, 56, 75, and 80, choose those which are not factors of 42
Answer:
5, 25, 28, 35, 56, 75 80 are not the factors of 42
a marathon is about 26 miles liong which of these shows to convert 26 miles to feet
Answer:
137,280 feet
Step-by-step explanation:
1 mile = 5280 feet
26 * 5280 = 137280
Best of Luck!
Answer:
A marathon is about 26 miles long. Which of these shows how to convert 26 miles to feet?
Step-by-step explanation:
Pretty sure thats the answer
A birdbath holds 4 liters of water. How many milliliters does it hold?
Answer:
4000
Step-by-step explanation:
Answer:
4000
Step-by-step explanation:
You have to multiply the volume value by 1000. So 4 x 1000=4000
Find the value of the following expression:
(28 ⋅ 5−5 ⋅ 190)−2 ⋅ 5 to the power of negative 2 over 2 to the power of 3, whole to the power of 4 ⋅ 228 (5 points)
Write your answer in simplified form. Show all of your steps. (5 points)
Answer:
25
Step-by-step explanation:
Answer:
5^2 = 25
Step-by-step explanation:
Terry’s garden is in the shape of a quarter-circle with radius 24 meters. What is the area of her garden?
Answer: 1809.56 let me know if it is right?
Step-by-step explanation:
WILL GIVE BRAINLIEST
Answer: a.
Step-by-step explanation:
If there is a negative mark next to the whole fraction, that means both of the numbers are negative.
I am not sure if this answer is accurate. Please inform me if I am incorrect. TY.
Solve for x in the equation x squared minus 10 x + 25 = 35.
Answer:
x = 10.92, -0.92.
Step-by-step explanation:
x^2 - 10x + 25 = 35
The left side is a perfect square:
(x - 5)^2 = 35
x - 5 = +/- √35
x = 5 +/- √35
x = 10.92, -0.92.
B on Edge 2020!
X = 5±\(\sqrt{35}\)
Just got it right on the quiz, hope this helps!!
Which function is graphed below?
Which of the following explains how ΔBEI could be proven similar to ΔCEH using the AA similarity postulate? Quadrilateral ABDC, in which point F is between points A and C, point G is between points B and D, point I is between points A and B, and point H is between points C and D. A segment connects points A and D, a segment connects points B and C, a segment connects points I and H, and a segment connects points F and G. Segments AD, BC, FG, and IH all intersect at point E. ∠BEI ≅ ∠CEH because vertical angles are congruent; rotate ΔCEH 180° around point E, then translate point C to point B to confirm∠IBE ≅ HCE. ∠BEI ≅ ∠CEH because vertical angles are congruent; reflect ΔCEH across segment FG, then translate point C to point B to confirm∠IBE ≅ HCE. ∠BEI ≅ ∠CEH because vertical angles are congruent; rotate ΔCEH 180° around point E, then dilate ΔCEH to confirm segment EB ≅ segment EC. ∠BEI ≅ ∠CEH because vertical angles are congruent; reflect ΔCEH across segment FG, then dilate ΔCEH to confirm segment EH ≅ segment EI.
∠BEI ≅ ∠CEH because vertical angles are congruent; rotate ΔCEH 180° around point E, then translate point C to point B to confirm∠IBE ≅ HCE.
i got it right on the test
This flower is made up of yellow hexagons, red trapezoids, and green triangles.Write sentences to describe the ratios orthe shapes that make up this pattern.1.|2. How many of each shape would be intwo copies of this flower pattern? 6:9
1) In the flower, there is one red trapezoid, six yellow hexagons and 10 green triangles. The ratio of red trapezoids to yellow hexagons is 1:6, the ratio of red trapezoids to green triangles is 1:10 and the ratio of yellow hexagons to green triangles is 6:10 = 3:5.
2) In one copy, there is one red trapezoid, six yellow hexagons and 10 green triangles.
So in two copies, 2*1 = 2 red trapezoids, 2*6 = 12 yellow hexagons and 2*10 = 20 green triangles.
Solve each equation by completing the square.
d² - 24d + c
Answer:
d² - 24d + c = (d - 12)² - 144 + c
Could someone help me with this calc question please
I hope this helps you...
Assume lines n and m are parallel. If μ(∠)1=147°
, find the following angle measures. (Type each answer as a number, in the corresponding blank below.)
The angle measures of the numbered angles from <1- 8 would be listed below as follows:
<1=147°
<2= 33°
<3= 147°
<4=33°
<5=33°
<6=147°
<7=33°
<8=147°
How to determine the measures of the missing angles?When two parallel lines a crossed by a transverse line then the following occurs:
the pair of corresponding angles is equal. That is <2=<4the pair of interior alternate angles is equal. That is; <6=<3 and <2=<7the pair of exterior alternate angles is equal. That is;<1=<8,<5=<4interior angles on the same side of transversal are supplementary.That is; <2+<3=180°Learn more about parallel lines here:
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The table shows the age of a painting (x) in years, and its estimated dollar value (y).
A 4-column table with 6 rows. Column 1 is labeled x with entries 50, 54, 62, 65, 68, sigma-summation x = 299. Column 2 is labeled y with entries 1,200, 1,500, 2,400, 3,200, 4,100, sigma-summation y = 12,400. Column 3 is labeled x squared with entries 2,500, 2,916, 3,844, 4,225, 4,624, sigma-summation x squared = 18,109. Column 4 is labeled x y with entries 60,000, 81,000, 148,800, 208,000, 278,800, sigma-summation x y = 776,600.
Which regression equation correctly models the data?
y = 41.47x + 0.09
y = 41.47x + 1,279.93
y = 153.32x – 6,688.54
y = 153.32x – 6,325.76
Regression equation correctly models the data is: y = -43.98x + 1,279.93
To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.
Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.
The slope (m) can be calculated using the formula:
\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)
Plugging in the values from the table:
m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)
m = (776,600 - 3,708,800 / 6(18,109) - 89,401)
m = (-2,932,200 / 66,654)
m ≈ -43.98
The y-intercept (b) can be calculated using the formula:
b = (Σy - m(Σx)) / n
Plugging in the values from the table:
b = (12,400 - (-43.98)(299)) / 6
b ≈ 1,279.93
The correct regression equation that models the data is:
y = -43.98x + 1,279.93
Out of the given options, the correct regression equation is:
y = -43.98x + 1,279.93
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Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 18, 24, and 30 and a second triangle labeled D prime with side lengths of 6, 8, and 10
Determine the scale factor used.
Scale factor of one third
Scale factor of 3
Scale factor of 4
Scale factor of one fourth
The scale factor used to dilate triangle D to create triangle D' is 1/3. This means that each side length in triangle D' is one-third of the corresponding side length in triangle D.
To determine the scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.
In triangle D, the side lengths are given as 18, 24, and 30. In triangle D', the corresponding side lengths are given as 6, 8, and 10.
To find the scale factor, we can divide the corresponding side lengths of D' by the corresponding side lengths of D.
Scale factor = Length of corresponding side in D' / Length of corresponding side in D
For the corresponding sides, we have:
Scale factor = 6/18 = 1/3
Please note that the scale factor can also be determined by comparing the area or perimeter of the two triangles. However, in this case, we used the corresponding side lengths to find the scale factor.
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Which polynomial is prime?
O 3x³ + 3x² - 2x - 2
O 3x³ − 2x² + 3x − 4
-
O
4x³ + 2x² + 6x + 3
O
4x³+4x²-3x - 3
Answer:
B
Step-by-step explanation:
a prime polynomial is one which does not factor into 2 binomials.
its only factors are 1 and itself
attempt to factorise the given polynomials
3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )
= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(3x² - 2) ← in factored form
--------------------------------------------------
3x³ - 2x² + 3x - 4 ( factor the first/second terms
= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored
thus this polynomial is prime
----------------------------------------------------
4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )
= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term
= (2x + 1)(2x² + 3) ← in factored form
-------------------------------------------------
4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )
= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(4x² - 3) ← in factored form
--------------------------------------------------
the only polynomial which does not factorise is
3x³ - 2x² + 3x - 4