Answer:
2D
Step-by-step explanation:
i times two is 5
Jorge wants to divide 3x2−x−2 by x + 4 using synthetic division. Which answer shows the correct process? Synthetic division problem with divisor negative four, and the dividends are three, negative one, and negative two. Under the negative one is negative twelve, and under the negative two is forty-four. Under the equals line are the numbers three, eleven, and forty-two. Image with alt text: Synthetic division problem with divisor negative four, and the dividends are three, negative one, and negative two. Under the negative one is negative twelve, and under the negative two is forty-four. Under the equals line are the numbers three, eleven, and forty-two. Synthetic division problem with divisor negative four, and the dividends are three, negative one, and negative two. Under the negative one is negative twelve, and under the negative two is fifty-two. Under the equals line are the numbers three, negative thirteen, and fifty. Image with alt text: Synthetic division problem with divisor negative four, and the dividends are three, negative one, and negative two. Under the negative one is negative twelve, and under the negative two is fifty-two. Under the equals line are the numbers three, negative thirteen, and fifty. Synthetic division problem with divisor four, and the dividends are three, negative one, and negative two. Under the negative one is twelve, and under the negative two is negative forty-four. Under the equals line are the numbers three, negative eleven, and negative forty-six. Image with alt text: Synthetic division problem with divisor four, and the dividends are three, negative one, and negative two. Under the negative one is twelve, and under the negative two is negative forty-four. Under the equals line are the numbers three, negative eleven, and negative forty-six. Synthetic division problem with divisor four, and the dividends are three, negative one, and negative two. Under the negative one is twelve, and under the negative two is negative fifty-two. Under the equals line are the numbers
The graph that shows the correct synthetic division process is given at the end of the answer.
How does synthetic division works?In synthetic division, the coefficients of a polynomial are each divided by a value.This value is the zero of the divided polynomial, which goes into the far left box.For this problem, we have that:
The divisor is: 3x² - x - 2, hence the coefficients are: 3, -1, -2.The dividend is: x + 4, hence the bottom left term is -4.Then, from the graph, we have that:
The first coefficient, 3 is pushed to the bottom of the table.Then, each bottom term is multiplied with -4(3 x -4 = -12) and added with the next coefficient to get the result.-1 - 12 = -13, -13 x -4 = 52.-2 + 52 = 50.Hence, the result of the division of 3x² - x - 2 by (x + 4) is 3x - 13 with a remainder of 50.
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Evaluate the expression when c = -4 and x=7.
-5x+c
Answer:
-39
Step-by-step explanation:
Hello, to do this problem, we need to use substitution.
c=-4 and x=7
-5x+c
-5(7)+-4
-35-4
=-39
Hope that helps
:D
Answer:
c = -4
x = 7
- 5 (7) + (- 4)
- 35 + (- 4)
= - 39
Hope this helps :)
NEEEEEDDDD HELPPPPPP PLEASE...........
Solve for [x]. Each figure is a trapezoid.
Answer:
11
Step-by-step explanation:
Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,
[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]
Gruman Company purchased a machine for $198,000 on January 2, 2017. It made the following estimates:
Service life 5 years or 10,000 hours
Production 180,000 units
Residual value $18,000
In 2016, Gruman uses the machine for 1,700 hours and produces 40,000 units. In 2017, Gruman uses the machine for 1,200 hours and produces 34,000 units. If required, round your final answers to the nearest dollar.
Required:
Compute the depreciation for 2016 and 2017 under each of the following methods:
a. Straight-line method
b. Sum-of-the-years'-digits method
c. Double-declining-balance method
d. Activity method based on hours worked
e. Activity method based on units of output
a. Straight-line method: $36,000 $36,000
b. Sum-of-the-years'-digits method: $60,000 $48,000
c. Double-declining-balance method: $79,200, $47,520
d. Activity method based on hours worked: $30,600, $21,600
e. Activity method based on units of output $40,000 $34,000
Straight-line methodb. Straight line method
Depreciation expense = (Cost of asset - Salvage value) / Useful life
Depreciation expense=( $198,000 - $18,000 ) / 5
Depreciation expense = $36,000
b. Sum-of-the-years'-digits method
Sum-of-the-year digits = (Remaining useful life / Sum of the years ) x (Cost of asset - Salvage value)
Sum of the years = (1 +2 +3 +4 + 5 )
Sum of the years = 15
Year 1 Depreciation expense = (5/15) × ( $198,000 - $18,000 )
Year 1 Depreciation expense = $60,000
Year 2 Depreciation expense = (4/15) x ( $198,000 - $18,000 )
Year 2 Depreciation expense = $48,000
c. Double-declining-balance method
Depreciation factor = 2 x (1/Useful life)
Depreciation factor =2 x(1/5)
Depreciation factor = 0.4
Year 1 Depreciation expense = 0.4 x $198,000
Year 1 Depreciation expense= $79,200
Year 1 Book value = $198,000 - $79,200
Year 1 Book value= $118,800
Year 2 Depreciation expense= 0.4 x $118,800
Year 2 Depreciation expense= $47,520
d. Activity method based on hours worked
Activity method = (Hours worked / Total machine hours) x (Cost of asset - Salvage value)
Year 1 Depreciation expense = (1,700 / 10,000) x ( $198,000 - $18,000 )
Year 1 Depreciation expense = $30,600
Year 2 Depreciation expense = (1,200 / 10,000) x ( $198,000 - $18,000 )
Year 2 Depreciation expense = $21,600
e. Activity method based on units of output
Activity method = (Output produced / Total machine output capacity) x (Cost of asset - Salvage value)
Year 1 Depreciation expense = ( 40,000 / 180,000) x ( $198,000 - $18,000 )
Year 1 Depreciation expense = $40,000
Year 2 Depreciation expense= ( 34,000 / 180,000) x ( $198,000 - $18,000 )
Year 2 Depreciation expense = $34,000
Therefore the Straight-line method is $36,000 $36,000.
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A piece of wood was 12 feet long. Kendra cut the wood into pieces __
2
3 foot
long. How many pieces did Kendra make? State what strategy you will use
to answer the question, explain your choice, and then find the answer.
The number of pieces are 18 if the piece of wood was 12 feet long. Kendra cut the wood into pieces 2/3 foot.
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:
A piece of wood was 12 feet long. Kendra cut the wood into pieces __
2/3 foot.
Let x be the number of pieces:
12/x = 2/3
x = 36/2
x = 18
Thus, the number of pieces are 18 if the piece of wood was 12 feet long. Kendra cut the wood into pieces 2/3 foot.
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which of the following number lines shows the solution to the inequality given below? 3x + 1 <_ -11 or 4x - 3 > 9
The number line which shows the solution to the inequality is option C
Number lines which shows the solution to the inequality3x + 2 ≤ -11
or
4x - 3 > 9
3x + 2 ≤ -11
substract 2 from both sides3x ≤ -11 - 2
3x ≤ -13
divide both sides by 3x ≤ -13/3
x ≤ -4.33
or
4x - 3 > 9
Add 3 to both sides4x > 9 + 3
4x > 12
divide both sides by 4x > 12 / 4
x > 3
Ultimately, the answer to the inequalities is x ≤ -4.33 and x > 3
Therefore, the number line which shows the solution to the inequality is option C
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Elimination method.
Written as a simplified polynomial in standard form, what is the result when
(2x + 5)2 is subtracted from 10?
the spread of data set X is greater than the spread of data set Y, and the data sets are normally distributed. Which statement is true? A. The mean of data set X is greater than the mean of data set Y. B. The median of data set X is less than the median of data set Y. C. The standard deviation of data set X is greater than the standard deviation of data set Y. D. The range of data set X is less than the range of data set Y. E. The mode of data set X is greater than the mode of data set Y.
here u go I hope this is the answer ur looking for!
Joanne has a toy box. the box contains three toy cars two dollars and five balls. without looking is Joanne chooses a toy from the box what is the probability of not selecting a toy car
Answer:mkpewmg pmblembmfe
Step-by-step explanation:
7 t8gt385uhg
can someone help me with this ?
The height of the ball is given as 7.74 ft.
How to find the height of the ballWe have the value of h(X) to be
-[tex]-\frac{44x^{2} }{v^{2} } +x+6[/tex]
The initial velocity is given as v which is = 26
v = 26² = 676
the value of x is given as 2
We have to put these values in the formula
[tex]-\frac{44(2)^{2} }{676 } +2+6[/tex]
= 44 * 4/676 + 2 + 6
= -0.26 + 2 + 6
= 7.74
Hence we can say that the height of the ball is given as 7.74 ft.
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Pleaseeee
help me solve this
Answer:
x = 155°
Step-by-step explanation:
Given hexagon ABCDEF, you want to find the measure of interior angle E. Angles at vertices A, B, C, D, and F are specified.
Angle sumThe sum of the interior angles of an n-sided polygon is ...
angle sum = (n -2)180°
For the 6-sided polygon given, the sum of interior angles is ...
(6-2)180° = 720°
ApplicationThe interior angle at vertex B is 360° -80° = 280°.
The interior angle at vertex D is 180° -115° = 65°.
Then the sum of interior angles is ...
A +B +C +D +E +F = 720°
85° +280° +30° +65° +x +105° = 720° . . . . . substitute known values
565° +x = 720° . . . . . . . collect terms
x = 155° . . . . . . . . . . subtract 565°
__
Additional comment
The angles in the attached figure are drawn to scale.
An alternate solution might draw segment CX through vertex B so that the figure containing angle x has no reflex interior angles. Then the interior angles of pentagon ABXEF will total 540°. Known angles in that figure are A=85°, B=100°, X=95°, F=105°. Then E=x=540° -385° = 155°.
We took this approach initially, to verify that the angle sum of the given hexagon remained 720° even with the reflex interior angle at B.
what are two different operations with at least four numbers that equal 12
Answer:
3+3+3+3=12
48-12-12-12=12
Step-by-step explanation:
common sense :)
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.6 days.
(a) X is distributed normally.
(b) The median recovery time is 3 days.
(c) The z score of the patient who takes 4.2 days to recover is 0.75.
(d) The probability of spending more than 2.3 days in recovery is 66.64 %.
(e) The probability of spending between 3.7 and 4.2 days in recovery is 10.7 %.
(f) The 85th percentile for recovery times is 5.24 days.
(a) We are informed that a certain surgical procedure's recuperation time for patients is typically distributed. As a result, X is distributed normally.
(b) The median will be equal to the mean because the patient recovery time has a normally distributed distribution. The median is therefore 3 days.
(c) The formula for z score is given as:
z = X - μ / σ
Now, we have the mean μ = 3 days.
Standard deviation, σ = 1.6 days
The observed value, X = 4.2 days
Therefore,
z = ( 4.2 - 3) / 1.6
z = 1.2 / 1.6
z = 0.75
(d) When X = 2.3 days
Then the z score will be:
z = X - μ / σ
z = 2.3 - 3 / 1.6
z = - 0.7 / 1.6
z = - 0.4375
The corresponding area for z = 0.4375 is 0.3336.
In order to determine the likelihood for a period longer than 2.3 days, we must look at the region to the right, which we can locate by deducting 0.3336 from 1.
Therefore, the probability will be:
p = 1 - 0.3336
p = 0.6664
p = 66.64 %
(e) Now, for the probability between X = 3.7 days and 4.2 days.
z₁ = (3.7 - 3) / 1.6 = 0.7/1.6 = 0.4375
z₂ = (4.2 - 3) / 1.6 = 1.2 / 1.6 = 0.75
The area for a z score of 0.4375 is 0.1664 and the area to left for a z score 0.75 is 0.2734.
Then the probability between 3.7 days and 4.2 days will be:
p = 0.2734 - 0.1664
p = 0.107
p = 10.7 %
(f) For the 85th percentile:
For 0.85 the z score from the table is 1.4.
So, z = 1.4
z = X - μ / σ
1.4 = ( X - 3) / 1.6
(1.4)(1.6) = X - 3
2.24 = X -3
X = 2.24 + 3
X = 5.24 days
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The complete question is mentioned below:
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.6 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.
a. What is the distribution of X?
b. What is the median recovery time? __________days
c. What is the Z-score for a patient that took 4.2 days to recover?
d. What is the probability of spending more than 2.3 days in recovery?
e. What is the probability of spending between 3.7 and 4.2 days in recovery?
f. The 85th percentile for recovery times is _________days.
how many terms are in the sequence given of the following d=5,a1=-9 and an=141
The number of terms in the sequence with d=5 , a₁ = -9 and aₙ=141 is 31 terms.
Arithmetic Sequence
The nth term of the sequence { a , a+d , a+2d , ... , a+(n-1)d } is given by
aₙ=a+(n-1)d ...(i)
where , a = first term ,
d = common difference ,
n = number of terms ,
aₙ = nth term of the sequence .
It is given in the question that
first term (a) = -9
common difference (d) = 5
and nth term (aₙ) = 141
Substituting the values in equation (i) we get ,
141 = -9 + (n-1)5
simplifying further we get
141+9=(n-1)5
150 = 5n - 5
150+5 = 5n
155 = 5n
n=155/5
n=31.
Therefore , There are 31 terms in the sequence with d=5 , a1 = -9 and aₙ=141 .
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(3x^-4)6/9x^-12 can you please solve? I’ll give brainly
The answer to this given simplification (3x^-4)6/9x^-12 is 2 x^8.
What are exponents?
The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. In this essay, let's study more about exponents.
given:
(3x^-4)6/9x^-12
=x^-4 . 3 . 6 / 9 . x^-12
= 2. x^-4 / x^-12
=2 x^8
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Solve for x and show work
[tex] \longrightarrow \: - 4 + \frac{x + 4}{3} - 2 = 2(x + 1) \\ \longrightarrow \: { -4} + \frac{x}{3} + \frac{4}{3} - {2} = 2x + 2 \\ \longrightarrow \: { - 4}+ \frac{4}{3} - {2} - 2 = 2x - \frac{x}{3} \\ \longrightarrow \: -4 - 2 - 2 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: - 8 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: \frac{ - 20}{3} = \frac{5}{3} x \\ \longrightarrow \:\frac{ - 20}{3} \times \:3\: = 5x \\ \longrightarrow \:-20 = 5x\\\longrightarrow \:\frac{-20}{5} = x \\\longrightarrow \:x = - 4[/tex]
Monique has $48, then the following events happen, in order: • She earns $20 babysitting. • She spends $32. • She doubles her money doing chores.
Answer:
72
Step-by-step explanation:
$48 + $20 = $68
$68 - $32 = $36
$36 × 2 = $72
A probability experiment consists of rolling a 6-sided die. Find the probability of the event bel
rolling a number less than 5
The probability is
(Type an integer or decimal rounded to three decimal places as needed.)
The probability of rolling a number less than 5 is 0.667.
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event asked. The value is expressed from zero to one. An outcome is a value we can obtain.
As we are given a 6-sided dice therefore,
Total possible outcomes = 6
Favorable outcomes (that is less than 5) = 4 [that are; 1, 2, 3, 4]
probability = number of favorable outcomes/number of possible outcomes
probability = 4/6
4/6 = 2/3
= 0.6666666666666
To round the value to three decimal places, we need to see if the fourth value after decimal is more than 5 or not. If it is more than 5, preceding digit is increased by 1. therefore, by applying the rule to the value we get
= 0.667 [rounded to three decimal places as needed]
therefore, the probability of the event given, that is rolling a number less than 5 is 0.667.
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What percent of 332.5 is 66.5?
After calculation the percentage, we have come to find that 66.5 20% percent of 332.5 .
What is percentage?A percentage is a number or ratio in mathematics that could be expressed as a fraction of 100. If we need to calculate a percentage of a number, divide it by 100. As a result, the percentage denotes a part out of a hundred. The word % means "per 100." The symbol for it is "%."
Percentages can also be expressed as decimals or fractions, for example, 0.6%, 0.25%, and so on. Academic grades are calculated in terms of percentages. Ram, for example, received a 78% on his final exam. As a result, this percentage is calculated based on Ram's total marks across all subjects.
To find out percentage, We multiply the fraction of given numbers with 100
= 66.5/332.5 × 100
= 1/5 × 100
= 20%
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Triangle PQR has vertices P (3,8), Q (-5, 7), and R (0, 2). What are the coordinates of the vertices of the image after a reflection in the y-axis?
A) P' (3,-8)
B) P (-3,8)
□C) Q' (5,7)
□D) Q' (5-7)
□E) R¹ (-2,0)
OF) R¹ (0,2)
After the picture is reflected along the y-axis, its vertices will have the coordinates P'Q'R.:
[tex]P' = (-3,8)\\Q' = (5,7)\\R'=(0,2)[/tex]
What is coordinates of the vertices?
The triangle's vertices' coordinates are [tex](x_{1} ,y_{1} )[/tex], [tex](x_{2},y_{2})[/tex], and [tex](x_{3},y_{3} )[/tex]. The line that connects the first two is split in the ratio l:k, and the line that runs from the division point to the opposing angular point is divided in the ratio m:k+l.
Given:
Triangle PQR and vertices of triangle are
[tex]P=(3,8)\\Q=(-5,7)\\R=(0,2)[/tex]
The following rule results in a reflection about the y-axis:
[tex](x, y) ---- > (-x, y)[/tex]
Using the rule on each of our vertices, we have:
[tex](3, 8) ---- > (-3, 8)\\(-5, 7) ---- > (5, 7)\\(0, 2) ---- > (0, 2)[/tex]
Therefore,
After the picture is reflected along the y-axis, its vertices will have the coordinates P'Q'R.
[tex]P' = (-3,8)\\Q' = (5,7)\\R'=(0,2)[/tex]
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13 square kilometers to square mile? Round to nearest tenth as needed
Answer:
5 square mile
Step-by-step explanation:
1 square km = 0.3 square mile
13 square km = 5.01 square mile
5.01 rounded equals 5
hope that helps <3
How to do this problem in the picture 8th grade math
Answer:
4.69 x 10⁵
Step-by-step explanation:
Step 1
To find a, take the number and move a decimal place to the right one position.
Original Number: 469,000
New Number: 4.69000
Step 2
Now, to find b, count how many places to the right of the decimal.
New Number: 4 . 6 9 0 0 0
Decimal Count: 1 2 3 4 5
There are 5 places to the right of the decimal place.
Step 3
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10b
a = 4.69 (Please notice any zeroes on the end have been removed)
b = 5
Now the whole thing:
4.69 x 10⁵
Step 4
Check your work:
105 = 100,000 x 4.69 = 469,000
Answer: [tex]4.61 \times 10^5[/tex]
Reason:
The original number is 461,000 or 461000
Place a decimal point between the first two nonzero values. Erase the zeros and we get 4.61
To get back to 461000, we need to move the decimal point 5 spaces to the right. This is the exponent for the [tex]10^5[/tex] portion.
So [tex]461,000 = 4.61 \times 10^5[/tex]
Enter an inequality that represents the graph in the box.
Graph of a linear inequality on a coordinate plane. The horizontal x-axis ranges from negative 8 to 8 in increments of 2. The vertical y-axis ranges from negative 8 to 8 in increments of 2. A solid line passes through begin ordered pair 0 comma negative 6 end ordered pair and begin ordered pair 2 comma 2 end ordered pair. The region above the solid line is shaded.
The linear inequality represented by the given graph in the attached image is y > -3x + 6.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The graph of the linear inequality. Let's pick two points from the graph to frame the linear equation
The slope-intercept form of the equation is Where m is the slope and b is the y-intercept is (0,6) from the graph so b=6.
Find out slope m by using the general formula. Pick two points (0,6) and (2,0).
Slope = ( y₂ - y₁) / ( x₂ - x₁ )
Slope = ( 0 - 6 ) / ( 2 - 6 )
Slope = -3
m = -3
So the equation is y = -3x + 6
Now we check the inequality sign by testing any point on the shaded area let's pick (4,0). let's plug in 4 for x and 0 for y
y= -3x + 6
0 = -3(4) + 6
0 > -6
Inequality: y > -3x + 6.
Therefore, the inequality represented by the given graph is y > -3x + 6.
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Answer: y≥4x−6
Step-by-step explanation: I took the test and this was the right answer for me.
Use the graph below to answer. Find f(1)
Answer:
f(1) = 9
Step-by-step explanation:
where x is 1, y is 9
what’s the measure of angle SQT?
Solve for [x]. Each figure is a trapezoid.
*
Question 1
Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,
[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]
Question 2
Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,
[tex]9x+30+7x-10=180 \\ \\ 16x+20=180 \\ \\ 16x=160 \\ \\ x=10[/tex]
Please help ASAP! Help greatly appreciated with step by step solutions
The nth terms of the arithmetic sequences;
I. Tn = 3 + √2 + ( n - 1) √2
ii. Tn = 2/ √3 + ( n - 1) 1/ √3
How to determine the nth termThe formula for the nth term of an arithmetic sequence is expressed as;
Tn = a + ( n - 1)d
Where;
Tn is the nth terma is the first term n is the number of termsd is the common differencei. a = 3 + √2
d = √2
Substitute the values, we have;
Tn = 3 + √2 + ( n - 1) √2
ii. a = 2/ √3
d = 1/ √3
Substitute the value, we have;
Tn = 2/ √3 + ( n - 1) 1/ √3
Thus, the nth terms of the arithmetic sequences are Tn = 3 + √2 + ( n - 1) √2 and Tn = 2/ √3 + ( n - 1) 1/ √3 respectively
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Fiona spent of her money on a dress and $39 on a bag. If she had $121 left, how much money did she have at first?
Answer:
She had $160 at first
Step-by-step explanation:
Fiona spent of her money on a dress and $39 on a bag. If she had $121 left, how much money did she have at first?
In order to find how much she had at first
we have to add how much she spent plus how much she has left with her
➟ $121 + $39
➟ $160
∴ She had $160 at first
A warehouse store sells 3.5-ounce cans of tuna in package of 3. A package of 3 cans costs $3.99. The store also sells 6.5-ounce cans in packages of 4 cans for $6.48. Which package is the best buy
