Answers
The Synthetic Division form of Given Division Problem is :
✿ [tex]-5\;\arrowvert\overline{\;4\;\;\;\;\;-13\;\;\;\;\;\;8}[/tex]
Option C is the Answer
In synthetic division for [tex]\( \frac{4x^2 - 13x + 8}{x + 5} \)[/tex], option C (-5 | 4 -13 8) correctly represents the coefficients, showcasing the division process with a remainder of 8.
The synthetic division problem given is [tex]\( \frac{4x^2 - 13x + 8}{x + 5} \)[/tex]. Synthetic division is a method used to divide polynomials, particularly when dividing by a linear factor of the form (x - c) . The correct representation in synthetic division form would be:
**C. -------------
- 5 | 4 - 13 8**
Here's the breakdown of the synthetic division:
1. The divisor x + 5 corresponds to c = -5, so the root is x = -5.
2. Write down the coefficients of the dividend 4x^2 - 13x + 8 in the synthetic division box.
3. Bring down the leading coefficient, which is 4 in this case.
4. Multiply the root (-5) by the leading coefficient (4) and write the result below the second column. Add the result to the second column.
5. Multiply the root by the result from step 4 and write the result below the third column. Add the result to the third column.
The final result in the bottom row represents the coefficients of the quotient, and the last number (8) is the remainder. The synthetic division in option C accurately reflects this process.
Related Questions
the consumer price index compares the cost of goods and services over various years, where 1967 is used as t=0. The same goods that cost $100 in 1967 cost $184.50 in 1977. Find an exponential function to model this data. Estimate what those goods would cost in 2005
Answers
Answer:
f(t) = 100·1.845^(t/10)$1025.15Step-by-step explanation:
(a) The given numbers can be put directly into the form ...
... f(t) = (initial value) · (ratio)^(t/(time to achieve that ratio))
Here, we have an intial value of $100, and a ratio of $184.50/$100 = 1.845. The time to achieve that multiplication is 10 years (1967 to 1977). So, the equation can be written ...
... f(t) = 100·1.845^(t/10)
(b) You want to find f(38).
... f(38) = 100·1.845^(38/10) = 100·1.845^3.8 ≈ 1025.15 . . . dollars
Final answer:
Using the provided CPI data, an exponential function is found to model the change in cost of goods over time. The estimated cost of the same goods in 2005, using this model, is approximately $1019.03, illustrating changes in purchasing power and the cost of living.
Explanation:
The question involves finding an exponential function to model the Consumer Price Index (CPI) data and estimate the cost of goods in a future year based on past data. The data provided includes the cost of the same goods being $100 in 1967 (t=0) and $184.50 in 1977. An exponential function of the form y = abt can be used, where y represents the cost of goods, t represents the year, and a and b are constants to be found.
Given that the goods cost $100 in 1967, our initial condition gives us a as $100. We then use the information from 1977 (t=10) to solve for b. Plugging in the values, we get $184.50 = 100*b10, which solves to b approximately equal to 1.0653. Therefore, the exponential function modeling the CPI data is y = 100(1.0653)t.
To estimate the cost of goods in 2005, we substitute t with 38 (2005 - 1967), resulting in an estimated cost of goods y ≈ 100(1.0653)³⁸ ≈ $1019.03. This estimation illustrates how the Consumer Price Index can indicate changes in purchasing power and the cost of living over time.
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year. Michigan's population was 9.9 million, increasing by 0.6 million each year. When will the two years have the same population? Let y represent the number of years.
Answers
Answer:-
[tex]11.4 + 0.5y = 9.9 + 0.6y[/tex] , then the two states have the same population.
Step-by-step explanation:
Let y represents the number of years
As per the statement:
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.
⇒ [tex]11.4 + 0.5y[/tex]
and
also, it is given that: Michigan's population was 9.9 million, increasing by 0.6 million each year.
⇒ [tex]9.9 + 0.6y[/tex]
When two states have the same population.
then the equation : [tex]11.4 + 0.5y = 9.9 + 0.6y[/tex].
Answer:
In 15 years the population will be same.
Step-by-step explanation:
Let y represent the number of years.
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.
[tex]x=11.4+0.5y[/tex]
Michigan's population was 9.9 million, increasing by 0.6 million each year.
[tex]x=9.9+0.6y[/tex]
We have to tell that when will the two years have the same population, so we will put both equations equal.
[tex]11.4+0.5y=9.9+0.6y[/tex]
=> [tex]11.4-9.9=0.6y-0.5y[/tex]
=> [tex]0.1y=1.5[/tex]
So, y = 15
Therefore, in 15 years the population will be same.
A store is going out of business. Everything is marked down 40%. How much do you pay now for an item that used to cost $150?
Answers
Steps for Solving :
$150/10 (to get 10 parts)
=15
15•4 (to get 40%)
=60
In a recent election the new mayor received three votes for every vote received by her opponent. The new mayor received 2058 votes. How many votes did her opponent receive?
Answers
As per the given values, the opponent received 686 votes.
Explanation:Total votes received by Mayor = 2058.
To find out how many votes the opponent received, we need to determine the ratio of votes received between the new mayor and her opponent. Given that the new mayor received three votes for every vote received by her opponent, we can set up the equation:
3x = 2058
where x represents the number of votes received by the opponent. To solve for x, we divide both sides of the equation by 3:
x = 2058 ÷ 3
= 686
Therefore, the opponent received a total of 686 votes.
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Write an equation of the line that passes through(0,4)and(0,-3)
Answers
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-4}{0-0}\implies \cfrac{-7}{0}\impliedby und efined[/tex]
when the slope of the points is undefined, is a flag that is a vertical line.
Check the picture below.
Hi there! :)
Step-by-step explanation:
[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{(-3)-4}{0-0}=\frac{-7}{0}=0[/tex]
Therefore, the slope is 0.
Undefined.
Final answer is 0.
I hope this helps you!
Have a nice day! :)
-Charlie
:D
HELP ASAP PLZ!!! Collin deposited $5,500 in a savings account that earns 4.5% simple annual interest. The formula that can be used for calculating simple interest is I=prt , where I represents interest, p is the principle, r is the rate and t is the time. How much interest is earned after 5 years if he makes no other deposits or withdrawals?
Answers
Answer:
$1237.50
Step-by-step explanation:
r = 4.5% = 0.045
I = prt
I = 5500*0.045*5
= $1237.50
A rocking horse has a weight limit of 60 pounds .What weight is 95 percent of the limit?
Answers
Answer:
57 pounds weight is 95 percent of the limit .
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
A rocking horse has a weight limit of 60 pounds .
Here
Percentage = 95%
Total value = 60 pounds
Put in the formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
[tex]95 = \frac{Part\ value\times 100}{60}[/tex]
[tex]Part value = \frac{95\times 60}{100}[/tex]
[tex]Part value = \frac{5700}{100}[/tex]
Part value = 57 pounds
Therefore 57 pounds weight is 95 percent of the limit .
Answer:
57 pounds is 95 percent of the limit.
Step-by-step explanation:
Given the statement: A rocking horse has a weight limit of 60 pounds.
⇒Weight limit of rocking horse = 60 pounds.
To find what weight is 95 percent of the limit.
Let x be the weight.
then;
x = 95% of 60
[tex]x = \frac{95}{100} \times 60[/tex]
or
x = [tex]\frac{95 \times 60}{100} = \frac{5700}{100} = 57[/tex]
therefore, 57 pounds is 95 percent of the limit.
A spherical scoop of ice cream with a diameter of 8 cm rests on top of a sugar cone that is 12 cm deep and has a diameter of 8 cm. What percent of the ice cream must be eaten to insure it does not overflow the cone when it melts?
Answers
Answer: 25% of the ice cream must be eaten to insure it does not overflow the cone when it melts.
Step-by-step explanation:
1. You must calculate the area of spherical scoop of ice cream with the following formula for calculate the volume of a sphere:
[tex]Vs=\frac{4}{3}r^{3}\pi[/tex]
Where [tex]r[/tex] is the radius ([tex]r=\frac{8cm}{2}=4cm[/tex])
[tex]Vs=\frac{4}{3}(4cm)^{3}\pi=268.08cm^{3}[/tex]
2. Now, you need to calculate the volume of the sugar cone with the following formula:
[tex]Vc=\frac{1}{3}r^{2}h\pi[/tex]
Where [tex]r[/tex] is the radius ([tex]r=\frac{8cm}{2}=4cm[/tex]) and [tex]h[/tex] is the height ([tex]h=12cm[/tex]):
[tex]Vc=\frac{1}{3}(4cm)^{2}(12cm)\pi=201.06cm^{3}[/tex]
3. When the ice cream melt, the percent of the cone that will be filled is:
[tex]P_f=(\frac{201.06cm^{3}}{268.08cm^{3}})100=75[/tex]%
4. Therefore, the percent of the ice cream that must be eaten to insure it does not overflow the cone when it melts, is:
[tex]P_e=100[/tex]%[tex]-75[/tex]%
[tex]P_e=25[/tex]%
Final answer:
To ensure the melted ice cream does not overflow the cone, 75% of the ice cream must be eaten. This is calculated by finding the volumes of the ice cream sphere and the cone and comparing them to get the percentage that can fit into the cone without overflowing.
Explanation:
The student's question involves determining what percent of a spherical scoop of ice cream (with a diameter of 8 cm) must be eaten to ensure it does not overflow a sugar cone (also with a diameter of 8 cm and 12 cm deep) when the ice cream melts. The ice cream and the cone have the same diameter, so they have the same base area. To prevent overflow, the volume of the melted ice cream must be less than or equal to the volume of the cone.
To solve this, we must first calculate the volume of the spherical scoop of ice cream, which can be determined using the formula for the volume of a sphere: V = (4/3)πr³. Subsequently, we need to calculate the volume of the cone using the formula for the volume of a cone: V = (1/3)πr²h. We shall compare these volumes to find out the percentage of ice cream that must be eaten.
Let's calculate the volume of the sphere (ice cream):
V_s = (4/3)π(4 cm)³ = (4/3)π(64 cm³) = 256π/3 cm³
Now let's calculate the volume of the cone:
V_c = (1/3)π(4 cm)²(12 cm) = (1/3)π(16 cm²)(12 cm) = 64π cm³
To prevent overflow, the volume of melted ice cream should be the same or less than the volume of the cone. Therefore, the portion which would fit into the cone without overflowing when melted is:
percent = (V_c / V_s) × 100 = (64π / 256π/3) × 100 = 75%
This means that 75% of the ice cream must be eaten to ensure it does not overflow the cone when it melts.
Donna used 30 buttons of different colors and sizes to make a design. She used 12 large blue buttons the rest were small and yellow or small and green there were the same number of yellow and green buttons how many buttons were small and yellow
Answers
[tex] \frac{(30 - 12)}{2} = 9[/tex]
9 small yellow buttons
What is the y-intercept of f(x)=-X^3+3x^2+1?
Answers
The y-intercept is
[tex](0,1)[/tex]
EXPLANATION
The given polynomial function is
[tex]f(x) = - {x}^{3} + 3 {x}^{2} + 1[/tex]
At y-intercept the value of x is zero.
Therefore we need to put
[tex]x = 0[/tex]
into the given polynomial function to determine the corresponding y-value.
[tex]f(0) = - {(0)}^{3} + 3 {(0)}^{2} + 1[/tex]
This will give us,
[tex]f(0) = 0 + 0+ 1[/tex]
We further simplify to obtain,
[tex]f(0) =1[/tex]
This means that when
[tex]x = 0[/tex]
the value of the function is
[tex]1[/tex]
Hence the y-intercept is
[tex](0,1)[/tex]
The expression shown is the cost a customer pays for an item, where c is the cost the store pays for the item and 0.85c is the 85% price increase the store adds to the item
Answers
Answer:0.85c
Step-by-step explanation:
Answer:
0.85c
Step-by-step explanation:
i did the diagnostic
A point of sale transaction occurs when an ATM withdrawal is made. Please select the best answer from the choices provided T F
Answers
Answer:
A point of sale transaction occurs when an ATM withdrawal is made- TRUE.
Step-by-step explanation:
A point of sale transaction occurs when an ATM withdrawal is made - This is TRUE.
A point of sale is the point when a transaction is finalized. This transaction is based on any form of payment like - cash, debit cards, credit cards etc.
Which is true about rational numbers? A Every rational number has a decimal representation that terminates. B Every rational number has a decimal representation that either repeats or terminates. C Every rational number has a decimal representation that repeats. D No rational number has a decimal representation, because rational numbers are written as fractions.
Answers
Answer:
B Every rational number has a decimal representation that either repeats or terminates.
Step-by-step explanation:
A rational number is a number that can be written as a fraction of integers. As a decimal, a rational number either terminates or repeats.
Answer: B Every rational number has a decimal representation that either repeats or terminates.
Every rational number has a decimal representation that either repeats or terminates. Option B is correct.
What is a rational number?In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.
What are irrational numbers?An irrational number is a type of real number that cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.
here,
From definition,
Rational numbers are the fractional values that give decimal values and every rational number has a decimal representation that either repeats or terminates.
Thus, option B is correct.
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In ∆PQR, PQ = 39 cm and PN is an altitude. Find PR if QN = 36 cm and RN = 8 cm.
Answers
Use the Pythagorean theorem two times:
[tex]NQ^2+NP^2=QP^2\\\\36^2+h^2=39^2\\\\1296+h^2=1521\qquad\text{subtract 1521 from both sides}\\\\h^2=225\to h=\sqrt{225}\\\\\boxed{h=15\ cm}[/tex]
second time:
[tex]PR^2=RN^2+NP^2\\\\x^2=8^2+15^2\\\\x^2=64+225\\\\x^2=289\to x=\sqrt{289}\\\\\boxed{x=17\ cm}[/tex]
Answer: PR = 17 cm.Answer:
17 cm
Step-by-step explanation:
We must first find the length of the height, PN. Since PN is an altitude, it makes a right angle with QR; this means that PNQ will be a right triangle, as will PNR. This means we will use the Pythagorean theorem:
a²+b² = c²
Letting h represent PR (since it is the height),
h²+36² = 39²
h²+1296 = 1521
Subtract 1296 from each side:
h²+1296-1296 = 1521-1296
h² = 225
Take the square root of each side:
√(h²) = √(225)
h = 15
PN is 15 cm.
Now we will use it and the other "base," RN, to find PR:
15²+8² = x²
225+64 = x²
289 = x²
Take the square root of each side:
√(289) = √(x²)
17 = x
sofia bought bananas ,cereal,and milk at the store.She spent all of her money.She spent 3/10 of her money on bananas and 4/10 on cereal.What fraction of her money did Sofia spend on milk?Write and solve equations.
Answers
because 3/10 + 4/10 = 7/10
then 10/10 - 7/10 = 3/10
Paul bought a soft drink and a sandwich for $9.90. What equation may be used to find the price of each item if the sandwich cost 3.5 times as much as the soft drink? A) x = 9.90 B) 2x = 9.90 C) 3.5x = 9.90 Eliminate D) 3.5x + x = 9.90
Answers
Answer:
D
Step-by-step explanation:
The other ones don't make sense. The answer is 3.5x+x=9.90
Alex mixes 2/3 pounds of walnuts with 3/5 pound of dried fruit. To create more of the same mixture, how many pounds of walnuts does Alex need to mix with one pound of dried fruit?
Answers
Alex needs to mix one pound of dried fruit with
[tex]1 \frac{1}{9} [/tex]
pounds of walnuts.
EXPLANATION
It was given that, Alex mixes
[tex] \frac{2}{3}[/tex]
pounds of walnuts with
[tex] \frac{3}{5} [/tex]
pounds of dried fruit.
We can write the ratio,
[tex] \frac{2}{3} : \frac{3}{5} [/tex]
Let
[tex]x[/tex]
represent how many pounds of walnuts Alex needs to mix with one pound of dried fruit.
Then we can again write the ratio,
[tex]x: 1[/tex]
We can therefore write the proportion,
[tex] \frac{2}{3} : \frac{3}{5} = x: 1[/tex]
This can be rewritten as,
[tex] \frac{ \frac{2}{3} }{ \frac{3}{5} } = \frac{x}{1} [/tex]
We solve for x to obtain,
[tex] \frac{2}{3} \times \frac{5}{3} = x[/tex]
This implies that,
[tex]x = \frac{10}{9} [/tex]
[tex]x = 1 \frac{1}{9} [/tex]
Hence Alex needs to mix
[tex] 1\frac{1}{9} [/tex]
pounds of walnuts with one pound of dried fruit.
Please help meeee!!!
Answers
Answer:
26, 37
Step-by-step explanation:
1,3,5,7,9,11
17 + 9 = 26
26 + 11 = 37
1+1=2
2+3=5
5+5=10
10+7=17
17+9=26
26+11=37
You add each odd number in order
there was a substance of a 450 milligrams of radioactive substance to start a study. Since then the sample has decayed of 5.4% each year. Let t be the number of years since the start of the study. Let Y be the mass of the sample in milligrams. Write an exponential function showing the relationship of the y and t
Answers
Answer: [tex]\bold{Y = 450e^{(.054t)}}[/tex]
Step-by-step explanation:
The general formula for decay is:
[tex]A = Pe^{rt}[/tex] ; where:
P is the initial massr is the rate (in decimal form)t is the timeGiven:
P = 450r = 5.4% = .054Equation:
[tex]Y = 450e^{(.054t)}[/tex]
A birdhouse has a shadow that is 12
12
feet long.
Jin is 5
5
feet tall, and he is standing next to the birdhouse.
Jin has a shadow that is 3
3
feet long.
Use this information to complete the statement about the birdhouse.
Answers
5/3=0.6
Then multiply the length of the birdhouse shadow by that scale factor
12*0.6=7.2 feet
So the new birdhouse shadow length is 7.2 feet
Hope this helps!
A. What is the sum of the squares of the roots of $x^2 - 5x - 4 = 0$?
B. One root of $x^2 + 12x + k = 0$ is twice the other root. Find $k.$
C. What is the sum of the roots of the quadratic $4x^2 - 4x - 4$?
D. Jimmy is trying to factor the quadratic equation $ax^2 + bx + c = 0.$ He assumes that it will factor in the form
\[ax^2 + bx + c = (Ax + B)(Cx + D),\]where $A,$ $B,$ $C,$ and $D$ are integers. If $a = 4,$ and Jimmy wants to find the value of $A,$ what are the possible values he should check, in order to find $A$?
E. Brandy is trying to factor the quadratic $3x^2 - x - 10.$ She starts by assuming that the quadratic factors as
\[3x^2 - x - 10 = (x + B)(3x + D),\]for some integers $B$ and $D.$ After some work, Brandy successfully factors the quadratic. Find the ordered pair $(B,D).$
Answers
Answer:
A. 33
B. k=32
C. 1
D. [tex]\pm 1,\ \pm 2,\ \pm 4[/tex]
E. [tex]B=-2,\ D=5[/tex]
Step-by-step explanation:
In all parts for the quadratic equation [tex]ax^2+bx+c=0[/tex] use Vieta's formulas
[tex]x_1+x_2=-\dfrac{b}{a},\\ \\x_1\cdot x_2=\dfrac{c}{a},[/tex]
where [tex]x_1,\ x_2[/tex] are the roots of the quadratic equation.
A. For the equation [tex]x^2-5x-4=0,[/tex]
[tex]x_1+x_2=5,\\ \\x_1\cdot x_2=-4.[/tex]
Then
[tex](x_1+x_2)^2=x_1^2+2x_1\cdot x_2+x_2^2,\\ \\5^2=x_1^2+x_2^2+2\cdot (-4),\\ \\x_1^2+x_2^2=25+8=33.[/tex]
B. One of the roots of [tex]x^2+12x+k=0[/tex] is twice the other root, then [tex]x_2=2x_1.[/tex] By the Vieta's formulas,
[tex]x_1+x_2=3x_1=-12,\\ \\x_1\cdot x_2=2x_1^2=k.[/tex]
Then [tex]x_1=-4[/tex] and [tex]k=2x_1^2=2\cdot (-4)^2=2\cdot 16=32.[/tex]
C. The sum of the roots of the quadratic [tex]4x^2-4x-4[/tex] is [tex]-\dfrac{b}{c}=-\dfrac{-4}{4}=1.[/tex]
D. Note that
[tex](Ax+B)(Cx+D)=ACx^2+x(AD+BC)+BD,[/tex]
then [tex]AC=a=4.[/tex] If [tex]A,\ B,\ C,\ D[/tex] are integers, then you should check [tex]A=\pm 1,\ \pm 2,\ \pm 4.[/tex]
E. Consider [tex]3x^2 - x - 10 = (x + B)(3x + D).[/tex] Note that
[tex]x_1+x_2=\dfrac{1}{3},\\ \\x_1\cdot x_2=-\dfrac{10}{3}.[/tex]
Then
[tex]x_1=2,\ x_2=-\dfrac{5}{3}.[/tex]
Then [tex]3x^2 - x - 10 = (x -2)(3x+5),[/tex] hence [tex]B=-2,\ D=5.[/tex]
A. The sum of the squares of the roots is 33, B. k = 32, C. The sum of the roots is 1, D. The possible values he should check are ±1, ±2, ±4, E. The ordered pair (B, D) is (2, -5).
Let's solve each part of the problem step-by-step:
A. First, find the roots of the quadratic equation using Vieta's formulas:
The sum of the roots (α + β) = -(-5) = 5.The product of the roots (αβ) = -4.Now, the sum of the squares of the roots is given by: (α² + β²) = (α + β)² - 2αβ. Substituting the known values:
Hence, α² + β² = 25 - (-8) = 25 + 8 = 33.
B. Let the roots be α and 2α. Using Vieta's formulas again:
The sum of the roots (α + 2α) = 3α = -12, thus α = -4.The product of the roots (α * 2α) = 2α² = k.Therefore, k = 2(-4)² = 2 * 16 = 32.C. The sum of the roots is given by -b/a:
Here, a = 4 and b = -4.Thus, the sum of the roots = -(-4)/4 = 1.D. The quadratic can be written as 4x² + bx + c. The coefficient of x² on the right-hand side must be AC. Since a = 4:
The possible integer values for A can be the pairs (A, C) where A * C = 4.Thus, the possible values for A are ±1, ±2, ±4.E. The quadratic can be factored as (x + B)(3x + D). Let's determine B and D:
3B + D = -1 (coefficient of x)BD = -10 (constant term)Solving these equations, we find B = 2 and D = -5.Thus, the ordered pair (B, D) is (2, -5).
(2,4) (1,8) Which Number Is y2 HELP!!
Answers
(2,4) because y2 is 1 = 2x
math help please!!!!!!!!!!! will mark brainly
Answers
Answer:
B)3/8
Step-by-step explanation:
So there are 3 yellow or blue in total. So 3/8.
Answer:
3/8
Step-by-step explanation:
There are 8 pieces of equal size (and thus equal probability). 3 of them qualify as "success" (yellow or blue), so 3 out of 8 is the probability.
The function f(x) goes through the point (2, 6). What point will this translate to in the function f(x) = (x + 2) – 3?
(0, 9)
(0, 3)
(4, 3)
(4, 9)
Answers
Answer:
(0,3)
Step-by-step explanation:
g(x) = f(x + 2) – 3
This is a shift of 2 to the left and a shift of 3 down
x moves from 2 to 2 units left (-2) so it becomes 0
y moves from 6 to 3 units down (-3) so it becomes 3
Answer:
the answer is B. or (0,3)
Step-by-step explanation:
It takes terrel 69 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 49 minutes. How long would it take them working together? Round to the nearest tenth of a minute
Answers
Answer: 28.7 minutes
Step-by-step explanation:
Terrel: [tex]\dfrac{1}{69}[/tex] of job per minute
Wife: [tex]\dfrac{1}{49}[/tex] of job per minute
Together: [tex]\dfrac{1}{x}[/tex] of job per minute
Terrel + Wife = Together
[tex]\dfrac{1}{69}+\dfrac{1}{49}=\dfrac{1}{x}[/tex]
[tex]\dfrac{1}{69}(69*49*x)+\dfrac{1}{49}(69*49*x)=\dfrac{1}{x}(69*49*x)[/tex]
49x + 69x = 69 * 49
118x = 3381
x = 28.7
What is the slope of a line parallel to the line with equation 5x + 3y = 7?
Answers
Answer:
-5/3
Step-by-step explanation:
Parallel lines are lines which have the exact same slope but different y-intercepts. We can find the slope by converting to slope-intercept form, y=mx+b from standard form.
We convert by using inverse operations to isolate y.
5x+3y=7
5x-5x+3y=7-5x
0x+3y=-5x+7
3y=-5x+7
[tex]\frac{3y}{3} =\frac{-5x+7}{3} \\y=\frac{-5}{3}x+\frac{7}{3}[/tex].
The slope is -5/3. SInce parallel lines have the same slope, the slope for a parallel line will be -5/3.
Solve the system for each variable. y + g = 12 and 2y + 3g = 16
Answers
Answer:
y + g = 12 ,2y + 3g = 16
y =12-g
Substitute y =12-g in the equation 2y + 3g = 16.
2(12-g)+ 3g = 16
24-2g+3g=16
24+g=16
g=16-24
g= -8
Substitute g= -8 in the equation y =12-g.
y =12-(-8)
=12+8
y =20
Step-by-step explanation:
The value of variable y is 20 and value of variable g is -8.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of equations are y+ g = 12 and 2y + 3g = 16
y+g=12
y=12-g...(1)
2y+3g=16..(2)
Substitute 1 in equation 2
2(12-g)+3g=16
24-2g+3g=16
Add the like terms
24+g=16
g=16-24
g=-8
Now substitute the g value in equation y+g=12
y-8=12
Add 8 on both sides
y=20
Hence, the value of variable y is 20 and value of variable g is -8.
To learn more on Equation:
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Factor the polynomial
5c2 - 17c - 14
(5c - 7)(c - 2)
(5c - 2)(c - 7)
(5c - 7)(c + 2)
Prime polynomial
Answers
Answer:
(5c-7)(c+2)
Step-by-step explanation:
what are the zeros of the polynomial functio ? f(x)=x^3+x^2-9x-9
Answers
Answer:
x = - 1
x1 = - 3
x2 = 3
Step-by-step explanation:
x^2(x + 1) - 9(x + 1) = f(x) x + 1 is a common factor
(x + 1) [ x^2 - 9] = f(x) factor x^2 - 9
(x + 1)(x - 3)(x + 3)
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x + 1 = 0
x = - 1
x - 3 = 0
x = 3
x + 3 = 0
x = - 3
====================
Answer
x = - 1
x1 = - 3
x2 = 3
Question:
What are the zeros of the polynomial function?
Step-by-step explanation:
Hope this helps!
Please help me out! :) !!!!!!
Answers
Answer:
your answer is 8/40 but is reduced to 1/5
Step-by-step explanation: