Answer: The correct option is (B) -7.
Step-by-step explanation: We are given to select the correct values of x that make the following rational expression undefined :
[tex]E=\dfrac{16-x}{7+x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
a rational expression is undefined at the points where the denominator becomes zero.
Therefore, the expression (i) will become undefined when
[tex]7+x=0\\\\\Rightarrow x=-7.[/tex]
Thus, the required value of x where the given expression is undefined is -7.
Option (B) is CORRECT.
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)
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:
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?
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
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.
A rocking horse has a weight limit of 60 pounds .What weight is 95 percent of the limit?
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.
Solve the system for each variable. y + g = 12 and 2y + 3g = 16
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.
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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.
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
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
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]
Officer Brimberry wrote 24 tickets for traffic violations last week, but only 21 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent.
Answer:3 percent because
Answer:
Percent = 62.5%
Step-by-step explanation:
A point of sale transaction occurs when an ATM withdrawal is made. Please select the best answer from the choices provided T F
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.
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?
Write a linear function for the line represented by the point-slope equation
y −4 = 3 (x − 4)
Must show your work to receive full credit.
Answer:
f(x) = 3x-8
Step-by-step explanation:
y −4 = 3 (x − 4)
We want to write the equation in y = mx+ b form
Distribute the 3
y-4 = 3x -3*4
y-4 = 3x -12
Add 4 to each side
y -4+4 = 3x-12+4
y = 3x-8
Since the want it in function form, f(x)
f(x) = 3x-8
4 Questions about The Polynomial Remainder Theorem
None of these questions have anything to do directly with the polynomial remainder theorem. The theorem says that the remainder upon dividing a polynomial [tex]p(x)[/tex] by [tex]x-c[/tex] is given by the value of [tex]f(c)[/tex].
For these questions, all you really have to do is evaluate the given polynomials at the given points, and IMO is much less work.
Question 2: [tex]f(5)=4(5)^2-5(5)+2=77[/tex]
Question 3: [tex]f(4)=3(4)^4-8)4)^2-2(4)+12=644[/tex]
Question 4: Here you have check the value of [tex]h(x)[/tex] and 2 and -2, then interpret them as points in the coordinate plane, [tex](x,h(x))[/tex].
[tex]h(-2)=2(-2)^5-4(-2)^4-2(-2)^2+15=-121[/tex]
[tex]h(2)=2(2)^5-4(2)^4-2(2)^2+15=7[/tex]
Question 5: Same as in question 4, but you have to check [tex]h(x)[/tex] at -4, -3, -2, -1.
[tex]h(-4)=72[/tex]
[tex]h(-3)=46[/tex]
[tex]h(-2)=26[/tex]
[tex]h(-1)=12[/tex]
- - -
If you insist on using the polynomial remainder theorem, it's a question of polynomial division. For instance, in question 2 you'd compute
[tex]\dfrac{4x^2-5x+2}{x-5}=4x+15+\dfrac{77}{x-5}\implies4x^2-5x+2=(4x+15)(x-5)+77[/tex]
so the remainder is 77, as we found by simply computing [tex]f(5)[/tex].
What is the slope of a line parallel to the line with equation 5x + 3y = 7?
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.
The price of milk tripled, and then rose another $0.75 per gallon. If the price now is AT LEAST $4.50 per gallon, which inequality expresses this situation? A) 3x + 0.75 ≤ 4.5 B) 3x + 0.75 ≥ 4.5 C) 3x - 0.75 ≥ 4.5 D) 3(x + 0.75) ≤ 4.5
This can be represented by the inequality:
3x + 0.75 ≥ 4.5
Inequality shows the non-equal comparison between two numbers or mathematical expressions.
Let x represent the price of milk per gallon.
Since the price of milk tripled, and then rose another $0.75 per gallon, hence:
Price of milk = 3x + 0.75
The price is now is AT LEAST $4.50 per gallon, hence this can be represented by the inequality:
3x + 0.75 ≥ 4.5
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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?
Answer:
$1237.50
Step-by-step explanation:
r = 4.5% = 0.045
I = prt
I = 5500*0.045*5
= $1237.50
Please help meeee!!!
Answer:
26, 37
Step-by-step explanation:
1,3,5,7,9,11
17 + 9 = 26
26 + 11 = 37
47=16384 write in logarithmic form
Answer:
[tex]\log_4{(16384)}=7[/tex]
Step-by-step explanation:
The base of the exponent is the base of the logarithm. The exponent is the logarithm. The value the exponential expression is equal to is the argument of the logarithm.
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
Answer:0.85c
Step-by-step explanation:
Answer:
0.85c
Step-by-step explanation:
i did the diagnostic
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 $(B,D).$
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).
Factor the polynomial
5c2 - 17c - 14
(5c - 7)(c - 2)
(5c - 2)(c - 7)
(5c - 7)(c + 2)
Prime polynomial
Answer:
(5c-7)(c+2)
Step-by-step explanation:
The directions on a sewing pattern say to cut an extra 15% of fabric to account for error. Chloe needs 0.75 yard of frantic to make a skirt, and she cuts 0.1125 yard. Did Chloe cut the right amount of fabric?
Answer:
Yes she did
Step-by-step explanation:
There is .75 yards and she cut .1125 of it, it make it 15% as .75 x .15 = .1125
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.
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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(2,4) (1,8) Which Number Is y2 HELP!!
(2,4) because y2 is 1 = 2x
Please help me out! :) !!!!!!
Answer:
your answer is 8/40 but is reduced to 1/5
Step-by-step explanation:
Identify the value of p. Give your answers in simplest radical form. HELP PLEASE!!
Answer:
C
Step-by-step explanation:
using the cosine ratio to find p
cos 45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{p}[/tex]
cross- multiplying gives
p × cos45° = 6 → [ cos 45° = [tex]\frac{1}{\sqrt{2} }[/tex]]
p × [tex]\frac{1}{\sqrt{2} }[/tex] = 6
multiply both sides by [tex]\sqrt{2}[/tex]
⇒ p = 6[tex]\sqrt{2}[/tex] ( third option on list )
To determine the value of p in simplest radical form, solve the equation by simplifying the denominator and taking the square root of both sides. The value of p is 2.
Explanation:To identify the value of p, we need to solve the equation and simplify it to the simplest radical form. Let's start by simplifying the denominator and expressing it as a perfect square.
Next, we can take the square root of both sides of the equation to eliminate the square. This will help us isolate p. Once we do that, we can solve for p by getting rid of the square root on the left side of the equation. After simplifying, we find that p = 2.
So, the value of p is 2.
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.
Combine and simplify these radicals. square root of 3 times the square root of 16
Answer:
[tex]\sqrt{3} * /sqrt{16} = 4\sqrt{3}[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
square root of 3 times the square root of 16 looks like this
[tex]\sqrt{3} .\sqrt{16}[/tex]
we try to break the numbers inside the radical to there prime factors
so
[tex]\sqrt{3} .\sqrt{2.2.2.2}[/tex]
the prime factors which are in pair , comes out of the radical so
[tex]\sqrt{3} .2.2[/tex]
which simplifies to
[tex]4\sqrt{3}[/tex]
Jared bought a package of pens containing 20 pens if 3/4 of the pens have black ink how do you determine the number of pens with black ink
Answer:
The number of black ink pen are 15 pens.
Step-by-step explanation:
As given
Jared bought a package of pens containing 20 pens.
[tex]if\ \frac{3}{4}\ of\ the\ pens\ have\ black\ ink.[/tex]
Thus
[tex]Number\ of\ black\ ink\ pens = \frac{3}{4}\times Total\ number\ of\ pens[/tex]
Putting the value
[tex]Number\ of\ black\ ink\ pens = \frac{3}{4}\times 20[/tex]
Number of black ink pens = 3 × 5
= 15 pens
Therefore the number of black ink pen are 15 pens.
Jared has 15 pens with black ink, which is calculated by multiplying 3/4 by the total number of pens he has (20 pens).
To determine the number of pens with black ink that Jared has, you need to multiply the total number of pens by the fraction representing the pens with black ink. Jared has a package containing 20 pens, and 3/4 of these have black ink. Here's how you calculate it:
Find the fraction of pens with black ink: 3/4 of the pens.
Multiply this fraction by the total number of pens: 3/4 × 20 pens.
Calculate the product to find the number of pens with black ink: 3/4 × 20 = 15 pens.
Therefore, Jared has 15 pens that contain black ink.
PLEASE ANSWER THIS QUESTION !! 30 POINTS AND BRAINLIEST TO THE FIRST PERSON!
Answer:
x<=11
Step-by-step explanation:
2(x-3 ) <= 16
Distribute the 2
2x -6 <= 16
Add 6 to each side
2x -6+6<= 16+6
2x <= 22
Divide by 2
2x/2 <= 22/2
x<=11