The required zeros of the given polynomial equation are x = 7/4 and x = -3.
Zeros of an equation is defined as the value of the independent variable where the equation or function gives zero.
here,
Given expression,
f(x) = 4x² + 5x - 21.
Putting the above expression equal to zero,
4x² + 5x - 21 = 0
Factorizing the above equaiton gives,
(x - 7/4)(x + 3) = 0
Now,
x = 7/4 and x = -3
Thus, the required zeros of the given polynomial equation is x = 7/4 and x = -3.
Learn more about zeros here:
https://brainly.com/question/16824818
#SPJ2
The city of austin can buy roads or light rail. if 10 miles of roads cost $1 million and 2 miles of light rail cost $10 million, what is the city's opportunity cost of 1000 miles of roads?
a. $1,000 million
b. 200 miles of light rail
c. 2 miles of light rail
d. $100 million
e. $50 million
A rope of length 2/5 m is cut into 4 equal cords. What is the length of each cord?
Find the radius of a cylinder with a volume of 208 cm3 and a height of 4 cm.
Which exponential equation is equivalent to the logarithmic equation below? c = ln 2
e^c=2
Step-by-step explanation:
What is the solution to the equation fraction 3 over 5 n minus fraction 4 over 5 equals fraction 1 over 5 n?
Answer:
n = 2
Step-by-step explanation:
As per statement of the question we will form the equation first.
[tex](\frac{3}{5})n-\frac{4}{5}=(\frac{1}{5})n[/tex]
Now we will solve the given equation to get the solution of n.
[tex](\frac{3}{5})n=\frac{4}{5}+(\frac{1}{5})n[/tex]
[tex](\frac{3}{5})n-(\frac{1}{5})n=\frac{4}{5}[/tex]
[tex](\frac{3-1}{5})n=\frac{4}{5}[/tex]
[tex](\frac{2}{5})n= \frac{4}{5}[/tex]
Now we cross multiply the fractions
(2×5)×n = 4×5
10.n = 20
[tex]n=\frac{10}{5}=2[/tex]
Therefore answer is n = 2
A business woman invests $38,000 into two accounts: one that returns 3.5% annual interest and one that returns 6.5% annual interest. After 1 year, she earns $1960. How much did she invest in each account?
$23,000 in the 3.5% interest account, $15,000 in the 6.5% interest account.
$26,000 in the 3.5% interest account, $12,000 in the 6.5% interest account.
$12,000 in the 3.5% interest account, $26,000 in the 6.5% interest account.
$17,000 in the 3.5% interest account, $21,000 in the 6.5% interest account.
Final answer:
The business woman invested $17,000 in the 3.5% interest account and $21,000 in the 6.5% interest account.
Explanation:
To find how much she invested in each account:
Let x be the amount invested at 3.5% interest and y be the amount at 6.5%.
We can set up a system of equations like this: x + y = $38,000 and 0.035x + 0.065y = $1,960.
Solving this system, we get x = $17,000 and y = $21,000.
Therefore, investment is $17,000 in the 3.5% interest account, $21,000 in the 6.5% interest account
An item is regularly priced at $ 40 . It is on sale for 40 % off the regular price. How much (in dollars) is discounted from the regular price?
$16 are discounted from the regular price of the item.
DiscountsGiven that an item is regularly priced at $40, and it is on sale for 40% off the regular price, to determine how much (in dollars) is discounted from the regular price, the following calculation must be performed:
40 - (40 x (1 - 0.4)) = X40 - (40 x 0.6) = X40 - 24 = X16 = XTherefore, $16 are discounted from the regular price of the item.
Learn more about discounts in https://brainly.com/question/1289629
This figure is a step in which construction?
A. a line parallel to <-AB-> through point P.
B. a line perpendicular to <-AB-> through point P.
Option: B is the correct answer.
B. a line perpendicular to <-AB-> through point P.
Step-by-step explanation:We know that a line perpendicular to a given line is constructed as follows:
1) Draw a line segment AB
2) Take a span of compass more than half the length of AB and keep the point of compass first at A and then at B to make a arc above AB.
3) Draw a straight line that passes through the intersection of arc and line AB such that it meets AB at point P which will act as a midpoint of line AB.
Hence, the correct option is:
Option: B
If Tim and Terry started to run in opposite directions with the speeds of 90 feet per minute and 11 feet per minute respectively, how far away from each other will they be in 18 minutes?
PLZ, FIRST CORRECT ANSWER AUTOMATICALLY GETS BRAINLIEST!!
To find the distance between Tim and Terry after 18 minutes, you can calculate the distance each has traveled based on their speed and time elapsed. Then subtract their distances to find the total distance between them.
To determine the distance between Tim and Terry after 18 minutes, you can add up the distances each has traveled according to their speeds and time elapsed. Tim covers 90 feet/minute, so in 18 minutes, he would have traveled 90 * 18 = 1620 feet. Terry covers 11 feet/minute, so in 18 minutes, he would have traveled 11 * 18 = 198 feet.
Calculating the total distance between them:
Distance = |1620 - 198| = 1422 feet
Lynn and dawn tossed a coin 60 times and got heads 33 times. What is the experimental probability of tossing heads using Lynn and dawn's results?
A rectangle has dimensions 10 cm by 6 cm. determine the measures of the angles at the point of where the diagonals intersect
The equation d = can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an equivalent equation solved for V?
The equation [tex]d=(m)/(V)[/tex] can be used to calculate the density, [tex]d[/tex], of an object with mass, [tex]m[/tex], and volume, [tex]V[/tex]. [tex](m)/(d)=V[/tex] is an equivalent equation solved for [tex]V[/tex].
To find the equation equivalent to [tex]d= m/V[/tex] solved for [tex]V[/tex], we need to isolate [tex]V[/tex]on one side of the equation.
Given the equation [tex]d= m/V,[/tex] where [tex]d[/tex] represents density, [tex]m[/tex] represents mass, and [tex]V[/tex] represents volume.
To solve for [tex]V[/tex] , we can rearrange the equation:
[tex]d= m/V[/tex]
First, let's get rid of the fraction by multiplying both sides by [tex]V[/tex]:
[tex]d*V=m[/tex]
Now, to isolate [tex]V[/tex], we need to divide both sides by [tex]d[/tex]:
[tex]V= m/d[/tex]
So, the equivalent equation solved for [tex]V[/tex] is:
[tex]V= m/d[/tex]
This corresponds to option C: [tex]m/d=V.[/tex]
COMPLETE QUESTION:
The equation [tex]d=(m)/(V)[/tex] can be used to calculate the density, [tex]d[/tex], of an object with mass, [tex]m[/tex], and volume, [tex]V[/tex]. Which is an equivalent equation solved for [tex]V[/tex]?
A. [tex]dm=V[/tex]
B. [tex](d)/(m)=V[/tex]
C. [tex](m)/(d)=V[/tex]
D. [tex]m-d=V[/tex]
due to the same law, persons earning $500,000 per year had lower taxes removed from their paychecks on the first $106,800 they earned, saving them 2% of this portion of their salary. The same persons also received $14,250 more on their federal tax return. Fill in the blanks to complete the statement below. A person earning $500,000 a year received $______ more or______ % more of their income. Round to the nearest dollar and to the nearest tenth of a percent.
Final answer:
A person earning $500,000 per year received an additional $16,386 or 3.3% more of their income due to tax changes.
Explanation:
To ascertain how much more a person earning $500,000 per year received due to tax changes, we need to calculate the savings from the first $106,800 at a 2% reduction, in addition to the increased federal tax return of $14,250.
Firstly, we calculate 2% of $106,800:
0.02 × $106,800 = $2,136
Now, we add this to the additional amount received from the tax return:
$2,136 + $14,250 = $16,386
Therefore, a person earning $500,000 per year has received an additional $16,386. To find the percentage this additional amount represents of their income, we perform the following calculation:
($16,386 / $500,000) × 100 = 3.277%
Rounded to the nearest tenth of a percent, it is 3.3%.
The statement completed would be: A person earning $500,000 a year received $16,386 more or 3.3% more of their income.
Compare the decimals 1,825.10 and 1,825.1. Which is correct? A. 1,825.10 > 1,825.1 B. 1,825.10 < 1,825.1 C. 1,825.10 = 1,825.1
ABC undergoes a dilation, with a scale factor of 6, to form A’B’C’
Side A’B’ is 6 times the length of slide AB
what is the area of A’B’C, compared to the area of ABC?
Please help me god bless you.
Sam can plant 261 cabbage plants in 1 row of his garden . How many rows in his garden must be used to plant 1044 plants
Let f(x)=5x3−60x+5 input the interval(s) on which f is increasing. (-inf,-2)u(2,inf) input the interval(s) on which f is decreasing. (-2,2) find the intervals on which f is concave up. (-inf,-2)u(2,inf) find the intervals on which f is concave down.
In a taxi, there is a pregnant lady that's 25 years old.An elder that's 76 years old. The taxi driver who's 34 years old. Who is the youngest?
A train arrives at the station with 150 passengers on board.2/5 of the passengers get off the train in Seattle,and then 35 passengers board the train.How many passengers are on the train when it leaves the station?
Jermiah bought 3 sanwiches for lunch if each sandwich cost $4 how much did Jeremiah spend in all
Suppose ABCD is a rectangle. Find AB and AD if point M is the midpoint of
BC,AM ⊥ MD , and the perimeter of ABCD is 34 in..
Someone answered this question but Ad is not 4 and AB is not 9. . Thank you
I substitute 1 in 2
AD²=2*[(17-AD)²+(AD/2)²]----> AD²=2*[289-34AD+AD²+0.25AD²]
AD²=578-68AD+2.50AD²--------> 1.50AD²-68AD+578
1.50AD²-68AD+578=0
using a graph tool to solve the quadratic equation
see the attached figure
AD1=11.33 in
AD2=34 in----------is not solution because (AB+AD=17)
Solution is AD=11.33 in
AB=17-11.33--------> 17-11.33-----> AB=5.67 in
the answer is
AD=11.33 in
AB=5.67 in
The price of milk is believed to increase by 54% over the next 3 years. If 2 gallons of milk costs $2.50 now, what will the price be in 3 years after the increase?
Final answer:
To find the future price of milk after a 54% increase, multiply the current price by 1.54. For 2 gallons of milk costing $2.50 now, the future price will be $3.85.
Explanation:
To calculate the future price of milk after a 54% increase over 3 years, we first need to determine the percentage increase in decimal form and then apply it to the current price. An increase of 54% is equivalent to a multiplier of 1.54 in decimal form.
Therefore, if 2 gallons of milk currently cost $2.50, we calculate the future cost by multiplying $2.50 by 1.54.
Here's the calculation:
Convert the percentage increase to a decimal: 54% = 0.54.
Add 1 to the decimal to account for the total value after the increase: 1 + 0.54 = 1.54.
Multiply the current price of 2 gallons of milk by the increase factor: $2.50 x 1.54 = $3.85.
After a 54% increase, the price for 2 gallons of milk will be $3.85.
In your lab, a substances temperature has been observed to follow the function T(x)=(x-2)^3+8. The turning point of the graph is where the substance changes from a solid to a liquid. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function.
In the sandwiches mode, select the "cheese" option and observe the equation given for the preparation of a cheese sandwich. in the equation, set the number of bread slices to "2" and the number of cheese slices to "1." you will see that the product formed by these three ingredients is one cheese sandwich. suppose you have 38 bread slices and 28 cheese slices. how many cheese sandwiches can you make?
Final answer:
You can make 19 cheese sandwiches with 38 bread slices and 28 cheese slices.
Explanation:
In this scenario, you have 38 bread slices and 28 cheese slices. The equation for a cheese sandwich is 1 sandwich = 2 slices of bread + 1 slice of cheese. So, if you set the number of bread slices to '2' and the number of cheese slices to '1', you can calculate how many cheese sandwiches you can make.
First, divide the number of bread slices (38) by 2 to get the number of sandwiches that can be made with the bread: 38 / 2 = 19 sandwiches.
Next, divide the number of cheese slices (28) by 1 to get the number of sandwiches that can be made with the cheese: 28 / 1 = 28 sandwiches.
Since you can only make 19 sandwiches with the available bread, the limiting factor is the bread. Therefore, you can make 19 cheese sandwiches with the given amounts of bread and cheese.
what is the reciprocal
In order to find the reciprocal of a number, we should just flop it over.
If we're asked to find the reciprocal of a fraction, then the numerator & denominator of the fraction switch places.
If we're asked to find the reciprocal of an expression, then we also flop it over, like so:-
[tex]\pmb{u^2-s^2}\longmapsto\pmb{\displaystyle\frac{u^2-s^2}{1} }\longmapsto\pmb{\displaystyle\frac{1}{u^2-s^2} }[/tex]
Explanation of steps:-
First, I turned the expression into a fraction by adding a denominator of 1.
Then, I flopped it over and found the reciprocal.
Hence, the reciprocal of u²-s² is:-
[tex]\bigstar{\boxed{\pmb{\displaystyle\frac{1}{u^2s^2} }}}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
In the figure, and . Complete the following statements to prove that and are supplementary angles. and , as they are corresponding angles for parallel lines cut by a transversal. Therefore, if , then by the . Therefore, and are supplementary angles by the . ° (1) , so (2) Applying the to (1) and (2), we get . Therefore, and are supplementary angles.
The Complete sentence is shown below.
What is Congruent Supplement theorem?Two angles are congruent if they are supplements of the same angle (also known as congruent angles).
The Complete sentences will be
∠EIA ≅ ∠IKC and ∠GJB is ≅ ∠ JLD (Corresponding angles)
∠EIA ≅ ∠GJB then ∠IKC ≅ ∠ JLD (Substitution Property of Congruency)
∠IKL + ∠IKC 180° (Linear Pair Theorem)
and ∠DLH + ∠JLD =180° (Linear Pair Theorem)
Then, m∠IKL + m∠IKC = 180°
Also, ∠IKC ≅ ∠JLD
m∠IKC = m∠JLD (Subtraction Property OF Congruency)
Thus, m∠IKL + m∠JLD = 180°
As, ∠IKL and ∠JLD are supplementary angles.
But ∠DLH and ∠JLD are supplementary angles.
∠IKL ≅ ∠DLH (Congruent Supplements Theorem)
Learn more about Congruent Supplements Theorem here:
https://brainly.com/question/29175829
#SPJ7
Convert y=2/3x-17 to standard form
Larry use a pattern of colors to make a Q train he use a regular a blue cube a Red Cube and another Red Cube before he start the pattern again he use 15 cubes how many red cubes are Larry use
Whole numbers are written on cards and then placed in a bag. Tyra selects a single card, writes down the number, and then places it back in the bag. She repeats this 62 times. Tyra calculates the relative frequency of each number card. Outcome 1 2 3 4 5 Relative Frequency 0.19 0.20 0.21 0.19 0.21 Which statement about Tyra's experiment is true? The outcomes do not appear to be equally likely, so a uniform probability model is a good model to represent the probabilities in Tyra's experiment. The outcomes do not appear to be equally likely, so a uniform probability model is not good model to represent the probabilities in Tyra's experiment. The outcomes appear to be equally likely, so a uniform probability model is a good model to represent the probabilities in Tyra's experiment. The outcomes appear to be equally likely, so a uniform probability model is not a good model to represent the probabilities in Tyra's experiment. will give BRAINLIEST
Answer: The outcomes appear to be equally likely, so a uniform probability model is a good model to represent the probabilities in Tyra's experiment.
Step-by-step explanation: Probability model, also known as Probability distribution, is a mathematical function that shows the probability of any outcome to occur in an experiment. When those probabilities of occurence are the same for all possible outcomes, it is a uniform probability distribution.
For example, if you roll a fair dice, the probability of having the number 1 is 1/6; for 2 is also 1/6 and etc,
In Tyra's experiment, when the calculates the frequency of each number card, the values are closer together. This means that the probability of taking a card with number 1 written on it is almost the same as taking a card with number 2 and so. In conclusion, Tyra's experiment is au uniform probability model.
The statement about Tyra's experiment is:The outcomes do not appear to be equally likely, so a uniform probability model is not a good model to represent the probabilities in Tyra's experiment.
In probability theory, a uniform probability model is one in which all outcomes in the sample space are equally likely to occur. This means that if there are n possible outcomes, the probability of each outcome is [tex]\( \frac{1}{n} \)[/tex].
In Tyra's experiment, she drew a card from a bag, recorded the number, and then replaced it before drawing again. This process is repeated 62 times, and she calculates the relative frequency of each number card. The relative frequency is the ratio of the number of times a particular outcome occurs to the total number of trials.
The given relative frequencies for outcomes 1 through 5 are as follows:
Outcome 1: 0.19Outcome 2: 0.20Outcome 3: 0.21Outcome 4: 0.19Outcome 5: 0.21If the outcomes were equally likely, we would expect the relative frequencies to be the same for all outcomes, especially after a large number of trials like 62. However, the relative frequencies vary from 0.19 to 0.21, indicating that some outcomes are occurring more frequently than others.
Since the relative frequencies are not the same for all outcomes, we can conclude that the outcomes do not appear to be equally likely. Therefore, a uniform probability model, which assumes equal likelihood for all outcomes, would not be a good fit for Tyra's experiment. Instead, the probabilities in Tyra's experiment seem to be non-uniform, and a different probability model that accounts for the varying likelihoods of the outcomes would be more appropriate.