For two binomials, the distributive property is:
[tex](a+b)\cdot(c+d)=a\cdot c+a\cdot d+b\cdot c+b\cdot d[/tex]So, let's solve this problem.
Step 01: Multiply the first term of the binomial (x - 3) by both terms of the binominal (4x + 2).
[tex](x-3)\cdot(4x+2)=x\cdot4x+x\cdot2+\cdots_{}[/tex]Step 02: Multiply the second term of the binomial (x - 3) by both terms of the binominal (4x + 2).
[tex](x-3)\cdot(4x+2)=x\cdot4x+x\cdot2+(-3)\cdot4x+(-3)\cdot2[/tex]Step 03: Multiply the terms.
[tex]=4x^2+2x-12x-6[/tex]Step 04: Add like terms.
[tex]=4x^2-10x-6[/tex]Answer:
[tex]4x^2-10x-6[/tex]Trini Cars break down on the highway.show me estimates that she is 20 to 30 miles from the nearest car repair shop she calls a towing company that charges a fee of $80 plus $3 per mile to tow a car.if training uses this towing company, which is the best estimate for the amount of money,m,she will pay for the company to tow her car.a .103 greater than sign and greater than sign 113 b.140 greater than sign M greater than sign 150 c.114 greater than 5 m greater than 170 d. 560 greater than 10 m > 70
We have that the cost is $80 plus $3 per mile, and also we now that the car is 20 to 30 miles from the car repair shop. So we have that Trini have to pay
[tex]\begin{gathered} 80\text{ + 3(20) }\leq\text{ M }\leq\text{ 80 + 3(30)} \\ 80\text{ + 60 }\leq\text{ M }\leq\text{ 80 + 90} \\ 140\text{ }\leq\text{ M }\leq170 \end{gathered}[/tex]So the answer is: b.140 greater than sign M greater than sign 150.
21.) Determine the distance between the points (-2, 3) and (4,9).A 142B 7146C 413D 6V222.) Infigure
The distance formula can be represented below
[tex]\begin{gathered} c^{}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} c=\sqrt[]{(4+2)^2+(9-3)^2} \\ c=\sqrt[]{(6)^2+(6)^2} \\ c=\sqrt[]{36+36} \\ c=\sqrt[]{72} \\ c=\sqrt[]{36\times2} \\ c=6\sqrt[]{2} \end{gathered}[/tex]The answer is D.
In a right triangle, if the hypotenuse is equal to 16 feet and the side adjacent to ∠θ is equal to 5 feet, what is the approximate measurement of ∠θ?
We have the diagram:
We use the trigonometric identity cosine:
[tex]\cos\theta=\frac{adjacent}{hypotenuse}[/tex]Substitute the values:
[tex]\begin{gathered} \cos\theta=\frac{5}{16} \\ \theta=\cos^{-1}(\frac{5}{16})=71.79 \end{gathered}[/tex]Answer: 71.79°
When you convert 0.0045 to scientific notation, the exponent will be
positive.
Or
negative.
find the sum to infinity 16,4,1,1/4
Answer:
The sum to infinity of the given series is;
[tex]S_{\infty}=21\frac{1}{3}[/tex]Explanation:
From the given series, we can see that the series is a Geometric Progression (GP) because it has a common ratio;
[tex]\begin{gathered} r=\frac{4}{16}=\frac{1}{4} \\ r=0.25 \end{gathered}[/tex]The formula to calculate the sum to infinity of a GP is;
[tex]\begin{gathered} S_{\infty}=\frac{a}{1-r} \\ \text{For;} \\ 0Where;a = first term = 16
r = common ratio = 0.25.
substituting we have;
[tex]\begin{gathered} S_{\infty}=\frac{16}{1-0.25}=\frac{16}{0.75} \\ S_{\infty}=21\frac{1}{3} \\ S_{\infty}=21.33 \end{gathered}[/tex]Therefore, the sum to infinity of the given series is;
[tex]S_{\infty}=21\frac{1}{3}[/tex]Fill in the blanks to find other expressions for 8%a. __ for every 100, b. __for every 50, c. 1 for every __, d. 0.5 for every __. 150
Using ratios, the sentences regarding a percentage of 8% are given as follows:
a. 8 for every 100.
b. 4 for every 50.
c. 1 for every 12.5.
d. 0.5 for every 6.25.
Ratio between two amountsThe ratio between two amounts a and b is given by the division of a by b, as follows:
r = a/b.
One example of ratio is a percentage, as a percentage of x% is equivalent to the ratio of x to 100, that is:
r = x/100.
Hence a percentage of 8% is equivalent to the following ratio:
r = 8/100.
That is, 8 for every 8.
Ratios are fractions, and they can be simplified, dividing both the numerator and the denominator by the same amount, as is the case in this problem:
r = 4/50 (simplifying by 2, four for every 50).r = 1/12.5 (simplifying by 4, one for every 12.5).r = 0.5/6.25 (simplifying by 2, 0.5 for every 6.25).More can be learned about ratios at https://brainly.com/question/2328454
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Which of the following correctly identifies the vertices that lie on the major axis of the conic section shown below? (x - 2) 3-2*) (y+5) = 1 4 9 O A. (2,-2) and (2,-8) O B. (-5,5) and (-5,-1) O C. (5,5) and (-1,-5) O D. (0,-5) and (4,-5)
General equation of an ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]where (h,k) is the center, and a and b are some constants.
If b² is greater than a², then the y-axis is the major axis.
In this case, the ellipse is defined by the next equation:
[tex]\frac{(x-2)^2}{4}+\frac{(y+5)^2}{9}=1[/tex]This means that:
[tex]\begin{gathered} b^2=9 \\ b=\sqrt[]{9} \\ b=3 \end{gathered}[/tex]And, h = 2, k = -5
The vertices on the major axis are computed as follows:
(h, k+b) and (h, k-b)
Substituting with h = 2, k = -5, and b = 3, the vertices are:
(2, -5+3) and (2, -5-3)
(2, -2) and (2, -8)
Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)
Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)
The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.
Given,
Belinda wants to invest $1,000.
The Table is:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Now, According to the question:
When the x-values are sequential (1, 2, 3, ...), the y-values will have a common difference for a linear function, and a common ratio for an exponential function.
For the two investment options, we notice Belinda earns 1300 -1000 = 300 the first year for either option. The difference is the same the next year for Option 2 (1600 -1300 = 300), but is not the same for Option 1. For that option, the ratio is the same for the second year as it was for the first year:
1690/1300 = 1.3 = 1300/1000
Part A :
(Option 1) can be represented by exponential function.
(Option 2) can be represented by a linear function.
Part B:
For Option 1:
To find the value of the investment f(n), in dollars, after n years.
The generic form of an exponential function is ...
f(n) = a·b^n
Now, Amount after 1 year = 1100
Principle (P) is = 1000
Using the formula :
A = P[tex](1+r)^n[/tex]
1100 = 1000[tex]([/tex][tex]1 + r)^1[/tex]
1.10 = 1 + r
r = 0.10
Amount after t years can be given by :
A = 1000(1.10)^t
For Option 2,
The generic form of an exponential function is ...
f(n) = a·n + b
Rate of change (m) = (1100 - 1000) / 1 = 100
Amount after t years can be given by
A = 1000 + 100 x t .
Part C:
Investment in (1) : 1000 [tex](1.10)^2^0[/tex]= $6727
Investment in (2): $3000
Hence, The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.
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282The number of germs in a sample can be measured by the equation f(x)=15x + 145. Temperature represents the domain of the sample while the range isthe number of germs. If a doctor wants to keep the amount of germs to be less than 300,what is the approximate domain of temperatures to keep the sample under 300?
Answer
The approximate domain temperature is 10
Step-by-step explanation:
Given the following model function
f(x) = 15x + 145
Mathematically
15x + 145 < 300
Collect the like terms
15x < 300 - 145
15x < 155
Divide both sides by 15
15x/15 < 155/15
x < 10.33
Find the exact value of sin A and cos A where a = 9 and b = 10 and
Given data:
a=9 , b = 10
use the phythagoras theorem,
[tex]c=\sqrt[]{a^2+b}^2[/tex][tex]\begin{gathered} c=\sqrt[]{9^2+10^2} \\ c=\sqrt[]{81+100} \\ =\sqrt[]{181} \end{gathered}[/tex]thus,
[tex]\sin A=\frac{opp}{\text{hypo}}[/tex][tex]\text{sinA}=\frac{9}{\sqrt[]{181}}[/tex]and,
[tex]undefined[/tex]you guess there are 80 marbles in a jar but there are actually 50. what is the percent of error
Calculate value = 80
Actual value = 50
[tex]\begin{gathered} \text{Percentage error = }\frac{Calculated\text{ value - Actual vale}}{\text{Actual value}}\text{ X 100\%} \\ =\text{ }\frac{80\text{ - 50}}{50}\text{ x 100} \\ =\text{ }\frac{30\text{ x 100}}{50} \\ =\text{ }\frac{3000}{50} \\ =\text{ 60\%} \end{gathered}[/tex]how do you calculate the volume of water in a lake? given is the area of the lake at 1.35 km2 and its depth is 4.0 m
Given
Area of lake = 1.35 square km
Depth = 4.0m
Find
Volume of water in a lake
Explanation
Volume of water in a lake is given by
[tex]area\times depth[/tex]first we have to make the units same
as we know 1 square km = 1000000
so , 1.35 square km = 1.35 * 1000000= 1350000 square meter
so , volume of water in a lake =
[tex]\begin{gathered} volume=1350000\times4 \\ volume=5400000\text{ }cubic\text{ meter} \end{gathered}[/tex]Final Answer
Therefore , the volume of water in a lake is 5400000 cubic meter
15. The new county park is one mile square. What would be the length of a road around its boundaries?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
County park:
area = 1 mile²
Step 02:
length of a road around:
area = side²
1 mile ² = s²
[tex]\begin{gathered} s^2=1 \\ s=\sqrt[]{1}=\text{ 1 } \end{gathered}[/tex]s = 1 mile
perimeter = 4 s = 4 * 1 mile = 4 miles
The answer is:
the length of a road around its boundaries is 4 miles
1.5 part 1 question 36 determine whether the graph represent a function explain your answer
Recall that for a graph to correspond to a graph it must pass the vertical line test. The vertical line test consists of drawing vertical lines and if two points of the graph are on the same vertical line then the graph does not represent a function.
Notice the following:
From the above graph, we get that points A B, and C are on the same vertical line, and the same happens for e and f, and m and n. Therefore the graph fails the vertical line test.
Answer: The graph does not represent a function.
Suppose that an airline uses a seat width of 16.2 in. Assume men have hip breadths that are normally distributed with a mean of 14 in. and a standard deviation of 1 in. Complete parts (a) through (c) below.
Given:
population mean (μ) = 14 inches
population standard deviation (σ) = 1 inch
sample size (n) = 126
Find: the probability that a sample mean > 16.2 inches
Solution:
To determine the probability, first, let's convert x = 16.2 to a z-value using the formula below.
[tex]x=\frac{\bar{x}-\mu}{\sigma\div\sqrt{n}}[/tex]Let's plug into the formula above the given information.
[tex]z=\frac{16.2-14}{1\div\sqrt{126}}[/tex]Then, solve.
[tex]z=\frac{2.2}{0.089087}[/tex][tex]z=24.6949[/tex]The equivalent z-value of x = 16.2 is z = 24.6949
Since we are looking for the probability of greater than 16.2 inches, let's find the area under the normal curve to the right of z = 24.6949.
Based on the standard normal distribution table, the area from the center to z = 24.6949 is 0.5
Since we want the area to the right, let's subtract 0.5 from 0.5.
[tex]0.5-0.5=0[/tex]Therefore, the probability that a sample mean of 126 men is greater than 16.2 inches is 0.
Identify the x intercept(s) from the graphType your answer using set notation {x,x} listing x values in order from least to greatest
The x-intercept is where the graph passes the x-axis.
The graph extends from {-5 ≤ x ≤ 3}
The x-intercept is {x = -1}.
What point in the feasible reign maximizes the objective function? constraints: x => 0 y => 0 y<= x - 4 x + y <= 6
Objective Function: C = 2x + y
The point in the feasible region maximizes the objective function is (5, 1)
How to determine the feasible region?The given parameters are
Objective function: C = 2x + y
Subject to (i.e. the constraints)
x >= 0, y >= 0
y <= x - 4, x + y <= 6
Represent y <= x - 4, x + y <= 6 as equations
y = x - 4 and x + y = 6
Substitute y = x - 4 in x + y = 6
So, we have
x + x - 4 = 6
Evaluate the like terms
2x = 10
This gives
x = 5
Substitute x = 5 in y = 6 - x
y = 6 - 5
Evaluate
y = 1
So, we have
(x, y)= (5, 1)
Hence, the coordinates is (5, 1)
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Robin Sparkles invests $3,760 in a savingsaccount at her local bank which gives 1.8%simple annual interest. She also invests$2,400 in an online savings account whichgives 5.3% simple annual interest. After fiveyears, which one will have earned moreinterest, and how much more interest will ithave earned, to the nearest dollar?
The formula for determining simple interest is expressed as
I = PRT/100
where
I = interest
P = principal or amount invested
T = time in years
R = interest rate
Considering the amount invested in her local bank,
P = 3760
R = 1.8
T = 5
I = (3760 x 1.8 x 5)/100 = 338.4
Considering the amount invested in online savings,
P = 2400
R = 5.3
T = 5
I = (2400 x 5.3 x 5)/100 = 636
After 5 years, the investment in the online savings account earned more interest.
The difference in interest earned is
636 - 338.4 = $298 to the nearest dollar
It has earned $298 more than the local bank's interest
y - 7.8= 5.5 I got 2.9 but I want to be sure I understand and took the right steps
Given the equation:
[tex]y-7.8=5.5[/tex]You need to solve for "y" in order to find its value. In this case, you need to apply the Addition Property of Equality, which states that, if:
[tex]a=b[/tex]Then:
[tex]a+c=b+c[/tex]Therefore, you need to add 7.8 to both sides of the equation in order to solve for "y":
[tex]\begin{gathered} y-7.8+(7.8)=5.5+(7.8) \\ y=13.3 \end{gathered}[/tex]Hence, the answer is:
[tex]y=13.3[/tex]Zaria is making pipe cleaner flowers for
her friends. She has 215 pipe cleaners.
How many flowers can she make with 3
pipe cleaners in each?
[?] flowers and pipe cleaners leftover
I
Answer
Enter
We can get the answer by dividing 215 by 3
What is dividing?
One of the four fundamental arithmetic operations, or ways to combine numbers to create new ones, is division. The other operations are multiplication, addition, and subtraction. The process of counting the instances in which one integer is included into the others is the most fundamental definition of the division of two natural numbers. This amount need not be an integer. For instance, if twenty apples are divided equally among four people, everyone will get five of them.
We can get the answer by dividing 215 by 3
215/3 = 71.67
Hence, 71 flowers are made
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you pull with 45nm on a torque wrench of 1m what's the tourqe at the end
The torque at the end is equal to 45 Nm.
What is torque?Torque can be defined as a measure of the amount of force which causes a physical object to rotate about an axis. This ultimately implies that, torque is a force which tends to cause the rotation of a physical object about an axis.
Mathematically, torque can be calculated by using this formula:
τ = Fd
Where:
τ represents the torque.F represents the force.d represents the perpendicular distance.In this scenario, we can reasonably infer and logically deduce that the torque at the end would be equal to 45 Newton meter (Nm) because the force was not applied over a perpendicular distance.
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Transforming the graph of a function by shrinking or stretching
So,
From the graph of the function f(x), we can notice it contains the points:
[tex]\begin{gathered} f(2)=-4\to(2,-4) \\ f(-2)=-2\to(-2,-2) \end{gathered}[/tex]If we use the transformation, we obtain the new points:
[tex]\begin{gathered} f(\frac{1}{2}x)\to f(\frac{1}{2}(2))=f(1)=-\frac{7}{2}\to(2,-\frac{7}{2}) \\ f(\frac{1}{2}x)\to f(\frac{1}{2}(-2))=f(-1)=-\frac{5}{2}\to(-2,-\frac{5}{2}) \end{gathered}[/tex]All we need to do to graph the new line is to plot the points:
[tex](2,-\frac{7}{2})\text{ and }(-2,-\frac{5}{2})[/tex]And form a line that passes through them.
How do I find the selling price if a store pays 3$ for a magazine. The markup is 5%
We need to find the selling price of a magazine. We know that the store pays $3 for it, and the markup is 5%.
So, we need to add 5% of the initial price to that initial price.
First, let's find:
[tex]5\%\text{ of }\$3=5\%\cdot\$3=\frac{5}{100}\cdot\$3=\frac{\$15}{100}=\$0.15[/tex]Now, adding the previous result to the initial price, we obtain:
[tex]\$3+\$0.15=\$3.15[/tex]Therefore, the selling price is $3.15.
Division Properties of Exponents HW.
Given the expressions:
[tex]\begin{gathered} \frac{4^5}{4^2} \\ \text{and} \\ \frac{4^2}{4^5} \end{gathered}[/tex]we can use the following property for exponents in quotients:
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]in this case, we have the following:
[tex]\begin{gathered} \frac{4^5}{4^2}=4^{5-2}=4^3 \\ \text{and} \\ \frac{4^2}{4^5^{}}=4^{2-5}=4^{-3} \end{gathered}[/tex]then, the difference between both expressions is that when they are simplified, they get opposite signs on their exponents.
Ms.Lee has 7 boys and 13 girls in her class. If she selects a student at random, what is the probability that she will select a boy?
Answer: 35 percent chance
Step-by-step explanation: 7+13=20 20x5=100 7x5=35 13x5=65 65+35=100
3/4 divided by 3/5 how do you work the problem
We copy the first number, change the division sign to multiplication, then flip the second fraction
Cancel the three's
If you want to simplify the improper fraction, divide the numerator by the denominator
5/4 = 1 1/4
What are the coordinates of the point on the directed line segment from (3,-3) to (7,5) thar oartitions the segment into a ratio of 5 to 3?
Answer:
(x, y) = (5.5, 2)
Explanation:
The coordinates of a point that divide the segment from point (x1, y1) to (x2, y2) into a ratio of a:b can be found using the following equations:
[tex]\begin{gathered} x=x_1+\frac{a}{a+b}(x_2-x_1) \\ y=y_1+\frac{a}{a+b}(y_2-y_1) \end{gathered}[/tex]So, replacing (x1, y1) by (3, -3), (x2, y2) by (7, 5) and the ratio a:b by 5:3, we get that the coordinates of the point are:
[tex]\begin{gathered} x=3+\frac{5}{5+3}(7-3) \\ x=3+\frac{5}{8}(4) \\ x=3+2.5=5.5 \\ y=-3+\frac{5}{5+3}(5-(-3)) \\ y=-3+\frac{5}{8}(5+3) \\ y=-3+\frac{5}{8}(8) \\ y=-3+5=2 \end{gathered}[/tex]Therefore, the coordinates of the point are (x, y) = (5.5, 2)
For the equation, complete the given table.
Answer:
Step-by-step explanation:
first row: 4
second: 2
third: 6
fourth: 9
plug in x for x in the equation/plug in y for y in the equation for whichever is given.
I need help with this page pls help me !!
N 6
we have
[tex]216=\frac{r}{2}+214[/tex]a ------> subtraction
subtract 214 both sides
[tex]\begin{gathered} 216-214=\frac{r}{2} \\ 2=\frac{r}{2} \end{gathered}[/tex]b ------> multiplication
Multiply by 2 both sides
[tex]\begin{gathered} 2\cdot2=2\cdot\frac{r}{2} \\ r=4 \end{gathered}[/tex]c ------> r=4
A spinner has the sections A through F. The spinner is spun and a 6-sided die is rolled. What is the probability that the outcome will be D and 5?1/361/181/121/6
To find the probability of having a D and %, we would use the concept of mutually exclusive events here
But probability is given as
[tex]P=\frac{\text{ number of favourable outcomes}}{\text{total number of }possible\text{ outcomes}}[/tex]The probability of choosing a D is
A, B, C, D, E and F. This can be found as
[tex]P_a=\frac{1}{6}[/tex]The probabilty of choosing a 5 out of 6 possible outcomes is
[tex]P_n=\frac{1}{6}[/tex]The probability of having a D and 5 would be
[tex]\begin{gathered} P=P_a\times P_n \\ P=\frac{1}{6}\times\frac{1}{6} \\ P=\frac{1}{36} \end{gathered}[/tex]From the calculations above, the answer to this question is 1/36