Jerry purchased items for his garden
Let the items purchased be x and y
He purchased plants for $15 and bags of soil for $15
Jerry used the expression: 15(x + y)
Valerie used the expression: 15x + 15y
The expressions are equivalent
Using the distributive property
a * (b + c ) = ab + ac
therefore, 15(x + y ) is equivalent to 15x + 15y
15(x + y) = 15 * x + 15 * y
15(x + y) = 15x + 15y
The country of Honduras has a population of 8.2 million. There were 7,172 homicide deaths there in 2014. a) Express the deaths per capita as a decimal. Round to 6 decimal places. b) Express the deaths per capita in Scientific Notation (using the digits you typed in part a). Type your answer as though you were typing it into your calculator--either with "E" or "x10^" notation-- no spaces in your answer!c) The United States has a population of about 320 million. If our homicide deaths were proportional to that of Honduras, how many deaths would we expect in the United States due to homicides? Round to the nearest person.
Population = 8.2 million = 8,200,000
Homicides = 7,172
a) Deaths per capita = Homicides / Population = 7,172 /8,200,000 = 0.000875 deaths per capita
b) 8.75 x 10 ^-4
c) Population : 320 million : 320,000,000
7,172 /8,200,000 = x / 320,000,000
Cross multiply:
320,000,000 ( 7,172 ) = 8,200,000 x
320,000,000 ( 7,172 ) / 8,200,000 = x
x = 279,883 Deaths
Need help with the attached - my last tutor and I lost connectivity as we were solving it
Answer:
[tex]18,24\text{ and 30}[/tex]Explanation:
Here, we want to get the legs of the triangle
Let the shorter length be x cm
The longer leg will be (x + 6) cm
The hypotenuse length will be (x + 12) cm
According to Pythagoras' theorem. the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides
Thus:
[tex]\begin{gathered} (x\text{ + 12\rparen}^2\text{ = \lparen x\rparen}^2\text{ + \lparen x + 6\rparen}^2 \\ x^2+24x\text{ + 144 = x}^2+12x\text{ + 36 + x}^2 \\ x^2+24x+144\text{ = 2x}^2+12x\text{ + 36} \\ 2x^2-x^2+12x-24x\text{ + 36-144 = 0} \\ x^2-12x\text{ -108 = 0} \end{gathered}[/tex]Solving the quadratic equation, we have it that:
[tex]\begin{gathered} x^2-18x+6x-108\text{ = 0} \\ x(x-18)+6(x-18)\text{ = 0} \\ (x+6)(x-18)\text{ = 0} \\ x\text{ = -6 or 18} \end{gathered}[/tex]We discard x = -6
This would give us a side length with 0 length
Now, using x = 18:
we have the side lengths as:
18, 18 + 6 and 18 + 12 :
18, 24 and 30
david invested 89000 in an account paying an intrest rate of 3.1% compounded continuously. assuming no deposits or with drawls are made how much money to the nearest ten dollars would be in the account after 15 years?
The information we have is:
Principal, the invested amount:
[tex]P=89,000[/tex]Interest rate:
[tex]r=3.1\text{ percent }[/tex]We will need the percent as a decimal, so we divide by 100:
[tex]r=0.031[/tex]Time of the investment in years:
[tex]t=15[/tex]Since the investment is compounded continuously, we need to use the formula for continuous compounding:
[tex]A=Pe^{rt}[/tex]Where P, r, and t are the values we defined earlier. And A is the Amount after 15 years. Also, e is a mathematical constant:
[tex]e=2.7183[/tex]Substituting these values into the formula:
[tex]A=(89,000)(2.7183)^{(0.031\times15)}[/tex]Solving the operations:
[tex]\begin{gathered} A=(89,000)(2.7183)^{(0.465)} \\ A=(89,000)(2.7183)^{(0.465)} \\ A=(89,000)(1.592) \\ A=141,689.7 \end{gathered}[/tex]Answer: $141,689.7
To round the answer to the nearest ten dollars, we should round the last three digits: 89.7 to the nearest tens which is 90.
So the rounded answer will be: $141,690
Maury's Motorcycle Shop has an average inventory of $289,900. What was the inventory turnover (to the nearest tenth) when annual sales were $1,395,870?3.64.14.85.7None of these choices are correct
Solution
Step 1
Deine terms and write an expression for the inventory turnover ratio
Annual sales = $1,395,870
Average inventory = $289,900
[tex]\text{Inventory turnover ratio =}\frac{Anualsales(\cos t\text{ of goods sold)}}{\text{Average inventory}}[/tex]Step 2
Calculate the inventory turnover ratio
[tex]\begin{gathered} \text{Inventory turnover ratio =}\frac{1395870}{289900} \\ \text{Inventory turnover ratio = 4.82} \end{gathered}[/tex]Therefore the inventory turnover ratio approximately = 4.8
Therefore, the correct option is option C (4.8)
Rewrite the following linear equation in slope intercept form. write your answer with no spaces. y-5=(x+1)
Answer:
y=x+6
Explanation:
The slope-intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Given the line:
[tex]y-5=\mleft(x+1\mright)[/tex]We add 5 to both sides to obtain:
[tex]\begin{gathered} y-5+5=x+1+5 \\ y=x+6 \end{gathered}[/tex]The slope-intercept form is y=x+6.
There are 28 students in a homeroom. How may different ways can they be chosen tobe elected President, Vice President, and Treasurer?
Since we have 28 students, there are 28 different ways for choosing the President. Then, there are 27 different ways for the Vice President and 26 ways for the Treasurer.
Therefore, there are
[tex]3P28=28\cdot27\cdot26=19656[/tex]ways to choose a President, Vice President and Treasurer. Therefore, the answer is: 19656
Express the product of 2x2 + 3x - 10 and x +5 in standard form.
The given expression :
[tex]2x^2+3x\text{ -10 and x +5}[/tex]set up the expressions next to each other in parenthesis:
[tex](x+5)(2x^2+3x-10)[/tex]Distribute the first term in the first set of parenthesis throughout each term in the second set of parenthesis:
[tex](x+5)(2x^2+3x-10)=x(2x^2+3x-10)+5(2x^2+3x-10)[/tex]Now, distribute x over 2x^2+3x-10 and 5 too
[tex]\begin{gathered} (x+5)(2x^2+3x-10)=x(2x^2+3x-10)+5(2x^2+3x-10) \\ (x+5)(2x^2+3x-10)=2x^3+3x^2-10x+10x^2+15x-50 \\ (x+5)(2x^2+3x-10)=2x^3+13x^2+5x-50 \end{gathered}[/tex]The digit 6 is placed in front of a 3-digit number abc, to form a 4-digit number. the sum of the 4-digit number and 300 is 8 times the original 3-digit number, find the abc
Step-by-step explanation:
abc = x
6 in front of abc means it is abc + 6000.
x + 6000 + 300 = 8x
x + 6300 = 8x
6300 = 7x
x = abc = 900
the variable y is directly proportional 2 x. if y equals -0.6 when x equals 0.24, find x when y equals -31.5.
y is directly proportional to x, so:
y = αx
Where α = constant of proportionality
If y = -0.6 and x = 0.24:
-0.6 = α0.24
Solving for α:
α = -0.6/0.24 = -2.5
Now, if y = -31.5 :
-31.5 = -2.5*x
Solving for x:
x = -31.5/-2.5 = 12.6
calculate the area of a triangle with a 3.5 cm base and a 2.6 cm height
calculate the area of a triangle with a 3.5 cm base and a 2.6 cm height
the area of triangle is equal to
A=(1/2)b*h
where
b is the base and h is the height
we have
b=3.5 cm
h=2.6 cm
substitute in the formula
A=(1/2)*(3.5)*(2.6)
A=4.55 cm2
area is 4.55 square centimeters
Use the decimals 3.43, 8.93, and 5.5 to write two different addition facts and two different subtraction facts.
We have that a number fact is an equation made up of three different numbers.
We can say that:
Addition facts:
3.43 + 5.5 = 8.93
And also that:
5.5 + 3.43 = 8.93
(In this case, we have the commutative property of the addition).
Subtraction facts:
8.93 - 3.43 = 5.5
8.93 - 5.5 = 3.43
Identify the terms the expression. 1.7 + 2x - 12 *
1.7, 2x, and -12.
1) In the expression we can identify the following parts of this expression:
2) So the terms are 1.7, 2x, and -12. 1.7 and -12 are called constants, 2 is the coefficient and x is the variable.
Question 6 of 10 If f(x) = 2x-3 -3 5 which of the following is the inverse of f(x)? > O A. f-'(x) = 5x+3 2 O B. f'(x) = 3x+2 5 O c. f'(x) 2x +3 5 O D. f-'(x) = 3x +5 2 SUBMIT
y = (2x-3)/5
To find the inverse, exchange x and y and solve for y
x = ( 2y-3)/5
Multiply each side by 5
5x = 2y-3
Add 3 to each side
5x+3 = 2y-3+3
5x+3 = 2y
Divide each side by 2
(5x+3)/2 = 2y/2
(5x+3)/2 = y
The inverse is (5x+3) /2
f^-1(x) = 5x+3
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2
Eugene is ready to purchase a new suit. It regularly sells for $132.45, but it is on sale for $89.95. What is the mark down?
Given:
The initial selling price, sp=$132.45.
The new selling price, SP=$89.95.
The mark down in selling price is,
[tex]\begin{gathered} D=sp-SP \\ =132.45-89.95 \\ =42.5 \end{gathered}[/tex]Therefore, the markdown is $42.5.
In the diagram below, describe what additional piece of information isneed to prove the triangles are congruent by SAS.
Remember that
(SAS for Similarity). In two triangles, if two sets of corresponding sides are proportional and the included angle is congruent, the triangles are similar.
so
in this problem
JK and AK ae congruent to NK and AK
is needed the measure of angle
therefore
answer is fourth optionThe triangle shown is rotated 90 degrees clockwise about the origin.Next, it is translated according to the rule (x, y) -> (x-5y-2).
1ST. Rotate 90° (red)
Image of A after first transformation= (-2,2)
Next, translate 5 units to the left along the x -axis , and down to units along the y-axis. (BLUE TRIANGLE)
image of A after both tranformations= (-7,0)
what is the ratio of 75:90
The ratio of two numbers can be gotten by dividing the first number by the second one, such that:
[tex]a\colon b=\frac{a}{b}[/tex]The question is provided to be:
[tex]75\colon90[/tex]Hence, we can rewrite the question to be:
[tex]75\colon90=\frac{75}{90}[/tex]We can simplify the fraction by dividing both the numerator and the denominator by 15:
Numerator:
[tex]\Rightarrow75\div15=5[/tex]Denominator:
[tex]\Rightarrow90\div15=6[/tex]Therefore, the ratio is:
[tex]\frac{5}{6}[/tex]ANSWER:
Fraction: ⁵/₆
Decimal: 0.833333
22. Distribute (c +4)(3c2-C-5).
We need to make the product of a binomial times a trinomial of the form:
[tex](c+4)\cdot(3c^2-c-5)[/tex]So we use distributive roerty, making sure that we multiply each term of the first binomial times each term of the trinomial.
We start by multiplying c times each of the three terms in the trinomial expression, and after that we do the product of "4" times each of the three terms of the trinomial:
[tex]\begin{gathered} c\cdot(3c^2)-c^2-5c+4\cdot(3c^2)-4c-20 \\ 3c^3-c^2-5c+12c^2-4c-20 \end{gathered}[/tex]and to follow this, we combine the like terms that we have produced in the product. These are the terms in c-squared, and the terms in c:
[tex]3c^3+11c^2-9c-20[/tex]A pre-image and its image have coordinates (-3,-6) and (-1, -2), respectively. Which of the following options representsthe scale factor used in the dilation?321/21/3
ANSWER
1/3
EXPLANATION
The pre-image has coordinates (-3, -6) and the image has coordinates (-1, -2)
The scale factor is the number by which the pre-image was increased or decreased in size through dilation.
To find that, we pick either of the x or y coordinates of the pre-image and image and then we have:
[tex]\text{scale factor =}\frac{coordinate\text{ of image}}{coordinate\text{ of preimage}}[/tex]Let us pick the x coordinates.
We have that the scale factor is:
[tex]SF\text{ = }\frac{-1}{-3}\text{ = }\frac{1}{3}[/tex]The scale factor is 1/3.
A person invests 4000 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5900 dollars?
Given:
A person invests 4000 dollars in a bank.
so, the initial balance = P = 4000
The interest rate = r = 5.75% = 0.0575
Compounded quarterly, n = 4
We will find the time (t) to reach 5900
We will use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Substitute with the given values then solve for (t)
[tex]\begin{gathered} 5900=4000(1+\frac{0.0575}{4})^{4t} \\ \frac{5900}{4000}=1.014375^{4t} \\ \end{gathered}[/tex]Taking the natural logarithm for both sides:
[tex]\begin{gathered} \ln \frac{5900}{4000}=4t\cdot\ln 1.014375 \\ \\ t=\frac{\ln \frac{5900}{4000}}{4\ln 1.014375}\approx6.8077 \end{gathered}[/tex]Rounding to the nearest tenth of a year
So, the answer will be t = 6.8 years
help!! im confused on this question of my study guide.
Solution:
Remember that corresponding Parts of Congruent Triangles are Congruent. According to this, we can conclude that the correct answer is:
CPCTC
7/8 +9/10 write your answer as a fraction in simplest form
Adding Fractions
We are required to find the sum:
[tex]\frac{7}{8}+\frac{9}{10}[/tex]In order to be able to find the sum, we first need to make both denominators with the same value, or a common denominator.
The procedure is called Least Common Multiple of the denominators and consists of finding the lowest multiple of both denominators, in this case:
LCM(8,10)
To find the LCM, we write the prime divisors of each number as follows:
8 = 2*2*2
10 = 2*5
Now we select all the divisors the maximum number of times they appear, that is:
LCM = 2*2*2*5 = 40
Now we divide the LCM by each denominator and multiply the result by each numerator:
[tex]\frac{7}{8}+\frac{9}{10}=\frac{5\cdot7}{40}+\frac{4\cdot9}{40}[/tex][tex]\frac{7}{8}+\frac{9}{10}=\frac{35}{40}+\frac{36}{40}[/tex]Operating:
[tex]\frac{7}{8}+\frac{9}{10}=\frac{35+36}{40}=\frac{71}{40}[/tex]The result is 71/40
evaluate the expression 9÷{17-8}
Solution
We have the following expression:
[tex]\frac{9}{17-8}=\frac{9}{9}=1[/tex]The reason is because we need to do the subtraction and then the division
Write an equation of a line in slope-intercept form that is perpendicular to the line to y = -2x - 1 and that passes through the point (-10,4)
The slope - Intercept form of the equation of a line is written as:
y = mx + c...........................(1)
where m is the slope and
c is the intercept
the equation given in this task is:
y = -2x - 1..........................(2)
Comparing equations (1) and (2)
m = -2
That is the slope of the line = -2
A line perpendicular to the line y = -2x - 1 will have a slope:
[tex]\begin{gathered} m_1=\text{ }\frac{-1}{m} \\ m_1=\text{ }\frac{-1}{-2} \\ m_1=\text{ }\frac{1}{2} \end{gathered}[/tex]The equation of the perpendicular line will be:
[tex]y-y_1=m_1(x-x_1)[/tex]The point through which the line passes is (-10, 4)
That is, x₁ = -10, y₁ = 4
The equation of the perpendicular line becomes:
[tex]\begin{gathered} y\text{ - 4 = }\frac{1}{2}(x\text{ - (-10))} \\ y\text{ - 4 = }\frac{1}{2}(x\text{ + 10)} \\ y-\text{ 4 = }\frac{x}{2}+\text{ }\frac{10}{2} \\ y\text{ - 4 = }\frac{x}{2}\text{ + 5} \\ y\text{ = }\frac{x}{2}\text{ + 5 + 4} \\ y\text{ = }\frac{x}{2}\text{ + 9} \\ y\text{ = }\frac{1}{2}x\text{ + 9} \end{gathered}[/tex]STATEMENTS KLASUN What could be the final reason in the proof below? ASA HL SAS CPCTC
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Diagram
Step 02:
We must apply the properties of parallel and transversal lines.
Statements Reasons
AB || CD , AB = CD 1. Given
∠ ABD = ∠ CDB 2. Alternate interior angles
BD = DB 3. Reflexive Property
ΔABD = ΔCBD 4. Side-angle-side SAS
That is the full solution.
The first two numbers in a sequence areh(1) = 4 and h(2) = 8a) If h(x) is an arithmetic sequence, write anequation:b) If h(x) is a geometric sequence, write anequation:
First term of sequence (a)=4
Second term of sequence =8
The recursive defination of arithmatic sequence is,
[tex]\begin{gathered} a_n=a_{n-1}+d \\ a_0=a=4 \\ \text{common difference d=8-4=4} \end{gathered}[/tex]The arithmatic sequence is written as,
[tex]\begin{gathered} h(x)=a_0+dn \\ h(x)=4+4n \\ h(x)=4,8,12,16 \end{gathered}[/tex]The recursive defination of geometric series is,
[tex]\begin{gathered} a_n=ra_{n-1} \\ \text{where a}_0=4 \\ 8=a_0r \\ 8=4.r \\ r=2 \\ \text{commom ratio = r=2} \end{gathered}[/tex]The geometrix series is written as,
[tex]\begin{gathered} a_n=a_{0^{}}r^n \\ h(x)=4(2)^n_{} \\ h(x)=4,8,16,\ldots\text{..} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} 1)h\mleft(x\mright)=4+4n \\ 2)h(x)=4(2)^n \end{gathered}[/tex]my son needs help with Algebra equation for GED test
we have
3x+7=8x+24
this is an equation
Solve for x
That means
Isolate the variab;e x
so
step 1
Group terms
8x-3x=7-24
step 2
Combine like terms
5x=-17
step 3
Divide both sides by 5
5x/5=-17/5
simplify
x=-17/5tell which property of equality was used. 53 = 318/w 53 × 61 = (318 / w) × 16
We have the expression:
[tex]\begin{gathered} 53=\frac{318}{w} \\ 53\cdot61=\frac{318}{w}\cdot61 \end{gathered}[/tex]In this case, we apply the same factor on both sides of the equality and it remains the same.
This property is the multiplication property.
In the coordinate plane, the points X(−11 4) Y( 10 2) and Z(−3− 5) are reflected over the y-axis to the points X′, Y′, and Z′, respectively. What are the coordinates of X′, Y′, and Z′?
We are given the points X(-11,4), Y(10,2) and Z(-3,-5) and asked to find their reflection over the y-axis. Note that given a point of the form
when we reflect it over the y-axis, we get the red dot
Note that the reflection over the y-axis gives you a point that has the same height. This means that when we reflect over the y-axis, we fix the y coordinate of the point. What changes is the x coordinate. The change is simply obtained by multiplying the x coordinate by -1. So, we get the following table
X(-11,4)--->X'(11,4)
Y(10,2)--->Y'(-10,2)
Z(-3,-5)-->Z'(3,-5)
hello whoever you are ,,,, i j need to check a question, in math, "determine the value of 9 log_24 2 + log_24 27" my answer is 3 but i'm not 100% sure if it's correct
Given:
[tex]\log _{24}2+\log _{24}27[/tex]Sol:.
Use log property then:
[tex]\log _xab=\log _xa+\log _xb[/tex]So:
[tex]\begin{gathered} =\log _{24}2+\log _{24}27 \\ =\log _{24}(27\times2) \\ =\log _{24}54 \\ =1.255 \end{gathered}[/tex]So the value is 1.255