To answer this question, we will define some things first.
For every mathematical expression or term, it consist of three parts:
1) Coefficient
2) Variable: a symbol that stands in for an unknown value in a mathematical expression
3) Constant
In the expression given:
[tex]\begin{gathered} 9+2z \\ 9\text{ is the constant} \\ 2\text{ is the coefficient} \\ z\text{ is the variable} \end{gathered}[/tex]So the variable in the expression is z.
How do I solve for x? Would my answer be 27?
SOLUTION
Exterior property of a triangle
An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.
Hence,
[tex](5x+13)^0=(4x+2)^0+(2x-9)^0[/tex]Simplify and evaluate for x
[tex]\begin{gathered} 5x+13^0=4x+2^0+2x-9^0 \\ 5x+13^0=4x+2x+2^0-9^0 \\ 5x+13^0=6x-7^0 \\ \text{Collect like terms} \\ 13^0+7^0=6x-5x \\ 20^0=x \\ \therefore x=20^0 \end{gathered}[/tex]Therefore,
[tex]x=20^0[/tex]Consider the equation below. 4(x - 4) + 6x = 14 Part A: Enter the value for x that makes the equation true. X = Part B: Explain the algebraic steps you took to get the solution. thea Part C: Explain how you know your solution in Part A is correct.
Part A) To find out the value for x that makes it an identity, (true), we need to solve it.
4(x-4) +6x=14 Distiribute
4x -16 +6x = 14 Combine like terms
2x -16 = 14 Add 16 to both sides
2x = 30 Divide both sides by 2
x =15
Part B) Above explained.
Part C) We can know it by plugging it into the original equation:
4(15 -4) +6(15) = 14
4(11) +90 = 14
44
Greg is ordering tile for a floor he is installing. The owner picks out tile that is 16in by 16in including the grout . The floor is 350 sq ft . (part 1) How many tile must Greg order for the floor ( assume no waste)(part 2) Each tile cost $ 1.75 plus 8% sales tax . How will the tile cost ?
ANSWER
(part 1) 196 tiles
(part 2) $ 1.89
EXPLANATION
(part 1)
First we have to find the area of each tile, that is the product of the dimensions because it is a rectangle,
[tex]A_{\text{tile}}=16in\cdot16in=256in^2[/tex]To compare it to the floor's area, we have to transform it into square feet. Knowing that 1 ft² = 144 in²,
[tex]256in^2\cdot\frac{1ft^2}{144in^2}=\frac{16}{9}ft^2[/tex]This is a partial result, so it is best if we leave it as a fraction so we don't miss any decimals.
Now, the area of the floor is 350 ft². To find how many tiles Greg has to order, we have to divide the area of the floor by the area of each tile,
[tex]\#tiles=\frac{A_{\text{floor}}}{A_{\text{tile}}}=\frac{350ft^2}{\frac{16}{9}ft^2}=196.875[/tex]But the number of tiles has to be an integer. If Greg buys 197 tiles they will have to cut some (waste). If he buys 196 there will be some of the floor not covered. However we were asked to assume no waste, so Greg will have to order 196 tiles.
(part 2)
To answer this question we have to add 8% to the cost of the tile. The 8% of 1.75 is,
[tex]1.75\cdot\frac{8}{100}=0.14[/tex]So the cost of each tile is,
[tex]1.75+0.14=1.89[/tex]How many apple pies did they sell and how many blueberry pies did they sell?
Let the number of apple pies x
Let the number of blue pies y
Since they sold 38 pies on Saturday, then
Add x and y, then equate the sum by 38
[tex]x+y=38\rightarrow(1)[/tex]Since they sold each apple pie for $11 and each blueberry pie for $13
Since they collected $460 on Saturday, then
Multiply x by 11 and y by 13, then add the products and equate the sum by 460
[tex]11x+13y=460\rightarrow(2)[/tex]Now, we have a system of equations to solve it
Multiply equation (1) by -13 to equate the coefficients of y in values and opposite them in signs to eliminate them
[tex]\begin{gathered} (-13)(x)+(-13)(y)=(-13)(38) \\ -13x-13y=-494\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3)
[tex]\begin{gathered} (11x-13x)+(13y-13y)=(460-494) \\ -2x+0=-34 \\ -2x=-34 \end{gathered}[/tex]Divide both sides by -2
[tex]\begin{gathered} \frac{-2x}{-2}=\frac{-34}{-2} \\ x=17 \end{gathered}[/tex]Substitute the value of x in equation (1) to find y
[tex]17+y=38[/tex]Subtract 17 from both sides
[tex]\begin{gathered} 17-17+y=38-17 \\ y=21 \end{gathered}[/tex]The y sold 17 apple pies and 21 blueberry pies
The answer is the last choice
Sonia has $725,000 she wants to save. If the FDIC insurance limit per depositor, per bank, is $250,000, which of these ways of distributing her money between three banks will guarantee that all her money is insured?
$220,000 in Bank A, $230,000 in Bank B, $275,000 in Bank C
$220,000 in Bank A, $250,000 in Bank B, $255,000 in Bank C
$240,000 in Bank A, $230,000 in Bank B, $255,000 in Bank C
$240,000 in Bank A,, $245,000 in Bank B 245,000 in Bank c
As per the dividing method, there are 3 ways of distributing her money between three banks.
Dividing method:
Division is the process of repeated subtraction.
This method, we start from the number called dividend in the number line and keep subtracting the number called divisor till we reach at 0 that is called remainder, and the number of steps we go on backward counting is the quotient or result of division.
Given,
Sonia has $725,000 she wants to save.
FDIC insurance limit per depositor, per bank, is $250,000
So, here we need to find the ways of distributing her money between three banks will guarantee that all her money is insured.
We know that, he limit is $250,000.
So, we have to divide the total amount within these limit across three bank.
Therefore, the possible ways of dividing the amount is given below:
Way 1:
if $250,000 deposited in bank A,
$250,000 deposited in bank B and
remaining money $175,000 will be deposited in bank C.
Way 2:
if $200,000 deposited in bank A,
$250,000 deposited in bank B,
$225,000 deposited in bank C.
Way 3:
If $225,000 deposited in bank A,
$225,000 deposited in bank B,
and $ 225,000 in bank C.
To know more about Dividing method here.
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Use synthetic division to find the quotient and remainder when2x^3+ 9x^2- 8x+ 4 is divided by x - 2
Solution:
Given;
[tex]\frac{2x^3+9x^2-8x+4}{x-2}[/tex]Using Synthetic division;
Thus, the solution is;
[tex]\frac{2x^{3}+9x^{2}-8x+4}{x-2}=2x^2+13x+18+\frac{40}{x-2}[/tex]The quotient is;
[tex]2x^2+13x+18[/tex]The remainder is;
[tex]18[/tex][tex]( - 2 \div 5) \leqslant (x + 4) \div 3 \ \textless \ x + 5[/tex]solve the inequalities
We will solve this problem first, by solving the inequality in the left hand side and next the inequality on the right hand side.
In the left hand side, we have
[tex]-\frac{2}{5}\le\frac{x+4}{3}[/tex]If we move 3 to the left hand side, we obtain
[tex]-\frac{2}{5}\cdot3\le x+4[/tex]which is equal to
[tex]-\frac{6}{5}\le x+4[/tex]Now, if we move 4 to the left hand side as -4, we have
[tex]\begin{gathered} -\frac{6}{5}-4\le x \\ -\frac{6}{5}-\frac{20}{5}\le x \\ \frac{-6-20}{5}\le x \\ -\frac{26}{5}\le x \end{gathered}[/tex]Now, in the right hand side, we have
[tex]\frac{x+4}{3}and if we move 3 to the right hand side, we obtain[tex]x+4<3(x+5)[/tex]we must note that, since 3 is positive, it doesnt flipt the inequality sign. Then, we obtain
[tex]x+4<3x+15[/tex]Now, if we move x to the right hand side we have
[tex]\begin{gathered} 4<3x-x+15 \\ 4<2x+15 \end{gathered}[/tex]and finally, we have
[tex]\begin{gathered} 4-15<2x \\ -11<2x \\ \frac{-11}{2}In summary, we have the following conditions:[tex]-\frac{26}{5}\le x[/tex]and
[tex]\frac{-11}{2}and we must choose one of them. We can see that
[tex]\begin{gathered} -\frac{11}{2}<-\frac{26}{5} \\ \text{because} \\ -5.5<-5.2 \end{gathered}[/tex]Therefore, the answer which fulfil both conditions is
[tex]-\frac{26}{5}\le x[/tex]what is the slope of (12 -18) (-15 -18)
Answer:
m = 0
Step-by-step explanation:
[tex]m=\frac{-18-(-18)}{-15-12)} \\m=\frac{0}{-27} \\m= 0/-27 = 0\\m=0[/tex]
A study of consumer smoking habits includes 177 people in the 18-22 age bracket ( 48 of whom smoke), 146 people in the 23-30 age bracket ( 31 of whom smoke), and 81 people in the 31-40 age bracket ( 28 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 18-22 or does not smoke.A. 0.319B. 0.854C. 0.173D. 0.729
From the question,
Age 18 - 22 has 177 people, 48 of whom smoke.
Age 23-30 has 146 people, 31 of whom smoke.
Age 31-40 has 81 people, 28 of whom smoke.
People who do not smoke = (177- 48)+(146-31)+(81-28) = 129 + 115 +53 = 297 people.
People within age 18-22 who do not smoke = 129
Total number of events = 404
[tex]\begin{gathered} p(18-22\text{ or does not smoke) = }\frac{(177+297-129)}{404} \\ p(18-22\text{ or does not smoke)}=\frac{345}{404}=0.853960396 \\ p(18-22\text{ or does not smoke)}\approx0.854 \end{gathered}[/tex]Hence, option B is the answer.
Solve the equation by identifying the quadratic form. Use a substitute variable(t) and find all real solutions by factoring. Type your answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. When typing exponents do not use spaces and use the carrot key ^ (press shift and 6). For example, x cubed can be typed as x^3.x^{10}-2x^5+1=0Step 1. Identify the quadratic formLet t= Answer. We now have:t^2-2t+1=0Step 2. FactorFactor this and solve for t to get t=Answer Step 3. Solve for xWe have solved for t now we need to use this value for t to help us solve for x. Revisit step 1 to remind you of the relationship between t and x. Type your real solutions (no extraneous) from smallest to largest.x= Answer
Given:
[tex]x^{10}-2x^5+1=0[/tex]Step 1: To identify the quadratic form of the given equation.
[tex]\begin{gathered} x^{10}-2x^5+1=0 \\ (x^5)^2-2x^5+1=0 \\ \text{Put x}^5=t,\text{ it gives} \\ t^2-2t+1=0 \end{gathered}[/tex]So, t = x²
Step 2: Factor the quadratic equation in step 1.
[tex]\begin{gathered} t^2-2t+1=0 \\ t^2-t-t+1=0 \\ t(t-1)-t(t-1)=0 \\ (t-1)(t-1)=0 \end{gathered}[/tex]Thus, the factors of the equation is
[tex](t-1)(t-1)=0[/tex]Step3: solve for x.
[tex]\begin{gathered} (t-1)(t-1)=0 \\ (x^5-1)(x^5-1)=0 \\ \Rightarrow x^5-1=0,x^5-1=0 \\ \Rightarrow x=1 \end{gathered}[/tex]Answer: x = 1
What is the area of this trapezoid? Enter your answer in the box. ft2
Given the figure, we can deduce the following information:
Upper base = 15 ft
Lower base = 37 ft
Height = 18 ft
To determine the area of a trapezoid, we use the formula:
[tex]A=\frac{a+b}{2}h[/tex]where:
A=Area
a=upper base
b=lower base
h=height
We plug in what we know:
[tex]\begin{gathered} A=\frac{a+b}{2}h \\ =\frac{15+37}{2}(18) \\ \text{Simplify} \\ A=\frac{52}{2}(18) \\ =\frac{936}{2} \\ A=468ft^2 \end{gathered}[/tex]Therefore, the area of the trapezoid is 468 ft^2.
Garvin earned $ 948.35 in net pay for working 24 hours. He paid $ 348.26 in federal and state taxes, and $ 145.06 in FICA taxes. What is Garrett's hourly wage? Round your answer to two decimal places. If answer doesn't have two decimal places include zeros to make two decimal places. For the units, use a word not a symbol. Be sure to attach your work to this question in order to receive credit for your answer.Your Answer:units:
ANSWER:
18.96 dollars per hour
STEP-BY-STEP EXPLANATION:
The 24-hour salary is calculated with the earnings and we subtract the taxes, as follows:
[tex]\begin{gathered} s=948.35-348.26-145.06 \\ s=455.03 \end{gathered}[/tex]Now, we divide by 24 to find out Garvin's hourly wage:
[tex]\begin{gathered} h=\frac{455.03}{24} \\ h=18.96 \end{gathered}[/tex]Therefore, the hourly wage is $18.96.
Given f(x)=6(1-x), what is the value of:a) f(-8)_____b) f(x) = -30 _____c) f(x) = 30____d) f(30)_____
Answer:
a) f(-8) = 54
b) f(x) = -30, x = 6
c) f(x) = 30, x = -4
d) f(30) = -174
Explanation:
Given the function:
f(x) = 6(1 - x)
To find f(-8), we replace x by -8 in the equation and then solve
f(-8) = 6[1 - (-8)8]
= 6(1 + 8)
= 6(9)
= 54
For f(x) = -30, we replace f(x) by -30 and solve for x
-30 = 6(1 - x)
Divide both sides by 6
1 - x = -30/6 = -5
Subtract 1 from both sides
-x = -6
Multiply both sides by -1
x = 6
For f(x) = 30, we replace f(x) by 30 and solve for x
30 = 6(1 - x)
Divide both sides by 6
1 - x = 30/6 = 5
Subtract 1 from both sides
-x = 4
Multiply both sides by -1
x = -4
f(30) = 6(1 - 30)
= 6(-29)
= -174
if 1ml = 0.00011 then 9ml= _____
if 1ml = 0.00011 then 9ml=
Apply proportion
0.00011/1=x/9
solve for x
x=9*0.00011
x=0.00099
answer is
0.00099Are the answers to question six part a b c and d correct?
- 32 + 2Determine for each 2-value whether it is in the domain of f or not.In domainNot in domain203
f(x) = x-3 / x+2
To be in the domain, we have to avoid 0 on the bottom of the fraction.
So, the bottom of the fraction is x+2.
x=-2
(-2)+2= 0
-2 is not in the domain
x= 0
(0)+2= 2
0 is in the domain
x=2
(2)+2=4
Solve 7x-2y = 17 for y
hello
the question here is an equation and we are asked to solve for y
we'll follow some steps here
[tex]7x-2y=17[/tex]step 1
take y to the left side of the equation and bring 17 to the right hand side of the equation
note: the sign changes once they cross equality sign
[tex]\begin{gathered} 7x-2y=17 \\ 7x-17=2y \end{gathered}[/tex]step 2
divide both sides by the coeffiecient of y which is 2
[tex]\begin{gathered} 2y=7x-17 \\ \frac{2y}{2}=\frac{7x-17}{2} \\ y=\frac{7x-17}{2} \end{gathered}[/tex]from the calculations above, the value of y = (7x - 17)/2
there are 66 utensils in the cafeteria. 22 of them are spoons and the rest are Forks. what is the ratio of the number of spoons to the total number of utensils?And what is the ratio of the number of forks to the number of spoons?
Let's begin by listing out the information given to us:
Total utensils = 66
Spoons = 22
Forks = 66 - 22 = 44
The ratio of spoons to the total utensil is given by the ratio of spoons to total utensils. We have:
22:66 ⇒ 1:3
Therefore, the ratio of spoons to total utensils is 1 spoon is to 3 utensils
The ratio of the number of forks to spoon is given by the ratio of forks to spoon. We have:
44:22 ⇒ 2:1
Therefore, the ratio of forks to spoon is 2 to 1. For every 2 forks, there is 1 spoon
Question 2 (7 points)Match the fractions and decimals to the corrects percentage.
we can change a fraction to a percentage multiplying the fraction by 100
also, we can change a decimal number to a percentage multiplying by 100
for example
1. 1/5
[tex]\frac{1}{5}\cdot100=20[/tex]In this case, 1/5 represent 20%
4. .625
[tex]0.625\cdot100=62.5[/tex]In this case, 0.625 represent 62.5%
If we do the same process to all the next numbers we will obtain the next solutions.
1. 1/5 ------ a. 20%
2. 8/10 ------ f. 80%
3. 0.08 ------ d. 8%
4. .625 ---- g. 62.5%
5. 32/100 ---- b. 32%
6. 1/2 ------ c. 50%
7. 1.25 ---- e. 125%
A farmer is planning on picking 1,000 bell peppers on the first day of the harvest. After picking the first 600, he finds that 70 percent of them are green and 30 percent of them are red. How many of the remaining peppers must he pick must be red in order for exactly half of the total number of peppers picked to be red?
Answer:
320 red bell peppers
Step-by-step explanation:
First, let's calculate how many green and red bell peppers the farmer harvest in the first time:
Green peppers: 600*70/100 = 420
Red peppers: 600*30/100 = 180
If the farmer wants that half (50%) of the pepper harvest are red:
The total number of red peppers harvest have to be:
100*50/100 = 500
For this reason, the amount of remaining red peppers that have to be harvest are:
500 - 180 = 320
Answer: The farmer has to harvest more 320 red bell peppers
Nick skates 2 1/8 miles in 1/2 of an hour. What is Nick's average speed, in miles per hour ?
Average speed = distance / time
From the question;
distance = 2 1/8 miles = 17/8 miles
time = 1/2
substitute the values into the formula;
[tex]\text{Average sp}eed\text{ =}\frac{\frac{17}{8}}{\frac{1}{2}}[/tex][tex]=\frac{17}{8}\times\frac{2}{1}[/tex][tex]=\frac{17}{4}[/tex][tex]=4\frac{1}{4}\text{ miles per hour}[/tex]If 260 is decreased by 65%, what is the new amount?
To find the new amount, substract the percent of the original amount to the original amount, this way:
[tex]260-0.65\cdot260=91[/tex]The new amount is 91.
WILL MARK BEST ANSWER BRAINLIEST
The system of conics has two solutions.
(x−1)2+(y+4)2=25(x−1)225+(y+4)2100=1
What are the solutions to this system of conics?
Enter your answer by filling in the boxes.
Answer:
(2,0) and (-2,0)
Step-by-step explanation:
pls mark me Brainliest
Answer: (-4,-4) (6,-4)
Step-by-step explanation:
I took the test and it said these were the corrects answers.
The sides of an L-shaped figure meet all the right angles
ANSWER:
24 ft²
STEP-BY-STEP EXPLANATION:
To determine the area of the figure, we must divide the L-shaped figure into two rectangles just like this:
We calculate the area of each rectangle and the sum of both areas would be the area of the L-shaped figure, in the following way:
[tex]\begin{gathered} A_1=L\cdot W=6\cdot2=12\text{ ft}^2 \\ \\ A_2=L\cdot W=3\cdot4=12\text{ ft}^2 \\ \\ \text{ Therefore:} \\ \\ A_t=A_1+A_2=12+12 \\ \\ A_t=24\text{ ft}^2 \end{gathered}[/tex]The area of the L-shaped figure is equal to 24 ft².
For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chumpkin hide
Let x and y be the number of holes dug by the chipmunk and the squirrel, respectively.
Therefore, the number of hidden acorns by each animal is given by the equations below
[tex]\begin{gathered} a_{chipmunk}=3x \\ a_{squirrel}=4y \end{gathered}[/tex]On the other hand, since the squirrel needed 4 fewer holes, and the number of hidden acorns is the same
[tex]\begin{gathered} y=x-4 \\ and \\ a_{chipmunk}=a_{squirrel} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow3x=4y \\ \Rightarrow3x=4(x-4) \\ \Rightarrow3x=4x-16 \\ \Rightarrow x=16 \end{gathered}[/tex]Hence,
[tex]\Rightarrow16*3=48[/tex]The chipmunk hid 48 acorns.How do you write 6 tens + 4 ones + 5 tenths + 2 hundredths + 8 thousandths
Answer:64.528 is the decimal
Step-by-step explanation:
how much is 2 gallons in quarts
how much is 2 gallons in quarts
Answer:
8 quarts
–8.38 as a mixed number.
Answer:
4 3/4
Step-by-step explanation:
This is matching:#1 If solving a problem with population growth compounding CONTINUOUSLY, which of the following formulas would you use?#2 If solving a problem with population growth compounding ANNUALLY, which of the following formulas would you use?#3 If solving a problem with population growth compounding QUARTERLY, which of the following formulas would you use?#4 If solving a problem with continuously compounding interest, which of the following formulas would you use?A: A(t)=P(1+r÷n)^ntB: A(t)=Pe^rtC: P(t)=P0(1+r)^tD: P(t)=P0^e^rt
#1
The formula for continuous compounding is:
[tex]A(t)=P_{}e^{r\cdot t}[/tex]#2
Since the population grows compounding annually, we have that:
[tex]P(t)=P_0(1+r)^t[/tex]#3
For a problem with population growth compounding quarterly, we have to divide the rate between n=4, therefore:
[tex]A(t)=P(1+\frac{r}{n})^{n\cdot t^{}}[/tex]#4
Finally, for continuously compounded interest we have the formula:
[tex]P(t)=P_0e^{r\cdot t}[/tex]How do i dilate a scale factor by 2?
The dilated figure is larger than the original figure if the dilation factor is greater than 1 and the dilated figure becomes smaller than the origial figure if the dilation factor is less than 1.
Since, the dilation factor is 2, the dilated image is larger than the original figure two times.
For the coordinate (x,y) in original figure, the coordiante in the dilated figure will be (2x,2y).