Answer:
x = 13 and x = 1
Step-by-step explanation:
(x-7)² = 36
simplify left side of equation
x² - 14x + 49 = 36
Our object now is to get every thing on the left side of the equal sign so we can factor. To do this, we subtract 36 from both sides
x² - 14x + 13 = 0
we then factor the left side of the equation
( x - 1 ) ( x - 13 ) = 0
we then set factors equal to 0 and solve both factors for x
x - 1 = 0
add 1 to both sides
x = 1
x - 13 = 0
add 13 to both sides
x = 13
The values of x are x = 13 and x = 1
Translate and solve using proportions: What number is 30% of 60
Answer: 18
Step-by-step explanation:
The question is asked to know 30% of 60, we get
60 x 30% = 60 x 0.3 = 18
Answer:
18
Step-by-step explanation:
We know that 30% means 30/100
30/100 multiplied by 60
hence, the answer is 18
A store pays $85 for a picnic table and marks the price up by 25%. What is the new price
B. If the point are in line ( vertical) then it is not a functiom
Answer:
True.
Step-by-step explanation:
If a relation forms a vertical line, then that means a given input has multiple outputs. Because of this, it is not a function.
The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 17.6 and 23.6 lb
Step-by-step explanation:
mean of 20 lb and a standard deviation of 9. If 9 fish are randomly selected,
what is the probability that the mean weight will be between 17.6 and 23.6
Ib? Write your answer as a decimal rounded to 4 places
What is the nth term of each linear pattern?
a) 5.4, 8.4, 11.4, 14.4, 17.4...
b) 85, 80, 75, 70...
c) 38 1/2, 43 1/2, 48 1/2, 53 1/2, 58 1/2
3 bombas de agua llenan una piscina en 10 días trabajando 5 horas diarias.
Si hay 5 bombas de agua, ¿cuántos días demoran en llenar la misma piscina, si trabajan 8 horas diarias?
5 bombas deben trabajar durante 4 dias para llenar la piscina.
¿cuántos días demoran en llenar la misma piscina, si trabajan 8 horas diarias?Cada bomba trabaja a un rate (razon de trabajo) R.
Sabemos que 3 bombas, trabajando 5 horas diarias por 10 días (un total de 50 horas), llena una piscina, entonces:
(3R)*50 horas= 1 piscina.
R = (1 piscina)/(150 horas).
Es decir, una sola bomba tarda 150 horas en llenar una piscina.
En el caso de que 5 bombas trabajen, tenemos que para llenar una piscina tienen que trabajar un tiempo T.
5*((1 piscina)/(150 horas))*T = 1 piscina.
(1 piscina)/(30 horas)
Resolviendo para T, obtenemos:
T = 1 piscina*(30 horas)/(1 piscina) = 30 horas.
Y sabemos que trabajan 8 horas diarias, es decir, las bombas deben trabajar durante:
30/8 = 3.75 ≈ 4 días.
5 bombas deben trabajar durante 4 dias para llenar la piscina.
Sí quieres aprender más sobre razones de trabajo.
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convert 25 __ 200 fluid ounces
use the Measures of Capacity to help u if u need it
which is greater
steps must be given
Will give branliest
brantty works 21.5 hours every week . if she earns 8.50 per hour how much does she earn in one week round part a to the nearest dollar
Step-by-step explanation:
1 hour - $8.50
21.5 hours (one week) - $8.50 × 21.5 = $182.75
One week = $183
Factor the following expression. x^2+9x+8
Answer:
(x+1)(x+8)
Step-by-step explanation:
I just got multiples of 8 that when added equal to 9. In this case, it was 1 and 8 which when you multiply is 8 and when you add, it's 9.
Solve: 2x^2 -x >15 Show your work.
Answer:
x>3
Step-by-step explanation:
Work:
2x^2-x>15
Subtract 15 on both sides:
2x&2-x-15>0
Factor the left side of equation to cancel out the ^2.
(2x+5)(x−3)>0
2x+5=0 or x−3>0
Then to make it easier we will do the x-3>0 one, add 3 to both sides = x>3
Find the distance between points A(−1, 5) and B(0, 4) to the nearest tenth.
Answer:
1.4
Step-by-step explanation:
Use the distance formula
d= √(x2-x1)² +(y2-y1)² , where x1, x2, y1, y2 are the coordinates of the points
A(x1 = −1, y1 = 5) and B(x2 = 0, y2 = 4)
d= √(0 - -1 )² +(4 - 5)²
d= √(1)² +(-1)²
d= √2
d= 1.414213562, round to the nearest tenth
d≈ 1.4
HELP NO LINKS THOUGH!!!!!!!!
[tex] \sf \longmapsto1 \frac{1}{3 } \div 1\frac{3}{4} [/tex]
[tex]\sf \longmapsto \frac{4}{3} \div \frac{7}{4} [/tex]
[tex]\sf \longmapsto \frac{4}{3} \times \frac{4}{7} [/tex]
[tex]\sf \longmapsto \frac{4 \times 4}{3 \times 7} [/tex]
[tex]\sf \longmapsto \frac{16}{21} [/tex]
Therefore, the answer is :
[tex]\sf \frac{16}{21} [/tex]
Lara made the table below of the predicted values for h(t), the height, in meters, of a penny t seconds after it is dropped off of the back of the bleachers.
A 2-column table with 9 rows titled Height of Penny over Time. The first column is labeled t with entries 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8. The second column is labeled h(t) with entries 2, 1.951, 1.804, 1.559, 1.216, 0.775, 0.236, negative 0.401, negative 1.136.
To the nearest tenth of a second, how much time would it take the penny to hit the ground?
0.5 seconds
0.6 seconds
0.7 seconds
0.8 seconds
Answer:
Step-by-step explanation:
as the chart is broken into steps with the same precision we're looking for. Just choose the one where height is closest to zero or 0.6 s
To do it mathematically
The equation is
h = 2 - ½gt²
to find g, plug in a time and height
0.236 = 2 - ½g(0.6²)
g = 9.8 m/s
check another one just to be sure
1.559 = 2 - ½(9.8)0.3²
1.559 = 1.559
now plug in zero elevation with an unknown time
0 = 2 - ½(9.8)(t²)
-2 = - ½(9.8)(t²)
t² = 4/9.8
t = 0.6388765...
t = 0.6 s
The time it takes for the penny to hit the ground is about 0.6 seconds.
Option B is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
To determine the time it takes for the penny to hit the ground, we need to find the point where the height of the penny is equal to zero.
Looking at the table,
We can see that the height of the penny is negative when t = 0.7 and becomes more negative for larger values of t.
So the penny must hit the ground between t = 0.6 and t = 0.7 seconds.
Now,
We can use linear interpolation to estimate the time at which the height of the penny is zero by finding the equation of the line that passes through the two points closest to zero on the table, namely (0.6, 0.775) and (0.7, -0.401).
So,
The slope of the line passing through these points.
= (change in height) / (change in time)
= (-0.401 - 0.775) / (0.7 - 0.6)
= -1.176
The equation of the line passing through these points.
y - 0.775 = -1.176(x - 0.6)
Simplifying
y = -1.176x + 1.438
Setting y to zero and solving for x.
0 = -1.176x + 1.438
x = 1.438 / 1.176
x ≈ 1.22
Therefore,
To the nearest tenth of a second, the time it takes for the penny to hit the ground is about 0.6 seconds.
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This class is algebra
Answer:
y = -1/2
Step-by-step explanation:
(3x + 4y = 4)
+
(2x - 4y = 6)
______________
5x = 10
x = 2
plug in x for any of the two equations ....
2(2) - 4y = 6
4 - 4y = 6
-4y = 2
y = -1/2
Find the domain of the function
Answer:
Here you go :)
Step-by-step explanation:
Identify the domain and range of each relation. Is the relation a function?
x y
5 3
8 6
10 11
Answer:
No
Step-by-step explanation:
Considering domain and range of a function, we first have to create the function based off the given points.
So this would mean first having to find the slope of the equation, which would be using the slop/point formula of [tex]\frac{y_{1} -y_{2} }{x_{1} -x_{2} }[/tex]
Taking the first 2 points, it would make the equation as follows:
[tex]\frac{y_{1} -y_{2} }{x_{1} -x_{2} } = \frac{6-3}{8-5} = \frac{3}{3} = 1[/tex]
To be sure, we take the 2nd pair of points (point 2 and point 3) and make the equation with those as well.
[tex]\frac{y_{1} -y_{2} }{x_{1} -x_{2} } = \frac{11-6}{10-8} = \frac{5}{2} = 2.5[/tex]
Since these 2 slopes do not match, this set of relations cannot be a function, and therefore a domain/range cannot be found.
Please help! Thanks!: If a 95% confidence interval was being calculated using the following expression:
3.2 ± 1.96 ⋅ 1.1
What would be the margin of error for this confidence interval?
If you can please give an explanation on how to solve?
The confidence interval can be calculated from the margin of error, and vice versa,
The margin of error of the confidence interval is 2.156
The confidence interval is given as:
[tex]\mathbf{CI = 3.2 \pm 1.96 \cdot 1.1}[/tex]
The formula of confidence interval is:
[tex]\mathbf{CI = \bar x\pm E}[/tex]
Where E represents the margin of error.
So, by comparison:
[tex]\mathbf{E = 1.96 \cdot 1.1}[/tex]
Multiply
[tex]\mathbf{E = 2.156}[/tex]
Hence, the margin of error of the confidence interval is 2.156
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2/3 of a cup of batter can make 5/6 of a batch of pancakes. How many cups of water are needed to make one batch of pancakes?
Answer:
1 11/12 cups of water
Work out the area of this semicircle.
Take a to be 3. 142 and write down all of the digits given by your calculator.
11 cm
Answer:
Step-by-step explanation:
A = πr²/2 = 3.142(11²)/2 = 190.091 cm²
You may use a calculator for this item,
Zach, Kolby, and Peyton are investing a total of $360,000 to open a cottee shop Their investments are in the radio
1:2:0.5, respectively
How much has Zach invested, in dollars?
Enter your answer in the space provided
Based on the investment ratio and the amount invested, the amount that Zach invested is $102,857.14.
First thing to do is to add up the numbers in the ratio:
= 1 + 2 + 0.5
= 3.5
The amount that Zach invested is:
= Zach's ration/ Sum of ratio x Amount invested
= 1 / 3.5 x 360,000
= $102,857.14
In conclusion, Zach invested $102,857.14.
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Write a possible equation for a polynomial with zeros at -4, -5, 0, 1/3.
[tex]\begin{cases} x = -4\implies &x+4=0\\ x=-5\implies &x+5=0\\ x = 0\implies &x=0\\ x=\frac{1}{3}\implies &x -\frac{1}{3}=0\\ &3\left( x -\frac{1}{3} \right)=3(0)\\ &3x-1=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x+4)(x+5)(x)(3x-1)=\stackrel{\textit{original equation}}{0} \\\\\\ (x^2+9x+20)(x)(3x-1)=y\implies (x^3+9x^2+20x)(3x-1)=y \\\\\\ (3x^4+27x^3+60x^2)+(-x^3-9x^2-20x)=y[/tex]
[tex]3x^4+27x^3+60x^2-x^3-9x^2-20x=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 3x^4+26x^3+51x^2-20x=y~\hfill[/tex]
Factor this completely thank you
Answer:
4(2x raise to power 2-4-7x)
Shape l and ll are what?
Answer:
a trapezoid:ll and a dented triangle:l
Find the exact valueFind sin theta:/2
See picture. Show steps
Answer:
Step-by-step explanation:
Use the half angle formulas
sin(θ/2) = ±√((1 - cosθ)/2)
sin(θ/2) = ±√((1 - (3/5))/2)
sin(θ/2) = ±√((2/5)/2)
sin(θ/2) = ±√(1/5)
knowing θ is in the 4th quadrant, θ/2 will be in the second quadrant where sines are positive.
sin(θ/2) = +√(1/5) = √0.2
Howards baseball team won 7/10 of its game. Jeremys team won 2/5 of its game. They both played the same number of games. Whose team won more games, or did they win the same amount?
Answer:
Jeremy's team won more games
Step-by-step explanation:
Let's transform these fractions into ratios:
[tex]\frac{7}{10} =7:10\\\\\frac{2}{5} =7:10[/tex]
Then, simplify:
[tex]7:10[/tex] ≈ [tex]1:1.4[/tex]
[tex]2:5=1:2.5[/tex]
Finally, compare:
[tex]1:1.4\neq 1:2.5[/tex]
Result:
Jeremy's team won more games since [tex]1:2.5>1:1.4[/tex]
Note:
The way I simplify the ratios may be confusing so here is a quick explanation;
Make the smaller of the two numbers in the ratio into one then divide the larger number by the smaller number for the other part of the ratio
Example:
5:10
5 turns into 1
10 divided by 5 equals 2
Simplified Ratio: 1:2
Jeremy won more games than Howard.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Howard Team won = 7/10
Jeremy team won = 2/5
Now, taking LCM (5, 10)= 10
So, Jeremy team won = 2/5
= 4/10
So, Jeremy won more games than Howard.
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Jenny has five basketball to treat soccer balls what fraction of the balls are basketballs
Answer:
5/8
Step-by-step explanation:
there is 8 total and 5 of them are basketballs
Balamma
Model with Math How many things are
used to make a guitars like the ones in the
picture Draw a bar diagram to show how
you found your answer
Answer:
Where is the questions picture so I know what I am about to answer
Step-by-step explanation:
I need a pic.
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100100100 pieces of sushi in total.
Sofia had already ordered and paid for 242424 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 121212 pieces and costs \$8$8dollar sign, 8.
Let RRR represent the number of additional rolls that Sofia orders.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
12+24R \leq 10012+24R≤10012, plus, 24, R, is less than or equal to, 100
(Choice B, Checked)
B
12+24R \geq 10012+24R≥10012, plus, 24, R, is greater than or equal to, 100
(Choice C)
C
24+12R \leq 10024+12R≤10024, plus, 12, R, is less than or equal to, 100
(Choice D)
D
24+12R \geq 10024+12R≥10024, plus, 12, R, is greater than or equal to,
Inequalities are used to represent unequal expressions.
The inequality is [tex]24 + 8R \ge 100[/tex]
The given parameters are:
[tex]Paid = 24[/tex]
[tex]Rolls = 12[/tex]
[tex]Cost = 8[/tex] --- the unit cost per roll.
Assume the number of additional roll is R.
So, the total number of sushi is:
[tex]Total=Paid + Cost \times R[/tex]
This gives
[tex]Total=24 + 8\times R[/tex]
Multiply 8 and R
[tex]Total=24 + 8R[/tex]
The sushi needed is at least 100.
This implies that:
[tex]Total \ge 100[/tex]
So, we have:
[tex]24 + 8R \ge 100[/tex]
Hence, the inequality is [tex]24 + 8R \ge 100[/tex]
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A color printer prints 5 pages in 9 minutes.
How many minutes does it take per page?
PLS HELPPPPPP
Answer: 1.8
Step-by-step explanation: Divide 9/5
Alexander is a car salesman. He earns 7% in commission each week. Last week, he sold $164,000 worth of cars. How much did he make last week in commission?
Answer:
$11,480
Step-by-step explanation: