Hello!
a. 48 ? (-8) = (-6) - divisionTo solve this exercise, let's think from right to left:
What operation between (-6) and (-8) results in 48?
When we do (-6) * (-8) we obtain 48, right?
As we are doing it in reverse, the opposite operation will be division, look:
48 ÷ (-8) = -6
b. (-40) ? 8 = (-5) - divisionLet's solve it in a similar way: what operation between (-5) and 8 results in 40?
(-5) * 8 = -40
So, (-40) divided by 8 = (-5)
c. 12 ? (-2) = 14 - subtractionThis will be a bit different:
Notice that the difference between these numbers is the middle number. So, let's try another operation now:
12 - (-2) = 14
Attention here: the - sign will invert the value of what is inside the parentheses.
d. 18 ? (-12) = 6 - additionThis is a addition, look:
18 + (-12) = 6
18 - 12 = 6
e. 18 ? (-20) = -2 - additionHere we have another addition between these numbers:
18 + (-20) = -2
18 - 20 = -2
f. 22 ? (-0.5) = -11 - multiplicationHere, (-0.5) is the same as (-1/2).
When we multiply something by 1/2, the result is half.
So:
22 * (-0.5) = 11
9. A zoo has two water tanks that are leaking. One tank contains 100 gal of water and is leaking at a constant rate of 4 gal/h. The second tank contains 60 gal of water and is leaking at a constant rate of 2 gal/h. When will the tanks have the same amount of water?
we can write an equation for each statement
One tank contains 100 gal of water and is leaking at a constant rate of 4 gal/h
[tex]y=100-4h[/tex]
where y are the total gallons and H the hours elapsed
he second tank contains 60 gal of water and is leaking at a constant rate of 2 gal/h.
[tex]y=60-2h[/tex]
where y are the total gallons and H the hours elapsed
When will the tanks have the same amount of water?
we must replace one equation in the other to find the time that its measure is equal,so
[tex]100-4h=60-2h[/tex]now solve h
[tex]\begin{gathered} 100-60=4h-2h \\ 40=2h \\ \frac{40}{2}=h \\ \\ h=20 \end{gathered}[/tex]the two tanks will have the same volume when 20 hours have passed
which of the following sets of numbers could not represent the the sides of a right triangle?{57, 76, 94}{39, 52, 65}{54, 72, 90}{9, 40, 41}
Answer:
{57, 76, 94}
Explanation:
For the set of numbers to represent the the sides of a right triangle, the square of the longest side must be equal to the sum of the square of other two sides
For the first option:
{57, 76, 94}
Longest side = 94
Square of the longest side = 94^2 = 8836
Sum of the square of other two sides = 57^2 + 76^2
Sum of the square of other two sides = 9025
Since both values are bot equal hence teh set of number {57, 76, 94} does not represent the sides of a right triangle.
CoursesStandard Normal DistributionCatalog and Study ToolsRental OptionsMasoStandard Devletion 10College Success TipsCareer Success Tips0 Help5000-500001 Give Feedback-2.0-1.00:00.00001.02.0P(Z > 2.00)P(Z > -1.00) =p(Z < 0.50) =p(z < 1.75) -Grade It NowSave & ContinueContinue without saving
From z table:
For P(Z > 2.00)
[tex]P(Z>2.00)=1-P(Z<2.00)=1-0.9772=0.0228[/tex]Answer: 0.0228
For P(Z > -1.00)
[tex]P(Z>-1.00)=1-P(Z<-1.00)=1-\text{0}.1587=0.8413[/tex]Answer: 0.8413
For p(Z < 0.50)
[tex]P(Z<0.50)=0.6915[/tex]Answer: 0.6915
For p(z < 1.75)
[tex]P(Z<1.75)=0.9599[/tex]Answer: 0.9599
Solve for x and y:x – 3y = -83x + 2y = 31Select one:a. (-11,-1)b.(11,-1)c. (5,8)d. (7,5)
We have two unknowns (x and y) and 2 equations.
We will clear one unknown in the first equation and then replace it in the second.
Then, we can solve for the other variable and solve backwards.
The first equation is:
[tex]\begin{gathered} x-3y=-8 \\ x=3y-8 \end{gathered}[/tex]We replace the value of x in the second equation:
[tex]\begin{gathered} 3x+2y=31 \\ 3(3y-8)+2y=31 \\ 9y-24+2y=31 \\ 11y=31+24 \\ 11y=55 \\ y=\frac{55}{11} \\ y=5 \end{gathered}[/tex]Then, with y=5, we can calculate the value of x:
[tex]x=3y-8=3\cdot5-8=15-8=7[/tex]The solution (x,y) is (7,5). The answer is Option D.
sara is packing for a trip. she has 16 pairs of shoes. if she has room to pack 5 pairs, how many ways can she choose which shoes to take
It i given that n = 16, which is the total number of shoes and r = 5.
The number of ways she can choose which shoes to take is determined by combination.
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]Substitute the values,
[tex]^{16}C_5=\frac{16!}{5!11!}=\frac{16\times15\times14\times13\times12\times11!}{5\times4\times3\times2\times1\times11!}[/tex]Hence the answer is 4368. The number of ways she
Write an equation in slope intercept form of a line passing through the given point and perpendicular to the given line(0, -6);3x-2y=5
Answer:
y = -2 /3 x - 6
Explanation:
Here we remind ourselves that if we have an equation of the form
[tex]y=mx+b[/tex]then the equation of a line perpendicular to the above line is
[tex]y=-\frac{1}{m}x+c[/tex]where c is the y-intercept.
Now for our case, the equation we have is
[tex]3x-2y=5[/tex]which isn't helpful since we cannot use it to find the equation of the perpendicular line.
Therefore, to make it useful, we first convert it to the slope-intercept form: y = mx + b.
Now, subtracting 3x from both sides gives
[tex]3x-2y-3x=5-3x[/tex][tex]-2y=5-3x[/tex]dividing both sides by -2 gives
[tex]\frac{-2y}{-2}=\frac{5-3x}{-2}[/tex][tex]y=\frac{3}{2}x-5[/tex]Now that our equation is in slope-intercept form, we can find the equation for the perpendicular line.
The equation of the line that is prependicular to the above line is
[tex]y=-\frac{1}{3/2}x+b[/tex][tex]y=-\frac{2}{3}x+b[/tex]Now, we are told that this line must pass through (0, -6). Therefore, we have to find a value of b such that the above line passes through (0, -6). To find b, we put x = 0 and y = -6 into the above equation to get
[tex]-6=-\frac{2}{3}(0)+b[/tex][tex]-6=b\text{.}[/tex]The value of b is -6.
Therefore, the equation of a line perpendicular to 3x - 2y = 5 line passing through (0, -6) is
[tex]\boxed{y=-\frac{2}{3}x-6.}[/tex]Which of the following is the graph of the quadratic function y=x+4x-12?-20-20A.20-20-20B.20C.-6D.
Given
The quadratic function,
[tex]y=x^2+4x-12[/tex]To find;
The graph representing the above function.
Explanation:
It is given that,
[tex]y=x^2+4x-12[/tex]That implies,
[tex]y=x^2+4x-12[/tex]Can you help me please I just paid 100 dollar for the tutor version and I can’t find one tutor
The Solution.
Given the function below:
[tex]f(x)=\frac{1}{x+9}\text{ and the interval \lbrack{}10,10+h\rbrack}[/tex]The average rate of change in the given interval is
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]In this case,
[tex]a=10,b=10+h[/tex]So,
[tex]f(a)=f(10)=\frac{1}{10+9}=\frac{1}{19}[/tex][tex]f(b)=f(10+h)=\frac{1}{10+h+9}=\frac{1}{19+h}[/tex]Substituting in the formula, we have
[tex]\text{Average rate of change =}\frac{\frac{1}{19+h}-\frac{1}{19}}{10+h-10}[/tex][tex]\begin{gathered} \text{Average rate of change =}\frac{\frac{19-(19+h)}{19(19+h)}}{h}=\frac{-h}{19h(19+h)}=\frac{-1}{19(19+h)} \\ \end{gathered}[/tex]So, the correct answer is
[tex]\frac{-1}{19(19+h)}[/tex]8What is the slope of the line that passes through the points (-2, 5) and (3, 4) in the standard (x,y) plane?
Answer
Slope = -(1/5) = -0.20
Explanation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (-2, 5) and (3, 4)
[tex]\text{Slope = }\frac{4-5}{3-(-2)}=\frac{-1}{3+2}=\frac{-1}{5}[/tex]Hope this Helps!!!
x+4y=4 I know how to solve it. But how. how do you plot it on a graph?
In order to plot it, we start by solving for y:
[tex]\Rightarrow4y=4-x\Rightarrow y=1-\frac{x}{4}[/tex]After this we simply replace values for x and we will get values for y inordered pairs, the
Can someone walk me through this? I know it’s familiar but I can’t recall how to do it.
18 dimes and 6 quarters
1) Let's recall that 1 dime = $0.10 and a quarter is $0.25
2) We can solve this by writing a Linear System of Equations:
[tex]\begin{gathered} x+y=24 \\ 0.1x+0.25y=3.3 \end{gathered}[/tex]Note that the second equation relates the quantities in dollars, 330 cents is the same as $3.30.
2.2) So now let's solve it using the Elimination Method multiplying one of those equations by -0.1:
[tex]\begin{gathered} 0.1x+0.25y=3.3 \\ -0.1x-0.1y=-2.4 \\ ---------------- \\ 0.15y=0.9 \end{gathered}[/tex]Let's divide both sides by 0.15:
[tex]\begin{gathered} \frac{0.15y}{0.15}=\frac{0.9}{0.15} \\ y=6 \end{gathered}[/tex]So we have 6 coins of quarters, now let's plug into the original equation x+y=24 to get the number of dimes:
[tex]\begin{gathered} x+6=24 \\ x+6-6=24-6 \\ x=18 \end{gathered}[/tex]3) Hence, there are 18 dimes and 6 quarters
For an unknown parent function f(x), write a function g(x) that is:-vertically stretched by a factor of 2,- shifted up 5 units, and - shifted right 4 units. Explain how your function accomplishes these transformations.
Given the parent function to be:
[tex]f(x)[/tex]Write the function g(x), when the parent function is
1. vertically stretched by a factor of 2 - Multiply the parent function by 2
[tex]g(x)=2f(x)[/tex]2. Shifted up 5 units - Add 5 units outside of the parent function
[tex]g(x)=2f(x)+5[/tex]3. Shifted right 4 units - Subtract 4 from within the parent function
[tex]g(x)=2f(x-4)+5[/tex]Therefore, the transformation of the parent function f(x) to g(x) is
[tex]g(x)=2f(x-4)+5[/tex]Which inequality represents the graph? -20 -15 -10 -5 0 5 10 5 10 15 20
EXPLANATION:
We can see in the graph that the value of -15 appears on the negative axis,
What we observe in the graph is that a closed circle is used, that means that the inequality is "less than or equal to" q
[tex]\begin{gathered} ANSWER\colon \\ q\leq-15 \end{gathered}[/tex]solve the following equation for f .
f = 3U/2
Explanation:[tex]U\text{ = }\frac{2}{3}f[/tex]cross multiply:
[tex]\begin{gathered} U\text{ = }\frac{2f}{3} \\ 3(U)\text{ = 2f} \end{gathered}[/tex]Divide both sides by 2:
[tex]\begin{gathered} \frac{3U\text{ }}{2}\text{= }\frac{\text{2f}}{2} \\ f\text{ = }\frac{3U\text{ }}{2} \end{gathered}[/tex]It’s two-parter question I would like the answer and how to solve
Answer:
x > 10 ; D
Step-by-step explanation:
2 One fluid ounce is approximately 30 milliliters. A water bottle holding 20 fluid ounces would holdmany milliliters (ml)?A 1.5 mLB 66.7 mlC 150 mLD 600 mL
answer:600mL
one fluid ounce holds 30mL
20 fluid ounces will hold 20*30ml
therefore, a water bottle will hold 600mL
The bird population of an island is declining at the rate of 2.2% per year the population was 3500 in the year 2016 which answer is the best prediction of the population in year 2022
ANSWER:
3063
STEP-BY-STEP EXPLANATION:
The first thing is to create an equation that models the situation with the data of the statement:
[tex]\begin{gathered} y=A\cdot(1-r)^x \\ \\ \text{ Where y is the best population prediction, A is the initial amount, r is the rate of decline, and x is the elapsed time.} \\ \\ \text{ We replacing:} \\ \\ y=3500(1-2.2\%)^x \\ \\ y=3500(1-0.022)^x=3500(0.978)^x \end{gathered}[/tex]We evaluate when x = 6, since the time elapsed between 2016 - 2022 is 6 years and we would be left with the following:
[tex]\begin{gathered} y=3500\cdot\left(0.978\right)^6 \\ \\ y=3062.676\approx3063 \end{gathered}[/tex]The best prediction of the population in the year 2022 is 3063
1,898,130,000,000,000,000,000,000,000 in scientific notation (round to two digts after the decimal
in scientific notation is
[tex]1.89\times10^{27}[/tex]Which of the following is a trinomial with a constant term? A. 4x5 + 2x - 2x2 B. 5x2 - 4 + x C. x2 - 6 D. -3 + 4x4
Step 1: What is a trinomial expression?
A trinomial is an algebraic expression composed of three terms and is normally of the form
[tex]ax^2\text{ + bx + c}[/tex]Where c is the constant term
A constant term is a term without x
Step 2:
From the options, it only options A and B that are trinomial.
[tex]Option\text{ B has a constant term }-4,\text{ because it is also a trinomial}[/tex]Step 3:
Final answer
[tex]\begin{gathered} Option\text{ B} \\ 5x^2\text{ - 4 + x} \end{gathered}[/tex]3/5t+ 7 = -8 What is t
The equation to solve is:
[tex]\frac{3}{5t}+7=-8[/tex]We take "7" to the right hand side:
[tex]\begin{gathered} \frac{3}{5t}+7=-8 \\ \frac{3}{5t}=-8-7 \\ \frac{3}{5t}=-15 \end{gathered}[/tex]Now, we cross multiply:
[tex]\begin{gathered} 3=5t\times-15 \\ 3=-75t \end{gathered}[/tex]Now we divide by -75 to solve for t:
[tex]\begin{gathered} 3=-75t \\ t=-\frac{3}{75} \end{gathered}[/tex]Assume lines that look tangent, are tangent.Find the value of x.(The ones that are crossed out don’t need answered)
Take into account that for secant and tangent lines related to circles, use the following formula:
x = 1/2·(larger arc - smaller arc)
Then, you have, for the first circle:
larger arc = 360° - 124° = 236°
smaller arc = 124°
x = 1/2·(236° - 124°)
x = 1/2·(112°)
x = 56°
For the second circle, the value of x is the same that the given arc:
x = 124°
For the fourth circle:
larger arc = 171°
smaler arc = 67°
x = 1/2·(171° - 67°)
x = 1/2·(104°)
x = 52°
For the fifth circle:
x = 1/2·(101° + 39°)
x = 70°
P varies jointly with Q and R,and P=6 when Q=3 and R=12.Find P Q=4 and R=16
Answer:
10.67
Explanation:
We're told that P varies jointly as Q and R, this can be represented as shown below;
[tex]\begin{gathered} P\propto QR \\ P=\text{kQR} \end{gathered}[/tex]where k = constant of proportionality
Given P = 6, Q = 3 and R = 12, let's go ahead and solve for k;
[tex]k=\frac{P}{QR}=\frac{6}{3\times12}=\frac{6}{36}=\frac{1}{6}[/tex]Knowing k = 1/6, let's solve for P when Q = 4 and R = 16;
[tex]P=\frac{1}{6}\times4\times16=\frac{64}{6}=10.67[/tex]Use the sum-to-product identities to rewrite the following expression as a product.sin(x) – sin(3x)
Given:
[tex]\sin x-\sin 3x[/tex]Sol:.
Formula of sin3A is:
[tex]\sin 3A=3\sin A-4\sin ^3A[/tex]Put the value of sin3x in given function:
[tex]\begin{gathered} =\sin x-\sin 3x \\ =\sin x-(3\sin x-4\sin ^3x) \\ =\sin x-3\sin x+4\sin ^3x \\ =-2\sin x+4\sin ^3x \\ =2\sin x(2\sin ^2x-1) \end{gathered}[/tex]Evaluate the factorial expression.10!/7!
To evaluate the expression we need to remember that:
[tex]n!=n(n-1)![/tex]Then we have:
[tex]\frac{10!}{7!}=\frac{10\cdot9!}{7!}=\frac{10\cdot9\cdot8!}{7!}=\frac{10\cdot9\cdot8\cdot7!}{7!}=10\cdot9\cdot8=720[/tex]Therefore:
[tex]\frac{10!}{7!}=720[/tex]The exact area of a circle is 2106.811 square miles.What is the radius?1mi
Answer:
[tex]r=26\text{ miles}[/tex]Step-by-step explanation:
The area of a circle is represented by the following equation:
[tex]\begin{gathered} A_o=\pi\cdot r^2 \\ \end{gathered}[/tex]If the exact area is 2106.811, plug it into the equation and solve for r(radius);
[tex]\begin{gathered} 2106.811=\pi\cdot r^2 \\ r=\sqrt[]{\frac{2106.811}{\pi}} \\ r=25.89 \\ \text{ Rounding:} \\ r=26\text{ miles} \end{gathered}[/tex]The rocket is at ground level at ( ) seconds and ( ) seconds.
Given the equation:
[tex]h=-16t^2+48t[/tex]Where (h) represents the height of the rocket, and (t) is the time
We will find when the rocket will be at the ground level
The ground will be at the ground level when (h=0), which means the x-intercepts of the given graph
As shown: the graph has two points of x-intercepts
The points are (0, 0) and (3, 0)
So, the answer will be:
The rocket is at ground level at ( 0 ) seconds and ( 3 ) seconds.
Find a formula for the nth termof the arithmetic sequence.First term -17Common difference 5an=[? ]n +Enter
The nth term of a sequence is given by the formula:
[tex]T_n_{}=a+(n-1)d[/tex]Where
[tex]\begin{gathered} T_n=\text{nth term} \\ a=\text{ first term} \\ n=\text{ number of terms} \\ d=\text{ common difference} \end{gathered}[/tex]From the question given
We are told that the first term is -17
the common difference is 5
We will simply substitute these values into the formula
[tex]T_n=-17+(n-1)\times5[/tex]Simplifying
we will have
[tex]\begin{gathered} T_n=-17+5n-5 \\ T_n=5n-17-5 \end{gathered}[/tex]Simplifying further, we will have
[tex]T_n=5n-22[/tex]So If we compare the answer above with what is required in the question, we will have
[tex]a_n=5n-22[/tex]Therefore we will have
Can you help me figure out the answer for 135 and -65?
135
For letter S, we have
x/3 + 10 = 55
Subtracting 10 from both sides of the equation, we have
x/3 + 10 - 10 = 55 - 10
x/3 = 45
x = 45 * 3
x = 135
Therefore,
Solve for x2x - 7 = -3x + 18
Given the following equation:
[tex]2x-7=-3x+18[/tex]You can solve it as follows:
1. Apply the Addition Property of Equality by adding this term to both sides of the equation:
[tex]3x[/tex]Then:
[tex]\begin{gathered} 2x-7+(3x)=-3x+18+(3x) \\ 5x-7=18 \end{gathered}[/tex]2. Apply the same property. Add 7 to both sides of the equation:
[tex]\begin{gathered} 5x-7+(7)=18+(7) \\ 5x=25 \end{gathered}[/tex]3. Finally, you can apply the Division Property of Equality by dividing both sides of the equation by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{25}{5} \\ \\ x=5 \end{gathered}[/tex]Therefore, the answer is:
[tex]x=5[/tex]If oats cost $0.02is the cost of theoats if thecontainer is full?
Given the cost of an oats = $0.02