we have
9(7 +5)
apply distributive property
9*(7)+9*(5)
63+45
combine like terms
108
7.If you raised $15 byday 2 and by day 7 youhad $75. What is therate of change?
We have the following:
the rate of change is equal to a slope, therefore we can calculate it as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{75-15}{7-2}=\frac{60}{5}=12[/tex]The rate of change is $12/day
Solve by graphing. If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initally. When will the amount left be 2 grams? Round to the nearest tenth of a day. Be sure to label your answer.
The exercise describes an exponential decay, you can express this using the general form:
[tex]y=ab^x[/tex]Where
a is the initial amount
b is the decay factor
x is the time intervals
y is the amount after x time intervals
The half-life of a substance indicates the time it takes for the amount to decrease by half.
If the initial amount is a=5 grams, the half-life indicates that after x=20 days, the amount will be
y= 5/2 = 2.5 grams.
You can replace these values on the formula above to obtain an expression where the decay factor will be the only unknown:
[tex]\begin{gathered} y=ab^x \\ 2.5=5b^{20} \end{gathered}[/tex]To solve for b, first, divide both sides of the equation by 5:
[tex]\begin{gathered} \frac{2.5}{5}=\frac{5b^{20}}{5} \\ 0.5=b^{20} \end{gathered}[/tex]Then apply the square root with index 20 to both sides of the equal sign no reach the value of b:
[tex]\begin{gathered} \sqrt[20]{0.5}=\sqrt[20]{b^{20}} \\ b=0.97 \end{gathered}[/tex]Now that you know the value of the decay factor, you can determine how much time it will take for the substance to decrease to 2grams.
The expression for the exponential decay in this case is:
[tex]y=5\cdot0.97^x[/tex]For y=2grams:
[tex]2=5\cdot0.97^x[/tex]Now, you have to solve the expression for x:
-Divide both sides by 5:
[tex]\begin{gathered} \frac{2}{5}=\frac{5\cdot0.97^x}{5} \\ 0.4=0.97^x \end{gathered}[/tex]-Apply the logarithm to both sides of the equal sign:
[tex]\begin{gathered} \log (0.4)=\log (0.97^x) \\ \log (0.4)=x\log (0.97) \end{gathered}[/tex]-Divide both sides by the logarithm of 0.97 to determine the value of x:
[tex]\begin{gathered} \frac{\log(0.4)}{\log(0.97)}=\frac{x\log (0.97)}{\log (0.97)} \\ x=30.08\approx30.1 \end{gathered}[/tex]It will take approximately 30.10 days to have 2 grams of substance left.
Can you help me with problem #1 I think I remember how to do it but just want to make sure
1)
[tex]3x-2y=-16[/tex]To convert this equation into slope-intercept form we have to isolate y. Subtracting 3x at both sides of the equation:
[tex]\begin{gathered} 3x-2y-3x=-16-3x \\ -2y=-3x-16 \end{gathered}[/tex]Dividing by -2 at both sides of the equation:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{-3x-16}{-2} \\ y=\frac{-3x}{-2}+\frac{-16}{-2} \\ y=\frac{3}{2}x+8 \end{gathered}[/tex]im on a bit of a time crunch so please go fast
Solution
[tex]undefined[/tex][tex]Slope=\frac{24-12}{4-2}=\frac{12}{2}=6[/tex]The final answer
[tex]6\text{ feets}[/tex]Solve for a.69a = = √ [?]Pythagorean Theorem: a2 + b² = c²a
1) In this problem, we need to find the leg "a". Note that in the Pythagorean Theorem the hypotenuse, the largest leg is opposed to the right angle.
2) So, we can write out the following:
[tex]\begin{gathered} 9^2=6^2+a^2 \\ 81=36+a^2 \\ 81-36=a^2 \\ a^2=45 \\ a=\sqrt{45} \end{gathered}[/tex]Note that we could simplify that, but since the question wants it all under the radical.
Would you be able to assist me in answering these questions ?
A direct variation is a relationship between 2 variables in which the changes are proportionate. The variables are related by a constant. This is also called a slope. Thus, the graph would always be a straight line. Therefore,
c) Direct variation models are always a type of linear models
a) The straight line always pass through the origin(0, 0)
b) A polynomial is an expression containing variables and coefficients. The variable can be in the form x^n where n can be any positive integer. This means that n can be 1,2,3,4.....If n is 1, the polynomial expression is linear. Thus, it can be a direct variation model. Therefore,
Direct variation models are sometimes a type of polynomial models
d) An exponential model is not linear. The form of a linear model is
y = ax
where a is the constant of pro
An exponential model is y = ab^x
The models are not the same. Thus,
Direct variation models are never a type of exponential model
what is the solution to the equation below? (round your answer to two decimal places.) 3•6^x= 15.57
Simplify the given expression as shown below
[tex]\begin{gathered} 3*6^x=15.57 \\ \Rightarrow6^x=\frac{15.57}{3}=5.19 \\ \Rightarrow xln(6)=ln(5.19) \end{gathered}[/tex][tex]\Rightarrow x=\frac{ln(5.19)}{ln(6)}\approx0.92[/tex]Thus, the answer is x=0.92, option D.QUESTIONS 13,14 I NEED HELP dont understand ssorry for the caps didnt mean to
Answer
• 13. vertical angles.
,• 14. corresponding angles
Explanation
Assuming r and s are parallel lines, and that the line u (marked with stars) is a transversal cutting r and s, then the angles formed (a, b, and c) acquire some special properties.
• 13
Regarding ∠a and ∠b are vertical angles, which means they have the same measure.
• 14
Regarding ∠a and ∠c they are corresponding angles, which means they have the same measure.
Astrid works in the oil and gas industry near Fort McMurray, Alberta. She earns $28.30/h and makes double time for hours worked beyond 40 each week. Calculate Astrid’s gross income for 45.25 hours worked last week.
We have that the first 40h are paid at $28.30 each hour, so this first 40h give $1132
[tex]28.30\cdot40=1132[/tex]Now the other 5.25 hours that are beyond 40h the last week are paid at the double of a normal hour this means are paid at $56.60 ($28.30 x 2). Now the 5.25h give 297.15
[tex]56.60\cdot5.25=297.15[/tex]So the total is $1429,15. The answer is $1429,15
Where are you most likely to build up enough static charge to receive a shock? O A. In a rain forest B. On a concrete sidewalk on a dry day O c. On a nylon carpet in a dry area O d. On a nylon carpet in a hotel by the beach
Where are you most likely to build up enough static charge to receive a shock?
The correct answer is option C on a nylon carpet in a dry area
Explanation:
As nylon is a good conductor of electricity, the static electricity accumulatedin the body does ntot flow to the ground. Also, when we touch a metal object directly connected to the ground, a difference in electric charges creates a static electric discharge.iAs a reult ,we receive a shock.
h(x) = x² – 5 – x; Find h(8)
hello
to solve this question, we simply need to substitute 8 as the value of x in the expression
[tex]\begin{gathered} h(x)=x^2-5-x \\ h(8)=8^2-5-8 \\ h(8)=64-5-8 \\ h(8)=51 \end{gathered}[/tex]from the calculation above, the value of h(8) is equal to 51
use the diagrams to answer the following questions Number 6
Explanation:
86 is the far arc and 18 is near intercepted arc
x = 1/2(far arc - near arc)
[tex]\begin{gathered} x\text{ = }\frac{1}{2}(86-18) \\ \text{ =34} \end{gathered}[/tex]Answer: x = 34
Which function's graph is shown below? ད་ལྟ་བ་དང་ o = A. Y = COS X O B. y = -cos x C. y = sin x OD. y = -sin
Given:
Consider the given graph in figure.
To find:
Select the correct option that shows the given function's graph.
Explanation:
Here, graph is in the form of,
[tex]y=acos(bx)[/tex]Where, a is amplitude and the period of a cosine function is the length of the shortest interval on the x axis over which the graph repeats.
[tex]\text{ period =}\frac{2\pi}{|b|}[/tex]Here, at x = 0, the y value is 1. so, the graph starts at (0, 1) which indicates the graph of
[tex]y=cosx[/tex]Consider the below graph:
So, the correct option is (A) y = cosx.
Final answer:
Hence, the required correct option is (A) y = cos
Can you help me solve the one with mrs Jones I want to know if I’m right
We know that
• 11 students own a cat.
,• 12 students own a dog.
,• 6 students own both a cat and a dog.
,• 3 students own neither.
First, let's draw a Venn diagram to visualize the problem.
First, we have to fund the total number of students inside the sets Cat and Dog. We need to subtract the number 6 once, otherwise, we'll count it twice.
[tex]11+12-6=17[/tex]Then, we include the students that own neither.
[tex]17+3=20_{}[/tex]Therefore, the total number of students is 20.Claire wants to determine how her math score, 690, on a standardized college entrance exam compares to her mother's score, 680, when she took the exam 20 years earlier. The year Claire took the exam, the mean math score was 510 with a standard deviation of 110 points. When Claire's mother took the exam, the mean math score was 490 with a standard deviation of 100 points. Who had the better relative performance? Claire did better because her Z-score is greater than her mother's. Claire's mother did better because her z-score is greater than Claire's. Claire did better because her z-score is closer to the mean than her mother's. Claire's mother did better because her z-score is closer to the mean than Claire's.
The z score tells us the number of standard deviations that a given value is from the mean. Recall, standard deviation tells us the spread of the values from the mean
For Claire, the mean score was 510 but she scored 690 which was higher than the mean score
The z score would be
(690 - 510)/110 = 1.63
For Claire's mother, the mean score was 490 but she scored 680 which was higher than the mean score
The z score would be
(680 - 490)/100 = 1.9
We can see that her mother had a higher z score. Compared to the average score, she had a better performance. Therefore, the correct option is
Claire's mother did better because her z-score is greater than Claire's.
Recall the perimeter of a figure is the distance around figure
To find the perimeter of the triangle you have to add the length of its sides:
[tex]\begin{gathered} P=a+b+c \\ P=\frac{4}{17}+\frac{5}{17}+\frac{8}{17} \\ P=\frac{4+5+8}{17} \\ P=\frac{17}{17} \\ P=1 \end{gathered}[/tex]The perimeter of the triangle is 1 inch
897 mL to liters ? L
We have to convert 897 mL to L.
We have to take into account the following equivalency between the two units:
[tex]1L=1000mL[/tex]If we write this as a unit factor, we have:
[tex]\frac{1L}{1000mL}=1[/tex]So we can use this factor to multiply the quantity and change the units without changing the actual measure:
[tex]897mL\cdot(\frac{1L}{1000mL})=\frac{897}{1000}L=0.897L[/tex]NOTE: this unit factors can be used to change multiple units in the same operation.
Answer: 0.897 liters
x^2+3x-6 Find the Discriminat and state how many solutions and type of zero
Solution
Discriminant
- The formula for the discriminant of a quadratic equation is:
[tex]\begin{gathered} \text{ Given,} \\ ax^2+bx+c \\ \\ \text{ The Discriminant is:} \\ D=b^2-4ac \end{gathered}[/tex]- Applying the formula, we have:
[tex]\begin{gathered} a=1,b=3,c=-6 \\ \\ \therefore D=3^2-4(1)(-6) \\ D=9+24 \\ D=33 \end{gathered}[/tex]- Discriminant is 33
How many solutions
- If the discriminant is > 0, then, the Quadratic equation has 2 solution.
- If the discriminant is = 0, then, the Quadratic equation has 1 solution
- If the discriminant is < 0, then, the Quadratic equation has no real solutions.
- The discriminant is 33 > 0, thus, the Quadratic equation has 2 solutions
Type of zero
- Since there are 2 solutions, then, it has real solutions
Final Answer
OPTION B
List all the possible rational roots, then find all the roots of the function
Take into account that for a polynomial function, the possible roots are given by the following quotient:
roots = p/q
where p is the constant of the function (and its factors) and q is the coefficient of the term with the greates degree (variable with greatest exponent) or its factors.
Then, based on the previous explanation, you have:
p = -9
q = 5
factors -9: -1, 1, -3, 3, -9, 9
factors 5: -1, 1, -5, 5
Hence, the possible factors are:
±1, ±3, ±9, ±1/5, ±3/5, ±9/5
and the roots:
roots = {i(√15)/5 , -i(√15)/5, √3, -√3}
The roots can be also obtained by using quadratic formula for x^2, and then, by applying square root to the result to obtain x.
pls help for brainliest
Answer:
9 nickels, 8 dimes
Step-by-step explanation:
Let n = number of nickels, and let
d = number of dimes.
n + d = 17--------->.05n + .05d = .85
.05n + .10d = 1.25---->.05n + .10d = 1.25
------------------------
.05d = .40
d = 8, n = 9
What is the distance between points (-8,5) and (7,-3)? (Hint. Use the distance formula)
SOLUTION:
We are to find the distance between points (-8,5) and (7,-3).
[tex]\begin{gathered} \sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \text{where x}_1=-8,x_2=7,y_1=5andy_2=-3_{} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{(7-(-8))^2+(-3-5)^2} \\ \\ \sqrt[]{(7+8)^2+(-8)^2} \\ \\ \sqrt[]{15^2_{}+(-8)^2} \\ \\ \sqrt[]{225+64} \\ \\ \sqrt[]{289} \\ 17\text{ units} \end{gathered}[/tex]CONCLUSION:
The distance between points (-8,5) and (7,-3) is 17 units.
Find the mean, median, and mode of the following data. If necessary, round to one more decimal place than the largest number of decimal placesgiven in the dataRate of Fatal Alcohol ImpairedCar Crashes per 100 MillionVehicle Miles of Travel0.29 0.45 0.69 0.53 0.600.37 0.59 0.43 0.61 0.300.54 0.43 0.70 0.40 0.760.38 0.72 0.43 0.60 0.73Copy DataPrevAnswer 2 PointsKeypadKeyboard ShortcutsSeparate multiple answers with commas, if necessary.Selecting a button will replace the entered answer value(s) with the button value. If the button is not selected, the entered answer is used.Mean:Median:Mode:O No mode
The mean of the given data set is 0.528, the median of the given data set is 0.535 and the mode of the given data set is 0.43.
The given data set is:
0.29, 0.45, 0.69, 0.53, 0.60, 0.37, 0.59, 0.43, 0.61, 0.30, 0.54, 0.43, 0.70, 0.40, 0.76, 0.38, 0.72, 0.43, 0.60, 0.73.
Arranging the given data set in ascending order:
0.29, 0.30, 0.37, 0.38, 0.40, 0.43, 0.43, 0.43, 0.45, 0.53, 0.54, 0.59, 0.60, 0.60, 0.61, 0.69, 0.70, 0.72, 0.73, 0.76.
The mean of the data is given by;
Mean = (Sum of the numbers)/(total numbers)
=(0.29 + 0.30 + 0.37 + 0.38 + 0.40 + 0.43 + 0.43 + 0.43 + 0.45 + 0.53 + 0.54 + 0.59 + 0.60 + 0.60 + 0.61 + 0.69 + 0.70 + 0.72 + 0.73 + 0.76) / 20
= 10.55 / 20
= 0.5275 ≈ 0.528
Median = (0.53 + 0.54) / 2
= 0.535
Mode = 0.43 (0.43 repeated most time)
Thus, the mean of the given data set is 0.528, the median of the given data set is 0.535 and the mode of the given data set is 0.43.
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A dog alte 5 feet away from its owner's 50-foot tall house. What equation could be used to find the angle of elevation? 60 8 tan = BO CON 60 bine BO 50 ban () = b
Answer:
The equation that could be used to find the angle of elevation is;
[tex]\tan \theta=\frac{50}{5}[/tex]Explanation:
Given that the dog sits 5 ft away from its owner's 50 ft tall house.
it can be represented with the drawing below;
Using Trigonometry;
Recall that;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]From the diagram;
opposite = 50 ft
adjacent = 5 ft
so, we have;
[tex]\tan \theta=\frac{50}{5}[/tex]Therefore, the equation that could be used to find the angle of elevation is;
[tex]\tan \theta=\frac{50}{5}[/tex]A flagpole 3m tall casts a shadow5m long at the same time a nearby hill casts a shadow62m long. How Tall is the hill.
Explanation:
We are given information about the height of a flagpole and its shadow, and we also have information about the shadow of a hill.
This information is represented in the following diagram:
Where the symbol '?' represents what we are trying to find:
How tall is the hill
We will call this h for reference:
Since these shadows are happening at the same time, the ratio between these values must be the same, this is to say that
3/5 must be equal to h/62:
[tex]\frac{3}{5}=\frac{h}{62}[/tex]From this equation, we solve to find h:
[tex]\begin{gathered} \frac{3}{5}\times62=h \\ \end{gathered}[/tex]Solving the operations the result is:
[tex]\begin{gathered} 0.6\times62=h \\ \downarrow \\ 37.2=h \end{gathered}[/tex]The hill is 37.2 m tall.
Answer:
37.2 m
Noah finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of the cutout squares used to make it. This is the graph Noah gets if he allows x to take on any value between -1 and 5.What is the approximate maximum volume for his box?
the real world domain would be 0 to 2.5, the maximum would be 15
On your own paper, solve the system of equations using substitution and identify the solution.4=16 +=2
Answer: (4,-2)
Explanation:
Given:
4x=16
x+y=2
We solve for x in 4x=16.
4x=16
Then, divide both sides by 4.
4x/4=16/4
Calculate
x=4
Substitute x=4 into x+y=2.
x+y=2
4+y=2
Simplify and rearrange
y=2-4
Calculate
y=-2
Therefore, x=4 and y=-2.
Me. Gray is going to save money until she can afford to buy a new television that cost $4,189 including tax. If she saves $60 each month
Given:
Ms. Gray wants to buy a new television that costs $4189.
She saves $60 each month.
To find the numbers of months will be required for her to save enough money to buy the television,
[tex]\frac{4189}{60}=69.8167\approx70[/tex]Verify,
[tex]\begin{gathered} \text{ \$ 60 for 70 months} \\ 60\times70=4200\text{ this is enough money to buy the television that costs \$4189} \end{gathered}[/tex]Answer: option J
At a local bakery, at a local bakery Ariel Bots for oatmeal cookies four $1.20 Mia bought 9 mil cookies for $2.70 Becky bought 12 oatmeal cookies for $3.60 Larry purchased 15 oatmeal cookies $4.5. Graph the data on the graph
EXPLANATION
Drawing given set data ni a graph, will give us:
As we can see in graph, this is a proportional relationship given by a straight line.
To find the missing length below, would you use Law of Sines or Law of Cosines?Find the missing length. There are 2 answers, Law of _____ and missing side length.
3,400 mL. 34 L I need help which one is bigger
Answer: 34L is bigger than 3400mL
Given data
3, 400 mL and 34L
Firstly, we need to convert mL to L for unit consistency
1000mL = 1L
3, 400Ml = xL
Cross multiply
1000 * x = 1 x 3400
1000x = 3400
Divide both sides by 1000
1000x / 1000 = 3400/ 1000
x = 3.4 L
Therefore, 3400mL = 3.4L
34L is bigger than 3400mL