Answers
The numeric value of f(a) + f(h) for f(x) = x² - 5x + 3 is given as follows:
A. f(a) + f(h) = a² + h² - 5a - 5h + 6.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is defined as follows:
f(x) = x² - 5x + 3.
Hence the numeric values are given as follows:
f(a) = a² - 5a + 3.f(h) = h² - 5h + 3.The only like term is the 3 for both expressions, hence the addition is given as follows:
f(a) + f(h) = a² + h² - 5a - 5h + 6.
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Related Questions
Write the equation of the line that has slope 3 and passes through the point
(-2,5).
Answers
y=mx +c
where m is the slope, c is a constant, and x and y are variables,
we know the slope is 3 so m=3
rewriting it
y=3x +c
to find c we substitute values x=-2 and y=3 into the equation y=3x +c
so
3= 3(-2) + c
c=9
thus, y=3x+ 9
Explanation:
y = kx+m is the equation of a line. The coefficient of x is the slope i.e 3. So we know that a part of the equation is y = 3x + m.
How to find M?
Well, we already have a point on the equation. Meaning we already have an x and a y. -2 = x and 5 = y.
The equation then becomes 5 = (3 x -2) + m.
Solve for m and the answer will be m = 11.
Now we have both m and K meaning that the whole equation is solved and it’s y = 3x + 11
How many shipments had at least 10 broken tiles but less than 20 broken tiles ?
Answers
Answer:
5 shipments had at least 10 broken tiles but less than 20 broken tiles.
The triangle above has the following measures.
a=8m
b=8 squared 3m
Use the 30-60-90 Triangle Theorem to find the length of the hypotenuse. Include correct units.
Show all your work.
Answers
The value of m∠Q as shown in the right-angled triangle is 54.718°.
The Formula used is:
m∠Q = cos⁻¹(s/r)........................ (1)
Where:
a = 8 m
b = 8√3 m
Now, Substitute these values into equation 1
m∠Q = cos⁻¹(8/8√3)
m∠Q = cos⁻¹(1/√3)
m∠Q = 54.718.
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At the toy store, 3 toy cars cost $2.46. How much does it cost to buy 25 toy cars?
Answers
Step-by-step explanation:
it says "college" in the headline of this question.
are you serious ?
this is an upper elementary or beginning of middle school problem.
if you have a problem with such a question in college, you really have a problem and would need intensive tutoring (you need to recover everything from the beginning of math).
in such problems, to find your way, always try to find the amount represented by 1 unit.
everything else can be then calculated in relation to that one unit.
3 cars cost $2.46
1 car costs therefore 1/3 of that :
2.46/3 = $0.82
and 25 cars cost then 25 times that of a single car :
0.82 × 25 = $20.50
in short, the direct approach is
$2.46 × 25/3 = $20.50
The value of y varies directly with x.
If y = 102 then x = 17
Solve for y when x = 13
k = 6
y = ?
Remember y = kx
Answers
The value of y at the value of x = 13 is,
⇒ y = 78
We have to given that;
The value of y varies directly with x.
And, at y = 102 then x = 17
Since, The value of y varies directly with x.
Hence, We get;
⇒ y = kx
at y = 102 then x = 17;
⇒ 102 = k × 17
⇒ k = 102 / 17
⇒ k = 6
Hence, Equation is,
⇒ y = 6x
Plug x = 13;
⇒ y = 6 × 13
⇒ y = 78
Thus, The value of y at the value of x = 13 is,
⇒ y = 78
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what 2 values can f have if f² is 16
Answers
Answer:
4 and -4
Step-by-step explanation:
4²=16
-4²=1
The two values that f could be if f² is 16 are +4 and -4 because both the positive and negative square roots are considered in solving the equation f² = 16.
Explanation:The solution to the equation f² = 16 is found by taking the square root of both sides. However, when we take the square root in solving an equation, we need to consider both the positive and negative roots. The square root of 16 is +4 and -4. These are the two possible solutions for f in the equation f² = 16.
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HELPPPPPPPPPSOZLSLALALLZ
Answers
Among the given options, the measure that cannot be the length of the third side of the triangle is 12 cm. The correct option is C 12 cm.
What is the length?Determining the length that cannot not be the measure of the third side of the triangle
From the question, we are to determine the length that cannot be the measure of the third side of the triangle
From the given information, Two sides of the triangle are 7 cm and 4 cm From one of the properties of a triangle, we know that the length of a side of triangle is greater than the difference of the two other sides and it is less than the sum of the two other sides.
Let the length of the third side of the triangle be x.
Therefore,
x < 7 cm + 4 cm
x < 11 cm and
x > 7 cm - 4 cm
x > 3 cm
Hence, the measure that cannot be the length of the third side is 12 cm.
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A box contains 2 red marbles, 5 green marbles and 8 blue marbles. Find the probability of the different events.
P ( 3 blue ) =
P (blue & green)
Answers
The value of the probability of the different events are,
The value of the probability P (3) is,
⇒ 1 / 5
And, The value of the probability P (blue & green) is,
⇒ 8/45
We have to given that;
A box contains 2 red marbles, 5 green marbles and 8 blue marbles.
Hence, Total marbles = 2 + 5 + 8 = 15
So, The value of the probability P (3) is,
⇒ 3 / 15
⇒ 1 / 5
And, The value of the probability P (blue & green) is,
⇒ 8/15 x 5/15
⇒ 8/15 x 1/3
⇒ 8 / 45
Thus, The value of the probability P (3) is,
⇒ 1 / 5
And, The value of the probability P (blue & green) is,
⇒ 8/45
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Help me please When writing a proof, how do you construct the first statement?
A) By writing the justification for the first statement in the right column.
B) By copying the “prove” statement(s) from the original problem.
C) By writing the next logical statement from the current one.
D) By copying the “given” statement(s) from the original problem.
Answers
The correct statement when writing a proof, how do you construct the first statement is,
⇒ By copying the “given” statement(s) from the original problem.
Since, We know that;
Evidence or argument establishing or helping to establish a fact or the truth of a statement.
Now, We just start any proof or derivation
By copying the “given” statement(s) from the original problem.
Thus, The correct statement when writing a proof, how do you construct the first statement is,
⇒ By copying the “given” statement(s) from the original problem.
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At a certain college, the mean math ACT score is a 21.8 with a standard deviation of 4.9. Assume that these scores have a normal distribution, what is the 30th percentile of math ACT scores at this college?
Answers
A math ACT score of 19.55 or lower corresponds to the 30th percentile of scores at this college.
To do this, we can use a standard normal distribution table or a calculator with a normal distribution function. The standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1.
By using a table or calculator, we can find the z-score that corresponds to the 30th percentile. The z-score represents the number of standard deviations away from the mean that a certain point is. Once we have the z-score, we can use it to find the actual math ACT score by using the formula:
actual score = mean + (z-score)(standard deviation)
If we use a standard normal distribution table, we can find that the z-score corresponding to the 30th percentile is -0.52. Therefore, the math ACT score that corresponds to the 30th percentile at this college is:
actual score = 21.8 + (-0.52)(4.9) = 19.55
In other words, 30% of the scores are below 19.55, and 70% of the scores are above 19.55.
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44. Dana attends a 90-minute dance class one day each week. Last week, she practiced
the following dances during class.
30 minutes on ballet
40 minutes on tap
20 minutes on jazz
Which display of data is most appropriate to show how Dana spent her practice
time in dance class last week?
A line plot
B circle graph
C
line graph
D tally chart
Answers
Answer:
B circle graph
Step-by-step explanation:
circle graph or pie chart is the best representation since bar chart is not present
Mast 1 broadcasts radio signals that can be heard within a radius of 15 km.
Mast 2 broadcasts radio signals that can be heard within a radius of 20 km.
Use ruler and compasses to work
out in which region radio signals can
be heard from both masts.
1 cm represents 10 km
The answer is region
Mast 1
71%
Mast 2
Answers
The intersection points are approximately (2.6, 1.29) and (2.6, -1.29).
How to explain the pointThe region where radio signals can be heard from both masts is the intersection of the two circles. We can find the intersection points by solving the system of equations:
(x - 1)² + y² = 1.5²
(x - 5)² + y² = 2²
Expanding the equations and subtracting them, we get:
10x - 26 = 0
So, x = 2.6. Substituting into either equation, we get:
y = ±✓(1.5² - (2.6 - 1)²) = ±1.29
The intersection points are approximately (2.6, 1.29) and (2.6, -1.29).
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Can u check my answer if its right
Answers
The correct option is c because the measure of the arc angle RE is 62° using the Angles of Intersecting Chords Theorem.
What is the Angles of Intersecting Chords Theorem
The Angles of Intersecting Chords Theorem states that the angle formed by the intersection of the chords is equal to half the sum of the intercepted arcs, and conversely, that the measure of an intercepted arc is half the sum of the two angles that intercept it.
66° = (RE + ST)/2
66° = (RE + 70)/2
RE + 70 = 2 × 66 {cross multiplication}
RE + 70 = 132
RE = 132 -70 {collect like terms}
RE = 62°
Therefore, the measures of the arc angle RE is 62° using the Angles of Intersecting Chords Theorem
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I suck at word problems can i get some help with this one
Answers
Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week. The function to keep track of his exercise is f(x) = 7x + 15. What do the f(x) and x represent in Luke's situation? (2 points)
Group of answer choices
f(x) represents the total number of hours; x represents the number of weeks he exercises this summer
f(x) represents the total number of weeks that he has exercised; x represents the number of hours
f(x) represents the number of hours he exercises per day; x represents the number of weeks
f(x) represents the total number of hours that Luke has exercised; x represents the number of weeks he exercises per day
Answers
The function is solved and f(x) represents the total number of hours; x represents the number of weeks he exercises this summer
Given data ,
Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week.
So , the function is given by
The function to keep track of his exercise is f(x) = 7x + 15
On simplifying the equation , we get
f(x) represents the total number of hours; x represents the number of weeks he exercises this summer
Hence , the function is f(x) = 7x + 15
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Zaid holds up a bag of coins.
The bag contains only 5p and 20p coins.
The ratio of 5p to 20p coins is 2:1
Zaid says
"If all the 5p coins became 20p coins and all the 20p coins became 5p coins
the total value of the coins in the bag would increase by £6."
Work out how many coins are in the bag.
Answers
the number of 5p = 2x
and the number of 20p = x
the total value = y
(2x)*(.05) + (x)*(.20)= y .......eqa1
if all 5p became 20p
20p = 2x
5p = x
(x)*(.05) + (2x)*(.20)= y+6 ..... eqa2
subtract the equations
eq2 - eq 1
======================
0.05x + 0.4x =y+6
-
0.1x + 0.2x = y
======================
0.45x= y+6
-
0.3x =y
= 0.15x = 6
x = 40
so number of 5p = 80 coins
and number of 20p = 40 coins
URGENT PLEASE HELP ME
Answers
The values of x in the absolute value function 5 - 9|4 - 8x| = -103 are (b) {-1, 2}
Calculating the value of x in the absolute value functionFrom the question, we have the following parameters that can be used in our computation:
5 - 9|4 - 8x| = -103
Subtract 5 from both sides of the equation
so, we have the following representation
- 9|4 - 8x| = -108
Divide both sides by -9
|4 - 8x| = 12
Remove the absolute bracket
Thisgives
4 - 8x = 12 or 4 - 8x = -12
So, we have
-8x = 8 or -8x = -16
Divide
x = -1 or x = 2
Hence, the values of x are (b) {-1, 2}
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K
J
L
5
M
Given that the rectangle above has a perimeter of 34 units, find mZKLJ. Round the answer to the nearest hundredth.
A. 8.46°
B. 22.62⁰
C. 24.62°
D. 65.38°
Answers
The measure of angle ZKLJ is approximately is 24.62°. Option C is right choice.
To find the measure of angle ZKLJ in the given rectangle:
Since a rectangle has opposite sides equal in length, we can divide the perimeter of 34 units by 4 to find the length of each side:
34 units / 4 = 8.5 units
Now, consider triangle ZKL. We know that ZK = 8.5 units and KL = 5 units.
Using the Pythagorean theorem, we can calculate the length of ZL:
[tex]ZL^2[/tex] = [tex]ZK^2 + KL^2[/tex]
[tex]ZL^2[/tex] = [tex](8.5 \:units)^2 + (5 \:units)^2[/tex]
[tex]ZL^2[/tex] = 72.25 + 25
[tex]ZL^2[/tex] = 97.25
ZL ≈ 9.86 units
Now, let's calculate the tangent of angle ZKL:
tan(ZKL) = KL / ZL
tan(ZKL) = 5 units / 9.86 units
tan(ZKL) ≈ 0.507
Using the inverse tangent (arctan) function, we can find the measure of angle ZKLJ:
ZKLJ ≈ arctan(0.507)
ZKLJ ≈ 27.46°
Therefore, rounding to the nearest hundredth, the measure of angle ZKLJ is approximately 27.46°.
The closest option to this answer is option C: 24.62°.
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Question-
Given that the rectangle above has a perimeter of 34 units, find mZKLJ. Round the answer to the nearest hundredth.
A. 8.46°
B. 22.62⁰
C. 24.62°
D. 65.38°
what do 47%, 36%, and 100% average together as a percentage?
Answers
Answer:
(.47 + .36 + 1)/3 = 1.83/3 = .61 = 61%
PLEASE HELP! Using a ton of my points on this one. Thx :)
A new curved projection system for a small media room states the optimal viewing angle is
74° (m/ACB = 74°) when you sit 10 feet from the center of the TV (length of CD = 10 ft). The
depth of the curved screen is 2 feet (length of DE = 2 ft). Find the length of line segment AB, in feet, that corresponds to the width of the television. (Round your answer to the nearest foot)
Answers
Answer:
12 ft
Step-by-step explanation:
See image
32° 7 Solve for c. CO 8 C C = [?] Round your your final answer to the nearest tenth. Law of Cosines: c² = a² + b² - 2ab-cosC
Answers
[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ c = \sqrt{7^2+8^2~-~2(7)(8)\cos(32^o)} \implies c = \sqrt{ 113 - 112 \cos(32^o) } \\\\\\ c \approx \sqrt{ 113 - (94.9814) } \implies c \approx \sqrt{ 18.0186 } \implies c \approx 4.2[/tex]
Make sure your calculator is in Degree mode.
The total number of hours each student spends volunteering in their
community is shown in the stem-and-leaf plot.
Hours Volunteered
Stem Leaf
1012479
2122578
303336
4 112
Which statement is supported by the data in the stem-and-leaf plot?
OA. The number of students who volunteered more than 30 hours is
greater than the number of students who volunteered fewer than
30 hours.
Answers
The most common number of hours volunteered is 22.
Option B is the correct answer.
We have,
A.
The number of students who volunteered more than 30 hours is greater than the number of students who volunteered fewer than 30 hours.
This can not be determined from the given stem-and-leaf plot as it only shows the frequency distribution of hours volunteered without any specific count of students.
The plot only indicates that there are some students who volunteered between 31-36 hours (stem 3, leaves 33, and 36) and one student who volunteered for 44 hours (stem 4, leaf 4).
Therefore, option A is not supported by the given data.
B.
The most common number of hours volunteered is 22.
From the stem-and-leaf plot, we can see that the mode is 22 as it has the highest frequency (stem 2, leaves 2, 5, 7, 8).
Hence, option B is supported by the given data.
C.
The number of students who volunteered between 9 and 20 hours is greater than the number of students who volunteered more than 40 hours.
This statement cannot be confirmed by the given stem-and-leaf plot as there are no leaves in stem 1, which means there are no students who volunteered less than 10 hours. Also, there are no leaves in stem 4, except for one leaf with a value of 44.
Therefore, we can not determine how many students volunteered between 9-20 hours and more than 40 hours. Hence, option C is not supported by the given data.
D.
The most common number of hours volunteered is 41.
There are no leaves in stem 4 except for the value of 44, which means there is no student who volunteered for 41 hours.
Hence, option D is not supported by the given data.
Therefore,
The most common number of hours volunteered is 22.
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what is the volume of this rectangular prism
Answers
Answer:
[tex] \frac{3}{5} \times \frac{4}{3} \times 3 = \frac{3}{5} \times 4 = \frac{12}{5} = 2 \frac{2}{5} [/tex]
The volume of this rectangular prism is
2 2/5 cm^3.
PLEASE HELP!
What is the value of the expression below?
A. 0.69
B. -5.76
C. -5.81
D. -5.96
Answers
Answer:
c.-5.81
Step-by-step explanation:
=-13/4 -2.56
=-581/100
=-5.81
If Sally invested $45,000 in an account that pays 11.9% interest, compounded continuously:
How much would be available after 10 years?
How much after 25 years?
How long will it take to double in value?
Answers
Answer: To solve this problem, we can use the formula for continuous compound interest:
A = Pe^(rt)
Step-by-step explanation:
A = Pe^(rt)
where A is the amount of money in the account after t years, P is the principal amount (initial investment), e is the mathematical constant (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years.
For Sally's investment:
P = $45,000
r = 0.119 (11.9% as a decimal)
a) After 10 years:
t = 10
A = 45000e^(0.119 x 10) = $158,086.34
Therefore, after 10 years, Sally would have approximately $158,086.34 in the account.
b) After 25 years:
t = 25
A = 45000e^(0.119 x 25) = $989,988.27
Therefore, after 25 years, Sally would have approximately $989,988.27 in the account.
c) To find how long it takes to double in value:
We can use the formula:
2P = Pe^(rt)
Simplifying this equation:
2 = e^(rt)
ln(2) = rt
t = ln(2)/r
Using the values of P and r from above:
t = ln(2)/0.119 = 5.81 years (rounded to two decimal places)
Therefore, it would take approximately 5.81 years for Sally's investment to double in value.
Step-by-step explanation:
The formula for continuously compounding interest is P(at the time t) = P(original) * [tex]e^{rt}[tex]
P(t) = value at time t
P(o)= original principal (amt invested)
r = nominal annual interest rate
t = length of time the interest is applied
r is expressed as a decimal, so 20% is 0.20, and in this example 11.9% would be 0.119.
After 10 years:
P(t) = 45,000 * e ^(0.119*10)
=$147,918.65
After 25 years:
P(t) = 45,000 * e ^(0.119*25)
= $881,533.05
To double in value, $45,000 x 2 = $90,000.
So the equation would be $90,000 = $45,000 * e^(0.119t)
Now solve for t.
90,000/45,000 = e^(0.119t)
2=e^(0.119t)
Take the log of both sides
log(2) = log(e^(0.119t))
The logarithm of a number raised to a power is the power times the logarithm of the number.
0.119t=log(2)/log(e)
0.119t= 0.693147
Now solve for t
t=5.82
You can go back to the original formula to check:
=45000*e^(0.119*5.82)
=90,000
log(2)
anita has a cellphone contract that cost her R100 per month plus 0.85 per peak time sms and0.75 per off peak time sms if she send 45 sms during peak time and 150 sms during off peak time in month,what will her monthly bill come to
Answers
Answer:
250.75
Step-by-step explanation:
Peak time cost = 0.85 × 45 = 38.25
Off peak time cost = 0.75 × 150 = 112.5
Monthly payment = R100
Total monthly bill = 100+112.5+38.25 = R 250.75
what are natural numbers
Answers
Answer:
Natural numbers are a set of positive integers (whole numbers greater than zero) that are used for counting and ordering things. They are denoted by the symbol "N" and the set of natural numbers includes 1, 2, 3, 4, 5, 6, 7, 8, 9, and so on.
(Hi there, do you like stories? if so, go into my profile for my questions. Read the excerpt and give me feedback if you can)
Example: 1,2,3,4,5,6 etc.
Can someone please help me with this question
Answers
Answer:
( 4t + 15 ) / 20
Step-by-step explanation:
Let me show you the formula for this type of question,
[tex] \frac{a}{c} + \frac{b}{d} = \frac{ad + bc}{cd} [/tex]
So here for you,
[tex] \frac{t}{5} + \frac{3}{4} = \frac{ 4t+15 }{20} [/tex]
Ms. Patterson proposes to give her daughter Claire an allowance of $0.05 on the first day of her 14-day vacation, $0.10 on the second day, $0.20 on the third day, and so on. Find the allowance Claire would receive on the last day of her vacation.
Answers
The amount of allowance Claire would have on the 14th day is given by the geometric progression and a₁₄ = $ 409.60
Given data ,
The pattern in which the allowance is increasing is a geometric sequence with first term $0.05$ and common ratio $r=2$ since each term is twice the previous term.
The given GP has a common ratio of 2. We can find the 14th term using the formula:
aₙ = arⁿ⁻¹
Here, a1 = 0.05 and r = 2. Therefore,
a₁₄ = 0.05 * 2^(14-1)
a₁₄ = 0.05 * 2^13
a₁₄ = 0.05 * 8192
a₁₄ = 409.6
Hence , the 14th term of the given GP is $ 409.60
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Hoku is buying uniform shirts for her employees. She pays the shirt company the following prices:
• A one-time fee of $880 for the shirt design and the first 50 shirts
• $12 per shirt for every shirt over 50 shirts
To determine the cost of shirts, y, for any number of shirts, x, over 50, she wrote the equation y = 12(x - 50) + p.
What is the value of p in her equation?
Enter the value of p in the response box.
P =
Answers
It is given that Hoku is paying the shirt company $880 for shirt design and the first 50 Shirts. So, the fixed price will be $880 for 50 shirts.
Now, for over & above 50 shirts the cost is $12 per shirt.
Now, adding both the amounts to get the total cost of uniform shirts for company. So, the equation for total cost for buying more than 50 uniform shirts becomes y = 12(x-50)+880.
Comparing the above equation with the given equation, the value of p comes out to be 880.
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