Answer:
15a) True 15b) False 15c) True
16)[tex]\frac{4*2}{5*2}=\frac{8}{25}=\frac{4*3}{5*3}=\frac{12}{15}[/tex]
[tex]\frac{5*2}{6*2}=\frac{10}{12}=\frac{5*3}{6*3}=\frac{15}{18}[/tex]
Step-by-step explanation:
*Rewriting the question with Retrieved missing information:
15. Mr. Clements painted his barn for hours in the morning. He painted his barn [tex]3\frac{3}{5}[/tex] hours in the morning. He painted the barn for [tex]5\frac{3}{4}[/tex] hours in the afternoon.Select True or False for each statement.
15a. A common denominator of the mixed numbers is 20.
15b. The amount of time spent painting in the morning can be rewritten as [tex]3\frac{15}{20}[/tex]
15c. Mr. Clements spent [tex]2\frac{3}{20}[/tex]
hours longer painting in the afternoon than the morning.
16. Tom exercised:
[tex]\frac{4}{5}[/tex]
hour on Monday and
[tex]\frac{5}{6}[/tex]
hour on Tuesday. Part A. Complete the calculations below to write equivalent fractions with a common denominator.
15a) True
Turning the Mixed Numbers into Improper ones:
He painted the his barn:
[tex]3\frac{3}{5}=\frac{18}{5}[/tex] Keep the denominator, and for the numerator multiply the denominator 5 by 3 and add 3 = 18. (In the morning).
[tex]5\frac{3}{4}=\frac{23}{4}[/tex] (In the afternoon)
The Prime factorization [tex]\frac{23}{4},\frac{18}{5}[/tex] help us to obtain the common denomination, i.e. 20
15b) False
This is a matter of simplification. In this mixed number, the fraction can be simplified this way:
[tex]3\frac{15}{20}=3\frac{15:5}{20:5}\Rightarrow 3\frac{3}{4}[/tex]
15c) True
Subtracting the working hours, knowing the common denominator by prime factorization is 20.
For Mixed Numbers:
[tex]5\frac{3}{4}-3\frac{3}{5}=5\frac{15}{20}-3\frac{12}{20}=2\frac{3}{20}[/tex]
For the same mixed numbers turned into improper fractions:
[tex]\frac{23}{4}-\frac{18}{5}=\frac{115-72}{20}=\frac{43}{20}[/tex]
Notice that:
[tex]2\frac{3}{20}==\frac{43}{20}=2.15[/tex]
16A
Equivalent fractions are fractions multiplied by a same constant, on the numerator and denominator:
[tex]\frac{4*2}{5*2}=\frac{8}{25}=\frac{4*3}{5*3}=\frac{12}{15}[/tex]
[tex]\frac{5*2}{6*2}=\frac{10}{12}=\frac{5*3}{6*3}=\frac{15}{18}[/tex]
15a is False as a common denominator isn't clear; 15b is False because the time in the morning is undefined; 15c is True assuming the morning was 3 hours. 16 needs further clarification.
15a ⇒False. To find the common denominator, we need to look at the fractions given. If there are fractions involved, more context is needed to validate this statement. Please provide relevant fractions.15b ⇒False. There is no concrete information given about the exact time spent in the morning to confirm this statement. If he spent 5 hours in the afternoon and the total time spent isn't specified, we cannot conclude the morning time is 3 hours.15c ⇒True. Since he painted for 5 hours in the afternoon, and we assume the morning time to be 3 hours (as per previous interpretations), Mr. Clements painted 2 hours longer in the afternoon (5 - 3 = 2).So, correct answer is 15a. False 15b. False 15c.True
PLEASE answer this I put the graph in the picture
amy and brittnay spent a total of $25 for lunch. Brittanys lunch cost $3 more than amy’s did. how much did amy spend for lunch?
Answer:
Amy spent $11 for lunch.
Step-by-step explanation:
x+y=25
x+(x+3)=25
2x+3=25
2x=25-3
2x=22
x=22/2
x=11
Answer:amy spent 11 dollars.
Step-by-step explanation:I did math
What number has to be added to each term of 2:5 to make the ratio 4:5?
Using [tex]a/b+c/b=(a+c)/b[/tex], we find that [tex]2/5+2/5=4/5[/tex].
Hope this helps.
What is 5 3/7 - 2 1/5?
Answer:
3 8/35 is the answer your welcome
A cooler contains fifteen bottles of sports drink: eight lemon-lime flavored and seven orange flavored
Answer:
Mutually exclusive,
[tex]P(\text{Lemon-lime or orange})=\frac{2}{3}[/tex]
Step-by-step explanation:
Please consider the complete question:
Determine if the scenario involves mutually exclusive or overlapping events. Then find the probability.
A cooler contains twelve bottles of sports drink: four lemon-lime flavored, four orange flavored, and four fruit-punch flavored. You randomly grab a bottle. It is a lemon-lime or an orange.
Let us find probability of finding one lemon lime drink.
[tex]P(\text{Lemon-lime})=\frac{\text{Number of lemon lime drinks}}{\text{Total drinks}}[/tex]
[tex]P(\text{Lemon-lime})=\frac{4}{12}[/tex]
[tex]P(\text{Lemon-lime})=\frac{1}{3}[/tex]
Let us find probability of finding one orange drink.
[tex]P(\text{Orange})=\frac{\text{Number of orange drinks}}{\text{Total drinks}}[/tex]
[tex]P(\text{Orange})=\frac{4}{12}[/tex]
[tex]P(\text{Orange})=\frac{1}{3}[/tex]
Since probability of choosing a lemon lime doesn't effect probability of choosing orange drink, therefore, both events are mutually exclusive.
We know that probability of two mutually exclusive events is equal to the sum of both probabilities.
[tex]P(\text{Lemon-lime or orange})=P(\text{Lemon-lime})+P(\text{Orange})[/tex]
[tex]P(\text{Lemon-lime or orange})=\frac{1}{3}+\frac{1}{3}[/tex]
[tex]P(\text{Lemon-lime or orange})=\frac{1+1}{3}[/tex]
[tex]P(\text{Lemon-lime or orange})=\frac{2}{3}[/tex]
Therefore, the probability of choosing a lemon lime or orange is [tex]\frac{2}{3}[/tex].
Please help me really quick pleasee
answer choices:
a)2
b)11
c)20
d)29
Answer:
C. [tex]x=20^{\circ}[/tex]
Step-by-step explanation:
Angle 6 and angle with measure 45° are vertical angles (opposite angles whan two lines intersect). By Vertical Angles Theorem, vertical angles are congruent, so
[tex]m\angle 6=45^{\circ}[/tex]
Angle 6 and angle with measure [tex]5x+35^{\circ}[/tex] are the same side interior angles when two parallel lines are cut by transversal. The same side interior angles add up to 180°, then
[tex]m\angle 6+5x+35^{\circ}=180^{\circ}\\ \\45^{\circ}+5x+35^{\circ}=180^{\circ}\\ \\5x=180^{\circ}-45^{\circ}-35^{\circ}\\ \\5x=100^{\circ}\\ \\x=20^{\circ}[/tex]
Sum1 help me in any of these
This seems confusing, like part of the question was cut off, but I'll try my best!
Answer: (For Part A)
I'm gonna assume that the $25.30 is the sum of all food and beverages.
So, if that's the case, the bill should be $27.32
Step-by-step explanation:
The meals tax is 8%, so all you have to do is multiply 25.30 (or 25.3) with 0.08 (8%) to get 2.024. Then you add 2.024 to the original number;
25.30 + 2.024 = 27.324
Finally you round to the nearest cent. So you get $27.32
However this might be incorrect because it looks like a part of the question is missing.
How to solve this?:
2x+2y=9
2x-y=3
Answer:
(2.5, 2 )
Step-by-step explanation:
Given the 2 equations
2x + 2y = 9 → (1)
2x - y = 3 → (2)
Rearrange (2) expressing y in terms of x
y = 2x - 3 → (3)
Substitute y = 2x - 3 into (1)
2x + 2(2x - 3) = 9 ← distribute left side and simplify
2x + 4x - 6 = 9
6x - 6 = 9 ( add 6 to both sides )
6x = 15 ( divide both sides by 6 )
x = 2.5
Substitute x = 2.5 into (3) for corresponding value of y
y = 2(2.5) - 3 = 5 - 3 = 2
Solution is (2.5, 2 )
Solve this using the elimination process.
They're already lined up so just solve!
2x + 2x = 4x
2y+ (-y) = 3y
9 + 3 = 12
4x + (-1y) = 12
Now solve.
4x + -1 x y = 12
4x - y = 12
4x = 12 + y
x = 12 + y / 4
First, when a problem is lined up with the same vales/terms, you can use the elimination process while doing math.
Then, make your equation by adding and subtracting the same terms.
Therefore, you finally get your answer.
Keep in mind not all answers will be a full number.
What is an equation of a line that passes through the points (8 , -3) (8 , 4)
Answer:
[tex]\displaystyle x = 8[/tex]
Step-by-step explanation:
Anything set to equal x is considered an undefined rate of change [slope], which is a vertical line. This is not a function, since it flunks the vertical line test.
I am joyous to assist you anytime.
please help me please
Write a ratio that is equivalent to 13:2, other than 13:2 itself
26:4
Hope this helps!
An equivalent ratio to 13:2 can be found by multiplying or dividing both terms of the ratio by the same number. For instance, when both terms are multiplied by 2, the equivalent ratio is 26:4 because the proportion remains unchanged.
Explanation:To find a ratio equivalent to 13:2, you need to multiply or divide both terms of the ratio by the same number. For example, if you multiply both terms of the ratio 13:2 by 2, you would get 26:4 which is an equivalent ratio. This is because the relationship or proportion between the two terms remains the same.
Here's the step-by-step calculation:
Multiply the first term of the ratio (13) by 2. That gives you 26.Multiply the second term of the ratio (2) by 2. That gives you 4.
So, the ratio that is equivalent to 13:2 is 26:4.
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HELP ASAP will give brainliest
A farmer is tracking the amount of wheat his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 75 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 5 to year 15.
The crop yield increased by 150 pounds per acre from year 5 to year 15.
The crop yield decreased by 15 pounds per acre from year 5 to year 15.
The crop yield decreased by 5 pounds per acre from year 5 to year 15.
The crop yield did not change from year 5 to year 15.
Average rate of change is 0
Interpretation: The crop yield did not change from year 5 to year 15
Solution:
The function that models the yield is:
[tex]f(x) = -x^2 + 20x + 75[/tex]
The average rate of change of f(x) from x = a to x = b is given by the formula:
[tex]\text{ average rate of change }=\frac{f(b)-f(a)}{b-a}[/tex]
Find and interpret the average rate of change from year 5 to year 15
[tex]f(5) = -(5)^2 + 20(5) + 75\\\\f(5) = -25 + 100 + 75\\\\f(5) = 150[/tex]
[tex]f(15) = - (15)^2 + 20(15) + 75\\\\f(15) = -225 + 300 + 75\\\\f(15) = 150[/tex]
Thus average rate of change:
[tex]\text {average rate of change}=\frac{f(15)-f(5)}{15-5}[/tex]
[tex]\text {average rate of change}=\frac{150-150}{10}=0[/tex]
Thus Average rate of change is 0
Interpretation: The crop yield did not change from year 5 to year 15.
Final answer:
The average rate of change in wheat yield from year 5 to year 15 is 0 pounds per acre per year, symbolizing that there was no change in the crop yield between these years.
Explanation:
To find the average rate of change of the wheat yield from year 5 to year 15, we will apply the function f(x) = −x² + 20x + 75 to these years and then calculate the rate of change. First, we'll find the yield for year 5 and year 15:
For year 5: f(5) = −(5)² + 20(5) + 75 = − 25 + 100 + 75 = 150For year 15: f(15) = −(15)² + 20(15) + 75 = − 225 + 300 + 75 = 150Next, we'll calculate the average rate of change using these yields:
Average rate of change = (f(15) - f(5)) / (15 - 5) = (150 - 150) / (10) = 0
Therefore, the crop yield did not change from year 5 to year 15. The function indicates that at both year 5 and year 15, the farmer's land yielded 150 pounds per acre, so the average rate of change in yield over this period is 0 pounds per acre per year.
A rhombus, COAL is centered at the origin. The longer diagonal is on the y-axis and has a
length of 27m. The shorter diagonal is on the x-axis and has a length of has diagonals with
length 19m. Determine the coordinates of the vertices.
Answer with Step-by-step explanation:
We are given that
COAL is a rhombus .
CA and LO are the diagonals of rhombus COAL.
CA=27 m
OL=19 m
We know that
Diagonals of rhombus are bisect to each other.
Let P(0,0) be the intersecting point of diagonals
Therefore, CP=PA
LP=PO
Length PO=[tex]\frac{1}{2}LO=\frac{19}{2}=9.5 m[/tex]
Length of CP=[tex]\frac{1}{2}PA=\farc{1}{2}(27)=13.5 m[/tex]
Let C([tex]0,y_2),O(x_1,0),A(0,y_1) \;and\;L(x_2,0)[/tex].
Distance formula:[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the formula
[tex]CP=\sqrt{(0-0)^2+(0-y_2)^2}=13.5[/tex]
[tex]\sqrt{y^2_2}=13.5[/tex]
[tex]y_2=\pm 13.5[/tex]
C(0,13.5) or (0,-13.5)
[tex]\sqrt{(y_2-y_1)^2}=27[/tex]
Substitute the value [tex]y_2=13.5[/tex]
[tex]\sqrt{13.5-y_1}=27[/tex]
[tex]13.5-y_1=\pm 27[/tex]
[tex]y_1=13.5-27=-13.5[/tex]
A(0,-13.5)
[tex]13.5-y_1=-27[/tex]
[tex]y_1=13.5+27=40.5[/tex]
A(0,40.5)
Substitute [tex]y_2=-13.5[/tex]
[tex]\sqrt{(-13.5-y_1)^2}=27[/tex]
[tex]-13.5-y_1=\pm 27[/tex]
[tex]-13.5-y_1=27[/tex]
[tex]y_1=-13.5-27=-40.5[/tex]
A(0,-40.5)
[tex]-13.5-y_1=-27[/tex]
[tex]y_1=-13.5+27=13.5[/tex]
A(0,13.5)
[tex]LP=\sqrt{(x_2-0)^2}=9.5[/tex]
[tex]\sqrt{x^2_2}=9.5[/tex]
[tex]x_2=\pm 9.5[/tex]
L(9.5,0) or L(-9.5,0)
[tex]\sqrt{x_2-x_1)^2}=19[/tex]
[tex](9.5-x_1)^2}=19[/tex]
[tex]9.5-x_1=\pm 19[/tex]
[tex]9.5-x_1=19[/tex]
[tex]x_1=9.5-19=-9.5[/tex]
[tex]9.5-x_1=-19[/tex]
[tex]x_1=9.5+19=28.5[/tex]
[tex](-9.5-x_1)=19[/tex]
[tex]-9.5-x_1=\pm 19[/tex]
[tex]-9.5-x_1=19[/tex]
[tex]x_1=-9.5-19=-28.5[/tex]
[tex]-9.5-x_1=-19[/tex]
[tex]-9.5+19=x_1[/tex]
[tex]x_1=9.5[/tex]
O(-9.5,0) or O(28.5,0) or (-28.5,0) or (9.5,0)
Caroline has 5 times as many paper clips as Trevon. After Trevon buys another 500 paper clips, he has 268 paper clips fewer than Caroline. How many paper clips does Trevon have now?
Trevon have 692 paper clips after buying 500 more clips.
Step-by-step explanation:
Let,
Paper clips Caroline have = x
Paper clips Trevon have = y
According to given statement;
x = 5y Eqn 1
After Trevon buys another 500 paper clips, he has 268 paper clips fewer than Caroline.
y + 500 = x - 268
y + 500 +268 = x
y + 768 = x Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]y+768 = 5y\\768=5y-y\\768 = 4y\\4y=768[/tex]
Dividing both sides by 4
[tex]\frac{4y}{4}=\frac{768}{4}\\y=192[/tex]
Number of paper clips Trevon has now = y+500 = 192+500 = 692
Trevon have 692 paper clips after buying 500 more clips.
Keywords: linear equation, substitution method
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To find out how many paper clips Trevon has now, we set up an algebraic equation and solve it to determine that Trevon originally had 192 paper clips. After buying an additional 500, he now has a total of 692 paper clips.
Explanation:The student's question involves solving a basic algebra word problem where Caroline has 5 times as many paper clips as Trevon. When Trevon buys another 500 paper clips, he has 268 paper clips fewer than Caroline. To solve this, we can set up the equation to find the original number of paper clips Trevon had:
Let T represent the number of paper clips Trevon originally had.Caroline has 5 times as many paper clips, so she has 5T.After Trevon buys 500 more, he has T + 500.At this point, Trevon has 268 fewer paper clips than Caroline, so 5T = T + 500 + 268.Solving this equation: 5T = T + 768.4T = 768T = 192So, Trevon originally had 192 paper clips. After buying another 500, Trevon now has 192 + 500 = 692 paper clips.
As a laboratory assistant, you measure chemicals using the metric system. For your current research, you need to measure out 45 grams of sodium chloride. The bottle you are using lists the amount in ounces. About how many ounces of sodium chloride will you need?
Answer:
There is 1.587 ounces of sodium chloride that he will need.
Since we have given that
Quantity of sodium chloride in grams = 45 grams
We need to find the number of ounces of sodium chloride.
As we know that
1 ounce = 28.35 gram
So, 1 gram =
So, 45 grams =
Hence, there is 1.587 ounces of sodium chloride that he will need.
Step-by-step explanation: Since we have given that
Quantity of sodium chloride in grams = 45 grams
We need to find the number of ounces of sodium chloride.
As we know that
1 ounce = 28.35 gram
So, 1 gram =
So, 45 grams =
Hence, there is 1.587 ounces of sodium chloride that he will need.
3.8 divided by 2 estimated
Answer:
Approx. 2
Step-by-step explanation:
round 3.8 to the nearest whole number, which is 4.
Divide 4 by 2.
3.8/2 is approx. 2.
(the exact answer would be 1.9)
To estimate the result of 3.8 divided by 2, you can round 3.8 to 4 which, when divided by 2, gives an estimate of 2. This method provides a result that is close to the actual answer of 1.9.
Explanation:The question '3.8 divided by 2 estimated' is asking for an approximate result of dividing 3.8 by 2. To estimate this, you can round 3.8 to 4 because it is close to this even number which makes mental math easier. Now, divide 4 by 2 to get 2. Although this is an estimate, the actual calculation of 3.8 / 2 yields 1.9. So, our estimated answer is close to the actual result.
When performing division, estimation can be a useful tool, especially when dealing with decimals. Estimating can also help in checking the reasonableness of answers obtained via calculators, which can sometimes provide more precision than necessary. For example, when using significant figures in calculations, a calculator does not limit the precision of the result, but estimating can help a user decide how many decimal places to report.
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alicia takes 4 white 2 red and 3 lue shirts on the trip. on the first day alicia will pick a shirt at random. what is the probability that she picks a red shirt?
Answer:
The Probability of Alicia picking a red shirt is [tex]\frac{2}{9}[/tex].
Step-by-step explanation:
Given,
Number of White shirts = 4
Number of Red shirts = 2
Number of Blue shirts = 3
Solution,
Total number of shirts = Number of White shirts + Number of Red shirts + Number of Blue shirts = [tex]4+2+3=9[/tex]
[tex]P(E)=\frac{Total\ number\ of\ possible\ outcomes}{Total\ number\ of\ outcomes}[/tex]
Therefore,
[tex]P(of\ red\ shirts)=\frac{2}{9}[/tex]
Hence The Probability of Alicia picking a red shirt is [tex]\frac{2}{9}[/tex].
How do you solve the following for x?
Answer:
Step-by-step explanation:
Is called a letter that stands for the number
Answer:
Step-by-step explanation:
√10x - 1 = 7
Square both sides,
10x - 1 = 7²
10x - 1 = 49
10x = 49 + 1
10x = 50
x = 50/10
x=5
20 pts and brainiest if correct
We have 1 square with side length 8 inches, and 4 triangles with a base length of 8 inches and a height of 15.
Surface area = (8 × 8) + 4(0.5 × 8 × 15)
The first part of this equation is the area of the square
The second part is the area of a triangle, multiplied by 4 (because there are 4 triangles)
= 64 + 4(60)
= 64 + 240
= 304 in²
The total surface area is 304 square inches.
Let me know if you need any clarifications, thanks!
Micheal is 4 times as old as Brandon and is also 27 years older than Brandon. How old is Brandon?
Answer: 108
Step-by-step explanation:
Please need help!!! Need in 10 monutes
Answer:
Step-by-step explanation:
16) 4 * y/5
The value of y should be greater than 5
For example if y = 6, then 4* 6/5 = 24/5 = 4.8
If y= 10, then 4* 10/5 = 4 * 2 = 8
y > 5
17) 1 pound = 16 ounce
3020 pounds =3020 * 16 = 48320 ounces
when 6 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution.
When 6 is subtracted from the square of a number, the result is 5 times the number, then the negative solution is -1
Solution:Given that when 6 is subtracted from the square of a number, the result is 5 times the number
To find: negative solution
Let "a" be the unknown number
Let us analyse the given sentence
square of a number = [tex]a^2[/tex]
6 is subtracted from the square of a number = [tex]a^2 - 6[/tex]
5 times the number = [tex]5 \times a[/tex]
So we can frame a equation as:
6 is subtracted from the square of a number = 5 times the number
[tex]a^2 - 6 = 5 \times a\\\\a^2 -6 -5a = 0\\\\a^2 -5a -6 = 0[/tex]
Let us solve the above quadratic equation
For a quadratic equation [tex]ax^2 + bx + c = 0[/tex] where [tex]a \neq 0[/tex]
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Here in this problem,
[tex]a^2-5 a-6=0 \text { we have } a=1 \text { and } b=-5 \text { and } c=-6[/tex]
Substituting the values in above quadratic formula, we get
[tex]\begin{array}{l}{a=\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(-6)}}{2 \times 1}} \\\\ {a=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5 \pm \sqrt{49}}{2}} \\\\ {a=\frac{5 \pm 7}{2}}\end{array}[/tex]
We have two solutions for "a"
[tex]\begin{array}{l}{a=\frac{5+7}{2} \text { and } a=\frac{5-7}{2}} \\\\ {a=\frac{12}{2} \text { and } a=\frac{-2}{2}}\end{array}[/tex]
a = 6 or a = -1We have asked negative solution. So a = -1
Thus the negative solution is -1
true or false...a triangle with sides of lengths 20,21 and 29 is a right triangle
Answer:
True
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
20 squared+21 sqaured= 29 squared
At this rate, how many dresses does Lucy sew in one hour?
Answer: Lucy sews [tex]\frac{16}{21}[/tex] of a dress in one hour.
Step-by-step explanation:
The complete question is:
"Lucy is a dress maker. She sew [tex]\frac{4}{7}[/tex] of a dress in [tex]\frac{3}{4}[/tex] hour. At this rate, how many dresses does Lucy sew in one hour?"
Let "x" represents the number of dresses that Lucy sews in one hour.
You need to analize the information given in the exercise.
According to the exercise, you know that, in [tex]\frac{3}{4}[/tex] hour, Lucy sews [tex]\frac{4}{7}[/tex] of a dress.
Then, knowing this data, you can set up the following proportion:
[tex]\frac{\frac{4}{7}}{\frac{3}{4}}=\frac{x}{1}[/tex]
Therefore, you must solve for "x" in order to find the he number of dresses that Lucy sew in one hour.
You get this result:
[tex](1)(\frac{4*4}{7*4})=x\\\\x=(1)(\frac{16}{21})\\\\x=\frac{16}{21}[/tex]
Then, Lucy sews [tex]\frac{16}{21}[/tex] of a dress in one hour.
What are the domain and range of the function f(x) = -3(x-5)2 +4?
domain: (-0,5)
range: -00,00)
domain: (-0,4]
range: -00,00)
domain: (-0,5]
range: (-0,4]
domain: -00,00
range: (-0,4]
Good evening ,
Answer:
domain: ]−∞,+∞[
range: ]−∞,4]
Step-by-step explanation:
Look at the photo below for more info.
:)
The domain of the function f(x) = -3(x-5)² +4 is all real numbers, written as (-∞, ∞). The range, or possible values of f(x), is (-∞, 4] since the parabola opens downwards and the maximum value is 4.
Explanation:The function f(x) = -3(x-5)² +4 is a parabola that opens downwards. The domain of a function is the set of all values that x can take. For any parabolic function, the domain is always all real numbers, which we could write as (-∞, ∞).
The range of a function refers to the possible values of f(x). In this case, since the parabola opens downwards, the maximum value of f(x) is at the vertex of the function. This parabola's vertex is at (5,4), so its maximum, and thus the upper boundary of the range, is 4. The parabola continues downwards to negative infinity, so the range is (-∞, 4].
Therefore, the domain is (-∞, ∞), and the range is (-∞, 4].
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The area of a triangle is given by the formula A=1/2bh. Solve this equation for the height, h, in terms of the base, b, and area, A.
The equation for the height, h, in terms of the base, b, and area, A is [tex]h = \frac{2A}{b}[/tex]
Solution:
Given that area of a triangle is given by the formula:
[tex]A = \frac{1}{2}bh[/tex]
Where,
A is the area of triangle
b is the base of triangle
h is the height of triangle
We have to find the equation for height in terms of base and area
So we have to arrange the equation in such a way that height can be found by using area and base
Given formula is:
[tex]A = \frac{1}{2}bh[/tex]
Keep "h" alone in L.H.S and move the other terms to other side of formula
[tex]A = \frac{bh}{2}\\\\2A = bh\\\\h = \frac{2A}{b}[/tex]
Thus height is expressed in terms of base and area
1. What is the period of the sinusoidal function? Please help thank you
The period will be the length for one cycle of the function.
answer: 10
Given f(x) and g(x) = f(k:x), use the graph to determine the value of k.
Answer:
k=2
Step-by-step explanation:
We are given that two function f(x) and g(x)
[tex]g(x)=f(kx)[/tex]
From given graph
[tex]g(-2)=0[/tex]
[tex]f(-4)=0[/tex]
[tex]g(-2)=f(-4)[/tex]
By comparing we get
x=-2 and
[tex]kx=-4[/tex]
[tex]k(-2)=-4[/tex]
[tex]k=\frac{-4}{-2}=2[/tex]
Hence, the value of k=2
Based on information provided, the value of k is 2.
Here's why:
1. Understanding the problem: We are given two functions, f(x) and g(x), where g(x) is defined as f(k * x). The graph shows both functions, and we are asked to find the value of k.
2. Analyzing the graph: The graph shows two lines:
- The red line represents f(x).
- The blue line represents g(x).
3. Key observation: We are given that g(-2) = 0. This means the blue line intersects the x-axis at x = -2.
4. Relating g(x) to f(x): Since g(x) = f(k * x), we know that the blue line is obtained by horizontally stretching or compressing the red line by a factor of k.
5. Finding k: To make the blue line intersect the x-axis at x = -2, we need to stretch the red line to the left by a factor of 2. This means k = 2.
Therefore, based on the given information and the analysis of the graph, the value of k is 2.
a coach bought some baseball bats and 5 baseball gloves. Let b represent the number of bats. Write an expression that can be used to find the total cost of bats and gloves. Then find the total cost if he bought three bats.
The expression for the total cost of bats and gloves is b*x + 5*y. To find the total cost when three bats are bought, you need to know the costs of a bat (x) and a glove (y), and substitute those into the expression.
Explanation:Assume that the cost of a baseball bat is 'x' dollars and each glove costs 'y' dollars. The total cost can be calculated by making 'b' the number of bats and adding the cost of 5 gloves. Therefore, the expression representing the total cost is b*x + 5*y.
Now, if the coach bought 3 bats, and we're given the costs for a bat and a glove, we can substitute '3' for 'b', 'x' for the cost of a bat, and 'y' for the cost of a glove.
For example, if a bat is $50 (x=50) and a glove is $20 (y=20), the total cost would be: 3*50 + 5*20 = 250 dollars.
Learn more about Algebraic Expressions here:https://brainly.com/question/34192827
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Final answer:
The expression for total cost of baseball bats and gloves is 'b times the number of bats plus 5 times the cost of a glove', where 'b' represents the cost of a bat. In the bat and ball problem, if a bat costs $1 more than the ball and together they cost $1.10, the ball costs $0.05. For three bats, the total cost is $3.15.
Explanation:
The question posed is a classic algebra problem from mathematics often used to illustrate a common cognitive error. To write an expression for the total cost of the baseball bats and gloves, let the cost of each bat be represented by 'b' and assume each glove has a fixed cost 'g'. The expression is then b times the number of bats plus 5 times the cost of a glove. However, we require additional information regarding the cost of individual gloves to complete this expression.
Turning to the bat and ball problem, if a bat and ball together cost $1.10, and the bat costs $1 more than the ball, we can set up the following equations where 'x' is the cost of the ball:
x + (x + $1) = $1.10
2x + $1 = $1.10
2x = $1.10 - $1.00
2x = $0.10
x = $0.05
Thus, the ball costs $0.05 and the bat costs $1.05. Finding the cost of three bats, we simply multiply $1.05 by 3 to get $3.15.
(-3, y) and (1, -7); m = -4
Step-by-step explanation:
If you're asking for an equation, the equation would be: [tex]y=-4x-3[/tex]
(probably what you're looking for) if you're looking for what y equals, the answer is: 9
for equation:
1. write an equation with the information you have
[tex]y=-4x+b[/tex]
2. Plug in the values for x and y
[tex]-7=-4(1)+b[/tex] where b equals -3
so your equation would be [tex]y=-4x-3[/tex]
for what y equals:
1. since you've figured out the equation, plug in the value for x and solve for y
[tex]y=-4(-3)-3[/tex] which then gives you [tex]y=9[/tex]