The graph would be affected by horizontally stretching the curve of f(x) = x^2 when the coefficient is changed
How to determine the change?The function is given as:
f(x) = x^2
When the coefficient of x^2 changes to 1/3, we have:
f(x) = 1/3x^2
The above represents a stretch of the function
This means that the graph would be affected by horizontally stretching the curve of f(x) = x^2 when the coefficient is changed
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Find the measure of side b.
b = _ yd
Complete the table. Each column should contain equivalent values. One column has been completed for you. Make sure the fractions are stated in simplest form.
Fraction Decimal Percent
0.39 39%
0.82
22%
0.8
The complete table will be:
Fraction Decimal Percent
39/100 0.39 39%
82/100 0.82 82%
22/100 0.22 22%
3/4 0.75 75%
80/100 0.8 80%
Percentage
The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:
[tex]\frac{25}{100} =0.25*100=25%[/tex]
The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks etc.
Line 1Fraction Decimal Percent
39/100 0.39 0.39*100=39%
Line 2Fraction Decimal Percent
82/100 0.82 0.82*100=82%
Line 3
Fraction Decimal Percent
22/100 0.22 22%
Line 4
Fraction Decimal Percent
3/4 0.75 0.75*100=75%
Line 5
Fraction Decimal Percent
80/100 0.8 0.80*100=80%
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Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
A function which could represent the graph is: C. f(x) = x⁴(x - a)(x - b)².
How to interpret the graph?The nature of the intercept on a polynomial graph highlights the nature of its multiplicity. Also, the polynomial graph has no single zero (factor) but bounced off the x-axis at three (3) different locations.
This ultimately implies that the polynomial graph has an even multiplicity at these three (3) points:
x⁴
x - a
(x - b)²
In conclusion, a function which could represent the graph is f(x) = x⁴(x - a)(x - b)².
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WHAT TWO EQAUL NUMBERS ADD TO THE EVEN NUMER 40
Answer:
20
Step-by-step explanation:
20+20=40
I need help with the slope
Answer:
Line A
Step-by-step explanation:
Hello!
Given that the x-values is the time in minutes, and the y-axis is the number of dishes stacked, for every minute, the line should go up by 7.
This means, that the value of y when x is 1 should be 7. The line that follows this rule is Line A. For every minute, 7 dishes are stacked.
The answer is Line A.
3. A rare species of aquatic insect was discovered in the Amazon rainforest. To protect the species, environmentalists declared the insect endangered and transplanted the insect to protected area. The population P(t) (in thousands) of insects in t months after being transplanted is
a. [3 pts] Determine the number of months until the insect population reaches 40 thousand (round to 2 decimal places).
b. [3 pts] What is the limiting factor on the insect population as time progresses? Explain your answer.
c. [3 pts] Sketch a graph of the function using the window and. Be sure to indicated the scale on the graph, label the axes, at least 2 points on the graph, and any asymptotes.
The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.
Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).
(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get
P(t)=40
(50(1+0.05t))/(2+0.01t)=40
Cross multiply both sides, we get
50(1+0.05t)=40(2+0.01t)
Apply the distributive property a(b+c)=ab+ac, we get
50+2.5t=80+0.4t
Subtract 0.4t and 50 from both sides, we get
50+2.5t-0.4t-50=80+0.4t-0.4t-50
2.1t=30
Divide both sides with 2.1, we get
t=14.29 months
(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get
[tex]\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end[/tex]
(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.
Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.
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f r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to (StartFraction r Over s EndFraction) (6)?
The equivalent expression to [tex]\mathbf{(\dfrac{r}{s})(6)= \dfrac{17}{13}}[/tex]
What are the equivalent expressions?Equivalent expressions are similar expressions that may have different forms but when a value is replaced with the variables in the same form provides the same answer.
From the information given, If:
r(x) = 3x - 1s(x) = 2x + 1Then the fractional form can be an expression as:
[tex]\mathbf{(\dfrac{r}{s})(x)= \dfrac{3x-1}{2x+1}}[/tex]
where;
x = 6[tex]\mathbf{(\dfrac{r}{s})(6)= \dfrac{3(6)-1}{2(6)+1}}[/tex]
[tex]\mathbf{(\dfrac{r}{s})(6)= \dfrac{18-1}{12+1}}[/tex]
[tex]\mathbf{(\dfrac{r}{s})(6)= \dfrac{17}{13}}[/tex]
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WHAT IS 5+6+6+^6 DIVDED BY 7
The value of the given expression is 11.57
Division of numberDivision are written as a ratio of two values. Given the expression below
5+6+6+2^6 ÷ 7
Simplify to have:
(11+6+64)÷ 7
Simplify the expression in parenthesis
81÷ 7
11.57
Hence the value of the given expression is 11.57
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Graph the following inequality. y ≤ 3x +5 Use the graphing tool to graph the inequality Click to enlarge graph
Please see the graph below
A. Reflection around the x-axis:
1. A (5, 1)→ A'
2. B (1, 3) B¹.
3. C (-2, 2)→ C'.
4. D (-5, 4) D'
B. Reflection around the y-axis:
1. A (5, 1)→ A'
2. B (1, 3) B¹.
3. C (-2, 2)→ C'_
4. D (-5, 4) D'
Part A
1) (5, -1)
2) (1, -3)
3) (-2, -2)
4) (-5, -4)
Part B
1) (-5, 1)
2) (-1, 3)
3) (2, 2)
4) (5, 4)
Find the slope and y-intercept of the line whose equation is y=6x=5
Answer:
the slope is 5 and the y intercept is 5
Step-by-step explanation:
I think that you meant to write y = 6x + 5.
y = mx + b
The number in in the m spot is the slope and the number in the b spot is the y intercept.
Which expression is equivalent to
xay
8
700
8√√√x
y
8√√y
Mark this and return
128x56
√ 2x75
? Assume x > 0 and y> 0.
Save and Exit
The equivalent expression of [tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex] is [tex]\frac{8\sqrt y}{x}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex]
Divide 128 by 2
[tex]\sqrt{\frac{64x^5y^6}{x^7y^5}}[/tex]
Apply the law of indices to the variables
[tex]\sqrt{\frac{64y^{6-5}}{x^{7-5}}}[/tex]
Evaluate the differences
[tex]\sqrt{\frac{64y}{x^2}}[/tex]
Take the square root of 64
[tex]8\sqrt{\frac{y}{x^2}}[/tex]
Take the square root of x^2
[tex]\frac{8\sqrt y}{x}[/tex]
Hence, the equivalent expression of [tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex] is [tex]\frac{8\sqrt y}{x}[/tex]
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Which of the following similarity statements about the triangles in the figure is true?
Right triangle P Q R has angle Q marked as a right angle. A segment is drawn from point Q to side P R. The point where the segment intersects side PR is point S. Angle P S Q is marked as a right angle.
A. Triangle P Q R is similar to triangle P S Q, which is similar to triangle Q S R.
B. Triangle R Q P is similar to triangle S Q P, which is similar to triangle R S Q.
C. Triangle Q R P is similar to triangle Q S P, which is similar to triangle Q S R.
D. Triangle P R Q is similar to triangle Q P S, which is similar to triangle R Q S.
Answer:
Answer B is correct
"The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200, with 200 being the highest level of motivation. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 30 students who are at least 29 years of age, and their mean was 135.2"
Calculate the observed test statistic (Zobt or Tobt) for hypothesis test. Round up to the second decimal place.
Using the z-distribution, the observed test statistic is given as follows:
z = 3.69.
What are the hypothesis tested?At the null hypothesis, it is tested if older students have the same mean as the general population, that is:
[tex]H_0: \mu = 115[/tex]
At the alternative hypothesis, it is tested if they have a greater mean, that is:
[tex]H_0: \mu > 115[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.For this problem, the parameters are:
[tex]\overline{x} = 135.2, \mu = 115, \sigma = 30, n = 30[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{135.2 - 115}{\frac{30}{\sqrt{30}}}[/tex]
z = 3.69.
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The transformation from parallelogram LMNO to parallelogram L'M'N'O' was carried out as shown in the coordinate plane below.
The transformation from parallelogram LMNO to parallelogram L'M'N'O' is a reflection across the x-axis
How to determine the transformation?The complete question is added as an attachment
From the graph, we have the following highlights:
Parallelogram LMNO and parallelogram L'M'N'O' are on either sides of the x-axisThey are equidistant from the x and y axesThey have equal dimensionsThis means that parallelogram LMNO is reflected across the x-axis to get parallelogram L'M'N'O'
Hence, the transformation from parallelogram LMNO to parallelogram L'M'N'O' is a reflection across the x-axis
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Integral of
11-3x/
x²+2x-3
dx
Answer:
2x+2
Step-by-step explanation:
x²+2x-3
=2(x^2-1)+2*1(2x^1-1)
Translate to a proportion and solve.
148.5 is 59 1/5% of what?
The actual value is 250.
Applying simple percentage formula here,
let x be the whole value
x=148.5/ 59 2/5%
x= 148.5/0.594
x=250.
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The actual value is 250.
Applying percentage formula here,
let x be the value:
x=148.5/ 59 2/5%
x= 148.5/0.594
x=250
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None of the pots in the kitchen have a lid.
For each statement below, determine whether it is a negation
All pots in the kitchen have a lid.
Not every pot in the kitchen has a lid.
At least one pot in the kitchen has a lid.
Some pots in the kitchen have a lid.
Yes
No
O
O
The first three statements are not a negation. Only the last statement is a negation.
What is negation?The opposite of the given mathematical statement is the negation of a statement in mathematics. If "P" is a statement, then "P" is the statement's negation. The words negation is used to denote a statement's denial.
It's vital to know the opposite of a given mathematical statement from time to time in mathematics. This practice is known as "negating" a statement. Remember that if a statement is true, then its negation must be false (and if a statement is false, then its negation is true).
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If the function is:
What is f(-4)?
Answer:
D. -11
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases}2x-3 & \textsf{if }x \leq -4\\x^2 & \textsf{if }-4 < x < 0\\x+5 & \textsf{if }x \geq 0\end{cases}[/tex]
Therefore, the function has three definitions:
[tex]f(x)=2x-3 \quad \textsf{ when x is equal to or less than -4}[/tex]
[tex]f(x)=x^2 \quad \textsf{ when x is greater than -4 or less than zero}[/tex]
[tex]f(x)=x+5 \quad \textsf{ when x is greater than zero}[/tex]
f(-4) means to substitute x = -4 into the function.
As x = -4 satisfies the interval of the first piece of the function, substitute x = -4 into f(x) = 2x - 3:
[tex]\begin{aligned}\implies f(-4) & =2(-4)-3\\& = -8 -3\\& = -11\end{aligned}[/tex]
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Answer is D. -11
Answer:
Solution Given:
f(-4) depends on the condition x≤-4,
so
f(-4)=2*-4-3=-8-3=-11
The diagram is supposed to be used for both question 7 and 8. WORTH 30 POINTS.
7. D. Arc JK = 124°
8. Applying the angle of intersecting chords theorem, m∠1 = 115°.
What is the Angle of Intersecting Chords Theorem?The angle of intersecting chords theorem states that the angle (∠1) formed by two chords in a circle, equals half of the sum of the intercepted arcs (arcs ML and JK).
Arc JMK = 2(118) = 236° [inscribed angle theorem]
Arc JK = 360 - arc JMK = 360 - 236
Arc JK = 124°
Arc ML = 236 - 70 - 60 = 106°.
m∠1 = 1/2(arc JK + arc ML)
m∠1 = 1/2(124 + 106)
m∠1 = 115°.
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do you have a picture of what the graph would look like?
The attached graph represents the piecewise function.
How to determine the graph of the equation?The piecewise function is given as:
f(x) = 3x - 5, x ≤ -1
= -2x + 3, -1 < x < 4
= 2, x ≥ 4
To plot the graph, we simply plot the equations together with their domains
i.e.
3x - 5 with the domain of x ≤ -1, -2x + 3 with the domain of -1 < x < 4 and 2 with the domain of x ≥ 4
See attachment for the graph of the function
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If (x, 68, 85) form a Pythagorean Triple, what is the value of x?
Answer:
x = 51Step-by-step explanation:
If (x, 68, 85) form a Pythagorean Triple, what is the value of x?
to solve we again use Pythagoras, x is the smallest number, so 68 is a cathetus and 85 the hypotenuse
x = √(85²- 68²)
x = (7225 - 4624)
x = √2601
x = 51
Answer:
x = 51
Step-by-step explanation:
The missing value of the Pythagorean triple can be found using the Pythagorean theorem, or it can be found by comparing the values in the triple to known triples.
What are Pythagorean triples?A Pythagorean triple is a set of integers {a, b, c} that satisfy the equation of the Pythagorean theorem:
a² +b² = c²
The smallest such triple is {3, 4, 5}. It is also the only triple that is an arithmetic sequence. Other triples of small integers are ...
{5, 12, 13}, {7, 24, 25}, {8, 15, 17}
There are an infinite number of "primitive" Pythagorean triples, ones that are not multiples of another triple.
What is this triple?The given values of the triple have the ratio ...
68/85 = (4·17)/(5·17) = 4/5
Only the values in the {3, 4, 5} triple and its multiples will have this ratio.
The value of x is 3·17 = 51, so the triple is {51, 68, 85}.
x = 51
__
Additional comments
Any primitive triple will have two odd numbers.
The ratios of numbers in a primitive triple are unique to that triple. That is, the numbers are mutually prime.
For any pair of positive integers m > n, there is a Pythagorean triple {2mn, m²-n², m²+n²}. Such triples will not be primitive if m and n have the same parity.
__
The above triple can be verified using the Pythagorean theorem:
51² +68² = 2601 +4624 = 7225 = 85²
Which is the statement is true about f(x)=-2/3|x+4|-6
Answer: The graph of f(x) is horizontally stretched
a group of mapuve CLC MLMS4 STUDENTS were questioned how they got to school.half of the students said they walk, one-third said they take a taxi,and the rest claimed they drive.calculate the number of students delivered by a car using proper fractions
The fraction of those who were delivered by car will be 1/6.
How to calculate the fraction?It should be noted that from the information given, the students were questioned on how they got to schoo and half of the students said they walk, one-third said they take a taxi,and the rest claimed they drive.
Therefore, the fraction of those who were delivered by car will be:
= 1 - (1/2 + 1/3)
= 1/2 - 5/6
= 1/6
In conclusion, the fraction of those who were delivered by car will be 1/6.
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By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 303 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol. By eating 2 eggs and 1 cupcake, a child consumes 570 mg of cholesterol. How much cholesterol is in each item?
Using a system of equations, the amounts of cholesterol in each item are given as follows:
Egg: 278 mg.Cupcake: 14 mg.Slice of pizza: 11 mg.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables for this problem are given as follows:
Variable x: Amount of cholesterol in an egg.Variable y: Amount of cholesterol in a cupcake.Variable z: Amount of cholesterol in a slice of pizza.By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 303 mg of cholesterol, hence:
x + y + z = 303.
3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol, hence:
3y + 4z = 90
y + 1.33z = 30.
By eating 2 eggs and 1 cupcake, a child consumes 570 mg of cholesterol, hence:
2x + y = 570.
Then, writing y and z as functions of x:
y = 570 - 2x.z = (30 - y)/1.33 = (30 - 570 + 2x)/1.33 = 1.5x - 406.Then, replacing on the first equation:
x + y + z = 303.
x + 570 - 2x + 1.5x - 406 = 303.
0.5x + 164 = 303.
x = (303 - 164)/0.5
x = 278.
The amounts for the cupcake and the slice of pizza are given as follows:
y = 570 - 2(278) = 14 mg.z = 1.5x - 406 = 1.5(278) - 406 = 11 mg.More can be learned about a system of equations at https://brainly.com/question/24342899
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PLEASE HELP AND GIVE A FULL EXPLANATION I WILL GIVE BRAINLEST PLEASE SOMEONE
Answer:
shown in explanation
Step-by-step explanation:
a) ∆EPB similar to ∆ERG
b) angle BEP = angle GER (common angle shared)
angle EPB = angle ERG (corresponding angles, PB//RG, parallelogram)
therefore through Angle-Angle similarity test, ∆EPB is similar to ∆ERG
or explanation can also be shortened to
∆EPB is similar to ∆ERG (AA, similarity)
c) since proven they are similar ∆, then we can proceed to use property of ratio of corresponding sides being equal
[tex] \frac{pb}{rg} = \frac{ep}{er} [/tex]
RG = 200+300=500m
[tex] \frac{200}{500} = \frac{ep}{ep + 350} [/tex]
cross multiply (from what I've learnt)
2ep+700=5ep
ep= 700/3 = 233 ⅓m (answer for length EP)
Do the same for length BE(using ratio of corresponding sides)
[tex] \frac{be}{ge} = \frac{pb}{rg} [/tex]
[tex] \frac{be}{be + 400} = \frac{200}{500} [/tex]
cross multiply again to get:
5BE = 2BE + 800
BE = 800/3 = 266 ⅔ m (answer for length BE)
What kind of transformation is illustrated in this figure?
The transformation illustrated in the figure is translation.
What is Translation?Translation is a Transformation process in which the size or shape of a figure is not changed rather it only changes the coordinates of the vertices that make up that shape by moving them from one point to another.
Analysis:
Both shapes are congruent, since all the vertices remain in their respective positions even though they were moved and no change in the shape or size, then the transformation process is Translation.
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The final result after substituting a value into an equation is the output.
A. true
B. false
Sets A,B , and C are subsets of the universal set U.
These sets are defined as follows.
U= {f,g,h,p.q.r.x.y.z}
A={f,h,p.q.r}
B={q,r,y,z}
C={g,h,p,q,y}
Find (B' U A) ∩ C.
Write your answer in roster form or as Ø.
[tex]B'=\{f,g,h,p,x\}\\B'\cup A=\{f,g,h,p,q,r,x\}\\(B'\cup A)\cap C=\{g,h,p,q\}[/tex]
Primer numbers list maths
Answer:
1 - 100 primes numbers
Step-by-step explanation:
2,3,5,7,11,13,17,19,23,29,31,37,41,47,57,59,61,67,71,79,83,8797