In 90 minutes, she would have created 36 drawings.
How many total drawings will Frankita have created at the end of 90 minutes?The first step is to establish a pattern between time and the number of drawing that Frankita creates.
When the question is studied, it can be deduced that every 15 minutes the rate of increase in drawing is (previous drawing + (1 + rate of increase of previous drawing.
Drawing created in 30 minutes = 15 + 2 = 17
Drawing created in 45 minutes = 17 + ( 1 + 2) = 20
Drawing created in 60 minutes = 20 + (3 + 1 ) = 24
Drawing created in 75 minutes = 24 + (4 + 1) = 30
Drawing created in 90 minutes = 30 + (5 + 1) = 36
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A girl get n cedis pocket money money each week. she saves her money for five weeks and buys a present for her mother which cost gh 7900 i. write an expression for the amount of the money left ii.what is the minimum amount she needs to save each week to be able to afford the gift
An expression for the amount of the money left = (5n-7900) cedis
The minimum amount she needs to save each week to be able to afford the gift: n = 7900/5.
What is a word problem?The term "word problem" refers to a type of math question where the answer is written as one or more sentences and asks students to use their mathematical understanding to solve a problem from "real world."
What is the first step in solving word problem?Read the problem in its full to get a clear understanding of what you need to do in order to solve it before you start. Following reading it, you may choose which components of the issue need to be resolved the most and which ones are not.
According to the given data:She gets n cedis a week.
she will get n x 5 cedis for 5 wks =5n cedis.
She buys a present worth 7900.
An expression for the amount of the money left = (5n-7900) cedis.
The minimum amount she needs to save each week to be able to afford the gift.
5n-7900 = 0
n = 7900/5.
7900/5 = ____ per week
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My brain stopped. I need help
Answer:
x = 99°
y = 91°
Step-by-step explanation:
For Cyclic quadrilateral, the sum of the opposite angles = 180°
Let's find x :-
x + 81° = 180°
x = 180 - 81
x = 99°
Let's find y :-
y + 89° = 180°
y = 180 - 89
y = 91°
Hope this helps you !
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
1.Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Answer:
[tex]y = -\frac{2}{3}x + 490[/tex]
gradient = = [tex]-\frac{2}{3}[/tex]
y-intercept = [tex]490[/tex]
Step-by-step explanation:
• The slope-intercept form of an equation takes the general form:
[tex]\boxed{y = mx + c}[/tex],
where:
m = slope,
c = y-intercept.
• We are given the equation:
[tex]2x + 3y = 1470[/tex]
To change this into the slope-intercept form, we must make y the subject:
[tex]3y = -2x + 1470[/tex] [subtract [tex]2x[/tex] from both sides]
⇒ [tex]y = -\frac{2}{3}x + \frac{1479}{3}[/tex] [divide both sides by 3]
⇒ [tex]y = -\frac{2}{3}x + 490[/tex]
• Comparing this equation with the general form equation, we see that:
m = [tex]-\frac{2}{3}[/tex]
c = [tex]490[/tex].
This means that the gradient is [tex]\bf -\frac{2}{3}[/tex], and the y-intercept is [tex]\bf 490[/tex].
if you double the side length of a cube how does it effect the volume
Step-by-step explanation:
Volume of the cube = Side
Since,
All the sides of the cube are equal
Then if the length of a side of the cube is
increased
So, the side of the cube becomes
Side of the cube = 2 × Side
Assume
Side of the cube be ‘s’
Side of the cube = 2s
Now,
Volume of the cube = 2s × 2s × 2s
Volume of the cube = (2s)
Volume of the cube = 8s
To find how many times the volume of the cube is
increased
A company needs to package 7,560 beads. A wooden container shaped like a rectangular prism can hold 180 beads. A plastic cylindrical container can hold 126 beads. The wooden container costs the company $0.70, while the plastic container costs $0.40.
Which container should the company use to minimize cost? Explain.
The wooden containers should be used because it will cost $5.40 more to use the plastic containers.
The plastic containers should be used because it will cost $5.40 more to use the wooden containers.
The wooden containers should be used because it will cost $16.20 more to use the plastic containers.
The plastic containers should be used because it will cost $16.20 more to use the wooden containers.
The plastic containers should be used by the company to minimize the cost because it will cost $5.40 more to use the wooden containers.
What are word problems in mathematics?A mathematical word problem is a question that is stated as one or more sentences and calls on students to use their understanding of arithmetic operations to solve a "real-life" problem.
As you are aware, word problems can include almost any operation, including addition, subtraction, division, and even many operations at once.
From the given information:
If the company uses a wooden container shaped-liked rectangular prism, the will need to use (7560/180) containers.
= 42 containers of wooden containers.
If the company uses a plastic cylindrical container, they will need to use (7560/126) containers.
= 60 containers of plastic containers.
To determine the container that the company should use that will minimize the cost:
If the company decided to use the wooden container, then they will spend = 42 × $0.70 = $29.4If the company decided to use the plastic container, then they will spend = 60 × $0.40 = $24Therefore, we can conclude that the company should use plastic containers because it will cost $5.40 more to use wooden containers.
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Answer:
B. The plastic containers should be used because it will cost $5.40 more to use the wooden containers.
Step-by-step explanation:
Kenneth wants to sew a tent, including the bottom so that it is entirely enclosed. He has a rectangular piece of canvas with dimensions of 12 feet by 20 feet. The front and back of the tent will be identical triangles, measuring 6 feet across at ground level, with two 5-foot sides meeting at the top. The depth of the tent will be equal to three times the height of the front of the tent. What is the depth of the tent?
Based on the calculations, the depth of tent is equal to 12 feet.
How to calculate the depth of the tent?Based on the diagram (see attachment) and information provided, we can logically deduce the following parameters (points):
Triangle ABC is an isosceles triangle (AB = AC).The front and back of the triangle are identical triangles.Side AD is perpendicular side BC.CD is the midpoint of BC i.e CD = BC/2 = 6/2 = 3 feet.Next, we would determine the height of the right-angled triangle (ADC) by applying Pythagorean theorem:
AC² = AD² + DC²
AD² = AC² - DC²
AD² = 5² - 3²
AD² = 25 - 9
AD² = 16
AD = √16
AD = 4 feet.
Also, we would determine the area of the triangle (ABC):
Area = 1/2 × b × h
Where:
b is the base area.h is the height.Substituting the given parameters into the formula, we have;
Area = 1/2 × 6 × 4
Area = 12 feet².
Depth of tent = 3 × height of ADC
Depth of tent = 3 × 4
Depth of tent = 12 feet.
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PLEASE HELP IM STUCK PLS
Answer:
The slope between these two points is m=-4.
Step-by-step explanation:
Greetings !
[tex]the \: equation \: for \: slope \: m \: is \\ m = \frac{Y₂-Y}{X₂-X₁}..substitute \: known \: values \\ m = \frac{ (-11 - 9) }{(3 - ( - 2)} \\ m = \frac{ - 20}{5} \\ m = - 4[/tex]
1. The accompanying table shows the number of movie theaters showing a popular film and the film's weekly gross earnings, in millions of dollars. Use the table to answer the questions 1), 2).
Number of Theaters (x)
443
456
493
530
569
657
723
1,054
Gross Earnings (y)
(millions of dollars)
2.57
2.65
3.73
4.05
4.76
4.79
5.15
9.63
1). Write the linear regression equation for this set of data, rounding values to five decimal places. Using this linear regression equation, find the approximate gross earnings, in millions of dollars, generated by 610 theaters. Round your answer to two decimal places.
2). Find the minimum number of theaters that would generate at least 7.65 million dollars in gross earnings in one week.
2. A real estate agent plans to compare the price of a cottage, y, in a town on the seashore to the number of blocks, x, the cottage is from the beach. The accompanying table shoes a random sample of sales and location data. Write a linear regression equation that relates the price of a cottage to it's distance from the beach. Use the equation to predict the price of a cottage, to the nearest dollar, located three blocks from the beach.
Number of Blocks
from the Beach
(x) Price of a Cottage
(y)
5 $132,000
0 $310,000
4 $204,000
2 $238,000
1 $275,000
7 $60,800
3. The table below represents a chart kept by a pediatrician tracking the circumference of babies heads at various months of age.
Age
(in months) Circumference
(in cm)
1 35.8
2 36.6
5 38.5
6 39.1
4 38.9
13 40.1
7 39.1
15 40.3
10 39.9
2 36.8
18 40.6
1). Determine the regression model that best fits the data, rounding all values to the nearest thousandth. Then predict the size of a baby's head at 24 months old. Round your answer to the nearest tenth.
2). The pediatrician measured a newborns head and found the circumference to be 35.1cm. Can he add the pair (0, 35.1) to the data set to calculate a new regression? Justify your answer.
The regression equation of this group of data is given as ŷ = 0.0108X - 1.98123.
How to solve for the amount generated by the theaterŷ = 0.0108X - 1.98123
x = 610
= 0.0108*610 - 1.98123
= 4.61 million dollars
2. the minimum number of theaters that would generate at least 7.65 million dollars in gross earnings in one week.
7.65= 0.0108x-1.98123
take like terms
x = 892
2. correlation coefficient of X and Y is r = -0.987
This shows a negative relationship
b)Linear Regression Equation =
Y = 313309 - 34740x
c) Y = 313309 - 34740x
Y = 313309 - 34740 * 3
209089
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What is the focus point of a parabola with this equation? y = 1 8 (x2 − 4x − 12)
The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p) exist (2, 0).
How to estimate the focus point of a parabola?Given: [tex]$y=\frac{1}{8} (x^{2} -4x-12)[/tex]
[tex]$y=\frac{x^{2}}{8}-\frac{x}{2}-\frac{3}{2}$$[/tex]
Use the form [tex]$a x^{2}+b x+c$[/tex] to find the values of a, b, and c.
[tex]$a=\frac{1}{8}$[/tex], [tex]$b=-\frac{1}{2}$[/tex] and [tex]$c=-\frac{3}{2}$[/tex]
Consider the vertex form of a parabola [tex]$a(x+d)^{2}+e$[/tex]
To estimate the value of d using the formula [tex]$d=\frac{b}{2 a}$[/tex].
Substitute the values of a and b into the formula
[tex]$d=\frac{-\frac{1}{2}}{2\left(\frac{1}{8}\right)}$$[/tex]
[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$[/tex]
Cancel the common factor 2 and 8.
[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{1}{4}}$$[/tex]
[tex]$d=-\frac{1}{2}(1 \cdot 4)$$[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]$d=-\frac{1}{2} \cdot \frac{1}{2\left(\frac{1}{8}\right)}$$[/tex]
[tex]$d=-\frac{1}{2} \cdot \frac{1}{\frac{2}{8}}$$[/tex]
equating, we get
[tex]$d=-\frac{1}{2}(1 \cdot 4)$$[/tex]
[tex]$d=-\frac{1}{2} \cdot 4$$[/tex]
The value of [tex]$d=-2$[/tex]
Find the value of e using the formula [tex]$e=c-\frac{b^{2}}{4 a}$[/tex].
Substitute the values of c, b and a into the above formula, and we get
[tex]$e=-\frac{3}{2}-\frac{\left(-\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$$[/tex]
simplifying the equation, we get
[tex]$e=-\frac{3}{2}-\frac{(-1)^{2}\left(\frac{1}{2}\right)^{2}}{4\left(\frac{1}{8}\right)}$[/tex]
Apply the product rule to [tex]$\frac{1}{2}$[/tex].
[tex]$e=-\frac{3}{2}-\frac{1\left(\frac{1}{4}\right)}{4\left(\frac{1}{8}\right)}$$[/tex]
[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{4\left(\frac{1}{8}\right)}$$[/tex]
[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4(1)}{8}}$$[/tex]
simplifying the above equation, we get
[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 \cdot 2}}$$[/tex]
[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{4 \cdot 1}{4 / 2}}$$[/tex]
[tex]$e=-\frac{3}{2}-\frac{\frac{1}{4}}{\frac{1}{2}}$$[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]$e=-\frac{3}{2}-\left(\frac{1}{4} \cdot 2\right)$$[/tex]
[tex]$e=\frac{-3-1}{2}$$[/tex]
[tex]$e=\frac{-4}{2}=2$[/tex]
Substitute the values of [tex]$a, d_{t}$[/tex] and e into the vertex form [tex]$\frac{1}{8}(x-2)^{2}-2$[/tex].
Set y equal to the new right side.
[tex]$y=\frac{1}{8} \cdot(x-2)^{2}-2$[/tex]
Use the vertex form, [tex]$y=a(x-h)^{2}+k$[/tex], to determine the values of a, h, and k.
[tex]$a=\frac{1}{8}$[/tex]
[tex]$h=2$[/tex]
[tex]$k=-2$[/tex]
Find the vertex [tex]$(h, k)$[/tex]
[tex]$(2,-2)$[/tex]
Find [tex]$\boldsymbol{p}$[/tex], the distance from the vertex to the focus.
To estimate the distance from the vertex to a focus of the parabola [tex]$\frac{1}{4 a}$[/tex]
Substitute the value of a into the formula
[tex]$\frac{1}{4 \cdot \frac{1}{8}}=\frac{1}{\frac{4(1)}{8}}$[/tex]
[tex]$\frac{1}{\frac{4 \cdot 1}{4-2}}=\frac{1}{\frac{4 \cdot 1}{4 \cdot 2}}$[/tex]
[tex]$\frac{1}{\frac{1}{2}}=2$[/tex]
The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down. (h, k + p)
Substitute the known values of h, p, and k into the formula, we get
(2,0).
Therefore, the correct answer is (2,0).
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The total mass of 2 similar clay pots and 2 similar metal pots was 13.2 kg. The mass of 1 such clay pot was 3 times the mass of a metal pot. What was the mass of a clay pot?
Answer:
mass of a clay pot = 4.95 kg
Kindly award branliest
Step-by-step explanation:
Let the mass of a clay pot be x
Let the mass of a metal pot be y
Thus; 2x + 2y = 13.2
And ;
x = 3 times y
x = 3y
2x + 2y = 13.2
2(3y) + 2y = 13.2
6y + 2y = 13.2
8y = 13.2
y = 13.2/8 = 1.65
x = 3y = 3(1.65) = 4.95
mass of a clay pot = 4.95 kg
3 rhombi are connected at a point, side by side. All sides are congruent.
Juan is making a model out of rhombi. Each rhombus will be connected to the one before it. Each rhombus will be 6 inches tall and 4 inches wide.
How much paper does he need for each rhombus?
square inches
If his wall is 11 feet long, how much paper does he use?
square inches
a. The amount of paper that he is going to need would given as 12 square inches.
b. If it is 11 inches what is needed to cover the wall is given as 396
a. How to solve for the amount of paper neededWe have the area of a rhombus to be given as
0.5 *d1 * d2
We have d1 = 6 inches
d2 = 4 inches
then area would be
0.5 * 6 * 4
= 12 inches
b. The amount of paper used as length is 11 feet long
1 ft = 12 inches
then 11 feet = 11 * 12
= 132
Number needed = 4
132/4 = 33
Then the area would be 33 * 12 inches to cover the wall
= 396
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Answer:
12 and 396
Step-by-step explanation:
In the diagram below, if < A = 97 °, < B = 46 °, < D = 97 ° and < F = 37 °, we can say that
The two triangles are similar by AA
There is not enough information to tell
The two triangles are not similar
Answer:
(a) The two triangles are similar by AA
Step-by-step explanation:
Similar triangles have congruent corresponding angles and proportional corresponding side lengths.
Third angleThe third angle in triangle ABC is found using the fact that the sum of angles is 180°.
∠C = 180° -∠A -∠B
∠C = 180° -97° -46° = 37°
Two of the angles, A and C, match the measures of two of the angles in triangle DEF. The matches are ...
∠A = ∠D = 97°
∠C = ∠F = 37°
The two triangles are similar by AA.
__
Additional comment
The similarity statement can be ΔABC ~ ΔDEF.
Solve each problem mentally. Type the answer in each box. 1. Bottle A contains 4 ounces of water, which is 25% of the amount of water in Bottle B. How much water is there in Bottle B? 2. Bottle C contains 150% of the water in Bottle B. How much water is there in Bottle C? 3. Bottle D contains 12 ounces of water. What percentage of the amount of water in Bottle B is this? %
Answer:
1. 16
2. 24
3. 75
Step-by-step explanation:
A skateboard halfpipe is being designed for a competition. the halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 40 ft above the ground. using the ground as the x-axis, where should the base of the halfpipe be positioned? which equation best describes the equation of the halfpipe?
The equation of the halfpipe is Option A , (0, 20); Y equals one over eighty times x squared plus 20.
The equation of the halfpipe is Y = X²/80 +20.
What is parabola ?
A parabola is the set of points in a plane that are the same distance from a given point and a given line in that plane. The given point is called the focus, and the line is called the directrix. The midpoint of the perpendicular segment from the focus to the directrix is called the vertex of the parabola.The equation of parabola is given by
(X-h)² = 4p(Y-k)²
In this case h = 0
So we get
Y = X²/4P +k
Focus point is (h, p+k) , (p+k) = 40
Hence h, k = (0,20)
P = 40-k = 20
Equation Y = X²/80 +20
Therefore, the equation of the halfpipe is Y = X²/80 +20
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The complete question is -
A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?
(0, 20); y equals one over eighty times x squared plus 20
(0, 20); y equals one over eighty times x squared minus 20
(0, 10); y equals one over forty times x squared plus 10
(0, 10); y equals one over forty times x squared minus 10
Are these lines perpendicular, parallel, or neither based off their slopes?
6x - 2y = -2
y = 3x + 12
Answer:
parallel
Step-by-step explanation:
//
Answer: these lines are parallel.
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{6x-2y=-2} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x-2y+2=0} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x+2=2y\ |:2} \atop {x=2}} \right. \\\\\left \{ {{3x+1=y} \atop {y=3x+12}} \right.\\ \\\left \{ {{y=3x+1} \atop {y=3x+12}} \right. \\So,\ these\ lines\ are\ parallel.[/tex]
Can someone please help me with this?
Answer: [tex]\Large\boxed{f(-9)=-189}[/tex]
Step-by-step explanation:
f(x) = -3x² - 6x
Requirements of the question
Find the value of f(-9)
Substitute values into the given function
f(x) = -3x² - 6x
f(9) = -3 (-9)² - 6 (-9)
Simplify the exponent
f(9) = -3 (81) - 6 (-9)
Simplify by multiplication
f(-9) = (-243) - (-54)
Simplify by subtraction
[tex]\Large\boxed{f(-9)=-189}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
5. In one game, the final score was Falcons 3, Hawks 1. What fraction and
percent of the total goals did the Falcons score? Show your work in the space
below. Remember to check your solution.
Answer:
3/4 or 75%
Step-by-step explanation:
Falcons scored 3 and Hawks scored 1, so in total 4 points were scored during the game. Falcons scored 3 out of 4 points, so they scored 3/4 of the points scored in the game.
To convert 3/4 to percentage, divide 3 by 4, multiply the quotient (result after division calculation) by 100, and add % sign after the number.
3/4 = 0.75
Therefore 3/4 is equivalent to 75%.
Answer:
[tex] \frac{3}{4} [/tex]
[tex]75\%[/tex]
Step-by-step explanation:
From the information given from the question, we can deduce:
Total goals scored by both teams = 3 + 1 = 4
Fraction of Goals Scored by Falcons =
[tex] \frac{goals \: scored \: by \: falcons}{total \: goals \: scored \: by \: both \: teams} \\ = \frac{3}{4} [/tex]
To get the percentage, we have to make sure the denominator is 100.
[tex] \frac{3}{4} \\ = \frac{3 \times 25}{4 \times 25} \\ = \frac{75}{100} \\ = 75\%[/tex]
What is the range of this function? (negative infinity, infinity) left-bracket negative 1, infinity) (negative 1, infinity) (0, infinity)
The range of the function [tex]f(x) = -2(6)^{x} +3[/tex] discovered using exponential function is ( -∞, 3).
What is the range?The difference between the greatest and smallest numbers is called the range.What is an exponential function?
The following equations represent an exponential function: [tex]y=ab^{x} +c[/tex]In which:
a is the initial value.b is the rate of change.c is the vertical shift.As for the range, we have:
If a > 0, the range is (c,∞).If a < 0, the range is (-∞,c).In this problem, the function is given by: [tex]f(x) = -2(6)^{x} +3[/tex]
The coefficients are a = -2 0, b = 6, and c = 3, and the range is (-∞,3).
Therefore, the coefficients are a = -2 0, b = 6, and c = 3, and the range is (-∞,3).
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The complete question is given below:
What is the range of the function f(x) = –2(6x) + 3? (negative infinity, negative 2 Right-bracket (negative infinity, 3) Left-bracket negative 2, infinity) Left-bracket 3, infinity)
Answer:B
Step-by-step explanation:edge lolololololololloll
Use the laplace transform to solve the given initial-value problem. y' + y = (t − 1), y(0) = 5
Using the Laplace transform, the value of y' + y = (t − 1), y(0) = 5 is y(t) = 5e ^ -t + u (t - 1)e^(1-t)
Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in regions of physics, electrical engineering, control optics, arithmetic and sign processing.
y' + y = (t − 1)
y (0) = 5
Taking the Laplace transformation of the differential equation
⇒sY(s) - y (0) + Y(s) = e-s
⇒(s + 1)Y(s) = (5+ e^-s)/s + 1
⇒y(t) = L^-1{5/s+1} + {e ^-s/s + 1}
⇒y(t) = 5 e^-t + u(t -1)e^1-t
The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.
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The table shows some values of a function of the form y
= ax² + bx + c.
V
4
21
5
32
6
45
7
60
8
77
The value of c, the constant of the function y = ax² + bx + c, exists -3.
What is an equation?An equation exists as an expression that indicates the relationship between two or more numbers and variables.
Given that: y = ax² + bx + c
At point (4, 21)
21 = a(4²) + 4b + c .......(1)
At point (5, 32)
32 = a(5²) + 5b + c .........(2)
At points (6, 45)
45 = a(6²) + 6b + c .......(3)
Therefore, the value of a = 1, b = 2 and c = -3.
The value of c, the constant of the function y = ax² + bx + c, exists -3.
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What is the independent variable in this function?
Answer:
p.
Step-by-step explanation:
p is the independent variable.
The dependent one is h.
The value of h depends on the value of p.
please help
the line ABC is tangent to a circle at B centre O with diameter EB the angle DAB = 28
(a) ABE=
(b) EDB=
(c) AOB=
(d) BOD=
(e) OBD=
(f)DBC=
Answer:
A 90°
B 90°
C 62°
D 118°
Hopefully this helps u
What is the independent variable in the following function?
The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
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What is the sign of s^67/t^9 when s < 0 and t > 0?
possible answers:
. positive
. negative
. zero
Answer:
negative
Step-by-step explanation:
[tex]s^{67}<0 \\ \\ t^9>0 \\ \\ \implies \frac{s^{67}}{t^9}<0
[/tex]
Answer:
negativeStep-by-step explanation:
The sign of a product or quotient cannot be determined by the positive number (t), so we can ignore it. The sign of the expression will be negative if and only if there are an odd number of negative factors.
Here, there are 67 (an odd number) negative factors, so the expression will be negative.
the product of 1540 and m is a square number. find the smallest possible value of m
The smallest possible value of m according to the task is; 1/1540.
What is the smallest possible value of m?Since it follows from the task content that the product of 1540 and m is a square number and the smallest possible small number is; 1.
The equation which holds true is; 1540 × m = 1
Consequently, m = 1/1540.
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In the student council elections, five students are running for president, two are running for vice president, two are running for treasurer and three are running for secretary. How many different possible student council teams could be elected from these students?
Using the Fundamental Counting Theorem, it is found that 60 different possible student council teams could be elected from these students.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Considering the number of options for president, vice president, treasurer and secretary the parameters are:
n1 = 5, n2 = 2, n3 = 2, n4 = 3.
Hence the number of different teams is:
N = 5 x 2 x 2 x 3 = 60.
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piecewise function f (x) is defined by f of x is equal to the piecewise function of 3 to the power of the quantity x minus 1 end quantity minus 4 for x is less than or equal to 3 and the quantity negative x squared plus 3 times x plus 4 end quantity over the quantity x squared minus 7 times x plus 12 end quantity for x is greater than 3 Part A: Graph the piecewise function f (x) and determine the range. (5 points) Part B: Determine the asymptotes of f (x). Show all necessary calculations. (5 points) Part C: Describe the end behavior of f (x). (5 points)
The range of the function f(x) is (-∝, 3]
Part A: Graph the piecewise functionThe function definition is given as:
[tex]f(x) = \left[\begin{array}{cc}3^{x-1}-4&x\le 3\\ \frac{-x^2 + 3x + 4}{x^2 - 7x + 12}&x > 3\end{array}\right[/tex]
There are two sub-functions and the domains in the above definition.
Each function would be plotted alongside its domain.
See attachment for the graph of the function f(x)
From the graph of the function, we have the following range of f(x)
Minimum = Negative Infinity
Maximum = 5
Hence, the range of the function f(x) is (-∝, 3]
The asymptotes of f(x)We have the domains to be
x <= 3 and x > 3
This means that the asymptote of f(x) is x = 3
The end behavior of f(x)From the graph, we have:
f(x) increases as x increasesf(x) decreases as x decreasesThis means that the end behavior of f(x) is as x approaches +∝, the function approaches +∝ and as x approaches -∝, the function approaches -∝
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Complete question
A piecewise function f (x) is defined by
[tex]f(x) = \left[\begin{array}{cc}3^{x-1}-4&x\le 3\\ \frac{-x^2 + 3x + 4}{x^2 - 7x + 12}&x > 3\end{array}\right[/tex]
Graph y=8.5x PLS VERY URGENT ANSWER QUICKLY!!!!!!!!!!!!!!!!
The slope of the line is 8.5 and the y-intercept is at the origin as shown in the graph below.
Graph of a linear functionA linear function is a function that has a leading degree of 1. The standard equation for a linear function is expressed as:
y = mx + b
where
m is the slope which is equal to the rate of change of y coordinate to x-coordinates.
b is the y-intercept
Given the following equation
y=8.5x
The slope of the line is 8.5 and the y-intercept is at the origin as shown in the graph below.
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Russ is solving an equation where both sides are linear expressions. he sets the expressions equal to y and graphs the system finding that they are the same line. how should russ interpret this outcome?
The correct option (D).
There are infinitely many intersection points.
What is liner equation?a two-variable equation that, when plotted on a graph, results in a straight line.
What does intersection point mean?The term "point of intersection" refers to the intersection of two lines.
According to the given information:Russ is attempting to solve an equation whose two sides are both linear expressions.
He graphs the system and finds that they are on the same line after setting the expressions to y.
Since both lines are the same, there are an endless number of junction places.
Russ should therefore consider the outcome to be option (D) There are a limitless number of intersections.
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I understand that the question you are looking for is:
Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome? There are no intersection points. There is exactly one intersection point. There are exactly two intersection points. There are infinitely many intersection points.Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome?
A. There are no intersection points.
B. There is exactly one intersection point.
C. There are exactly two intersection points.
D. There are infinitely many intersection points
find the value of p and of q for which x-3 is a common factor of the expressions [tex]x^{2} + (p + q)x-q[/tex] and [tex]2x^2 + (p-1)x + (p+2q)[/tex]
WILL GIVE BRAINLIEST PLS ANSWER
Step-by-step explanation:
Use the Factor Theorem,
" if x-a is a factor of f(x), then f(a) =0,
So here, since x-3 is a factor then f(3)=0,
So first step, plug in 3 for x for the serperate equations.
[tex] {3}^{2} + ( p + q)3 - q = 0[/tex]
[tex]2(3) {}^{2} + (p - 1)3 + (p + 2q) = 0[/tex]
Simplify both equations,
[tex]9 + 3p + 2q = 0[/tex]
[tex]15 + 4 p + 2q = 0[/tex]
Isolate the constants,
[tex]3p + 2q = - 9[/tex]
[tex]4p + 2q = - 15[/tex]
We have a system of equations so let eliminate a variable, by subtracting the two equations.
[tex] - p = 6[/tex]
[tex]p = - 6[/tex]
Plug p back in for any one of the equations to find q.
[tex]3( - 6) + 2q = - 9[/tex]
[tex] - 18 + 2q = - 9[/tex]
[tex]2q = 4.5[/tex]
So p is -6
q is 4.5
