Increasing the value of a increases the initial value of our exponential, and also increases the rate of growth of the function.
How would increasing the value of a change the graph?
Y assume we have an exponential equation of the form:
y = a*b^x + c
In this case, a is what we know as the "initial value" of the exponential.
Notice that when we evaluate in x = 0, we get:
y = a*b^0 + c
y = a + c
So increasing a will increase the initial value of what we are representing, but it will also increase the "rate" at which our function increases when x increases.
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What is the slope of the line that passes through the points (10, 3) and
(7,0)? Write your answer in simplest form.
Answer:
slope = 1
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (10, 3 ) and (x₂, y₂ ) = (7, 0 )
m = [tex]\frac{0-3}{7-10}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1
xy =8 inches wy =24 and xz=48 inches height from the ground to the base of the window is?
The height of the ground from the base of the window is 144 inches.
How to find the side of a right angle triangle?One angle of a right angle triangle is equals to 90 degrees.
Therefore, the sides and angles of the right triangle can be found using trigonometric ratios.
tan x = WY / XY
tan x = opposite / adjacent
tan x = 24 / 8
x = tan⁻¹ 3
x = tan⁻¹ 3
x = 71.5650511771
x = 71.60°
tan 71.60 = h / 48
cross multiply
h = 48 tan 71.60
h = 48 × 3
h = 144 inches
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Can someone help me please?
A.1/5
B.7/10
C.3/10
D.1/2
Using it's concept, the probability that a student plays basketball or soccer is given as follows:
B. 7/10.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
P(A or B) is the probability that a student plays basketball or soccer, hence, from the Venn diagram:
7 students play at least one of the sports, which are: Fran, Juan, Ian, Ella, Mickey, Mai and Marcus.There is a total of 10 students, which are the 7 that plays at least one of the sports, plus Karl, Jada and Gabby.Hence the probability P(A or B), that is, the probability that a student plays basketball or soccer, is given as follows:
p = 7/10.
Which means that option B is correct.
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Can you please help me with this question
When you have negative exponents, you flip it around. Let me give you two examples below.
[tex]x^{-5} = \frac{1}{x^{5} }[/tex]
[tex]10^{-2} = \frac{1}{10^{2} }[/tex]
Therefore you will be doing: [tex]\frac{4}{1} * \frac{1}{10^{2} } = \frac{4}{1} * \frac{1}{100} } = \frac{4}{100} = \frac{1}{25}[/tex]
Your final answer is 1/25.
Brainliest would make my day :)
la+xl/2 - la-xl/2, if a= -2, x= -6
HELP!!!
Answer: 2
Step-by-step explanation:
1) substitute
2) calculate the difference before the absolute value
3) calculate the absolute value
4) convert into whole numbers/reduce
5) subtract the whole numbers
this is what i think might be wrong
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
The surface area of the shape is 117.8 km²
Surface area of a coneFrom the question, we are to determine the surface area of the figure
The given figure is a cone.
Total surface area of a cone = Area of circular part + Curved surface area
Total surface area of a cone = πr² + πrl = πr(r + l)
Where r is the radius
and l is the slant height
From the given information,
r = 3 km
l = 9.5 km
The total surface area of the cone = π×3(3+9.5)
The total surface area of the cone = 3π(12.5)
The total surface area of the cone = 117.8 km²
Hence, the surface area of the shape is 117.8 km²
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HEY PLEASE HELP ASAP
Answer:
[tex]\dfrac{8y-43}{(y-1)(y-8)}[/tex]
Explanation:
[tex]\rightarrow \dfrac{5}{y-1} +\dfrac{3}{y-8}[/tex]
make the denominators similar
[tex]\rightarrow \dfrac{5(y-8)}{(y-1)(y-8)} +\dfrac{3(y-1)}{(y-8)(y-1)}[/tex]
Join both the fraction
[tex]\rightarrow \dfrac{5(y-8)+3(y-1)}{(y-1)(y-8)}[/tex]
simplify the expression
[tex]\rightarrow \dfrac{5y-40+3y-3}{(y-1)(y-8)}[/tex]
[tex]\rightarrow \dfrac{8y-43}{(y-1)(y-8)}[/tex]
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's simplify ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{5}{y - 1} + \cfrac{3}{y - 8} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{5(y - 8) + 3(y - 1)}{(y - 1)(y - 8)} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{5y -40 + 3y - 3}{y {}^{2} - y - 8y + 8} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{8y -43}{y {}^{2} - 9y + 8} [/tex]
Identify an equation in standard form for a hyperbola with center (0, 0), vertex (−5, 0), and focus (−6, 0).
An equation in standard form for a hyperbola with center (0, 0), vertex (-5, 0), and focus (-6, 0) is given by y²/25 - x²/9 = 1.
What is an equation?An equation can be defined as a mathematical expression which is used to show and indicate that two (2) or more numerical quantities are equal.
How to determine the equation of a hyperbola?Mathematically, the equation of a hyperbola in standard form is given by:
[tex]\frac{(y\;-\;k)^2}{a^2} - \frac{(x\;-\;h)^2}{b^2} = 1[/tex]
Given the following data:
Center (h, k) = (0, 0)
Vertex (h+a, k) = (-5, 0)
Foci, F = (h+c, k) = (-6, 0) and F' = (6, 0)
Also, we can logically deduce that the value of a and c are -5 and -6 respectively.
For the value of b, we would apply Pythagorean's theorem:
c² = a² + b²
b² = c² - a²
b² = (-6)² - (-5)²
b² = 36 - 25
b² = 9.
b = √9
b = 3.
Substituting the given parameters into the equation of a hyperbola in standard form, we have;
[tex]\frac{(y\;-\;k)^2}{a^2} - \frac{(x\;-\;h)^2}{b^2} = 1\\\\\frac{(y\;-\;0)^2}{-5^2} - \frac{(x\;-\;0)^2}{3^2} = 1\\\\\frac{y^2}{-5^2} - \frac{x^2}{3^2} = 1\\\\\frac{y^2}{25} - \frac{x^2}{9} = 1[/tex]
y²/25 - x²/9 = 1.
In conclusion, we can logically deduce that an equation in standard form for a hyperbola with center (0, 0), vertex (-5, 0), and focus (-6, 0) is given by y²/25 - x²/9 = 1.
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Select the correct answer from each drop-down menu.
Since AC, MN, and DB intersect at O,
( A. Transitive property of congruence.)
( B. Linear pair postulate.)
( C. Congruent supplements theorem.)
( D. Vertical angles theorem.)
It is given that
( A. Linear pair postulate.)
( B. Vertical angles theorem.)
( C. Transitive property of congruence.)
( D. Congruent supplements theorem.).
The paragraph looks like:
Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.
In the question, we are asked to convert the given proof to the paragraph format, where the proof is already given to us.
The proof given to us is:
Statements________________________Reasons
1. AC, MN, and DB intersect at O.______1. given
2. ∠AOM ≅ ∠NOC__________________2. vertical angles theorem.
3. ∠MOD ≅ ∠BON__________________3. vertical angles theorem.
4. ∠BON ≅ ∠NOC__________________4. given.
5. ∠AOM ≅ ∠MOD_________________5. transitive property of congruence.
To convert this proof to the paragraph format, we need to translate each statement along with its reason in the paragraph.
Thus, the paragraph looks like:
Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.
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3.
Determine how much this home would cost to replace: 2,600 square feet at $86.00 per square foot
Answer: $
Answer: $223,600
Step-by-step explanation:
Since it is $86 per square foot and you're replacing the 2,600 square foot house you would just take 2,600 × 86 and get 223,600 dollars.
Fifteen students were divided into two classrooms in a ratio of 1:2.
How many students were in each classroom?
14) Adelina is comparing prices for two brands of health and energy bars at the local grocery store.
She wants to get the best price for each bar. Feel Great energy bars are $18 for 12 bars. Super
Power bars cost $21.75 for 15 bars.
a) Write an equation to find the price for each bar of the Feel Great brand.
b) Write an equation to find the price of each bar for the Super Power brand.
c) Which bar should Adelina buy? Explain your reasoning.
The bar which Adelina should buy is super power brand because it cost less than feel great energy bar at $1.45 per bar
Unit priceFeel great energy bars = Total cost / number of bars
= $18 / 12
= $1.5 per bar
Super power brand = Total cost / number of bars
= $21.75 / 15
= $1.45 per bar
Therefore, the bar which Adelina should buy is super power brand because it cost less than feel great energy bar at $1.45 per bar
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Re-write the quadratic function below in Standard Form y=-5(x+1)²+7
Answer:
y = - 5x² - 10x + 2
Step-by-step explanation:
y = - 5(x + 1)² + 7 ← expand (x + 1)² using FOIL
= - 5(x² + 2x + 1) + 7 ← distribute parenthesis by - 5
= - 5x² - 10x - 5 + 7 ← collect like terms
= -5x² - 10x + 2 ← in standard form
Answer: y = -5x² - 10x + 2
Step-by-step explanation:
Given quadratic function
y = -5 (x + 1)² + 7
Given requirement
Quadratic Standard Form: y = ax² + bx + c
Simplify the exponents
y = -5 (x + 1) (x + 1) + 7
y = -5 (x² + x + x + 1) + 7
y = -5 (x² + 2x + 1) + 7
Expand the parenthesis by distributive property
y = (-5) · x² + (-5) · 2x + (-5) · 1 + 7
y = -5x² + (-10x) + (-5) + 7
y = -5x² - 10x - 5 + 7
Combine like terms
[tex]\Large\boxed{y=-5x^2-10x+2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The summary of the given data is are as follows :-
Minimum: 11
Lower quartile:11
Median:24
Upper quartile:34
Maximum:45
Interquartile range:23
Given :- 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45
Minimum = The smallest number of data
Thus Minimum = 11
Maximum = The largest number of data
Thus Maximum = 45
Median = The middle number of the data if data consists of odd number of elements
Thus Median = 45
Lower quartile = The median of the lower half of data
Thus Lower quartile = 11
Upper quartile = The median of the upper half of data
Thus Upper Quartile = 34
Interquartile range = The difference of upper and lower quartiles,
Thus Interquartile range = 34 -11 = 23
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Adult men have heights with a mean of 69. 0 inches and a standard deviation of 2. 8 inches. find the z-score of a man who is 71. 9 inches tall. (to 4 decimal places)?
The value of the z score is 1.03.
According to the statement
we have given that the value of mean and standard deviation and we have to find the value of the z score.
So, For this purpose we know that the
Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.
And the given values are:
mean value = 69 inches
s.d value = 2.8 inches
And the value of x is 71.9 inches.
So, The Z score is
z = x - mean / standard deviation
substitute the values in it then
z = 71.9 - 69 / 2.8
then
z = 2.9 /2.8
z = 1.03
So, The value of the z score is 1.03.
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Which of the following is true with respect to the following functions:
The option that is true with regard to the following functions is Option B. "The domain g(x) and h(x) include all real number while the domain of i(x) and h(x) are restricted"
What is the explanation for the above?Lets examine f(x) = 3x + 14Note that this function is indicative of a straight-line. See the attached graph for function 1. Note that it doesn't have any end points. That is, it is Asymptote.
Let us examine h(x) = 3ˣ + 1This represents an exponential graph. Just like the function above it doesn't have any end point. It however has an asymptote:
y = 0
Let us look at F'(x) = Log₃ (x = 1).
This is indicative of logarithm graph. It doesn't have any end but has an asymptote x == 0
Let us take a look at g(x) = X⁴ + 3x² - 14Notice that in the mid point there is an end point given as (0, -14). Thus, it is correct to state that the function in Option B is the only one that exhibits end behavior and as such is restricted.
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Urgent!!!!!!!!!!!!!!!!!!
A bucket contains exactly 3 marbles, one red, one blue and one green. a person arbitrarily pulls out each marble one at a time. What is the probability that the last marble removed is non-red?
The probability that the last marble removed is non-red is 2/3.
According to the given question.
Total number of marbles in a bucket = 3
And, a person arbitary pulls out each marble one at a time.
So, there are 6 possible sequences of removing 3 marbles.
Let R be the red marble, B be the blue marble and G be the green marble.
The possible sequences or sample space for removing marbles are: {RBG, RGB, BGR, BRG, GRB and GBR}.
Let A denotes the event of removing the non-red marbles at the last.
The favorable cases for event A are: RBG, RGB, BRG and GRB.
As, we know that probability of any event is calculated as by taking the ratio of total number of favorable outcomes to the total number of outcomes.
Thereofre,
The probability that the last marble removed is non-red
= 4/6
= 2/3
The probability that the last marble removed is non-red is 2/3.
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Which expression represents the following statement? Multiply 6 by 3, and then subtract the quotient of 18 and 9.
A) 6 x (3 ÷ 18) + 9
B) 6 + 3 + (18 ÷ 9)
C) (6 x 3) − 18 ÷ 9
D) 6 x (3 + 18) + 9
Answer:
C) (6 x 3) - 18 ÷ 9
Step-by-step explanation:
I'll solve this question by writing down every step and doing it one by one.
1. Multiply 6 by 3
--> This will be represented as 6 x 3.
2. Subtract the quotient of 18 and 9
--> The quotient is a number resulting in a division of another number. In this case, 18 is bigger than 9, so the quotient will be: 18 ÷ 9.
--> Since we are subtracting this from the equation we got earlier, it can be expressed as (6 x 3) - (18 ÷ 9)
This equation is the same as C) (6 x 3) - 18 ÷ 9, so C is our final answer.
Which monomial is a perfect cube
Answer:
A perfect cube monomial must have three identical root , such that the product of the roots equal the perfect square monomial . The coefficient of the monomial must be divisible by 3 . Any monomial can be a perfect cube root .
Step-by-step explanation:
1.)1000=10 cube
2.) 729=9 cube
3.) 512=8 cube
4.) 343=7 cube
5.) 216=6 cube
6.) 125=5 cube
7.) 64=4 cube
8.) 27=3 cube
9.) 8=2cube
10.) 1=1 cube
HELP PLEASE. Hector built a tent shaped like a rectangular pyramid. The volume of the tent is 56 cubic ft. The area of the base of the tent is 24 square ft. What is the hieght of Hectors tent in feet?
The height of the rectangular pyramid is 7 ft.
How to get the height of the rectangular pyramid?
First, we know that the volume of a rectangular pyramid is given by:
[tex]V = B*H/3[/tex]
Where B is the base, H is the height.
First, we know that the volume is 56 ft³, and the base is 24ft², then we can replace these two in the volume equation to get:
[tex]56 ft^3 = 24ft^2*H/3[/tex]
Solving that for H, we get:
[tex]H = 3*(56ft^3/24ft^2) = 7ft[/tex]
The height of the rectangular pyramid is 7 ft.
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15 The tennis team is selling tickets to a car wash for $6. When they do not
sell very many tickets, the team decreases the price 25%. What is the
new cost of a ticket?
Show your work.
Answer: $4.50
Step-by-step explanation:
Original Price: $6
Discount: 25%
Discounted Price: 6*25%= $1.5
$6-$1.5= $4.5
PLEASE ITS MY LAST QUESTION
Answer:
[tex]y = - \frac{1}{4} x - 10[/tex]
Step-by-step explanation:
The negative reciprocal of 4 is -1/4.
Let's substitute in our values, to find the y-intercept:
[tex]y = - \frac{1}{4} x + c[/tex]
[tex] - 11 = - 1 + c[/tex]
[tex]c = - 10[/tex]
Finally, our full equation is:
[tex]y = - \frac{1}{4} x - 10[/tex]
.Which statement is true about two ordered pairs
that are the same except for the signs of the
numbers?
A. Their points are reflections.
B. Their points are on the horizontal axis.
C. Their points are on the vertical axis.
D. Their points are in different quadrants.
Answer
The statement that is true about two ordered pairs that are the same except for the signs of the numbers is their points are in different quadrants. Option D
What are ordered pairs?Ordered pairs are known to be pairs of numbers that are used locate a point in the rectangular coordinate plane
They are written as (x ,y)
where
x is the x-coordinate y is the y-coordinateIt is important to note that the location of the ordered pair in the quadrants determines the sign of the x and y coordinates.
The signs of the ordered pairs are given as;
When (x , y) is in Quadrant I then both x and y are positive
(x , y) is in Quadrant II then x is negative and y is positive (x , y) is in Quadrant III then both x and y are negative (x , y) is in Quadrant IV then x is positive and y is negativeTherefore, the statement that is true about two ordered pairs that are the same except for the signs of the numbers is their points are in different quadrants. Option D
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PLEASE ANSWER QUICKLY!!!! THE FIRST ONE GETS BRAINLIEST OR 5 STARS!!! For consecutive weeks, the manager of a local restaurant collected data on the number of cheese pizzas sold each week. The data is shown in the scatterplot below.
Can the given line be used to make reasonable predictions of the number of cheese pizzas that Will be sold in upcoming weeks? Explain. (graph is below)
Answer:
Yes
Step-by-step explanation:
The given line is an average of the data points.
2. Select true or false for each statement about the data above.
A. The most common length of ribbon is 11/
B. The sum of the longest and shortest lengths is 20¹
C. The difference between the longest and shortest
lengths is 2.
X
+
11
-
215
Part Two
A group of children picked oranges and made orange juice. The line plot below shows
the amount of juice each child made. Use the line plot below to answer questions 3-7.
X
x x
X
+
N
X
+
+ +
2²/12 2²/ 2/²/
Quarts of Orange Juice Made
3. What is the greatest amount of juice?
True False
416
True False
True False
XX
+
N
516
4. What is the least amount of juice?
5. What is the sum of the least and greatest amount of juice? Show your work.
X
+
M
6. What is the difference between the greatest and least amount of juice? Show your
work.
7. If the children were to share the juice equally, how much would each child get?
Show your work.
A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
What is a line plot?A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
Based on the data provided in the complete question, we can logically deduce the following points:
Length of ribbon (11 1/4) = 3.Length of ribbon (10 3/4) = 1.Length of ribbon (10 1/2) = 1.Length of ribbon (10 7/8) = 1.Length of ribbon (10 5/8) = 1.Length of ribbon (9 7/8) = 1.In conclusion, graph C shown in the image attached below is a line plot which correctly shows the data from the table above.
The most common length of ribbon is 11 1/4: True.
The sum of the longest and shortest lengths is 20 1/8: False.
Sum = 11 1/4 + 9 7/8
Sum = 21 9/8 ≠ 20 1/8.
The difference between the longest and shortest lengths is 2 1/8: False.
Difference = 11 1/4 - 9 7/8
Difference = 1 3/8 ≠ 2 1/8 .
Part Two.The greatest amount of juice is equal to 3.
The least amount of juice is equal to 1 4/6.
The sum of the least and greatest amount of juice is:
Sum = 1 4/6 + 3
Sum = 4 4/6 = 4 2/3.
The difference between the greatest and least amount of juice is:
Difference = 3 - 1 4/6
Difference = 8/6 = 4/3.
How much would each child get?If the children were to share the juice equally, the amount of juice each would get should be calculated by determining the mean:
Mean = [F(x)]/n
Mean = (1 4/6 + 2 + 2 + 2 + 2 2/6 + 2 5/6 + 2 5/6 + 3)/8
Mean = 18.7/8
Mean = 2.3375 = 2 27/80.
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Complete Question:
Katie recorded the length, in inches, of the ribbon pieces she was going to use for a project. Use this information for questions 1 and 2.
11 1/4, 11 1/4, 10 3/4, 10 1/2, 10 7/8, 10 5/8, 9 7/8, 11 1/4,
1. Which line plot correctly shows the data?
The two rectangles are similar. which is the correct proportion for corresponding sides?
Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.
According to the statement
we have given that the two rectangle which are similar to each other and we have to find the correct proportion for corresponding sides of rectangles.
So, we know that the
For the two rectangles to be similar, it means the ratio of their corresponding sides must be the same.
Looking at the two rectangles, the corresponding sides are pf the rectangles are:
4 m side corresponds to 8 m side in rectangle A
12m side corresponds to the 24 m side in rectangle B.
Then
The ratios of the both rectangles are:
In rectangle A is 8/4 = 2
In rectangle B is 24/12 = 2
From this it is clear that the ratios are equal.
Thus, the scale factor is 2
Since 8/4 = 24/12, we can rearrange to get;
12/4 = 24/8.
So, Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
The two rectangles are similar with sides 4 m side corresponds to 8 m side in rectangle A and 12m side corresponds to the 24 m side in rectangle B.which is the correct proportion for corresponding sides?
A. 12/3 = 24/12.
B. 12/2 = 27/8.
C. 11/4 = 23/8.
D. 12/4 = 24/8.
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PLEASE HELP!!
Part C
What is the difference of the x-coordinate of point A and the x-coordinate of point B?
The difference of the x-coordinate of point A and the x-coordinate of point B is 0
Coordinates of a pointThe coordinate of a point on an xy-plane is written in the form (x, y). The given figures are circles A and B where the circle A is greater than circle B.
The position of the dots in both sides are positioned at the centre and as such the coordinate point at the centre of both circle will be the origin (0, 0)
According to the question, we are to find the difference of the x-coordinate of point A and the x-coordinate of point B
x-coordinate of pint A = 0
x-coordinate of point B = 0
Take the difference
Difference = 0 - 0
Difference = 0
Hence the difference of the x-coordinate of point A and the x-coordinate of point B is 0
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When rolling two dice what is the probability of rolling a sum of six or two even numbers.
The probability of rolling a sum of six or two even numbers.
is P = 1/3
How to find the probability?
Here we are rolling two dice, and each dice has 6 possible outcomes, then the total number of outcomes is:
6*6 = 36
Now, the outcomes that given a sum of 6 are:
dice 1 dice 2.
1 5
5 1
2 4
4 2
3 3
We have 5 outcomes there.
The outcomes where both numbers are even are:
dice 1 dice 2.
2 2
2 4
4 2
4 4
4 6
6 2
6 4
6 6
We have 8 outcomes here (such that 2 are in the ones we counted before).
Then the total number of outcomes that either add to 6 or have both even numbers are:
5 + 8 - 2 = 12
Then 12 out of 36 outcomes either add to 6 or have both even numbers, this means that the probability is:
P = 12/36 = 1/3
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This year consumers purchased 5,234,267,990 bottles of water. Last year
consumers purchased 1,000,900,999 bottles of water. Which is the best
estimate of the number of bottles sold this year and last year?
OA) 4,000,000,000
OB) 6,000,000,000
OC) 6,235,168,989
OD) 7,000,000,000
Answer: B
Step-by-step explanation:
First, find the sum of the bottles, which is 6,235,168,989 which is not an estimate.
Rounding it to the nearest billion, the answer is 6,000,000,000 or B)
