The new function that can be formed after f(x) transforms horizontally 4 units to the right and then vertically 7 units upwards is
H(x) = h(x) = x² + 11x + 37.
How to shift an equation horizontally?
For a function, f; a brand new function d(x) = f(x - h), where h is a constant, is a horizontal shift of the function f; for positive 'h' the graph shifts right and for negative 'h' the graph shifts left.
How to shift an equation vertically?
For a function, f; a brand new function d(x) = f(x) + k, where k is a constant, is a vertical shift of the function f; for positive 'h' the graph shifts up and for negative 'h' the graph shifts down.
Given, the equation is f(x) = x² + 3x + 2
The new equation formed will be = h(x)
Also, the function horizontally shifts 4 units to the right.
Therefore, h(x) = f(x + 4) = (x + 4)² + 3(x + 4) + 2 = x² + 11x + 30
Again, the function formed in h(x) vertically shifts up by 7 units.
Thus, new equation for h(x) is = h(x) + 7 = x² + 11x + 37
Therefore, the required equation for H(x) = h(x) = x² + 11x + 37
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what is 5/3x +1/3 = 13/1/3 + 8/3x
Answer: x = − 116/3
Step-by-step explanation:
Evaluate 5/3x + 1/3 = 13/1/3 +8/3x
Multiply the numbers 5x/3 + 1/3 = 13/1/3 + 8/3x
Simplify 5x/3 + 1/3 = 39 + 8x/3
Multiply both sides 5x/3 × 3 + 1/3 × 3 = 39 × 3+ 8/3x × 3
Simplify the expression 5x+1=117+8x
Move the variable to the left side 5x+1−8x=117
Subtract the terms −3x+1=117
Move the constant to the right side −3x=117−1
Subtract the terms −3x=116
Divide both sides −3x/-3 = 116/-3
Simplify −3x/-3 = 116/-3
Solution x = − 116/3
What is the number in standard form?
QUESTION:
5.8×10−10
Options:
A.0.00000000088
B.0.00000000005008
C.0.0000508
D.0.00000005008
E.0.0000000508
F.0.0000058
5.8×10^-10 in standard form is: 0.00000000058.
What is standard form?Standard form can be defined as the way of written a number of digit in a simple form for easy understanding.
Given data:
5.8 × 10 ^ -10
Now let this scientific notation 5.8 × 10 ^-10 into a standard form.
We know that 5.8×10^-10 can be re-written as :
5.8 ÷ 10 ^-10
= 5.8 × 10×10×10×10×10×10×10×10×10×10
= 5.8 ÷ 10000000000
= 0.00000000058
Hence,
5.8×10^-10 = 0.00000000058
Therefore we can conclude that 0.00000000058 is the standard form of 5.8 ×10 ^-10.
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picture down below
PLS HURRY FIRST GETS BRAINLIEST
Step-by-step explanation:
come on, this is really simple.
you need to put the given values of x into the places, where x appears in the functional expression.
which expression to be used ? that depends on the given value.
x = -1
is -1 >= 0 (to use the case for x >= 0) ? no, it is not.
-1 < 0, so we need to use the expression for x < 0.
y = -1 - 2 = -3
x = 0
is 0 >= 0 ? yes, it is.
so, we need to use the expression for x >= 0.
y = 3×0 + 1 = 0 + 1 = 1
x = 1
is 1 >= 0 ? yes, it is.
so, we need to use the expression for x >= 0.
y = 3×1 + 1 = 3 + 1 = 4
x = 2
is 2 >= 0 ? yes, it is.
so, we need to use the expression for x >= 0.
y = 3×2 + 1 = 6 + 1 = 7
График функции y=-0,5(10-x) Дополнительная информация -2≤x≤12
Leah can run 720 yards in 4.5 minutes. How many yards can she run in 2 minutes at the same rate?
A. 350
B. 320
C. 160
D. 110
By the concept of unitary method she can run 320 yards in 2 minutes at the same rate.
What is meant by unitary method?The unitary method is a technique used to determine the value of a single unit from the value of many units and the value of multiple units from the value of a single unit. We typically utilize it for math calculations. This approach might be helpful for answering questions on ratio and proportion, algebra, and other subjects. "It is a method where we get the value of a single unit from the value of many units and the value of multiple units from the value of a single unit." bra, geometry, etc. Before determining the value of additional or less items, we must first determine the value of one item by dividing it. There are two categories of unitary approaches.
Direct VariationIndirect Variation720 yards = 4.5 minutes
1 minute = 720/4.5
= 160 yards
2 min = 160(2)
= 320 yards
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0.0 mi/hr to 70.0 mi/hr in 10.0 seconds, what would be its final velocity after 5.0 seconds if its starting velocity was 50.0 mi/hr
Based on the calculations, the final velocity of this car is equal to 85.0 mi/hr.
How to calculate the final velocity of this car?In order to determine the final velocity of this car, we would first calculate its acceleration based on the parameters provided. Mathematically, the acceleration of an object can be calculated by using this formula:
a = (V - U)/t
Where:
a represents the acceleration.V represents the final velocity.U represents the initial velocity.t represents the time measured in seconds.Substituting the given parameters into the formula, we have:
a = (70.0 - 0)/10
a = 70.0/10
Acceleration, a = 7.0 mi/hr².
Now, we can determine the final velocity of this car as follows:
V = U + at
V = 50.0 + (7.0)(5)
V = 50.0 + 35.0
Final velocity, V = 85.0 mi/hr.
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Complete Question:
If a car can go from 0.0 mi/hr to 70.0 mi/hr in 10.0 seconds, what would be its final velocity after 5.0 seconds if its starting velocity was 50.0 mi/hr
Evaluate the expression,in simplest form c= 7/10 y=2/15-3y+c
Let's begin by listing out the information given to us:
[tex]undefined[/tex]how many groups of 10 milliliters are in 1 liter explains
There are 100 groups of 10 milliliters in 1 liter
How to determine the number of groups?From the question, the given parameters are
Volume 1 = 10 milliliters
Volume 2 = 1 liter
The number of groups of the first group in the second is calculated as
Groups = Volume 2/Volume 1
Substitute the known values in the above equation
So, we have the following equation
Groups = 1 liter/10 milliliters
Evaluate the quotient
Groups = 100
Hence, the number of groups is 100
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X=-3±2√2
Solve for x
answers are in the photo
goodluck
(12)^1/6
—————
(3)^1/2 (2)^1/3
Answer:
I can't tell if this is division or two separate answers. So, I'll answer both!
Division: 0.222
Answer to (12)^1/6: 2
Answer to (3)^1/2(2)^1/3: 1
Does this table show a proportional relationship? If so, what is the constant of proportionality?
A Yes; 1/5
B Yes; 5
C Yes; 10
D The quantities are not proportional.
We can conclude that (A) yes, the table shows the constant of proportionality of 1/5.
What is the constant of proportionality?The ratio connecting two given values in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.So, the constant of proportionality of the given table:
Formula: k = y/x
So, substitute the values in the formula as follows:
8/40 = 1/510/50 = 1/512/60 = 1/514/70 = 1/5So, yes, the table shows the constant of proportionality of 1/5.
Therefore, we can conclude that (A) yes, the table shows the constant of proportionality of 1/5.
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Which of the following may produce bias? Select all that apply.
The question uses an inaccurate tool.
Some subgroups may be at a disadvantage due to prior experiences.
A medical research study assigns the healthier patients to the group using the new treatment and the sicker patients to the group using the traditional treatment.
Asking school children how they use apps to organize their day.
All students find the question easy.
The things that can lead to bias include:
The question uses an inaccurate tool.
Some subgroups may be at a disadvantage due to prior experiences.
A medical research study assigns the healthier patients to the group using the new treatment and the sicker patients to the group using the traditional treatment.
What is bias?It should be noted that bias simply means anything that leads to a systematic difference between the true parameter.
It should be noted that in a situation where the question uses an inaccurate tool. This will lead to bias and bring about inaccuracy.
Also, using different tools for the patients can lead to bias.
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What's the circumference of a circle with a radius of 5 inches
Answer:
31.4
Step-by-step explanation:
C=2πr=2·π·5≈31.41593in
Leah runs M miles everyday during the week except for Wednesday or Sunday. A. write an algebraic expression that represents the total number of miles leah runs each week B. there are 52 weeks in a year. write an algebraic expression that represents the total number of miles leah runs in a year
A. The algebraic expression that represents the total number of miles Leah runs each week is 5*M.
B. The algebraic expression that represents the total number of miles Leah runs in a year is 260*M.
Leah runs M miles everyday during the week except for Wednesday or Sunday.
We need to write the algebraic expression that represents the total number of miles Leah runs each week. Leah runs for 5 days in a week. The total number of miles run in a week is 5*M.
We need to write the algebraic expression that represents the total number of miles Leah runs in a year. Leah runs 5*M miles in a week. The total number of miles run in a year is (5*M)*52 = 260*M.
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two non-decreasing sequences of nonnegative integers have different first terms. each sequence has the property that each term beginning with the third is the sum of the previous two terms, and the seventh term of each sequence is . what is the smallest possible value of ?
The smallest possible value of the seventh term of the sequence is 104 .
A sequence is an ordered group of items in mathematics where repetitions are permitted and order is important.
Similar to a set, it has members (also called elements, or terms). The size of the series is the amount of elements (potentially infinite). In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important.Let the first two terms of the first sequence be a and b and the first two of the second sequence be c and d.
Computing the seventh term,
we see that 5a + 8b = 5c + 8d.
Note that this means that a and c must have the same value of |8|.
To minimize, let one of them be 0;
We assume that a= 0.
Thus, the smallest possible value of c is 8; and since the sequences are non-decreasing we get d > 8.
To minimize, let d = 8. Thus, 5c + 8d = 40 + 64 = 104.
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Tea that sells for $2.00 a pound is mixed with a different tea that sells for
$5.00 a pound to produce 40 pounds of a custom blended tea that will
sell for $4.25 a pound. How many pounds of the less expensive tea
should be used in the mixture?
(1) 10
(2) 15
(3) 25
(4) 30
Pls help hellooooo I’ve asked this 5 times and nobody as helped me pls pls pls lsl
Answer:
3 should be the answer to your question
My daughter needs help with her homework I’m confused she’s supposed to fill in the missing digits
Answer:
A is 5
B is 3
C is 2
D is 4
E is 3
F is 5
What is the discriminant of the quadratic equation -x^2+6x-4=0?
Answer:
[tex]x = - 3 + - \sqrt{13} [/tex]
Step-by-step explanation:
formula is x=-b+-sqrt b^2-4ac/2a
construct a 95% confidence interval for the mean number of defects per screen for all screens produced by this manufacturer. a) what is the lower limit on the interval? give your answer to three decimal places. 2.077 incorrect: your answer is incorrect. b) what is the upper limit on the interval? give your answer to three decimal places. 2.203 incorrect: your answer is incorrect.
The 99% confidence interval for the population proportion p is 0.833< p < 0.863.
Given that,
x = 3059
n = 3604
Point estimate = sample proportion = x / n =3059/3604=0.848
[tex]1 - \hat p[/tex] = [tex]1-0.848 =0.152[/tex]
At 99% confidence level the z is ,
[tex]\alpha[/tex] = 1 - 99% = 1 - 0.99 = 0.01
[tex]\alpha[/tex]/ 2 = 0.01 / 2 = 0.005
[tex]Z\alpha[/tex]/2 = [tex]Z*0.005[/tex] = 2.576 ( Using z table )
Margin of error = E = [tex]Z\alpha / 2 * (\sqrt(((\hat p * (1 - \hat p)) / n)[/tex]
= [tex]2.576* (\sqrt((0.848*0.152) /3604 )[/tex]
=0.015
A 99% confidence interval for population proportion p is ,
[tex]\hat p - E < p < \hat p + E[/tex]
0.848-0.015< p <0.848+ 0.015
0.833< p < 0.863
Hence, the 99% confidence interval for the population proportion p is 0.833< p < 0.863.
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20. If the measure of angle 5 = x, which angles have a measure of 180 - x? Select all that apply.
(A) angle 2
B angle 3
C) angle 7
D angle 11
Answer:
my best answer is C) angle 7. But there is not much context so i'm not 100% sure
Step-by-step explanation:
Can someone please help me solve for Y and X. Question number 5
Using the triangle sum theorem, x = 7 and y = 18.
What is the Triangle Sum Theorem?The theorem that says that all the interior angles of a triangle will be equal to 180 degrees is referred to as the triangle sum theorem.
In the diagram given, since vertical angles are congruent, therefore:
(11x - 9) + (6x - 2) + 72 = 180 [triangle sum theorem]
Solve for x
11x - 9 + 6x - 2 + 72 = 180
17x + 61 = 180
17x = 180 - 61
17x = 119
x = 7
Also,
(5y - 8) + (11x - 9) + 30 = 180 [triangle sum theorem]
5y - 8 + 11x - 9 + 30 = 180
5y + 13 + 11x = 180
Plug in the value of x
5y + 13 + 11(7) = 180
5y + 13 + 77 = 180
5y + 90 = 180
5y = 180 - 90
5y = 90
y = 90/5
y = 18
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In the figure below, N lies between M and P.
1
Find the location of N so that MN is of MP.
1/2 of MP
Answer:
8
Step-by-step explanation:
See attached image.
I need some help please. Given the functions, complete the sections. a) Find the intercepts with the axes. b) Indicate the basic function that you will use to graph it. c) Identify the transformations that your graph will undergo, starting from its basic function. d) Draw the sketch showing the transformations, taking into account all the previous sections. Highlight f(x) with a pen or marker. e) Determine its domain and range.[tex]f(x) = - \frac{1}{4} \sqrt{8 - 4x} + 1[/tex]
a)
The x-intercept can be found as:
[tex]\begin{gathered} f(x)=0 \\ so\colon \\ -\frac{1}{4}\sqrt[]{8-4x}+1=0 \\ -\frac{1}{4}\sqrt[]{8-4x}=-1 \\ \sqrt[]{8-4x}=4 \\ 8-4x=16 \\ 4x=8-16 \\ 4x=-8 \\ x=-\frac{8}{4} \\ x=-2 \end{gathered}[/tex]Therefore, the x-intercept is: (-2,0)
The y-intercept can be found evaluating the function for x = 0, so:
[tex]\begin{gathered} f(0)=-\frac{1}{4}\sqrt[]{8-4(0)}+1 \\ f(0)=1-\frac{\sqrt[]{2}}{2} \\ f(0)\approx0.29 \end{gathered}[/tex]b) The parent function for this is given by:
[tex]g(x)=\sqrt[]{x}[/tex]c)
1st: A reflection over y-axis:
[tex]\begin{gathered} y=g(-x) \\ y=\sqrt[]{-x} \end{gathered}[/tex]2nd: A horizontal compression:
[tex]\begin{gathered} y=g(-4x) \\ y=\sqrt[]{-4x} \end{gathered}[/tex]3rd: A horizontal translation 8 units to the left:
[tex]\begin{gathered} y=g(x+8) \\ y=\sqrt[]{-4x+8}=\sqrt[]{8-4x} \end{gathered}[/tex]4th: A reflection over y-axis:
[tex]\begin{gathered} y=-g(x) \\ y=-\sqrt[]{8-4x} \end{gathered}[/tex]5th: A vertical compression:
[tex]\begin{gathered} y=\frac{1}{4}g(x) \\ y=-\frac{1}{4}\sqrt[]{8-4x} \end{gathered}[/tex]6th: A vertical translation 1 unit up:
[tex]\begin{gathered} y=g(x)+1 \\ y=-\frac{1}{4}\sqrt[]{8-4x}+1 \end{gathered}[/tex]d)
Where the blue graph is the parent function:
[tex]g(x)=\sqrt[]{x}[/tex]And the red graph is the function after the transformations:
[tex]f(x)=-\frac{1}{4}\sqrt[]{8-4x}+1[/tex]e)
The domain and the range are:
[tex]\begin{gathered} D\colon\mleft\lbrace x\in\R\colon x\le2\mright\rbrace \\ R\colon\mleft\lbrace y\in\R\colon y\le1\mright\rbrace \end{gathered}[/tex](04.01 HC)
A person with type A blood can donate red blood cells to people with type A or type AB
blood. About 31% of the US population has type A blood. You are asked to design a
simulation to determine the probability that at least 4 of 10 people will have type A blood.
Part A: Conduct five trials using the following table of random digits: (5 points)
96299 07196 98642 20639 23185 56282
94168
86280
59225
69929 14125 38872
18192 08710 80777 84395 69563
70406 18564 69273 72532 78340 36699
46376 58596 14365 63685 56555 42974 72944 96463 63530 24152
47352 04266 74017 79319 70170 96572 08523 56025 89077 57678
71622 35940 81807
03272 41230 81739
74797
Part B: Based on your simulation, what is the probability that at LEAST 4 of 10 people will
have type A blood? (5 points)
Answer:31%
Step-by-step explanation:
Let f (x) = 2x - 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following. Find f(x) + h(x)
The value of f(x) + h(x) when f(x) = 2x - 1 and h(x) = x² + 1 is x² + 2x.
Addition of linear functions:
Addition of two individual functions, a(x) and b(x); linearly, results in the formation of the functional addition, c(x) of the two functions, such as:
c(x) = a(x) + b(x) = (a+b)(x) – (i)
The addition of the functions strictly restricts to simple linear addition without any pre-defined constraints.
Given, f(x) = 2x - 1, g(x) = 3x and h(x) = x² + 1
Using the available formula in (i), we get
f(x) + h(x) = (f + h)(x) = (2x - 1) + (x² + 1) = x² + 2x = x(x + 2), which is a quadratic equation.
Thus, the required value of f(x) + h(x) is x² + 2x.
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Susan is unpacking a full box after moving. She removes a 9 in. x 18 in. x 20 in. computer from the box below. How much volume do the rest of the items in the box take up (in cubic inches)?
The volume the rest of the items in the box take up (in cubic inches) is (x-3240) cu in.
What is volume?
Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m^3, cm^3, in3, etc.Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.Various forms have various volumes.Let the volume of the full box be = x cu in
The volume of the computer box = 9 in. x 18 in. x 20 in. = 3240 cu in
Volume the rest of the items in the box take up (in cubic inches)
= x cu in - 3240 cu in = (x-3240) cu in
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A store owner mixes 2 Ib of candy that costs x dollars per pound with 3 Ib of candy that costs $1.50 per pound. She sells the mix for $2.50 per pound.
The 2lb candy cost the owner $8 and the 3lb candy cost the owner $4.5
What is the cost of 2lb candyThe total weight of the candy is
[tex]3 + 2 = 5[/tex]
Let's write equation for this.
[tex]3(1.50) + 2x = 2.5(5)\\4.5 + 2x = 12.5\\12.5 - 4.5 = 2x \\8 = 2x\\x = 4[/tex]
The cost of the 2 pound candy is $4 per unit and the store owner spent $8 in the 2lb candy.
The cost of 3 pound candy was $4.5
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Justin is playing tennis. When serving, he stands 12 feet away from the net, which is 3 feet tall. The ball is served from a height of 7.5 feet. Justin thinks the ball travels about 21.4 feet before it hits the ground 8 feet from the net on the opposite side.
a) How far does the ball travel?
b) What assumptions did you make to solve the distance the ball travels?
c) What mathematical practice did you use to solve this problem?
Regarding the situation described, we have that:
a. The ball travels 21.4 feet.
b. The assumption is that the ball was served at an angle of 90º.
c. The Pythagorean Theorem was used to solve this problem.
Pythagorean TheoremThe Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, it is found that:
The vertical change in the height of the ball was of 7.5 feet, as it was served from a height of 7.5 and hit the ground.The horizontal change in the height of the ball is of 12 + 8 = 20 feet, as he served 12 feet from the net, and the ball hit the ground 8 feet from the net on the opposite side.Assuming that the ball was served at an angle of 90º, the distance traveled by the ball is the hypotenuse of a right triangle of legs 7.5 feet and 20 feet, hence:
d² = 7.5² + 20².
d = sqrt(20² + 7.5²)
d = 21.4 feet. (which is Justin's estimate).
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Suppose that 11 inches of wire costs 66 cents.
At the same rate, how much (in cents) will 21 inches of wire cost?
Answer:
8 inches can be purchased for 32 cents.
Write the equation of the line that passes through the points (7,-6)(7,−6) and (3,8)(3,8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The equation of the line is y = -0.35x – 3.55
Given,
The gradient of the line between two points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).
Since the line passes through the points (7,-6) and (3,8),
• (x₁, y₁) = (7,-6) and
• (x₂, y₂) = (3,8).
So, substituting the values of the variables into the equation, we have
m = (y₂ - y₁)/(x₂ - x₁).
m = (8 - (-6))/(3 - 7).
m = (8 + 6)/ -4
m = 14/-4
m = -3.5
The equation of the line passing through the point (x₁, y₁) in point-slope form is given by
y - y₁ = m(x - x₁) where
• m = gradient =- 0.35 and
• (x₁, y₁) = (7, -6)
So, substituting the values of the variables into the equation, we have
y - y₁ = m(x - x₁)
y - (-6) = -0.35(x - 7)
y + 6 =-0.35 (x - 7)
y = (-0.35x + 2.45 – 6)
y = -0.35x – 3.55
So, the equation of the line is y = -0.35x – 3.55
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