To solve a, we need to replace x = 0 in the formula of the function:
[tex]\begin{cases}f(x)=x^2+5 \\ x=0\end{cases}\Rightarrow f(0)=0^2+5=5[/tex]The y value when x = 0 is 5.
b is asking the same as a but in a different way. The y-intercept of a function is when x = 0, we just calculated that. The point of y-intercept is (0, 5)
Finally, to solve c, we need to find the values of x that gives us a value of f(x) = 46:
[tex]f(x)=46\Rightarrow46=x^2+5[/tex]Then solve:
[tex]\begin{gathered} x^2=46-5 \\ x=\pm\sqrt[]{41} \end{gathered}[/tex]Remember that we must that plus-minus the value when we take square root. ± √41 is the answer to c.
Which is a counterexample for the conditional statement shown?
If the numerator of a fraction is larger than the denominator of the fraction, then the fraction is greater than 1.
any fraction with a denominator of 0
any fraction with a numerator of 0
any fraction with a positive numerator and a negative denominator
any fraction with a negative numerator and a positive denominator
Answer: Choice C
any fraction with a positive numerator and a negative denominator
======================================================
Explanation:
Consider the fraction 10/(-5) where we divide 10 over -5
The numerator 10 is larger than the denominator -5, as any positive number is larger than a negative number. But 10/(-5) simplifies to -2 which is not greater than 1.
This is one counterexample to show that the original conditional statement is false.
Determine whether the sequence 15,13,11,9 is an arithmetic sequence if yes, identify the common difference.
The sequence is not an arithmetic sequence because. The n-term for an arithmetic sequence is:
[tex]a_n\text{ = }a_1\text{ + }(n-1)d[/tex]where d is the difference between two consecutive numbers. In this case d = 2. Because
15-13 = 2
13-11 = 2
11- 9 = 2
now, the first term for 15,13,11,9 is 15 = a_1, the second term would be:
[tex]a_2\text{ = }a_1\text{ + }(2-1)d\text{ }[/tex]that is equivalent to say:
[tex]a_2\text{ = 15 + }(2)2=19\ne13\text{ }[/tex]So we can conclude that 15,13,11,9 is not an arithmetic sequence.
The combination of both integer and rational numbers gives
Answer:
Step-by-step explanation: Answer is real number
Give a parametric representation of the parabola y = (x+7)^2 -5
We have to find the parametric representation of the parabola y = (x+7)² - 5, which is represented in vertex form.
Parametric representations use a third variable on which we define x and y.
We will call this variable t.
We can start with defining t as:
[tex]\begin{gathered} t=x+7 \\ \Rightarrow x(t)=t-7 \end{gathered}[/tex]We then have already x in function of t.
Then, we can use the definition of t to find y(t):
[tex]\begin{gathered} y(t)=(x(t)+7)^2-5 \\ y(t)=(t-7+7)^2-5 \\ y(t)=t^2-5 \end{gathered}[/tex]We then have x and y defined in function of t.
Answer: we can represent the parabola in a parametric form as
x(t) = t-7
y(t) = t² - 5
five friends are going to share 1/2 of a pizza. How much of a whole pizza will each friend eat?which equation can be used to solve the problem above?A.5÷1/2=nB.1\2÷5=nC.n÷5=1/2D.n÷1\2=5
In this case the answer is very simple .
Step 01:
Data
5 friends
1/2 pizza
Step 02:
We must distribute the pizza among 5 friends.
[tex]\frac{\frac{1}{2\text{ }}\text{ pizza}}{5\text{ friends}}\text{ = n}[/tex]The answer is:
Option B.
1\2÷5=n
A family has 6 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 6 girls if it is known the family has at least one girl.
The probability that the family has 6 girls if it is known the family has at least one girl is; 3.125%
What is the Probability?
We are told that each child has the same chance of being a boy or a girl and as such we can say that probability is 1 in 2, or 0.50 or 50%.
Since the family must have at least one girl, if we assume that the first child is a girl, the the probability of the second child being a girl is 50%.
The probability of the other 5 children all being girls is:
(1/2) * (1/2) * (1/2) *(1/2) * (1/2) = 1/32.
This Probability expressed as a decimal or percentage represents a probability that we have as; 1/32 = 0.03125 = 3.125%.
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y + 7 ≥ –1 and y∕4 + 3 ≤ 5.
Answer:
first one
y can be every number so it can be a -6 to infinity
[tex] - 1 < y [/tex]
[tex]y = - 6 \: or \: \infty [/tex]
second two
y<8
[tex]y < 8 \: or \infty [/tex]
The bill at a restaurant came to $136.40. The patrons decided to leave a 15% tip. What was the total bill including tip?
Answer: 156.86
Step-by-step explanation:
the supplement of an angle is 30 degrees more than the measure of the
what is the measure of
the angle?
angle,
Answer:
x = 75°
Step-by-step explanation:
supplementary angles sum to 180°
let x be the angle then x + 30 is the supplementary angle , so
x + x + 30 = 180
2x + 30 = 180 ( subtract 30 from both sides )
2x = 150 ( divide both sides by 2 )
x = 75
x + 30 = 75 + 30 = 105
the angle is 75° and the supplementary angle is 105°
0,2% of what number is 8?
LE THE UNKNOWN NUMBER BE x WHEN I SOLVE
[tex] \frac{0.2}{100} \times x = 8 \\ \frac{0.2x}{100} = 8 \\ [/tex]
I WILL USE CROSS MULTIPLICATION
[tex]0.2x = 8(100) \\ 0.2x = 800 \\ \frac{0.2x}{0.2} = \frac{800}{0.2} \\ x = 4000[/tex]
OF ( 4000) IS 0.2% OF 8.
HOPE THIS HELPS.
Simplify 3^2 + 3(6 - 2^2) ÷ 6.
Fractions simplification
Apply PEMDAS method. Eliminate parenthesis first.
Then (3^2 + 3•6 - 3•2^2 )/ 6 = (3^2 + 3•6 - 3•2^2 )/ 6
now eliminate exponents
= [3• 3 + 3•6 + 3•4] / 6
= 3•5/6 now multiplicate
3•5= 15
Then
= 15/6 = 2 + 3/6 = 2 + 1/2 = 2.5
A board 172 inches wide is cut to three-fourths of its original width
Answer: 129 inches
Step-by-step explanation:
172 inches x 3/4 original with = 129 inches
if a varies equal directly with b, and a=8 when b=20 what is the value of a when b= 14.5
Hey there Ms or Mr could you please help me out with this problem? Just a heads up, this is my assignment not a quiz. My assignment is about distance and midpoint formula.
EXPLANATION
Let's see the facts:
Midpoint = (-2,5)
A=(4,7)
Let the point of B as B=(x,y)
Then,
[tex]\frac{x+4}{2}=-2,\frac{y+7}{2}=5[/tex]Multiplying the frist equation by 2:
[tex]x+4=-2\cdot2[/tex]Subtracting -4 to both sides:
[tex]x=-4-4[/tex]Simplifying:
[tex]x=-8[/tex]Multiplying the second equation by 2:
[tex]y+7=2\cdot5[/tex]Subtracting -7 to both sides:
[tex]y=10-7=\text{ 3}[/tex]The coordinates of the point B are:
B=(-8,3)
What is the diameter of a sphere with a volume of 80487 in^3, to the nearest tenth ofan inch?
EXPLANATION
If the volume of a sphere is 80487 in^3, the diameter would be given by the following relationship:
[tex]\text{Volume}=\frac{4}{3}\cdot\pi\cdot r^3[/tex]Replacing terms:
[tex]80487=\frac{4}{3}\cdot\pi\cdot r^3[/tex]Isolating r^3:
[tex]\frac{80487}{\pi}\cdot\frac{3}{4}=r^3[/tex]Applying the cubic root to both sides:
[tex]\sqrt[]{\frac{80487}{\pi}\cdot\frac{3}{4}}=r[/tex]Switching sides:
[tex]r=\sqrt[]{\frac{80487}{\pi}\cdot\frac{3}{4}}[/tex]Multiplying numbers:
[tex]undefined[/tex]the numberof blocks has 9 in the ones places.The number in the hundreds place is one more than the number in the tens place. Those two numbers equal 11. How many blocks are there?
Based on the given information, we can express the following
[tex]\begin{gathered} h=1+t \\ h+t=11 \end{gathered}[/tex]Because the digit of hundreds is 1 more the tens, and they sum 11. Let's combine the function to find t
[tex]\begin{gathered} h+t=11 \\ 1+t+t=11 \\ 2t=11-1 \\ t=\frac{10}{2}=5 \end{gathered}[/tex]So, the digit of tens is 5.
Let's find the hundreds.
[tex]h=1+t=1+5=6[/tex]The number of hundreds is 6.
Hence, the number of blocks is 659.How would you find the area of each of your rooms without furniture?
Given that you have a room that has dimensions l and w wherein l is the length of the room while w is the width of the room (shown in a diagram below).
the area of the room can be computed using the equation
[tex]A_{room}=l\times w[/tex]Basically, we just multiply the length and the width of the room.
There are 151 people in the 6th
grade class. It costs $24 for each
person to go snorkeling. How
much did they pay altogether?
Answer:
Step-by-step explanation:
it cost $3,624
2x – 1 over 5 - 3x +2 over 4
we have
(2x-1)/5-(3x+2)/4
{4(2x-1)-5(3x+2)}/20
{8x-4-15x-10}/20
{-7x-14}
5-(3x+2)/4
4(2x-1
What are the x intercept of the equation f(x)=3(x-7)(4x+2)
The x-intercepts are
x = 7
and
x = -1/2
SOLUTION:
we need to find the value of x where y or f(x) is 0
the expression x-7 will be zero if x=7
the expression 4x+2 will be zero if x = -1/2
cual es la raiz cuadrada de 4096 y 529
The square root of 4096 is 64 and the square root of 529 is 23.
The square root of a number x in mathematics is a number y whose square (the outcome of multiplying the number by itself, or y·y), is equal to x.
For instance, since 4² = (-4)² = 16, 4 and -4 are the square roots of 16.The square root of x is rational if and only if x is a rational integer that can be expressed as the ratio of two perfect squares. (The square root of 2 for proof that this number is illogical; the quadratic irrational for evidence against all non-square natural numbers.) The square root function changes rational numbers into algebraic numbers, which are a superset of rational numbers.The given numbers are 4096 and 529.
Let us find the factors of 4096:
4096 = 2¹²
Therefore the square root of 4096 = √4096 = √(2¹²) = 2⁶ = 64 .
Let us find the factors of 529:
4096 = 23 × 23
Therefore the square root of 529 = √529 = √(23²) = 23 .
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Disclaimer : The question in English is :
What is the square root of 4096 and 529.?
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Write an equation for the function whose graph is shown to the right
In this problem we have that
the parent function or original function is
[tex]y=\sqrt[]{x}[/tex]the transformation is a translation of 2 units at left
so
the rule is
(x,y) ------> (x-2,y)
therefore
the equation of the given graph is
[tex]y=\sqrt[]{x+2}[/tex]A university claims its recent graduates earn an average annual salary of
$45,000. You draw a random sample of 40 recent graduates and find that their
average salary is $46,000, and calculate the standard error of the sample mean
as 436.81. What is the t ratio for this result?
Answer:
t-ratio = 0.362
Step-by-step explanation:
In hypothesis testing,
The t-ratio is given by the formula:
[tex]\dfrac{X-\mu}{s}[/tex]
where μ is the hypothesized mean, X the sample mean and s the sample standard deviation
The Standard Error of the Mean SEM = [tex]\large \text{{$\dfrac{s}{\sqrt{n}}$}}[/tex] where n is the sample size.
We We are given:
X = 46,000
μ= 45,000
SEM = 436.81
n = 40
We can find the sample standard deviation
s = SEM x √n
s = 436.81 x √ 40
s = 2762.3
Therefore
t-ratio = (46000 - 45000)/2762.3 = 0.362
b. Triangle DEF with coordinates D(-2, 2), E (1,5), and F (4, -1) is rotated 90° counterclockwise aboutthe origin
Please help I couldn’t go to school today and I don’t understand
Answer:
the value of x is 2
Step-by-step explanation:
3x + 6
x = 6 ÷ 3
x = 2
3x + 6
3× 2 + 6
6+6
12
-4 + 8x
-4 + 8×2
-4+16
12
Helppppppp will give brainiest to first right answer
Answer:
1 degrees F
Step-by-step explanation:
-3+12-6=3
3/3 = 1
1 degrees F
:]
what is probability that it is from the 70s is
Given :
the total number of collections = 60 vinyl
There are six from the 70s
So, the probability that is from 70s is :
[tex]\frac{6}{60}=\frac{1}{10}[/tex]I need an answer for 1,2,3,4,5, and 6
Using alternate exterior angles,
[tex]3x-31=x+59\\\\2x=90\\\\x=45\\\\\implies 3x-31=x+59=104[/tex]
So,
[tex]\angle 1[/tex]: 76 degrees using linear pairs
[tex]\angle 2[/tex]: 104 degrees using corresponding angles
[tex]\angle 3[/tex]: 76 degrees using vertical angles
[tex]\angle 4[/tex]: 104 degrees using same-side interior angles
[tex]\angle 5[/tex]: 76 degrees using linear pairs
[tex]\angle 6[/tex]: 76 degrees using vertical angles
Which are the better statistics to use to compare the team scores
Step 1
We are given two team scores
Required; Which are the better statistics to use to compare the team scores
Step 2
The box plot displays the 5 number summary
-Minimum data value
-Maximum data value
-Median
-First Quartile, and
Third Quartile
The Interquartile Range (IQR) of the data can also be calculated by finding the difference between the First Quartile, and the third Quartile.
The Interquartile Range (IQR) helps us to determine the variability of the data set. The IQR is often seen as a better measure of spread than the range as it is not affected by outliers.
The median that is gotten from the box pot measures the center tendency of the data. The median is the most informative measure of central tendency for skewed distributions or distributions with outliers.
Therefore, the better statistics to use for comparing the scores of the teams are;
Median and IQR.
Complete the point slope equation of the line through -2,6 and 1,1
Answer:
3y = -5x + 8
Step-by-step explanation:
Point Slope Equation Of A Straight Line:
y - y1 = m(x - x1)
where m = slope of the line and (x1, y1) is any point on the line
Slope is given by rise/run
For any two point (x1, y1) and (x2, y2) on the line
rise = y2 - y1
and
run = x2 - x1
Given points (-2, 6) and (1, 1)
rise = 1 - 6 = -5
run = 1 - (-2) = 1 + 2 = 3
rise/run = m = -5/3
Equation using the point (1, 1) is
y - 1 = -5/3(x - 1)
y - 1 = -5/3x + 5/3
Multiply both sides by 3 to get
3(y - 1) = 3 x (-5/3)x + 3(5/3)
3y - 3 = -5x + 5
3y = -5x + 8