Answer: −33.5 or - 67x over 2 -4
i might be wrong
Step-by-step explanation:
8. Write an equation of the line perpendicular to y = x + 4 that contains (3,-3). Please write the
equation in point-slope form.
Answer:
y + 3 = - (x - 3)
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x + 4 ← is in slope- intercept form
with slope m = 1
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{1}[/tex] = - 1
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - 1 and (a, b ) = (3, - 3 ) , then
y - (- 3) = - 1 (x - 3) , that is
y + 3 = - (x - 3)
The sum of two numbers is 38 and their product is 165. Find the larger number. PLEASE HELP
Answer:
The larger number is 33
Step-by-step explanation:
Writing and solving a system of equations
Let x and y be the numbers
sum of two numbers is 38
x+y = 38
their product is 165
xy = 165
x = 38-y
Substitute this into xy =165
(38-y) * y = 165
38y - y^2 = 165
-y^2 + 38y -165 = 0
Multiply by -1
y^2 - 38y + 165 =0
Factor
( y-33) ( y-5) = 0
Using the zero product property
y -33 =0 y-5 =0
y =33 y=5
Now we can find x for each solution
x = 38-33 =5 x = 38-5 = 33
The two numbers are 33 and 5
The larger number is 33
is у = 3х3 – 3 linear?
Given the equation :
[tex]y=3x^3-3[/tex]It is a cubic function because the power of x = 3
The cubic function is not linear function
The linear function has the form : y = m * x + b
The power of x for the linear function = 1
so, the answer is : No
One number is chosen from the list 2,4,6, and 8. Another is selected from the list 6, 7 and 8. Find the probability that they are the same. a. 0 b.1/6 c. 2/3 d. 1/3
There are 2 options to get the same number, they choose 6 from both lists or they choose 8 from both lists.
Then, the probability to select 6 from the first list is:
[tex]\frac{1}{4}[/tex]Because we have 4 options ( 2, 4, 6, 8) and 1 of then is number 6. At the same way, the probability to select 6 from the second list is:
[tex]\frac{1}{3}[/tex]Because there are 3 numbers and one of them is 6.
Finally, the probability to choose 6 from both lists is the multiplication of the probabilities above, so:
[tex]P_6=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12}[/tex]We can also calculate the probability to choose 8 from both lists as:
[tex]P_8=\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12}[/tex]Because 1/4 is the probability to choose 8 from the first list and 1/3 is the probability to select 8 from the second list.
Therefore, the probability that both numbers are the same is the sum of the probability to choose 6 from both lists and the probability to choose 8 form both lists.
[tex]\begin{gathered} P=P_6+P_8 \\ P=\frac{1}{12}+\frac{1}{12} \\ P=\frac{1}{6} \end{gathered}[/tex]Answer: b. 1/6
8(y+4)-2(y-1)=70-3y
solve for y
Answer:
y = 4
Step-by-step explanation:
8(y + 4) - 2(y - 1) = 70 - 3y ← distribute parenthesis and simplify left side
8y + 32 - 2y + 2 = 70 - 3y
6y + 34 = 70 - 3y ( add 3y to both sides )
9y + 34 = 70 ( subtract 34 from both sides )
9y = 36 ( divide both sides by 9 )
y = 4
show your stepsWhat is the solution of the equation?SEE IMAGE
Given the equation
[tex]\begin{gathered} 3\text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ + 3 = 27} \\ \end{gathered}[/tex]Subtract 3 from both sides
[tex]\begin{gathered} 3\text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ + 3-3 = 27}-3 \\ \\ 3\text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ = }24 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ = }\frac{24}{3} \\ \text{ }\sqrt[5]{(x+2)^3\text{ }}\text{ = 8} \\ \end{gathered}[/tex]Raise both sides to power 5 to remove the 5th root on the left hand side
[tex]\begin{gathered} \text{ (}\sqrt[5]{(x+2)^3\text{ }})^5=8^5 \\ \\ (x+2)^3=(8^{})^5 \\ (x+2)^3=\text{ 32768} \\ \end{gathered}[/tex]Take the cube root of both sides
[tex]\begin{gathered} \sqrt[3]{(x+2)^3}^{}=\sqrt[3]{32768} \\ (x+2\text{ )= 32} \\ \end{gathered}[/tex]Subtract 2 from both sides
x + 2 = 32
x = 32 - 2
x = 30
The solution to the equation is x = 30
Write a quadratic function that fits the points (0, 6), (2, 4), and (3, 6).
The quadratic equation y = x² - 3 · x + 6 fits the points (0, 6), (2, 4) and (3, 6).
How to find a quadratic equation that fits a set of three points
Herein we find a set of three points that fits in a quadratic equation, that is, a polynomial of the form y = a · x² + b · x + c, where a, b, c are real coefficients. It is possible to find a quadratic equation as the number of points is equal to the numbers of real coefficients.
First, obtain the system of linear equations by substituting the values of x and y on each case:
(x, y) = (0, 6)
a · 0² + b · 0 + c = 6
c = 6
(x, y) = (2, 4)
a · 2² + b · 2 + c = 4
4 · a + 2 · b + c = 4
(x, y) = (3, 6)
a · 3² + b · 3 + c = 6
9 · a + 3 · b + c = 6
Second, solve the system of linear equations by numerical methods:
(a, b, c) = (1, - 3, 6)
Third, write the resulting quadratic equation:
y = x² - 3 · x + 6
To learn more on quadratic equations: https://brainly.com/question/1863222
#SPJ1
Hi, can you help me answer this question please, thank you
Given:
The test claims that the proportion of men who own cats is smaller than the proportion of women who owns cat.
The null and atlernative hypothesis is given as,
[tex]\begin{gathered} \mu_M=\text{ Men who own cats} \\ \mu_F=\text{ Women who own cats} \end{gathered}[/tex]So,
[tex]\begin{gathered} H_0\colon\mu_M=\mu_F_{} \\ H_1\colon\mu_M<\mu_F \end{gathered}[/tex]Answer: option c)
Answer:
what he said^^
Step-by-step explanation:
because of blablablablabla
Write an equation of the line that passes through the point (-2,6) and is parallel to the line that passes through the points (0,-4) and (3,2)
We have the points:
p(0,-4) & q(3,2)
then, our directional vector will be:
pq(3,6)
now we have the equation of the line that we need to be parallel with:
(x,y)=(0,-4)+t(3,6)
We get (3,6) as follows:
we determine the directonal vector using the two point given:
p(0,-4) & q(3,2)
pq(3-0,2+4) =>pq=(3,6)
Now, the point of the line that is parallel to the one we got is: (-2,6):
Since a condition for being parallel is that the directional vector from one line is a product of the other, then:
(x,y) = (-2,6) + t(6,12)
As can be seen, the directional vector is parallel to the one found before (one is multiple of the other)
As for before, the equation of the line that passes by the point (-2,6) and is parallel to the line (x,y) = (0,-4) + t(3,6) is:
[tex](x,\text{ y) = (-2,6) + t(6,12)}[/tex]write an equation of the line described
passes through (8,8)
parallel to the line y = -7/4x - 4
Answer:
y = -7/4x + 22
Step-by-step explanation:
linear equation: y = mx +c, where m is the slope
when a line is parallel to another line, it means they have same slope
so the line slope, m = -7/4
now you need to find c to complete the equation
you have x,y information
replace that into linear equation together with slope value
8 = (-7/4)8 + c
8 = -14 + c
8+14 = c
c = 22
substitute m,c into the equation, you get
y = -7/4x + 22
15. An object that weighs exactly 1pound is placed on a digital scalethat measures weight in ounces. Ifthe scale is precise but notaccurate, what weight might beshown on the scale?
The rate of conversion between pounds and ounces is shown as;
16 ounces = 1 pound
Then you have a digital scale that measures weight in ounces. If you put an object that weighs "exactly 1 pound" on the digital scale, its supposed to display 16 ounces.
However the scale has been described as "not accurate," which implies that the calibration (fine tuning) has been altered either accidentally or on purpose. This also implies that the result would not be 100 percent correct, but it might be a little over or below 16 ounces. Hence the scale might display what in mathematics is termed as "plus or minus" and is denoted by the sign ±
The scale therefore might display 15 ounces or 17 ounces (that is ± 16)
±
Determine algebraically if f(x)=|x+2|is a functioneven, odd, or neither.
The absolute value function is given below as
[tex]f(x)=|x+2|[/tex]Concept: We will have to explain what is meant by an odd function, even function, or neither
Even function: A function is said to be even if it has the equality below
[tex]f(x)=f(-x)[/tex]is true for all x from the domain of definition.
An even function will provide an identical image for opposite values.
Odd function:A function is odd if it has the equality below
[tex]f(x)=-f(-x)[/tex]is true for all x from the domain of definition.
An odd function will provide an opposite image for opposite values.
Neither: A function is neither odd nor even if neither of the above two qualities is true, that is to say:
[tex]\begin{gathered} f(x)\ne f(-x) \\ f(x)\ne-f(-x) \end{gathered}[/tex]Given that
[tex]\begin{gathered} f(x)=|x+2| \\ f(-x)=|-x+2| \\ f(x)\ne f(-x) \end{gathered}[/tex]Also,
[tex]\begin{gathered} f(x)=|x+2| \\ -f(-x)=-|-x+2| \\ f(x)\ne-f(-x) \end{gathered}[/tex]Therefore,
We can conclude that f(x) = |x+2| is NEITHER an even nor a odd function
y=-2x+10 in standard form
Answer:Y+2x=10
Step-by-step explanation:
Answer:
2x+y=10
Step-by-step explanation:
The standard form is x+y=#
y=-2x+10
flip it around:
10-2x=y
add 2x
10=2x+y
2x+y=10
PLEASE ANSWER. I REALLY NEED THIS A+++
Answer: the first one is yes and the second one is no
Step-by-step explanation: that’s the answer i took the test
Lindsey bought a picnic basket originally priced at $40 but on sale for 50% off. After 10% sales tax, what was the total cost?
$
The total cost price of the basket is $22.
What is Discount ?
The discount is determined by dividing the purchase price by the item's par value. The discount is a type of cost price reduction or deduction for a product. It is primarily employed in consumer interactions when discounts on various goods are offered to customers. A percentage represents the discount rate.
Here ,
Original cost price of the basket = $40
After 50% offer the cost price of the bag is,
=> 40- 50% of 40
=> 40 - 20
=> $20.
Now the sales tax is 10% then,
=> 20+ 10% of 20
=> 20+ 2
=>$22
Therefore the total cost is $22 after discount.
To learn more about discount
https://brainly.com/question/24711235
#SPJ1
How do u Arranging the order of polynomials
Answer: You must put the highest exponent of the variable first, and then proceed in descending order.
Step-by-step explanation:
This is done to keep track of the powers much easier and also just looks nicer. ^^
Can you please help me
Step 1: Write out the formula for finding the area of a rhombus
[tex]\begin{gathered} \text{Area }=\frac{AC\times DB}{2} \\ \text{ Where} \\ AC\text{ and DB are the diagonals of the rhombus } \end{gathered}[/tex]Step 2: Substitute the given values to find AC
[tex]\begin{gathered} \text{ Area }=45\text{ square units} \\ DB=6\text{units} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{6AC}{2}=45 \\ 3AC=45 \\ \text{ Dividing both by 3, we have} \\ \frac{3AC}{3}=\frac{45}{3} \\ AC=15 \end{gathered}[/tex]Hence, AC is 15 unitsConsider the following solutions Please help on my question I’m confused
The function f(x) and g(x) is given as follows:
[tex]f(x)=4x+5;\; g(x)=2x-1[/tex]The composite function is defined as:
[tex](f\circ g)(x)=f(g(x))[/tex]Replace x with g(x) in the expression given for f(x):
[tex]f(g(x))=4(g(x))+5[/tex]Substitute g(x)=2x-1 into the right-hand side of the equation:
[tex]\begin{gathered} f(g(x))=4(2x-1)+5 \\ \Rightarrow f(g(x))=8x-4+5=8x+1 \end{gathered}[/tex]Recall that,
[tex]\begin{gathered} (f\circ g)(x)=f(g(x)) \\ \Rightarrow(f\circ g)(x)=8x+1 \end{gathered}[/tex]Notice that the composite function is a polynomial function of degree one (linear).
Recall also, that the domain of all polynomial functions is the set of real numbers.
Hence, the domain of the composite function (fog)(x) is the set of real numbers.
The set of real numbers in interval form is:
[tex](-\infty,+\infty)[/tex]The answer is:
[tex]\begin{gathered} (f\circ g)(x)=\boxed{8x+1} \\ \text{The domain of }(f\circ g)(x)\text{ is }\boxed{(-\infty,+\infty)} \end{gathered}[/tex]Martin is a manager at a restaurant. He receives a straight commission of 8% on food sales for the month. What were his March earnings if the restaurant sold $31,902 in food?
Martin's commission earning is $2552.16
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, Martin receives a straight commission of 8% on food sales for the month,
31,902*8/100 = 2552.16
Hence, Martin's commission earning is $2552.16
For more references on percentage, click;
https://brainly.com/question/29306119
#SPJ1
If the charge for shipping and handling is 8%, what is the total charge for an online order of $45?
We need to calculate the 8% of $45
[tex]45\cdot\frac{8}{100}=3.60[/tex]The total charge will be
[tex]45+3.60=48.60[/tex]ANSWER
The total charge is $48.60
Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 60 yd from B and 105 yd from A, with angle ACB measuring 69.3 . How far apart are A and B (to the nearest yard)?A. 101 yardsB. 110 yardsC. 119 yardsD. 128 yards
Let's draw a diagram of this problem:
This triangle can be seen as follows:
We can use the Law of Cosines to find the length of side c, since we know the measure of angle C:
[tex]c^2=a^2+b^2-2ab\cos (C)[/tex]In our case:
[tex]c^2=105^2+60^2-2(105)(60)\cos (69.3)[/tex][tex]c^2=11025+3600-12600\cos (69.3)=14625-12600\cos (69.3)[/tex]Taking the square root of both sides we get:
[tex]c=\sqrt[]{14625-12600\cos (69.3)}[/tex]which, using a calculator or online resource to calculate the right side of the equation will give us:
[tex]c=100.9[/tex]To the nearest yard, A and B are 101 yards apart, so option A. is correct.
Eight minus six and two-fifths
Answer:
1 and three-fifth or 1.6
A café has 60 tables. 35% of the tables have 2 chairs at each table. The remaining 65% of the tables have 4 chairs at each table. How many tables have 4 chairs?
The value for 39 tables have 4 chairs.
What is percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Percentage formula = (Value/Total value) × 100
Given,
total number of tables = 60
Percentage of tables have 4 chairs = 65%
Number of tables have 4 chairs = 65(60)/100
= 39
To know more about percentage, visit:
https://brainly.com/question/27574467
#SPJ1
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Width = 5.7 ft, Length = 10.5 ft
Step-by-step explanation:
Let the width be [tex]w[/tex]. Then, the length is [tex]2w-0.9[/tex].
[tex]w(2w-0.9)=59.85 \\ \\ 10w(20w-9)=5985 \\ \\ 200w^2-90w-5985=0 \\ \\ 40w^2-18w-1197=0 \\ \\ (4w+21)(10w-57)=0 \\ \\ w=5.7 (w>0) \\ \\ \implies 2w-0.9=2(5.7)-0.9=10.5[/tex]
Annie's mother asked Annie to go buy oranges, dog food, and bug spray. Each square's side length is 1 block. How many blocks will Annie have to walk in all if she visits the fruit stand, the pet store, and the supermarket, in that order, before returning home?
Here using the length of square, it is obtained that
Annie walked 14 blocks in total.
What is a square?
Square is a two dimensional four sided figure.
Here,
Length of each side of one square = 1 block
From Annie's home to the supermarket, Annie will have to walk 1 block
From Supermarket to pet store, Annie will have to walk 1 block straight and then 2 blocks to the left
From pet store to the fruit vendor, Annie will have to walk 1 block straight and then 2 blocks to the left
Total number of blocks walked by Annie from home = 1 + 1 + 2+ 1 + 2
= 7 blocks
Total number of blocks walked by Annie while returning home
= 1 + 1 + 2+ 1 + 2
= 7 blocks
Total number of blocks walked by Annie = 7 + 7 = 14 blocks
To learn more about square, refer to the link-
https://brainly.com/question/25092270
#SPJ1
Complete Question
The figure has been attached
A bottle rocket is launched straight up. Its height in feet (y) above theground x seconds after launch is modeled by the quadratic function: y =-16x2 + 132x + 6.How many seconds did it take the rocket to reach its maximum height?
Answer:
(C)4.125 seconds
Explanation:
The quadratic function modeling the rocket's movement is:
[tex]y=-16x^2+132x+6[/tex]To determine the number of seconds it takes the rocket to reach its maximum height, we are being asked to find the equation of the line of symmetry.
For a quadratic function of the form y=ax²+bx+c, the equation of the line of symmetry is:
[tex]x=-\frac{b}{2a}[/tex]In the given equation:
a = -16, b = 132
Therefore:
[tex]\begin{gathered} x=-\frac{132}{-2\times16} \\ x=4.125 \end{gathered}[/tex]It takes the rocket 4.125 seconds to reach its maximum height.
What is the purpose of the vertical line test for functions?
Answer:
The purpose of the vertical line test is to determine if the function is in fact a function. (Option C)
Explanation:
Once a vertical line is drawn to every part of the function and it only hit one point on the graph, then it is a function. For example,
If the vertical line hits two points or more on the graph, then the graph is not a function. For example, a circle is not a function.
The table below gives select values for the differentiable function f and g, and f' , the derivative of f, at select values of x. If...
Answer: for this problem. What we're going to do essentially, this is an exercise of using the formula for finding the derivative of the inverse of a function. So we have the derivative of the inverse of F would be equal to one over the derivative of F. So F prime evaluated at f inverse of X. So in this case we have X equals three. So F inverse of three, prime will be equal to one over F prime evaluated at f inverse of three. Now, looking at the table of values that you have, well, F inverse of three is going to be the X value such that X equals, or the the X values such that F equals three. So we can see that F equals three when X equals negative one. So we have one over F prime evaluated at negative one and F prime of negative one, we can see it is equal to one. So we'd have won over one or just one is the final answer.
Step-by-step explanation:
Use the dilation to find the value of y.
According to definition of dilation and the characteristics of the geometrical system in the picture, we find that the misssing side has a length of 25 units. (Correct choice: C)
How to determine the length of the missing side associated to two proportional triangles
The figure shows a geometrical system of two proportional right triangles generated about the point C, in which two pairs of sides related to the same side ratio for a dilation. Mathematically speaking, a dilation is defined by the following expression:
k = AB / A'B'
Where:
k - Scale factorAB - Original sideA'B' - Dilated sideThe ratio formula associated to the figure is shown below:
y / 35 = 15 / 21
y = (15 / 21) · 35
y = 25
The missing length is equal to 25.
To learn more on dilations: https://brainly.com/question/13176891
#SPJ1
If you make $75.00 a week at your job and want to save $250.00 over 3 months, saving an equal amount each week, how much spending money will you have each week?
The amount of spending money you will have each week is $54.17 .
How to find the spending money available?You make $75.00 a week at your job and want to save $250.00 over 3 months, saving an equal amount each week.
The amount of spending money available each week can be calculated as follows:
Therefore,
3 months = 12 weeks
let
x = amount saved every week.
Therefore,
12x = 250
x = 250 / 12
x = 20.83 dollars
Hence,
Amount of spending money each week = 75 - 20.83
Amount of spending money each week = $54.17
learn more on savings here:https://brainly.com/question/2871328
#SPJ1