Answers
the slope seems to be 2 and y intercep tis -1 so 2x-1
right equation is x is greater than or equal to 1
slope is 1 and y intercept is 4 so x+4
top left blank is x+4, top right blank is x is greater than or equal to 1
bottom left blank is 2x-1, bottom right blank is x is less than or equal to -1
Hence, we have:
f(x)= 2x-1 when x ≤ -1
x+4 when x ≥ 1
Step-by-step explanation:After looking at the graph we observe that in the region: x ≤ -1The graph is a straight line that passes through (-1,-3) and (-2,-5)
Hence, the equation of line is:
[tex]f(x)-(-3)=\dfrac{-5-(-3)}{-2-(-1)}\times (x-(-1))\\\\\\f(x)+3=\dfrac{-5+3}{-2+1}\times (x+1)\\\\\\f(x)+3=2(x+1)\\\\\\f(x)=2x+2-3\\\\\\f(x)=2x-1[/tex]
Also, in the interval x ≥ 1The graph is a straight line that passes through (1,5) and (2,6)
Hence, the equation of line is:
[tex]f(x)-5=\dfrac{6-5}{2-1}\times (x-1)\\\\\\f(x)-5=x-1\\\\\\f(x)=x-1+5\\\\\\f(x)=x+4[/tex]
Related Questions
Evaluate the determinant for the following matrix: [1 4 4 5 2 2 1 5 5]
(This is a 3x3 matrix)
Answers
1 4 4
5 2 2
1 5 5
To determine the determinant of the matrix, you must multiply the number diagonally. For a 3×3 matrix, you must also form 3 diagonals up and 3 diagonals down. To do this, you copy the the first two columns and place it next to the third column.
1 4 4 1 4
5 2 2 5 2
1 5 5 1 5
The sum of the products of the diagonals down is subtracted to the sum of the products of the diagonals up. In other words,
Determinant = ∑(products of diagonal down) - ∑(products of diagonal up)
Determinant = [(1*2*5)+(4*2*1)+(4*5*5)]-[(1*2*4)+(5*2*1)+(5*5*4)]
Determinant = 0
The determinant of the matrix is zero.
Final answer:
The determinant of the given 3x3 matrix [1 4 4 5 2 2 1 5 5] is calculated by expanding across the first row and is found to be -60.
Explanation:
To evaluate the determinant of a 3x3 matrix, you can use the method of expansion across any row or any column. Given the matrix [1 4 4 5 2 2 1 5 5], let's expand across the first row:
The determinant of the matrix is the sum of the products of each element in the chosen row or column and the determinant of the 2x2 matrix that remains after removing the row and column of that element.
Multiply the first element of the first row by the determinant of the remaining 2x2 matrix, then subtract the product of the second element and its associated 2x2 matrix, and add the product of the third element and its 2x2 matrix.
Calculating the values, we get: 1*(2*5 - 2*5) - 4*(5*5 - 2*1) + 4*(5*2 - 2*1) = 1*0 - 4*23 + 4*8 = 0 - 92 + 32.
Therefore, the determinant of the given matrix is -60.
Assume that y varies inversely with x. If y=6.4when x=4.4, find y when x=3.2
Answers
y = k/x
where k = constant.
When x=4.4, y=6.4. Therefore
k/4.4 = 6.4
k = 6.4*4.4 = 28.16
The required relation is
y = 28.16/x
When x = 3.2, obtain
y = 28.16/3.2 = 8.8
Answer: 8.8
the answer is 8.8
that is the answer
In a fast-food restaurant, the ratio of people eating hamburgers to people eating chicken is 4 : 3. There are 84 people in the restaurant. How many people are eating hamburgers and how many are eating chicken? A. 36 people are eating hamburgers; 48 people are eating chicken. B. 12 people are eating hamburgers; 72 people are eating chicken. C. 48 people are eating hamburgers; 36 people are eating chicken. D. 21 people are eating hamburgers; 63 people are eating chicken.
Answers
48:36 = 4:3 once both are divided by 12
48 + 36 = 84, everyone accounted for
Final answer:
By using the ratio 4:3 and the total number of people (84), we calculate that each part of the ratio represents 12 people. Multiplying 4 parts by 12 gives us 48 people eating hamburgers, and multiplying 3 parts by 12 gives us 36 people eating chicken, making option C correct.
Explanation:
To solve the problem of determining how many people are eating hamburgers and how many are eating chicken given the ratio and the total number of people, we need to divide the total number of people by the sum of the parts of the ratio to find out the value of each part. The ratio given is 4:3, which means for every 4 people eating hamburgers, there are 3 people eating chicken. To find the value of each part of the ratio, we add the parts of the ratio (4 + 3 = 7) and divide the total number of people in the restaurant (84) by this sum.
84 ÷ 7 = 12. This means that each part of the ratio is equivalent to 12 people. Now, we need to multiply the number of each part by the number of people that each part represents. For hamburgers, it's 4 parts, so 4 × 12 = 48 people. For chicken, it's 3 parts, so 3 × 12 = 36 people.
Therefore, the correct answer is C: 48 people are eating hamburgers and 36 people are eating chicken.
The slopes of perpendicular line segments are 1/2 and d/3 What is the value of d?
d=-6
d=-3/2
d=3/4
d=6
Answers
solve for "d"
so
1/2 times d/3=-1
d/6=-1
times both sides by 6
d=-6
Pretty sure this is super easy I'm just an idiot pls help!
Answers
7x + 3x - x
Combine like-terms first.
10x - x
9x
This is equivalent to 9x^1, or 9x to the degree of 1. This is known as a monomial.
A monomial is a number/product of numbers and variables with whole number exponents.
Some examples are as follows:
I hope this helps!
Can square root of 27 be simplified
Answers
[tex] \sqrt{27}= \sqrt{9*3}=3 \sqrt{3} [/tex]
To take 9 out, write the root on the left side (3) and write what is left on the right (3 since 9 times 3 is 27) The answer to root 27 simplified is 3 root 3
We use ________ to determine the actual rate of change over intervals.
the dependent variable
the independent variable
absolute value
none of the above
Answers
On a rotating turntable, how do tangential speed and rotational speed vary with distance from the center?
Answers
Solve the inequality. Check your solutions.
7−(2/b)<(5/b)
im not surehow to answer this, it's supposedly in a number form but I'mcompetely lost. Maybe a _
Answers
[tex]7- \frac{2}{b}\ \textless \ \frac{5}{b}[/tex]
write 7 as 7b/b to have all the expressions in common denominator:
[tex] \frac{7b}{b} - \frac{2}{b}\ \textless \ \frac{5}{b}[/tex]
[tex]\frac{7b-2}{b} \ \textless \ \frac{5}{b}[/tex]
[tex]\frac{7b-2}{b}- \frac{5}{b}\ \textless \ 0[/tex]
[tex]\frac{7b-2-5}{b}\ \textless \ 0[/tex]
[tex]\frac{7b-7}{b}\ \textless \ 0[/tex]
[tex]\frac{7(b-1)}{b}\ \textless \ 0[/tex]
here b=1 is a root and b=0 is not in the domain of the expression, but it still has an effect in the sign of the expression.
the sign table of [tex]\frac{7(b-1)}{b} [/tex] is :
+++++++[0] --------[1] +++++
this means that for values of b to the left of 0 and to the right of 1, the expression is positive, and for values of b in (0, 1), the expression is negative.
that is [tex]\frac{7(b-1)}{b}\ \textless \ 0 [/tex] for b∈(0, 1)
Answer: (0, 1)
F leonard bought 2 packs of batteries for x amount of dollars, how many packs of batteries could he purchase for $5.00 at the same rate
Answers
The rate at which Leonard bought was 2 packs per x dollars,
that is his buying rate was (2 packs)/(x dollars)=2/x (p/$)
2.
with 1 $ Leonard buys 2/x packs
then
with 5 $ Leonard buys (2/x)*5 = 10/x packs.
Answer: 10/x packs
Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)
Answers
The equation of a hyperbola is:
(x – h)^2 / a^2 - (y – k)^2 / b^2 = 1
So what we have to do is to look for the values of the variables:
For the given hyperbola : center (h, k) = (0, 0)
a = 3(distance from center to vertices)
a^2 = 9
c = 7 (distance from center to vertices; given from the foci)
c^2 = 49
By the hypotenuse formula:
c^2 = a^2 + b^2
b^2 = c^2 - a^2
b^2 = 49 – 9
b^2 = 40
Therefore the equation of the hyperbola is:
(x^2 / 9) – (y^2 / 40) = 1
Answer:
Hope this helps :)
Step-by-step explanation:
i need help with this question
Answers
case (i):
the output of the first machine ([tex]\sqrt{x-5}[/tex]) is the input of the second machine, so we plug ([tex]\sqrt{x-5}[/tex]) or g(x) in function h and calculate, as follows:
[tex]h(g(x))=h(\sqrt{x-5})[/tex], now h is the function which squares whatever the input is and subtracts 6:
[tex]h(\sqrt{x-5})=(\sqrt{x-5}) ^{2}-6=x-5-6=x-11[/tex]
case (ii): we plug h in g:
[tex]g(h(x))= \sqrt{h(x)-5}= \sqrt{ x^{2} -6-5}= \sqrt{ x^{2} -11} [/tex]
a.
case1
[tex]h(g(x))=x-11=5 [/tex]
x=16
so for x=16, h(g(x))=5
case2
[tex]g(h(x))= \sqrt{ x^{2} -11}=5[/tex]
[tex] x^{2} -11=25[/tex]
[tex] x^{2} =36[/tex]
x=-6 or x=6
for both these values, g(h(x))=5
so since her input was 6, the order was g(h(x)), that is h(x) was the input of g(x)
b.
case1
[tex]h(g(x))=x-11=-5[/tex]
x=11-5=6,
so for x=6, h(g(x))=-5
case2
[tex]g(h(x))= \sqrt{ x^{2} -11}=-5[/tex]
the square root cannot be a negative number
Answer:
A. order is g(h(x))
B. yes, for h(g(x)) only
Find the distance between each pair of points
Answers
First point is at (-1, -2) and the second is plotted at (-1, 3). We x-coordinates don't change. Just take the absolute value of the difference between the -2 and 3.
|3 - (-2)| =
|3 + 2| =
|5| = 5
So, 5 units is the answer.
The ratio of the number of girls to the number of boys was 3 to 5 . of 2,520 were presented, how many were girls and how many were boys
Answers
3/8(2520) = 7560/8 = 945 girls <==
5/8(2520) = 12600/8 = 1575 boys <==
There were 945 girls and 1575 boys respectively.
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b or a/b
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. The numerator is the upper quantity in the fraction and the denominator is the lower quantity in the fraction). Remember that the ratio should always be taken of quantities with the same unit of measurement. Also, the ratio is a unitless(no units) quantity.
We have been given that the ratio of the number of girls to the number of boys was 3 to 5.
The ratio girls to boys;
3 to 5
The Total = 8
The number of boys was 3 to 5 . of 2,520, Then;
3/8(2520) = 7560/8
girls = 945
5/8(2520) = 12600/8
boys = 1575
Therefore, there were 945 girls and 1575 boys respectively.
Learn more about ratios here:
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On Saturday Mike ran 5.5 kilometers swam 300M and invite 23 hectometers how many kilometers did he travel in total
Answers
What is the formula for finding the area of a regular polygon with perimeter P and apothem length a?
Answers
Answer:
[tex]A=\frac{1}{2}Pa[/tex]
Step-by-step explanation:
Let
P------> the perimeter of a regular polygon
a-----> the apothen
A-----> the area of a regular polygon
we know that
The formula to calculate the area of a regular polygon is equal to
[tex]A=\frac{1}{2}Pa[/tex]
The formula for finding the area of a regular polygon with
perimeter P and apothem length a is 1/2Pa.
What is a Polygon?This is referred to as a plane figure which has a finite number of
straight line segments connected to form a closed polygonal
chain.
The formula for calculating the area of a regular polygon is
1/2Pa where P is the perimeter of a regular polygon and a is the
apothem.
Read more about Polygon here https://brainly.com/question/1592456
Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2). Find the coordinates of the center of the circle.
Answers
Knowing that the distance between any two points is:
d^2=(x2-x1)^2+(y2-y1)^2 and these distances are all equal we can say
d^2=(x-0)^2+(y-0)^2, (x+3)^2+(y-0)^2, (x-1)^2+(y-2)^2
d^2=x^2+y^2, x^2+6x+9+y^2, x^2-2x+1+y^2-4y+4 now getting differences
0=-6x-9, 8x+4+4y
Since both of the equations above are equal to zero we can see that:
-6x-9=0
-6x=9
x=-9/6
x=-1.5, making 8x+4+4y=0 become:
8(-1.5)+4+4y=0
-12+4+4y=0
-8+4y=0
4y=8
y=2
So the center of this circle is at the point (-1.5, 2)
ROUND 47342.6653106 TO 1 DECIMAL PLACE HELP!
Answers
If there are x teams in a sports league, and all the teams play each other twice, a total of n(x) games are played, where n(x)equals
Answers
Consider a group of n objects. Assume we want to form groups of r, from these n objects.
There are in total [tex]C(n, r)= \frac{n!}{r!(n-r)!} [/tex] many ways of doing so.
where, r! is "r factorial", calculated as 1*2*3*...*(r-1)*r
2.
C(x, 2) is the total number of pairs out of x objects, that we can form.
so let the x objects represent the x teams, and 2, represent a group of 2, which means a game.
The total number of games is:
n(x)=2*C(x, 2) = [tex]2* \frac{x!}{2!(x-2)!}= \frac{x!}{(x-2)!}= \frac{x(x-1)(x-2)!}{(x-2)!}=x(x-1)= x^{2} -x [/tex]
Remark, we multiplied by 2, since there will be 2 matches for each pair of teams.
Answer: [tex] x^{2} -x[/tex]
Scientists are studying the temperature on a distant planet. Let y represent the temperature (in degrees Celsius).
Let x represent the height above the surface (in kilometers). Suppose that x and y are related by the equation =y−235x .
Answer the questions below. Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the temperature change for each kilometer we go up from the surface?
Answers
Final answer:
For each kilometer increase in altitude, the temperature on the distant planet decreases by 235 degrees Celsius, according to the given equation y = -235x.
Explanation:
The question pertains to the relationship between altitude and temperature on a distant planet. Given the equation y = -235x, where y represents the temperature in degrees Celsius and x represents the height above the surface in kilometers, we are asked to determine the temperature change for each kilometer as we increase elevation from the surface.
To find the temperature change per kilometer, we examine the coefficient of x in the equation. Since the coefficient is -235, it signifies that for every kilometer increase in altitude, the temperature on this planet decreases by 235 degrees Celsius.
The table below represents the distance of a car from its destination as a function of time: Time (hours) x Distance (miles) y 0 900 1 850 2 800 3 750 Part A: What is the y-intercept of the function, and what does this tell you about the car? (4 points) Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3, and tell what the average rate represents. (4 points) Part C: What would be the domain of this function if the car traveled the same rate until it reached its destination? (2 points)
Answers
The y-interception is y=900 or(0,900) which means that a car must travel 900 miles for the final destination. And every hour driven is 50 miles.
The average rate of change isIt represents how many miles per one hour changes the distance from a destination.
Domain of this function if the car traveled the same rate until it reached its destination:
0=-50x+900
50x=900
x=900/50=18
Domain: x∈ [0, 18].
Find the length of the hypotenuse of a right triangle whose legs measure 6 and 5
Answers
c^2 = a^2 + b^2
where c is the hypotenuse
We calculate as follows:
c^2 = a^2 + b^2
c^2 = 6^2 + 5^2
c^2 = 61
c = √61
Therefore, the hypotenuse of the right triangle with sides 6 and 5 would be √61 which, clearly, is longer than the two sides.
The length of the hypotenuse is: [tex]\[ c = \sqrt{61} \][/tex]
To find the length of the hypotenuse of a right triangle with legs measuring 6 and 5, we use the Pythagorean theorem, which states:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Given:
a = 6
b = 5
We need to find c . Plugging the values into the Pythagorean theorem, we get:
[tex]\[ 6^2 + 5^2 = c^2 \][/tex]
Calculating the squares:
[tex]\[ 36 + 25 = c^2 \][/tex]
Adding the numbers:
[tex]\[ 61 = c^2 \][/tex]
To find c , we take the square root of both sides:
[tex]\[ c = \sqrt{61} \][/tex]
Therefore, the length of the hypotenuse is:
[tex]\[ c = \sqrt{61} \][/tex]
A triangle has an area of 180 cm2 and the base that is 20 cm long. what is the height of the triangle answers
Answers
Height (h) = ?
Area = 180 cm²
[tex] \frac{1}{2}bh = 180 [/tex]
[tex] \frac{1}{2} * 20 *h = 180[/tex]
10h = 180
h = 18
Hence, the height is 18 cm.
Some facts about powers of ten are shown.
Use what you know about powers of ten to enter numbers that make the equation true
Enter numbers to write 256,000 in scientific notation.
Answers
Multiply 2.56 and 100,000 and you get 256,000.
First box is 100,000 and the second box is 5
The number 256,000 can be written as 2.56 x [tex]10^5[/tex] in scientific notation
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
Scientific notations value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
To write 256,000 in scientific notation.
[tex]10^5[/tex] is followed by 5 zeros, so, it is 100,000.
Now Multiply 2.56 and 100,000 we get
2.56 x 100,000 = 256,000.
Therefore, First box is 100,000 and the second box is 5
Learn more about scientific notation here:
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Choose the answer that best represents the situation described below. Kurt is buying a new cell phone. He knows that the more features the cell phone has, the more expensive it will be. A. The cost of the cell phone is a function of the number of features. B. The size of the cell phone is a function of the number of features. C. The number of features is a function of the cell phone company Kurt chooses.
Answers
The cost of the cell phone is a function of the number of features.
Explanation:The answer that best represents the situation described is option A. The cost of the cell phone is a function of the number of features.
In this case, as Kurt is buying a new cell phone, he knows that the more features the cell phone has, the more expensive it will be. This implies that the cost of the cell phone is dependent on the number of features it has.
For example, if a cell phone with basic features costs $200, a cell phone with additional features like a better camera, more storage, and waterproof capabilities may cost $400 or more.
Solve 3x2 + 13x = 10
a. x = two over three and x = −5
b. x = 3 and x = −3
c. x = −2 and x = five over three
d. x = −7 and x = 13
Answers
Write the equation as
3x² + 13x - 10 = 0
Use the quadratic formula to obtain
x = (1/6) [ -13 +/- √{13² - 4*3*(-10)} ]
= (1/6) [-13 +/- √289]
= (1/6) [-13 +/- 17]
x = -30/6 = -5
or
x = 4/6 = 2/3
The solution is x = 2/3 and -5.
Answer: a
Answer:
A. x = two over three and x = -5
The equation 3x^2 + 13x = 10 can be solved using the quadratic formula. The solutions are given by:
[tex]$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$[/tex]
Substituting the values from the equation (where a = 3, b = 13, and c = -10), we get:
[tex]$$x = \frac{-13 \pm \sqrt{13^2 - 4*3*(-10)}}{2*3}$$[/tex]
This simplifies to:
[tex]$$x = \frac{-13 \pm \sqrt{289}}{6}$$[/tex]
So, the solutions are:
[tex]$$x = \frac{-13 + \sqrt{289}}{6} = \frac{2}{3}$$[/tex]
and
[tex]$$x = \frac{-13 - \sqrt{289}}{6} = -5$$[/tex]
So, the correct answer is A. x = two over three and x = −5.
what is the maximum value of the function y = −3x2 − 15x + 9?
Answers
The graph of this equation is an n-shape. It will go up to a maximum point and then arc back downwards.
In order to find this point, there are two ways I can think of, I will show the one I prefer:
First, take out the coefficient of the x² terms:
y = -3(x² + 5x - 3)
Now, CTS (complete the square):
y = -3((x + 5/2)² - 25/4 - 3)
y = -3(x + 5/2)² + 111/4
Maximum Point: (-5/2, 111/4) or (-2.5, 27.75)
If x and y are not both equal to zero 1/x+y = 1/x + 1/y
Look at the picture provided below
|
V
Answers
Answer:
True
Step-by-step explanation:
All work is shown and pictured
I'm studying for a test and i seriously can't figure this out. I took a screenshot. Please help and thanks. :) :P :D
Answers
What we are dealing with is called "Pythagorean Theorum", also known as the famous equation "A^2 + B^2 = C^2." The side length "A" is usually the side length opposite of the hypotenuse, which is the side length "C" that is directly across from the right angle of the triangle. The side length "B" is adjacent to the hypotenuse.
Let's apply this to our current triangle.
We have the side length "A", which is 12 in., and our side length "B", which is 6 in.
Now, let's plug in our numbers to our variables in order to solve for C.
A^2 + B^2 = C^2
Replace A with 12 and B with 6.
12^2 + 6^2 = C^2
Simplify the exponents.
144 + 36 = C^2
Simplify the left side.
180 = C^2.
Now, we must solve for C. As C is being squared, we must apply the opposite mathematical term, which is square rooting.
C^2 = 180.
Square root both sides to solve for C.
C = [tex] \sqrt{180} [/tex] in.
Your answer is (C).
I hope this helps!
Suppose three out of every five people said they would prefer a television over a computer. If we surveyed 5,000 people, how many would prefer a television? A. 1,875 B. 5,000 C. 3,125 D. 3,000
Answers
60% of 5000 is equal to 0.6*5000=3000
Final answer: D