Make two equations representing the position of each animal, p and k, for the puppy and kitten respectively.
p=25t and k=180+20t
The puppy will catch the kitten when p=k so we can say:
25t=180+20t subtract 20t from both sides
5t=180 divide both sides by 5
t=36
So the puppy will catch the kitten after 36 seconds.
Answer:
36
Step-by-step explanation:
x y
0 3
1 1
2 -1
Which set of values in the RANGE corresponds to the set {0,2} in the DOMAIN?
2, -1. I think, possibly.
Answer:
3, -1
Step-by-step explanation:
Which is the graph of y = cos(x) + 3? HURRYY!!
Answer:
See attachment
Step-by-step explanation:
The given function is [tex]y=\cos x +3[/tex]
The base function is [tex]y=\cos x[/tex]
The single transformation applied to this function is a vertical upward shift by 3 units.
Therefore the graph of [tex]y=\cos x +3[/tex] is graph of [tex]y=\cos x [/tex] shifted up 3 units.
See attachment
Answer: B
Step-by-step explanation:
Just did the test on edge
If f(x)=3x-1+4 and g(x)=4x-7 what is (f-g)(x)
Answer: [tex](f-g)(x)=-x+10[/tex]
Step-by-step explanation:
Given the function f(x):
[tex]f(x)=3x-1+4[/tex]
And given the function g(x):
[tex]g(x)=4x-7[/tex]
You must subtract both functions is order to find [tex](f-g)(x)[/tex].
You need to remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(+)(-)=-[/tex]
Then:
[tex](f-g)(x)=3x-1+4-(4x-7)[/tex]
Now, you must distribute the negative sign:
[tex](f-g)(x)=3x-1+4-4x+7[/tex]
And finally, add the like terms. Then you get that [tex](f-g)(x)[/tex] is:
[tex](f-g)(x)=-x+10[/tex]
Identify the following equation as that of a line, a circle, an ellipse, a parabola, or a hyperbola.
y = x 2 + 1
Answer:
The equation [tex]y=x^2+1[/tex] will be a parabola when it is graphed
Answer:
It's a parabola
Step-by-step explanation:
The equation seems to a parabolic function. The parabola is defined as:
[tex]y=Ax^2+b[/tex]
where b is a displacement, we can notice that in our case A=1 and b=1
so it is a parabola with a vertical displacement of one unit.
Finish this simile. Use your imagination to complete the description.
Writing similes is like . . .
Flying a plane through your own imagination. This implies how dominoes make you think and create, using your mind to make comparisons. The other option is like banging my head against the wall. It’s pointless and painful.
Answer:
writing answers to math questions
Step-by-step explanation:
writing a sentance
writing an add
writing a book
Find the range. 4.7 6.3 5.4 3.2 4.9 3.1 –3.1 9.5 –9.5
Answer:
The range is 19
Step-by-step explanation:
First, you have to order the numbers from least to greatest:
-9.5, -3.1, 3.1, 3.2, 4.7, 4.9, 5.4, 6.3, 9.5
Then, you have to find the difference between the largest number and and smallest number. You do this by subtracting them:
9.5 - (-9.5)= 19
So, the range is 19
Graph the linear equation. Find the three points that solve the equation then plot on the graph. -y=x+0
Answer:
Step-by-step explanation:
We can first make y the subject of the formula by multiplying both sides of the equation by -1 ;
y = -x + 0
This is the equation of a line with a slope of -1, the coefficient of x, and passing through the origin.
In order to find three points that solve the equation, we can let x be;
0, 1, 2
then determine the corresponding values of y.
When x = 0, y = -(0) + 0 = 0
When x = 1, y = -(1) + 0 = -1
When x = 2, y = -2 + 0 = -2
Therefore, we have the following three sets of points that can be used to graph the linear equation;
(0,0)
(1,-1)
(2,-2)
Find the attached for the graph of the equation;
Answer: (-1,1) (0,0) (2,-2)
Step-by-step explanation:
A bag contains 10 marbles. Four of the marbles are purple. What is the probability you will choose a purple marble from the bag
1/2
3/10
2/5
1/5
Answer:
2/5
Step-by-step explanation:
There are 10 marbles and 4 of them are purple. That would give you the fraction 4/10. 4/10 can be simplified to 2/5. So, you have a 2/5ths chance of choosing a purple marble.
The probability of selecting a purple marble from a bag containing 10 marbles, 4 of which are purple, is 2/5.
The question asks: "A bag contains 10 marbles. Four of the marbles are purple. What is the probability you will choose a purple marble from the bag?" To find the probability, you divide the number of favorable outcomes (choosing a purple marble) by the total number of outcomes (all the marbles in the bag). Here, there are 4 purple marbles and 10 marbles in total.
The probability is therefore 4/10, which can be simplified to 2/5. So, the probability of choosing a purple marble from the bag is 2/5.
A rectangular prism has a volume of 144 cubic inches. If the length is 2 times the width and the width is 4, find the height of the prism.
Show your work.
V = Bh
144 = (8 x 4)h
144 = 32h
4.5 = h
Final answer:
To calculate the height of the rectangular prism, we use the formula for volume and the given values to solve for height, resulting in a height of 4.5 inches.
Explanation:
To find the height of a rectangular prism with a given volume where the length is two times the width and the width is known, we use the formula for the volume of a rectangular prism: volume = length × width × height.
Given that the volume is 144 cubic inches, the width is 4 inches, and the length is two times the width, which is 2 × 4 inches = 8 inches, we can substitute these values into the formula:
144 in³ = 8 in × 4 in × height
Next, we need to isolate 'height' by dividing both sides of the equation by the length times the width of the prism:
144 in³ / (8 in × 4 in) = height
144 in³ / 32 in² = height
4.5 in = height
Therefore, the height of the rectangular prism is 4.5 inches.
A car travels 102 miles on 3gallons of gas. How far can it travel on 11 Gallons of gas
Answer:
374 miles
Step-by-step explanation:
To see how many miles each gallon gets, divide 102/3 which is 34 meaning there are 34 miles per gallon so if you multiply 34 x 11 gallons it equals 374 miles.
Hope this helps!
To solve this problem, we will use the concept of a unit rate, which in this scenario is the car's miles per gallon (mpg). A unit rate compares a quantity to one unit of another quantity. Here's how to do it step by step:
1. **Find the unit rate (mpg).**
The car travels 102 miles on 3 gallons of gas. To find out how many miles it travels per gallon, we'd divide the total number of miles by the number of gallons of gas used:
\[ \text{mpg} = \frac{\text{miles traveled}}{\text{gallons used}} \]
\[ \text{mpg} = \frac{102 \text{ miles}}{3 \text{ gallons}} \]
\[ \text{mpg} = 34 \text{ miles per gallon} \]
So the car travels 34 miles per gallon of gas.
2. **Calculate the distance the car can travel on 11 gallons of gas.**
Now that we know the car travels 34 miles on one gallon of gas, we can find out how far it travels on 11 gallons by multiplying the mpg by the number of gallons:
\[ \text{distance} = \text{mpg} \times \text{gallons available} \]
\[ \text{distance} = 34 \text{ miles/gallon} \times 11 \text{ gallons} \]
\[ \text{distance} = 374 \text{ miles} \]
So, the car can travel 374 miles on 11 gallons of gas.
How do you write 900.5 and expanded form and word form?
(9 x 100) + (5 x 0.1)
OR
900 + .5
Nine hundred and five tenths
Hope this helped!
Hello!
-EXPANDED FORM- To make the number 900.5 in expanded form, We use 900 and then add 0.5 which is also 1/2.
-WORD FORM- To make the number 900.5 in word form, the answer would be nine hundred and five tenths
F(x)=x^2+3x+2 is shifted 2 units right the reuslt is g(x) what is g(x)
Answer:
[tex]g(x)=x^2-x[/tex]
Step-by-step explanation:
Given function is [tex]F\left(x\right)=x^2+3x+2[/tex].
Function [tex]F\left(x\right)=x^2+3x+2[/tex] is shifted 2 units right and gives result to a new function g(x).
Now we need to find about what is the equation of g(x).
We know that f(x-h) indicates right shift by "h" units.
So to get 2 units shift, replace x by (x-2) into given function
[tex]g(x)=F\left(x-2\right)[/tex]
[tex]g(x)=(x-2)^2+3(x-2)+2[/tex]
[tex]g(x)=x^2-4x+4+3x-6+2[/tex]
[tex]g(x)=x^2-x[/tex]
Hence final answer is [tex]g(x)=x^2-x[/tex].
What is the equation of the line that passes through the point (3, 0) and is perpendicular to the line 2x – y = 5?
Answer:
[tex]\large\boxed{y=-\dfrac{1}{2}x+\dfrac{3}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ 2x-y=5.\\\\\text{Convert to the slope-intercept form y = mx + b:}\\\\2x-y=5\qquad\text{subtract 2x from both sides}\\\\-y=-2x+5\qquad\text{change the signs}\\\\y=2x-5\to m_1=2\\\\\text{Therefore}\ m_2=-\dfrac{1}{2}.[/tex]
[tex]\text{The equation of the searched line:}\ y=-\dfrac{1}{2}x+b.\\\\\text{The line passes through }(3,\ 0).\\\\\text{Put the coordinates of the point to the equation.}\ x=3,\ y=0:\\\\0=-\dfrac{1}{2}(3)+b\\\\0=-\dfrac{3}{2}+b\qquad\text{add}\ \dfrac{3}{2} \text{to both sides}\\\\b=\dfrac{3}{2}[/tex]
Write a second inequality with the same meaning. −18 ≤ b
ANSWER
[tex]b \geqslant - 18[/tex]
EXPLANATION
The given inequality is:
[tex] - 18 \leqslant b[/tex]
We can rewrite this as:
[tex]b \geqslant - 18[/tex]
The above two inequalities have the same meaning.
Reading from right to left, the first inequality says, "b is greater than or equal to negative 18."
Reading from left to right, the second inequality says, "b is greater than or equal to negative 18."
Therefore the two inequalities have the same meaning.
Step-by-step Answer:
Many inequalities are possible, for example:
Keeping the less than or equal to sign, we could write
-18-b<=0
or, switching sides,
b>= -18 (just by switching sides)
b+18>=0 (by transposing -18 to the left)
Then again, we can multiply both sides by -1, but we need to change the direction of the inequality:
18>=-b
or equivalently, by transposing 18 to the other side
0>=-b-18
and similarly
b+18>=0 (we already had this above)
Guess time to stop!
A tank with a volume of 61.25 cubic meters is filled with pull. The oil has a density of 865 kilograms per cubic meter that is the mass in kilometers of the oil?
Answer:
Step-by-step explanation:
Density is mass divided by volume:
ρ = M / V
So mass is density times volume:
M = ρV
If the density is 865 kg/m³ and the volume is 61.25 m³:
M = (865 kg/m³) (61.25 m³)
M = 52981.25 kg
Final answer:
To find the mass of oil in a tank, multiply the tank's volume (61.25 cubic meters) by the oil's density (865 kg/m³), resulting in 52,981.25 kilograms. The mass is not measured in kilometers, which suggests a typo in the original question.
Explanation:
The question concerns the calculation of the mass of oil if its density and the volume of the tank it fills are known. To find the mass, you would multiply the volume of the oil by its density:
Step-by-Step Calculation:
Determine the volume of the oil. In this case, the volume is already given as 61.25 cubic meters.
Identify the density of the oil. According to the question, it is 865 kilograms per cubic meter.
Multiply the volume by the density to get the mass. That is:
61.25 m³ × 865 kg/m³ = 52,981.25 kilograms.
In terms of mass in kilometers, there appears to be a typo, as mass is not measured in distances like kilometers. The correct unit should likely be kilograms.
please help i am timed
Answer:
Step-by-step explanation:
2x-10 is your answer
Answer:
D. 2x+5
Step-by-step explanation
All you have to do is put them all together and there you have it your answer of D 2x+5
convert 0.5 to a percent value
0.5 as a percent is 50%
0.5 to a percent value is 50%
Which stamens is true about f(x)=-6|x+5|-2?
A.) The graph of f(x) is horizontally compressed.
B.) The graph of f(x) is horizontally stretched.
C.) The graph of f(x) opens upward.
D.) The graph of f(x) opens to the right.
ANSWER
A.) The graph of f(x) is horizontally compressed.
EXPLANATION
The given absolute value function is
[tex]f(x) = - 6 |x + 5| - 2[/tex]
The parent function is
[tex]y = |x| [/tex]
Since the factor -6 has an absolute value greater than 1, the graph of the given function will be narrower than the graph of the base function.
Hence the graph is horizontally stretched by a factor of 6.
The graph opens downwards because of the negative sign.
It has vertex at (-5,-2)
Find the product , select the simplest form
Answer:
the answer is 3
Step-by-step explanation:
21/8 simplify is 3
Yeah, The answer is 3
If the endpoints of have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of ?
A.
(5, 3)
B.
(4, 5)
C.
(5, 5)
D.
(4, 3)
Your answer is D. (4,3)
ANSWER
D(4,3)
EXPLANATION
The endpoints of AB have the coordinates A(9, 8) and B(-1, -2).
To calculate the coordinates of the midpoint of AB, we use the midpoint formula,
[tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )[/tex]
We substitute the coordinates of the endpoints into the formula to get,
[tex]( \frac{9+ - 1}{2},\frac{8+ - 2}{2} )[/tex]
[tex]( \frac{8}{2},\frac{6}{2} )[/tex]
We simplify further to obtain,
[tex]( 4,3)[/tex]
f(x)=x^2+x-30
complete the square
f(x)= x[tex]x^2+x-30[/tex
= [tex](x)^2+2*x*\frac{1}{2} +(\frac{1}{2} )^2-(\frac{1}{2} )^2-30[/tex]
= [tex](x+\frac{1}{2} )^2-\frac{1}{4} -30[/tex]
= [tex](x+\frac{1}{2} )^2-\frac{121}{4}[/tex]
=[tex](x+\frac{1}{2} )^2-30\frac{1}{4}[/tex] (Answer)
Solve |x| > 3
{-3, 3}
{x|x < -3 ∪ x > 3}
{x|x < -3 ∩ x > 3}
Answer: Second Option
{x| x< -3 ∪ x > 3}
Step-by-step explanation:
To solve the inequality
[tex]| x | >3[/tex] there are two cases:
Case 1. [tex]x>0[/tex]
[tex]x > 3[/tex]
Case2. [tex]x<0[/tex]
[tex]-x > 3[/tex]
[tex]x < -3[/tex]
The final solution is the union of the solution of each case
This is:
[tex]x < -3[/tex] or [tex]x > 3[/tex]
{x| x< -3 ∪ x > 3}
Please help will give brainliest
No, two ordered pairs in this list have a repeated of the domain element.
Step-by-step explanation:We know that the definition of functions tells us that a function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).
So here is important to know the term exactly one element, Why? because if you don't have this, you don't have a function. From the figure, two ordered pairs in this list have a repeated of the domain element. This can be proven by plotting these three points as indicated below. As you can see, the element 4 in the domain matches both 2 and -2 in the range. In conclusion, this relation is not a function.
the hypotenuse of a right triangle is 20 centimeters. one of the legs is 4 cm longer than the other leg. find the area of the triangle.
Answer:
hypotenuse = 20
leg = x + 4
other leg = x
From the Pythagorean Theorem we know that
20^2 = (x + 4)^2 + x^2
400 = x^2 + 8x + 16 + x^2
2 x^2 + 8x -384 = 0
Solving the quadratic equation we get
x = 12 and x = -16
x = 12 and so the lengths of the 2 legs are:
12 and 16
Right Triangle Area = (leg1 * leg2) / 2
Right Triangle Area = (12 * 16) / 2
Area = 192 / 2
Area = 96 square centimeters
Step-by-step explanation:
To find the area of the triangle, we used the Pythagorean theorem to solve for the legs, obtaining lengths of 16 cm and 12 cm. The area is then calculated using the formula for the area of a right triangle (1/2 * base * height), resulting in an area of 96 cm².
We are given a right triangle with a hypotenuse of 20 cm and two legs where one leg (let's call it a) is 4 cm longer than the other leg (let's call it b). Using the Pythagorean theorem, we can express the relationship between the legs and the hypotenuse: a² + b² = 20². We know that a = b + 4, so if we substitute a into the equation, we get:
(b + 4)² + b² = 400
b² + 8b + 16 + b2 = 400
2b² + 8b - 384 = 0
Dividing everything by 2, we get:
b² + 4b - 192 = 0
Using the quadratic formula or factoring, we find that b = 12 (b can't be negative). Consequently, a = 16. The area of the triangle is given by 1/2 * base * height, which is:
Area = 1/2 * a * b
Area = 1/2 * 16 * 12
Area = 1/2 * 192
Area = 96 cm²
How many choices are possible with 1 topping
The answer is 45, I believe so
Please Help Quickly!!!
If lim x--> 4 f(x) = 5
Answer:
D
Step-by-step explanation:
Value of the function [tex]\lim_{x \to 4} \dfrac {g}{h}(x)[/tex] is zero.
Correct option is b.
What is limit?Limits are defined as values to which the function approximates the output for given input values. The limit is the unique real numbers. Given a real-valued function "f" and a real number "c", the limit is usually defined as [tex]\lim_{x \to c} f(x) = L[/tex]. We read that "the limit of f of x is equal to L as x approaches c". "lim" represents the limit, and the right arrow indicates that the function f(x) approaches the limit L as x approaches c.
Given functions,
[tex]\lim_{x \to 4} f(x) = 5 , \lim_{x \to 4} g(x) = 0, \lim_{x \to 4} h(x) = -2[/tex]
[tex]=\lim_{x \to 4} \dfrac {g}{h}(x)[/tex]
[tex]=\lim_{x \to 4} \dfrac {g(x)}{h(x)}[/tex]
[tex]=\dfrac{\lim_{x \to 4} g(x)} {\lim_{x \to 4} h(x)}[/tex]
= 0/-2
= 0
Hence, 0 is the value of function [tex]\lim_{x \to 4} \dfrac {g}{h}(x)[/tex] .
Learn more about limit here:
https://brainly.com/question/12207539
#SPJ2
Determine the slope of a line parallel to a line whose slope is -5
Answer:
-5
Step-by-step explanation:
A line that is parallel to another line must have the same slope.
Answer:
-5
Step-by-step explanation:
Parallel lines all have the same slope (as each other). Both of the parallel lines you are describing have a slope of -5.
Evaluate: −4 + 12 ÷(−3)/10 + 3(−2)
Answer:
Step-by-step explanation:
First we calculate (-3)÷10 = -0.3
Then 12÷(-0.3) = -40
After that -4 + (-40) = -44
3(-2) = -6
Finally -44 + (-6) = -50
For this case we have that the order of algebraic operations is determined by PEMDAS:
P: Perform any calculation inside the parentheses, making the most internal ones first.
E: Simplify any exponential expressions.
MD: Do all the multiplications and divisions, from left to right, as they appear.
AS: Do all the addition and subtraction, from left to right, as they appear.
Then, we have the following expression:
-4 + 12 ÷ (-3) ÷ 10 + 3 (-2) =
-4-4 ÷ 10 + 3 (-2) =
-4-0.4 + 3 (-2) =
-4-0.4-6 =
-4.4-6 =
-10.4
Answer:
-10.4
If the ratio of a circle’s sector to its total area is 1/3, what is the measure of its sector’s arc?
1/3 = 33%
33% * 390 = 118.8
Your answer 118.8 degrees
Answer: 120 degrees
Step-by-step explanation:
Just did it.
Daniel is choosing between two cellphone plans. "Plan A" charges $80 per month, which includes unlimited text messaging. "Plan B" costs $20 per month plus $0.15 per text message.
What is the system of equation that represents the fees of both "Plan A" and "Plan B"? Identify what your variables represent.
Answer:
Plan A:
C = $80
C = cost
Plan B:
C = 0.15t + 20
C = cost; t = amount of text messages
Step-by-step explanation:
Let C = cost.
Let t = amount of text messages.
Plan A:
C = $80
Plan B:
C = 0.15t + 20
If the next question asks for you to solve when Plan B will be equal to Plan A, set the two equations equal to each other.
80 = 0.15t + 20
Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 20 from both sides.
80 (-20) = 0.15t + 20 (-20)
80 - 20 = 0.15t
60 = 0.15t
Divide 0.15 from both sides.
(60)/0.15 = (0.15t)/0.15
60/0.15 = t
t = 400
Those who use Plan B must send at least 400 text message to have the same price as Plan A.
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