Answer:
D) The relationship between y-intercepts cannot be determined.
Step-by-step explanation:
We have been given two different functions f(x) and g(x). Now we need to find about what can be determined about their y-intercepts. Then match with the correct choice from the given choices:
A) The function f(x) has a higher y-intercept.
B) The function g(x) has a higher y-intercept.
C) They both have the same y-intercept.
D) The relationship between y-intercepts cannot be determined.
We know that y-intercept is the y of function value when x=0.
In the table of g(x), we don't see any point that has x=0
So we can't find the y-intercept for g(x)
Hence correct choice is :
D) The relationship between y-intercepts cannot be determined.
The answer is:
C) They both have the same y-intercept.
Why?In order to find the correct option, we need to find the equation of the function g(x), and then, compare its y-intercept with the y-intercept of the f(x) function.
So,
- Finding the equation of the g(x):
Calculating the slope of the function, using the first two points (-1,8) and (1,0), we have:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-8}{1-(-1)}=\frac{-8}{2}=-4[/tex]
Now, calculating the value of "b" using the first point (-1,8) and the slope of the function, we have:
[tex]y=mx+b[/tex]
[tex]y=-x+b[/tex]
[tex]8=-4(-1)+b[/tex]
[tex]b=4[/tex]
So, the equation of g(x) is:
[tex]y=-4x+4[/tex]
- Comparing the y-intercepts of f(x) and g(x):
Finding the y-intercept of f(x), by making "x" equal to 0, we have:
[tex]y=x+4\\\\y=4[/tex]
We have that the function f(x) has its y-intercept at "y" equal to 4.
Finding the y-intercept of g(x), by making "x" equal to 0, we have:
[tex]y=-4x+4[/tex]
[tex]y=-4*(0)+4[/tex]
[tex]y=4[/tex]
We have that the function g(x) has its y-intercept at "y" equal to 4.
Hence, we have that both functions have their y-intercepts at the same point, so, the correct option is:
C) They both have the same y-intercept.
Have a nice day!
The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.
PLZZZZZ I NEED LE HELP FROM LE FELLOW STUDENTS!!!
Answer:
44 and 46
Step-by-step explanation:
Let
x,x+2-----> the two consecutive positive even integers
we know that
[tex](x+x+2)^{2}=x^{2}+(x+2)^{2} +4,048[/tex]
Solve for x
[tex](x+x+2)^{2}=x^{2}+(x+2)^{2} +4,048\\ \\4x^{2} +8x+4=x^{2}+x^{2} +4x+4+4,048\\ \\2x^{2} +4x-4,048=0[/tex]
Solve the quadratic equation by graphing
The solution is x=44
see the attached figure
therefore
the numbers are
x=44
x+2=46
Find the measure of the third angle of a triangle given the measure of two angles: x and 50
Answer:
is it a right triangle or no ?
Step-by-step explanation:
A person drove 36 miles per hour on a trip. If he had driven 48 miles per hour he would have arrived 4 hours earlier. What was the distance the person drove?
Answer:
d = 576
Step-by-step explanation
Think of the two different speeds as belonging to 2 different cars going to the same place, taking the same route and going to the same place.
Let the time traveled by the fast car = t
Let the time traveled by the slower car = t+4
Let the rate of travel of the slow car = 36 mph
Let the rate of travel of the fast car = 48 mph
===========
d = 36*(t + 4)
d = 48 * t
Since the distance is the same, they can be equated.
48t = 36(t + 4) Remove the brackets.
48t = 36t + 144 Subtract 36t from both sides.
48t - 36t = 144 Combine
12t = 144 Divide by 12
t = 144/12
t = 12
Therefore the faster car takes 12 hours to get where it is going.
d = 48 * t
d = 48 * 12
d = 576
(HELP ASAP PLEASE)
Brenna wrote a business plan for an entrepreneurship class, and now she has to make bound copies. Brenna could use a printer who charges a setup fee of $52 and $5 for every copy printed. Another possibility is to go to the office supply store, where she could pay an up-front fee of $24 and $12 per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How many copies is that? How much would the copies cost?
For ___ copies, the cost is $ ___ .
Answer:
for four copies the cost is $72
Step-by-step explanation:
52 + 5a = 24 + 12a
28 + 5a = 12a
28 = 7a
a = 4
52 + 20 = 72
for four copies the cost is $72
The graph of y = 1/x is vertically stretched by a factor of 3, reflected across the y-axis and shifted to the left by 2 units. What it the function of the resulting graph?
y = 3/(x-2)
y = (-3)/(x+2)
y = 1/(3x-6)
y = (-1)/(3x+6)
y = (-1)/(3x-6)
ANSWER
[tex]y = - \frac{3}{x + 2} [/tex]
EXPLANATION
The given parent function is:
[tex]y = \frac{1}{x} [/tex]
When this function is vertically stretched by a factor of 3, then we have
[tex]y = \frac{3}{x} [/tex]
A reflection across the y-axis transforms the function to;
[tex]y = - \frac{3}{x} [/tex]
When the resulting function is shifted to the left, the transformed function becomes;
[tex]y = - \frac{3}{x + 2} [/tex]
Which of the following nonlinear inequalities is graphed below?
ANSWER
[tex] \frac{( {x + 3)}^{2} }{16} - \frac{( {y + 4)}^{2} }{36} > 1[/tex]
EXPLANATION
The given non-linear function is a hyperbola with equation:
[tex] \frac{( {x + 3)}^{2} }{16} - \frac{( {y + 4)}^{2} }{36} = 1[/tex]
Since the boundary lines are dashed lines, the inequality should be either < or >.
Since the outer portion is shaded, the inequality is
[tex] \frac{( {x + 3)}^{2} }{16} - \frac{( {y + 4)}^{2} }{36} > 1[/tex]
The radius of a small ornament in the shape of a sphere is 2 inches. What is the approximate volume of the ornament? Use 3.14 for pi. Round to the nearest tenth of a cubic inch.
Answer:
34
Step-by-step explanation:
The volume is calculated as approximately 33.5 cubic inches when rounded to the nearest tenth.
The question asks us to calculate the volume of a sphere with a known radius using the value of 3.14 for pi. The formula for the volume of a sphere is V = (4/3)πr³. Given that the radius (r) is 2 inches, we substitute the given values into the formula to find the volume:
V = (4/3)πr³
V = (4/3) × 3.14 × (2 inches)³
V = (4/3) × 3.14 × 8
V ≈ 33.51 cubic inches
We then round the result to the nearest tenth to get the final answer:
The approximate volume of the ornament is 33.5 cubic inches.
Probability question. Please answer with work attached.
Step-by-step Answer:
There is a total of 10 coins, 5 dimes, 2 quarters and three pennies.
By picking a coin, it could be any that shows up out of the 10, so the probability of picking any coin in particular is 1 / 10.
If there are 5 dimes, the probability of picking ANY one particular dime is 1/10, so with 5, the probability of picking ANY of the five dimes is 5/10 = 1/2.
Going along the same line of thought, the probability of picking any of quarters and pennies would be 2/10+3/10 = 5/10 = 1/2 as well.
What is the value of x?
A. 13
B. 17
C. 119
D. 169
Answer:
13
Step-by-step explanation:
x² = 5²+12²
x² = 25+144
x² = 169
x² = 13²
x = 13
Given the equation 2X +4/3 Y equals one and Y -9/13 x=9 by what Vector would you multiply the first equation so that combining the two equations would eliminate x
A -9/26
B 9/26
C 1/2
D -9/13
Answer: Option B
B. [tex]\frac{9}{26}[/tex]
Step-by-step explanation:
We have the following equations:
[tex]2x + \frac{4}{3}y = 1[/tex] (1)
[tex]y -\frac{9}{13}x=9[/tex] (2)
Let us call "a" the coefficient of the variable x in the first equation and call "b" the coefficient of the variable x in the second equation.
Then we must multiply the number "a" by a value z such that when adding [tex]az + b[/tex] the result is zero.[tex]a = 2[/tex]
[tex]b = -\frac{9}{13}[/tex]
So
[tex]2z-\frac{9}{13} = 0[/tex]
We solve the equation for z
[tex]2z=\frac{9}{13}[/tex]
[tex]z=\frac{9}{26}[/tex]
The first equation must be multiplied by a value of [tex]\frac{9}{26}[/tex]
Find the area of a regular hexagon with the given measurement.
4-inch side
A = sq. in.
bruh what is the answer
Answer: [tex]24\sqrt{3}in^2[/tex] or [tex]41.56in^2[/tex]
Step-by-step explanation:
You can find the area of a regular hexagon with the following formula:
[tex]A_{(hexagon)}=\frac{3\sqrt{3}s^2}{2}[/tex]
Where "s" is any side of the regular hexagon.
For this hexagon you know that the length of each side is 4 inches. Then, you must substitute [tex]s=4in[/tex] into the formula [tex]A_{(hexagon)}=\frac{3\sqrt{3}s^2}{2}[/tex].
Therefore, the area of this regular hexagon is:
[tex]A_{(hexagon)}=\frac{3\sqrt{3}(4in)^2}{2}[/tex]
[tex]A_{(hexagon)}=24\sqrt{3}in^2[/tex] or [tex]A_{(hexagon)}=41.56in^2[/tex]
Answer:
the answer is 24 square root 3
Step-by-step explanation:
Solve for X
A: 12.5
B: 5
C: 6[tex]\sqrt{3}[/tex]
D:12
Answer:
D. 12Step-by-step explanation:
(LOOK AT THE PICTURE)
ΔADC and ΔCDB are similar (AAA). Therefore the corresponding sides are in proportion:
[tex]\dfrac{AD}{CD}=\dfrac{CD}{DB}[/tex]
We have
[tex]AD=16,\ CD=x,\ DB=9[/tex]
Substitute:
[tex]\dfrac{16}{x}=\dfrac{x}{9}[/tex] cross multiply
[tex]x^2=(9)(16)\to x=\sqrt{(9)(16)}\\\\x=(\sqrt9)(\sqrt{16})\\\\x=(3)(4)\\\\x=12[/tex]
bear in mind that, a perpendicular line stemming from the right-angle like so, creates three similar triangles, a large one, containing the other two smaller ones, a medium and a small.
so.. .we can just use the medium and small proportions.
Check the picture below.
38. Express these rates in the lowest terms.
a. $56: 16 kg
b. There are six teachers for every 108 students
39. Change to unit rates.
a. $20 for five T-shirts
b. 45 miles in half an hour
Answer:
38: is A
39: is A
Step-by-step explanation:
To express rates in the lowest terms, divide both the numerator and denominator by their greatest common divisor. For unit rates, calculate the rate per single unit of item or time. Example: $7 for 2 kg simplifies to a rate of $3.50 per kg, six teachers for 108 students simplifies to one teacher for 18 students, $20 for 5 T-shirts becomes $4 per T-shirt, and 45 miles in half an hour translates to 90 miles per hour.
Explanation:Question 38: Our goal is to express the rates in the lowest terms.
$56 for 16 kg: To find the simplest form, we divide both the numerator (dollars) and the denominator (kilograms) by the greatest common divisor. $56 and 16 kg both are divisible by 8, so dividing by 8 gives us $7 for 2 kg.Six teachers for every 108 students: The simplest form is found by dividing both numbers by their greatest common divisor, which is 6 in this case. So, 1 teacher for every 18 students is the rate in the lowest terms.Question 39: Here, we will convert the given rates to unit rates.
$20 for five T-shirts: A unit rate is the rate for one unit of the item. To find the unit rate for one T-shirt, divide $20 by 5. This gives $4 per T-shirt.45 miles in half an hour: To find the distance traveled in one hour (unit time), multiply the distance by 2. So, the unit rate is 90 miles per hour.The graph shows the population of a school from year to year what is the rate of change in terms of number of students per year?
Answer:
The number of students per year increasing
The following examples illustrate the associative property of multiplication.
(5 · 3) · 6 = 5 · (3 · 6)
2 · (1.1 · 0.1) = (2 · 1.1) · 0.1
Study the examples, then choose the statement that best describes the property.
a · (b · c) = (a · b) · c
a · b · c = c · a · b
b · c · a = (b · c · a)
(a · b) · c = a · b
Answer:
The first example: a · (b · c) = (a · b) · c
Step-by-step explanation:
The associative property regroups values by changing the location of parentheses. If you notice, the order of the values is not changed. Both sides have a x b x c, only the parentheses have been moved. Moving the parentheses changes the progression of what is multiplied (whatever is in the parentheses is multiplied together first) but doesn't change the final answer.
The statement a. (b . c) = ( a . b ) . c describes the correct property.
What is associative property ?Associative property for multiplication states that rearranging the terms and brackets places in a multiplication of two or more than two terms does not change the result of the multiplication.
There are more properties multiplication is commutative also for example a×b = b×a
a . ( b . c ) = ( a . b) . c is the right answer here brackets have been changed according to the statement.
Learn more about Associative property :
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What is the correct solution to the expressions 3 + 5^2
Answer:
28
Step-by-step explanation:
3+5^2
3+25
28
Answer:
28
Step-by-step explanation:
5^2=5*5
5*5=25
25+3=28
Solve each equation. 6.97a = 27.88
Answer:
a=4
Step-by-step explanation:
6.97a = 27.88
Divide 6.97a on both sides
6.97a/6.97a = 27.88/6.97a
a=4
6.97a = 27.88
Divide both sides by 6.97.
6.97a/6.97 = 27.88/6.97
a = 4
PLZ HURRY IT'S URGENT!
What is the distance between the points (4, 7) and (4, –5)? A. 2 units B. 0 units C. 4 units D. 12 units
Answer:
D. 12 units
Step-by-step explanation:
The distance between two points is found by
d = sqrt( (x2-x1)^2 + (y2-y1)^2)
sqrt( (4 -4)^2 + (-5-7)^2)
sqrt((0^2 + (-12)^2)
sqrt(0+144)
sqrt(144)
12
How many 2/3 cup servings of rice are in a 6 cup bag
Answer:
9
Step-by-step explanation:
namely, how many times does 2/3 go in 6?
[tex]\bf 6\div\cfrac{2}{3}\implies \cfrac{6}{1}\div\cfrac{2}{3}\implies \cfrac{6}{1}\cdot \cfrac{3}{2}\implies \cfrac{3}{1}\cdot \cfrac{6}{2}\implies 3\cdot 3\implies 9[/tex]
Determine the coordinates of the y-intercept of 5x − 5y = 4
Final answer:
The coordinates of the y-intercept of 5x − 5y = 4 are (0, -4/5).
Explanation:
The y-intercept of a linear equation represents the point where the line intersects the y-axis. To determine the coordinates of the y-intercept, we set the x-coordinate to 0 and solve for y. In the equation 5x - 5y = 4, To determine the coordinates of the y-intercept of the equation 5x − 5y = 4, we set the x-value to 0 since, by definition, the y-intercept occurs where the line crosses the y-axis (x=0). The equation simplifies to -5y = 4. we substitute x=0 and solve for y:
5(0) - 5y = 4
-5y = 4
y = -4/5
Therefore, the coordinate of the y-intercept is (0, -4/5).
Solve the following equation. Then place the correct number in the box provided. x/1.2=15
Answer:
x = 18
Step-by-step explanation:
The equation to solve is:
[tex]\frac{x}{1.2}=15[/tex]
This basically means, "what number" (x), divided by 1.2 would give us 15??
We can cross multiply and simply solve for x:
[tex]\frac{x}{1.2}=15\\x=1.2*15\\x=18[/tex]
Correct answer x = 18
Answer:
x=18
Step-by-step explanation:
x/1.2=15
Multiply each side by 1.2
x/1.2 * 1.2 =15 * 1.2
x = 18
What are the real zeros of the function g(x) = x3 + 2x2 − x − 2?
For this case, to find the roots of the function, we equate to zero.
[tex]x ^ 3 + 2x ^ 2-x-2 = 0[/tex]
We rewrite how:
[tex]x ^ 3 + 2x ^ 2- (x + 2) = 0[/tex]
We factor the maximum common denominator of each group:
[tex]x ^ 2 (x + 2) -1 (x + 2) = 0[/tex]
We factor the polynomial, factoring the maximum common denominator[tex](x + 2):[/tex]
[tex](x + 2) (x ^ 2-1) = 0[/tex]
By definition of perfect squares we have to:
[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]
ON the expression[tex](x ^ 2-1):[/tex]
[tex]a = x\\b = 1[/tex]
So:
[tex](x ^ 2-1) = (x + 1) (x-1)[/tex]
Thus, the factorization of the polynomial is:
[tex](x + 2) (x + 1) (x-1) = 0[/tex]
[tex]x_ {1} = - 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]
ANswer:[tex]x_ {1} = - 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]
a small refrigerator is a cube with a side length of 16in use the formula s equals 6s to the second power to find the surface area of the cube
Answer:
1536 in²
Step-by-step explanation:
S = 6s²
We are told that s = 16 inches, so plugging in:
S = 6 (16)²
S = 1536 in²
What is the degrees in arc AE?
Answer:
[tex]\boxed{27^{\circ}}[/tex]
Step-by-step explanation:
BD is a diameter of the circle, so
mDE + mAE + mAB = 180°
63° + mAE + 90° = 180°
mAE + 153° = 180°
mAE = 27°
The measure of arc AE is [tex]\boxed{27^{\circ}}[/tex]
29. Find the circumference.
a. 3.14
b. 69.08
c. 121
36
Answer:
b. 69.08Step-by-step explanation:
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
r - radius
We have r = 11. Substitute:
[tex]C=2\pi(11)=22\pi[/tex]
[tex]\pi\approx3.14\to C\approx(22)(3.14)=69.08[/tex]
The answer is B.
Hope this helps :)
Select the correct answer. Rectangle ABCD is dilated by a scale factor of 2 with the origin as the center of dilation, resulting in the image A′B′C′D′. If the slope of is -2, what is the slope of ? A. -4 B. -1 C. -2 D. 0
Answer:
i think its -2
because the object increased in size but nothing else changed the slope stays the same the slope is the same as the original shape
if i am wrong i apologize
Step-by-step explanation:
The slope of the rectangle will be the same as ABCD option (B) -2 is correct, which is the slope of the ABCD.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We have:
Rectangle ABCD is dilated by a scale factor of 2 with the origin as the center of dilation, resulting in the image A′B′C′D′.
As we know, if dilate the rectangle by factor 2 the slope of the sides will not change.
Thus, the slope of the rectangle will be the same as ABCD option (C) -2 is correct, which is the slope of the ABCD.
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Find volume of cylinder
Show work
For this case we have that by definition, the volume of a cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where:
A: It is the radius of the cylinder
h: It's the height
We have according to the data that:
[tex]r = \frac {34} {2} = 17 \ m\\h = 27 \ m[/tex]
Substituting in the equation we have:
[tex]V = \pi * (17) ^ 2 * 27\\V = \pi * 289 * 27\\V = 24501.42\ m^3[/tex]
ANswer:
[tex]V = 24501.42\ m^3[/tex]
Eduardo's average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged
40 miles per hour. If the round trip took him 1.25 hours, which expression represents the distance, in miles, for his trip home
that is missing from the table?
Rate
(mi/h)
55
Time
(h)
Distance
(miles)
55t
Commute to
Work
Commute to
Home
40
Answer:
The answer is 40(1.25 – t) C.
Step-by-step explanation:
That's the answer for e2020 students!!
Answer:
c
Step-by-step explanation:
big brain
Kamal solved an equation as shown below. 3(x-8)=x+2x+7 3x-24=3x+7 -24=7 What is the solution to Kamal’s equation?
Answer:
No solution
Step-by-step explanation:
The given equation is [tex]3(x-8)=x+2x+7[/tex].
Kamal expanded first and simplified the RHS to get: [tex]3x-24=3x+7[/tex]
He then subtracted 3x from both sides of the equation to get: -24=7
Since the last statement is false, it means the given equation is inconsistent.
Hence the equation has no solution.
Answer:Its No Solution i just took the Unit Test.
Step-by-step explanation:
Which quotient is the same as the quotient 4.85÷0.7? 1. 48.5÷7 2. 48.5÷70 3. 485÷0.07 4. 485÷7
Answer:
1. 48.5÷7
Step-by-step explanation:
4.85÷0.7
We can multiply both terms by 10 without changing the division problem
4.85 * 10 = 48.5
.7 * 10 = 7
48.5 ÷ 7 is the same as 4.85 ÷ .7