Answer:
Step-by-step explanation:
The parabola y=x^2 is shifted up by 7 units and to the left by 1 unit.
Answer:
y=(x+1)^2 +7
When the parabola y=x² is shifted up by 7 units and to the left by 1 unit then the equation of the new parabola is y = (x-1)² + 7.
When a parabola is shifted vertically or horizontally, its equation changes accordingly.
In this case, the parabola y = x² is shifted up by 7 units and to the left by 1 unit.
Adding a constant value to the function shifts the graph vertically.
In this case, adding 7 to the original function y = x² will shift it up by 7 units:
y = x² + 7
Subtracting a constant value from the input of the function shifts the graph horizontally.
In this case, subtracting 1 from the x-values of the function y = x² + 7 will shift it to the left by 1 unit:
y = (x-1)² + 7
Hence, the equation of the new parabola after both shifts is y = (x-1)² + 7.
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2x + 4y = 15
6x +12y = 45
What would the solution to the system of equations be?
Answer:
They both have an infinite number of solutions.
Step-by-step explanation:
Given system of equations:
a) 2x + 4y = 15
b) 6x + 12y = 45
Slope-intercept form: y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Rewrite both equations into slope-intercept form:
a) 2x + 4y = 15
⇒ 2x + 4y = 15 [subtract 2x from both sides]
⇒ 2x - 2x + 4y = 15 - 2x
⇒ 4y = - 2x + 15 [divide both sides by 4]
⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)
[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
b) 6x + 12y = 45
⇒ 6x + 12y = 45 [subtract 6x from both sides]
⇒ 6x - 6x + 12y = 45 - 6x
⇒ 12y = - 6x + 45 [divide both sides by 12]
⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)
[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
New equations:
[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.
System of equations can have the following:
No Solution: the same slope (both lines will be parallel)
One Solution: different slopes and different y-intercepts
Infinitely Many Solutions: the same slope and y-intercept
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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.
Slope-Intercept Form ⇒ [tex]y = mx + b[/tex]m = slopeb = y-interceptEquation #1
Subtract 2x from both sides
[tex]2x + 4y = 15[/tex][tex]2x - 2x + 4y = 15 - 2x[/tex][tex]4y = -2x + 15[/tex]Divide both sides by 4
[tex]\frac{4y}{4} = \frac{-2}{4}x + \frac{15}{4}[/tex][tex]y = \frac{-2}{4}x + \frac{15}{4}[/tex][tex]y = -0.5x + 3.75[/tex]Equation #2
Subtract 6x from both sides
[tex]6x + 12y = 45[/tex][tex]6x - 6x + 12y = 45 - 6x[/tex][tex]12y = -6x + 45[/tex]Divide both sides by 12
[tex]\frac{12y}{12} = \frac{-6}{12}x + \frac{45}{12}[/tex][tex]y = \frac{-6}{12}x + \frac{45}{12}[/tex][tex]y = -0.5x + 3.75[/tex]Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other. Therefore, there are infinite solutions as they will always continue on top of each other.
f(x)=√x +3. Find the inverse of f(x) and its domain.
Answer:
f(x) = √x + 3
y = √x + 3
√x = y - 3
x = (y - 3)²
Hence inverse of f(x) = (x - 3)² and its domain is x >= 3.
Step-by-step explanation:
hope this helps
What additional piece of information would prove △LMK≅△NMK by Side Angle Side?
Answer:
angle M
Step-by-step explanation:
if you are using side angle side the two sides may be
line LK and NK
and angle M
If 8x + y = -1 is a true equation, what would be the value of y + 8x
The y-intercept is the place where a line crosses the y-axis. hat is true about the y-intercept?
A. It always has an x coordinate of 0.
B. It always has any coordinate of 0
C. Both x and y coordinates are 0.
Answer:
It always has an x coord of 0
The first step that we must take before attempting to solve a problem is to understand what it is asking for and what is given to us to help solve the problem. Looking at the problem statement, we can see that they are asking what is true about the y-intercept. We are given the information that the y-intercept is the place where a line crosses the y-axis.
Now that we have collected all that information, let us move onto understanding and solving the problem. So first of all, using the information that was given to us, we know that the y-intercept is the place where a line crosses the y-axis. The y-axis occurs where the x-coordinate is 0 and the x-axis occurs where the y-coordinate is 0. Therefore, the option that would best fit the description that we have would be option A, it always has an x coordinate of 0.
A particle is moving along the curve y= 4sqrt(5x+11) . As the particle passes through the point (5,24) , its -coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant
The rate of change of the distance from the particle to the origin at this instant is 3 units per second.
What is the rate of change?The instantaneous rate of change is the rate of change at a particular instant.
A particle is moving along the curve
[tex]y= 4\sqrt{5x+11} .[/tex]
The rate of change of y is given as:
dy / dx = 2
by differentiating both sides,
[tex]\dfrac{dy}{dx} = 4\dfrac{1}{2\sqrt{5x+11} } 5\dfrac{dx}{dt} \\\\\dfrac{dy}{dx} = \dfrac{10}{\sqrt{5x+11} }\dfrac{dx}{dt}\\\\[/tex]
From the question, we have:
(x, y) = (5,24)
Substitute 5 for x and dy / dx = 2
[tex]\dfrac{dy}{dx} = \dfrac{10}{\sqrt{5x+11} }\dfrac{dx}{dt}\\\\\\5= \dfrac{10}{\sqrt{5(5)+11} }\dfrac{dx}{dt}\\\\\\\sqrt{5(5)+11} = 2\dfrac{dx}{dt}\\\\\\\dfrac{dx}{dt} = 6/ 2 = 3[/tex]
Hence, the rate of change of the distance from the particle to the origin at this instant is 3 units per second.
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what is the volume of the solid
Answer:
A.264
Step-by-step explanation:
((Area Of triangle*height)=Volume
Area of triangle is the base of the triangle multiplied by height of triangle divided by 2
((8*6)/2)*11=264
Sophia determined that the expression Negative (4 x minus 5) + 2 (x minus 3) is equivalent to –2x – 5 by using the steps below.
Expression: Negative (4 x minus 5) + 2 (x minus 3)
Expression: –2x – 5
Step 1:
Choose a value of x
Choose x = 1.
Choose x = negative 1.
Step 2: Substitute
Negative (4 (1) minus 5) + 2 (1 minus 3)
Negative 2 (negative 1) minus 5
Step 3: Evaluate
Negative (4 (1) minus 5) + 2 (1 minus 3) = negative (negative 1) + 2 (negative 2) = negative 3
Negative 2 (negative 1) minus 5 = 2 minus 5 = negative 3
Step 4:
Compare
Since –3 = –3, the two expressions are equivalent.
Which explains whether Sophia is correct?
She is correct because the value of the two expressions are the same in Step 3.
She is correct because she substituted opposite values in Step 1.
She is not correct because she did not substitute the same number in both expressions in Step 1.
She is not correct because she did not perform the correct order of operations in Step 3.
The correct statement is:
"She is not correct because she did not substitute the same number in both expressions in Step 1."
Is Sophia correct?First, let's see if Sophia is correct.
She starts with the expression:
-(4x - 5) + 2*(x - 3) = -2x - 5
Expanding the left side:
-4x + 5 + 2x - 6 = -2x - 5
-2x -1 = -2x - 5
So the constant term is different.
Now, what Sophia does is evaluating in x = 1 and x = -1. You can't do that when finding equivalent expressions. (never evaluate in different numbers).
"She is not correct because she did not substitute the same number in both expressions in Step 1."
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Which statement best describes Inflation?
О А. Inflation decreases the amount of goods and services that can be purchased with a dollar.
Inflation Increases the amount of goods and services that can be purchased with a dollar.
Inflation increases the purchasing power of a dollar.
O C.
OD.
Inflation decreases the prices of goods and services.
O E. Inflation doesn't affect the prices of goods and services but increases wages.
Answer:
A
Step-by-step explanation:
Inflation decreases the amount of goods and services that can be purchased with a dollar.
Match each graph with the function it represents.
A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The graph of the function f(x) and g(x) can be plotted as shown in the below image.
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2 x 3 4/5 as a mixed number.
Answer:
7 3/5
Step-by-step explanation:
2 x 3 4/5
2 x 19/5
2x19/1x5 = 38/5 = 7 3/5
Work out the length of
x.
Give your answer rounded to 3 significant figures.
The triangle is an isosceles right triangle. Then the value of x will be 1.27 cm.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The right-angle triangle is given below.
The given triangle is an isosceles right triangle.
P = B = x
Then we have
1.8² = x² + x²
2x² = 3.24
x² = 1.62
x = 1.27 cm
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The ratio of boys to girls is 3:2. f the class has 27 boys. How many pupils are in the class?
Answer:
the answer is 45
see the attachment photo!
what is 0.02 to the power of 4? HELP NEEDED SOON
Answer:
1.6e-7, or .00000016
Step-by-step explanation:
6-2 6 grade home work
Answer:
list five solution to the energy crisis of nepal
Please solve the whole page please please
1d) ↑ (Do the same but turned if that's easier)
1a) 199
1b) 193
1c) 217
1e) Based on the box plot, we can for example, find the lowest and greatest values, the range (largest - smallest), the mean (all values / # values), and the median middle value or q2 given by the second line in the box.
2b) 7
2c) 9.5
2d) ↑
2e) because the data is not ordered, it is difficult to determine the quartile data. Once it is ordered like 6, 7, 7, 7, 8, 8, 9, 10, 10. The data can be visualized alot easier. With the box plot we can determine q3 of the data by looking at the 3rd line, using the whiskers of the box to find the minimum and maximum values.
3)
You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.
In this case the ordered data would be: 4,6,8,8,9,11,12,14,14,16.
[4, 6, 8, 8, 9] [] [11, 12, 14, 14, 16]
4 is the minimum, 16 is the maximum, q1 is 8, q3 is 14, and median is 10.
4) ↑
5)
You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.
In this case the ordered data would be:
45, 45, 50, 55, 60, 70, 70, 75, 80, 85
[45, 45, 50, 55, 60] [] [70, 70, 75, 80, 85]
45 is the minimum, 85 is the maximum, q1 is 50, q3 is 75, and median is 65.
6) ↑
add 6370 square to 6370 square
The table gives information about the speeds, in kilometres per hour, of 80 motorbikes as each pass under a bridge.
Speed
(s kilometres per hour) Frequency
40 < s 50 10
50 < s 60 16
60 < s 70 19
70 < s 80 23
80 < s 90 12
(a) Write down the modal class
(b) Work out an estimate for the mean speed of the motorbikes as they pass under the bridge.
Give your answer correct to 3 significant figures.
The modal class is 70 - 80 and the mean speed is 66.4
How to determine the modal class?The table of values is given as:
Speed Frequency
40 - 50 10
50 - 60 16
60 - 70 19
70 - 80 23
80 - 90 12
The modal class is the class with the highest frequency
The class 70 - 80 has the highest frequency of 23
Hence, the modal class is 70 - 80
How to determine the mean?Rewrite the frequency table to include the class midpoints
x f
45 10
55 16
65 19
75 23
85 12
The estimate of the mean speed is then calculated as:
[tex]\bar x =\frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{45* 10 + 55 * 16 + 65 * 19 + 75 * 23 + 85 * 12}{80}[/tex]
Evaluate
[tex]\bar x = 66.4[/tex]
Hence, the mean speed is 66.4
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EASY POINTS LM is the midsegment of & ABC. If IM is 8 centimeters long, how long is AC
I think it's 12 because here it comes out
Solve for D: 70D + 2 - 14D = 79 + 12D - 20
70d+2-14d= 79+12d-20
70d-14d-12d= 79-20-2
44d= 57
d= 57/44
a quadrilateral is inscirbed in circle o. the angle measures the quadrilateral in degrees are given by the expressions shown in the figure.
what is the measure of angle c?
(will mark branliest + 20points)
Answer:
A. 65 degrees
Step-by-step explanation:
The required measure of the angle c in the quadrilateral is given as 65°.
As mentioned in the question,
A quadrilateral is inscribed in a circle o. the angle measures the quadrilateral in degrees is given by the expressions shown in the figure.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
In a quadrilateral, the sum of the composite angle is equal to 180°,
∠A + ∠C = 180
130 -x + 95 -2x = 180
-3x = 180 - 225
x = 15
Now,
∠c = 95 - 2x
∠c = 95 - 2×15
∠c = 65
Thus, the required measure of the angle c in the quadrilateral is given as 65°.
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can you please help me? 2.1.3
[tex]~~~~~~2I_2 - A\\\\\\=2\begin{bmatrix}1&0\\0&1 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2&0\\0&2 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2-4&0-2\\0-3&2+3 \end{bmatrix}\\\\\\=\begin{bmatrix}-2&-2\\-3&5 \end{bmatrix}[/tex]
HELP!!!!!! 100 POINTS!!!!!!
Kyle and Lauren teach swimming lessons during the summer. Kyle has 8 classes with g students in each class and 6 classes with h students in each class. Lauren has 5 classes with g students in each class and 10 classes with h students in each class.
If Kyle has a total of 62 students and Lauren has a total of 70 students, which equation shows the solution to the system of equations that represents this situation?
The equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
Kyle and Lauren teach swimming lessons during the summer. Kyle has 8 classes with g students in each class and 6 classes with h students in each class. Lauren has 5 classes with g students in each class and 10 classes with h students in each class.If Kyle has a total of 62 students and Lauren has a total of 70 students,The equation made by the given situation is:-
For kyle, there are g students attending 8 classes sp total number of students will be 8g similarly for h students there are 6 classes so the total number of h students will be 6h. The total number of students for both g and h students attending kyle's class is 62. So the equation will be given as:-
8g + 6h = 62
Now for Lauren, there are g students attending 5 classes so the total number of students will be 5g similarly for h students there are 10 classes so the total number of h students will be 10h. The total number of students for both g and h students attending Lauren's class is 70. So the equation will be given as:-
5g + 10h = 70
Therefore the equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.
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what is the decimal equivalent for 15 1/4
Answer:
15.25
Step-by-step explanation:
1/4 is also 0.25 in decimals so add that to your 15 and you get 15.25.
Step-by-step explanation:
the fraction 1/4 is also equivalent to the decimal for of .25 + 15 equals 15.25
Find the equation of the exponential function represented by the table below:
Y
8
0
1
2
3
3
12
48
192
no I dont feel like it is the answer
What is the value of F(x)=-x+9 if x=-7
Answer: F = - 2/7
Step-by-step explanation:
[tex]f(x) = x + 9\\f(-7) = -7 + 9\\f(-7) = 2\\f = -\frac{2}{7}[/tex]
What is the solution to this equation? (1/27)2-x =9^3x
Answer:
x = -2
Step-by-step explanation:
Prime factorize, 27 and 9
27 = 3 *3 * 3 = 3³
9 = 3*3 = 3²
[tex]\sf \left(\dfrac{1}{27}\right)^{2-x}=9^{3x}\\\\[/tex]
[tex]\left(\dfrac{1}{3^3}\right)^{2-x}=9^{3x}\\\\(3^{-3})^{2-x}=(3^2)^{3x}\\\\3^{(-3)*(2-x)}=3^{2*3x}\\\\3^{-6+3x} = 3^{6x}[/tex]
Bases are same, so now compare the exponents
-6 + 3x = 6x
3x = 6x + 6
3x - 6x = 6
-3x = 6
x = 6/(-3)
[tex]\sf \boxed{\bf x = -2}[/tex]
Exponent law:[tex](x^m)^n=x^{m*n}\\\\\left(\dfrac{1}{a^{m}}\right)=a^{-m}\\[/tex]
help?
what fraction of a dollar is 236 cents?
236/100, 59/25, or 2 9/25
Step-by-step explanation:
There are 100 cents in a dollar, so 236/100 is your starting fraction. The simplest improper fraction would be 59/25. But if you're looking for a mixed number, you get 2 9/25.
236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.
To solve this problem,
We need to convert 236 cents into dollars.
Since there are 100 cents in one dollar,
we can divide 236 by 100 to get the equivalent dollar value.
⇒ 236 cents ÷ 100 cents per dollar = 2.36 dollars
Now that we know that 236 cents is equivalent to 2.36 dollars,
we can express it as a fraction of a dollar.
To do this, we'll use the fact that one dollar is equivalent to 100 cents, which means that one dollar can be expressed as the fraction 100/100.
To find the fraction of a dollar that 2.36 dollars represents,
we'll divide 2.36 by 1.
⇒ 2.36 ÷ 1 = 2.36/1
To express this as a fraction of a dollar,
Multiply both the numerator and denominator by 100 to get,
⇒ (2.36 x 100) / (1 x 100) = 236/100
Simplifying this fraction, we get,
⇒ 236/100 = 118/50
Therefore,
236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.
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what is the answer ???
Answer: Heyaa!~
- Write 63 as the product of prime factors -
Since, the prime factors of 63 are 3, 7. Therefore, the product of prime factors = 3 × 7 = 21.- Write the prime factors in ascending order -
I think it would be 3/7- what's the highest common factor of 63 and 105 -
21, divides both 63 and 105, i.e., 21.Hopefully this helps you! ^^^
A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a jack .
Answer:
2/52 so the chance is unlikely.
Step-by-step explanation:
well I think I’m right because sometimes when my family has time we play blackjack in my house for fun or another card game so I should be right.