y = (x - 1)² - 10 is the vertex form of the equation y = x² - 2x - 9.
Given, y = x² - 2x - 9
The equation is already in standard form : y = ax² + bx + c
where a=1, b=-2 and c=-9 according to the equation y = x² - 2x - 9.
The vertex form of parabola is: y = a (x - h)² + k
The "a" in y = ax² + bx + c equation and the "a" in equation y = a (x - h)² + k are the same attributes of a parabola, therefore, substitute 1 for "a" in equation y = a (x - h)² + k: y = (x - h)² + k.
"h" is the x coordinate of the axis of the vertex: h = [tex]\frac{-b}{2a}[/tex]
Substitute in the values: h = - ( -2 ) ÷ 2(1)
∴ h = 1
Then, Substitute the value of h into the y = (x - h)² + k.
y = (x - 1)² + k.
Using the coordinates x and y from the above equations,
k = 1² - 2(1) - 9
k = 10
Now, Substitute the value of k into the equation y = (x - 1)² + k.
y = (x - 1)² - 10.
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Masha is training for a marathon. she is doing tempo runs to get faster. in tempo runs, a runner varies their pace during the race. masha jogs 1 mile , then runs at a fast pace for 11 miles. she finishes by walking 2 miles to cool down. write a numerical expression to model the number of miles masha runs, jogs, or walks?
The numerical expression for model the number of miles to Masha runs, jogs or walks will be;
⇒ 1 + 11 + 2
⇒ 14
What is Addition?
Addition in math is the process of combining two or more numbers. Addends are the numbers added, and the result or the final answer.
Now,
Masha is training for marathon.
Masha jogs 1 mile.
And, runs at a fast pace for 11 miles.
And, For finishing by walking she walk 2 miles to cool down.
Now,
The numerical expression for model the number of miles to Masha runs, jogs or walks will be;
⇒ Miles in jogs + miles in runs + miles in walk
⇒ 1 + 11 + 2
⇒ 14 miles.
Therefore,
The numerical expression for model the number of miles to Masha runs will be;
⇒ 1 + 11 + 2
⇒ 14
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You collect a total of $160 in donations from three people. The three donations are in the ratio 5 : 5 : 10. How much do the two people donate that donate the same amount? How much greater is the largest donation than the smaller donations?
1. The amount donated by the people with same ratio is $40.
2. The amount greater is $40.
How to calculate the value?From the information, there's a total of $160 in donations from three people and the three donations are in the ratio 5 : 5 : 10.
It should be noted that the amount donated by the people with same ratio will be:
= 5/(5 + 5 + 10) × $160
= 5/20 × $160
= $40
The amount donated by the person with largest ratio will be;
= 10/20 × $160
= $80
Therefore, the difference will be:
= $80 - $40
= $40
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Find the equation of the line.
The perpendicular bisector to the line segment with endpoints (-7, 6) and (5,2).
3x - y = -7 is the required equation of the line, which will bisect the line segment with endpoints (-7, 6) and (5,2).
the equation for the perpendicular bisector of the line with end points [tex](x_{0},y_{0})\\[/tex] and [tex](x_{1},y_{1})[/tex] are given by:
[tex]2(x_{1} - x_{0})x+2(y_{1}-y_{0})y = x^{2} _{1}-x^{2} _{0}+y^{2}_{1}-y^{2}_{0}[/tex]
in the given case we have,
[tex](x_{0},y_{0})\\[/tex] = (-7,6)
and
[tex](x_{1},y_{1})[/tex] = (5,2)
now substituting the given values in the above equation we get,
2(5-(-7))x + 2(2-6)y = 5²- (-7)² + 2²- 6²
= 24x - 8y = 25 - 49 + 4 - 36
= 24x - 8y = -56
on simplifying by dividing the LHS and the RHS by 6 we get our equation to be,
3x - y = -7
What is a perpendicular bisector?
A line or segment that is perpendicular to another segment and passes through its midpoint is called a perpendicular bisector.
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Complete the proof
Given: Line AB intersects line DC at point E ; AEB and DEC are straight angles.
Prove: AEC = DEB
∠ AEC = ∠ DEB by using the property of the straight lines.
We are given the two lines AB and CD.
We are given that they intersect at point E and both are the straight lines.
Now, we know that, the sum of angles of a straight line will be equal to 180° (straight line property).
Now, For line AB, we get that:
∠ AED + ∠ DEB = 180° …(1)
For line CD, we get that,
∠AED + ∠ AEC = 180° … (2)
Now, we will subtract (1) from (2) and we get that:
∠ AED + ∠ DEB - ∠AED - ∠ AEC = 180° - 180°
∠ DEB - ∠ AEC = 0
∠ DEB = ∠ AEC
∠ AEC = ∠ DEB
Hence proved.
Therefore, we get that, ∠ AEC = ∠ DEB by using the property of the straight lines.
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you estimate that you can do 30 math problems in 45 minutes. How many minutes should it take you to do 40 math problems?
Answer:
60 minutes
Step-by-step explanation:
Proportions:Number of problems done, and the time taken to finish them are in proportion.
Let the time taken to finish 40 problems = 'x'
30 : 45 = 40 : x
Product of extremes = 30 *x = 30x
Product of means = 45 * 40
Product of extremes = Product of means
30 *x = 45 * 40
[tex]\sf x = \dfrac{45*40}{30}[/tex]
x = 15 * 4
x = 60 minutes
At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44 adult and baby camels at the zoo.
Complete the table.
The number of baby camels at the zoo is 44.
Given: The number of adult camels is 6 and the number of baby camels is 5 for every 6 camels respectively.
To find :We have to find how many baby camels are at the zoo.
Explanation:
Step 1:The ratio of adult camels and baby camels is 6:5
Step 2:Let the number of adult camels = 6x .
Step 3:Let the number of baby camels = 5x
Step 4:It is given that the total number of adult camels and baby camels is 44 at the zoo. So According to the questions,
⇒6x+5x=44
⇒11x=44
⇒x=44/11
⇒x=4
∴The number of adult camels = 6×4
= 24
And the number of baby camels at the zoo.
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If f(a)= -4 what is the value of a
If the distance from 0 to x on a number line is greater than 0, then -5 + x is positive?
True or false
True.
Given the statement 'If the distance from 0 to x on a number line is greater than 5, then -5+x is positive' is True.
For the given question,
The distance from 0 to x on a number line is greater than 5
We write the above statement in mathematical expression form as,
⇒ |x - 0| > 5
⇒ |x| > 5
⇒ x > 5
We need to determine the value of an expression -5 + x
From (1),
⇒ x > 5
Subtract -5 from both sides,
⇒ -5 + x = -5 + 5
⇒ -5 + x > 0
From the above expression, we observe that the value of the expression is always greater than 1.
This means the value of an expression -5 + x is positive.
Therefore, the given statement 'If the distance from 0 to x on a number line is greater than 5, then -5+x is positive' is True.
In mathematics, a number line can be described as a figure that symbolizes numbers on a consecutive line. The digits on a number line are positioned successively with equal spacing along its length. It can be infinitely expanded in any direction and is often depicted horizontally.
Absolute value is the distance between a digit and zero on a number line. Since the space is forever positive, the absolute value will always be positive.
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PLEASE HELP ME
(03.03 MC)
A bacteria is growing by a factor of 2 every hour from 1 p.m. to 11 p.m. The function below shows the number of bacterial cells, f(x), after x hours from 1 p.m.: f(x) = 20(2)* Which of the following is a reasonable domain for the function?
A. All positive integers
B. 1≤x≤ 11
C. 0≤x≤ 20
D. 0≤x≤ 10
Answer:
D. 0 ≤ x ≤ 10
Step-by-step explanation:
I took the quiz.
The domain of the function is 0 ≤ x ≤ 10 if the function is f(x) = 20(2)ˣ which represnts the exponential function option (D) is correct.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
It is given that:
A bacteria is growing by a factor of 2 every hour from 1 p.m. to 11 p.m.
The function is:
f(x) = 20(2)ˣ
The value of x represents the domain of the exponential function.
The domain of the function is:
0 ≤ x ≤ 10
Thus, the domain of the function is 0 ≤ x ≤ 10 if the function is f(x) = 20(2)ˣ which represnts the exponential function option (D) is correct.
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Solve the following problems using special product. SHOW YOUR SOLUTION.
2.) What is the area of a rectangle if its length measures (10y+4w)cm and its with measures (10y-4w)cm.
[tex]a = l \times w \\ a = (10y + 4w)(10y - 4w) \\ a = 10y(10y - 4w) + 4w(10y - 4w) \\ a = 100 {y}^{2} - 40wy + 40wy - 16 {w}^{2} \\ a = 100 {y}^{2} - 16 {w}^{2} [/tex]
ATTACHED IS THE SOLUTION
Hamburgers are sold in packages of 20 well buns are sold in packages of 12 what are the least number of packages you should buy in order to have the same number of hamburgers and buns
60 number of packages needed to have the same number of hamburgers and buns.
In this problem, we are using the concept of Least Common Multiple. The least common multiple (LCM) of two numberts is the smallest number that can be partitioned by both numbers. To have the same number of buns and hamburgers, we just need to calculate the least common multiple of 20 and 12
12's Multiples = 12, 24, 36, 48, 60, 72, 90
20's Multiples = 20, 40, 60, 80, 100
Here we can see the common multiple of 20 and 12 is 60, and the LCM of 20 and 12 is 60. Therefore they need to buy 60 packages in order to have the same number of hamburgers and buns
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PLEASE HELP! When you set up your 6-feet-tall beach umbrella this morning, it cast an 8 foot shadow on the sand. How long is the shadow of your little sandcastle, which is proudly standing at 1.5 feet tall?
(Please answer in terms of feet)
Answer:
2 feet
Step-by-step explanation:
Answer:
3.5
Step-by-step explanation:
6 plus 2 equals 8 and if you add 2 to 1.5 you get3.5
Solve 2x - y = y for x
A. 2y - 2 B. y - 2 C. y. D. 0
Kylie went into a grocery store and bought 3 apples and 4 bananas, costing a total of
$6.50. Lily went into the same grocery store and bought 10 apples and , bananas,
costing a total of $17.50. Write a system of equations that could be used to determine
the price of each apple and the price of each banana. Define the variables that you
use
to write the system.
Answer:
0.87 cent
if i did this right.
Step-by-step explanation:
17.50 divided by 2 = 8.75
8.75 divided by 10 = 0.87
I am less than a whole. I am 3 decimal places.when rounded to the nearest tenth I am 0.78.what number am i
The number that is less than a whole, in 3 decimal places and when rounded to the nearest tenth is 0.78 will be 0.775.
When is a decimal?A fraction expressed in a particular way is called a decimal. As an alternative to expressing 1/2, you might write 0.5 instead, with the zero in the ones place and the five in the tenths position. The word decimus, which means tenth in Latin, is derived from the base word decem, or 10.
It should be noted that 0.775 is in 3 decimal places. In this case, the last 5 will be converted and this will become 0.78.
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Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x − 2)?
A) The graph of y = f(x) will shift left 2 units.
B)The graph of y = f(x) will shift right 2 units.
C) The graph of y = f(x) will shift up 2 units.
D) The graph of y = f(x) will shift down 2 units.
We have a horizontal translation of 2 units to the right, so the correct option is B.
"The graph of y = f(x) will shift right 2 units."
Which effect will have it on the graph?
For any function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left.
if N < 0, the translation is to the right.
In this case we have the function written as:
y = f(x - 2)
So we have N = -2, which means that we have a translation of 2 units to the right.
Then the correct option is B.
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The Sydney Opera House can house no more than 5738 people. Luisa Miller always brings crowds of at least 4,000 people. What is the maximum number of empty seats that might not be filled during her performance?
What's the inequality for this story?
Write the steps to solve it
What is the solution?
When this inequality is graphed will the limit be an open or closed circle?
When this inequality is graphed will the line have an arrow pointing to the right or to the left?
The maximum number of seats that might not be filled during her performance is 1738 , the the inequality representing this story is 4000+x≤5738 .
In the question ,
it is given that
Luisa Miller always brings crowds of at least 4,000 people, and
Sydney Opera House can house no more than 5738 people
no more than is represented by the inequality "≤" .
let x be the number of empty seats during her performance .
So, according to the question , the inequality becomes
4000+x≤5738
on solving further , we get
x ≤ 5738-4000
x ≤ 1738
So, maximum number of seats that might not be filled during her performance is 1738 .
When the inequality x ≤ 1738 , will be graphed then the limit will be an closed circle as equal to sign is included in the inequality .
as when the numbers decreases , it move towards left side
So, When the inequality is graphed, the line will have an arrow pointing towards the left .
Therefore , the maximum number of seats that might not be filled during her performance is 1738 ,
the the inequality representing this story is 4000+x ≤ 5738 ,
the limit of graph will be closed circle and arrow will be pointing towards left .
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shureka washburn has scores of 69,80,71, and 90 on her algebra tests
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 77 or higher, given that the final exam counts as two tests.
b. Explain the meaning of the answer to part (a).
Help please
The inequality to find the scores she must make on the final exam to pass the course with an average of 77 or higher is (310 + x) / 5 >= 77.
The meaning is that she should have a score of 75 or higher to pass.
How to calculate the value?From the information, Shureka washburn has scores of 69,80,71, and 90 on her algebra tests and she must make on the final exam to pass the course with an average of 77 or higher.
Therefore, the inequality to express the information will be:
(69 + 80 + 71 + 90 + x)/5 >= 77
(310 + x) / 5 >= 77
Crops multiply
310 + x >= 77 × 5
310 + x >= 385
x >= 385 - 310
x >= 75
She needs 77 or more in order to pass the course.
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500 divided by 2/3 = 500 x _ = _ feet
Answer:
500 divided by 2/3 = 500 * 3/2= 750
Step-by-step explanation:
If the ratio of m to n is equal to 5 then which of the following is true?
If ratio of m to n is equal to 5 then, m = 5n
What are ratios?Ratios :- The quantitative relation between two amounts showing the number of times one value contains or is contained within the other are known as ratios.
m/n = 5
m = 5
Therefore, option b is correct i.e. m = 5.
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I think of number double it and subtract two i get nine
Answer: the number in question is 5.5
Step-by-step explanation: brainliest please? i could really use it
assume that y is normally distributed n (, 2). moving from the mean () 1.96 standard deviations to the left and 1.96 standard deviations to the right, then the area under the normal p.d.f. is:
assume that y is normally distributed n (, 2). moving from the mean () 1.96 standard deviations to the left and 1.96 standard deviations to the right then P( -1.96 ≤ Z≤ 1.96) = 0.95
assume that y is normally distributed n (, 2). moving from the mean () 1.96 standard deviations to the left and 1.96 standard deviations to the right
Given that the z -scores -1.96 and 1.96
we have to find Probability( -1.96 ≤ Z≤ 1.96)
Probability( -1.96 ≤ Z≤ 1.96) = |A(1.96)+A(-1.96)|
= |A(1.96)+A(-1.96| (∵A(-Z) = A(Z))
= 0.4750+0.4750
= 2×0.4750
= 0.95
The probability lies between -1.96 to 1.96
P( -1.96 ≤ Z≤ 1.96) = 0.95
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Solve for n. −2(n − 3.5) > 15 n > −4 n < −4 n > 4 n < 4
Answer: N > -4
Step-by-step explanation:
Cuz It's Right
The solution for inequality is n < -4.
The given inequality is −2(n − 3.5) > 15
An inequality will have the sign < , > , ≥ or ≤ instead of an equality in an equation. That is, an inequality compares two quantities on either sides of the inequality sign.
We are asked to solve the inequality −2(n − 3.5) > 15. That is, to find the possible values for n.
−2(n − 3.5) > 15
Dividing throughout by 2,
-(n - 3.5) > 15/2
⇒ -n +3.5 > 7.5
Subtracting 3.5 from both sides,
⇒ -n > 7.5 - 3.5
⇒ -n > 4
Multiply -1 on both sides of the inequality and the inequality will be reversed,
⇒ n < -4 is the solution for n.
The solution is the values of n less than -4.
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In 2008, Evan bought a car. In 2010, Evan sold the car to Grace. Evan made a loss of 25%. In 2018,
Grace sold the car for £15225 Grace made a profit of 45% Work out how much Evan bought the car
for in 2008.
The price in which Evan bought the car for in 2008 is 75 percentage or £14000
What is Percentage ?
Percentage (%), which is a relative figure used to denote hundredths of any quantity. One percent is represented by the symbol 1%; hence, 100 percent denotes the entire amount, and 200 percent designates double the amount.
Given,
Loss% = 25%
Profit% = 45%
selling price = £15,225
The price of the car before getting the profit of 45%
= 15225 / 145 x 100
= 105 x 100
= 10500
The price of the car before getting the profit of 45% is £10500
Now, he had a loss of 25%
=100% - 25%
= 75%
So, the price will be
= 10500 / 75 x 100
= 14000
Hence, Evan bought the car for £14000 in 2008
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Ar 1:00am the temperature in the Gardem City was -8°F. by noon, the temperature was 25°F. What was the change in temperature, in degrees Fahrenheit, from 1:00am to noon
The change in temperature was 25 F - (-8F) = 33 F.
Answer:
Explanation:
The change in temperature is the difference between the two temperatures. In our case this is 25 F - (-8F) = 33 F. Notice that the subtracting the negative number changes the sign of the operation and turns it into an addition problem25 F+ 8 F = 33 F.
In ∆OPQ, q =18cm, o=96cm and
Given the information on the problem, we can use the law of cosines to find the length of p with the following equation:
[tex]p^2=q^2+o^2-2q\cdot o\cdot\cos P[/tex]substituting the values at hand, we get the following:
[tex]\begin{gathered} p^2=(18)^2+(96)^2-2(18)(96)\cos 142 \\ \Rightarrow p^2=324+9216+2723.37 \\ \Rightarrow p^2=12263.37 \\ \Rightarrow p=\sqrt[]{12263.37}=110.74 \\ p=110.7\operatorname{cm} \end{gathered}[/tex]therefore, the length of p is 111 cm
what is the horizontal asymptote as $x$ approaches positive infinity of $$\sqrt{4x^2 5x} - \sqrt{4x^2 x}?$$the horizontal asymptote is in the form $y
the horizontal asymptote as x tends to infinity that is approaches positive infinity of \sqrt{4x^2+ 9x} - \sqrt{4x^2 +x} is 2
What do the asymptotes mean?
Definition of asymptote
a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the
slope of the line
[tex]f(x)=\sqrt{4x^2+9x}-\sqrt{4x^2+x} \\\\f(x)=2x(1+\frac{9}{4x}) ^{\frac{1}{2} } -2x(1+\frac{1}{4x})^\frac{1}{2}[/tex]
[tex]f(x)=2x( 1+\frac{1}{2} .\frac{9}{4x} +...... -1 -\frac{1}{2} .\frac{1}{4x} - ......)[/tex]
all the other terms involve 1/powers of x which vanish as x tends to infinity
[tex]f(x)=\frac{9}{4} -\frac{1}{4} +...[/tex]
Hence
[tex]\lim_{x \to \infty} f(x)=2[/tex]
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If A= -2, 2, 0, -5, 7, 9, C=-1, -1, -2, -7, 3, 2, and A - B = C, what is B?
B = [tex]\left[\begin{array}{ccc}-1&3&2\\2&4&7\end{array}\right][/tex] if A-B = C and values of A and C is given .
What is Matrix and determinants ?In linear algebra, determinants and matrices are used to solve linear equations by applying Cramer's rule to a collection of non-homogeneous equations that are expressed in linear form. Determinants are only determined using square matrices. If a matrix's determinant is zero, it is referred to as a singular determinant; if it is one, it is referred to as a unimodular matrix. For the system of equations to have a single solution, the determinant of the matrix must be nonsingular, or its value must be nonzero.In this post, we will discuss the definition of determinants and matrices, as well as their many types, characteristics, and instances.Calculation:
since A-B=C
so, A-C=B
plugging in the values :-
[tex]\left[\begin{array}{ccc}-2&2&0\\-5&7&9\end{array}\right] \left[\begin{array}{ccc}-1&-1&-2\\-7&3&2\end{array}\right][/tex] = B
B = [tex]\left[\begin{array}{ccc}-1&3&2\\2&4&7\end{array}\right][/tex]
Hence the value of B is = [tex]\left[\begin{array}{ccc}-1&3&2\\2&4&7\end{array}\right][/tex]
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4. Joe Shmoe is guaranteed a minimum of $450 salary plus 3.75% of his
total sales. What are his total sales for a week in which his gross pay was
$650?
Answer:
the total sales are 361 sales a week i did this i got a 100
A salad dressing is made by mixing oil and mayonnaise in the ratio 5 : 2
Jack makes 700 ml of the salad dressing.
How much oil does he use?
Give your answer in millilitres (ml).
The oil he use in the salad 291.66ml
What is Ratio ?
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
The formula below can be used to determine how much oil Jack consumes:
Jack uses x amount of mayonnaise to make y amount of salad dressing * (5 / (5 + 7)) ---. (1)
If we change the number of ml of salad dressing Jack prepares in equation (1), we get the following result:
Jack uses 291.66 ml of oil, which is equal to 700ml * (5/ (5 +7))
Hence, it will take 291.66ml of oil
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