Hello there. To solve this question, we need to remember some properties about quadratic functions and its key features.
Let f(x) = ax² + bx + c, for a not equal to zero.
The main key feature we can see at first glance is the leading coefficient a.
If a < 0, the parabola (the graph of the function) will have its concavity facing down.
If a > 0, the parabola will have its concavity facing up.
It also means the function will have either a maximum or a minimum point on its vertex, respectively.
Another key feature of the function is the y-intercept, i. e. the point in which the x-coordinate is equal to zero, is (0, c).
The x-intercepts of the graph (in plural), are the roots of the function.
If b² - 4ac > 0, we'll have two distinct real roots.
If b² - 4ac = 0, we'll have two equal real roots.
If b² - 4ac < 0, we'll have two conjugate complex roots (not real roots)
This b² - 4ac is the discriminant of the function.
The roots can be found by the formula:
x = (-b +- sqrt(b² - 4ac))/2a
The vertex of the graph can be found on the coordinates (xv, yv), in which xv is calculated by the arithmetic mean of the roots
xv = ((-b + sqrt(b²-4ac))/2a + (-b-sqrt(b²-4ac))/2a)/2 = -b/2a
The yv coordinate can be found by plugging in xv in the function
yv = a(-b/2a)² + b(-b/2a) + c, which will be equal to -(b²-4ac)/4a.
What is a plane that is perpendicular to the base of a Cube and slices through the cube
The figure formed will be hexagonal
how the position of the decimal point changes in a q u o t i e n t as you divide by Precinct power of 10.
When we divide a number by a power of 10, the decimal point changes its position. Specifically, the decimal points will move to the left according to the exponent of the power. For example, let's say we have the following division.
[tex]\frac{542}{10^3}[/tex]As we said before, we just have to move the decimal point to the left. In this case, we have to move it to 3 spots.
[tex]\frac{542}{10^3}=0.542[/tex]Hence, the division is equivalent to 0.542.
That's how the division works when you divide by a power of 10.
BUSINESS MATH calculate the state income tax owed on a 50,000 per year salary
Hello there. To solve this question, we have to remember some properties about income and taxes.
The following table shows the progressive tax rate for calculating individual income tax:
We want to calculate the state income tax owed on a $50,000 per year salary.
For this, notice this value is contained in the interval 17,001 and up, hence the progressive tax rate for this value is 5.75%.
In this case, the tax is simply given by the product between the value and the rate:
Don't forget to divide the percentage value by 100% before multiplying.
[tex]50000\cdot\dfrac{5.75}{100}=\$2,875[/tex]This is the state income tax owed by one whose salary is $50,000 per year.
write the equation of the polynomial with the following zeros in standard form
Answer:
x² - (5 + √7)x + 5√7
Explanation:
A polynomial with zeros at x = a and x = b can be written as:
(x - a)(x - b)
So, if the roots are x = √7 and x = 5, we can write the equation for the polynomial as follows:
(x - √7)(x - 5)
Then, to write it in standard form, we need to apply the distributive property, so:
[tex]\begin{gathered} (x-\sqrt[]{7})(x-5)=x\cdot x+x(-5)-\sqrt[]{7}x-\sqrt[]{7}(-5) \\ (x-\sqrt[]{7})(x-5)=x^2-5x-\sqrt[]{7}x+5\sqrt[]{7} \\ (x-\sqrt[]{7})(x-5)=x^2-(5+\sqrt[]{7})_{}x+5\sqrt[]{7} \end{gathered}[/tex]Therefore, the answer is:
x² - (5 + √7)x + 5√7
Solve each word problem using a system of equations. Use substitution or elimination. 1. One number added to three times another number is 24. Five times the first number added to three times the other number is 36.
ANSWER
The first number is 3 and the second number is 7
EXPLANATION
Let the first number be x.
Let the second number be y.
The first line of the word problem is:
One number added to three times another number is 24.
This means that:
x + 3(y) = 24
=> x + 3y = 24 ______(1)
The second line of the word problem is:
Five times the first number added to three times the other number is 36.
5(x) + 3(y) = 36
5x + 3y = 36 ______(2)
Now, we have a system of equations:
x + 3y = 24 ____(1)
5x + 3y = 36 ___(2)
From the first equation, we have that:
x = 24 - 3y
Substitute that into the second equation:
5(24 - 3y) + 3y = 36
120 - 15y + 3y = 36
Collect like terms:
-15y + 3y = 36 - 120
-12y = -84
Divide through by -12:
y = -84 / -12
y = 7
Recall that:
x = 24 - 3y
=> x = 24 - 3(7) = 24 - 21
x = 3
Therefore, the first number is 3 and the second number is 7.
Graph the line with the given slope m and y-intercept b.
m = 1, b =0
Answer:
See graph
Step-by-step explanation:
Compare f(0) and g(0)f(0) is <, =, or > to g(0)
From the graph of f(x), it can be obseved that function f(x) value at x = 0 is -3, which means that f(0) = -3.
From the graph of g(x), it can be observed that g(0) = 0.
As value 0 is greater than -3. So f(0) is lesser than g(0).
Answer: f(0) < g(0)
8. In order to reach the top of a hill which is 250 feet high, one must travel 2000 feet straight up a road
which leads to the top. Find the number of degrees contained in the angle which the road makes with the
horizontal.
7.18° the angle which the road makes with the horizontal.
Define Trigonometric functions
The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given,
Height of hill = 250 feet
Length of the slope = 2000 feet
find the angle,
we know, sin(x) = perpendicular / hypotenuse
sin(x) = 250 / 2000
x = sin^-1 (0.125)
x = 7.18°
Hence, 7.18° the angle which the road makes with the horizontal.
To read more about Trigonometric functions.
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y = 3× - 1y = -3× + 1
Given two equations,
[tex]\begin{gathered} y=3x-1 \\ y=-3x+1 \end{gathered}[/tex]Comapring both equations,
[tex]\begin{gathered} 3x-1=-3x+1 \\ 3x+3x=1+1 \\ 6x=2 \\ x=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Therefore, x = 1/3.
sorry its blurry[tex] \frac{3x - 2}{4} = 2x - 8[/tex]
the given expression is,
[tex]\frac{3x-2}{4}=2x-8[/tex][tex]\begin{gathered} 3x-2=4(2x-8) \\ 3x-2=8x-32 \\ 8x-3x=32-2 \end{gathered}[/tex][tex]\begin{gathered} 5x=30 \\ x=\frac{30}{5} \\ x=6 \end{gathered}[/tex]thus, the answer is x = 6
May I please get help with this math problem. I have been trying many times to find all correct answers to each length.
To draw a triangle, you cannot take three random line segments, they have to satisfy the triangle inequality theorems.
0. Triangle Inequality Theorem One: the lengths of any two sides of a triangle must add up to more than the length of the third side.
Procedure:
• Evaluating the first values given: (adding the two smallest values)
[tex]5.2+8.2=13.4[/tex]Now, we have to compare this addition with the bigger value. As 13.4 > 12.8, these can be side lengths of a triangle.
• Evaluating the second values given: (adding the two smallest values)
[tex]5+1=6[/tex]Comparing this addition with the bigger value, we can see that 6 < 10, meaning that these values cannot be side lengths of a triangle.
• Evaluating the third values given: (adding the two smallest values)
[tex]3+3=6[/tex]Comparing, we can see that 6 < 15. Therefore, these cannot be side lengths of a triangle.
• Evaluating the final values given:
[tex]7+5=12[/tex]We can see that 12 < 13, so these cannot be side lengths of a triangle.
Answer:
• 12.8, 5.2, 8.2: ,can be side lengths of a triangle.
,• 5, 10, 1: ,cannot be side lengths of a triangle.
,• 3, 3, 15: ,cannot be side lengths of a triangle.
,• 7, 13, 5: ,cannot be side lengths of a triangle.
What do the following two equations represent?y-3=2(x - 3)y+5 = 2(x + 1) a. the same lineb. distinct parallel linesc. perpendicular linesd. intersecting, b it not perpendicular
Option A: The same line
Explanations:The slope-intercept form of the equation of a line can be written as:
y = mx + c
Where m is the slope
and c is the intercept
Let us express the two equations given in the slope-intercept form
For the first equation:
y - 3 = 2(x - 3)
y - 3 = 2x - 6
y = 2x - 6 + 3
y = 2x - 3
The slope, m = 2
The intercept, c = -3
For the second equation:
y + 5 = 2(x + 1)
y + 5 = 2x + 2
y = 2x + 2 - 5
y = 2x - 3
We can see that both equations simplify to y = 2x - 3, this means the both equations represent the same line
The sum of 3 and r is less than 7.What number sentence represents the statement?
The sum of 3 and r can be represented by "3 + r"
If this sum is less than 7, we can use the symbol "lesser than" (<) to compare the sum with the number 7, so our number sentence is:
[tex]3+r<7[/tex]Kayla bought 2 1/2 yards of blue cloth for 6.97 and 1 1/2 yards of yellow cloth for half as much. She used 1/4 of the blue cloth to make her mother a apron. How much cloth did it take to make the apron
She used 1/4 of the blue cloth to make her mother a apron:
[tex]\frac{5}{2}\times\frac{1}{4}=\frac{5}{8}=0.625[/tex]She used 5/8 yd or 0.625yd of blue coth to make the apron
Find the missing number to make the fractions equivalent. 3/4 = 9/?
We have the following:
[tex]\frac{3}{4}=\frac{9}{x}[/tex]solving:
[tex]\begin{gathered} x=\frac{9\cdot4}{3} \\ x=12 \end{gathered}[/tex]Therefore, the answer is [B] 12
what are the two moves you can use to get the first figure to the second figure (dilation,rotation, reflection,and translation)
ANSWER:
Dilation and translation
EXPLANATION:
Looking at the figures, the two moves used to get the first figure to the second figure is dilation and translation.
The figure was translated 6 units right and 7 units down.
The translation rule that occured here is==> (x+6, y-7)
Also, a dilation with a scale factor of 2 occured here.
Therefore, a dilation and translation occured in order to get the first figure to the second figure.
Evaluate the expression 10 to the 2 power + (3 +5 to the power 2) -5
The answer is 159
The value of the expression 10 to the 2 power + (3 +5 to the power 2) -5 is 159.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The expression will be illustrated thus:
10² + (3 + 5)² - 5
= 100 + 8² - 5
= 100 + 64 - 5
= 164 - 5
= 159
The value is 159.
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What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why.
An example of situation involving quantitative comparison is:
The game-plan of an offensive coach for a NFL game.
What are quantitative variables?
Quantitative variables are variable that assume numbers as results, instead of labels such as yes/no or good/bad.
When an NFL offensive coordinator is game-planning, he has to consider numeric stats of the opponent defense, such as these ones:
Average passing yards allowed per play.Average rushing yards allowed per play.These stats are also compared to the NFL average to verify if the weak point of the opponent defense is the run or the pass, hence the game-plan is adjusted accordingly as follows:
Bad run defense: the coordinator should call more running plays.Bad pass defense: the coordinator should call more passing plays.A similar problem, also about quantitative variables, is given at https://brainly.com/question/15212082
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two systems of equations are given below. for each system, choose the best description of its solution. if applicable, give the solution.
Let:
[tex]\begin{gathered} x-4y=8_{\text{ }}(1) \\ -x-4y=8_{\text{ }}(2) \\ \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (1)+(2) \\ x+(-x)+(-4y)+(-4y)=8+8 \\ -8y=16 \\ y=\frac{16}{-8} \\ y=-2 \end{gathered}[/tex]Replace the value of y into (1):
[tex]\begin{gathered} x-4(-2)=8 \\ x+8=8 \\ x=8-8 \\ x=0 \end{gathered}[/tex]The system has unique solution:
[tex](x,y)=(0,-2)[/tex]I need help I am doing 8th grade conversion factors and there is only one way my teacher wants me to do it.
Conversion factors are the numbers for which we need to multiply a certain variable to convert it to another unit. In this case we need to convert gallons to cups, which have a conversion factor of 16 and minutes to seconds, which has a conversion rate of 60. Doing this we have:
[tex]\text{capacity = 24 gallons }\cdot\text{ 16 = }384\text{ cups}[/tex][tex]\text{time = 5 minutes }\cdot\text{ 60 = }300\text{ s}[/tex]The rate is:
[tex]\text{rate = }\frac{384}{300}\text{ = }1.28\text{ }\frac{cups}{s}[/tex]simplifying with like terms; 2(m+10)
In order to simplify the expression, we would multiply the terms inside the bracket by the term outside. It becomes
2 * m + 2 * 10
= 2m + 20
Select the correct answer. Which equation, when solved, gives 8 for the value of x? OA. +3 = =+14 OB. 5-9=31-12 OC. 21-2=r-4 OD. 5.-7=*=+14
Let's solve for each and see which gives 8
For A
5/2 x + 7/2 = 3/4 x + 14
collect like term aand solve for x
5/2 x - 3/4 x = 14 - 7/2
[tex]\frac{10x-3x}{4}=\frac{28-7}{2}[/tex][tex]\frac{7x}{4}=\frac{21}{2}[/tex][tex]x=\frac{21}{2}\times\frac{4}{7}=6[/tex]For B
5/4 x - 9 = 3/2 x -12
collect like term and solve for x
[tex]\frac{5}{4}x-\frac{3}{2}x=-12+9[/tex][tex]=\frac{5x-6x}{4}=-3[/tex][tex]-\frac{x}{4}=-3[/tex][tex]x=12[/tex]For C
5/4 x - 2 = 3/2 x - 4
collect like term and then solve for x
[tex]\frac{5}{4}x-\frac{3}{2}x=-4+2[/tex][tex]\frac{5x-6x}{4}=-2[/tex][tex]-\frac{x}{4}=-2[/tex][tex]x=8[/tex]For D
5/4 x - 7 = 3/4 x + 14
collect like term and solve for x
[tex]\frac{5}{4}x-\frac{3}{4}x=14+7[/tex][tex]\frac{2x}{4}=21[/tex][tex]x=42[/tex]Therefore, the correct option is C
i am stuck and need help ASAP with itfind the area
Given:
Required:
We want to find the area of given
Explanation:
As we can see that measurement of given figure is 5 by 5 so it is square and the area of square is
[tex]5*5=25\text{ unit}^2[/tex]Final answer:
25 sq unit
A __ is a polynomial with one term.
ANSWER
Monomial
EXPLANATION
A polynomial is a expression that contains variables, coefficients and sometimes constants.
These terms relate with one another by the use of mathematical signs like addition, subtraction, multiplication, etc
A polynomial with just one term is called monomial.
An example of a polynomial is:
[tex]x^2\text{ + x + 1}[/tex]An example of a monomial is:
[tex]\begin{gathered} x^2 \\ or\text{ } \\ \frac{x}{2} \end{gathered}[/tex]Answer:
monomial
Step-by-step explanation:
How does the graph of f(x) = (x + 7)^3 − 8 compare to the parent function g(x) = x^3
The ways in which the graph of f(x) = (x + 7)^3 − 8 compare to the parent function g(x) = x^3 are as follows:
Shifted 7 units to the left.Shifted 8 units down. What is a translation?In Mathematics, the translation a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Geometry, g(x + 7) simply means shifting a graph 7 units to the left while subtracting 8 from the function simply means moving the graph down.
In this context, we can reasonably infer and logically deduce that the parent function g(x) was shifted 7 units to the left and 8 units down.
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Use the graph to find the horizontal asymptote of the rational function
Horizontal Asymptote
Observing the graph with the red dashed line, the horizontal asymptote of the function is at y = 6
Vertical asymptote
If we draw a line the graph we have the following
This indicates that the vertical asymptote is at x = 2.
60% discount on $500 sweater
The discount price of the sweater will be, the original price minus the percentage of discount of the original price.
First, express the percentage of discount as a decimal:
60% = 60/100 = 0.6
so:
[tex]\begin{gathered} 500-0.6\cdot500 \\ 500-300=200 \end{gathered}[/tex]The discount price of the sweater is $200
Match each expression on the left to its equivalent value on the right. Some answer options on the right will not be used.
Let us write out our expressions:
[tex]\begin{gathered} -29+(-7) \\ -34+(-94) \\ -8+(-14) \\ -12+(-48) \end{gathered}[/tex]The trick here is to get rid of the minus, then solve the sum as usual, and add a minus to the result. Let us do that for each of them:
-29+(-7)] Step one gives us:
[tex]29+7[/tex]Step two gives us:
[tex]36[/tex]Step three gives us:
[tex]-36[/tex]Then, -29+(-7) should be linked to -36.
-34+(-94)] Step one gives us:
[tex]34+94[/tex]Step two gives us:
[tex]128[/tex]Step three gives us:
[tex]-128[/tex]Thus, -34+(-94) should be linked to -128.
-8+(-14)] Step one gives us:
[tex]8+14[/tex]Step two gives us:
[tex]22[/tex]And step three gives us:
[tex]-22[/tex]This implies that -2+(-14) should be linked to -22.
-12+(-48)] Step one gives us:
[tex]12+48[/tex]Step two gives us:
[tex]60[/tex]And step three gives us:
[tex]-60[/tex]Then, -12+(-48) should be linked to -60.
the probability he chooses orange fruit
Consider that the total number of fruits are 10. The probability to get some fruit is given by the quotient in between the number of suc a fruit and the total number of fruits.
Then, at the first time, the probability of getting a kiwi is:
p1 = 1/10 = 0.1 (becasue there is one kiwi)
After the kiwi is taken out, the number of fruits are 9. In this case, the probability of getting one orange is:
p2 = 3/9 = 0.33 (because there are three oranges)
THe probability of the two previous events, that is, to obtain one kwi and then one orange is the product of the probabilities p1 and p2:
P = p1*p2 = (0.1)(0.33) = 0.03
Hence, the probabilty is approximately 0.03
Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey costs $3 per pound at Store A and $4.50 per pound at Store B. Ham costs $4 per pound at Store A and $6 per pound at Store B. Michael spends $18 at Store A, and Ashley spends $27 at Store B. Could Michael and Ashley have bought the same amount of turkey and ham?
Step 1
Michael spends $18 at store A
He buys x pounds of turkey and y pounds of ham.
But turkey costs $3 in-store A and ham costs $4 in-store A
Therefore, we will have the following equation for Michael
[tex]3x+4y=18---(1)[/tex]Step 2
Ashley spends $27 in-store B
She buys x pounds of turkey and y pounds of ham.
But turkey costs $4.50 in-store B and ham costs $6 in-store B.
Therefore, we will have the following equation for Ashley
[tex]4.5x+6y=27----(2)[/tex]Step 3
Solve the equations graphically
If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. Since the graphs are the same, then there are infinitely many solutions true for both equations.
For instance, the points if we test for the points on the graph, we will conclude if both Michael and Ashley bought the same amount of turkey and ham.
[tex]\begin{gathered} 3x+4y=18_{} \\ 4.5x+6y=27 \\ At\text{ x =2 and y=3} \\ we\text{ have,} \\ 3(2)+4(3)=18_{} \\ 6+12=18 \\ 18=18 \\ 4.5(2)+6(3)=27 \\ 9+18=27 \\ 27=27 \\ \text{At x=6, y=0} \\ we\text{ have} \end{gathered}[/tex][tex]\begin{gathered} 3(6)+4(0)=18 \\ 18=18 \\ 4.5(6)+6(0)=\text{ 27} \\ 27=27 \end{gathered}[/tex]Therefore yes, Michael and Ashley could have bought the same amount of turkey and ham.