EXPLANATION
The slope of a line is given by the following expression:
[tex]\text{Slope = }\frac{rise}{run}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]In this case, we have that the slope is represented by the generic form:
y = mx + b
Where m is the slope and b is the y-intercept.
So, the slope is -7.
Answer: m=-7
Please see the picture below. Indeed help with parts of the question
Given
[tex]\frac{(x-4)^2}{4}-\frac{y^2}{9}=1[/tex]Find
Values of a and b for this conic section
Explanation
As we know the standard equation for conic section is given by
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]where (h , k) be the vertex
vertices (h+a , k) and (h-a , k)
given equation can be rewrite as
[tex]\frac{(x-4)^2}{2^2}-\frac{y^2}{3^2}=1[/tex]on comparing , we get
a = 2 and b = 3
Final Answer
Therefore , the value of a = 2 and b = 3
Write an equation to find the necessary score on the final exam for a student to earn an A (90%) in the class.
For the given table:
We will find the necessary score on the final exam for a student to earn an A (90%) in the class.
so,
The equation will be:
[tex]92\cdot(0.2)+95\cdot(0.3)+88\cdot(0.2)+x\cdot(0.3)=90[/tex]now, solve the equation to find x:
[tex]\begin{gathered} 64.5+0.3x=90 \\ 0.3x=90-64.5 \\ 0.3x=25.5 \\ x=\frac{25.5}{0.3} \\ \\ x=85 \end{gathered}[/tex]So, the answer will be:
The student needs a score of 85% on the final exam to earn a 90%
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 11z
Answer:
smaller x value: -1,-8larger x value: 5,16The parenthesis part is already taken care of by the teacher.
=================================================
Explanation:
y is equal to x^2-9 and also 4x-4. We can equate those two right hand sides and get everything to one side like this
x^2-9 = 4x-4
x^2-9-4x+4 = 0
x^2-4x-5 = 0
Then we can use the quadratic formula to solve that equation for x.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-5)}}{2(1)}\\\\x = \frac{4\pm\sqrt{36}}{2}\\\\x = \frac{4\pm6}{2}\\\\x = \frac{4+6}{2} \ \text{ or } \ x = \frac{4-6}{2}\\\\x = \frac{10}{2} \ \text{ or } \ x = \frac{-2}{2}\\\\x = 5 \ \text{ or } \ x = -1\\\\[/tex]
Or alternatively
x^2-4x-5 = 0
(x-5)(x+1) = 0
x-5 = 0 or x+1 = 0
x = 5 or x = -1
------------------------------
After determining the x values, plug them into either original equation to find the paired y value.
Let's plug x = 5 into the first equation:
y = x^2-9
y = 5^2-9
y = 25-9
y = 16
Or you could pick the second equation:
y = 4x-4
y = 4(5)-4
y = 20-4
y = 16
We have x = 5 lead to y = 16
One solution is (x,y) = (5,16)
This is one point where the two curves y = x^2-9 and y = 4x-4 intersect.
If you repeat the same steps with x = -1, then you should find that y = -8 for either equation.
The other solution is (x,y) = (-1,-8)
Answer:
[tex](x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=x^2-9\\y=4x-4\end{cases}[/tex]
To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2-4x-5&=0\\x^2-5x+x-5&=0\\x(x-5)+1(x-5)&=0\\(x+1)(x-5)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for x:
[tex]\implies x+1=0 \implies x=-1[/tex]
[tex]\implies x-5=0 \implies x=5[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}x=-1 \implies y&=4(-1)-4\\y&=-4-4\\y&=-8\end{aligned}[/tex]
[tex]\begin{aligned}x=5 \implies y&=4(5)-4\\y&=20-4\\y&=16\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
need answer with steps[tex]( - 3 - 5i) + (4 - 2i)[/tex][tex](7 + 9i) + ( - 5i)[/tex]
We are given the following complex numbers
[tex](-3-5i)+(4-2i)[/tex]To perform the addition of the complex numbers, simply add the like terms together.
[tex](-3-5i)+(4-2i)=(-3+4)+(-5i-2i)=(1-7i)[/tex]Similarly,
[tex](7+9i)+(-5i)=\mleft(7\mright)+\mleft(9i-5i\mright)=(7+4i)_{}[/tex]Therefore, the result of the complex addition is
[tex]\begin{gathered} 19.\: (1-7i) \\ 20.\: (7+4i) \end{gathered}[/tex]Sketch one cycle of the graph of each function 16. y= -2 sin 8x
Answer:
• Amplitude = 2
,• Period = π/4
Explanation:
Given the function:
[tex]y=-2\sin(8x)[/tex]In order to sketch the graph of y, we need to find its amplitude and period.
Comparing the function with the general sine function:
[tex]y=a\sin(bx+c)+d[/tex]We have that:
[tex]\begin{gathered} Amplitude=|a|=|-2|=2 \\ Period=\frac{2\pi}{|b|}=\frac{2\pi}{8}=\frac{1}{4}\pi \end{gathered}[/tex]Next, using these values, we sketch one cycle of the graph below:
I need to solve this problem and name the concepts used in the problem
In a pie chart, the sum of the angles for each variable or item is 360 degrees. also, the total percentage is 100
Looking at each flavor,
27% chose Glazier freeze, = 27/100 * 360 = 97.2 degrees
25% chose Fierce grape = 25/100 * 360 = 90 degrees
15.5% chose Extreme Citrico = 15.5/100 * 360 = 55.8 degrees
13.5% chose Cool Blue = 13.5/100 * 360 = 48.6 degrees
11.5% chose Lemon ice = 11.5/100 * 360 = 41.4
We want to determine the degrees for others
Therefore,
97.2 + 90 + 55.8 + 48.6 + 41.4 + others = 360
333 + others = 360
others = 360 - 333
others = 27 degrees
The correct option is C
The concept used is converting the given percentages to degrees and equation them to 360 degrees
100% is equivalent to 360 degrees
What's the sum of ten terms of a finite arithmetic series if the first term is 13 and the last term is 89?
The sum of the n first terms in an arithmetic series is given by the following formula
[tex]S_n=n\cdot(\frac{a_1+a_n}{2})[/tex]Where a_1 represents the first term, a_n represents the n-th term, and n the amount of terms we want to sum.
The first term of our sequence is 13, the tenth term is 89 and the amount of terms is 10. Plugging those values in our formula, we have
[tex]S_{10}=10\cdot(\frac{13+89}{2})=10\cdot51=510[/tex]This sum is equal to 510.
show that the triangles are similar by measuring the lengths of their sides and comparing the ratios of their corresponding sides
ANSWER
EXPLANATION
The ratio between corresponding sides of similar triangles is constant - in other words, the ratio between each pair of corresponding sides gives the same value.
As shown in the questions, the ratios between corresponding sides are,
[tex]\begin{gathered} \frac{DE}{AB}=\frac{3}{2}=1.5 \\ \frac{DF}{AC}=\frac{1.5}{1}=1.5 \\ \frac{EF}{BC}=\frac{2.4}{1.6}=1.5 \end{gathered}[/tex]Since the three ratios between corresponding sides are the same, 1.5, the triangles are similar.
You want to enlarge a picture by a factor of 4.5 from its current size of 4 inches by 6 inches. What is the size of the enlarged picture?a. 18 in. by 27 in.b.8.5 in. by 10.5 in.c. 18 in. by 10.5 in.d. 8.5 in. by 27 in.
If we want to enlarge the picture by a factor of 4.5, the perimeter will also increase by the factor of 4.
[tex]\begin{gathered} \text{New dimension =}4.5\text{ (old dimension)} \\ \text{New dimension=4.5 (4 by 6)} \\ \text{New dimension=18 inches by 27 inches} \end{gathered}[/tex]Hence, the correct option is Option A
A researcher wants to study the amount of protein in pet food. Which one of the following is most likely to give theresearcher more accurate results?-take a sample of cat foods alone-take a sample of dog foods alone-take a sample of all pet foods mixed together-divide the pet foods into two different groups, cat and dog, and take a sample from each group
He will need to take sample of at least two different sample of pet food in order to analyze it more accurate. So, the researcher should:
divide the pet foods into two different groups, cat and dog, and take a sample from each group.
Practice questions to use for study guide/ my notes please help want to Ace test!
We have, From the graph it can be seen that when x tends to zero on the right, y
If the ones digit in a two-digit number is even, the number is a composite number. Which odd ones digit also tells you the number must be a compositenumber? Explain.
Okay, here we have this:
Considering that a composite number is a number that is not prime, the only number one of the units that tells us that a two-digit number is composed is 5, since every number ending in 5 is a multiple of 5.
I need help with this question please. This is non graded.
To determine the factor of the given polynomial, first, we rewrite it as follows:
[tex](16x^2+4x)+(-20x-5).[/tex]Now, notice that:
[tex]\begin{gathered} 16x^2+4x=4x(4x^+1), \\ -20x-5=-5(4x+1). \end{gathered}[/tex]Factoring out the 4x+1, we get:
[tex](16x^2+4x)+(-20x-5)=(4x-5)(4x+1).[/tex]Answer: [tex](4x+1).[/tex]When 27 is subtracted from the square of anumber, the result is 6 times the number. Findthe negative solution.
Given: A statement, "When 27 is subtracted from the square of a
number, the result is 6 times the number."
Required: To determine the number.
Explanation: Let the number be x. Then according to the question-
[tex]x^2-27=6x[/tex]Rearranging the equation as -
[tex]x^2-6x-27=0[/tex]The quadratic equation can be simplified as follows-
[tex]\begin{gathered} x^2-9x+3x-27=0 \\ x(x-9)+3(x-9)=0 \\ (x+3)(x-9)=0 \\ x=-3\text{ or }x=9 \end{gathered}[/tex]Final Answer: The negative solution is-
[tex]x=-3[/tex]Calculating number of periods?How long will an initial bank deposit of $10,000 grow to $23,750 at 5% annual compound interest?
For an initial amount P with an annually compounded interest rate r, after t years the total amount A is is given by:
[tex]A=P(1+r)^t[/tex]Then we have:
[tex]\begin{gathered} \frac{A}{P}=(1+r)^t \\ \ln\frac{A}{P}=t\ln(1+r) \\ t=\frac{\ln\frac{A}{P}}{ln(1+r)} \end{gathered}[/tex]For P = $10,000, A = $23,750 and r = 0.05, we have:
[tex]t=\frac{\ln\frac{23750}{10000}}{\ln(1+0.05)}\approx17.73\text{ years}[/tex]What is the equation of the line that passes through the given points (2,3) and (2,5)
Solution:
The equation of a line that passes through two points is expressed as
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ where \\ (x_1,y_1)\text{ and} \\ (x_2,y_2)\text{ are the coordinates of the points } \\ through\text{ which the line passes} \end{gathered}[/tex]Given that the line passes through the points (2,3) and (2, 5), this implies that
[tex]\begin{gathered} x_1=2 \\ y_1=3 \\ x_2=2 \\ y_2=5 \end{gathered}[/tex]By substitution, we have
[tex]\begin{gathered} y-3=\frac{5-3}{2-2}(x-2) \\ \Rightarrow y-3=\frac{2}{0}(x-2) \\ multiply\text{ through by zero} \\ 0(y-3)=2(x-2) \\ \Rightarrow0=2x-4 \\ add\text{ 4 to both sides} \\ 0+4=2x-4+4 \\ \Rightarrow4=2x \\ divide\text{ both sides by the coefficient of x, which is 2} \\ \frac{4}{2}=\frac{2x}{2} \\ \Rightarrow x=2 \\ \end{gathered}[/tex]Hence, the equation of the line that passes through the given points (2,3) and (2,5) is
[tex]x=2[/tex]5.Find the measures of themissing side of the righttriangle usingPythagorean Theoremequation.106K
Pythagoras Theorem:
In a right angle triangle, the sum of square of base and perpendicular is equal to the square of Hypotenuse .
Hypotenuse² = Perpendicular² + base²
In the given figure, we have:
Base = k
Hypotenuse = 10
Perpendicular = 6
Substitute the valus and solve for k,
[tex]\begin{gathered} \text{Hypotenuse}^2=Perpendicular^2+Base^2 \\ 10^2=6^2+k^2 \\ 100=36+k^2 \\ k^2=100-36 \\ k^2=64 \\ k=\sqrt[]{64} \\ k=8 \\ \text{Base, k = 8} \end{gathered}[/tex]The missing side is 8
Answer: 8
Find from first principles the derivative of f:x maps to (x+2)all squared
Given:
[tex]f(x)=(x+2)^2[/tex]Required:
To find the first principles
Explanation:
First principle,
[tex]\lim_{h\to0}\frac{f(x+h)-f(x)}{h}[/tex][tex]=\lim_{h\to0}\frac{(x+h+2)^2-(x+2)^2}{h}[/tex][tex]=\lim_{h\to0}\frac{x^2+(h+2)^2+2x(h+2)-x^2-4-4x}{h}[/tex][tex]=\lim_{h\to0}\frac{h^2+4+4h+2xh+4x-4-4x}{h}[/tex][tex]\begin{gathered} =\lim_{h\to0}\frac{h^2+4h+2xh}{h} \\ \\ =\lim_{h\to0}\frac{h(h+4+2x)}{h} \\ \\ =\lim_{h\to0}(h+4+2x) \\ =2x+4 \end{gathered}[/tex]Final Answer:
[tex]2x+4[/tex]find the slope of the line that passes through these two points (0, -2) (5, 3) slope= ?
Find the slope of the line that passes through these two points
P1 = (0, -2)
P2 = (5, 3)
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{3-(-2)}{5-0} \\ m=\frac{3+2}{5} \\ m=\frac{5}{5} \\ m=1 \end{gathered}[/tex]The slope would be 1
At a particular restaurant, each mozzarella stick has 100 calories and each slider has
200 calories. A combination meal with mozzarella sticks and sliders is shown to have
1500 total calories and 9 more mozzarella sticks than sliders. Determine the number
of mozzarella sticks in the combination meal and the number of sliders in the
combination meal.
There are
mozzarella sticks and
sliders in the combination meal.
The 1,500 calories in the combination meal and the amount of calories per mozzarella stick and per each slider gives an equation with the following solution;
There are 11 mozzarella sticks and 2 sliders in the combination meal.
What is a mathematical equation?An equation in mathematics is a statement that two mathematical expressions are equal.
The number of calories in each mozzarella stick = 100
Number of calories in each slider = 200
Number of calories in the combination meal = 1,500
Number of mozzarella sticks in the combination meal = 9 + The number of sliders
Let s represent the number of sliders in the combination meal, we have;
Number of mozzarella in the combination meal = s + 9
The equation that gives the amount of calories in the meal is therefore;
200·s + 100·(s + 9) = 1,500
200·s + 100·s + 900 = 1,500
300·s = 1,500 - 900 = 600
s = 600 ÷ 300 = 2
The number of sliders in the combination meal, s = 2
The number of mozzarella in the meal = 2 + 9 = 11
Learn more about writing equations in algebra here;
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A fence is purchased and constructed as shown. There are 250 feet of fence used for the chorale. Determine the values for x and y that will maximize the area. Round your answers to the nearest tenth if needed. Type the value for the x dimension in the first blank (you do not need to type x = , but label your answer). Type the value for y in the second blank (you do not need to type y =, but label your answer).
2x + 3y = 250
y = (250 - 2x)/3 (1)
S = x * y
= (-2/3x + 250/3)*x
= -2/3(x - 125/2)^2 + 125^2/6
x = 125/2
Replacing the value of x in (1)
y = 125/3
Nintendo previously projected that it would sell 19 million units of the console for the year ending in March. If it ended up selling 26.5 million after several upward versions to the forecast. How many selling off were their estimate
Simplify using exponential notation. 5a^6 x 7a^7
Given:
[tex]5a^6\times7a^7[/tex]Let's simplify using exponential notation.
To simplify, multiply the the base, then use law of indicies to add the exponents
We have:
[tex]undefined[/tex]The length of your step is 34 inches (in.). If you walk 10,000 steps in a day, how many feet (ft.) will you walk? ?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
step length = 34 inches
walking = 10000 steps
Step 02:
feet to inches
1 feet = 12 inches
1 step --------------- 34 inches
10000 steps ------- x
1 * x = 10000 * 34
x = 340000
340000 inches * ( 1 feet / 12 inches)
28333.33 feet
The answer is:
You will walk 28333.33 feet .
40 model A cars were sold that week. what else can you say about this bar model?
From the diagram
Ratio of model A car to model B car = 4:6
Ratio of model A to model B = 4:6
Ratio of model B to model A = 6:4
Ratio of model A to total = 4:10
Ratio of model B to total = 6:10
If 40 model A cars sold
I know that 60 model B cars was sold.
Dr. Wells saw 960 patients last year. This year, the number of patients he saw was 25%higher. How many patients did Dr. Wells see this year?
.Since the old number of patients is 960
Since it is increasing by 25%, then
We will find the amount of 25% of 960, then add it to 960
[tex]\begin{gathered} I=\frac{25}{100}\times960 \\ I=240 \end{gathered}[/tex]Add it to 960 to find the new number of patients
[tex]\begin{gathered} N=960+240 \\ N=1200 \end{gathered}[/tex]Dr Wells saw 1200 patients
A kitty in a tuxedo walks into a bank deposit of $4000 in an investment account. the account earns 8% interest, compounded monthly. after 10 years how much money will the fancy kitty have?
Answer:
The amount of money Kitty would have is;
[tex]\text{ \$}8,878.56[/tex]Explanation:
Given that Kitty invested $4000 into an account that earns 8% interest compounded monthly for 10 years;
[tex]\begin{gathered} \text{ Principal P = \$4000} \\ \text{ Rate r = 8\% = 0.08} \\ \text{ Time t =10 years} \\ \text{ number of times compounded per time n = 12} \end{gathered}[/tex]Applying the formula for compound interest;
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]Substituting the given values;
[tex]\begin{gathered} F=4000(1+\frac{0.08}{12})^{12(10)} \\ F=4000(1+\frac{0.08}{12})^{120} \\ F=4000(2.2194) \\ F=\text{ \$}8,878.56 \end{gathered}[/tex]Therefore, the amount of money Kitty would have is;
[tex]\text{ \$}8,878.56[/tex]Please Help me solve I know I am supposed to use the quadratic formula But I’m still not getting the right answers
To find the maximum profit we need to maximize the function.
First we need to find the critical points, to do this we need to find the derivative of the function:
[tex]\begin{gathered} \frac{dy}{dx}=\frac{d}{dx}(-2x^2+105x-773) \\ =-4x+105 \end{gathered}[/tex]now we equate it to zero and solve for x:
[tex]\begin{gathered} -4x+105=0 \\ 4x=105 \\ x=\frac{105}{4} \end{gathered}[/tex]hence the critical point of the function is x=105/4.
The next step is to determine if the critical point is a maximum or a minimum, to do this we find the second derivative:
[tex]\begin{gathered} \frac{d^2y}{dx^2}=\frac{d}{dx}(-4x+105) \\ =-4 \end{gathered}[/tex]Since the second derivative is negative for all values of x (and specially for x=105/4) we conclude that the critical point is a maximum.
Hence the function has a maximum at x=105/4. To find the value of the maximum we plug the value of x to find y:
[tex]\begin{gathered} y=-2(\frac{105}{4})^2+105(\frac{105}{4})-773 \\ y=605.125 \end{gathered}[/tex]Therefore the maximum profit is $605
Solve the system of equations 2x - 3y = 4 and 9x - 8y = - 26 by combining the
equations.
[tex]\sf \Large \boxed{\sf +}\\ \sf \Large \boxed{\sf +}\\\\ \sf \Large \boxed{\sf 11x+-11y=-22}\\\\ 2x+9x-3y-8y=4-26\\Combine\\11x-11y=-22\\Simplify\\x-y=-2\\x=y-2\\Plug\ the\ value\ in\ the\ equation\\2(y-2)-3y=4\\2y-4-3y=4\\-y-4=4\\-y=8\\y=-8\\Solve\ for\ x\\9x-8(-8)=-26\\9x+64=-26\\9x=-90\\x=-10[/tex]
Triangle MNO was reflected over the x-axis Given M(-5,-1)Find the coordinate M
When we perform the reflection of a figure over the x-axis, we just have to change the sign of the y-coordinate of each point, like this: P(x,y) -> P'(x,-y).
Then after a reflection of the triangle, the point M goes from (-5,-1) to (-5, 1)
Then the correct answer is the last option (-5, 1)