Step 1
Given; Find the slope of the line passing through the points (-3, 5) and (-6, 4).
Step 2
Slope is given as;
[tex]\begin{gathered} y_2=4 \\ y_1=5 \\ x_2=-6 \\ x_1=-3 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{4-5}{-6-(-3)} \\ m=\frac{-1}{-3}=\frac{1}{3} \end{gathered}[/tex]Answer;
[tex]slope=\frac{1}{3}[/tex]X= 7 4. Find the equation of a line passing through (5, -6) perpendicular (b) 3x + 5y = (d) 7x - 12y (f) x = 7 (a) 2x + y = 12 (c) x + 3y = 8 (e) 2y = 5 Find the equation of the line connecting the points of intersect (a) S x + y = 4 S 3x - y = 12 (b) Sy= and 2x=6 = -6 X=
Given data:
The first set of equations are x+y=4, and x=6.
The second set of equations are 3x-y=12 and y=-6.
The point of intersection of first set of te equations is,
6+y=4
y=-2
The first point is (6, -2).
The point of intersection of second set of te equations is,
3x-(-6)=12
3x+6=12
3x=6
x=2
The second point is (2, -6).
The equation of the line passing through (6, -2) and (2, -6) is,
[tex]\begin{gathered} y-(-2)=\frac{-6-(-2)}{2-6}(x-6) \\ y+2=\frac{-6+2}{-4}(x-6) \\ y+2=x-6 \\ y=x-8 \end{gathered}[/tex]Thus, the required equation of the line is y=x-8.
What is the remainder when j(x)=x4+2x3−5x2+2x+4 is divided by x+3
From the problem, we have a function :
[tex]j(x)=x^4+2x^3-5x^2+2x+4[/tex]The remainder when j(x) is divided by x + 3 is the value of the function when x = -3
x = -3 comes from :
x + 3 = 0
x = -3
Substitute x = -3 to the function,
[tex]\begin{gathered} j(-3)=(-3)^4+2(-3)^3-5(-3)^2+2(-3)+4 \\ j(-3)=81-54-45-6+4 \\ j(-3)=-20 \end{gathered}[/tex]The answer is -20
Simplify this expression. Assume that x is nonzero.– 11.7X<-11.x?(Type exponential notation with positive exponents.)
If two numbers have the same base ( the number below the exponent) then the multiplication of the two of them is the number with the same base but with the sum of its exponents (rule of exponents)
[tex]x^{-11}\cdot x^7=x^{-11+7}=x^{-4}[/tex]On the other hand, if a number is to the power a negative number, it means that it is the reciprocal elevated to the number, in this case
[tex]x^{-4}=(\frac{1}{x})^4[/tex]12 more than the product of 5 and a number x
Answer: (5*x) + 12 or 5x + 12
Step-by-step explanation: differant sites let you do it defferent ways but if the multipaction sign in an "x" I would do the 2nd one :) Hope it's right, have a great day!
which equation shows x^2+6x-4=0 rewritten by completing the squarea) (x+3)^2=36b) (x+3)^2=4c) (x+3)^2=9d) (x+3)^2=13
Solution
Step 1
Write the equation:
[tex]x^2\text{ + 6x - 4 = 0}[/tex]Step 2:
Rewrite the equation:
[tex]x^2\text{ + 6x = 4}[/tex]Step 3
[tex]\begin{gathered} Add\text{ }\frac{b^2}{4a\text{ }}\text{ to both sides to get a perfect square.} \\ \text{a = 1, b = 6} \\ \frac{b^2}{4a}\text{ = }\frac{6^2}{4\times1}\text{ = }\frac{36}{4}\text{ = 9} \end{gathered}[/tex][tex]\begin{gathered} x^2\text{ + 6x + 9 = 4 + 9} \\ Add\text{ similar terms:} \\ (x\text{ + 3\rparen}^2\text{ = 13} \end{gathered}[/tex]Final answer
[tex]d)\text{ \lparen x + 3\rparen}^2\text{ = 13}[/tex]Match the steps to put them in the correct order of something. You will not use all of the options.
SOLUTION
[tex]\begin{gathered} Given \\ 2h+9=21 \end{gathered}[/tex][tex]\begin{gathered} Step\text{ 1:} \\ Subtract\text{ 9 from both sides} \\ 2h+9-9=21-9 \\ 2h=12 \end{gathered}[/tex][tex]\begin{gathered} Step\text{ }2: \\ Divide\text{ both sides by 2} \\ \frac{2h}{2}=\frac{12}{2} \\ h=6 \end{gathered}[/tex][tex]\begin{gathered} Final\text{ answer:} \\ h=6 \end{gathered}[/tex]c. If x= 3 is specifically a hole (removable discontinuity) of f(x), then what would be true about g(3) and h(3)? Explain your reasoning.
Solution
We have the following function given:
f(x)= g(x)/h(x)
We have a point of discontinuity on x=3
c. If x= 3 is specifically a hole (removable discontinuity) of f(x), then what would be true about g(3) and h(3)? Explain your reasoning.
For this case we can conclude that g(3)/h(3) is not defined since f(3) is not defined for the function and that means that the function is not fully connected on x=3
The sum of two numbers is 20. The difference between three times the first rumber and twice the second is 40. Find the two numbers.
Let the first number is x and second number is y.
According to given conditions:
The sum of two numbers is 20.
[tex]x+y=20[/tex]And The difference between three times the first rumber and twice the second is 40.
[tex]3x-2y=40[/tex]Now multiply equation 1 with 2 and add in second eqution;
[tex]\begin{gathered} 2(x+y)+(3x-2y)=2(20)+40 \\ 2x+2y+3x-2y=40+40 \\ 5x=80 \\ x=16 \end{gathered}[/tex]Now put the value of x in equation 1:
[tex]\begin{gathered} 16+y=20 \\ y=4 \end{gathered}[/tex]So the first number is x=16 and second number is y=4.
According to given co
1) P(A) = 0.6 P(B) = 0.45 P(A and B) = ? O 0.35 0.65 O 0.75 O 0.27
We are given the following probabilities:
[tex]\begin{gathered} P(A)=0.6 \\ P(B)=0.45 \end{gathered}[/tex]We are to find P(A and B), to do that we will use the following relationship:
[tex]P(\text{AandB)=P(A) x P(B)}[/tex]Replacing we get:
[tex]P(AandB)=0.6\times0.45[/tex]Solving the operations:
[tex]P(\text{AandB)}=0.27[/tex]Therefore, the probability of A and B is 0.27.
60% of the
students take the
bus. If there were
120 students on the
busses, how many
total students are
there?
Answer:
168
Step-by-step explanation:
60%=120
40% of 120
10%12
10%12
10%12
10%12
12×4=48
120+48=168
what digit is in the
The number given in the statement is
2.113 pints.
To write in word form,
Two and one hundred thirteen thousandths.
As in the number from last we have thousand , hundred, tens and ones.
So, we can write the given number in word form.
Two and one hundred thirteen thousandths.
Hence the correct option is c.
Find the inverse of the function. g(x)= -5x – 20/7
Given the function:
[tex]g(x)=\frac{-5x-20}{7}[/tex]To find the inverse function, let us first write it as:
[tex]y=\frac{-5x-20}{7}[/tex]Make x the subject of the equation
[tex]\begin{gathered} -5x-20=7y \\ -5x=7y+20 \\ x=\frac{-7y-20}{5} \end{gathered}[/tex]Replace x by y, and y by x to obtain the inverse function
[tex]y=\frac{-7x-20}{5}[/tex]Where
[tex]y=g^{-1}(x)[/tex]Jada and Priya are trying to solve the equation 2/3 + x = 4 Jada says I think we should multiply each side by 3/2 because that is the reciprocal of 2/3 Priya since I think we should add -2/3 to each side because that is the opposite of 2/3
The equation they are trying to solve is
[tex]\frac{2}{3}+x=4[/tex]In order to solve this equation, they need to add -2/3 on each side (the opposite of 2/3).
[tex]\begin{gathered} \frac{2}{3}-\frac{2}{3}+x=4-\frac{2}{3} \\ x=4-\frac{2}{3} \end{gathered}[/tex]Hence, Priya is correct because they need to use the opposite of 2/3, not the reciprocal.
An equation that can be solved using Jada's strategy is
[tex]\frac{2}{3}x=4[/tex]This equation would need to use a reciprocal, as Jada said.
true or false18. In the circle: x^2+(y-2)^2=12, the radius is 12
The general equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center and r is the radius of the circle.
Comparing the given equation of a circle and the above general equation we get:
[tex]r^2=12[/tex]Then, the radius of this circle is:
[tex]r=\sqrt[]{12}[/tex]In conclusion, the sentence is false.
directly as Vi and inversely as y°. If: = 61 when = 36 and y = 9, find a if r = 64 and y = 6. (Round off your answer to the nearest hundredth.)
Given: z directly varies as √x and inversely varies as y³
when x = 36 and y = 9 then z = 61
To find:
when x = 64 and y = 6 then z = ?
explanation:
z ∝ √x / y³
z = k √x / y³
when x = 36 and y = 9 then z = 61
[tex]z=\text{ }\frac{k\text{ }\sqrt{x}}{y^3}[/tex][tex]\begin{gathered} 61=\frac{k\text{ * }\sqrt{36}}{9^3} \\ 61=\frac{k*6}{729} \\ k=\frac{61*729}{6}=\frac{61*243}{2}=\frac{14823}{2} \end{gathered}[/tex]when x = 64 and y = 6
[tex]z=\text{ }\frac{14823}{2}*\frac{\sqrt{64}}{6^3}=\frac{14823*8}{2*216}=\frac{4941*4}{72}=\frac{4941}{18}=274.5[/tex]the value of z = 274.5
final answer:
z = 274.5 ≈ 300 when rounded off to the nearest hundredth
Solve the equation for A: 2*Cos A + 2 = 3.
Answer:
A=60 degrees
Explanation:
Given the equation:
[tex]2\cos A+2=3[/tex]Subtract 2 from both sides of the equation.
[tex]\begin{gathered} 2\cos A+2-2=3-2 \\ 2\cos A=1 \end{gathered}[/tex]Divide both sides by 2:
[tex]\begin{gathered} \frac{2\cos A}{2}=\frac{1}{2} \\ \cos A=\frac{1}{2} \end{gathered}[/tex]Finally, solve for A.
[tex]\begin{gathered} A=\arccos (\frac{1}{2}) \\ A=60\degree \end{gathered}[/tex]A local health clinic surveys its patients about their water drinking habits it found data is normally distributed the mean amount of water consumed daily is 62 ounces and the standard deviation is 5.2how much water in ounces do approximately 95% of the patients drink each day
The approximate amount of water consumed by 95% of the patients will be given as a range which can be gotten by
[tex]P=x\pm2S[/tex]Where
P = Amount of water.
x = mean
S = Standard Deviation
Therefore,
The lower limit is
[tex]\begin{gathered} x-2s \\ =62-2(5.2) \\ =62-10.4 \\ =51.6\text{ ounces} \end{gathered}[/tex]The upper limit is
[tex]\begin{gathered} x+2s \\ =62+2(5.2) \\ =62+10.4 \\ =72.4\text{ ounces} \end{gathered}[/tex]Therefore, the amount of water that 95% of the patients drink approximately is 51.6 ounces to 72.4 ounces.
In how many months were there more than two days with thunderstorms? 1 3 5 7
To find how many months have more than 2 days look at the heights
of the bars
You need to count the bars which height more than 2
There are 5 bars that have a height of more than 2
The answer is 5
a jacket at Rick's clothing store originally costs $27 the store is having a 45% off sale on all of its merchandise what is the sale price of the jacket
Let:
Op = Original price
Sp = Sale price
r = Discount
Express the discount percentage as a decimal:
45% = 45/100 = 0.45
The sale price will be given by:
[tex]\begin{gathered} Sp=Op-0.45Op \\ where \\ Op=27 \\ so\colon \\ Sp=27-12.5 \\ Sp=14.85 \end{gathered}[/tex]$14.85
explain how you solve a quadratic equation. How many answers do you expect to get for a quadratic equation?
1. There are several ways to solve (Quadratic Formula, Graphing, Newton's Identities, Factoring) the most common is using the Quadratic Formula.
2. We can always expect two roots, either identical or different.
1) There are some ways to solve a quadratic equation. We can solve it using the Quadratic Formula, Graphing it or via Newton's Identities, or even factoring
The most common way is via Quadratic Formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}[/tex]Which a, b, and c are the coefficients of a Quadratic Equation, say:
x²+6x+9, a= 1, b=6, and c=9.
[tex]x=\frac{-6\pm\sqrt[]{6^2-4(1)(9)}}{2(1)}=x_1=x_2=-3[/tex]Note that in this case, both roots were equal to -3
2) We can always expect two roots. When the Quadratic Formula yields just one answer then we can call it double root, or 1 root with multiplicity 2, actually there are two roots with the same value.
3) Thus the answer is:
1. There are several ways to solve (Quadratic Formula, Graphing, Newton's Identities, Factoring) the most common is using the Quadratic Formula.
2. We can always expect two roots, either identical or different.
Jake, Becky, and Max are meeting at Charley's Pizza for dinner and then plan to go
pizza place,
each one of them has a different coupbn. They decide to use the coupon that will give them the best deal. movie. When they arrive. the
Jake's coupon is $19.99 for a pizza and pasta meal deal, Becky's
of the menu price; and Max's coupon is for three mediun
coupon is for two large one topping pizas-each at ]
one-topping pizzas - each at -off the menu price. Accordling
to the menu, a medium one-topping pizza is $8.99, and
large one-topping pizza $14.89. They also spend $1.25
for sodas and $5.00 on the tip. At the movie theater. Max has › coupon that's good for ãoff a third movie ticket when
you purchase two other movie tickets at the regular price.
The regular price of each movie ticket is $9.80.
Although Jake, Becky, and Max plan to split the cost of the pizza and movie, they decide that with the coupons, it's just
easier if one of them pays at each place. So, the friends agree that Jake will pay for the pizza and Becky will pay for the
movies. At the end of the night, they'll figure out how much Max owes
both Jake and Becky.
After all costs
split evenly, how much will each person contribute?
between $14 and $15
• between $15 and $16
• between $16 and $17
O between $17 and $18
Answer:
$16 and $17
Step-by-step explanation:
Can someone please help me with my math ;( ?
Step 1:
copy and complete the table below by inputting the data provided.
The marginal frequency numbers are the numbers at the edges of the table except for the number at the bottom right-most corner.
B) Marginal relative frequency is the ratio of the sum of the joint relative frequency in a row or column and the total number of data values
Hence,
[tex]\text{ the lowest marginal frequency }=\frac{107}{232}=0.461[/tex]Joint relative frequency the ratio of the frequency in a particular category and the total number of data values
Therefore,
[tex]\text{ the largest joint frequency }=\frac{63}{111}=0.568[/tex]C)For the circled number, the preferred style is Gothic given that the member is male and the percentage is 0.57
D) The total number of males surveyed = 111
the total number of members surveyed = 232
Hence, the percentage of the total number of choir students surveyed that were males are:
[tex]\frac{111}{232}=0.48[/tex]Use substitution to solve each system of equations.y + 1/2x = 34y + 2x = 6
Answer:
No solution
Explanation:Given the system of eqations:
[tex]\begin{gathered} y+\frac{1}{2}x=3 \\ 4y+2x=6 \end{gathered}[/tex]From the second equation, find x.
[tex]\begin{gathered} 2x=6-4y \\ x=\frac{6-4y}{2} \\ =3-2y \end{gathered}[/tex]Substitute the obtained value of x into the first equation.
[tex]\begin{gathered} y+\frac{1}{2}(3-2y)=3 \\ y+\frac{3}{2}-y=3 \\ \frac{3}{2}=3 \end{gathered}[/tex]which isnotpossible. So, no solution exists.
Decide whether the given orderd pair is a solution to the stystem of equations?I don’t know how to to the bottom equation.
Given:
[tex]\begin{gathered} y=2x-6 \\ x+y=8 \end{gathered}[/tex]solve the equation for x and y then
[tex]\begin{gathered} x+y=8 \\ \text{put the value of y} \\ x+2x-6=8 \\ 3x=8+6 \\ 3x=14 \\ x=\frac{14}{3} \end{gathered}[/tex]so value of y is:
[tex]undefined[/tex]You invested $28,000 in two accounts paying 7% and 9% annual interest, respectively. If the total interest earned for the year was $2180, how much was invested at each rate?
We are given the following information:
total of $28,000 invested in 2 accounts
7% and 9% interest rates for each account
total interest was $2,180
We are asked to calculate the amount invested at each rate.
To do this, let us first identify our variable and what it stands for. Let us use the variable x to represent the amount invest at 7%. That leaves us t
Use the properties of exponents to simplify. Express all answers using positive exponents.each)35x10 over 5x^5
Consider the given expression,
[tex]\frac{35x^{10}}{5x^5}[/tex]Consider the property,
[tex]\frac{x^m}{x^n}=x^{m-n}[/tex]Then the given expression can be simplified as follows,
[tex]\begin{gathered} \frac{35x^{10}}{5x^5} \\ =\frac{35}{5}\times\frac{x^{10}}{x^5} \\ =7\times x^{10-5} \\ =7\times x^5 \\ =7x^5 \end{gathered}[/tex]Thus, the given expression is simplified as,
[tex]\frac{35x^{10}}{5x^5}=7x^5[/tex]What is the greatest common factor of 48x^2?and 32x^3?A. 16x^2B. 96x^3C. 8x^2D. 16x
greatest common factor (GCF) of 2 algebraic terms is the largest monomial that evenly divides the two expressions.
We have
[tex]\begin{gathered} 48x^2 \\ \text{and} \\ 32x^3 \end{gathered}[/tex]There are two parts, the numbers and variables.
From the numbers, the largest number we can divide 48 and 32 by is:
16
From the variables, the largest factor is x^2
Putting them together, we can say the GCF is:
[tex]16x^2[/tex]Correct Answer: A
A student is taking a test in which items of type A are worth 8 points and items of type B are worth 12 points. It takes 3 min to complete each item of type A and 6 min to complete each item of type B. The total time allowed is 60 min and Anna answers exactly 16 questions. How many questions of each type did she complete? Assuming that all her answers were correct, what was her score? She completed questions of type A.
Type A questions are worth 8 points each.
Type B questions are worth 12 points each.
it takes 3 minutes to answer a Type A question
it takes 6 minutes to answer a Type B question.
total time allowed = 60 minutes
She answered a total of 16 questions.
let
number of question answer on type A = x
number of question answered on type B = y
Therefore,
3x + 6y = 60
x + y = 16
then,
[tex]\begin{gathered} 3x+6y=60 \\ x+y=16 \\ x=16-y \\ 3(16-y)+6y=60 \\ 48-3y+6y=60 \\ 3y=60-48 \\ 3y=12 \\ y=\frac{12}{3} \\ y=4 \\ x=16-4 \\ x=12 \end{gathered}[/tex]She answered 12 questions on type A and 4 questions on type B.
If all her answer is correct her score can be computed below
[tex]undefined[/tex]f(x) = -x2 + 7x - 13 Find f(-3)
Given the function :
[tex]f(x)=-x^2+7x-13[/tex]To find f(-3) , substitute with x = -3 , into the given function:
So,
[tex]\begin{gathered} f(-3)=-(-3)^2+7\cdot-3-13 \\ \\ f(-3)=-9-21-13 \\ \\ f(-3)=-43 \end{gathered}[/tex]
Which expression is equivalent to 1-51 +131? —8 ООО O2 o 8
Theg given expression : |-5|+|3|
Since modulus is express as |-a|=a and |a|=a
[tex]undefined[/tex]