The line parallel to y = 3x +7 and passes through the point (-4,-8) is
y=3x+4
What is a slope-intercept form?It gives the graph of a straight line and it is represented in the form
y= mx +c. It is one of the form used to calculate the equation of a straight line. We have to calculate the slope of the line from the equation. The slope calculated can be used in the slope-intercept form. It is the most popular form of a straight line.
We need to find the slope to the line y = 3x +7.
The slope of a line is m
Here, from the equation y=3x+7, m=3
So, m=3
The slope-intercept form is,
y= mx +c
-8 = 3(-4)+c
-8=-12+c
c=4 and m=3
Now, the above equation equation becomes,
y=3x+4
The line parallel to y = 3x +7 and passes through the point (-4,-8) is
y=3x+4
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What value is a discontinuity of x^2+5x+2/x^2+2x-35
Solution:
Given the expression:
[tex]\frac{x^2+5x+2}{2x^2+2x-35}[/tex]A function f(x) has disconituity at x=a if
[tex]\lim_{x\to a}f(x)[/tex]exists and is finite.
The function is thus undefined at x=a or when
[tex]\lim_{x\to a}(f(x))\ne f(a)[/tex]From the given function, we have
[tex]\begin{gathered} \frac{x^2+5x+2}{x^2+2x-35} \\ factorize\text{ the denominator,} \\ \frac{x^2+5x+2}{x^2-5x+7x-35}=\frac{x^2+5x+2}{x(x-5)+7(x-5)} \\ \Rightarrow\frac{x^2+5x+2}{(x-5)(x+7)} \end{gathered}[/tex]The function is undefined at
[tex]\begin{gathered} x-5=0 \\ \Rightarrow x=5 \\ x+7=0 \\ \Rightarrow x=-7 \end{gathered}[/tex]Hence, there is discontinuity at
[tex]x=5,\text{ x=-7}[/tex]The gas/oil ratio for a certain chainsaw is 50 to 1.a. How much oil (in gallons) should be mixed with 13 gallons of gasoline? b. If 1 gallon equals 128 fluid ounces, write the answer to part a in fluid ounces.
1) We can write the following ratio for this, considering the ratios and the quantities:
a)
[tex]\begin{gathered} \frac{50}{1}=\frac{13}{x} \\ 50x=13 \\ x=\frac{13}{50}\text{ (or 0.26g)} \end{gathered}[/tex]Notice that on the left side, the ratio gas/oil, and on the right side is the quantity of gas and the unknown quantity of oil.
So, so far we have 13/50 gallons of oil that must be mixed with gasoline.
b) For now, we need to convert that from gallons to fluid ounces so we can write out the following product:
[tex]\begin{gathered} x=\frac{13}{50}\times128 \\ x=33.28fl\text{ oz} \end{gathered}[/tex]So 13/50 or 0.26 gallons of oil. b) 33.28 fl oz.
Americans said money mistakes cost them $1,230, on average, last year alone, According to U.S. Census Bureau data from 2018, the latest release, the median household income was $61,372. What percent of their income did they lose on mistakes?
EXPLANATION.
The first thing to do is analyze the data that the exercise gives us, it tells us that a year the cost of error for money was 1230, but the income was 61,372, for this exercise we must find the percentage with a rule of three .
The exercise is as follows.
The total income 61,372 represents 100 percent, how much does 1230 represent?
[tex]undefined[/tex]which value must be added to the expression x^2 + x to make it a perfect-square trinomial
A perfect square trinomial is written in the form
[tex]undefined[/tex]What is the range 12 ,20,18,25,6
The maximum of data is 25
The minimum of data is 6
Then, the range is:
range = maximum - minimum
range = 25 - 6
range = 19
Find the equation of the line using the given information and the point slope form. Express the equation in slope intercept form points (5,6) Points(-1,4)
step 1
Find out the slope
m=(4-6)/(-1-5)
m=-2/-6
m=1/3
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=1/3
point(5,6)
substitute
6=(1/3)(5)+b
solve for b
6=(5/3)+b
b=6-5/3
b=13/3
therefore
y=(1/3)x+13/3Multiply 1.42 x 0.3
the given problem is 1.4*0.3
here the answer is 0.42
[tex]undefined[/tex]How many pounds of candy that sells for $0.85 per Ib must be mixed with candy that sells for $1.22 per lb to obtain 9 lb of a mixture that should sell for $0.92 per lb? 50.85-per-lb candy: 73 lb (Type an integer or decimal rounded to two decimal places as needed.) $1.22-per-b candy
This system gives two equations
[tex]\frac{0.85x+1.22y}{9}=0.92[/tex][tex]x+y=9[/tex]where x is the number pounds of $0.85/lb candy and y is the number of pounds of $1.22/lb candy.
The solution to the system is
[tex]x=7.297[/tex][tex]y=1.70[/tex]Hence, 7.297 lb of $0.85 candy is required in order that if we mix them with 1.70 lb of $1.22 candy, we will get a 9 lb solution of 0.92 /lb candy.
Write a quadratic equation with 7 and 2/5 as its roots. Write the equation in the form ax2 + bx+c= 0, where a, b, and c are integers.
As given by the question
There are given that the roots: 7 and 2/5.
Now,
Since the roots are integers, we can write the equation in the given form using a = 1.
Then,
b is the opposite of the sum of the roots
So,
[tex]\begin{gathered} b=-((7)+(\frac{2}{5})) \\ b=-(\frac{35+2}{5}) \\ b=-\frac{37}{5} \end{gathered}[/tex]And
c is the products of the roots
So,
[tex]\begin{gathered} c=7\times\frac{2}{5} \\ c=\frac{14}{5} \end{gathered}[/tex]Now,
The desired quadratic equation is:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x^2-\frac{37}{5}x+\frac{14}{5}=0 \\ 5x^2-37x+14=0 \end{gathered}[/tex]Hence, the correct option is A.
To get rid of radicals in the denominator of a fraction, you should rationalize the denominator by multiplying the fraction by a helpful form of _____.A.the denominatorB.xC.1D.the numerator
Given:
To get rid of radicals in the denominator of a fraction
Required:
you should rationalize the denominator by multiplying the fraction by what
Explanation:
In fraction, a number is said to be a quotient, in which the numerator is divided by the denominator.
there are three types of fraction
1. Proper fraction
2. Improper fraction
3. Mixed
Final answer:
But to get rid of radival in the denominator of a fraction, you should rationalize the denimonator by multiplying the fraction with 1
the sum of 6 times a number and 8 equals 7? translate into equation
Let:
x = Unknown number
the sum of 6 times a number:
[tex]6x+[/tex]and 8 equals 7, so:
[tex]\begin{gathered} 6x+8=7 \\ \text{solve for x:} \\ \text{subtract 8 from both sides:} \\ 6x=7-8 \\ 6x=-1 \\ \text{divide both sides by 6:} \\ x=-\frac{1}{6} \end{gathered}[/tex]3x and 8x are like terms.true or false
Like terms are those terms whose variable and its corresponding exponent are the same. Here we have 3x and 8x. Both terms have the number:
[tex]x^1[/tex]Which means that they have the same variable and the same exponents. Then they are like terms and the answer is True.
Is there any other further step I need to do? The answer is very close but not exact so I’m unsure.
Given the matrices:
[tex]A=\begin{bmatrix}{10} & {4} & {0} \\ {1} & {3} & {1}\end{bmatrix},B=\begin{bmatrix}{4} & {1} & \\ {2} & {2} & {} \\ {0} & {-1} & \end{bmatrix}[/tex]we will find the value of AB + I
First, we will find the product of AB as follows:
[tex]AB=\begin{bmatrix}{10} & {4} & {0} \\ {1} & {3} & {1}\end{bmatrix}\cdot\begin{bmatrix}{4} & {1} & \\ {2} & {2} & {} \\ {0} & {-1} & \end{bmatrix}=\begin{bmatrix}{10\cdot4+2\cdot4+0\cdot0} & {1\cdot01+4\cdot2+0\cdot-1} & {} \\ {1\cdot4+3\cdot2+1\cdot0} & {1\cdot1+3\cdot2+1\cdot-1} & {} \\ {} & {} & {}\end{bmatrix}[/tex]simplifying the answer:
[tex]AB=\begin{bmatrix}{48} & {18} & {} \\ {10} & {6} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Now, we will add the unity matrix to the answer:
[tex]AB+I=\begin{bmatrix}{48} & {18} & {} \\ {10} & {6} & {} \\ {} & {} & {}\end{bmatrix}+\begin{bmatrix}{1} & {0} & {} \\ {0} & {1} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{49} & {18} & {} \\ {10} & {7} & {} \\ {} & {} & {}\end{bmatrix}[/tex]So, the answer will be option D
Solve the given equation over the interval [0,2%): 3 tanº x+tan x = 0.7%x= 0 and x= - and x=6.6x= 0 and x=76and x=11%657 119x= 0 and x= and x=66es andSTx= 0 and x= - and x =6od x = F and =
OPTION C
Can someone please help me find the value of X?
Remember that
the sum of the interior angles in any polygon is equal to
S=180(n-2)
where
n is the number of sides of polygon
In this problem
we have
n=6 (hexagon)
so
substitute
S=180(6-2)
S=720 degrees
step 2
Adds the interior angles
720=120+(5x-6)+(4x+14)+(7x)+(8x-8)+(6x)
solve for x
combine like terms
720=30x+120
30x=720-120
30x=600
x=20determine whether the binomial expression is a factor to the following polynomial.[tex]p(x) = {x}^{3} - 9x + 1 \: \: \: \: \: \: \: \: \: (x - 3)[/tex]the binomial expression is (x-3) ^^answer choicesA. yesB. no
We can find if (x-3) is a factor by dividing P(x) by (x-3).
A simpler way is replacing x with 3 and if the value of P(x) is 0, then (x-3) is a factor of P(x). This is because x=3 is a root of P(x) and therefore it can be factorized with the term (x-3).
Then, we calculate P(3):
[tex]P(3)=3^2-9\cdot3+1=9-27+1=-17[/tex]As x=3 is not a root of P(x), then (x-3) is not a factor of P(x).
Answer: No.
Translate to an algebraic expression, but do not simplify.the difference of 10 and -16Simplify the translated phrase if possible.
When you have a phrase as the difference of a and b, the algebraic expression is b being subtractd from a.
The difference of 10 and -16:
[tex]10-(-16)[/tex]Simplify:
[tex]\begin{gathered} =10+16 \\ =26 \end{gathered}[/tex]Then, the algebraic expression is; 10-(-16) and simplified is 26Solve the following equation for x by using the quadratic formula. If there is more than one solution, enter your solutions as a comma-separated list, like "1, 3".2x^2+9x+7=0
Answer:
Explanation:
Given the equation:
[tex]2x^2+9x+7=0[/tex]• The coefficient of x², a=2
,• The coefficient of x, b=9
,• The constant, c=7
Substitute these values into the quadratic formula:
[tex]\begin{gathered} x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\ \implies x=\dfrac{-9\pm\sqrt[]{9^2-4(2)(7)}}{2\times2}=\dfrac{-9\pm\sqrt[]{81-56}}{4}=\dfrac{-9\pm\sqrt[]{25}}{4} \\ \implies x=\dfrac{-9\pm5}{4} \end{gathered}[/tex]Thus, the values of x are:
[tex]undefined[/tex]
The table below shows the cost of downloading songs from a website.Number of Songs Total Cost11$10.5613$12.4818.$17.28At this rate, what is the cost per song?Answer: $per song
To know the cost per song we make a division between the total Cost and the number of songs, then we can take any pair of data
I will use 11 songs and $10.56
[tex]\frac{10.56}{11}=\frac{24}{25}=0.96[/tex]to check we can use another pair (18 songs and $17.28)
[tex]\frac{17.28}{11}=\frac{24}{25}=0.96[/tex]then the cost per song is $0.96
can someone please help?just in case if the picture seems blurry, the question says the take off ramp is parallel to the waiting ramp, and the interest ramps are parallel. Given that the measure of angle a is 88 find the measure of each remaining angles
Which point shows the number with the greatest absolute value? А B + + D TH 30 40 50 -50 -40 -30 - 20 -10 0 10 20 O Point A O Point B O Point C O Point D ہ
We are shown points A, B, C, and D on a number line.
We are asked to find out which point shows the number with the greatest absolute value?
Recall that the absolute value of a number is always positive.
The negative values of points A and B will become positive.
As you can see from the number line, point A is closer to -40 and the point D is closer to 30
The absolute value of point A will be closer to |-40| = 40
Since 40 is greater than 30, point A shows the number with the greatest absolute value.
Therefore, the correct answer is Point A.
You have $5,000 to invest and want it to grow to $20,000 in two years. What interest rate would you need to find to make this possible?I wan answer and explanation.
ANSWER
The interest rate is 150%
EXPLANATION:
Given that;
The initial amount is $5000
The total amount $20, 000 after 2 years
Total period of the investment is 2 years
To find the interest rate, follow the steps below
1. Find the interest on the investment after two years
In the given data,
The initial amount (principal) is $5000
The total amount after 2 years is $20, 000
Recall that,
Total amount = Interest + principal
20, 000 = interest + 5000
subtract 5000 from both sides of the equation
20, 000 - 5,000 = interest + 5000 - 5000
15,000 = interest
Therefore, the interest on the investment after 2 years is $15, 000
Step 2; Find the interest rate using the simple interest formula
[tex]\text{ I }=\text{ }\frac{P\times R\times T}{100}[/tex]Where
I is the interest
P is the principal
R is the interest rate
T is the time of the investment
[tex]\begin{gathered} \text{ 15, 000 }=\text{ }\frac{5000\times\text{ r}\times\text{ 2}}{100} \\ \text{ } \\ \text{ 15000 }=\text{ }\frac{10,000r}{100} \\ \text{ 15, 000 }=\text{ 100r} \\ \text{ Divide both sides by 100} \\ \frac{15,000}{100}\text{ }=\text{ }\frac{100r}{100} \\ \text{ r }=\text{ 150\%} \end{gathered}[/tex]Therefore, the interest rate is 150%
Use synthetic division to find the result when 4x3 + 13x2 + 6x + 9 is divided byx + 3.
To solve this question, observe the figure and observe the steps below:
1) Organize the coefficient of the dividend according to the figure.
2) Write the zero of the divisor according to the figure.
3) Write down the first coefficient (4).
4) Multiply the coefficient by -3 and write it below 13 (second coefficient). Then, sum the result (-12) with 13. Write the answer (1).
5) Do the same with the other values, according to the figure.
6) The coefficients of the quotient are the values in green and the remainder is the value in red.
Answer: The quotient is:
[tex]4x^2+1x+3[/tex]Could you help me with how to multiply polynomials(5x - 1)(2x^2 -3x + 4)
ANSWER:
[tex](5x\: -\: 1)(2x^2\: -3x\: +\: 4)=10x^3-17x^2+23x-4[/tex]STEP-BY-STEP EXPLANATION:
We have the following multiplication of polynomials:
[tex]\mleft(5x-1\mright)\mleft(2x^2-3x+4\mright)[/tex]When multiplying two polynomials we must bear in mind that all the terms of the first polynomial must be multiplied by all the terms of the second polynomial, like this:
[tex]\begin{gathered} \mleft(5x-1\mright)\mleft(2x^2-3x+4\mright)=5x\cdot2x^2+5x\cdot-3x+5x\cdot4+(-1)\cdot2x^2+(-1)\cdot-3x+(-1)\cdot4 \\ (5x\: -\: 1)(2x^2\: -3x\: +\: 4)=10x^3-15x^2+20x-2x^2+3x-4 \\ (5x\: -\: 1)(2x^2\: -3x\: +\: 4)=10x^3-17x^2+23x-4 \end{gathered}[/tex]Solve for h.A=3h Can anyone help me?
You have the following expression:
[tex]A=3h[/tex]In order to solve for h, use the division property of equality. In this case divide by 3 both sides:
[tex]\begin{gathered} \frac{A}{3}=\frac{3h}{3} \\ \frac{A}{3}=h \end{gathered}[/tex]Hence, the solution for h = A/3
6<-3kWhy is the answer -2Shouldn’t it be positive 2
we are given the following inequality:
[tex]6<-3k[/tex]To solve for "k" we will divide both sides by -3, since we are dividing by a negative number we will change the direction of the inequality sign, we get:
[tex]\frac{6}{-3}>-\frac{3k}{-3}[/tex]Solving the operations we get:
[tex]-2>k[/tex]Therefore, the solution is the numbers that are smaller than negative 2.
Callie's grandmother pledged R150, 00 for every mile Callie walked in her walk-a-thon. Callie walked 14.5 km. How much does her grandmother owe? ( assume 8 km = 5miles)
Given:-
Callie walked 14.5 km. And also given 8 km=5 miles.
At first we convert 14.5 km to miles. we get,
[tex]\begin{gathered} 14.5\times\frac{5}{8}=\frac{72.5}{8} \\ \text{ =9.0625} \end{gathered}[/tex]So 14.5 km is 9.0625 miles.
Callie's grandmother pledged Rs. 150 for every mile. so for 9.0625 miles it is,
[tex]9.0625\times150=1359.375[/tex]So her grandmother owe Rs. 1359.375
5.Line AB is 14 inches long. What is the approximate area of this circle?АBa. 42 square inchesb. 615 square inchesc. 160 square inchesd. 154 square inches
The area of a circle is given as
A =
Solve for x. 4x-39>-43 and 8x+31<23with an example of a graphic line
Given:
[tex]4x-39>-43and8x+31<23[/tex]Solve the inequality separately,
[tex]\begin{gathered} 4x-39>-43 \\ 4x>-43+39 \\ 4x>-4 \\ x>-1 \end{gathered}[/tex]Also,
[tex]\begin{gathered} 8x+31<23 \\ 8x<23-31 \\ 8x<-8 \\ x<-1 \end{gathered}[/tex]As the given inequality give x > -1 and x < -1 it shows that there is no solution for the given inequality.
The graph is given as,
The red region shows the inequality 4x -39 > -43 and blue region shows 8x +31 < 23.
Answer: Option D.
given the function f defined by the formula f(x)=2x+1 find the following: Evaluate f(0)
At a given function:
[tex]\text{ f(x) = 2x + 1}[/tex]At f(0), it means that we substitute x by 0.
We get,
[tex]\text{ f(x) = 2x + 1}[/tex][tex]\text{ f(0) = 2(0) + 1}[/tex][tex]\text{ f(0) = 1}[/tex]Therefore, f(0) = 1.