In general, the slope-intercept form of a linear equation is
[tex]\begin{gathered} y=mx+b \\ m,b\rightarrow\text{ constants} \end{gathered}[/tex]Thus, in our case,
[tex]\begin{gathered} y-2=-5(x-2) \\ \Rightarrow y-2=-5x+10 \\ \Rightarrow y=-5x+12 \end{gathered}[/tex]The answer is y=-5x+1220. Connie's pool has 50 cubic yards of water in it and is draining at a rate of 3 cubic yards per second. Paula's pool has 9 cubic yards of water currently in it and is filling at a rate of 4 cubic yards per second. After how many seconds will Connie's pool have less water than Paula's?
write the equation for the Connie's pool and Paula's pool
Connie's
[tex]y=50-3x[/tex]y=cubic yards of water remaining in the pool
x=time in seconds
Paula's
[tex]y=9+4x[/tex]y=cubic yards of water in the pool
x=time in seconds
write the inequality in order for connie's pool to have less water
[tex]\begin{gathered} 50-3x<9+4x \\ \end{gathered}[/tex]solve the inequality for x
[tex]\begin{gathered} 50-9<3x+4x \\ 41<7x \\ x>\frac{41}{7} \end{gathered}[/tex]After 41/7 seconds Connie's pool will have less water than Paula's.
The hallway of an apartment building is 44 feet long
and 6 feet wide. A landlord has 300 square feet of carpet. Does she have
enough carpet to cover the hallway? Explain.
Answer:
Yes, there is enough carpet to cover the hallway. We know this because the area of the floor is shown as 44 times 6, which equals 264 feet. With 300>264, there is enough feet of carpet to cover
Step-by-step explanation:
44 times 6 = 264
Find the remaining zer Degree 3; zeros: 5, 7- i The remaining zero(s) of f is
Answer:
The remaining zero is;
[tex]7+i[/tex]Explanation:
Given that two of the zeros of a polynomial are;
[tex]\begin{gathered} 5 \\ 7-i \end{gathered}[/tex]to get the remaining zero.
Recall that according to complex conjugates, complex roots/zeros comes in pairs;
[tex]\begin{gathered} a+bi \\ \text{and} \\ a-bi \end{gathered}[/tex]where a and b are real numbers.
Applying the rule to the given roots.
Since we have a complex root;
[tex]7-i[/tex]we must also have the other pair of the complex root;
[tex]7+i[/tex]Therefore, the remaining zero is;
[tex]7+i[/tex]which of tje following proportion are true16/28=12/216/16=4/1430/40=24/3510/15=45/30
Notice that:
1)
[tex]\frac{16}{28}=\frac{4\cdot4}{7\cdot4}=\frac{4}{7}=\frac{4\cdot3}{7\cdot3}=\frac{12}{21}\text{.}[/tex]2)
[tex]\frac{6}{16}=\frac{2\cdot3}{2\cdot8}=\frac{3}{8}\ne\frac{2}{7}=\frac{2\cdot2}{2\cdot7}=\frac{4}{14}\text{.}[/tex]3)
[tex]\frac{30}{40}=\frac{10\cdot3}{10\cdot4}=\frac{3}{4}\ne\frac{2}{3}=\frac{12\cdot2}{12\cdot3}=\frac{24}{36}.[/tex]4)
[tex]\frac{10}{15}=\frac{5\cdot2}{5\cdot3}=\frac{2}{3}\ne\frac{9}{10}=\frac{5\cdot9}{5\cdot10}=\frac{45}{50}.[/tex]Answer: The only proportion that is true is the first one.
What are the solutions to the following system?{-2x+y=-5y=-3x2 + 50 (0, 2)O (1, -2)o (12.-1) and (- 12.-1):o 15.-10) and (-75-10
Answer:
[tex](\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}[/tex]Explanation:
Here, we want to solve the system of equations
Since we have y in both equations, let us start by rewriting the second equation to look like the first
We have that as:
[tex]\begin{gathered} -2x^2+y\text{ = }-5 \\ y+3x^2\text{ = 5} \end{gathered}[/tex]Subtract equation ii from i
We have it that:
[tex]\begin{gathered} -5x^2=\text{ -10} \\ 5x^2=10 \\ x^2=\text{ 2} \\ \\ x\text{ = }\pm\sqrt[]{2} \end{gathered}[/tex]when x = positive root 2, we have it that:
[tex]\begin{gathered} -2x^2+y\text{ = -5} \\ -2(\sqrt[]{2\text{ }})^2+y\text{ = -5} \\ -4+y\text{ = -5} \\ y\text{ = -5+4} \\ y\text{ = -1} \end{gathered}[/tex]when x = negative root 2:
We will still get the same answer as the square of both returns the same value
Thus, we have the solution to the system of equations as:
[tex](\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}[/tex]Does the function f(x) or g(x) have a greater value at x=2? f(x)=4∙2^x
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph: g(x)
function: f(x) = 4 * 2 ^ x
Step 02:
greater value ==> x = 2:
graph: g(x)
x = 2 , y = 18
g(2) = 18
function: f(x) = 4 * 2 ^ x
[tex]f(2)\text{ = 4 }\cdot2^2=\text{ 4 }\cdot\text{ 4 = 16}[/tex]The answer is:
g(x) has a greater value at x = 2
Hi , i need help with this question: what is the anwser to the division problem. 9÷4590
Problem
what is the anwser to the division problem.
9÷4590
Solution
We have the following number given:
[tex]\frac{9}{4590}[/tex]The first step would be simplify the fraction and we can divide both numbers by 9 and we got:
[tex]\frac{9}{9}=1,\frac{4590}{9}=510[/tex]So then our fraction becomes:
[tex]\frac{1}{510}[/tex]And if we convert this into a decimal we got 0.00196.
If ST = x + 4, TU = 10, and SU = 9x + 6, what is ST?
Given:
[tex]\begin{gathered} ST=x+4 \\ \\ TU=10 \\ \\ SU=9x+6 \end{gathered}[/tex]Find-:
The value of "x."
Explanation-:
The line of property
[tex]SU=ST+TU[/tex]Put the value is:
[tex]9x+6=x+4+10[/tex][tex]\begin{gathered} 9x+6=x+14 \\ \\ 9x-x=14-6 \\ \\ 8x=8 \\ \\ x=\frac{8}{8} \\ \\ x=1 \end{gathered}[/tex]So, the value of "x" is 1.
Graph the following:X>y^2 + 4y
Solution:
Given the inequality;
[tex]x>y^2+4y[/tex]The graph of inequality without an equal sign is done with broken lines,
The y-intercept is;
[tex]\begin{gathered} 0>y^2+4y \\ \\ 0>y(y+4) \end{gathered}[/tex]Thus, the graph is;
Fergus gets paid $5.25 an hour with time-and-a-half for overtime(over 40 hours). How much did he earn one week when he worked 48hours?a. $63.04b. $190.90c. $210d. $273.04
The correct answer is d. $273
Fergus worked 48 hours in the week. This means that for 40 hours he was paid $5.25 per hour; And for 8 hours he was paid 150% of the normal (150% is one and a half time)
Then for the regular paid hours:
$5.25 per hour by 40 hours => 5.25*40= $210
Now for the 8 remaining hours we need to calculate how much Fergus is paid by hour.
Then 50% of $5.25 is the same as 5.25 divided by 2: 5.25/2 = $2.625
Then the 150% is equal to 100% + 50%. The 100% is $5.25 and the 50% is $2.625
5.25 + 2.625 = $7.875
This is what Fergus gets paid for every overtime hour. This week he worked 8 overtime hours.
Then, $7.875 * 8 = $63
Now the total earning of the week is equal to $210 + $63 = $273 and that's option D.
1 + xThe function g is defined by g(x)=7+2xFind g(a+5).
The function is given as:
[tex]g(x)=\frac{1+x}{7+2x}[/tex]We need to find the expression g(a + 5).
This means that we are going to plug in "a + 5" into "x" of the function. So, substituting, it gives us,
[tex]\begin{gathered} g(x)=\frac{1+x}{7+2x} \\ g(a+5)=\frac{1+(a+5)}{7+2(a+5)} \end{gathered}[/tex]Now, we need to simplify the expression. Steps are shown below:
[tex]\begin{gathered} g(a+5)=\frac{1+(a+5)}{7+2(a+5)} \\ =\frac{1+a+5}{7+2a+10} \\ =\frac{6+a}{17+2a} \end{gathered}[/tex]Answer[tex]\frac{6+a}{17+2a}[/tex]Hi I need help with this question please thank you!
To answer this question we will factorize each term.
Notice that:
[tex]20x^4y=5xy(4x^3),[/tex][tex]10x^3y^3=5xy(2x^2y^2),[/tex][tex]5xy^2=5xy(y).[/tex]Therefore, the greatest common factor of the terms is:
[tex]5xy\text{.}[/tex]Answer:
[tex]5xy\text{.}[/tex]
f(x)=x^3-4x^2+x+6 find all the real zeros of the function
The zeroes of the polynomial f(x)= x³ - 4x² + x + 6 = 0 are x - 1, x = 2
and x = 3.
We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, f(x)= x³ - 4x² + x + 6 = 0.
Now, zeroes of the polynomial should be factors of 6 they are ±1, ±2. ±3, ±6.
Now at x = 1 f(x) = 4 so not a zero, at x = - 1, f(x) = 0 so x = - 1 a zero
at x = 2 f(x) = 0 so x = 2 is a zero,
at x = 2 f(x) = so x = 3 is a zero.
learn more about polynomials here :
https://brainly.com/question/20121808
#SPJ2
Drag and drop a phrase to make the statement true. TrianglesABC and DEF are Response area.similar or not similar
Solution:
Given two triangles;
Triangle ABC and DEF are similar only if;
[tex]\begin{gathered} \angle A\cong\angle D \\ \angle B\cong\angle E \\ \angle C\cong\angle F \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} \angle A=180^o-80^o-60^o \\ \angle A=40^o=\angle D \end{gathered}[/tex]Also,
[tex]\angle B=\angle E=80^o[/tex]Also,
[tex]\begin{gathered} \angle F=180^o-80^o-40^o \\ \angle F=60^o=\angle C \end{gathered}[/tex]FINAL ANSWER: Triangle ABC and DEF are similar triangles
7/8 = X/16 X=how do I solve it
x= 14
1) Let's solve this equation considering that we're dealing with two ratios.
Then we can cross multiply and simplify them this way:
[tex]\begin{gathered} \frac{7}{8}=\frac{x}{16} \\ 8x=16\cdot7 \\ \frac{8}{8}x=\frac{16\cdot7}{8} \\ x=2\cdot7 \\ x=14 \end{gathered}[/tex]2) So the answer is x= 14
What is the speed of a jet plane that flies 8100 km in 9 hours (in km/hr)
V = d/t
Speed = distance/time
V = 8100km/9hr = 900Km/hr
Answer:
V = 900 km/h
Determine if each of the following relationships form a function.(1,1), (3,2), (5,4), (-9,6)
Determine if each of the following relationships form a function.
(1,1), (3,2), (5,4), (-9,6)
we know that
A relationship between x and y form a function, if for one value of x there is only one value of y
In this problem we have that
for one value of x there is only one value of y
therefore
Yes, form a function
Use Cramer's Rule to solve the system. You may use the calculator for computations only - do not use any matrix functions. Show all work
Solution
Therefore the value of
[tex]\begin{gathered} x=-1 \\ y=\frac{5}{2}=2.5 \end{gathered}[/tex]1 5/6 - (-2 4/5)[tex]1 \frac{5}{6} - ( - 2 \frac{4}{5} )[/tex]
We have the following:
[tex]1\frac{5}{6}-(-2\frac{4}{5})[/tex]solving:
[tex]\begin{gathered} 1\frac{5}{6}=\frac{11}{6} \\ 2\frac{4}{5}=\frac{14}{5} \\ \frac{11}{6}+\frac{14}{5}=\frac{11\cdot5+14\cdot6}{30}=\frac{55+84}{30}=\frac{139}{30} \\ \frac{139}{30}=4\frac{19}{30} \end{gathered}[/tex]The answer is 4 19/30
Evaluate with no calculator sin(sin^-1(3/8))
Since the sine ratio is opposite side/hypotenuse
Then in
[tex]\sin (\sin ^{-1}\frac{3}{8})[/tex]This means the angle has opposite side 3 and hypotenuse 8 in a right triangle
Then use this rule to evaluate without a calculator
[tex]\sin (\sin ^{-1}\frac{a}{b})=\frac{a}{b}[/tex]Because sin will cancel sin^-1
[tex]\sin (\sin ^{-1}\frac{3}{8})=\frac{3}{8}[/tex]The answer is 3/8
y = 3x ÷ 9 and x = -6 what is the output?
y = 3x ÷ 9 and x = -6
y = 3(-6) ÷ 9 = -18 ÷ 9 = -2
y = -2
Answer:
y = -2
ubtract. - B the model to help
As you can see in the model
[tex]\frac{1}{2}=\frac{4}{8}[/tex]Then
[tex]\frac{5}{8}-\frac{1}{2}=\frac{5}{8}-\frac{4}{8}=\frac{5-4}{8}=\frac{1}{8}[/tex]This is the same as if you removed 4 pieces of 1/8 from the 5 pieces of 1/8, resulting in 1 piece of 1/8.
Therefore, the result of the subtraction is
[tex]\frac{1}{8}[/tex]General MathematicsProblem:What interest rate would yield ₱1,200 interest on ₱10,000 in 2 years?
Answer
Interest rate = 6%
Explanation
From the information given in the question,
Interest, I = ₱1,200
Principal, P = ₱10,000
Time, T = 2 years
Interest rate, R = ?
Using Simple Interest formula:
[tex]I=\frac{PRT}{100}[/tex]Since I, P and T are know, we shall substitute these values into the formula to get R.
[tex]\begin{gathered} 1200=\frac{10000\times R\times2}{100} \\ 1200=200R \\ \text{Divide both sides by 200} \\ \frac{1200}{200}=\frac{200R}{200} \\ R=6 \end{gathered}[/tex]Therefore, the interest rate is 6%
Below is a model of the infield of a baseball stadium. How long is each side of the field Hurry pleaseee
We have the following:
[tex]\begin{gathered} A=s^2 \\ s=\sqrt{A} \end{gathered}[/tex]A = 81, replacing:
[tex]A=\sqrt{81}=9[/tex]therefore, each side measures 9 in
does any know how to find the variance using n=122 p= 0.64
The formula to find the variance of a binomial distribution given the values n and p is:
[tex]\begin{gathered} \sigma^2=n\cdot p\cdot q \\ \text{ Where} \\ q=1-p \end{gathered}[/tex]In this case, you have:
[tex]\begin{gathered} n=122 \\ p=0.64 \\ q=1-p \\ q=1-0.64 \\ q=0.36 \end{gathered}[/tex]Then
[tex]\begin{gathered} \sigma^2=n\cdot p\cdot q \\ \sigma^2=122\cdot0.64\cdot0.36 \\ \sigma^2=28.11 \\ \text{ Rounding to the nearest tenth} \\ \sigma^2=28.1 \end{gathered}[/tex]Now, the standard deviation is the square root of the variance. So, you have
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{28.1} \\ \sigma=5.3 \end{gathered}[/tex]Therefore, the variance and standard deviation of the binomial distribution with the given values n y p are
[tex]\begin{gathered} \sigma^2=28.1\Rightarrow\text{ Variance} \\ \sigma=5.3\Rightarrow\text{ Standard deviation} \end{gathered}[/tex]A regular plot of land is 70 meters wide by 79 meters long. Find the length of the diagonal and, if necessary, round to the nearest tenth meter
Given :
The length is given l=79 m and width is given w=70m.
Explanation :
Let the length of diagonal be x.
To find the length of diagonal , use the Pythagoras theorem.
[tex]x^2=l^2+w^2[/tex]Substitute the values in the formula,
[tex]\begin{gathered} x^2=79^2+70^2 \\ x^2=6241+4900 \\ x^2=11141 \\ x=\sqrt[]{11141} \\ x=105.55m \end{gathered}[/tex]Answer :
The length of the diagonal is 105.6 m.
The correct option is D.
Kevin went for a drive in his new car. He drove for 377.6 miles at a speed of 59 miles per hour. For how many hours did he drive ?
We know that the average speed (v) can be calculated as the quotient between the distance D and the time t.
As v = 59 mi/h and D = 377.6 mi., we can calculate the time as:
[tex]v=\frac{D}{t}\longrightarrow t=\frac{D}{v}=\frac{377.6\text{ mi}}{59\text{ mi/h}}=6.4\text{ h}[/tex]Answer: he drove for 6.4 hours.
I need to find out which ones are true and which ones I have to change to get the answers correct please help me.
Solution
- In order to solve this question, we need to apply the following rules:
[tex]\begin{gathered} Given \\ f(x)=ax^2+bx+c \\ \\ |a|>1:\text{ } \\ \text{ The graph gets narrower the larger }|a|\text{ gets} \\ \\ 0<|a|<1: \\ \text{ The graph gets wider the closer }|a|\text{ is to zero} \\ \\ a<0: \\ \text{ The graph has a peak} \\ \\ a>0: \\ \text{ The graph has a valley} \end{gathered}[/tex]- Applying this rule, we can proceed to solve this question.
- Based on these rules above, we can select the correct options as follows:
Drag and drop numbers into the equation to complete the equation of the line in slope-intercept form.The line passes through (8, 19) and (5, 1).
we are given two points
(8,19) and (5,1)
firstly, we need to calculate the slope
slope = y2 - y1 / x2 - x1
from the points
x1 = 8, y1 = 19, x2 = 5, y2 = 1
slope = 1 -19 / 5 - 8
slope = -18/-3
negative will cancel each other
slope = 18/3
slope = 6
slope intercept equation is
y - y1 = m(x - x1)
m = slope = 6
y1 = 19 and x1 = 8
y - 19 = 6(x - 8)
open the parentheses
y - 19 = 6*x - 6*8
y - 19 = 6x - 48
make y the subject of the formula
y = 6x - 48 + 19
y = 6x - 29
One friend claims that to find the height of the platform, you need to use the tangent ratio. Explain why her approach is or is not a reasonable approach to finding the height of the platform.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the trigonometric ratios
[tex]\begin{gathered} \sin\theta=\frac{opposite}{hypotensue} \\ \cos\theta=\frac{adjacent}{hypotenuse} \\ \tan\theta=\frac{opposite}{adjacent} \end{gathered}[/tex]STEP 2: Analyze the given scenario to get the details given
We were given the length of the piece of wood needed to make the ramp as 3.5m long, this implies that the length of the side is 3.5m. From the given image, this is the hypotenuse.
[tex]hypotenuse=3.5m[/tex]The angle of elevation is 28 degrees,
[tex]\theta=28\degree[/tex]The height of the platform from the image will be opposite since it is the side that is facing the angle 28 degrees.
[tex]opposite=height\text{ }of\text{ }platform[/tex]Joining all these together, we have a right-angled triangle given below:
From the given ratios in step 1, since we know tha hypotenuse and the opposite and also the theta, therefore the correct ratio to use is:
[tex]\begin{gathered} \sin\theta=\frac{opposite}{hypotenuse} \\ \\ \sin28=\frac{height}{3.5} \\ height=3.5\times\sin28 \end{gathered}[/tex]Therefore, the given claim of needing tangent ratio to find the height of the platform is not a reasonable approach because the adjacent which is the base is not given.