y=3x - 5....(i)
6x+3y=15.....(ii)
Then,
Keeping value of y in (ii)equation;
or,6x+3(3x-5)=15
or,6x+9x-15=15
or,15x=15+15
or,x=30/15
:x=2
Now, Keeping value of x in (i) equation;
y= 3x-5
or, y= 3×2 - 5
or,y= 6-5
: y=1
What is an equation for the parabola with focus (0, -12) and directrix y = 12
Given:
Focus of a parabola is (0, -12) and directrix is y = 12.
To find:
The equation of the parabola.
Solution:
General form of a parabola is
[tex](x-h)^2=4p(y-k)[/tex] ...(i)
where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.
Focus is (0, -12).
[tex](h,k+p)=(0,-12)[/tex]
[tex]h=0[/tex]
[tex]k+p=-12[/tex] ...(ii)
Directrix is y = 12.
[tex]k-p=12[/tex] ...(iii)
Adding (ii) and (iii), we get
[tex]2k=0[/tex]
[tex]k=0[/tex]
Putting k=0 in (ii), we get
[tex]0+p=-12[/tex]
[tex]p=-12[/tex]
Putting h=0, k=0 and p=-12 in (i).
[tex](x-0)^2=4(-12)(y-0)[/tex]
[tex]x^2=-48y[/tex]
[tex]-\dfrac{1}{48}x^2=y[/tex]
Therefore, the required equation of parabola is [tex]y=-\dfrac{1}{48}x^2[/tex].
A fruit juice company includes 1.872 ounces of orange juice in a 6.65-ounce bottle of a mixed fruit
juice. How much of the bottle of mixed fruit juice is NOT orange juice?
ounces
(Type a whole number or a decimal.)
Answer:
4.778 ounces
Step-by-step explanation:
Given that:
Ounces of orange juice in mixed fruit juice = 1.872
Ounces of mixed fruit juice = 6.65 ounces
Ounces of Mixed fruit juice that is not orange juice :
(Ounces of mixed fruit juice - Ounces of orange juice)
(6.65 - 1.872) ounces
= 4.778 ounces
The graph of f^ prime is shown. Find and sketch the graph of f given that fis continuous and f(0) = 1 .
(#72 in the pic)
9514 1404 393
Answer:
see attached (blue line)
Step-by-step explanation:
The slope in the first interval (0 to 2) will be -1, down from the y-intercept of 1.
The slope in the second interval will be 2. After that, the slope is zero, so the graph is a horizontal line.
The blue line in the attached is the graph of f(x).
Help please giving brainliest!!
Answer:
Step-by-step explanation:
-1 = -3x + 5
add 3x on both sides
3x - 1 = 5
add 1 on both sides
3x = 6
divide both sides by 3 to get x by itself
x = 2
tor. Factor each expression. 2x + 8
Answer:
The factorized form of 2x + 8 is 2(x+4).
Step-by-step explanation:
Given the expression
2x + 8Let us factorize the expression
2x + 8
Rewrite 8 as 2·4
[tex]2x\:+\:8=2x+2\cdot \:\:4[/tex]
Factor out common term 2
= 2(x+4)
Therefore, factorized form of 2x + 8 is 2(x+4).
A group of researchers wants to know whether men are more likely than women to contract a novel coronavirus. They surveyed two random samples of 390 men and 360 women who were tested and found that 47 men and 52 women in the samples tested positive. Can you conclude that the proportion of positive tests among men is different from the proportion of positive tests among women? Use level of significance 10%. Procedure: Two means T (pooled) Hypothesis Test Step 1. Hypotheses Set-Up: H 0 : Select an answer = , where Select an answer the Select an answer and the units are Select an answer H a : Select an answer ? , and the test is Select an answer Step 2. The significance level α = % Step 3. Compute the value of the test statistic: Select an answer = (Round the answer to 3 decimal places) Step 4. Testing Procedure: (Round the answers to 3 decimal places) CVA PVA Provide the critical value(s) for the Rejection Region: Compute the P-value of the test statistic: left CV is and right CV is P-value is Step 5. Decision: CVA PVA Is the test statistic in the rejection region? Is the P-value less than the significance level? ? ? Conclusion: Select an answer Step 6. Interpretation: At 10% significance level we Select an answer have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
Answer:
Test statistic Z= 0.13008 < 1.96 at 0.10 level of significance
null hypothesis is accepted
There is no difference proportion of positive tests among men is different from the proportion of positive tests among women
Step-by-step explanation:
Step(I):-
Given surveyed two random samples of 390 men and 360 women who were tested
first sample proportion
[tex]p_{1} = \frac{360}{390} = 0.9230[/tex]
second sample proportion
[tex]p_{2} = \frac{47}{52} = 0.9038[/tex]
Step(ii):-
Null hypothesis : H₀ : There is no difference proportion of positive tests among men is different from the proportion of positive tests among women
Alternative Hypothesis:-
There is difference between proportion of positive tests among men is different from the proportion of positive tests among women
[tex]Z = \frac{p_{1}- p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } } }[/tex]
where
[tex]P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1}+n_{2} }[/tex]
P = 0.920
[tex]Z= \frac{0.9230-0.9038}{\sqrt{0.920 X0.08(\frac{1}{390}+\frac{1}{52} } )}[/tex]
Test statistic Z = 0.13008
Level of significance = 0.10
The critical value Z₀.₁₀ = 1.645
Test statistic Z=0.13008 < 1.645 at 0.1 level of significance
Null hypothesis is accepted
There is no difference proportion of positive tests among men is different from the proportion of positive tests among women
a philanthropist deposits 2,000$, in a trust fund that pays 6.0%interest , compunded continuously. The balance given to the college from which the has earned interest for 20 years. How much will the college receive? round to the nearest tenth
Answer:
$6414
Step-by-step explanation:
Step one
given
Principal=$2,000
rate= 6%= 0.06
Time= 20 years
Required
The final amount.
Step two:
The compound interest formula is
A= P(1+r)^t
substituting we have
[tex]A=2000(1+0.06)^2^0\\\\ A= 2000(1.06)^2^0\\\\ A=2000*3.207\\\\A=6414[/tex]
The amount given to the college is $6414
Question 4
Which equation has a graph perpendicular to the graph 3y = 2x - 9?
3x + 2y = 7
2x + 3y = 4
y = 2/3x - 1
y = 2x + 5
Answer:
slope of the line 3y = 2x - 9 , m = 2/3
therefore slope of line perpendicular to given line
m2 = -1/m1 = -3/2
then the general equation of line with slope -3/2 is given by
y = -3/2 ( x ) + c
where c = y-intercept which can be found when more data is provided
Name an equivalent ratio for with a denominator of 8.
Please select the best answer from the choices provided
A: 4/8
B: 1/8
C: 5/8
D: 3/8
Answer:
(A)
Step-by-step explanation:
4+4=8,4/8 is an equalivent ratio. So the best answer would be A!
Hope this helps:)!
Determine the next three terms in the following sequence: -1, 1/2, - 1/4, 1/8
Answer:
-1/16, 1/32, and -1/64.
Step-by-step explanation:
Basically, all you have to do is find the pattern in the sequence in front, which in this case is division by -2. Hence, you can apply this onwards to get (1/8) / -2 = -1/16, (-1/16) / -2 = 1/32, and (1/32) / -2 = -1/64.
Hope this helped! Merry Christmas!
The user manual for Layla’s phone notes that the device can be damaged when operated at temperatures below -20°C and above 45°C. Layla wants to know what these ranges are in degrees Fahrenheit and writes these inequalities to rewrite the relationship where F is degrees Fahrenheit.
5/9 (f - 32) 45
Which statement best describes the temperature ranges Layla should avoid while using her phone?
A.Layla should avoid using her phone in temperatures below -4°F and above 113°F.
B.Layla should avoid using her phone in temperatures above 21°F and below 57°F.
C.Layla should avoid using her phone in temperatures below 21°F and above 57°F.
D.Layla should avoid using her phone in temperatures above -4°F and below 113°F.
Layla should avoid using her phone in temperatures below -4°F
and above 113°F.
calculate the slope of the line
Answer:
-5/4 or -1.25
Step-by-step explanation:
the points are (-6, -3) and (-2, -8)
the formula for slope is y2-y1/x2-x1
y2 is -8
y1 is -3
x2 is -2
x1 is -6
(-8+3)/(-2+6)
(-5)/(4)
-5/4 or -1.25
Saba's dance class is 3 miles from her home. Her music class is 12 miles from her
home. Write an equation that shows the number of times farther Saba's music
class is from her home than her dance class is from her home.
Answer:
The number of times Saba's further is 4, because 12/3 = 4
Step-by-step explanation:
Ricky spends $103. 19 in additional interest and charges on monthly payments as the result of a prior bankruptcy. If Ricky had been able to save this money for one year and then put it into a savings account earning 3.1% simple interest, how much money could he have in savings after two more years?
a $1,238.28
b. $1,276.67
c. $1,315.06
d. $2,476.56
Answer:
C. 1,315.06
Step-by-step explanation:
................
express 25 as a power with base 5
Answer: 5
Step-by-step explanation:
Answer:
5^2 or 5 to the power of 2
Step-by-step explanation:
5x5=25
TRIGNOMETRY TEST DUE AT 10:02 PLZ HELP ME I DONT WANT TO FAIL THIS ONE!!! PLEASE SOMEONE MATH EASY HELP 123 ADDING SUBTRACTING
Answer:
7. 33 degrees
8. 17 degrees
9. 41 degrees
10. 75 degrees
This is all i can do I'd have to look up how to do 11-13
I hope this helps a little
Step-by-step explanation:
Angie divides the polynomial function f(x)=x3+3x2−7x−21 by (x + 3). What can she conclude from the fact that the remainder is equal to 0?
Answer:
See below
Step-by-step explanation:
Given function
f(x)=x³ + 3x²- 7x - 21We can find its factors:
x³ + 3x² - 7x - 21 =x²(x + 3) - 7(x + 3) =(x² - 7)(x + 3)We can conclude that the given polynomial function is fully divisible by (x + 3) and the quotient is (x² - 7)
Also one of zeros of the function is -3
1) 2 + 24 + 40 + 39- (33 - 30)
=
Answer:
102
Step-by-step explanation:
hope this helps
Answer:
2+24+40+39-(33-30)
105-33+30
135-33
132
Need help on number 2 plz I appreciate it thank you so much
Answer:
[tex] \angle PQR [/tex], [tex] \angle SQR [/tex], and [tex] \angle PQS [/tex]
Or
angle PQR, angle SQR and angle PQS
Step-by-step explanation:
The three different angles in the diagram are angle PQR, angle SQR and angle PQS.
Another way of writing this is using an angle sign before the alphabets follows. Thus:
[tex] \angle PQR [/tex], [tex] \angle SQR [/tex], and [tex] \angle PQS [/tex]
Find f(-3) of the function below
F(x)=2x^3-9x^2-5x
Answer:
your answer is -120
Step-By-Step Explanation:
2(-3)^3 - 9(-3)^2 -5(-3)
2 (-27) - 9(9) +15
-54 -81 +15
-135 +15
-120
i hope this helps :)
Answer: -120
Hope this helps :)
Isabella baked 10 cookies with 2 scoops of flour. How many scoops of flour does Isabella need in order to bake 45 cookies? Assume the relationship is directly proportional
Answer:
9 scoops
Step-by-step explanation:
If 10 cookies took 2 scoops of flour, then 4 scoops would make 20 cookies, 6 scoops would make 30, 8 scoops would make 40. If you need 5 cookies, then split 2 scoops in half, which would be one scoop. 8 scoops(which is 40 cookies)+ 1 scoop(5 cookies) = 9 scoops (45 cookies)
An employee works 22 days
per month. If they work an
average of 8 1/4 hours per
day, how many hours do they
work per month?
8.25 x 22 = 181.5
181.5 divided by 60 = 3.025
each month, they would work about 3 hours
Identify the pattern for the following sequence. Find the next three terms in the sequence.
-15, -11, -7, -3 ____, _____, _____,...
A: Subtract 4; -7, -11, -15
B: Add 4; 2, 6, 10
C: Subtract 4; 1, 5, 9
D: Add 4; 1, 5, 9
Answer:
D: Add 4; 1, 5, 9
Step-by-step explanation:
Firstly, we can look at the preceding sequence: -15, -11, -7, and -3. It's pretty much impossible to be subtract 4, since -15 - 4 = -19, and it only goes downhill from there, deviating from the original sequence. Hence, the front sequence should be following the pattern of add 4.
Now, to decide between B and D, all you have to do is add 4 to the last term of the sequence to continue it. In this case, that would be -3 + 4 = 4 - 3 = 1. Hence, we can instantly identify the correct option is D: Add 4; 1, 5, 9.
Hope this helped!
Answer:
D is the answer: 4, 1, 5, 9
Step-by-step explanation:
A car can travel 400 miles on 16 gallons of gasoline. How much gasoline will it need to go 275 miles?
*HELP WILL GIVE BRAINLIEST!!!*
Answer:
11 miles.
Step-by-step explanation:
[tex]\frac{16 gallons}{400 miles} =\frac{x}{275 m}[/tex]
So x is the number of miles. This is a ratio problem, so if we had a situation like 1:2, when 1 changes 2 will accordingly change. 2:4. And 1:2 = 2:4.
So now to solve the equation. Cross multiply 16 and 275 = 4400. Cross multiply 400 and x. You'll end up with an equation like 400x = 4400. Then solve and you'll get x = 11. Hope this helps!
The tables shows the amount of sugar and the amount of water used in the fall. How many cups of sugar would be needed for 15 cups of water in the Fall Mixture?
Answer:
30
Step-by-step explanation:
it's x2 for the rest and 15x2 =30
-34 > -10 + 4x
Help ASAP
Step-by-step explanation:
-34 > -10 + 4x
-24 > 4x
x < -6.
Answer:
Hope it will help u plz brain-list the answer
Step-by-step explanation:
-34 > -10 + 4x
by transitive property of in-equality we get,
-10+4x<-34
4x<-34+10 ( adding 10 to both sides
4x<-24
x<-24/4 ( dividing 4 to both sides
x<-6 AnsShaun estimated that the attendance at a college game was 1,200 people. The actual attendance was 1,158. What is the percent error of Shaun's estimate? (Round your answer to the nearest tenth)
Answer:
3.6%
Step-by-step explanation:
The formula for percent error is [ |va-ve/ve| * 100% ].
1200-1158/1158 * 100%
42/1158 * 100%
0.036 * 100%
3.6%
Best of Luck!
The percentage error should be 3.6%
Given that,
Shaun estimated that the attendance at a college game was 1,200 people. The actual attendance was 1,158.Based on the above information, the calculation is as follows:
[tex]= (1200-1158)\div 1158 \times 100\%\\\\= 42\div 1158 \times 100\%\\\\= 0.036 \times 100\%\\\\[/tex]
= 3.6%
learn more; https://brainly.com/question/1691136?referrer=searchResults
Do subtraction with monetory values.
$49.68 -$7.89=?
Answer:
U have $41.79 left i hope it is helpful have a nice day and merry Christmas
if you have $49.68 to spend and buy a $7.89 gingerbread set, you'll have 1 amazing gingerbread house.
-3(x + 6) idk what the answer is.
Answer:
-3x-18
Step-by-step explanation:
-3(x+6)
-3x-3x x 6
-3x-18
VY=27. VZ = 18, and Ww=8, find WX
Х
W
Z
Answer:
D. 4
Step-by-step explanation:
∆VWZ ~ ∆VXY, therefore:
[tex] \frac{VW}{VX} = \frac{VZ}{VY} [/tex]
VW = 8
VX = 8 + WX
VZ = 18
VY = 27
Plug in the values
[tex] \frac{8}{8 + WX} = \frac{18}{27} [/tex]
Cross multiply
[tex] 8 * 27 = (8 + WX)*18 [/tex]
[tex] 216 = 144 + 18WX [/tex]
Subtract 144 from each side
[tex] 72 = 18WX [/tex]
Divide both sides by 18
[tex] 4 = WX [/tex]
WX = 4