Answer:
x = 7 , -1
Step-by-step explanation:
SOLUTION :-
[tex]4(x-3)^2-11 = 53[/tex]
Add 11 to both the sides.[tex]=> 4(x-3)^2-11+11=53+11[/tex]
[tex]=> 4(x-3)^2 = 64[/tex]
Divide both the sides by 4.[tex]=> \frac{4(x-3)^2}{4} = \frac{64}{4}[/tex]
[tex]=> (x-3)^2 = 16[/tex]
Root square both the sides.[tex]=> \sqrt{(x-3)^2} = \sqrt{16}[/tex]
[tex]=> x-3 = +4 \; or -4[/tex]
Here , x will have two values -
1) [tex]x-3 = 4[/tex]
[tex]=> x = 4 + 3 = 7[/tex]
2) [tex]x - 3 = -4[/tex]
[tex]=> x = -4 + 3 = -1[/tex]
VERIFICATION :-
When x = 7 ,
[tex]4(x-3)^2 - 11 = 4(7 - 3)^2 - 11[/tex]
[tex]= 4 \times 4^2 - 11[/tex]
[tex]= 4 \times 16 - 11[/tex]
[tex]= 64 - 11[/tex]
[tex]= 53[/tex]
When x = -1 ,
[tex]4(x-3)^2 - 11 = 4(-1 - 3)^2 - 11[/tex]
[tex]= 4 \times (-4)^2 - 11[/tex]
[tex]= 4 \times 16 - 11[/tex]
[tex]= 64 - 11[/tex]
[tex]= 53[/tex]
Find the value of x in the figure
Answer:
x = 100
Step-by-step explanation:
180-57 would equal 123 which means 123 = x +23 and you can simplify this equation by moving 23 over to 123 and subtracting them leaving x = 100
123 = x+ 23
-23 + 123 = x
100 = x
x = 100
sorry, i'm really bad at explaining
180 degree angles when added
180-57 (for known angle)= 123
x+23=123<- we need to take off the all known angles to get x
123-123=100
x=100 is the answer
Suppose a quadratic equation is given as follows:
(k – 1)x² + x + 1 = 0
Select all values of k for which the above equation has two real and unequal roots
0
.25
0.5
0.75
1
1.25
1.5
1.75
Answer:
k>1.25
Step-by-step explanation:
The given quadratic equation is :
(k – 1)x² + x + 1 = 0
We need to find all values of k for which the above equation has two real and unequal roots.
For a quadratic equation ax²+bx+c=0, for real and unequal roots,
b²-4ac>0
Here, a = (k-1), b = 1 and c = 1
Put all the values,
1²-4×(k-1)1>0
1-4k+4>0
5-4k>0
k>1.25
S, k can take values more than 1.25. Hence, it can take values 1.5, 1.75.
Find missing number from letter n ! Please
Answer:
1. n= 20 /13
2. n=10
3. n=35
4. n=9
That's all I could do, I got tired of typing lol
Step-by-step explanation:
1. 4/n=13/5 we cross multiply, (4)*(5)=13*n, 20=13n Flip the equation. 13n=20, divide 13 on both sides, 13n/13=20/13, n= 20 /13
2. 9/6= 15/n, we cross multiply 9*n=(15)*(6), 9n=90, Divide both sides by 9. 9n/9=90/9 n=10
3. 28/4=n/5 Cross-multiply, (28)*(5)=n*(4), 140=4n Flip the equation.4n=140 Divide both sides by 4. 4n/4=140/4 n=35
4. n/6=6/4 we cross multiply,n*(4)=(6)*(6), 4n=36, Divide both sides by 4 4n/4=36/4. n=9
Will choose brainliest! Please help! (This is Khan Academy)
Answer:
Option B. A = (5/6)^-⅛
Step-by-step explanation:
From the question given above, we obtained:
(5/6)ˣ = A¯⁸ˣ
We can obtain the value of A as follow:
(5/6)ˣ = A¯⁸ˣ
Cancel x from both side
5/6 = A¯⁸
Recall:
M¯ⁿ = 1/Mⁿ
A¯⁸ = 1/A⁸
Thus,
5/6 = 1/A⁸
Cross multiply
5 × A⁸ = 6
Divide both side by 5
A⁸ = 6/5
Take the 8th root of both sides
A = ⁸√(6/5)
Recall
ⁿ√M = M^1/n
Thus,
⁸√(6/5) = (6/5)^⅛
Therefore,
A = (6/5)^⅛
Recall:
(A/B)ⁿ = (B/A)¯ⁿ
(6/5)^⅛ = (5/6)^-⅛
Therefore,
A = (5/6)^-⅛
find the missing angle measure in each triangle. Then classify the triangle as acute, right, or obtuse. PLEASE ANSWER QUICK ILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
17
Answer: The missing angle is 32 degrees.
Step-by-step explanation: All the degrees in a triangle sum up to 180 degrees. Add the two known angles and subtract the sum from 180
Hope this helps! :)
Can please send answers with step
Answer:
A. 14 Sq.cm
Step-by-step explanation:
The area of the circle is 56 cm Sq.
Half of it is 28 Sq.cm
If you combine the 2 triangles it will make an area of 7sq.cm
then the Curved shaded part is also 7sq.cm together of the shaded part will create a quarter of the whole figure
So
56/4 Sq.cm
= 14Sq.cm
Thank you!!
Mark me as brainliest :>>>
Round the decimal to the nearest hundreth. If decimal cannot be rounded, state this.
194.59
The decimal cannot be rounded. It is already rounded to the nearest hundredth.
What is the value of log
?
1/100
I hope this is gelpful for u
Eric borrowed a total of $3000 from two student loans. One loan charged 4% simple interest and the other charged 3.5% simple
interest, both payable after graduation. If the interest he owed after 2 years was $215, determine the amount of principal for each
loan.
Answer:
$ 500 was the principal of the loan at 4%, and $ 2,500 was the principal of the loan at 3.5%.
Step-by-step explanation:
Given that Eric borrowed a total of $ 3000 from two student loans, and one loan charged 4% simple interest and the other charged 3.5% simple interest, both payable after graduation, if the interest he owed after 2 years was $ 215, to determine the amount of principal for each loan, the following calculation must be performed:
4 x 2 = 8
3.5 x 2 = 7
1500 x 0.08 + 1500 x 0.07 = 225
1400 x 0.08 + 1600 x 0.07 = 224
100 x 0.08 + 2900 x 0.07 = 211
500 x 0.08 + 2500 x 0.07 = 215
Therefore, $ 500 was the principal of the loan at 4%, and $ 2,500 was the principal of the loan at 3.5%.
When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is:________
Answer:
zero
Step-by-step explanation:
The optimally fitted straight line via the locations and points on a graph is determined via linear regression. You may use regression equations to see if your data can indeed be fitted into a formula. If you want to create assumptions from your data, either future forecasts or indicators of previous behavior, using the Regression equation is highly beneficial.
The regression line is expressed as:
[tex]Y_i = a +bx_i[/tex]
where;
[tex]Y_i[/tex] = dependent variable
a = intercept
b = slope
[tex]x_i[/tex] = independent variable
So, when [tex]Y_i[/tex] is independent of the variation of [tex]x_i[/tex], it means that [tex]Y_i[/tex] does not linearly depend on [tex]x_i[/tex] . Thus, the slope of the regression will be zero.
12.
What is the
equation of a circle with center (-7, -3) and radius 2?
Answer:
(x + 7)^2 + (y + 3)^2 = 4
Step-by-step explanation:
The standard equation of a circle is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center and r is the radius. We can substitute the information given to obtain:
(x + 7)^2 + (y + 3)^2 = 4
solve the equation
x + -18 = 3x + 54
Answer:
-36
Step-by-step explanation:
See image below:)
Answer:
x = -36
Step-by-step explanation:
subtract 'x' from each side to get:
-18 = 2x + 54
subtract 54 from each side to get:
-72 = 2x
x = -72/2
x = -36
Can y’all help me on question 26?!
Answer:
im pretty sure the answer is D. let me kno if im right
A square with sides x ft long has a
perimeter of 343 ft. How long are the
sides of the square?
Can I get help with this problem?
Answer:
4+1=5(0+1)
Step-by-step explanation:
The formula is y2-y1=slope(x2-x1)
Find the slope by using the formula y2-y1/x2-y1.
Suppose the mean percentage in Algebra 2B is 70% and the standard deviation is 8% What percentage of students pass the class with an 86% or better? Enter the value of the percentage without the percent sign.
Answer:
Z-value is what we called the number of standard deviations from the mean. 62% is 8% one standard deviation to the left, or a Z-value of -1. 94 is 24% to the right of the mean, or 3 standard deviations for a z-value of three. You can look on a Z-table to find the area between -1 and 3, which is .840 or 84%
Step-by-step explanation:
Please mark me as brainlist
Among 35 students in a class, 20 of them earned A's on the midterm exam, 13 earned A's on the nal exam, and 12 did not earn A's on either examination. What is the probability that a random
Answer:
The correct answer is "[tex]\frac{2}{7}[/tex]".
Step-by-step explanation:
According to the question,
Number of students,
= 35
A ! mid term A,
[tex]n(A) = 20[/tex]
B : final A,
[tex]n(B) = 13[/tex]
Didn't start,
[tex]n(A^c \cap B^c) = 12[/tex]
Now,
⇒ [tex]n(A \cup B)=35-12[/tex]
[tex]=23[/tex]
then,
⇒ [tex]n(A \cup B)=20+13-23[/tex]
[tex]=10[/tex]
hence,
The probability will be:
⇒ [tex]P(A \cap B)=\frac{10}{35}[/tex]
⇒ [tex]=\frac{2}{7}[/tex]
pls i need this one n i pass the class pls pls help me
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
The two triangles are similar by the ASA theorem. The ratio of long side to short side in each right triangle is the same:
x/3 = 7.5/4.5
x = 3(7.5/4.5) . . . . multiply by 3
x = 5
Innocent until proven guilty? In Japanese criminal trials, about 95% of the defendants are found guilty. In the United States, about 60% of the defendants are found guilty in criminal trials. Suppose you are a news reporter following four criminal trials.
a) If the trials were in Japan, what is the probability that all the defendants would be found guilty? What is the probability if the trials were in the United States?
b) Of the four trials, what is the expected number of guilty verdicts in Japan? What is the expected number in the United States? What is the standard deviation in Japan? What is the standard deviation in the United States?
c) As a U.S. news reporter, what is the smallest number of trials n you would need to cover to be at least 99% sure of two or more convictions? What is the smallest number of trials n you would need if you covered trials in Japan?
Step-by-step explanation:
Let X be the number of guilty defendants in Japan
Let y be the number in the US
we have n = 4
p = 0.95
a.) prob of trials in Japan
p(x=4)
= 0.95⁴
= 0.8145
prob of trials in US
p(X=4)
= 0.60⁴
= 0.1296
B. expected number in Japan
E(X) = n*p
= 4*0.95
= 3.8
we find the variance
= n*p(1-p)
= 4*0.95(1-0.95)
= 0.19
standard deviation for japan
= √0.19
= 0.4359
expected number for US
E(X) = n*p
= 4*0.60
= 2.4
we find the variance
= n*p(1-p)
= 4*0.60(1-0.6)
= 0.96
standard deviation for US
= √0.96
= 0.979
c. 2*4 = 8
please help i’ll give brainliest
7.)What is the maximum number of texts received?
8.)All of the following are true except -
A.The range of the data is 190.
B.At least one student received no texts at all.
C.Most of the students received 65 or fewer texts.
D.50% of students received between 65 and 160 text messages.
9.)Which of the following cannot be determined from analyzing the boxplot?
A.
Mean
B.
Median
O.
Minimum D.
Range
10.) What percent of students receive more than 65 texts in a single day?
Answer:
7. 190
8. C
9. A
10. ~66% (not sure about this one though)
Step-by-step explanation:
How stopwatch can measure accurate reading?
answer in picture
stay safe (..
Answer:
Hello There!!
Step-by-step explanation:
Reading gives the required time interval.Some precise stopwatches are electronically connected to the time event.Therefore, making it more accurate.
hope this helps,have a great day!!
~Pinky~
convert 0.13 into a fraction
explain whether 8t - 3y - 4t is equivalent to 7t +(-3t) - 3y.
Answer:
4t - 3y
Step-by-step explanation:
8t - 3y - 4t
8t - 4t - 3y
4t - 3y
7t +(-3t) - 3y
7t - 3t - 3y
4t - 3y
Answer:
These expressions are equivalent, as both of them simplify down to (4t - 3y).
Step-by-step explanation:
In order to determine if (8t - 3y - 4t) is equivalent to (7t + (-3t) - 3y) one must simplify each equation. Combine like terms by performing the operations between the coefficients of the variables.
8t - 3y - 4t
= 4t - 3y
7t + (-3t) - 3y
= 7t - 3t - 3y
= 4t - 3y
3 boxes are stacked on top of each other. One box is 6 feet 8 inches tall, one is 5 feet 11 inches tall, and one is 5 feet 6 inches tall. How high is the stack?
Answer:
Step-by-step explanation: 16 ft 7 in, I correctly believe:
A statistics student is studying if there is a relationship between the price of a used car and the number of miles it has been driven. She collects data for 20 cars of the same model with different mileage, and determines each car’s price using a used car website. The analysis is given in the computer output.
Predictor Coef SE Coef t-ratio p
Constant 24157.2 2164.1 2.965 0.046
Mileage -0.181 0.024 5.377 0.000
S = 3860.7 R-Sq = 68.0% R-Sq(Adj) = 67.5%
Using the computer output, what is the equation of the least-squares regression line?
ŷ = –0.181 + 24157.2x
ŷ = 24157.2 – 0.181x
ŷ = 2164.1 + 0.024x
ŷ = 0.024 + 2164.1x
========================================================
Explanation:
Simply look at the "coef" column to find the values you need. The constant is the term that isn't attached to the variable. The mileage coefficient is basically the slope.
You can think of it like
price = constant + (mileage coefficient)*(mileage)
The mileage coefficient being negative tells us we have negative correlation going on here. As x increases, y decreases. This makes sense because the car's value is expected to go down the more mileage is added on it.
What is the coordinate point of letter F
If PQ = 4i+3j+2k, find /PQ/
Answer:
| PQ | = [tex]\sqrt{29}[/tex]
Step-by-step explanation:
Given
PQ = ai + bj + ck , then
| PQ | = [tex]\sqrt{a^2+b^2+c^2}[/tex]
Here PQ = 4i + 3j + 2k , then
| PQ | = [tex]\sqrt{4^2+3^2+2^2}[/tex] = [tex]\sqrt{16+9+4}[/tex] = [tex]\sqrt{29}[/tex]
The question is on the picture
answer:
ABCD is not congruent to KLMN
ABCD cannot be mapped onto KLMN
Out of 350 applicants for a job, 158 are female and 66 are female and have a graduate degree. Step 2 of 2 : If 110 of the applicants have graduate degrees, what is the probability that a randomly chosen applicant is female, given that the applicant has a graduate degree
Answer:
33/55
Step-by-step explanation:
Total applicants, n(T) = 350
Female applicants, n(F) = 158
Female and Graduate applicants, n(FnG) = 66
Graduates, n(G) = 110
Probability of female Given that applicant has graduate degree; this is a conditional probability problem;
Recall :
P(A given B) = P(A|B) = P(AnB) / P(B)
Therefore ;
P(F|G) = P(FnG) / P(G) = 66 / 110 = 33/55
The ratio of boys to girls in Mr. Johnsons after school club is the same as the ratio is the same to the ratio of boys to girls in Mr. Greene's after school club. There are 4 boys and 12 girls in Mr. Johnsons club. There are 6 boys in Mr. Greene's club. How many girls are in Ms. Greene's club?
Answer:
18 GIRLS
Step-by-step explanation:
1. Lets write a fraction (4 boys/12 girls)
[tex]\frac{4 \\boys}{12 \\ \\girls}[/tex]
2. Now lets plug the value in
[tex]\frac{6 \\boys}{x girls}[/tex]
3. In the original equation, the amount of girls is 3 times the amount of boys
4. multiply 6 and 3 = 18
5. 18 girls
Answer:
18 <3
Step-by-step explanation: