Answer:
The intermediate step is determining what a is, knowing also that (x+a)²=x²+(2a)x+a².
Also, x²-16x= -68 (in the form (x+a)²=b) is (x-8)²=-4
Step-by-step explanation:
x²-16x=-68
x²-16x+68=0
I suppose the intermediate step is finding (x+a)².
Remember that (x+a)²=x²+(2a)x+a², so 'a' will be half the coefficient of x (number beside x, not x²). The coefficient of x here is -16, so a is -8.
(x-8)²=x²-16x+64
So, if we can create 'x²-16x+64' out of 'x²-16x+68', we'll be on our way:
x²-16x+68=0
(x²-16x+64)+4=0
(x-8)²+4=0
(x-8)²=-4
What is
is 1/4 + 9/10y -3/5y +7/8 written in simplest form?
Answer:
Step-by-step explanation:
[tex]\frac{1}{4}+\frac{9}{10}y - \frac{3}{5}y+\frac{7}{8}\\\\=\frac{1}{4}+\frac{7}{8}+\frac{9}{10}y-\frac{3}{5}y\\\\[/tex]
Combine like terms. 1/4 and 7/8 are like terms and LCD of 4 and 8 is 8
9/10y and -3/5y are like terms and LCD of 10 , 5 is 10
[tex]= \frac{1*2}{4*2}+\frac{7}{8}+\frac{9}{10}y-\frac{3*2}{5*2}y\\\\=\frac{2}{8}+\frac{7}{8}+\frac{9}{10}y-\frac{6}{10}y\\\\=\frac{9}{8}+\frac{3}{10}y[/tex]
Answer:
3 • (4y + 15)
-----------------
40
Step-by-step explanation:
Long explanation get ready
STEP
1
:
7
Simplify —
8
Equation at the end of step
1
:
1 9 3 7
((—+(——•y))-(—•y))+—
4 10 5 8
STEP
2
:
3
Simplify —
5
Equation at the end of step
2
:
1 9 3 7
((—+(——•y))-(—•y))+—
4 10 5 8
STEP
3
:
9
Simplify ——
10
Equation at the end of step
3
:
1 9 3y 7
((— + (—— • y)) - ——) + —
4 10 5 8
STEP
4
:
1
Simplify —
4
Equation at the end of step
4
:
1 9y 3y 7
((— + ——) - ——) + —
4 10 5 8
STEP
5
:
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 4
The right denominator is : 10
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 1 2
5 0 1 1
Product of all
Prime Factors 4 10 20
Least Common Multiple:
20
Calculating Multipliers :
5.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 5
—————————————————— = ——
L.C.M 20
R. Mult. • R. Num. 9y • 2
—————————————————— = ——————
L.C.M 20
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
5 + 9y • 2 18y + 5
—————————— = ———————
20 20
Equation at the end of step
5
:
(18y + 5) 3y 7
(————————— - ——) + —
20 5 8
STEP
6
:
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 20
The right denominator is : 5
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 0 2
5 1 1 1
Product of all
Prime Factors 20 5 20
Least Common Multiple:
20
Calculating Multipliers :
6.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 4
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (18y+5)
—————————————————— = ———————
L.C.M 20
R. Mult. • R. Num. 3y • 4
—————————————————— = ——————
L.C.M 20
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
(18y+5) - (3y • 4) 6y + 5
—————————————————— = ——————
20 20
Equation at the end of step
6
:
(6y + 5) 7
———————— + —
20 8
STEP
7
:
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 20
The right denominator is : 8
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 3 3
5 1 0 1
Product of all
Prime Factors 20 8 40
Least Common Multiple:
40
Calculating Multipliers :
7.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 2
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (6y+5) • 2
—————————————————— = ——————————
L.C.M 40
R. Mult. • R. Num. 7 • 5
—————————————————— = —————
L.C.M 40
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
(6y+5) • 2 + 7 • 5 12y + 45
—————————————————— = ————————
40 40
STEP
8
:
Pulling out like terms :
8.1 Pull out like factors :
12y + 45 = 3 • (4y + 15)
(2, 4) after a reflection over the x-axis?
Find the surface area of the composite solid.
Answer:
185ft squared
Step-by-step explanation:
since this is a composite solid, all we have to do is use the 2 formulas:
b x h / 2 (Triangles on the pyramid)
l x w (Rectangular faces)
to solve the surface area of the composite figure.
simplify
[tex] {a}^{3} + {b}^{3} [/tex]
Answer:
[tex]{a}^{3} + {b}^{3} [/tex]
[tex] = (a + b)( {a}^{2} - ab + {b}^{2} )[/tex]
Hence, simplified
what does the model predict for the number of prizes won when you buy 10 tickets?
a - the model predicts that you will win 6 prizes when you buy 10 tickets.
b - the model predicts that you will win 19 prizes when you but 10 tickets.
c - the model predicts that you will win 4 prizes when you buy 10 tickets.
d - the model predicts that you will win 22 prizes when you buy 10 tickets.
Answer:
the answer is b
Step-by-step explanation:
top right corner
Answer:
the answer is b
Step-by-step explanation:
What is 672 divided by 12?
Answer:
56
Step-by-step explanation:
Answer:
56
Step-by-step explanation:
672 ÷ 12 = 56
So who’s tryna help me ☝
Answer:
4
Step-by-step explanation:
5+3=8 and 5-3=2 which is 8/2=4
Gordon is trying to save up $2000 for a new saxophone he makes 12.50 per hour at his job at the coffee shop but he needs to set aside half of his hourly wage to pay his regular bills How many 40-hour weeks will he need to work before he can afford the saxophone?
A. 320 Weeks
B. 40 Weeks
C. 8 Weeks
D. 6.25 Weeks
Answer:
he will need to work 8 40-hour weeks.
Explanation:
since gordon has to set aside half of his wage to pay his bills, he can only save $12.50 ÷ 2 = $6.25 for the saxophone.
we can find how much money gordon saves from a 40-hour week by multiplying this by 40: $6.25 × 40 = $250.
now, divide the total amount of money he has to save by the amount he saves each week: $2000 ÷ $250 = 8.
he will need to work 8 40-hour weeks before he can afford the saxophone.
i hope this helps! :D
Plz help if correct ill give Brainlyest
Answer:
x=21
Step-by-step explanation:
x=(16.8 * 2.5) /2=21
Ethan ran 11 miles in 2 hours. What is the unit rate of miles to hour?
A. 5.5 miles per hour
B. 0.18 miles per hour
C. 5.5 hours per mile
D. 0. 18 hours per mile
Answer:
A
Step-by-step explanation:
11miles/2hours
11 divide by 2 = 5.5 miles/1 hour
5.5 miles per hour
Answer:
5.5 miles per hour
Step-by-step explanation:
Please helppp, 15 points
Answer:
they are adding by 3 1 and 0
Step-by-step explanation:
Answer:
Step-by-step explanation: Mean= 400/15 =26.6
Median = 27
Mode= 35 - 16 =19
No
What are the mean,median and range for the monthly sales of the product?
Answer:
Option D
Step-by-step explanation:
mean=(∑x/N)=(1100+5000+2000+10100+8000/6)
=(34200/6)=$5700
________________-
median: =>
$1100,$2000,$5000,$8000,$8000,$10100
==>(5000+8000/2)=$6500
_______________
Range=maximum-minimum=10100-1100
==>$9000
so your answer is Option D
hope it helps...
have a great day!!
Ivy deposited some money into a savings account that earns 1%
annual simple interest. At the end of 5 years, she earned $32.50 in
interest. How much money did she put into the account initially?
Round to the nearest dollar.
Answer:
Ivy initially put $ 650 in the account.
Step-by-step explanation:
Given that Ivy deposited some money into a savings account that earns 1% annual simple interest, and at the end of 5 years, she earned $ 32.50 in interest, to determine how much money did she put into the account initially, the following calculation must be performed:
32.50 / 5 = 6.5
1 = 6.5
100 = X
100 x 6.5 = X
650 = X
Therefore, Ivy initially put $ 650 in the account.
Which of the following is not a true statement about the angles shown below? A H 3x x + 15 Z D x + 15 A. The measure of ZAHD is 30°. B. The measure of ZHDZ is 45°. C. The measure of ZHZD is 45°. D. The value of x is 30.
Answer:
A is not true
Step-by-step explanation:
Find x. Round to the nearest tenth if necessary.
Answer:
1)From ΔACB
tan 36= x/7
x= 7.tan 36
x= 5.086
2) Sin63=Opp/Hyp= 12/x
=>x=12/Sin63°
x= 13.47
3) Sin=x/MP
Sin 15°=x/12x=125 in 15°
x=3.11
hope it helps...
have a great day!!
Which of the following is NOT an example of a right angle?
A.The corner of a door
B.The corner of a book
C.The point of a pencil
D.The corner of a piece of notebook paper
Answer:
C.........................
Answer:
c.The point of a pencil if u go and check all of the other stuff are right triengle the point of a pencil is like an acute trienagle
Step-by-step explanation:
Which expression is equivalent to root 36/25
Answer:
6/5
Step-by-step explanation:
√36/25 =6/5
because root 36 is 6 and root 25 is 5.
Students painted 1/2 the wall in the gym with 3 colors. Each color takes up the same amount of space on the wall. What fraction of the wall does each color occupy?
t = p + 50
The variable p represents the number phone calls she routes, and the variable t represents
the number of minutes she is on the phone. In all, how many phone calls does Shivani have
to route to spend a total of 93 minutes on the phone?
Find the surface area of the prism,
2.5 m
2 m
4 m
4 m
Answer:
68
Step-by-step explanation:
2.5×4×2=20
2×4×2=16
4×4×2=32
20+16+32=68
Which two factors of 48 contain a factor that is a prime number
Answer:
3 and 16
Step-by-step explanation:
Question 10 of 10
Given the polynomial function below, find F(-5).
F(x) = x2 - 2x-7
O A. -22
B. 42
O C. 8
D. 28
Answer:
D. 28
Step-by-step explanation:
We are given the following polynomial function:
[tex]F(x) = x^2 - 2x - 7[/tex]
Find F(-5).
This is the value of F for which [tex]x = -5[/tex]. So
[tex]F(-5) = (-5)^2 - 2(-5) - 7 = 25 + 10 - 7 = 28[/tex]
28, which means that the correct answer is given by option D.
i don't really understand this
Answer:
sum
1.-28
2.5/4
3. -9.4
4. 33
5. 4.6
6. 2.4
7. -4.2
DIFFERENCE
8. -2.5
9. -7
10. 3/10
11. -31/36
12. -29/18
13. 16
14.-5/9
Step-by-step explanation: hoped this helped :))
If the probability of winning a slot machine is 5% and you are going to play 500 pulls. Using a normal approximation. What’s the probability that you win less than 40?
Answer:
0.9986 = 99.86% probability that you win less than 40
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
The probability of winning a slot machine is 5% and you are going to play 500 pulls.
This means that [tex]p = 0.05, n = 500[/tex]
Mean and Standard deviation:
[tex]\mu = E(X) = np = 500*0.05 = 25[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.05*0.95} = 4.8734[/tex]
What’s the probability that you win less than 40?
Using continuity correction, this is P(X < 40 - 0.5) = P(X < 39.5), which is the pvalue of Z when X = 39.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{39.5 - 25}{4.8734}[/tex]
[tex]Z = 2.98[/tex]
[tex]Z = 2.98[/tex] has a pvalue of 0.9986
0.9986 = 99.86% probability that you win less than 40
HURRY TIMED!!!!
Find the equation of the graphed line.
On a coordinate plane, a line goes through (0, negative 6) and (6, 0).
a.
y = negative x minus 6
c.
y = x minus 6
b.
y = x + 6
d.
y = negative x + 6
Answer:
y = x -6
Step-by-step explanation:
First find the slope
m= ( y2-y1)/(x2-x1)
= (0- -6)/(6-0)
=( 0+6)/(6-0)
= 6/6
= 1
The slope is 1 and the y intercept is -6
The slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = x -6
Answer:
the answer is C
Step-by-step explanation:
y = x -6
Solve for a.
ab +c= d
a= b+ c/d
a= b/ (c-d)
a= d-c/ b
Answer:
[tex]ab + c = d \\ ab = d - c \\ a = \frac{(d - c)}{b} [/tex]
Answer:
A=d-c/b
Step-by-step explanation:
just took the test
23, Corey bought the mailing tube shown at the right
mail a poster of the Gators Little League baseball
a, The mailing tube has the shape of which polyh
b. How many faces does the mailing tube have?
6, When Corey bought the mailing tube, it was
and looked like a net, What polygons would
Answer:
answer is b
Step-by-step explanation:
answer is b
3 1/4+3/8equals to what?
Answer:
6 5/8
Step-by-step explanation:
Answer:
it equals 29/8 you can also write it as 3 5/8
Step-by-step explanation:
first you would convert the mixed fraction to 13/4 then add te two fractions. i hope this helps
I need help asap !! Thank youuuuuuuuuuu
Answer:
Step-by-step explanation: 107.49/36 would give you 2.985833...
the question says to the nearest cent, so the answer would be $2.98
What is the surface area of the given figure?
A. 2564 cm
B. 2276 cm
C. 2184 cm
D. 1160 cm
Answer:
A
Step-by-step explanation:
