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Answer: [tex]\textsf{y = 4/11}[/tex]
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Given: [tex]\textsf{2y + 14 = 6(4y + 1)}[/tex]
Find: [tex]\textsf{Solve for y}[/tex]
Solution: In order to solve for y we need to distribute the ride side of the expression, simplify, subtract 14 from both sides, subtract 24y from both sides, and divide both sides by -22.
Distribute and simplify
[tex]\textsf{2y + 14 = (6 * 4y) + (6 * 1)}[/tex][tex]\textsf{2y + 14 = 24y + 6}[/tex]Subtract 14 from both sides
[tex]\textsf{2y + 14 - 14 = 24y + 6 - 14}[/tex][tex]\textsf{2y = 24y + 6 - 14}[/tex][tex]\textsf{2y = 24y - 8}[/tex]Subtract 24y from both sides
[tex]\textsf{2y - 24y = 24y - 24y - 8}[/tex][tex]\textsf{2y - 24y = -8}[/tex][tex]\textsf{-22y = -8}[/tex]Divide both sides by -22
[tex]\textsf{-22y/-22 = -8/-22}[/tex][tex]\textsf{y = -8/-22}[/tex][tex]\textsf{y = 8/22}[/tex][tex]\textsf{y = 4/11}[/tex]Therefore, the expression simplifies down to y = 4/11.
What are the vertex and x-intercepts of the graph of y=x² - 2x - 24? Select
one answer for the vertex and one for the x-intercepts.
A. x-intercepts: (4,0), (-6, 0)
B. x-intercepts: (-4,0), (-6, 0)
C. Vertex: (1, -25)
D. Vertex: (1, 23)
E. Vertex: (-1, -21)
OF. x-intercepts: (-4, 0), (6, 0)
Answer:
C. Vertex (1;-25)
F. x-intercepts: (-4;0), (6;0).
Step-by-step explanation:
1) x-coordinate of the vertex: -b/2a=1; y-coordinate of the vertex: -25;
2) for x-intercepts it needed to solve the equation x²-2x-24=0;
x=6;-4;
3) finally, correct answers are: C. Vertex (1;-25) and F. x-intercepts: (-4;0), (6;0).
Giving brainliest :)
Answer:
I think it would be D the last answer on the page I am pretty confident in the answer but if for some reason it's wrong then I'm sorry.
Step-by-step explanation:
Help plsss there’s a timer
Answer:
[tex]a=27, b=81[/tex]
Step-by-step explanation:
Plug in the values
[tex]a=3^3\\b=3^4\\\\a=27\\b=81[/tex]
A vase with a circular base exerts a force of 15 N on a table with a pressure of 750 N/m2.
Find the radius of the base of the vase in cm to 2 dp.
The radius of the base of the vase in cm to 2 dp is 0.08m
Pressure of an objectThe formula for calculating the pressure of a object is expressed as;
Pressure = Force/Area
Area = Force/Pressure
Area = 15/750
Areas = 0.02m²
Since the area of the circular base is πr², then;
πr² = 0.02
r² = 0.02/3.14
r = 0.0798m
Hence the radius of the base of the vase in cm to 2 dp is 0.08m
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Complete the identity: sec(t) - cos(t) = ?
1) sec(t)csc(t)
2) -2tan²(t)
3) 1 + cot(t)
4) sin(t)tan(t)
Step-by-step explanation:
[tex] \sec( \alpha ) - \cos( \alpha ) [/tex]
[tex] \frac{1}{ \cos( \alpha ) } - \cos( \alpha ) [/tex]
[tex] \frac{1}{ \cos( \alpha ) } - \frac{ \cos {}^{2} ( \alpha ) }{ \cos( \alpha ) } [/tex]
[tex] \frac{ \sin {}^{2} ( \alpha ) }{ \cos( \alpha ) } [/tex]
[tex] \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \times \frac{ \sin( \alpha ) }{1} [/tex]
[tex] \tan( \alpha ) \sin( \alpha ) [/tex]
4 is the option
6(m + 2 + 7m)
Part A: Write two expressions that are equivalent to the given expression. (3 points)
Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)
Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)
Part A: 6 ( 8m + 2) and 48m + 12
Part B: 48m - 48m = 12 - 12
Part C: 6 (10) = 6(10)
How to determine the expressions1. The two expressions could be gotten thus;
6(m + 2 + 7m)
Collect like terms in the bracket
6 ( 8m + 2) ⇒ first expression
6(m + 2 + 7m)
Expand the bracket
6m + 12 + 42m
Collect like terms
6m + 42m + 12
48m + 12 ⇒ second expression
Part B:
6(m + 2 + 7m) = 48m + 2
Expand the bracket
6m + 12 + 42m = 48m + 2
Collect like terms
48m - 48m = 12 - 12
0 = 0
Part C:
Let the expression from A be 6 ( 8m + 2)
6(m + 2 + 7m) = 6 ( 8m + 2)
Let the number be m = 1
Substitute the values
6(1 + 2 + 7(1) ) = 6 (8(1) + 2)
6 ( 1 + 2 + 7) = 6 (10)
6 (10) = 6(10)
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The lateral surface area of cone A is equal to the lateral surface area of cylinder B.
True or False?
Answer:
True.
Step-by-step explanation:
Lateral Surface area of cone=πrl=πr×2h=2πrh
Lateral surface area of cylinder=2πrh
I have tried this problem multiple times now and don't get the correct answer. Please help!
The confidence interval is (-1.1059, 7.70459).
What is confidence interval in statistics?Image result for what is confidence interval
A confidence interval is the mean of your estimate plus and minus the variation in that estimate.
The sample mean is M=3.3
The sample size is N=44
So, σM= s/√N = 16.6/ √44
= 16.6/ 6.633
= 2.621
and, the degree of freedom
df= n-1
=44-1
=43
So, The t-value for a 90% confidence interval and 43 degrees of freedom is t=1.681.
Now, Margin of error = 2.261* 1.681 = 4.4059
Now, the lower and upper bound of the confidence interval are:
LL = 3.3- 4.40459 = -1.1059
UL = 3.3+ 4.40459 = 7.70459
Hence, the confidence interval is (-1.1059, 7.70459).
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$15,074 is invested, part at 14% and the rest at 5%. If the interest earned from the amount invested at 14% exceeds the interest earned from the amount invested at 5% by $1694.07, how much is invested at each rate? (Round to two decimal places if necessary.)
The rate at 14% and 5% are $12, 883 and $2191 respectively.
How to determine the rateGiven that;
Invested amount = $ 15, 074 at 14% and 5%
Let rate at 14% = x
rate at 5% = y
We have rate at 9% exceeds that of 5% by $1694. 07
Hence,
0. 14x = 0. 05y + $1694. 07 ⇒ equation 1
x + y = $15, 074 ⇒ equation 2
Make 'x' the subject
x = [tex]15, 074 - y[/tex]
Substitute in equation 2
[tex]0. 14(15, 074 - y) = 0. 05y + $1694. 07[/tex]
Expand the expression
[tex]2, 110. 36 - 0. 14y = 0.05y + 1694. 07[/tex]
Collect like terms
[tex]416. 29 = 0. 19y[/tex]
Make 'y' the subject
y = [tex]\frac{416. 29}{0. 19}[/tex]
y = [tex]$2, 191[/tex]
Substitute the value in equation 2
x + y = $15, 074
x = $15, 074 - y
x = [tex]$15, 074 - 2191[/tex]
x = $12, 883
Therefore , the rate at 14% and 5% are $12, 883 and $2191 respectively.
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4(4 - x) - 8(-2 + 4x)
If you want the answer simplified, its
-36x + 32
Latesha justifies whether the expression 4x – 3 is equivalent to one-half (4 x minus 6) minus 2 x (1 minus 3) by letting x = 2 in both expressions. which values should latesha compare to justify whether the expressions are equivalent? 2 and 5 5 and 9 5 and 5 9 and 9
Answer:
5 and 9
Step-by-step explanation:
Answer:b
Step-by-step explanation: took the test
Graph the line with slope -3 passing through the point(-3,-2) .
The attached graph represents the graph of the line
How to plot the graph?The given parameters are:
Slope, m = -3
(x1, y1) = (-3, -2)
The equation is calculated as:
y = m(x - x1) + y1
So, we have:
y = -3(x + 3) - 2
Expand
y = -3x - 9- 2
Evaluate the difference
y = -3x - 11
See attachment for the graph of y = -3x - 11
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The sum of 8 times a number and 10 is 34. Find the number.
Answer: 3
8x+10=34
sub 10
8x=24 divide by 8
x=3
Step-by-step explanation:
If 7 spiders make 7
webs in 7 days, then 1
spider will make 1
web in how many
days?
Answer:
1 day
Step-by-step explanation:
since 7 spider =7 days
1 spider =? day
cross multiply
7 days × 1 spider = 7 spider × ? days
7 spider = 7 spider × ? days
7 spider 7 spider
= 1 days
2+2*+456+5367+63784+464749=
Answer:534360
Step-by-step explanation:
I did have to remove the multiplication though
Gathering information from individuals in a sample is known as _______________. A. data dumping B. data collection C. data diving D. data displaying
Gathering information from individuals in a sample is known as : Data collection. ( B )
What is statistics?Statistics is the science of collecting and analyzing data in quantities, especially for the purpose of informing.
Analysis:
sample collection is the first approach to analyzing any information.
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Form the table of backward differences for the function f(x) = x³ +5x-7 for x = -1, 0, 1, 2, 3, 4 5 and 6.
The table of values is
x -1 0 1 2 3 4 5 6
f(x) -13 -7 -1 11 35 77 143 139
How to form the table?The function is given as:
f(x) = x³ +5x-7
And the values of x are
x = -1, 0, 1, 2, 3, 4 5 and 6.
Substitute these values in the function
f(-1) = (-1)³ +5(-1) - 7 = -13
f(0) = (0)³ +5(0) - 7 = -7
f(1) = (1)³ +5(1) - 7 = -1
f(2) = (2)³ +5(2) - 7 = 11
f(3) = (3)³ +5(3) - 7 = 35
f(4) = (4)³ +5(4) - 7 = 77
f(5) = (5)³ +5(5) - 7 = 143
f(6) = (6)³ +5(6) - 7 = 239
Hence, the table of values is
x -1 0 1 2 3 4 5 6
f(x) -13 -7 -1 11 35 77 143 139
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Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.)
{2, 6, 10, 14, 18, . . . }
The formula for the general term of the sequence is Tn = 4n - 2
How to determine the formula?The sequence is given as:
{2, 6, 10, 14, 18, . . . }
The above sequence is an arithmetic sequence with the following features:
First term, a = 2Common difference, d = 4 i.e. 6 - 2The formula for the general term is calculated using:
Tn = a + (n - 1) * d
This gives
Tn= 2 + (n - 1) * 4
Expand
Tn = 2 + 4n - 4
Evaluate the like terms
Tn = 4n - 2
Hence, the formula for the general term of the sequence is Tn = 4n - 2
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There are chocolates in a box, all identically shaped. There are 8 filled with nuts, 16 with caramel, and 14 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.
Answer:
P = [tex]\frac{91}{703}[/tex] ≅ 12.95%.
Step-by-step explanation:
The total amount of chocolates in the box is 8 + 16 + 14 = 38, 14 of which are solid.
Let's calculate the probability of getting a solid chocolate in the first selection:
[tex]P(1S) = \frac{14}{38} = \frac{7}{19}.[/tex]
Given that the first piece was solid, there are now 37 pieces of chocolate in the box, 13 of which are solid. Let's now calculate the probability of selecting another solid chocolate:
[tex]P(2S\,|\,1S) = \frac{13}{37}.[/tex]
Thus, the probability of selecting two solid chocolates in a row is the product of the two probabilities calculated above:
[tex]P = \frac{7}{19}\,.\,\frac{13}{37} = \frac{91}{703}.[/tex]
Which type of parent function is f(x) = -
1/?
O A. Absolute value
OB. Reciprocal
OC. Square root
OD. Linear
Answer: B. Reciprocal
Step-by-step explanation:
This is a fact.
The parent function represented by f(x) = -1/x is the reciprocal function.
Therefore, the correct answer is option B.
Reciprocal functions, also known as rational functions, are defined by an algebraic expression where the dependent variable is in the denominator. In this case, the dependent variable is x, and it appears in the denominator as 1/x.
The negative sign in front of the fraction simply indicates that the function is reflected over the x-axis.
The general form of a reciprocal function is f(x) = a/x, where "a" is a constant. In the given function f(x) = -1/x, a is equal to -1.
In the case of f(x) = -1/x, the graph of the function is a hyperbola that opens downwards in the first and third quadrants. It approaches the x-axis as x moves towards positive or negative infinity, and it moves away from the x-axis as x approaches 0.
Therefore, the correct answer is option B, the reciprocal function.
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la mitad mas el tercio mas la cuarta parte de los años que tiene manuel, suman los años que tiene mas tres ¿que edad tiene manuel? ·
Resolviendo una ecuación lineal veremos que que Manuel tiene 36 años.
¿Qué edad tiene Manuel?Vamos a definir la edad de Manuel como x.
Sabemos que la mitad mas el tercio mas la cuarta parte de x es igual que x más 3, entonces:
x/2 + x/3 + x/4 = x + 3
Ahora podemos resolver esta ecuación lineal para x:
x/2 + x/3 + x/4 - x = 3
x*( 1/2 + 1/3 + 1/4 - 1) = 3
x = 3/(1/2 + 1/3 + 1/4 - 1) = 36
Así, concluimos que manuel tiene 36 años.
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FAST HELPPPPPPP
The point at which three or more lines intersect is the point of
A.equality.
B.concurrency.
C.parallelism.
D.tangency.
Answer:
B.concurrency.
Step-by-step explanation:
Three or more lines when met at a single point are said to be concurrent and the point of intersection is point of concurrency.
h(t)=t^4+3t^2-t+3
h'?
Answer: [tex]h'(t)=4t^3 + 6t-1[/tex]
Step-by-step explanation:
Use the power rule for differentiation.
Write -3.65 as a mixed number.
Answer:
-3 13/20
Step-by-step explanation:
-3.65=
-3 65/100=
-3 13/20
Consider the rectangle enlargement. a smaller rectangle has a length of 4.3 millimeters and width of 4.5 millimeters. a larger rectangle has a length of x millimeters and width of 24.3 millimeters. the perimeter of the original rectangle is . the side length of the enlarged rectangle is . the perimeter of the enlarged rectangle is .
The perimeter of the original rectangle is 17.6mm. The side length of the enlarged rectangle is 23.22mm and the perimeter of the enlarged rectangle is 95.04mm
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2(l +w)
If the smaller rectangle has a length of 4.3 millimeters and width of 4.5 millimeters while a larger rectangle has a length of x millimeters and width of 24.3 millimeters, then;
4.3/x = 4.5/24.3
Cross multiply
4.5x = 104.49
x = 23.22mm
Perimeter of original rectangle = 2(4.3 + 4.5)
Perimeter of original rectangle = 17.6mm
Perimeter of enlarged rectangle = 2(23.22 + 24.3)
Perimeter of enlarged rectangle = 95.04mm
The perimeter of the original rectangle is 17.6mm. The side length of the enlarged rectangle is 23.22mm and the perimeter of the enlarged rectangle is 95.04mm
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Answer:
17.6mm, 23.22mm, 95.04mm
Step-by-step explanation:
the sum of two numbers is 24 and the quotient is 3. what are the to numbers
Answer:
18 and 6
Step-by-step explanation:
18+6=24
18/6=3
please mark brainliest
the students in Mrs. Aubrey's class brought in 15 cans during week 1 of the food drive. during week 2 the students brought in 4 times as many cans. how many cans did the students bring in during week 2?
Answer:
30 cans :)
Step-by-step explanation:
We need to divide to solve so lets do that now :)
15 x 4 = 60
60/2 = 30
Have an amazing day!!
Please rate and mark brainliest!!
Find the total surface area of the cylinder shown. Leave the answer in terms of pi radius 4 height 6
Answer: [tex]80\pi[/tex]
Step-by-step explanation:
- the equation for the surface area of a cylinder is [tex]A=2\pi rh+2\pi r^{2}[/tex]
- the equation for this cylinder will be [tex]A=2\pi (4)(6)+2\pi (4^{2})\\[/tex]
- so, [tex]2\pi (4)(6) = 150.7964474[/tex] and [tex]2\pi (4^{2})\\ = 150.7964474[/tex]
- then [tex]150.7964474 + 150.7964474= 251.3274123[/tex]
- finally, [tex]251.3274123/\pi = 80[/tex]
- so the answer in terms of [tex]\pi[/tex] is [tex]80\pi[/tex]
hope this helps :)
465 draws will be made at random with replacement from the box [0 0 1]. The number of 1’s among the draws will be around…
The number of 1’s among the draws will be 155.
How to find that a given condition can be modelled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
The expected value is given as
E(X) = np
465 draws will be made at random with replacement from the box [0 0 1].
The number of 1’s among the draws will be
p = 1/3
n = 465
Then the expected value is given as
E(x) = 465 × 1/3
E(x) = 155
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The equation y minus 1 = negative 7 (x minus 3). is written in point-slope form. What is the y-intercept of the line?
Answer:
(0, 22)
Step-by-step explanation:
So you have the equation:
[tex]y-1=-7(x-3)[/tex]
So first let's define what the "y-intercept" is. The y-intercept, of a line is like the name implies, when the line intercepts or "passes" the y-axis. And if you were to take any point on the y-axis, the y-value may vary, but there is one value that doesn't change, and that's the x-value. the x-value is always going to be zero, no matter where you are on the y-axis. So to find the y-intercept simple plug 0 in as x. This gives you the equation:
[tex]y-1 = -7(0-3)[/tex]
[tex]y-1 = -7(-3)[/tex]
[tex]y-1=21[/tex]
[tex]y=22[/tex]
So the y-intercept is at (0, 22)