Answer:
11/5
Step-by-step explanation:
5x-7=4
5x=4+7
5x=11
x=11/5
The required solution of the function at x = 4 is f(4) = 13.
Given that,
A function is given f(x) = 5x - 7, the value of the function at x = 4 is to be determined.
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Given function,
f(x) = 5x - 7
put the value x = 4 in the above equation,
f(4) = 5 * 4 - 7
f(4) = 20 -7
f(4) = 13
Thus, the required solution of the function at x = 4 is f(4) = 13.
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If cos x= sin(20 + x)° and 0° < x < 90°, what is the value of x
If cos x= sin(20 + x)° and 0° < x < 90° then value of x is 35 degrees
Solution:
Given that:
[tex]cos x= sin (20 + x)[/tex]
We know that,
[tex]sin (a+b)=sin a \times cos b+cos a \times sin b[/tex]
[tex]cos x= sin (20 + x) = sin 20 cos x + cos 20 sin x[/tex]
[tex]cos x-sin20 \times cos x=cos 20 \times sin x[/tex]
Taking cos x as common,
[tex]cos x(1-sin 20)=cos 20 \times sin x[/tex]
[tex]\frac{(1-sin 20)}{(cos 20)}=\frac{sin x}{cos x }\\\\tan x = \frac{(1-sin 20)}{(cos 20)}[/tex]
By trignometric functions,
sin 20 = 0.34202
cos 20 = 0.939692
So,
[tex]tan x = \frac{1 - 0.34202}{0.939692}\\\\tan x = 0.7002[/tex]
Therefore,
x = arc tan (0.7002)
x = 35 degrees
Therefore value of x is 35 degrees
Method 2:cos x = sin (20 + x)
sin and cos are co - functions, which means that:
cos x = cos [90 - (20 + x)]
cos x = cos (90 - 20 - x)
cos x = cos (70 - x)
Therefore, x = 70 - x
x + x = 70
2x = 70
x = 35
Therefore value of x is 35 degrees
Rewrite x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers, to determine the a and b values.
Answer 1: a = 4 and b = 3
Answer 2: a = 3 and b = 2
Answer 3: a = 2 and b = 1
Anwser 4: a = 1 and b = 4
Answer:
Therefore values of a and b are
[tex]a=3\ and\ b = 2[/tex]
Step-by-step explanation:
Rewrite [tex]x^{2}-6x+7=0[/tex] in the form
[tex](x-a)^{2}=b[/tex]
where a and b are integers,
To Find:
a = ?
b = ?
Solution:
[tex]x^{2}-6x+7=0[/tex] ..............Given
Which can be written as
[tex]x^{2}-6x=-7[/tex]
[tex](\frac{1}{2} coefficient\ of\ x)^{2}=(\frac{1}{2}\times -6)^{2}=9[/tex]
Adding half coefficient of X square on both the side we get
[tex]x^{2}-6x+9=-7+9=2[/tex] ...................( 1 )
By identity we have (A - B)² =A² - 2AB + B²
Therefore,
[tex]x^{2}-6x+9=x^{2}-2\times 3\times x+3^{2}=(x-3)^{2}[/tex]
Substituting in equation 1 we get
[tex](x-3)^{2}=2[/tex]
Which is in the form of
[tex](x-a)^{2}=b[/tex]
On comparing we get
a = 3 and b = 2
Therefore values of a and b are
[tex]a=3\ and\ b = 2[/tex]
Answer 2: a = 3 and b = 2
45 POINTS!! A JCpenny dress originally costs $69.00, but the final price is $20.70. What is the discount percentage? (Example: 50% off $20.00 is $10.00)
Answer:
70%
Step-by-step explanation:
69 - 20.70 = 48.3
48.3 / 69 = 0.7
0.7 x 100 = 70
The discount percentage for the JCPenney dress, discounted from an original price of $69.00 to a final price of $20.70, is calculated to be 70% off.
To calculate the discount percentage for the JCPenney dress, we need to find the difference between the original price and the final price, and then divide that by the original price. We can then multiply the result by 100 to get the percentage.
The original price of the dress is $69.00, and the final price is $20.70. The difference between these two prices is $69.00 - $20.70 = $48.30. This is the amount of the discount.
To find the discount percentage, we divide the discount amount by the original price: $48.30 / $69.00 = 0.7. To convert this decimal to a percentage, we multiply by 100: 0.7 imes 100 = 70%.
Thus, the dress is discounted by 70%.
Complete the equation of the line through ( − 9 , 7 ) and ( − 6 , − 3 ) Use exact numbers. y =
Answer:
Step-by-step explanation:
first we need to find the slope using the slope formula :
slope = (y2 - y1) / (x2 - x1)
(-9,7)...x1 = -9 and y1 = 7
(-6,-3)....x2 = -6 and y2 = -3
now we sub
slope = (-3 - 7) / (-6 - (-9) = -10 / (-6 + 9) = -10 / 3
so our slope is -10/3
now we use y = mx + b....with m representing the slope
slope(m) = -10/3
use either of ur points....I will use (-9,7)...x = -9 and y = 7
we are solving for b, the y intercept
now we sub
7 = -10/3(-9) + b
7 = 30 + b
7 - 30 = b
- 23 = b
so ur equation is : y = -10/3x - 23
Final answer:
To find the equation of the line through (-9, 7) and (-6, -3), calculate the slope, which is -10/3, and then use the point-slope form to derive the equation y = -10/3 x + 23.
Explanation:
To complete the equation of the line through the points (-9, 7) and (-6, -3), we need to find the slope (m) and use one of the points to find the y-intercept (b) in the slope-intercept form y = mx + b.
Step 1: Find the slope (m):
Slope (m) is equal to the rise over run. We calculate it using the formula:m = (y2 - y1) / (x2 - x1)Plugging the given points into the formula:m = (-3 - 7) / (-6 - (-9))m = (-10) / (3)m = -10/3Step 2: Use point-slope form to find equation:
Using the slope and one of the points, say (-9, 7), we plug the values into the point-slope form:y - y1 = m(x - x1)y - 7 = (-10/3)(x - (-9))We then distribute the slope and move the y1 to the other side to solve for y:y - 7 = -10/3 x - 30y = -10/3 x + 23The completed equation of the line is y = -10/3 x + 23.
Dev has 9 shells. Zoe has 55 shells, Zoe gives some shells to Dev. Now zoe has 3 times as many shells as dev. How many shells does Zoe give to Dev.
Answer:
number of shells zoe gives to dev = 7
number of shells zoe is left with = 55-7= 48
number of shells dev has = 9+7=16
Step-by-step explanation:
let the initial number of shells that dev has be A, and initial number of shells that zoe has be B.
let the number of shells that zoe gives to dev be x.
after giiving x shells zoe is left with 3 times the number of shell as that of dev.
therefore number of shells with zoe = 3×number of shells with dev.
number of shells with zoe = initial shells - x = 55-x
number of shells with dev = initial shells + number of shells he gets
= 9+x
therefore (55-x)=3×(9+x)
55-x = 27+3x
55-27=3x+x
4x = 28
x= 7
therefore number of shells zoe gives to dev = 7
number of shells zoe is left with = 55-7= 48
number of shells dev has = 9+7=16
Answer:
Zoe laverne!!~!!!!!!!~~~!~~!~!~!
Step-by-step explanation:
Find the variable x.
Answer:
x = 7
Step-by-step explanation:
The inscribed angle (5x - 3) is equal to half the measure of the intercepted arc
5x - 3 = 0.5(9x + 1) ← multiply both sides by 2
10x - 6 = 9x + 1 ( subtract 9x from both sides )
x - 6 = 1 ( add 6 to both sides )
x = 7
help ill give you 20 points
Answer:
The top left graph is the correct one.
Step-by-step explanation:
The graph of y = 1/2x - 4 will rise to the right , have a slope of 1/2 and pass through the point (0, -4) on the y-axis.
Since the inequality sign is 'less than or equal to' the line will be continuous and the shading will be below this line.
What is the opposite of the number of 5 and 1/2
Answer:
the answer will be -5 and 1/2
Answer:
5 is a regular number and 1/2 is a fraction
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Step-by-step explanation:
Find the maximum value of P=3x+2y subject to the following constraints:
Please help me!!!
Answer:
maximum value of P is 33
Step-by-step explanation:
Sketch the lines represented by the constraints
5x + y = 16
with intercepts ([tex]\frac{16}{5}[/tex], 0) and (0, 16)
2x + 3y = 22
with intercepts (11, 0) and (0, [tex]\frac{22}{3}[/tex])
The solutions to both are below the lines.
Solve 5x + y = 16 and 2x + 3y = 22 simultaneously to find the point of intersection at (2, 6)
The coordinates of the vertices of the feasible region are
(0, 0), (0, 16), (2, 6), 11, 0)
Evaluate the objective function at each vertex
P = 3(0) + 2(0) = 0 + 0 = 0
P = 3(0) + 2(16) = 0 + 32 = 32
P = 3(2) + 2(6) = 6 + 12 = 18
P = 3(11) + 2(0) = 33 + 0 = 33
The maximum value of P is 33 when x = 11 and y = 0
A bookstore carries 72 magazines. 50% of the magazines are women's magazines. How many women's magazines does the bookstore carry?
Answer:
36
Step-by-step explanation:
72/2=36 50% of 72 is 36
Answer:
36
Step-by-step explanation:
72 divided by 2 to get a quotient of 36
Find the missing number so that the equation has no solutions x - 7 - 7x = -5x - 12
The equation is simplified to -x = 5, yet a negative x value indicates that the identity is not true. Hence, there is no solution to this equation.
Explanation:To solve this equation, we should first try to simplify both sides of the equation.
On the left side, combine like terms. This gives us -6x - 7.
On the right side, we already have -5x - 12.
Setting these expressions equal to each other yields: -6x - 7 = -5x - 12.
Adding 5x to both sides gives us -x - 7 = -12.
Then adding 7 to both sides gives us -x = 5.
However, a negative x value would indicate that the identity is not true, thus the equation has no solution.
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A baby was born and then began to gain weight at a rate of 1.5 pounds per month. After 4 months, the baby's weight was 16 pounds. Write an equation for the function
W
(
t
)
,
W(t), representing weight, in pounds, of the newborn baby
t
t months after birth.j
Answer: y = (4/3)x + 8
Step-by-step explanation:
A line has a slope of - 2/3 and passes through the point (-3, 8) what is the equation of the line
Answer:
y - 8 = (-2/3)(x + 3)
y - 8 = (-2/3)x - 2
y = (-2/3)x + 6
please help brainlyest+10 points=0ne big thank u if u cant see sorry
What is the value of the expression shown below?
8
8 and 1 over 6
8 and 1 over 8
79
Evaluate.
Follow PEMDAS.
7+(10-4)²÷4×(1/2)³
parentheses and exponents first
7+36÷4×(1/8)
multiplication next
7+9×(1/8) ----> 7+(9/8)
addition
8 1/8
answer: third choice
62,591 + 7.1 X 10-2 in standard notations
If 3x−y=12, what is the value of
8x
2y
?
If 3x-y=12, what is the value of 8x/2y?
Answer:
[tex]\frac{8x}{2y} =\frac{4x}{3x-12}[/tex]
Step-by-step explanation:
[tex]3x-y=12[/tex]
[tex]-y=12-3x[/tex]
[tex]y=3x-12[/tex]-------------------------(equation 1)
Now,
[tex]\frac{8x}{2y} =\frac{8x}{2(3x-12)}[/tex]---------(from equation 1)
[tex]=\frac{8x}{6x-24}[/tex]
[tex]=\frac{8x}{2(3x-12)}[/tex]
[tex]=\frac{4x}{3x-12}[/tex]
Therefore, the value of [tex]\frac{8x}{2y} =\frac{4x}{3x-12}[/tex]
What is the value of y in the equation 2(3y + 7 + 5) = 196 − 16? (1 point) Group of answer choices 13 14 26 28
Answer:
26
Step-by-step explanation:
2(3y+12)=180
3y+12=90
3y=78
y=26
Answer:
Option c) is correct.
The value of y in the given equation is 26 ie., y=26
Step-by-step explanation:
Given equation is
[tex]2(3y+7+5)=196-16[/tex]
Now to the find the value of y in the above equation.
To find y simplify the above equation
[tex]2(3y+7+5)=196-16[/tex]
[tex]2(3y+12)=180[/tex]
Now apply distributive property
[tex]6y+24=180[/tex]
[tex]6y=180-24[/tex]
[tex]=\frac{156}{6}[/tex]
Therefore y=26
Option c) is correct.
The value of y in the given equation is 26 ie., y=26
Which equation can be use to solve for x in the parallelogram below ?
Answer:
Below.
Step-by-step explanation:
I can't read it very well but one equation might be
2x + 8 = 3x - 12
(because the opposite sides of a parallelogram are congruent.
Explanation:
Opposite angles of a parallelogram are equal.
B. (3x - 12)° = (2x + 8)°
This equation can be used to solve x.
3x - 12 = 2x + 8
3x - 2x = 12 + 8
x = 20°
Verification:
3(20) - 12 = 2(20) + 8
60 - 12 = 40 + 8
48° = 48°
Hence, verified.
How many real cube roots does
-216 have?
Answer:
-216 has three real cube roots.
Step-by-step explanation:
A department Store sells a pair of shoes with an 87% markup. If the store sells the shoes for 192.61 dollars then what is their non-markup price?
Answer:
$103
Step-by-step explanation:
192.62 divided by 1.87
answer is $103
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If the markup price of the shoes is $192.61 then the original price of the shoes will be equal to $25.04.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the given information in the question,
Let the original price of the shoes is x.
Markup Price = $192.61, which is 87% more than the original price.
Price markup = 192.61 × 87/100 = $167.57
Original Price, x = $192.61 - $167.57
x = $25.04.
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Which ordered pair is a solution of the equation?
-3x+4y=14
A- Only (2,5)
B- Both (2,5) and (4,6)
C-Neither
Final answer:
The ordered pair (2,5) satisfies the equation -3x+4y=14, making it the correct solution, while the ordered pair (4,6) does not satisfy the equation.
Explanation:
To determine which ordered pair is a solution to the given linear equation -3x+4y=14, we need to plug in the x and y values from each pair into the equation and see if the equation holds true.
For the ordered pair (2,5), substituting x with 2 and y with 5 gives us:
-3(2) + 4(5) = -6 + 20 = 14Since the equation is satisfied, (2,5) is a solution to the equation.
For the ordered pair (4,6), substituting x with 4 and y with 6 gives us:
-3(4) + 4(6) = -12 + 24 = 12Since -12 + 24 does not equal 14, the equation is not satisfied, and hence, (4,6) is not a solution to the equation.
Therefore, the correct answer is A- Only (2,5)
There are 80 grams of salt in a 32% solution. Find the weight of the solution.
Answer: 250 grams.
Step-by-step explanation:
Let x be the weight of the solution.
Given : There are 80 grams of salt in a 32% solution.
That means , 32% of x = 80 grams
[tex]\Rightarrow\ 0.32x=80[/tex] [convert percent into decimal by dividing it by 100]
[tex]\Rightarrow\ x=\dfrac{80}{0.32}=\dfrac{8000}{32}=250[/tex]
i.e. Total solution = 250 grams.
Hence, the weight of the solution = 250 grams.
What kind of Theorem is this? AAS, SAS, SSS, ASA, HL, or NP?
Answer:
SAS
Step-by-step explanation:
WX = ZY
ANGLE W = ANGLE Y (90 DEGREE)
YZ = YZ
SAS CONGRUENCY
I hope this answer is correct
Anyways do confirm
Explain how to model represents 5 divided by 1/3 = 15
Answer:
Step-by-step explanation:
5 ÷ 1/3
= 5 × 3/1
= 15
Write in slope-intercept form an equation of the line that passes through the given points.
(-2,-2),(4,10)
what is y equals negative five over two times negative two
Answer:
y = - 5/2 * - 2
y = 10/2
y = 5
Step-by-step explanation:
Which rule represents the translation from the pre-image,
ДАВС, tо thе іmаge, ДАВ'C'?
x x
оооо
x x
(x, y) — (х + 7, y+6)
О (x, y) — (х+7, у– 6)
=(x – 6, y + 7)
о(x, y) — (х+6, y+7)
Answer:(x,y)-(x+7,y+6)
Step-by-step explanation:
If (3, 10) is the endpoint of a line segment, and
(-2, 3) is its midpoint, find the other endpoint.
Answer:
The required points of the given line segment are ( - 7, - 4 ).
Step-by-step explanation:
Given that the line segment AB whose midpoint M is ( - 2, 3 ) and point A is ( 3, 10), then we have to find point B of the line segment AB -
As we know that-
If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and ( [tex]x_{2}, y_{2}[/tex] )then the mid points M are-
M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1} + y_{2} }{2}[/tex] )
Here,
Let A ( 3, 10 ), B ( x, y ) with midpoint M ( - 2, 3 ) -
then by the midpoint formula M are-
( - 2, 3 ) = ( [tex]\frac{ 3 + x}{2}[/tex] , [tex]\frac{ 10 + y}{2}[/tex] )
On comparing x coordinate and y coordinate -
We get,
( [tex]\frac{ 3 + x}{2}[/tex] = - 2 , [tex]\frac{ 10 + y}{2}[/tex] = 3)
( 3 + x = - 4, 10 + y = 6 )
( x = - 4 - 3, y = 6 - 10 )
( x = - 7, y = -4 )
Hence the required points A are ( - 7, - 4 ).
We can also verify by putting these points into Midpoint formula.
Final answer:
To find the other endpoint of a line segment with a known endpoint (3, 10) and midpoint (-2, 3), use the midpoint formula in reverse to calculate the coordinates, resulting in the other endpoint being (-7, -4).
Explanation:
To find the other endpoint of a line segment when given one endpoint and the midpoint, you can use the midpoint formula in reverse. The midpoint formula in two dimensions is
( (x1+x2)/2, (y1+y2)/2 ), where (x1, y1) and (x2, y2) are the endpoints of the line segment. Given that (3, 10) is one endpoint and (-2, 3) is the midpoint, we can set up equations to find the coordinates of the unknown endpoint (x2, y2).
To find x2, we use the formula for x-coordinate of the midpoint: (-2 + 3)/2 = (x2 + 3)/2. Solving for x2 gives us x2 = -2 - 3 = -7.
To find y2, we use the formula for y-coordinate of the midpoint: (3 + 10)/2 = (y2 + 10)/2. Solving for y2 gives us y2 = 2*3 - 10 = 6 - 10 = -4.
Therefore, the other endpoint of the line segment is (-7, -4).
The average height of a giraffe and a baby giraffe is 6m. If the baby giraffe has a height which is 2/3 that of the giraffe, what is the height of the baby giraffe?
To find the height of the baby giraffe given the average height of it and a giraffe is 6m, and it is 2/3 the giraffe's height, first solve for the giraffe's height to find it is 7.2m. Then, calculate 2/3 of this to get the baby giraffe's height, which is 4.8m.
Explanation:The question asks to determine the height of a baby giraffe given the average height of a giraffe and a baby giraffe together is 6m, and the baby giraffe's height is 2/3 that of the giraffe's height. Let X be the height of the giraffe. Then, the baby giraffe's height would be 2/3 X. Given the average of these two heights is 6m, the equation to find the height of the baby giraffe is:
(X + (2/3)X) / 2 = 6
By solving this equation:
First, find a common denominator to add X and 2/3 X, which gives us (3/3)X + (2/3)X = (5/3)X.Then, multiply both sides by 2 to eliminate the division by 2, resulting in (5/3)X = 12.Finally, multiply each side by 3/5 to solve for X, which gives X = 12 * (3/5) = 7.2m.Since the baby giraffe is 2/3 the height of the giraffe, its height is 2/3 * 7.2 = 4.8m.Hence, the height of the baby giraffe is 4.8m.
Which is the graph of g(x) =[2/3]x -2
Answer:
slope: 2/3
y intercept: - 2
x-0,3
y - 3 0
Answer:
graph C
Step-by-step explanation: