Answer:
x= 15/8
Step-by-step explanation:
we need to solve the equation to find the value of x by adding like terms and then finding the value of x.
[tex](\frac{1}{2})x+(\frac{3}{2})(x+1)-(\frac{1}{4})=5\\(\frac{1}{2})x + (\frac{3}{2})x + (\frac{3}{2}) - (\frac{1}{4}) = 5\\Adding\,\,like\,\,terms\,\\(\frac{(1+3)x}{2}) + (\frac{6-1}{4})=5\\(\frac{4x}{2}) + (\frac{5}{4})=5\\2x= 5- \frac{5}{4}\\2x = \frac{20-5}{4}\\2x= \frac{15}{4}\\x= \frac{15}{4*2}\\x= \frac{15}{8}[/tex]
The value of X is ratio of fifteen to eight. That is, x = 15/8
ALGEBRIAC EQUATIONAlgebraic equation comprises of unknown variables with equality sign.
To evaluate 1/2x+3/2(x+1)-1/4 = 5, Find the LCM in the left hand side.
[tex]\frac{x}{2}[/tex] + [tex]\frac{3(x+1)}{2}[/tex] - [tex]\frac{1}{4}[/tex] = 5
At the Left hand side, the L.C.M is 4
[tex]\frac{2x+6(x+1)-1 }{4} = 5[/tex]
Cross multiply
2x + 6x + 6 - 1 = 20
8x + 5 = 20
Collect the like terms
8x = 20 - 5
8x = 15
Make x the subject of the formula
x = 15/8
Therefore, x = 15/8 in the given algebraic equation.
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What is the area of this parallelogram
Answer:
17.15 cm²
Step-by-step explanation:
The area (A) of a parallelogram is calculated using the formula
A = bh ( b is the base and h the perpendicular height )
here b = AE + EB = 1.4 + 3.5 = 4.9 and h = BF = 3.5, hence
A = 4.9 × 3.5 = 17.15
Find the values of x and y that fit both the equation 2x - 3y = 8 − = and 4x + 3y = -2.
Answer:
Step-by-step explanation:
In other words, solve the system
2x - 3y = 8
4x + 3y = -2
Let's use the method of elimination. Mult. the first equation by -2:
-4x + 6y = -16
4x + 3y = -2
----------------------
8y = -18, so y = -9/4. If y = -9/4, then 2x - 3(-9/4) = 8, and:
2x + 27/4 = 8, or
2x + 27/4 = 32/4, or
2x = 5/4, or
x = 5/8
Then the solution is (5/8, -9/4).
If this does not match any of the possible answer choices, please check to ensure that y ou have copied down this problem correctly. Where do the "- =" symbols following the '8' come from?
To find the values of x and y that fit both equations, we can solve the system of equations using the elimination method. The values of x and y that fit both equations are x = 1 and y = -2.
Explanation:To find the values of x and y that fit both the equations 2x - 3y = 8 and 4x + 3y = -2, we can solve the system of equations. This can be done using the elimination method or the substitution method. Let's use the elimination method:
Multiplying the first equation by 4 and the second equation by 2, we get:
8x - 12y = 32
8x + 6y = -4
Subtracting the second equation from the first, we get:
-18y = 36
Dividing both sides by -18, we find that y = -2. Substituting this value back into the first equation, we can solve for x:
2x - 3(-2) = 8
2x + 6 = 8
2x = 2
x = 1
Therefore, the values of x and y that fit both equations are x = 1 and y = -2.
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what is the factorization of the expression below 16x^2-25y2
For this case we must factor the following expression:
[tex]16x ^ 2-25y ^ 2[/tex]
By definition, the formula of square difference states that:
[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]
In this case:
[tex]a = 4x\\b = 5y[/tex]
Then, we can factor the expression as:
[tex](4x + 5y) (4x-5y)[/tex]
Answer:
[tex](4x + 5y) (4x-5y)[/tex]
Final answer:
The expression [tex]16x^2-25y^2[/tex]is a difference of squares and factors into the product of two binomial conjugates, which is (4x + 5y)(4x - 5y).
Explanation:
The expression [tex]16x^2-25y^2[/tex] is a difference of squares, which is a special factoring case where you have two perfect squares separated by a subtraction sign. The difference of squares can be factored into the product of two binomials that are conjugates of each other. This means that they are identical except for the sign between their terms.
The factorization is:
Identify the square root of each term: [tex]\(4x\) and \(5y\)[/tex]Write the expression as the difference of squares: [tex]\((4x)^2 - (5y)^2\)[/tex]Factor into two binomials:[tex]\((4x + 5y)(4x - 5y)\)[/tex]Therefore, the factorization of the given expression is[tex]\((4x + 5y)(4x - 5y)\).[/tex]
Jenna wrote the expression (8 + x)- 32 for "the sum of 8 and x less than 32".What mistake did Jenna make? Show and explain how to write the correct expression.
Answer:
(8+x)<32
Step-by-step explanation:
What Jenna wrote is "the sum of 8 and x minus 32"
Jenna made a mistake by interpreting the phrase "the sum of 8 and x less than 32" as if it suggested that one should calculate the sum of 8 and x and then subtract 32 from it. This interpretation led her to write the expression as (8 + x) - 32. However, this expression actually represents the value that is 32 less than the sum of 8 and x, which is not what the phrase intends to convey.
The phrase "the sum of 8 and x less than 32" means that when we add 8 and x together, their total should be less than 32. This is a statement about the relationship between the sum of 8 and x and the number 32. It involves a comparison, not an arithmetic operation like subtraction.
To correct the expression according to the original phrase's intent, we need to write an inequality that compares the sum of 8 and x with 32. The phrase suggests that the sum (8 + x) should be smaller than 32. This inequality is written as:
8 + x < 32
This correct expression states that when you add 8 to x, the result should be less than 32. It does not involve subtracting 32 from the sum, but rather compares the sum directly to 32 with a "less than" sign, effectively expressing the original phrase mathematically.
HELP!!
What is the value of x?
Answer:
The value of x = 34° ⇒ first answer
Step-by-step explanation:
* Lets revise some facts about the circle
- A chord of a circle is a straight line segment whose endpoints
both lie on the circle
- When two chords, intersect inside a circle then the measure
of the angles formed is one-half the sum of the measures of the
intercepted arcs.
* Now lets solve the problem
- There are two chords intersect inside the circle
∵ AC and DB are two chords intersect each other at point O
- The measures of the angles between them is 1/2 the measure
of their intercepted arc
∵ ∠AOB subtended by arc AB
∵ ∠COD subtended by arc CD
∴ m∠AOB = m∠COD = 1/2[measure arc AB + measure arc CD]
∵ The measure of arc AB = 45°
∵ The measure of arc CD = 23°
∴ m∠AOB = m∠COD = 1/2[45 + 23] = 1/2[68] = 34°
- The measure of angle AOB represented by x
∴ m∠AOB = x
∴ The value of x = 34°
If you substitute the value 22.5 for h into the equation
h = 11.25, does it make the statement true or false?
Answer:
Step-by-step explanation:
False, because plugging it in would imply that 22.5 = 11.25
False
its false
The answer is false ok. there
find surface area of regular pyramid
Answer: Surface Area= 40
Step-by-step explanation:
The surface area is the sum of all areas of the triangle. To find the area of the triangle you would multiply the base(4) times the height(3) and divide it by 2. 4x6/2=6. This will give you the area of 6 for one triangle. Since there are 4 triangles you would multiply it by 4. This will give you 24. Now all you got to do is add the square's area which is 4 times 4 giving you 16. Add 16 and 24 and you get 40.
Plz help me with this
Answer: C) 2
Step-by-step explanation:
The red curve is: y = eˣ
The blue line is: y = 2x + 3
The intersect at two coordinates: (-1.4, 0.2) & (2, 7)
The only x-value option provided in your answer choices is: x = 2
Faith Franklin sells furniture and earns 8% commission on her total sales. Last month she had $33,500 in sales. How much did she earn?
$2,976.00
$2680.00
$3,015.00
$3685.00
Answer:
$2680.00
Step-by-step explanation:
We are informed that Faith Franklin sells furniture and earns 8% commission on her total sales. She sold $33,500 last month. We are required to determine her earnings for that month;
We simply evaluate 8% of $33,500
[tex]\frac{8}{100}*33500=2680[/tex]
Therefore, she earned $2680.00
Carmen was hired as a salaried computer programmer for $42,000 per year. What is her bi-weekly (26 weeks) salary?
Question 1 options:
$1,615.38
$807.69
$1,000.00
$3,500.00
Answer:
$1,615.38
Step-by-step explanation:
Remember that
1 year=52 weeks
we know that
Carmen was hired as a salaried computer programmer for $42,000 per year
or
was hired as a salaried computer programmer for $42,000 per 52 weeks
using proportion
Find out how much is the salary per 2 weeks
[tex]\frac{42,000}{52}=\frac{x}{2}\\\\x=42,000*2/52\\\\x=\$1,615.38[/tex]
What is P(A or B)...?
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.5 + 0.4 - 0.15
P(A or B) = 0.75
6! = (4! x (6-4)!) =
Answer:
6! = 720(4! × (6 - 4)!) = 48Step-by-step explanation:
n! = 1 · 2 · 3 · 4 · ... · n
6! = 1 · 2 · 3 · 4 · 5 · 6 = 720
(4! × (6 - 4)!) = (1 · 2 · 3 · 4 × 2!) = 24 × 1 · 2 = 24 × 2 = 48
The triangle shown below has an area of 10 units. Find x.
Answer:
The value of x (which is also the height of this triangle) is x = 5 units.
Step-by-step explanation:
The formula for the area of a triangle of base b and height h is
A = (1/2)(b)(h).
Here A = 10 units² = (1/2)(4 units)(x).
Multiplying both sides by 2 yields 20 units² = (4units)(x), and thus
20 units²
x = ------------------ = 5 units
4 units
The value of x (which is also the height of this triangle) is x = 5 units.
Answer:
x=5
Step-by-step explanation:
Which inequality can be represented by the graph below ?
Answer:
Option F. [tex]y\geq x+b[/tex]
Step-by-step explanation:
we know that
The solution of the inequality of the graph is the shaded area above the solid line
step 1
Find the equation of the solid line
The intercepts are
The y-intercept is the point (0,b)
The x-intercept is the point (-b,0)
Find the slope
[tex]m=\frac{b-0}{0+b} =1[/tex]
The equation of the solid line is
[tex]y=x+b[/tex]
step 2
The solution of the inequality is the shaded area above the solid line
therefore
the inequality is equal to
[tex]y\geq x+b[/tex]
Answers????? Very confused
Answer:
Step-by-step explanation:
12/7 cups of blueberries
Answer:
111 g
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
2 + 3 = 5
185 ÷ 5 = 37
2 : 3
( × 37 )
74 : 111
Peyton wants to purchase a new refrigerator that has a larger capacity than his current refrigerator. The length, width, and height of his current refrigerator are shown below.
What is the volume of his current refrigerator?
A. 2 1/24 cu. m.
B. 3 17/60 cu. m
C. 7/12 cu. m
D. 1 1/48 cu. m
Answer:
the answer is D. 1 1/48 cu.m
Step-by-step explanation:
V = 7/10 * 5/6 * 7/4
V = 245/240 cu.m
V = 49/48 cu.m
V = 1 1/48 cu. m
The answer is D I hope this helped
Select the correct answer from each drop-down menu.
m^2-5/2m=-11/2 , m=___±___.
1st options:
1/4
1
5/4
2nd options:
(3i square root 7)/4
(i square root 21)/2
(square root 113)/4
Answer:
correct option for first blank is 5/4 and for second blank is [tex]\frac{ 3i\sqrt{7}}{4}[/tex]
i.e m= [tex]\frac{5}{4}\pm\frac{ 3i\sqrt{7}}{4}[/tex]
Step-by-step explanation:
The given equation
[tex]m^2 - \frac {5m}{2} = \frac{-11}{2}[/tex]
and we have to find m= ______ ± ________
We can use quadratic formula to solve this question.
The above equation can be written as: [tex]m^2 - \frac {5m}{2} + \frac{11}{2} = 0[/tex]
and the formula used will be:
[tex]m= \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Putting values of a= 1, b= -5/2 and c= 11/2 and solving we get:[tex]m=\frac{-\frac{-5}{2}\pm\sqrt{{(\frac{-5}{2})}^2-4(1)(\frac{11}{2})}}{2(1)}\\\\m=\frac{\frac{5}{2}\pm\sqrt{(\frac{25}{4})-22}}{2}\\m=\frac{\frac{5}{2}\pm\sqrt{(\frac{-63}{4})}}{2}\\m= \frac{\frac{5}{2}}{2}\pm\frac{\sqrt{(\frac{-63}{4})}}{2}\\m= \frac{5}{4}\pm\frac{\sqrt{-63}}{4}[/tex]
Since there is - sign inside the √ so [tex]\sqrt{-1}[/tex] is equal to i and we have to divide [tex]\sqrt{63}[/tex] into its multiples such that the square root of one multiple is whole no so,
[tex]\sqrt{63}[/tex] = [tex]\sqrt{9}* \sqrt{7}[/tex]=[tex]3* \sqrt{7}[/tex]
Putting value of [tex]\sqrt{63}[/tex] and [tex]\sqrt{-1}[/tex]
the value of m= [tex]\frac{5}{4}\pm\frac{ 3i\sqrt{7}}{4}[/tex]
so, correct option for first blank is 5/4 and for second blank is [tex]\frac{ 3i\sqrt{7}}{4}[/tex] .
Simplify: −6( 1 4 x - 2 3 x + 5 6 x) A) -2 1 2 x B) -x C) 2x D) 3 4 x
Answer:
-282x
Step-by-step explanation:
− 6( 1 4 x - 2 3 x + 5 6 x)
− 6(47 x) = -282x
Answer:
a
Step-by-step explanation:
-6(
1
4
x -
2
3
x +
5
6
x)
-6(
3
12
x -
8
12
x +
10
12
x)
-6(
5
12
x)
-2
1
2
x
A sequence is defined by the recursive function f(n + 1) = –10f(n).
If f(1) = 1, what is f(3)?
3
–30
100
–1,000
Answer:
100
Step-by-step explanation:
f(n+1) = -10f(n)
f(1) = 1
f(2) = -10f(1) => f(2) = -10·1 => f(2) = -10
f(3) = -10f(2) => f(3) = -10·(-10) => f(3) = 100
Answer:
100
Step-by-step explanation:
daniels spinner is divided into 8 equal sections. he plans to spin it 80 times. which equation predicts the number of times he could spin green?
Answer:
B) P(green)=2/8(80)
Step-by-step explanation:
Answer:
B. P(green)=2/8(80)
Step-by-step explanation:
what would be a reasonable estimate for 31+m=307
Answer:275 276
Step-by-step explanation:
the answer is m = 276
to get the answer you need to subtract 307 - 31 which equals 276
please give me brainliest ^_^
This is really stressing me out i need this don’t by tonight for extra credit please help?!!!!!
Answer:
1. 1/6 , 2/9 , 1/4 , 5/18
2. 1/3 , 4/9 , 1/2 , 5/9
3. 5/12 , 5/9 , 5/8 , 25/36
Hope this helps!
If you accept you are going to die at anytime, then you might not be as ambitious as you are.
Answer:
Nice quote!
Step-by-step explanation:
<:)
The discussion reflects on how accepting the inevitability of death might influence one's ambition, with perspectives ranging from it being a motivator to live more purposefully to a potential cause for nihilism or inaction.
The question delves into philosophical reflections on mortality and ambition, suggesting that acknowledging the inevitability of death might dampen one's drive to achieve. This idea taps into a broader discussion on how our perceptions of life and death can shape our motivations and actions. Ancient philosophies and modern thought leaders offer varying perspectives on this issue.
For instance, sources suggest that embracing the certainty of death can lead to a life lived with greater purpose and less fear, implying that the awareness of mortality can actually enhance one's ambition by instilling a sense of urgency and focus. This is supported by the notion that knowing each day could be our last encourages us to grow, reach out to others, and live authentically. Conversely, others argue that an excessive preoccupation with death may lead to nihilism or inaction, driven by the belief that all efforts are ultimately futile in the face of mortality. The balance between these viewpoints highlights the complex relationship between accepting death and pursuing ambition.
mrs. West took her class on a field trip to the museum cost of admission for the girls was $90 and the cost of admission for the boys who $75 each ticket cost the same amount what is the cost of each ticket
Answer:
15
Step-by-step explanation:
we know that the boys in total cost 75 dollars and the girls cost 90.
75 and 90 share but one common factor and that is 15.
Therefore, we can conclude that the tickets cost $15.
Answer:
15
Step-by-step explanation:
The data below represents the number of canoes rented each month from May through October. find the mean absolute deviation. round to the nearest hundredth 15, 29, 36, 45, 31, 12
The mean absolute deviation from the data representing the number of canoes rented each month from May through October is 9.67. The process involves finding the average of the data set, calculating each number's deviation from that mean, and then averaging those deviations.
Explanation:To calculate the mean absolute deviation of the provided data set: 15, 29, 36, 45, 31, 12, we take the following steps:
First, find the mean (average) of the data set. This is found by adding all the values together and then dividing by the number of values: (15 + 29 + 36 + 45 + 31 + 12) / 6 = 28 Next, find the absolute deviation of each number in the set by subtracting the mean from each number and taking the absolute value: |15 - 28|=13, |29 - 28|=1, |36 - 28|=8, |45 - 28|=17, |31 - 28|=3, |12 - 28|=16 Then, find the mean of these deviations by adding them together and dividing by the number of values: (13 + 1 + 8 + 17 + 3 + 16) / 6 = 9.67 (rounded to the nearest hundredth)
So, the mean absolute deviation of the data set is 9.67.
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What is the measure of the angle
Answer:
is 235
Step-by-step explanation:
shown in the image attached
Hope this helps
For this case we have that by definition, a flat angle is one that measures 180 degrees. It is observed that a flat angle is formed from the first to the second quadrant.
Now, we must add 55 degrees of the third quadrant, then:
[tex]180 + 55 = 235[/tex]
Thus, the angle formed is 235 degrees.
Answer:
235 degrees
Option A
IS the slope ( -3, -3) ( 3, 1)
A=positive
B= negative
C= no slope
D = undefined
and find the slope
The correct answer is A - positive
Answer:
A and the slope is 8/12
Step-by-step explanation:
Use the figure below to determine the length of side x help plz
The right answer for this one is C.
The length of side x is 4√3
What is tan of an angle?The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle.
Given
Height = 12
θ = 60
tan θ = height/base
tan 60 = 12/base
√3 = 12/x
x = 12/√3 = 4√3
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which methods could you use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15)?
A. Count by hand
B. Divide 15 by 2.
C. Add the endpoint.
D. Divide 1 by 15.
The y-coordinate of the midpoint of the vertical line segment is calculated by method B. Divide 15 by 2, which gives the midpoint's y-coordinate as 7.5.
Explanation:To calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15), you can use the method of dividing the y-coordinates of the endpoints by 2. In this case, you would divide 15 by 2 to find the midpoint's y-coordinate, which is method B. Divide 15 by 2. This is because the midpoint of a line segment is found by averaging the coordinates of the endpoints, and for the y-coordinates you add them together and then divide by 2. So, the calculation is (0 + 15) / 2, which equals 7.5. Thus, the midpoint of the segment is at the point (0, 7.5).
Write an equation of the line that passes through the points.
(0, - 2), (4, - 2)
Answer:
y = -2
Step-by-step explanation:
As we move from the point (0, -2) to the point (4, -2), x increases by 4, but y stays the same. Thus, the slope of this line is m = rise / run = 0/4 = 0.
Since the line passes through y = -2, that is the only descriptor needed for this line. The slope need not appear in this equation, although we certainly could write y = 0x - 2. Simplify this to y = -2.