The value of the equation for x is 32
What is PEDMAS?PEDMAS is described as a mathematical acronym that represents the important operations during calculations.
The alphabets represents;
ParenthesesExponentsDivisionMultiplicationAdditionSubtractionFrom the information given, we have;
-(-2)+√(-2)²-4(1)(-8)
expand the brackets
2 + -2 -4(-8)
multiply the values
2 -2 + 32
Add the values
32
Hence, the value is 32
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At the start of a party, a drink dispenser contains 912 quarts of iced tea. After the party only 7 cups of tea remain.How many cups of iced tea did people drink during the party?
Answer:
3,641 cups drank
Step-by-step explanation:
A quart is 4 cups
At the start of the party, there were 912 quarts, multiply that by 4 to get 3,648 cups
At the end of the party, only 7 cups remained
3648 - 7 = 3,641 cups drank
In AUVW, u = 6.7 inches, ZW=19° and ZU=5°. Find the area of AUVW, to the
nearest 10th of an square inch.
The required, area of the triangle to the nearest 10th of a square inch is 34.1 square inches.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°
Here,
Calculating unknown angle v,
Since the sum of the angles in the triangle is equal to 180,
u + w+ v = 180
5 + 19 + v = 180
v = 180 - 24
v = 156°
Now,
Calculating the unknown side w,
U/sinu = W/sinw
6.7/sin5° = W/sin19°
W =25.0277
Now,
Area of the triangle is given as
= 1/2 UW sinv
= 1/2× (25.027)×(6.7)×(sin156°)
= 34.1 square inch
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using addition and subtraction signs make 1 2 3 4 5 6 7 8 9 equal 30
The numbers can be arranged as follows
(1 - 1) + 2 - (3 + 4) + (5 + 6 + 7 + 8 + 9) = 30 How to solve the math questionThe math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as
the full meaning include
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
Applying the sequence the to make the expression 1 2 3 4 5 6 7 8 9 equal to 30 using addition and subtraction signs:
(1 - 1) + 2 - (3 + 4) + (5 + 6 + 7 + 8 + 9) = 30
You can use parentheses to group the numbers and then add or subtract the groups to get the desired result.
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What is the value of k such that (x³ + x² - 9x - 36) + (x + 4) has a rernainder
of zero? Show your work.
Answer:x^3+x^2-8x-32
Step-by-step explanation:
In a fair out of 5 people 2 are men and 2 are women and the remaining are children there are 2500 people at the fair. what percentage of people are adult?
Answer:
Percentage of adults = 80%
Number of adults = 2000
Step-by-step explanation:
Percentage of men = 2/5 x 100 = 40%
Percentage of women = 2/5 x 100 = 40%
Percentage of adults = 40+ 40= 80%
If there are 2500 people, then number of adults
= 2500 x 80%
= 2500 x 80/100
= 2000 adults
Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the Green were Planes?
There are 16% of the Green were Planes.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Total number of green planes = 250
The total number of all planes = 1550
The percent of green planes = (number of green planes/number of total planes ) x 100
The percent of green planes = (250/1550) x 100
The percent of green planes = 0.1612 x 100
The percent of green planes = 16.129
Round to the nearest percent, and we get
The percent of green planes = 16%
Thus, 16% of the Green were Planes.
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A cupcake shop makes 25 dozen
cupcakes every 2 days. At this rate, how
many cupcakes does the shop make in
five days?
A. 600
B. 650
C. 750
D. 900
I got a bit confused with this pls help.
Answer:
The correct answer is c. 750
Step-by-step explanation:
if the shops makes 25 dozen in two days that makes it 300 cupcakes In two days because 1 dozen is 12 cupcakes, so you will see that they make 50 dozen in 4 days which is 600 then you know he/she is going to make half of the 25 dozen on the 5th day so you will take half of 300 which is 150 and add it all together, so will get 300+300+150= 750 as your answer.
Sami is 5 feet 8 inches tall and his younger sister is 4 feet 11 inches tall. How many inches taller is sami than his sister?.
The number of inches Sami is taller to his younger sister as per their respective given heights is equal to 9 inches.
Height of Sami in feet and inches is equal to 5 feet 8 inches
Height of Sami's younger sister is equal to 4 feet 11 inches
Convert all height into inches we get,
1 feet = 12inches
5 feet = 5 × 12 inches
= 60 inches
4 feet = 4 × 12 inches
= 48 inches
Number of inches Sami's is taller than his younger sister is equal to
= ( 5 feet 8 inches ) - ( 4 feet 11 inches )
= ( 60 + 8 ) inches - ( 48 + 11 ) inches
= 68 inches - 59 inches
= 9 inches
Therefore, the number of inches Sami is taller than his younger sister is equal to 9 inches.
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2/12 Help me answer please
Answer:
Step-by-step explanation:
Let's call the present value of the loan P. The payments of $1,550 in 1 year and $2,400 in 4 years can be expressed as an ordinary annuity with semi-annual payments. We can calculate the present value of this annuity using the formula:
PV = A * (1 - (1 + r)^-n) / r
where
A = $1,550 / 2 = $775 (semi-annual payment)
n = (4 x 2) + 2 = 10 (number of semi-annual periods)
r = 0.045 / 2 = 0.0225 (semi-annual interest rate)
So,
PV = $775 * (1 - (1 + 0.0225)^-10) / 0.0225 = $8,100.40
Thus, the present value of the loan is P = $8,100.40.
Next, we can calculate the present value of the payment of $1,050 in 24 months and the balance in 30 months.
The payment of $1,050 in 24 months can be expressed as a single amount due in 24 months. The present value of this payment can be calculated as:
PV = $1,050 / (1 + 0.0225)^(24/2) = $1,000.54
So, the balance of the loan after this payment would be P - $1,000.54 = $8,099.86.
The balance in 30 months can be expressed as an ordinary annuity due with semi-annual payments. We can calculate the present value of this annuity using the formula:
PV = A * (1 - (1 + r)^-n) / r
where
A = ($8,099.86) / 6 = $1,349.98 (semi-annual payment)
n = 6 (number of semi-annual periods)
r = 0.0225 (semi-annual interest rate)
So,
PV = $1,349.98 * (1 - (1 + 0.0225)^-6) / 0.0225 = $7,999.86
Therefore, the payment required in 30 months for the rescheduled option to settle the loan is $1,349.98 per semi-annual period.
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Satellites Sputnik, Yeltsin, and Plekov often temporarily line up in order in a great circle. The circumferen
is 24,900 miles, and the satellites orbit at about 200 miles above the surface. If, while in a great circle, Sp
miles from Yeltsin, and Yeltsin is 11,500 miles from Plekov, how far apart are Sputnik and Plekov?
11,500
Yeltsin
2
9,000
Sputnik
26,156 miles
25,528 miles
5,656 miles
5.277.2 miles
Plekov
Answer:
Step-by-step explanation:
The satellites Sputnik, Yeltsin, and Plekov are in a great circle, which is a circular path on the surface of a sphere that passes through the center of the sphere. The circumference of this great circle is 24,900 miles, and the satellites orbit at a height of approximately 200 miles above the surface of the sphere.
If Sputnik is 2 miles from Yeltsin, and Yeltsin is 11,500 miles from Plekov, then the total distance from Sputnik to Plekov can be found by adding the distance between Sputnik and Yeltsin to the distance between Yeltsin and Plekov. So, the total distance is 2 miles + 11,500 miles = 11,502 miles.
However, this distance is not the direct distance between Sputnik and Plekov, since they are not on a straight line but on a curved path on the surface of the sphere. To find the actual distance between Sputnik and Plekov, we can use the formula for the great-circle distance between two points on a sphere, which is:
d = acos(sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(long2 - long1)) * R
where lat1 and lat2 are the latitudes of the two points, long2 - long1 is the difference in longitudes of the two points, R is the radius of the sphere, and acos is the inverse cosine function.
Using this formula, we can calculate the distance between Sputnik and Plekov to be approximately 26,156 miles.
Decide which of the two given prices is the better deal and explain why. You can buy shampoo in a 6-ounce bottle for $4.19 or in a 14-ounce bottle for $10.89.
Answer:
6-oz bottle is a better deal
Step-by-step explanation:
To find which is a better value, find the unit rates for both types of bottles
The bottle with the lower unit rate is the better deal
6-ounce bottle costs $4.19
Unit rate = 4.19/6 oz = $0.70 per oz
14-ounce bottle costs $10.89
Unit rate = 10.89/14 = $0.78 per oz
Hence the 6-oz bottle is a better deal
If Gabe buys 20 yards of fabric, uses 6 2/3 yards to make some pillow cases and another 10 1/4 yards to make curtains for his room, how many yards of fabric will he have left?
Answer:
3 and 1/12 left
Step-by-step explanation:
When put on a coordinate plane, 1st street has the equation y = 6x - 7. 2nd street is parallel to 1st street and
goes through the point (2, 9). Write the equation for 2nd Street in slope-intercept form.
by
The linear equation for the parallel line will be y=6x-3.
What exactly is a linear equation?
The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
Line parallel to line y=6x-7 will have same slope which will be m=6
as general equation is y=mx+c where m=slope and c=constant.
For parallel line c will be as it is passing through (2,9)
9=6*2+c
c=9-12
c=-3
then the equation will be y=6x-3
Hence,
The equation for the parallel line will be y=6x-3.
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find the value of each variable show proofs
Answer:
Answer is in the attached photo
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note for this question, Sine rule can be used to find both x and y as well instead of Pythagoras' Theorem.
x=18, y=9√3
There is a theorem with 30 degrees 30 degrees 90 degrees triangles, it is that the side opposite of 30 degrees angle is a, the hypotenuse is 2a, and the other leg opposite the 60 degree angle is a√3
So, since a=9, x=2a=18 and y=a√3=9√3
Line AB contains point A(−4, 1) and point B (−1, 3). Find the coordinates of A′ and B′ after a dilation with a scale factor of 2 with a center point of dilation at the origin.
Answer:
To find the coordinates of A′ and B′ after a dilation with a scale factor of 2 and with the center of dilation at the origin (0, 0), we need to apply the dilation formula:
(x', y') = (2 * (x - 0) + 0, 2 * (y - 0) + 0) = (2x, 2y)
For point A, the original coordinates are (-4, 1), so we substitute these values into the dilation formula:
(x', y') = (2 * (-4 - 0) + 0, 2 * (1 - 0) + 0) = (-8, 2)
So, after the dilation, the new coordinates of point A are (-8, 2).
For point B, the original coordinates are (-1, 3), so we substitute these values into the dilation formula:
(x', y') = (2 * (-1 - 0) + 0, 2 * (3 - 0) + 0) = (-2, 6)
So, after the dilation, the new coordinates of point B are (-2, 6).
Answer:
Step-by-step explanation:
Step 1: Understanding the Dilation
A dilation with a scale factor of 2 and a center of dilation at the origin is a transformation that enlarges or shrinks an object by a factor of 2, with the origin (0, 0) as the center of the dilation.
Step 2: Using the Formula
To find the coordinates of the dilated points, we use the formula:
(x', y') = (2 * x, 2 * y)
Where (x, y) are the original coordinates of the points, and (x', y') are the coordinates of the dilated points.
Step 3: Finding the Coordinates of A′
We are given that the original coordinates of point A are (-4, 1), so we substitute these values into the formula:
A′ = (2 * -4, 2 * 1) = (-8, 2)
Step 4: Finding the Coordinates of B′
We are given that the original coordinates of point B are (-1, 3), so we substitute these values into the formula:
B′ = (2 * -1, 2 * 3) = (-2, 6)
Step 5: Conclusion
So, after a dilation with a scale factor of 2 and a center of dilation at the origin, the new coordinates of A′ and B′ are (-8, 2) and (-2, 6) respectively.
3
10
x 100 = 0,3 x 100 =
Answer:
The answer is thirty (30)
Please I could really use some help
Answer:
-1/2
Step-by-step explanation:
cos(-360+60)=-1/2
[tex]\cos(\alpha - \beta)= \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ -300\implies 30-330\hspace{5em}\cos(-300^o)\implies \cos(30^o-330^o) \\\\\\ \cos(30^o-330^o)\implies \cos(30^o)\cos(330^o)+\sin(30^o)\sin(330^o) \\\\\\ \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{3}}{2}~~ + ~~\cfrac{1}{2}\cdot \cfrac{-1}{2}\implies \cfrac{3}{4}~~ + ~~\cfrac{-1}{4}\implies \cfrac{3}{4}-\cfrac{1}{4}\implies \cfrac{2}{4}\implies \boxed{\cfrac{1}{2}}[/tex]
What is (−2) ( 3 4/7 ) ? step by step
Answer:-50/7 or -7.143
Step-by-step explanation:
you have to turn the 3 4/7 into an improper fraction by this:
3x7=21
21+4=25
which makes it 25/7
(25/7)x(-2) = -50/7 or -7.143
Talking on the telephone causes cancer.
6. There are marbles of four different colors in a bag. The
ratio of red to white to blue marbles is 3:4:5. There are half
as many green marbles as there are blue marbles. What is
the least possible number of marbles in the bag?
(A) 12
(B) 24
(C) 29
(D) 58
Answer:
(C) 29
Step-by-step explanation:
Answer:
the least possible number of marbles in the bag is 12.
Step-by-step explanation:
As for the question about the marbles, let's call the number of red marbles "x". Then the number of white marbles is 4x, the number of blue marbles is 5x, and the number of green marbles is (1/2) * 5x = 2.5x.
The total number of marbles in the bag is x + 4x + 5x + 2.5x = 12.5x.
To find the least possible number of marbles, we need to find the smallest possible value of x, which will give us the smallest total number of marbles. Since x represents the number of red marbles, it must be a positive integer. The smallest positive integer value of x is 1.
So, if there is one red marble, there are 4 white marbles, 5 blue marbles, and 2.5 green marbles. The total number of marbles in the bag is 1 + 4 + 5 + 2.5 = 12.5.
Therefore, the least possible number of marbles in the bag is 12.
At a carnival game, the player pays a dollar, then flips a quarter, rolls two dice, and draws two cards from a standard deck. If the result is heads, 11, and a pair of aces, he wins $1000. What is the probability of this happening?
(Round your answer to seven decimal places)
The probability of winning is…?
The probability of it happening will be 0.0000628
How to calculate the probabilityProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
The number of outcomes based on the information will be:
= 2(36)[52C2)
= 72 × 52! / 50!2!
= 1/95472
Number of favorable outcome is:
= 4!/2!2!
= 6
The probability will be;
= 6 / 95472
= 0.0000628
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Find the perimeter of the large triangle below
The perimeter of the triangle is equal to 28.7 using the trigonometric ratio
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;
sine, cosine and tangent.
tan60 = q/4 {opposite/adjacent}
q = 4 × tan60 {cross multiplication}
q = 6.9282
sin60 = q/r {opposite/hypotenuse}
sin60 = 6.9282/r
r = 6.9282/sin60 {cross multiplication}
r = 8
sin45 = q/s {opposite/hypotenuse}
sin45 = 6.9282/s
s = 6.9282/sin45 {cross multiplication}
s = 9.8
cos45 = p/s {adjacent/hypotenuse}
cos45 = p/9.8
p = 6.9282 {cross multiplication}
perimeter of the triangle = 4 + p + s + r
perimeter of the triangle = 4 + 6.9282 + 9.8 + 8
perimeter of the triangle = 28.7282
Therefore, the perimeter of the triangle is equal to 28.7 using the trigonometric ratio.
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Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $1000 deposit in an account with an APR of 3%. The balance in the account after 1 year is approximately
The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
What is meant by continuous compounding?
If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.
Given,
rate per period = 3%
Principal amount = $1000
Compounding is done after 1,5 and 20 years.
But we are asked to find the amount after continuous compounding after 1 year.
The formula of the amount after continuous compounding is:
[tex]A = Pe^{rt}[/tex]
where A = amount after continuous compounding
r = rate of period
t = time period
P = principal amount
[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45
Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]
n = times it compounds per year = 365
r = 0.03
AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]
= 3.04%
Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
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rewrite the equation in vertex form. y^2-4y-x+9=0
In the vertex form the equation can be rewritten as x = 1×(y - 2)² + 5
The equation is given in the standard form y²-4y-x+9 = 0 and we have to convert it into vertex form
So basically, the general vertex form of any equation is x = a(y - k)² + h
⇒ y²-4y-x+9 = 0
Shifting the x to RHS,
⇒ x = y²- 4y + 9
Writing y²- 4y in the form of (a-b)²,
⇒ x = y²- 4y + 4 + 5
⇒ x = 1×(y - 2)² + 5,
Hence the equation is now converted to vertex form
⇒ where a = 1, k = 2 and h = 5
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find the value of each variable provide proofs
x= 19, y=19
There is a theorem with 45 degrees 45 degrees 90 degrees triangles, it is that the two legs are equal to a and the hypotenuse is equal to a√2
So, since we know the hypotenuse is 19√2, a=19
so x = 19and y = 19
7) Given the geometric sequence
9, 3, 1, 1/3, ...
What is the sum of the first 8 terms?
The sum of the first 8 terms is 13.5
What is the sum of the first 8 terms?From the question, we have the following parameters that can be used in our computation:
9, 3, 1, 1/3, ...
Using the above as a guide, we have the following:
First term, a = 9
Common ratio, r = 1/3
The sum of GP (of n terms) is calculated as
Sum = Sn = a(r^n - 1) / (r - 1)
substitute the known values in the above equation, so, we have the following representation
Sum = 9 * ((1/3)^8 - 1)/((1/3) - 1)
Evaluate
Sum = 13.5
Hence, the sum is 13.5
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An angle measures 17.4° more than the measure of its complementary angle. What is the measure of each angle?
45 and 27.6 degrees are the two complementary angles.
What are the angles' measurements?The various angles or measurements include:
Measure an acute angle between 0° and 90°.Measure the obtuse angle between 90° and 180°.Right Angle: The measurement is 90 degrees.Straight Angle: The measurement is 180 degrees.Measure the reflex angle from 180° to 360°.Complete or full angle: 360° is the exact measurement.Angles that are complementary are those whose sum is 90 degrees. If the smaller angle has a measure of x, then the complementary angle's measure is 90 - x.
The issue shows that the greater angle (x + 17.4) is 17.4 degrees larger than the corresponding angle's measurement (90 - x). To find x, we can construct the following equation:
x + 17.4 = 90 - x + 17.4
When we simplify and find x, we obtain:
2x = 55.2
x = 27.6
The greater angle's measure is x + 17.4 = 45 degrees, while the smaller angle's measure is x = 27.6 degrees.
The two complementary angles are 27.6 and 45 degrees as a result.
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please help i am so confused its eulerian circuit
According to the information in the graph, the cheapest route to travel through all cities would be: Atlanta - Dallas - San Francisco - Los Angeles - New York - Detroit - Atlanta.
How to calculate the cheapest option to travel to all cities?To calculate the cheapest option to travel to all cities, we must identify our starting point in the city of Atlanta and analyze which is the cheapest option to travel. In this case, it would be the Detroit or Dallas option (at this point we can choose either one).
Once we choose Dallas, we must apply a location strategy so that the next move leaves us in a suitable position to go to the cities of the east coast. Therefore, the best option would be San Francisco and then Los Angeles.
After this, the best (cheaper) option would be to take transportation to New York, Detroit, and finally to Atlanta. Finally, we must add the values of the displacements to know what the total value is:
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Which equation represents a proportional relationship?
y=-x
y = 5x + 1
y = −5 (x + 1)
o y =15x
Help me with this Quadratic function graph the function
The graph of the quadratic function can be seen on the image at the end.
How to graph the quadratic function?The only way to graph or sketch a function by hand, is by finding some points on the graph and then connecting them.
To find the points we need to evaluate the quadratic equation.
if x = 0
y = 5*0^2 + 2 = 2
So we have the point (0, 2)
if x = 1
y = 5*1^2 + 2 = 7
So we have the point (1, 7)
if x = -1
y = 5*(-1)^2 + 2 = 7
So we have the point (-1, 7)
And so on, once you have enough points, you can graph them on the coordinate axis and then connect them. The graph of the quadratic equation can be seen on the image at the end.
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An observer standing at the top of a vertical cliff spots a house in the adjacent valley at an angle of depression of 12 degrees. The cliff is 60 meters tall. How far is the house from the base of the cliff?
Distance of the house from the base of the cliff is 282.27 m.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
From the figure attached,
AB = Height of the cliff = 60 m
Let the distance between the base of the cliff and the house 'C' = x m
If the angle of depression = 12°
Then angle of elevation of the top of the cliff from the house = 12°
Now from right triangle ABC,
tan12=60/x
x=60/tan 12
x=60/0.21256
x = 282.27 m
Therefore, distance of the house from the base of the cliff is 282.27 m.
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