Answer:
Let x represents the number of apple tree and y represents the number of pear tree and z represents the number of cherry tree in an orchard.
From the given statement: The number of apple trees is 8 more than twice the number of pear trees.
⇒ [tex]x = 2y + 8[/tex] .....[1]
Also, It is given that the number of cherry and pear trees combined is 11 more than the number of apple trees.
⇒[tex]y + z = x + 11[/tex] ......[2]
The farmer plants 143 trees total.
⇒[tex]x +y +z =143[/tex] .....[3]
Substitute equation [2] into [3] we get;
[tex]x + x + 11 = 143[/tex]
Combine like terms;
[tex]2x +11 = 143[/tex]
Subtract 11 on both sides we get;
2x + 11 -11 =143 -11
Simplify:
2x = 132
Divide both sides by 2 we get;
x = 66
Substitute the value of x in equation [1];
66 = 2y + 8
Subtract 8 on both sides we get;
[tex]66 -8 =2y + 8 -8[/tex]
Simplify:
58 = 2y
Divide by 2 on both sides we get;
y = 29
Substitute the value of x and y in equation [3];
we have;
29 + 66 + z = 143
95 + z =143
Subtract 95 on both sides, we get;
95+ z -95 = 143- 95
Simplify:
z = 48
The framer plant in the orchard = 66 apple trees , 29 pear trees and 48 cherry trees
A circle has an area of 5050 square meters. Which answer is closest to the measure of its diameter?
A dress is selling for $100 after a 20 percent discount. What was the original selling price?
The original selling price if, A dress is selling for $100 after a 20 percent discount is $125.
What is the percentage?
A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Given:
A dress is selling for $100 after a 20 percent discount,
Calculate the original price as shown below,
Original price - 20% original price = 100
Original price(1 - 0.2) = 100
Original price = 100 / 0.8
Original price = $125
Thus, the original price is $125.
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Im sorry, finals have me stressed and I cant think straight.
Answer:
Yes, the triangles are similar.
x=7.2
Step-by-step explanation:
Similar triangles are triangles which have the same shape not not the same size. This can be seen when triangles have the same exact angle measures. The triangles in number 4 have the exact same angle measures and are therefore similar. Because they are similar, their sides have a special relationship. They are proportional on each triangle. We can set a proportion to find an unknown length.
A proportion is a ratio between two related quantities. We will write a proportion from one triangle side to the corresponding side on the other.
[tex]\frac{3}{5} =\frac{x}{12} \\[/tex]
We can cross multiply and isolate x to solve.
[tex]\frac{3}{5} =\frac{x}{12}\\3(12)=5(x)\\36=5x\\\frac{36}{5} =\frac{5x}{5} \\7.2=x[/tex]
The perimeter of a square field is 344
yards. How long is each side?
Answer: s = 324/4 = 81 yards
Answer:
s=81 yards
Step-by-step explanation:
A cookie recipe calls for 1/4 of a cup of sugar for one batch. How many complete batches can you make if you have 3 cups of sugar?
Iva deposits $2,000 into an interest-bearing savings account that is compounded continuously at an interest rate of 5%. She decides not to deposit or withdraw any money after the initial deposit. We can represent the account balance of the savings account after t years by an exponential function:
A(t) = $2,000 ∙ e^0.05t.
Approximately how many years will it take for the initial deposit to double?
Answer:
13.863 years
Step-by-step explanation:
Initial deposit is $2,000.
The rate of interest is 5% compounded continuously.
The account balance of the savings account after t years by an exponential function:
A(t) = $2,000 ∙ e^0.05t.
It says to find out the time when it takes for the initial deposit to double, i.e. A(t) = $4,000
Mathematically, we can set them equal and solve for t as follows:-
A(t) = $2,000 ∙ e^0.05t = $4,000.
e^(0.05t) = 4000/2000 = 2
0.05t Ln(e) = Ln(2)
t/20 = Ln(2)
t = 20 * Ln(2) = 13.86294361
So, it takes 13.863 years for the initial deposit to double.
Answer:
hope it hepls
Step-by-step explanation:
Gregory predicts that 310 people will attend the spring play there was an actual total of 220 people who attended the spring play. What is the percent error round to the nearest whole percent
Answer:
41%
Step-by-step explanation:
To calculate the percent error:
We find the difference between the predicted and the actual.We divide the absolute value of the difference by the actual recorded value.Convert to a percent by multiplying by 100 and adding a % sign.Gregory predicted 310 and 220 actually came.
1. 310-220=90
2. 90/220=0.41
3. 0.41(100)=41%
Answer:
the percent error is 41%
Step-by-step explanation:
If lisa has 2,134 buttons that needed to be sorted equally into 12 jars.How many buttons will be in each jar.
Answer:
Either 177 or 188 buttons
Step-by-step explanation:
2134/12=177.83
Lisa can place 177 buttons into each jar when she distributes 2,134 buttons equally among 12 jars.
Explanation:To determine the number of buttons Lisa can distribute into each jar, we perform a simple division: dividing her total button count, 2,134, by the number of jars, which is 12. This calculation results in approximately 177.83 buttons per jar. However, since you can't have a fraction of a button, we must round down to the nearest whole number, which is 177. Consequently, each jar will be filled with exactly 177 buttons. This fair distribution ensures that all 12 jars are equally supplied, making it practical and straightforward for Lisa to organize her collection.
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Celeste wants to have her hair cut and permed and also go to lunch she knows she will need $50 the perm cos twice as much as her haircut and she needs $5 for lunch how much does the permcost
True or False ? A remainder of 1 or more in the process of doing synthetic division tells you that you have found a root of the polynomial function and a factor of the polynomial.
Answer:
False
Step-by-step explanation:
If the value is a root of the polynomial, then the remainder will be 0. This means that the root as a factor will multiply to make the polynomial.
Joseph needs to find the quotient of 3,216 divided by 8 in what play is the first digit in the quotient
Answer:
3216/8 is = to 402
Step-by-step explanation:
So I am not sure what you are asking sorry
5x^2-(3xy-7x^2)+(5xy-12x^2)
When x=-0.25, and y=4
[tex]5x^2-(3xy-7x^2)+(5xy-12x^2)=5x^2-3xy+7x^2+5xy-12x^2=2xy\\\\ 2\cdot(-0.25)\cdot4=-2[/tex]
Answer:
-2
Step-by-step explanation:
5x^2-(3xy-7x^2)+(5xy-12x^2)
5x^2-3xy+7x^2+5xy-12x^2
[(5x^2+7x^2-12x^2)=0]
-3xy+5xy= -3(-.25)(4)+5(-.25)(4)
-3(-.25)(4)+5(-.25)(4)= 3-5= -2
-2
A ball is dropped from a heigh of h feet and repeatedly bounces off the floor. After each bounce, the ball reaches a height that is 2/3 of the height feom which it oreviously fell. For example, after the first bounce, the ball reaches a height of 2/3h feet. What represents the total number of feet the ball travels between the firat and the sixth bounce?
Answer:
[tex]s = \sum^5_1 {(2h)(\frac{2}{3})^i},[/tex]
Step-by-step explanation:
The initial height of the ball is h
After the first bounce the height is [tex]\frac{2}{3}h[/tex]
After the second bounce the height is [tex]\frac{2}{3}(\frac{2}{3})h[/tex]
After the i-th rebound the height is [tex](\frac{2}{3}) ^ i[/tex]
Then, distance s traveled by the ball is the sum of the heights reached between the first and fifth bounces.
[tex]s = 2 [\frac{2}{3}h + \frac{2}{3}(\frac{2}{3})h +, ..., + (\frac{2}{3}) ^ n h][/tex]
The equation is multiplied by 2 because the distance the ball travels when it goes up is the same as it travels down.
Finally the distance is a geometric series as shown:
[tex]s = \sum^5_1 {(2h)(\frac{2}{3})^i},[/tex]
The total distance traveled by the ball between the first and sixth bounce is [tex]\( \frac{23}{3}h \)[/tex] feet.
Step 1: Find the distance traveled during the first fall:
- The ball is dropped from a height of [tex]\( h \)[/tex] feet.
- So, the distance traveled during the first fall is [tex]\( h \)[/tex] feet.
Step 2: Find the distance traveled during each subsequent bounce:
- After each bounce, the ball reaches a height that is [tex]\( \frac{2}{3} \)[/tex] of the height from which it previously fell.
- During each bounce, the ball travels twice the distance of the height it reached.
- Therefore, during each bounce, the total distance traveled is [tex]\( \frac{4}{3}h \)[/tex] feet.
Step 3: Find the total distance traveled between the first and sixth bounce:
- Since we're asked for the distance between the first and sixth bounce, we have 5 subsequent bounces.
- The total distance traveled between the first and sixth bounce is the sum of the distance traveled during the first fall and the total distance traveled during the subsequent five bounces.
- So, it's [tex]\( h + 5 \times \left(\frac{4}{3}h\right) \)[/tex]feet.
Step 4: Calculate the total distance:
- Substitute the values and calculate: [tex]\( h + \frac{20}{3}h = \frac{23}{3}h \)[/tex]feet.
Therefore, the total number of feet the ball travels between the first and sixth bounce is [tex]\( \frac{23}{3}h \).[/tex]
30 points help!!!! Plz
Answer:
i took a long time figuring it out lol but here it is let me know if you got them all correct
Step-by-step explanation:
A) 3.6 × 10^(-1) B) 3.1 × 10^(6) C) 5.3 × 10^(-6) D) 4.2 × 10^(-1)
What are the zeros of the polynomial function? f(x)=x^3−x^2−4x+4
Select each correct answer.
-3
-2
-1
0
1
2
3
Answer: (B) -2, (E) 1, (F) 2
Step-by-step explanation:
x³ - x² - 4x + 4
= x²(x - 1) - 4(x - 1)
= (x² - 4) (x - 1)
= (x - 2)(x + 2)(x - 1)
Set each factor equal to zero to find the roots:
x - 2 = 0 x + 2 = 0 x - 1 = 0
x = 2 x = -2 x = 1
Answer:
-2,1,2
Step-by-step explanation:
PLEASE HELP!!
Diagonal AC divides the trapezoid ABCD (with bases AD and BC, AD>BC) into two similar triangles, △ABC and △DCA. Find AC if BC=4 cm and AD=9 cm.
Answer:
6 cm
Step-by-step explanation:
Let k represent the scale factor between ΔABC and ΔDCA. Then ...
... CA = k·BC
... AD = k·CA
So, AD/BC = k·(k·BC)/BC = k² = 9/4
Then k = √(9/4) = 3/2, and ...
... CA = (3/2)·BC = (3/2)·(4 cm)
... CA = 6 cm
Final answer:
To find the length of diagonal AC in trapezoid ABCD, we utilize the properties of similar triangles created by the diagonal. Since triangles △ABC and △DCA are similar, we set up a proportion using the sides BC and AD, and solve for AC to find that AC is 6 cm.
Explanation:
The question asks us to find the diagonal AC of trapezoid ABCD where it's given that BC = 4 cm and AD = 9 cm, and triangles △ABC and △DCA are similar. To find AC, we can use the properties of similar triangles which dictate that corresponding sides are proportional. Let us consider that the trapezoid is split into two triangles by AC. The ratio of the smaller triangle's base to the larger triangle's base (BC:AD) must be the same as the ratio of any other pair of corresponding sides in these two similar triangles. Furthermore, the ratio of the longer leg of △ABC (which is AC) to its base BC is equal to the ratio of the longer leg of △DCA (which is also AC) to its base AD. Using these ratios, we can set up a proportion to solve for AC:
AC/BC = AC/AD
Since the length of AC is the same in both ratios, we can multiply both sides by BC*AD to get:
[tex]AC^2 = BC * AD[/tex]
By substituting the given values for BC and AD into the equation we get:
[tex]AC^2 = 4 cm * 9 cm[/tex]
[tex]AC^2 = 36 cm^2[/tex]
To find AC, we take the square root of both sides:
AC = √36 cm
AC = 6 cm
Hence, the length of diagonal AC is 6 cm.
What is the circumference of the circle shown below? Use 3.14 for π, round your answer to the nearest tenth.
A. 131.9 cm
B. 65.9 cm
C. 13.2 cm
D. 6.6 cm
The most popular pizza at pavone's pizza is a 10-inch personal pizza with one topping.What is the area of a pizza with a diameter of 10 inches?Round your answer to the nearest hundredth
a= [tex]\pi[/tex] [tex]r^{2}[/tex]
The area of a pizza with a diameter of 10 inches is 78.5.
NEED HELP someone,anyone, please help im sturggling
Answer:
10. 1 right 2 acute 0 obtuse angles
11. x=6
Step-by-step explanation:
10. A triangle has 3 angles.
If it is a right triangle is has 1 right angle which is 90 degrees.
90 + x+y = 180 where x and y are the other 2 angles
Subtract 90 from both sides
x+y = 90
So the 2 angles that are left can only add to 90.
An obtuse angle is greater than 90 degrees, so we cannot have an obtuse angle. Acute angles are less than 90 degrees.
A right angle is 90 degrees. If one of the angles left is 90 degrees, the other one is zero, and that does not make a triangle.
So we must have 1 right angle and 2 acute angles (no obtuse angles)
11. Since the 2 sides are the same the triangle is isosceles. That means the two angles have the same measurements.
90 + y+y = 180
y+y=90
2y = 90
y = 45
Each angle must equal 45 degrees
7x+3 = 45 degrees
Subtract 3 from each side
7x+3-3 =45-3
7x =42
Divide each side by 7
7x/7 =42/7
x =6
The weight of water is 62 and one half lb per cubic foot. What is the weight of 18 and one fourth cubic feet of? water? How much does 18 and one fourth cubic feet of water? weigh?
Answer:
Water - 62.5 pounds per cubic foot
18.25 cubic feet would weigh 18.25 * 62.5 =
1,140.625 pounds.
Step-by-step explanation:
h(x)=17+ x/6
find x.
i will give brainliest 100 points
Answer:
x = -11
Step-by-step explanation:
h(x) = 17 + x/6
times 6
6 = x + 17
subtract 17
-11 = x
Answer:
H x − x 6 = 17
Step-by-step explanation:
WXYZ is a kite. If the measure of angle WXY is 120°, the measure of angle WZY is 4x° and the measure of angle ZWX is 10x°, find the measure of angle ZYX.
Answer:
100 degrees
Step-by-step explanation:
Remark
The endpoints of the smaller diagonal of a kite, intersect the vertexes of 2 equal angles. Put in simpler language, if x is at the top of the kite and x is the vertex of the larger angle between the top and bottom angles, then the other two angles (left and right) are equal.
In still simpler language. <W = <Y
Equation
<X + <W + <Z + <Y = 360 All quadrilaterals have 360 degrees for their interior angles.
Givens
<X = 120<W = 10x<Z = 4x <Y = 10xSolution
120 + 10x + 10x + 4x = 360 Gather like terms on the left120 + 24x = 360 Subtract 120 from both sides120- 120 + 24x = 360 - 120 consolidate 24x = 240x = 10Answer
Since <ZYX = 10x<ZYX = 10*10 = 100 degrees.Answer:
100
Step-by-step explanation:
Angle ZWX and angle ZYX are congruent.
360 = 120 + 4x + 10x + 10x
360 = 120 + 24x
240 = 24x
10 = x
The measure of angle ZYX is equal to 10(10) = 100°
Use the Distributive Property to rewrite each of the expressions -6(r-8)
Answer:
-6r+48
Step-by-step explanation:
(-6)(r)+(-6)(-8)
=-6r+48
Answer:
-6r +48
Step-by-step explanation:
The distributive property has us distribute the number on the outside to the numbers on the inside
-6(r-8)
-6 *r -6 * (-8)
-6r +48
Help!!! #2 Problem Set
Answer:
Independent: time (minutes)
Dependent: Distantce (inches)
Step-by-step explanation:
A large asteroid crashed into a moon of another planet causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic progression 18,54, 90,126, . Find the distance that the projectile traveled in the eighth second.
Answer:
270 feet
Step-by-step explanation:
From the sequence given, we can see that the asteroid travels 36 feet more with each second. (as seen [tex]54-18=36[/tex] and [tex]90-54=36[/tex] etc.)
So 5th second, it will travel: [tex]126+36=162[/tex]
6th second, it will travel: [tex]162+36=198[/tex]
7th second, it will travel: [tex]198+36=234[/tex]
8th second, it will travel: [tex]234+36=270[/tex]
Hence, in the eighth second, the projectile traveled 270 feet.
The distance the projectile travels in the eighth second is found to be 270 feet.
The question asks for the distance a projectile travels in the eighth second, given that the distances it covers each second form an arithmetic progression with initial distances given as 18, 54, 90, 126, etc. In an arithmetic progression, the difference between any two consecutive terms is constant, known as the common difference.
To find the common difference (d), we subtract the first term from the second term:
d = 54 - 18 = 36
The nth term of an arithmetic sequence can be found using the formula:
T(n) = a + (n - 1)d
Here, a represents the first term, which is 18, and d is the common difference we found to be 36. Substituting the values to find the eighth term:
T(8) = 18 + (8 - 1) x 36T(8)
= 18 + 7 x 36T(8)
= 18 + 252T(8) = 270
Thus, the distance the projectile travels in the eighth second is 270 feet.
Everyday day Marvin exercises for 48 minutes.How many days will it take him to exercise for 576 minutes.
"Match the vocabulary word with the correct definition. (altitude of a triangle, base angles, base of an isosceles triangle, centroid, median of a triangle, orthocenter, vertex angle )
1. The two angles that include the base of an isosceles triangle.
2. A point on the interior of a triangle in which the three medians of the triangle intersect.
3. A segment from a vertex perpendicular to the opposite side.
4. A point in which the three altitudes of the triangle intersect. It is possible for the orthocenter to occur on the triangle, on the interior of the triangle or on the exterior of the triangle.
5. The angle formed by the two equal sides of an isosceles triangle.
6. A segment from a vertex to the midpoint of the opposite side.
7. The third, unequal side of an isosceles triangle."
1. base angles
2. centroid
3. altitude of a triangle
4. orthocenter
5. vertex angle
6. median of a triangle
7. base of an isosceles triangle
Answer:
1.Base angles.
2.Centroid.
3.Altitude of a triangle.
4. Orthocenter.
5.Vertex angle.
6.Median of triangle.
7. Base of an isosceles triangle.
Step-by-step explanation:
1. Base angles: The two angles that include the base of an isosceles triangle.
2. Centroid: A point on the interior of a triangle in which the three medians of the triangle intersect.
3.Altitude of a triangle:A segment from a vertex perpendicular to the opposite side.
4.Orthocenter: A point in which the three altitudes of the triangle intersect .It is possible for the orthocentre to occur on the triangle ,on the interior of the triangle or on the exterior of the triangle.
5.Vertex of angle:The angle formed by the two equal sides of an isosceles triangle.
6.Median of triangle:A segment from a vertex to the midpoint of the opposite side .
7.Base of an isosceles triangle: The third , unequal side of an isosceles triangle.
A rectangle is inscribed in a semicircle of radius 8 cm. What is the maximum area of the rectangle?
The maximum area of a rectangle inscribed in a semicircle of radius 8 cm is found by maximizing the product of its width and height, which occurs when the rectangle's height is half the radius. Using the Pythagorean theorem, the optimal dimensions are calculated, leading to a maximum area of approximately 27.71 cm².
Explanation:To find the maximum area of a rectangle inscribed in a semicircle of radius 8 cm, we can employ a geometrical approach. Let the width of the rectangle be w and the height h. Because the rectangle is inscribed in a semicircle, the diagonal of the rectangle will be the radius of the semicircle, and the width of the rectangle will span from the midpoint of the diameter to a point on the circumference of the semicircle. Given the Pythagorean theorem, we have w² + h² = (2r)², where r is the radius. For our case, r = 8 cm.
Maximum area occurs when the rectangle's area is maximized. The area of the rectangle is A = w × h. By using the relation obtained from the Pythagorean Theorem, and knowing that for a rectangle inscribed in a semicircle the height will be half the radius when the area is maximized, we find h = r/2 = 4 cm. Substituting back into the Pythagorean Theorem, we find w = √(8² - 4²) = √64 - 16 = √48 = 4√3 cm. Therefore, the maximum area of the rectangle is A = w × h = 4√3 × 4 = 16√3 cm². This is approximately 27.71 cm².
This question combines geometry and basic principles of optimization to find the maximum area of a geometric shape within defined constraints, showcasing the application of mathematical reasoning in problem-solving.
What is the 17th term in the arithmetic sequence described by this explicit formula? A(n)=77+ (n-1) (-5)
Answer:
[tex]a_{17}[/tex] = - 3
Step-by-step explanation:
to find the 17 th term substitute n = 17 into the explicit formula
A(17) = 77 + (16 × - 5 ) = 77 - 80 = - 3
the answer is -3
have a blessed day!
It costs $23 per hour plus a flat fee of $16 for a plumber to make a house call. What is the equation of the form y = mx + b for this situation? A) y = 16x B) y = 23x C) y = 16x + 23 D) y = 23x + 16
Answer:
It is D 100%
Step-by-step explanation: