Final answer:
The solution to the system of equations 3x + 4y = -23 and 2y - x = -19, found using the elimination method, is (x, y) = (-61, -40).
Explanation:
To solve the system of equations 3x + 4y = -23 and 2y - x = -19, we can use the method of substitution or elimination. Let's use elimination to find the solution for (x, y).
Multiply the second equation by 2 to align the x terms: 2(2y - x) = 2(-19), which gives us 4y - 2x = -38.
Rewrite the equations to align like terms:
3x + 4y = -23
-2x + 4y = -38
Add the two equations together to eliminate y: (3x - 2x) + (4y + 4y) = -23 - 38, resulting in x = -61.
Substitute x back into the second original equation: 2y - (-61) = -19, which simplifies to 2y + 61 = -19.
Solve for y by subtracting 61 from both sides: 2y = -80, and then dividing by 2 gives us y = -40.
So, the solution to the system of equations is x = -61 and y = -40.
A single card is drawn from a deck. find the probability of selecting a heart or a 8.
Answer with Step-by-step explanation:
Let
A:selecting a heart
Total cards=52
number of hearts=13
P(A)=13/52
B:selecting a 8
number of 8=4
P(B)=4/52
A∩B:selecting a heart with 8 on it
number of hearts with 8 on it=1
P(A∩B)=1/52
A∪B:selecting a heart or a 8
We have to find P(A∪B)
P(A∪B)=P(A)+P(B)-P(A∩B)
= [tex]\dfrac{13}{52}+\dfrac{4}{52}-\dfrac{1}{52}[/tex]
=[tex]\dfrac{13+4-1}{52}[/tex]
= 16/52
= 4/13
Hence, the probability of selecting a heart or a 8 is:
4/13
If all terms of a series are positive, the series sums to a positive number?
A.
The statement is false because the series could converge to a negative number.
B.
The statement is true because the series will converge to a positive number because the series contains no negative terms.
C.
The statement is true because the series cannot diverge since all the terms are positive.
D.
The statement is false because the series could diverge.
A geometric series is the sum of an unlimited number of terms with a fixed ratio between them. The correct option is B.
What is geometrical series?A geometric series is the sum of an unlimited number of terms with a fixed ratio between them.
The given statement "If all terms of a series are positive, then the series sums to a positive number" is true because the series will converge to a positive number because the series contains no negative terms.
Hence, the correct option is B.
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Each shape is 1 whole. What fraction is represented by the shaded part of the model?
Fraction is a way to describe a part of a whole. The fraction is represented by the shaded part of the model is [tex]\dfrac{2}{1}[/tex].
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25
If we look at each of the shapes, we can observe that the whole of the shape is shaded therefore, the shaded part of the shape is equal to the shape which is represented by 1.
Now, in the image, there are two shapes given each of which is completely shaded, and the whole shape is represented by 1. therefore, these two shapes will be represented by 2.
The shaded shape can be written as,
[tex]2 = \dfrac{2}{1}[/tex]
Hence, the fraction is represented by the shaded part of the model is [tex]\dfrac{2}{1}[/tex].
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Can every even number be written as a sum of two primes?
Final answer:
No, not every even number can be written as a sum of two primes. This is known as the Goldbach Conjecture, which states that every even number greater than 2 can be expressed as the sum of two prime numbers.
Explanation:
No, not every even number can be written as a sum of two primes. This is known as the Goldbach Conjecture, which states that every even number greater than 2 can be expressed as the sum of two prime numbers. So far, this conjecture has been tested for even numbers up to at least 4, and no counterexamples have been found. However, it has not been proven to be true for all even numbers.
For example, the number 4 can be expressed as the sum of two primes (2 + 2), but the number 6 cannot be expressed as the sum of two primes. On the other hand, the number 8 can be expressed as the sum of two primes (3 + 5). This pattern continues, with some even numbers being expressible as the sum of two primes and others not.
If x = 3 inches, y = 10 inches, w = 5 inches, and z = 5 inches, what is the area of the object?
A.33 square inches
B.40 square inches
C.20 square inches
D.60 square inches
If x = 3 inches, y = 10 inches, w = 5 inches, and z = 5 inches. Then the area of the given figure is 40 inches.
What is area?"The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc."
What is the area of the square ?The area of the square is side times side i.e., a^2.
What is area of the rectangle ?The area of the rectangle is length times width i.e., l*b.
Here,
x = 3 inches, y = 10 inches, w = 5 inches, z = 5,
In the given figure:
Area of the square BCDE is a^2 = 5^2 = 25
Area of the rectangle ABFG is l*b = 5*3 = 15
Total area of the figure is = area of the square + area of the rectangle = 25+15 = 40.
Hence, the answer is option B.
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In the figure the horizontal lines are parallel and AB=CB=CD, if LM=5 find JM
Please help will be pleasured:)
In the neighborhood park there is a circular grassy picnic area, but half of the grass has died. The city wants to replant the grads, but needs to know the square footage of the damaged area. If the circular picnic are is 150 feet across what is the square footage of the damaged area
Answer: The damaged area is equal to 8831.25ft^2
Step-by-step explanation:
We know that we have a circular area, where half of the grass has died. We know that the circular picnic is "150 feet across" I guess this means that if you walk in a straight line from the edge of the circular area, through the middle, and to the next edge, the distance is 150ft.
This would mean that the diameter is equal to 150ft.
With this we can calculate the total area of the circle; this is:
A = pi*r^2
where r is the radius, that is half the diameter, so we have r = 150ft/2 = 75ft
and pi = 3.14
so we have:
A = 3.14*(75ft^)^2 = 17662.5ft^2
And we know that half of that area has the grass damaged, so the amount of square feet of grass needed is equal to A/2 = (17662.5ft^2)/2 = 8831.25ft^2
find the product of 3 and 3/4 and 1 1/10 how do you find the product and how did you come up with it could you show your work
The shampoo you like to use is on sale. But you only get the lower price if you buy 3 bottles. You want to know how much you'll save.
Write a formula that will help you determine how much you'll save by buying 3 bottles
on sale.
Let's let
s = sale price per bottle
r = regular price per bottle
c = cost savings
name AND define the two ways to classify polynomials
Rita rode her bicycle out into the country at a speed of 20 miles per hour and returned along the same route at 15 miles per hour. If the round trip took 5 hours and 50 minutes, how far out did she ride?
What is the radius of a circle circumscribed about a rectangle with a length of 8 centimeters and a width of 6 centimeters?
Answer:
I think its 5
Step-by-step explanation:
I may be wrong
find the value of r so that the line passes through (1,2) and (5,r) has a slope of -8
solve this equation for x. round to the nearest hundredth. 0.8=logx
Five coins are tossed. let x be the number of heads and y be the number of tails. find the expectation
find the limit of the function by using direct substitution. lim(x^2-1) x->0
Answer:
-1
Step-by-step explanation:
Direct substitution is just filling in the limit for x then solving. So in this case the limit is 0.
x^2-1
0^2-1
-1
Evaluate the dot product of (6,-3) and (8,5).
62, 52, 52, 52, 64, 69, 69, 76 for the given sample data, find
which of the following statements are true? Select all that apply.
a) The image of the point (-3,-5) under a reflection across the x-axis is (3,-5).
b) The image of the point (1,9) under a reflection across the y-axis is (1,-9).
c) The image of the point (8,7) under a reflection across the line y=-x is (-7,-8).
d) The image of the point (-6,-6) under a reflection across the y=x is (-6,-6).
e) The image of the point (2,4) under a reflection across the y-axis followed by a reflection across y=xis (-2,-2).
f) Point K (3,-1)is reflected across the x-axis to creak point K'.The line x+3y=6 passes through point K'.
Answer: The answer in order are false, false, true, true, false and (3,1)
Step-by-step explanation:
We know that image of a point (x,y) under the y-axis
is (-x,y) i.e. the sign of x coordinate changes
Similarly in case of x-axis sign of y coordinate changes
i.e (x,y) is reflected to (x,-y)
Also the reflection of (x,y) under the line y=x is (y,x)
and the reflection of (x,y) under the line y=-x is(-y,-x)
So
a) Given image of (-3,-5) under x-axis is (3,-5).
Hence statement is false
b) Given image of (1,9) under y-axis is (1,-9)
Hence the statement is false
c) Given image of (8,7) under y=-x is (-7,-8)
i.e. the statement is true
d) Given image of (-6,-6) under y=x is (-6,-6)
i.e the statement is true
e) Given image of (2,4) under y axis followed by x-axis is (-2,-2)
Hence the statement is false
f) (3,-1) is reflected in x-axis to (3,1)
Hence the point k is (3,1)
Answer:
a
b
e
g
Step-by-step explanation:
I just did the assignment lol-
The area of a trapezoid is 69.6 in2 and its altitude is 8.7 in. Find the perimeter of the trapezoid if the sum of its legs is equal to the sum of its bases.
A trapezoid is a quadrilateral having one set of opposing sides that are parallel to each other. The perimeter of the trapezoid is equal to 32 inches.
What is a trapezoid?A trapezoid is a quadrilateral having one set of opposing sides that are parallel to each other. It can have right angles (a right trapezoid) and congruent sides (isosceles), but neither is necessary.
As is mentioned that the area of the trapezoid is 69.6 in², while its altitude is 8.7 inches. Therefore, the sum of the bases of the trapezoid can be written as,
[tex]\rm \text{Area of trapezoid} = \dfrac{1}{2} \times (Base_1 + Base_2) \times Altitude[/tex]
[tex]69.6 = \dfrac{1}{2} \times (b_1 + b_2) \times 8.7\\\\(b_1 +b_2) = 16\rm\ inches[/tex]
Now, it is mentioned that the sum of the legs of the trapezoid is equal to the sum of its bases. Therefore, the perimeter of the trapezoid is,
[tex]\text{Perimeter of Trapezoid} = (\text{Sum of its bases}) +(\text{Sum of its legs})\\\\\text{Perimeter of Trapezoid} = 16+16 = 32\rm\ inches[/tex]
Hence, the perimeter of the trapezoid is equal to 32 inches.
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A(n)___ schedule is a table that gives the details of loan payments.
Solve the inequality and graph on a number line. 7x + 4 ≤ x – 2
Convert 5x + 6y = -5 to slope-intercept form. Simplify your answer
A baker has 34 cup of sprinkles to spread on cupcakes. Each cupcake needs 18 cup of sprinkles.
The baker uses the fraction model that is partially shown to find the number of cupcakes that will have sprinkles.
mediaIMG7358611486128321.jpg34=6
Which is the correct division equation that describes the model?
A. 18 ÷
B. 34÷18=8
C. 34÷18=6
D. 18÷34=332
a local post office sells stamps in packs of 4, 6 and 7. andy bought several packs of 4. erin bought several packs of 6. jarred bought several packs of 7. each of the three friends ended up with the same number of stamps that each person could have purchased?
The number of stamps each could have purchased is 84
How to determine the number of stamps each purchased
From the question, we have the following parameters that can be used in our computation:
Andy = packs of 4
Erin = packs of 6
Jarred = packs of 7
Expand 4, 6 and 7
So, we have
4 = 2 * 2
6 = 2 * 3
7 = 7
The LCM of 4, 6 and 7 is then calculated as
LCM = 2 * 2 * 3 * 7
Evaluate
LCM = 84
Hence, the number of stamps each could have purchased is 84
Finn bought 2 packs of stickers. Each pack had the same number of stickers. A friend gave him 4 more stickers. Now he has 24 stickers in all. How many stickers were in each pack. Explain how you solved it.
Let the number of stickers in each pack be 'x'
Finn bought 2 packs of stickers.
Number of stickers in 2 packs = [tex] 2 \times x [/tex] = 2x
According to the question, a friend gave him 4 more stickers and now he has 24 stickers in all.
Therefore, [tex] 2x+4=24 [/tex]
[tex] 2x=24-4 [/tex]
[tex] 2x=20 [/tex]
x = 10
Therefore, number of stickers in each pack are 10.
Based on the table of values below, find the slope between points where x = 3 and where x = 7. x y 3 1 4 6 7 9
Answer: The required slope is 2.
Step-by-step explanation: We are given to find the slope between the points where x = 3 and x = 7 from the following table :
x 3 4 7
y 1 6 9
We know that
the slope of a line between the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
At x = 3, y = 1 and at x = 7, y = 9.
Therefore, the slope between the points (3, 1) and (7, 9) is given by
[tex]m=\dfrac{9-1}{7-3}=\dfrac{8}{4}=2.[/tex]
Thus, the required slope is 2.
x+y= -9
x+2y= -25
According to the system of equations above, what is the value of y?
Bill needs to find the area of the ground covered by a conical tent. The tent is 12 feet tall and makes a 70° angle with the ground. Which expression can be used to find the area?
a) π · (12 · tan 70°)2
b) 36 · π
c) π · (12tan 70°12tan 70°)2
d) π · (tan 70°12tan 70°12)2
a) π · (12 · tan 70°)2. To find the area of the ground covered by the conical tent, use the formula for the surface area of a cone, A = πr(r+√(r^2+h^2)).
Explanation:To find the area of the ground covered by the conical tent, we can use the formula for the surface area of a cone. The formula is A = πr(r+√(r^2+h^2)), where r is the radius and h is the height of the cone.
In this case, the height of the cone is 12 feet and the angle it makes with the ground is 70°. To find the radius, we can use trigonometry. The radius is given by r = h tanθ, where θ is the angle with the ground. Plugging in the values, we get r = 12 tan(70°).
Now, substituting the value of r into the formula for the surface area of the cone, we get A = π(12 tan(70°))(12 tan(70°)+√((12 tan(70°))^2 + 12^2)). This simplifies to option a) π · (12 · tan 70°)2.