Answer: -44
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A. How many real solutions does the system { y = x² {} y = 2x have?
The system of equations has one real solution (2,4).
What is a system of equations?Simultaneous equations or systems of equations are two or more equations in algebra that must be solved simultaneously (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a unique solution.The given system of equations is:
y = x²
y = 2x
Substitute the value of y in the second equation,
x² = 2x
x²- 2x = 0 ( Factorize it)
x(x - 2) = 0
x = 0 and x = 2
Putting the value of x in the equations to obtain the value of y,
y = x² = 0
y = 2x = 2(0) = 0
y = x² = 2² = 4
y = 2x = 2(2) = 4
Therefore the system of equations has only one real solution (2,4).
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Estimate the area covered by the drum picture. Pls help thanks
Answer:
Step-by-step explanation:
Area = L times w ( length times width.)
Your lengthyot Length is 4 units and width is 4. so what is 4 times 4?
your right, its 16. Answer A is correct.
Find the area of the shaded region
need this ASAP!
ALL THE SHAPES HERE ARE RECTANGLES AND THE AREA OF A RECTANGLE IS =L×B
TO GET THE AREA OF THE SHADED PART WE SAY THE AREA OF THE OUTSIDE SHAPE SUBTRACT THE AREA OF THE INNER SHAPE.
LET US FIND THE AREA OF THE OUTSIDE RECTANGLE FIRST.
[tex]a1 = (x + 5)(x - 1) \\ = {x}^{2} - x + 5x - 5 \\ a = {x}^{2} +4 x - 5[/tex]
NOW LET US FIND THE AREA OF THE INNER RECTANGLE.
[tex]a2 = (x + 1)(x - 4) \\ a = {x}^{2} - 4x + x - 4 \\ \\ a = {x }^{2} - 3x - 4[/tex]
the area of the shaded part is given by
[tex]a1 - a2 = ( {x}^{2} +4 x - 5) - ( {x}^{2} - 3x - 4) \\ = {x}^{2} + 4x - 5 - {x }^{2} + 3x + 4 \\ = {x}^{2} - {x}^{2} + 4x + 3x - 5 + 4 \\ areashaded = 7x - 1[/tex]
Simplify: -2(3x – 2) -5(7 – x)
The simplified expression for the given algebraic expression -2(3x – 2) -5(7 – x) will be ( -x - 31)
As per the question statement, we are supposed to find the simplified expression for the given algebraic expression -2(3x – 2) -5(7 – x).
For solving the above expression, we should be having good knowledge of all mathematical operators and BODMAS.
Let y = -2(3x – 2) -5(7 – x)
y = -6x + 2*2 - 5*7 + 5x
y = -6x + 4 - 35 +5x
y = -x - 31
Therefore, the simplified expression for the given algebraic expression -2(3x – 2) -5(7 – x) will be y = ( -x - 31)
Algebraic Expressions: An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)To learn more about the Algebraic Expressions click on the link given below:
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the angle of elevation to a nearby tree from a point on the ground is measured to be 45 degrees. How tall is the tree if the point on the ground is 79 feet from the tree? Round your answer to the nearest hundredth of a foot
The tree is 79 feet tall if the ground is 79 feet from the tree and the angle of elevation is 45°.
Angle of elevation:
The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
Therefore, the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
Given,
The angle of elevation to a nearby tree from a point on the ground is measured to be 45 degrees.
Here we need to find how tall is the tree if the point on the ground is 79 feet from the tree and we have also need to round the answer to the nearest hundredth of a foot.
Here we know that
The angle of elevation = 45°
Distance of the point from the tree = 79 feet
Suppose h is the height of the tree.
Then the value of h is calculated as,
=> h / 79 = tan 45°
We know that, the value of tan 45° = 1,
So,
=> h/79 = 1
Then the value of h is,
=> h = 79
Thus, the height of the tree is 79 feet.
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What amount of pure acid must be added to 600 mL of a 50% acid solution to produce a 60% acid solution?
That indicates that in order to make a solution that is 60% acid, you will need to add a total of 300 milliliters of pure acid into the mixture.
This is further explained below.
What amount of pure acid must be added?In general, pure acid refers to an acid concentration of 100%. It is feasible to formulate the following equation if you assume that X represents the volume addition of the pure acid:
[tex]Va=100 \%X + 600 * 40 \%[/tex]
[tex]Va= (600+X)60 \% (M_1V_1=M_1 V_2)[/tex]
100X + 24000 = 36000 + 60x
X = 300.
In conclusion, That implies in order to generate a solution that is 60% acid, you will need to add 300 milliliters of pure acid.
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The scatter diagram shows the scores of 10 students in their paper 1 and paper 2 Maths GCSE exams.
a. The graph shows a positive correlation.
b. Using the line of best fit, his predicted score in his second paper could have been between 60 - 65.
What is a Positive Correlation?A positive correlation is a type of correlation whereby two variables move in the same direction. That is, as one increases, the other increases also.
In a scatter plot, a positive correlation exist when both variables appear to move towards the same direction as the line of best fit slopes upwards from left to your right.
a. The scatter plot shows an upward trend on the line of best fit, therefore, the type of correlation shown by the graph is: positive correlation.
b. Using the line of best fit to make prediction, if he got 50 in his paper 1, then the score of the student in his paper 2 could have been between 60 and 65.
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Sarita bought eggs at rupees 8.40 at what price per 100must she sell them so as to earn a profit of 15 percent
Answer:
Cost per egg = 8.4/12 = 0.7
Cost per hundred egg =Rs70
Let selecting price per hundred be Rs.y
⇒ 70/y-70 ×100 = 15
⇒ 10y−700 = 105
⇒ y = 80.5Rsplease help thank you
The interest of the CD account's of Ethan after 6 year is $756.
What is termed as the simple interest?Simply multiplying the everyday interest rate by both the principal and the amount of time between payments yields simple interest.Customers who pay their loans in full or early each month benefit from simple interest.Auto loans as well as short-term personal loans seem to be typically interest-only loans.For the given question;
Ethan deposit $7,000 into a certificate of deposit CD for 6 years.
The formula for finding the simple interest is;
SI = PRT/100
where,
SI = simple interest P = principal amount ($7,000)R = rate of interest (1.8%)T = time duration (6 years)Put the values in the formula,
SI = 7,000×1.8×6/100
Simplifying;
SI = 756.
Thus, the simple interest gained after 6 years will be $756.
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Watch help video What is the domain of the function shown in the graph below? 8 19 10 10 e a 4 5 4 14 6 10 W INCOR6 9 8 in to 5 1 2 3 4 5 6 17
The domain of any function represents the set of values of x for which the function is true.
The function shown in the graph starts at x=3 and continues towards +∞
The domain of the function is all values of x greater than or equal to 3.
[tex]\lbrace{x|x}\ge3\rbrace[/tex]Add 0.74 and 0.19! How many tenths are in the sum?
Answer: 0.93
There are 9 tenths
Step-by-step explanation:
The base angle of an isosceles triangle measures 40 degrees. What is the measure of the
top, vertex angle?
O 80°
O 140°
O 100°
O 40°
The measure of the top, vertex angle of an isosceles triangle is option c 100 degrees
Given,
The base angle of an isosceles triangle = 40 degrees
We have to find the top, vertex angle:
Isosceles triangle:
Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
Here,
We know that total interior angle of a triangle is 180°
In an isosceles triangle base angles will be equal.
Here, base angle is 40 degrees.
Now, the top, vertex angle = total angle - base angle × 2
= 180 - 40 × 2
= 180 - 80
= 100
That is, the top, vertex angle of an isosceles triangle is 100°
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Helppppppppppppp pls
Answer: x = -1 , F
Step-by-step explanation:
Hard to see your pic, but
[tex](-b+\sqrt{b^{2}-4ac } )/2a\\(-b-\sqrt{b^{2}-4ac } )/2a[/tex]
[tex](-5-\sqrt{5^{2}-16} ) / 8 = -1[/tex]
Your answer is: x = -1
Madelyn went to the hardware store and bought 7 identical wooden boards. when madelyn placed all the boards end-to-end, the line was 1.9 meters long. to the nearest tenth of a meter, how long was each board?
The length of each wooden board bought by Madelyn was 0.27 meters.
What is defined as the division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 separated into three equal groups adds up to 4 in each group in division.Each component of a division equation has its own name.Dividend: The dividend is indeed the number divided during the division process.Divisor: The divisor is the number with which the dividend is divided.Quotient: A quotient is an outcome of the division process.Quotient: A quotient is an outcome of the division process. emainder: We can't always divide things exactly. There could be an extra number. The leftover number is known as the remainder.The following explains the connection between these four parts: Dividend = Divisor x Quotient + RemainderFor the given question.
The number of wooden board bought by Madelyn = 7.
The length of all boards = 1.9 meters.
Thus, to find the length of each wooden board, simply divide the total length by the total board as each board is identical.
Each length = total length/number of boards
Each length = 1.9/7
Each length = 0.27 meter.
Thus, the length of each board bought by the Madelyn is 0.27 meters.
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AB=3x, BC=x+5 and AC=24. what is the midpoint of ac?
IF AB=3x, BC=x+5 and AC=24 then the midpoint of AC is point B.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
WE have given that AB=3x, BC=x+5 and AC=24. Since B is the midpoint, then we have:
AB = BC = AC/2
Now Substitute and solve for x:
AB = BC
x + 5 = 3x
x + -3x = -5
2x = 5
x = 5/2
AB = 3(5/2) = 15/2
BC = x + 5 = 5/2 + 5 = 15/2
Hence, the midpoint of AC is point B.
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true or false each of these reparents proportional relations y= 3/4x
Answer: true
Step-by-step explanation:
You bring 1.5 dozen bagels to school.
A dozen bagels cost $5.98.
You used a coupon that took $1.00 off the total.
How much did you pay for the bagels?
Answer: You would pay $7.97 for the bagels.
Step-by-step explanation:
(Price per Dozen * Amount) - Coupon = Price of Bagels
(5.98 * 1.5) - 1 = Price of Bagels
8.97 - 1 = Price of Bagels
Price of Bagels = $7.97
can u help me on b pleasee
a) By definition of standard form, a light-year is equal to 5.880 × 10¹² miles.
b) By simple rule of three, a magnitude of 4.25 light-year is equivalent to a magnitude of 2.499 × 10¹³ miles.
How to convert miles to light-years and viceversa
In this problem we need to convert a magnitude in miles to an equivalent magnitude in light-years and another magnitud in light-years to an equivalent magnitude in miles. Standard form is a notation used to represent both large and small number with no significant loss of precision. This form is described by the following form:
a.b × 10ⁿ
Where:
a - Whole number between 0 and 10.b - Significant decimalsn - Order of magnitudea) A light-year is equal to 5.880 × 10¹² miles.
b) The equivalent magnitude in miles is found by the following simple rule of three:
x = 4.25 ly × (5.880 × 10¹² mi / ly)
x = 2.499 × 10¹³ mi
A magnitude of 4.25 light-year is equivalent to a magnitude of 2.499 × 10¹³ miles.
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AB is a straight line workout the size of angle X
The x value will be 109°. The straight line formed a 180° angle. Solving the equation yields the angle.
What are supplementary angles?Supplementary angles are two angels whose sum is 180°. When a straight line intersects a line, two angles form on each of the sides of the considered straight line.
Those two-two angles are supplementary angles in two pairs. That is, if two supplementary angles are adjacent to each other, their exterior sides form a straight line.
The straight line formed a 180° angle. The resulting equation is as follows:
⇒x+42°+29°=180°
⇒x=109°
Hence, the value of the x will be 109°
The complete question is:
AB is a straight line.
Work out the size of angle x.
Not drawn accurately
42°
Х
29°
А
B
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How do you write 52 in scientific notation?
× 10
Answer:
5.2 × 10 to the power of 1
Step-by-step explanation:
Given f(x) = ax + b, where a and b are nonzero real numbers, which of the following describes the differences between the graph of f and the graph of the output of f multiplied by
On multiplying by [3], the slope becomes 3 times the original slope and
y - intercept becomes 3 times of the original value.
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following problem -
f(x) = ax + b, where [a] and [b] are nonzero real numbers. Now, the function f(x) is multiplied by 3.
The given straight line is -
y = f(x) = ax + b
After multiplied by [3], we get -
y' = 3f(x) = 3(ax + b) = (3a)x + (3b)
Therefore, on multiplying by [3], the slope becomes 3 times the original slope and y - intercept becomes 3 times of the original value.
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[Complete question - Given f(x) = ax + b, where a and b are nonzero real numbers, which of the following describes the differences between the graph of f and the graph of the output of f multiplied by 3 ]
Help ! Pleaseeeeeeee asap
1. f(x) = 3x² + 18x + 32
The zeroes of the equation f(x) is 3x² + 18x + 32 is x = -18 -7.75/ 6 and x = -18 + 7.75/ 6
What is polynomial?Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.
Given f(x) = 3x² + 18x + 32
3x^2 + 18x + 32 = 0
Here, a = 3
b = 18
c = 32
-b ±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
-18 ± [tex]\frac{\sqrt{18^2-4(3)(32)} }{2(3)}[/tex]
-18 ± [tex]\frac{\sqrt{324-84} }{6}[/tex]
-18 ± [tex]\frac{\sqrt{-60} }{6}[/tex]
-18 ± [tex]\frac{-7.75}{6}[/tex]
X = -18 (-7.75)/ 6 and x = -18 – (-7.75)/ 6
X = -18 -7.75/ 6 and x = -18 + 7.75/ 6
Therefore, the zeroes of the polynomial are X = -18 -7.75/ 6 and x = -18 + 7.75/ 6
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Casilde and Oziel walk from a restaurant in the same direction. If Casilde has walked five-eighths of a mile and Oziel has walked seven-tenths of a mile, how far apart are they?
For the first 4 home football games, the
concession stand sold 600 hotdogs. If
that ratio stays constant, how many
hotdogs will sell for all 10 home games?
Answer:
1500
Step-by-step explanation:
600 divided by 4 to see how much hotdogs are sold EACH home football game. This gives you 150 each game so you multiple it by ten in order to get the total for ten home games
[tex]2x-3=x+5[/tex]hjgctyrksrykfy.gulh/
Answer: x=8
Step-by-step explanation:
2x-3+x+5
2x-3+3=x+5+3 (Add 3 to both sides)
-2x=x+8
_____________
2x=x+8
2x-x=x+8-x (Subtract x from both sides)
_____________
Combine like terms
_____________
2x-x=x+8-x
1x=x+8-x
Multiply by 1
1x=x+8-x
x=x+8-x
_____________
Combine like terms
x=x+8-x
[x=8]
The weight of 6 eggs is shown. Identify the constant of proportionality of total weight to number of eggs.
The weight of 6 eggs is 264 g.
Answer:
44
Step-by-step explanation:
Let the number of eggs be N, and the weight be M
M is directly proportional to N.
.: M= kN
264 = 6k
.; k(the constant of proportionality is) = 264/6
k = 44.
PLEASE HELP MATH QUESTION
Answer:
Proved below.
Step-by-step explanation:
Parallel lines and angles:
Given: p // q and ∠1≅ ∠2
Proof:
p //q, l is transversal,
∠3 ≅ ∠1 -----(I) {Corresponding angles are congruent}
∠1 ≅ ∠2 ---------(II) {Given}
From (II) & (I),
∠3 ≅ ∠2
∠3 and ∠2 are alternate interior angles. Alternate interior angles are congruent only if the lines are parallel.
⇒ l // m
PLEASE HELP!!!!!!!!! WILL MARK BRAINLIEST IF CORRECT
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
A baseball coach takes her team out for pizza every time they win a game. Not everyone can come each time, so she orders the pizzas based on how many players are coming. After last week's victory, she bought 3 small pizzas and 4 large pizzas, the perfect amount for the 19 players going out for pizza. This week, there were 25 players going, so she ordered 5 small pizzas and 5 large pizzas, which was also just the right amount. How many people does each size of pizza feed?
Each small pizza feeds
people, and each large pizza feeds
people.
1 small pizza and 4 large pizza feeds people according to the system of equations.
Let the number of small pizza be x and the number of large pizza be y.
So, we get the two equations as:
3 x + 4 y = 19 ...(1)
5 x + 5 y = 25 ...(2)
Taking 5 common from equation 2, we get that:
x + y = 5
x = 5 - y
Put it in equation 1, we get that:
15 - 3 y + 4 y = 19
15 + y = 19
y = 4
x = 5 - 4 = 1
Therefore, we get that, 1 small pizza and 4 large pizza feeds people according to the system of equations.
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A sphere had a 6-inch radius (r).
volume of the sphere?
A. 24 cubic inches B. 32 cubic inches
C. 216 cubic inches
D. 288 cubic inches
The volume of sphere in terms of is 288 cubic inches, if the sphere has a radius of 6 inches.
What is the volume of sphere?
In mathematics, the volume of the sphere defines the capacity of a sphere. It is measured in the cubic unit. Basically, it tells the amount of the air it can hold inside the sphere.
According to the question, the given data state that the sphere has a radius of 6 inches
Using standard formula for volume of sphere is,
Volume of the sphere = (4/3)πr³
where, r - radius of sphere and it is 6 inches
Therefore, volume of sphere = (4/3)π(6)³ = (4/3)π(216) = 288 Cubic inches
Hence, the volume of sphere in terms of is 288 cubic inches, if the sphere has a radius of 6 inches.
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