The solution to the given system of equations y = x² + 10x + 11, y = x² + x - 7 is x = -2, y = -5.
The given set of equations
y = x² + 10x + 11 --- eqn(1)
y = x² + x - 7 --- eqn(2)
Solving the equations by elimination method
⇒ Subtracting eqn 2 from eqn 1, we get
⇒ y - y = x² + 10x + 11 - (x² + x - 7)
⇒ 0 = x² + 10x + 11 - x² - x + 7
⇒ 0 = 9x + 18
⇒ 9x = -18
⇒ x = -2
Put the value of x in eqn 1, and we get
⇒ y = (-2)² + 10(-2) + 11
⇒ y = 4 - 20 + 11
⇒ y = -5
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Please help!! I would love to learn how to understand this.
A step-by-step would be great. Thank you.
Answer:
BC = 143
JC = 10
Step-by-step explanation:
Similar triangles:In similar triangles, the corresponding sides are in same ratio.
ΔABC ~ ΔAGH
[tex]\sf \dfrac{BC}{GH} = \dfrac{AB}{AG}\\\\\\\dfrac{BC}{22}=\dfrac{130}{20}\\\\[/tex]
[tex]\sf BC =\dfrac{130}{20}*22[/tex]
= 13 * 11
[tex]\sf \boxed{BC = 143}[/tex]
11) ΔJLK ~ ΔJBC
[tex]\sf \dfrac{JC}{JK} = \dfrac{JB}{JL}\\\\\\\dfrac{JC}{40}=\dfrac{12}{48}\\\\JC = \dfrac{12}{48}*40\\\\JC = \dfrac{1}{4}*40\\\\JC = 1*10\\\\\boxed{\bf JC = 10}[/tex]
How do you determine the coordinates of a point after a reflection in the y-axis?
The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the -value the same.
A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection.
When a point is reflected across the Y-axis, the Y-coordinates remain the same, and the X-coordinates are transformed into their opposite signs.
Therefore, the reflection of the point (x, y) across the Y-axis is (-x, y).
A reflection of a point, a line, in the Y axis reflects the image over the Y axis to create a mirror image. In this way, the Y axis would be called the axis of reflection.
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if sam can buy 3 pounds of apples for 4.35, how many can he get for 11.52?
46+46 +y+ y= 180 *plug y in to solve for x
The value of y in the equation is 44.
What is equation ?
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A lot of specialists, such as air traffic controllers, architects, computer programmers, and carpenters, employ equations on a daily basis.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
46 + 46 + y + y = 180
2y = 180 - 46 - 46
2y = 180 - 92
y = 88 / 2
y = 44
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Scott is using a 12-foot ramp to help load furniture into the back of a moving truck. If the back of the truck is 3.5 feet from the ground, what is the horizontal distance from where the ramp reaches the ground to the truck? Round your answer to the nearest tenth.
Answer:
11.5 (this is a decimal)
Which graph shows the function f(x)=−ln(x−1)
The graph that shows the function f(x) = -ln (x - 1) is graph C.
Option C is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
f(x) = -ln (x - 1)
When x = 1, f(1) = - ln 0 = ∞
When x = 2, f(2) = - ln (2 -1) = -ln 1 = 0
When x = 3, f(3) = - ln (3 - 1) = - ln 2 = - 0.30
These coordinates are seen in graph C.
The graph in option C represents f(x).
Thus,
The graph in option C represents f(x).
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PLEASE HELP!! The Great Pyramid of Cheops has a square base whose sides each measure 230 meters. The altitudes of the triangular faces of the pyramid each make an angle of 51.8 degrees with the base.
What is the height of the pyramid? What is the shortest distance you would have to climb up a triangular face to reach the top?
Triangular (comparative more triangular, superlative most triangular) (comparative more triangular, superlative most triangular) a triangle-shaped form.
What is the height of the square pyramid?The entire area bounded by any triangle's three sides is referred to as the triangle's area. In essence, it is equivalent to 1/2 of base times height, or A = 1/2 b times h.
The Great Pyramid held the record for the world's highest building for more than 4,000 years, standing at 146.5 m (481 ft) tall. After losing 9.5 meters (31 feet) off the top, it is now 137 meters (449.5 feet) high.
S2(A2)2 is a formula that calculates the height of a square pyramid. In this example, a represents the length of the square base edge and s represents the square pyramid's slant height. Given by a2(h3) is the volume of the square pyramid.
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Number of miles driven in a week.
Person. Miles
Vani 30
Ryan 18
Fatoumata 42
For every ___ miles Vani drove, Ryan drove __ miles.
The number of miles driven by Taub in a week is 3 times the number of miles driven by Valeria in a week.
How to express ratio in simplest form?The United States Department of Transportation Federal Highway Administration said that the average driver traveled 12,724 miles in 2020. That's down from 14,263 average annual miles in 2019. The 2020 average equates to 1,060 miles per month per driver, or about 35 miles per day.Although it's possible, you cannot drive 1000 miles in a day safely with a single driver. This would involve approximately 16 hours of driving before accounting for traffic and rest stops. Assuming a total travel time of 20 hours, you would need to depart in the early hours and share the driving.Often, 100,000 miles is considered a cut-off point for used cars because older vehicles often start requiring more expensive and frequent maintenance when mileage exceeds 100,000.The average American spends 18 days driving per year, with an average of eight hours and 22 minutes per week, a OnePoll study conducted on behalf of Cooper Tire found.Number of miles driven by each person in a week:
Valeria = 7
Taub = 21
Ruby = 35
Number of miles driven by Taub : Number of miles driven by Valeria
= 21 : 7
= 21/7
= 3/1
= 3 : 1
Therefore, the number of miles driven by Taub : number of miles driven by Valeria in a week is 3 : 1 in it's simplest form.
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Use properties of operations to find the product of 8 and 88.
Fill in the blanks below.
8 x 88 = 8x (90-a)
= (8 x 90)-(8x a), a =
= 720-
||
A
The value of a for the given expression will be 2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression will be 8 x 88 = 8x (90-a). The value of a will be calculated as,
8 x 88 = 8x (90-a)
88 = 90 - a
a = 90 - 88
a = 2
Hence, the value of a will be 2.
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Lindsay earned a 98 on her final exam for biology. The mean score was 78.2 and the standard deviation was 8.4. What was Lindsay’s z-score?
Lindsay's z - score, given the mean score, the standard deviation, and her score, is 2. 35.
How to find the z - score ?To calculate a z-score, you subtract the mean from the individual score and then divide by the standard deviation.
The formula is:
z = (x - μ) / σ
Where
x is the individual score
μ is the mean
σ is the standard deviation.
So, to find Lindsay's z-score:
z = (98 - 78.2) / 8.4
z = 19.8 / 8.4
z = 2.35
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What are the solutions of 6t − 1 ≥ 4t + 13?
Answer:
t ≥ 7
Step-by-step explanation:
6t - 1 ≥ 4t + 13 ( subtract 4t from both sides )
2t - 1 ≥ 13 ( add 1 to both sides )
2t ≥ 14 ( divide both sides by 2 )
t ≥ 7
Answer:
Inequality Form: t ≥ 7
Interval Notation: [ 7, ∞ }
Step-by-step explanation:
1) Move all terms that contain "t" to the left side of the inequality by subtracting 4t from both sides.
a) 6t – 1 – 4t ≥ 13, THEN subtract 4t from 6t
b) 2t – 1 ≥ 13
2) Move terms that do not contain "t" to the right side of the inequality:
a) ADD 1 to both sides ––> 2t ≥ 13 + 1
b) ADD 13 and 1 ––> 2t ≥ 14
3) Divide each term by 2, then simplify:
= 2t/2 ≥ 14/2
4) Simplify the left side:
t = 14/2
5) Simplify the right side:
t ≥ 7
ANSWER:
Inequality Form: t ≥ 7
Interval Notation: [ 7, ∞ }
Hi
I know there are answers but I just want the methods used to get the answers please
Thank you:)
Answer:
Step-by-step explanation:
add a better picture
which of the following is the graph of the piecewise function
Step-by-step explanation:
[tex]\displaystyle\\f(x)=\left\{\begin{array}{ccc}\sqrt{-x-1}\ \ \ if}\ \ \ x\leq -1 \\\frac{x}{x^2-x-2}\ \ \ if\ \ \ -1 < x < 2 \\log_2(x-1)\ \ \ if\ \ \ x\geq 2\end{array}\right[/tex]
Answer:
In LMN MN=15cm, LP is perpendicular to MN, LP=100 angle PLN=PNL. Calculate the length of LN
The length of LN is approximately 101.12 cm.
What is the length of the hypotenuse?
In a right triangle, the hypotenuse is the side opposite to the right angle and it is the longest side of the triangle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In a right triangle, the length of the hypotenuse is given by the Pythagorean theorem: c^2 = a^2 + b^2.
In this case, we are given that LN is the hypotenuse, and LP and MN are the other two sides.
We are also given that LP = 100 and MN = 15, and that angle PLN = PNL which means that the triangle is a right triangle.
We can use the Pythagorean theorem to find the length of LN:
LN^2 = LP^2 + MN^2
LN^2 = 100^2 + 15^2
LN^2 = 10000 + 225
LN^2 = 10225
LN = √10225
LN ≈ 101.12 cm
So the length of LN is approximately 101.12 cm.
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10 packages of bacon cost $20.50 at the grocery store. How much will 1 pack of bacon cost?
A.$2.05
B.$2.25
C.$2.00
D.$2.10
Answer: $2.05
[tex]$20.50/10=2.05[/tex]
Suppose one friend decided to pay for a bag of pretzels
and a drink for all 4 of them.
If x equals the cost of the pretzels and y equals the cost of
the drink, what expression represents the total cost?
A 4+x+y
B 4(x+y)
c 4x+y
D x+4y
Answer:
C
Step-by-step explanation:
4x is really just 4 times the cost of the drinks +the cost of the pretzel bag so ita 4x+y
PLEASE HELP ASAP!!!!!
Answer:
answer B
Step-by-step explanation:
Did this one on a test got it right last week
can someone please help
Answer:
For the hexagon, the sum of all angles must be equal to 360. So, we have 360 divided by 6 and we have 60 and this is the angle for the hexagon. For the pentagon, again, the sum of all the angles must be equal to 360, so each angle is equal to 360/5 = 72.
The difference between 72 and 60 is equal to y which is 12.
Step-by-step explanation:
What is substitution table method?
Substitution table method is a method for solving systems of linear equations. It involves writing out the equations in a table with one variable per column, and then substituting one variable for the other until the equations are solved. This method can help students visualize the equations and make it easier to keep track of the values of each variable.
Solving Systems of Linear Equations Using the Substitution Table MethodThe substitution table method is a simple but effective way of solving systems of linear equations. It involves writing out the equations in a table with one variable per column. Then, one variable is substituted for the other until the equations are solved. This method is useful because it provides a visual way of keeping track of the values of each variable. It can also help students understand which variable values need to be substituted into which equations. Once the table is complete, the equations can be solved by using the values of the variables in the table. This method can be used to solve both two-variable and multi-variable systems of linear equations.
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Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon. K = 4
The vertices of the polygon before and after dilation are shown below
preimage Image
S (-5, 2) S' (-20, 8)
T (-3, 4) T' (-12, 16)
U (-1, 1) U' (-4, 4)
V (3, -1) V' (12, -4)
What is dilation?Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
Applying the rule to the vertices of the polygon we have
preimage Image
S (-5, 2) (4 * -5, 4 * 2) S' (-20, 8)
T (-3, 4) (4 * -3, 4 * 4) T' (-12, 16)
U (-1, 1) (4 * -1, 4 * 1) U' (-4, 4)
V (3, -1) (4 * 3, 4 * -1) V' (12, -4)
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What is the height of a triangle if its base is 24 cm and its area is 216 cm2?
The height of a triangle is calculated to be 18 cm if its base is 24 cm and its area is 216 cm².
Given that,
Base = 24 cm
Area = 216 cm²
Height = ?
The formula to find out the area of the triangle is given by,
Area A = 1/2 × Base b × Height h
A = 1/2 × b × h
Making h as subject, we have,
h = (2 A)/b = (2× 216)/24 = 18 cm
Thus, the required height of a triangle is calculated to be 18 cm if its base is 24 cm and its area is 216 cm².
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Select the correct answer. What is the slope of the line represented by this equation? -3x + 8y = 12 a. B. C. D.
With the help of the given equation, we know that the required slope is (A) 3/8.
What is a slope?In math, the gradient of a line is a number that tells you how steep it is and in which direction it goes in.
The point-slope form is a way of writing equations (y-y₁=m(x-x₁)) to emphasize the slope and a point on the line that isn't the y-intercept.
To highlight the same line's slope and y-intercept, you can rewrite the equation in slope-intercept form (y=mx+b).
So, we have the equation:
-3x + 8y = 12
Calculate the slope as follows:
We need to change it into a more general format.
-3x+8y=12
⇒ 8y = 3x+12
⇒ y = 3x/8+12/8
⇒ y = 3x/8+3/2
If you look at it in terms of y = mx+c, the m would be 3/8.
Therefore, with the help of the given equation, we know that the required slope is (A) 3/8.
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Complete question:
Select the correct answer. What is the slope of the line represented by this equation? -3x + 8y = 12
a. 3/8
B. 4/8
C. 8/4
D. 2
The product of two consecutive integers is 156. What are the numbers?
Answer:
12 and 13!
12 * 13 = 156
Step-by-step explanation:
Hope it helps! =D
Answer: The answer to your question is 12 and 13= 156
In your own words define energy transformation
Your answer Daryl finds a pair of pants for $17.00. If the pants are on sale for 35% off, what is the sale price of the pants?
Answer:
$11.05
Step-by-step explanation:
First, you make the percent into a decimal
35% - 0.35
Next, you multiply 17 and 0.35
17* 0.35= 5.95
Then, you subtract the discount which is $5.95 from $17
17-5.95= 11.05
So, the answer is $11.05
Hope this helps :)
Answer: $11.05
Step-by-step explanation:
First how much 35% of 17:
35% = 0.35
0.35 x 17 = 5.95
Next, subtract this discount off of the total:
17 - 5.95 = 11.05
Now adding the dollar sign makes it $11.05
What is the formula of minor sector and minor segment?
The formula of the minor sector = (θ/360°) × π r²
The formula of the minor segment = (θ / 360°) × πr² - (1/2) r² sin θ (OR) r² [πθ/360° - sinθ / 2] if 'θ' is in degrees
What is a segment of a circle?
A circle's arc and chord together define a segment, which is the area within that region. Let's go over what a circle's arc and chord signify once more.
What is a sector of a circle?
The term "Minor Sector" refers to the tiny area of a circle that is removed by two circle radii. The minor sector is a tiny area occupied by two radii.
Here,
We have to find the formula of the minor sector and minor segment.
We concluded that
The formula of the minor sector = (θ/360°) × π r²
The formula of the minor segment = (θ / 360°) × πr² - (1/2) r² sin θ (OR) r² [πθ/360° - sinθ / 2] if 'θ' is in degrees.
Hence, the formula of the minor sector is (θ/360°) × π r².
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if there are 20 oranges in one basket then how man in 12 baskets use the distribuive strategy to solve
Answer: There would be 240 oranges in 12 baskets.
Step-by-step explanation:
So, if there's 20 oranges per basket, you would just need to multiply 20 oranges by the 12 baskets.
20 x 12 = 240.
Explain how you can compare the cost of two items that are different sizes.
Answer:
You could compare the ounces or weight, the price per unit, or overall quality.
Step-by-step explanation:
You could use the ounce/weight to check which weighs more, or has more in it. Then figure out which is more reasonable. You could use the price per unit, and the ounce/weight because the price per unit/ price per ounce could be more expensive, or less expensive and make more sense to buy. Or you could just use overall quality. You can have an item with more in it, but have lower quality contents, when you could have a smaller amount with better quality contents, which might cost a little more.\
-Hope this helped
There is a soccer tournament with 16 teams. Each team must play every other team. You want to know how many games will be played. Explain how you would create a simpler problem to help solve this problem.
it’s 12
Step-by-step explanation:
Answer:ontinuing this process shows that for 16 teams, there are 8 + 4 + 2 + 1, or 15 total games. Using brackets can be done for any number of teams.
Step-by-step explanation:
Any help would be greatly appreciated!
scale factor is 2/3
Step-by-step explanation:
because