Answer: x = -2 y = 2
Step-by-step explanation:
There are different ways to solve systems of equations. I will set them equal to each other.
First, I have to divide 2 from both sides of the first equation, which gives
y = -4x - 6
Now I can set them equal to each other and solve for x.
-4x - 6 = 2x^2 + 4 x + 2
0 = 2x^2 + 8x + 8
Now we factor it. If you cannot see the factors right away, you can use the quadratic formula, but I see that
(2x+4)(x+2) = 2x^2 + 8x + 8 = 0
so, because (2x+4)(x+2) = 0, one (or both) of the parenthesis must equal zero.
Solve for each parenthesis.
2x+4=0 => 2x = -4 => x = -2
x+2=0 => x = -2
As we see here, there is only one value for x. Now we can plug it into either one of the original equations. I'll do the first since there are no squares.
2y = -8(-2) -12
2y = 16 - 12
2y = 4
y = 2
Please help me pleaseeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!
Answer: 3.32 * 10^4
Step-by-step explanation:
1) Set up the equation
4.00 * 10^4 - 6.8 * 10^3
2) Set the scientific notions the same
You can do this by multiplying 10 or dividing 10 on a notion
4.00 * 10^4 - 0.68 * 10 ^4
3) Factor the scientific notions out
10^4(4.00 - 0.68)
4) Subtract
10^4(3.32)
3.32 * 10^4
A horse that is ill needs medication. The medication costs the veterinarian $17.50 to buy. He marked up the medication 54.2% before selling it to the customer. Find the final selling price of the horse’s medication.
Answer:
$26.99
Step-by-step explanation:
17.50 original cost plus a 54.2% increase
First, divide percentage by 100 to get a decimal to divide by 54.2/100=0.542
Then multiply the new decimal by the original cost to find the amount marked up. 17.50 x 0.542= 9.485
Now add 9.485 to the original cost
17.50+9.485=26.985-> 26.99 rounded for the final answer
13-14 question gemetri 10 grade
The angle measures formed by the parallel lines are:
9. m∠10 = 69°
10. m∠6 = 115°
11. m∠7 = 118°
12. m∠11 = 108°
13. m∠14 = 66°
14. m∠12 = 86°
How to Find the Angle Measures Formed by Parallel Lines?The angle measures can be determined by using the special angle relationship between the angles involved when a transversal crosses two lines that are parallel.
9. x and y are parallel lines
m∠5 = 69°
m∠10 = m∠5 [alternate interior angles theorem]
m∠10 = 69° [substitution]
10. x and y are parallel lines
m∠9 = 115°
m∠6 = m∠9 [alternate interior angles theorem]
m∠6 = 115° [substitution]
11. x and y are parallel lines
m∠12 = 118°
m∠7 = m∠12 [alternate interior angles theorem]
m∠7 = 118° [substitution]
12. x and y are parallel lines
m∠4 + m∠11 = 180 [supplementary angles]
72 + m∠11 = 180 [substitution]
m∠11 = 180 - 72
m∠11 = 108°
13. m∠4 + m∠14 = 180 [supplementary angles]
114 + m∠14 = 180 [substitution]
m∠14 = 180 - 114
m∠14 = 66°
14. m∠5 = 86° [given]
m∠12 = m∠5 [congruent angles]
m∠12 = 86°
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You are completing a math assignment. The number of questions you complete and the time it takes you to complete them have a proportional relationship, as shown in the table.
Number of questions 4 and 7
Time (in minutes) 6 and ?
How much time does it take to complete 7 questions ?
Answer choices
3 min
5 min, 30 sec
9 min
10 min, 30 sec
I think your answer is 10 minutes and 30 seconds. . .
Step-by-step explanation:What I did was I took 6 and 7 and multiplied them together, then i divided 42 by 4, and got 10.5. which would give you 10 minutes and 30 seconds.
6*7=42/4=10.5 (aka 10min 30sec)
Divide.
2/7÷1/3
Responses
6/7
2/14
1/4
2/21
Answer:
6/7
Step-by-step explanation:
2Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/3 is 3/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - two sevenths divided by one third is six sevenths.
can someone help me answer this please?? Thank you so much is you help!! :)
The value of g(f(x)) will be 3(1-x²) and the value of g(f(2)) will be -9 for the f(x)=4-3x² and g(x)=x-1.
What is Function?A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
What are the 4 types of functions?Functions are broadly classified into four categories. Element-based: one-to-one function, many-to-one function, onto function, one-to-one and onto function, into function.
Here, f(x)=4-3x² and g(x)=x-1
g(f(x))=(4-3x²)-1
g(f(x))=4-3x²-1
=3-3x²
=3(1-x²)
g(f(2))=3(1-2²)
=3*-3
=-9
For f(x)=4-3x² and g(x)=x-1, the value of g(f(x)) is 3(1-x²) and the value of g(f(2)) is -9.
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can someone helpp me with this i will give brainlest :)
Answer:
Step-by-step explanation:
1slice=280 and 6 slices so 280x6 so 0x6=0 then 80x6=6+6x4=48x10=480
then 200x6= 6x2=12x100=1200
add all 0+480+1200=1680
sry i'm not used to showing work i usually do it all in my head
Alan sees this offer.
Refurbished phone
45% OFF
Now only £88
How much was the phone before the discounted price?
The cost of the phone before the discounted price is $160.
Given that, Refurbished phone 45% OFF now only £88.
What is the discount?Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price. The List price or Marked price is the price of an article as declared by the seller or the manufacturer, without any reduction in price. Selling price is the actual price at which an article is sold after any reduction or discounts in the list price.
Let the original price of the phone be x.
Now, x - 45% of x = 88
⇒ x - 45/100 × x = 88
⇒ x - 0.45x = 88
⇒ 0.55x = 88
⇒ x = 88/0.55
⇒ x = 160
Therefore, the cost of the phone before the discounted price is $160.
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The wholesale price for a necklace is $10.the mark up percent is 200%.what is the mark up
The mark up is $30.
What is markup?As stated, markup is the distinction between a product's selling price and its cost price. Retail minus Cost is markup. The term "markup" describes the discrepancy between a product's selling price and its actual cost. It is specified as a percentage over the price. In other words, the seller makes a profit when the price of the commodity or service is higher than the overall cost. A unit's gross profit, which is the sales price less the cost to create or buy it for resale, is divided by its cost to determine the markup %. The markup percentage is computed as (12 - 8) / 8 and is equal to 50% if an item costs the business $8 to produce but is sold for $12.
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 The measures of the angles of a triangle are shown in the figure below. Solve for x.
46°
34°
x°
Answer:
x = 100
Step-by-step explanation:
180 = 46 + 34 + x
180 = 80 + x
100 = x
PLEASE HELP BRO WILL GIVE BRAINLI
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠n + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? (4 points)
Step 2; it should be m∠o − m∠p = 90 degrees (complementary angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
Step 3; it should be m∠m + m∠n + m∠o = m∠o + m∠p
Answer:
Step 3; it should be angle m + angle n + angle o = angle o + angle p
Step-by-step explanation:
yes, the sum of the inner angles of the triangle, m, n, o must be 180°.
yes, the sum of supplementary angles (which the pair of inner and outer angles always is) p and o must be 180°.
so, step 3 wants to show that the sum of the 3 inner angles is the same as the sum of the inner/outer angle pair. m + n + o = o + p = 180.
but instead of o the student suddenly wrote n in the right side of the equation. and that is wrong. n + p can't be 180°, as both are inner angles, and that would make the third inner angle 0°, which is not really possible.
so, once n is replaced by o on the right side of the equating in step 3, all is correct again.
and step 4 is correct anyway (it fixed the mistake in step 3 of the original proof by another mistake, coming to the right conclusion just by coincidence), now that step 3 is corrected.
The coordinates of the endpoints of QR are Q(6, 2) and R(18, 18). Point S is on QR and divides it such that QS:RS is 3:1. What are the coordinates of S? Write your answers as integers or decimals.
Check the picture below.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ Q(6,2)\qquad R(18,18)\qquad \qquad \stackrel{\textit{ratio from Q to R}}{3:1} \\\\\\ \cfrac{Q\underline{S}}{\underline{S} R} = \cfrac{3}{1}\implies \cfrac{Q}{R} = \cfrac{3}{1}\implies 1Q=3R\implies 1(6,2)=3(18,18)[/tex]
[tex](\stackrel{x}{6}~~,~~ \stackrel{y}{2})=(\stackrel{x}{54}~~,~~ \stackrel{y}{54}) \implies S=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{6 +54}}{3+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{2 +54}}{3+1} \right)} \\\\\\ S=\left( \cfrac{ 60 }{ 4 }~~,~~\cfrac{ 56}{ 4 } \right)\implies {\Large \begin{array}{llll} S=(15~~,~~14) \end{array}}[/tex]
Simplify: 18c - 49 + 1 -2c
Answer:
16c - 48
Step-by-step explanation:
combine like terms : 18c - 2c - 49 + 1
then you get 16c - 48
The vertices of triangle SRQ have coordinates S (1, 1), R (3, 4), and Q (7, 0). If triangle SRQ is rotated about the origin 180°, what are the resulting coordinates of the point R?
Answer:
Step-by-step explanation:
its 3 4
R' (-3,-4) are the resulting coordinates of the purpose R.
A rotation may be a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point. The fixed point is named the center of rotation . The quantity of rotation is called the angle of rotation and it is measured in degrees. Use a protractor to live the specified angle counterclockwise.
Using the rule for a 180° rotation to seek out the vertices of the rotated triangle.
T: (x, y) ⇒ (-x, -y)
Given points of triangle: S(1,1) , R (3, 4) and Q (7, 0).
Rotation 180° about the origin.
S (1, 1) → S' (-1,-1)
R (3,4) → R' (-3,-4)
Q (7,0) → Q' (-7,0)
Hence, the coordinate of the R is: R' (-3,-4).
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What is the value of x in this figure?
x = 22
x = 68
x = 90
I don't know.
100 POINTS + BRAINLEIST IF CORRECT!
[tex]\huge\boxed{\sf 16}\\\\ \sf The\ two\ right\ triangles\ are\ a\ reflection\ of\ each\ other.\\ Both\ sides\ are\ equal\ in\ size. \\\\ 5x+1=4x+4\\5x-4x=4-1\\1x=3\\\\ Plug\ the\ value\ of\ x\ back\ into\ any\ of\ the\ two\ equations.\\\\ 5(3)+1 =15+1=16[/tex]
write an equation of a line that passes through the point (2,-2) and is parallel to the line 5x-2y=4
The equation of line is y= 5/2x -7.
What is equation of line?The slope of the line and a point on the line may be used to create the equation of a line. To better comprehend how the equation for a line is formed. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.
One of the significant forms used to express a straight line algebraically is the two point form.
Written as, y- y1= m (x- x1), where m is slope.
Given:
a line passes through the point (2, -2) and parallel to 5x-2y = 4
Now, writing the given equation of line in the form of slope intercept form
5x- 2y=4
2y = 5x -4
y= 5/2x -2
Here the slope is 5/2 and the required line will also have the same slope as parallel line.
then, m=5/2
Now using y=mx +c
put y=-2 and x=2
-2 = 5/2(2) + c
-2 -5 = c
c=-7
Hence, the equation of line is y= 5/2x -7.
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You overhear your friend explaining how to find intercepts to a
classmate. Your friend says, "When you want to find the x-intercept, just substitute 0 for x
and continue to solve the equation."
Is your friend's explanation correct?
The friend's explanation is not correct.
They are mixing up x and y intercepts.
To find the y intercept, plug in x = 0 to find y.
To find the x intercept, plug in y = 0 and solve for x.
Please help me with this please please please
Answer:
undefined
Step-by-step explanation:
We all know that any number multiplied by zero equals zero. Consequently, the division by zero operation is impossible.
so, your answer is undefined
Write the equation of the line that goes between the two points (6, -5) and (2, 3).
The equation of the line that passes through points (6, -5) and (2, 3) is y = -2x + 7.
How to determine the equation of line from two points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point 1 ( 6, -5 )
x₁ = 6y₁ = -5Point 2 ( 2,3 )
x₂ = 2y₂ = 3First, we determine the slope of the line.
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m = ( 3 - (-5) ) / ( 2 - 6 )
Slope m = ( 3 + 5 ) / ( 2 - 6 )
Slope m = ( 8 ) / ( -4 )
Slope m = -2
Now that the value of slope is known, we determine the y-intercept 'b' by plugging the slope and one point into equation of line formula.
y = mx + b
-5 = (-2)(6) + b
-5 = -12 + b
b = -5 + 12
b = 7
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (-2)x + 7
y = -2x + 7
Therefore, the equation of the line is y = -2x + 7.
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How do you solve an equation like this?
Answer:
Step-by-step explanation:
[tex]\displaystyle\\(64x^\frac{2}{3})^{-\frac{1}{3}} =\\\\(4^3x^\frac{2}{3})^{-\frac{1}{3}}=\\\\ 4^{3*(-\frac{1}{3})}x^ {\frac{2}{3}*(-\frac{1}{3} )}=\\\\ 4^{-1}x^{-\frac{2}{9} }=\\\\\frac{1}{4} x^{-\frac{2}{9} }=\\\\\frac{1}{4} (\frac{1}{x^\frac{2}{9}} } )=\\\\\frac{1}{4\sqrt[9]{x^2} }[/tex]
-3(v + 2) - 2v simplify and use distributive property
Answer: -5v-6
Step-by-step explanation:
Mark is looking at a blueprint of a skateboard that shows the ramp's length that is 11.4 inches. If the scale on the blueprint is 1 inch: 6 feet, find the actual length of the ramp.
(Someone answer Asap please.)
Applying the scale factor the actual dimension of the ramp in the blueprint Mark was looking at was found to be 0.158 inches
What is scale factor?Scale factor represent the amount the image is increased or reduced in the map.
How to find the actual length of the rampinformation from the question include
the scale on the blueprint is 1 inch: 6 feet
the ramp's length that is 11.4 inches
finding the scale factor
1 inch ⇒ 6feet = 72 inches
the scale factor is 1/72
finding the actual dimension
1 inch ⇒ 72 inches
? = 11.4 inches
cross multiplying gives
72 * ? = 1 * 11.4
? = 1/72 * 11.4
? = 0.158 inches
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Please help me im getting stressed with solution
7/12r + 3/4 < -5/24 + 5/6r = ? I need some help. again. please. I need to know what the answer is. I need to clear the fraction. and I'm HORRIBLE at math...
seven more then a number is equal to 18. what is the number
Answer:11
Step-by-step explanation:
The personal assets and liabilities of a plumber are listed below.
What is the total value of the plumber's liabilities?
$149,367
$167,925
$241,231
$273,881
The total value of the plumber's liabilities = $441,806
How to calculate the total of something?One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.
It is one of the fundamental mathematical operations we employ on a daily basis. We employ number addition in a variety of contexts. When we work with time or money, such as when adding up invoices and receipts, adding numbers is one of the most frequently used operations in daily life.
The total value of the plumber's liabilities :
is to simply add all the values and we will get
$441,806
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Answer:
Option B.) $167,925
Step-by-step explanation:
Liability is money you owe to another person or institution, including a credit card balance, mortgage and so on.
So the plumber's liabilities
= 149,367 + 6,283 + 12,275
= $167,925
The average rainfall for Key West, Florida is 1.51 inches for February and 5.45 inches for September. On average, how many more inches of rainfall are expected in September than in February?
The inches that are expected more in September than in February is 3.94
What is average and how to calculate it?
Average is ratio of the sum of all elements of dataset and total number of elements in the dataset. To calculate first find the sum of all elements of the dataset and then divide it by total number of elements in the dataset
The average rainfall for key west is 1.52 inches in February and 5.45 inches in month of September
To find the more inches we subtract the two We get,
[tex]5.45-1.51=3.96[/tex] inches
Hence The inches that are expected more in September than in February is 3.94 inches
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Daniel walks at a speed of 4 miles per hour. Daniel leaves his house at 1:00 p.m. and walks toward a playground that is exactly 2 miles away.
How long does it take Daniel to walk 1 mile?
Answer: 30 minutes to get to the playground
Step-by-step explanation:
a ladder 16 ft long rests against a vertical wall. let theta be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. if the bottom of the ladder slides away from the wall, how fast (in ft/rad) does x change with respect to theta when
If the bottom of the ladder slides away from the wall, then x changes by 12cosθ with respect to theta and when θ = π/6, x changes by 6[tex]\sqrt{3}[/tex] inches with respect to θ.
Here, we are given that a ladder 16 ft long rests against a vertical wall and theta is the angle between the top of the ladder and the wall.
We know that, sin of an angle = opposite / hypotenuse
Thus, sinθ = x/16
⇒ x = 16 sinθ
The rate of change of x with respect to θ will be given by dx/dθ
dx/dθ = d/dθ (12sinθ)
= 12 d/dθ (sinθ)
= 12cosθ
Now, we need to find the value of dx/dθ when θ = π/6,
= 12 cosπ/6
= 12 ([tex]\sqrt{3}[/tex]/2)
= 6[tex]\sqrt{3}[/tex]
Thus, when θ = π/6, x changes by 6[tex]\sqrt{3}[/tex] inches with respect to θ.
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Your question was incomplete. Check for full content below-
A ladder 12 feet long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall, and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π/6?