Answer:
{x = 1/2 , y = 3/2
Step-by-step explanation:
Solve the following system:
{3 x + y = 3 | (equation 1)
{x + y = 2 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{3 x + y = 3 | (equation 1)
{0 x+(2 y)/3 = 1 | (equation 2)
Multiply equation 2 by 3:
{3 x + y = 3 | (equation 1)
{0 x+2 y = 3 | (equation 2)
Divide equation 2 by 2:
{3 x + y = 3 | (equation 1)
{0 x+y = 3/2 | (equation 2)
Subtract equation 2 from equation 1:
{3 x+0 y = 3/2 | (equation 1)
{0 x+y = 3/2 | (equation 2)
Divide equation 1 by 3:
{x+0 y = 1/2 | (equation 1)
{0 x+y = 3/2 | (equation 2)
Collect results:
Answer: {x = 1/2 , y = 3/2
Answer:
[tex]\large\boxed{x=\dfrac{1}{2}\ and\ y=1\dfrac{1}{2}\to\left(\dfrac{1}{2},\ 1\dfrac{1}{2}\right)}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}3x+y=3\\x+y=2&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x+y=3\\-x-y=-2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=1\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=\dfrac{1}{2}}\\\\\text{Put the value of x to the second equation:}\\\dfrac{1}{2}+y=2\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\boxed{y=1\dfrac{1}{2}}[/tex]
What is the solution to this equation? X/2-7=15
Answer:
x = 44Step-by-step explanation:
[tex]\dfrac{x}{2}-7=15\qquad\text{add 7 to both sides}\\\\\dfrac{x}{2}-7+7=15+7\\\\\dfrac{x}{2}=22\qquad\text{multiply both sides by 2}\\\\x=44[/tex]
Which graph represents a quadratic function that has no real zeros?
Answer:
2nd graph (in the attached pics)
Step-by-step explanation:
Graphically, the x-intercepts of the graph of a quadratic function are its zeroes.
There can be
no zeroes (where graph doesn't cut the x-axis at all),1 zero (where graph touches the x-axis at one point only), and2 zeros (where the graph cuts the x-axis at 2 points)Looking at the figures, the 2nd graph has no real zeroes, because the graph doesn't cut the x-axis at all!
So, the answer is the second graph.
The graph that represents a quadratic function that has no real zeros is the second graph
For a graph to be a quadratic function, and not have real zeros, then the following must be true
The graph must be a parabolaThe graph must not cross or touch the x-axisFrom the list of given options, the second graph does not touch the x-axis
Hence, the graph that represents a quadratic function that has no real zeros is the second graph
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What is greater 12 gallons or 50 quarts
50 quarts is greater than 12 gallons.
Given that, 12 gallons and 50 quarts.
Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, 1 quarts = 0.25 gallons
Here, 50 quarts = 50×0.25
= 12.5 gallons
So, 12.5 gallons > 12 gallons
Therefore, 50 quarts is greater than 12 gallons.
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Which value of y below is the solution to the system shown below. A) y=6 B) y=-1 C) y=-4 D) y=8
Equations: x+2y=27
2x+3y=46
Answer:
D
Step-by-step explanation:
given the 2 equations
x + 2y = 27 → (1)
2x + 3y = 46 → (2)
Rearrange (1) expressing x in terms of y by subtracting 2y from both sides
x = 27 - 2y ← substitute into (2)
2(27 - 2y) + 3y = 46
54 - 4y + 3y = 46
54 - y = 46 ( subtract 54 from both sides )
- y = - 8 ( multiply both sides by - 1 )
y = 8 → D
Determine which ordered pair is not a solution of y=-5x-4 a. (10,-52) b.(7,-39)c.(-7,31) d(8,-44)
Final answer:
The ordered pair (10, -52) is not a solution to the equation y = -5x - 4 because when x is substituted with 10, the equation yields -54, not -52.
Explanation:
To determine which ordered pair is not a solution of the equation y = -5x - 4, you need to plug the x-value from each ordered pair into the equation and see if the y-value matches the result.
For the pair (10, -52), substitute x with 10: y = -5(10) - 4 = -50 - 4 = -54, which does not match the y-value of -52.For the pair (7, -39), substitute x with 7: y = -5(7) - 4 = -35 - 4 = -39, which matches the y-value.For the pair (-7, 31), substitute x with -7: y = -5(-7) - 4 = 35 - 4 = 31, which matches the y-value.For the pair (8, -44), substitute x with 8: y = -5(8) - 4 = -40 - 4 = -44, which matches the y-value.The ordered pair that is not a solution is thus (10, -52).
what’s the value of
tan (3arc cos 3/4)
This trigonometric function can be written as:
[tex]tan (3 cos^{-1} (\frac{3}{4}))[/tex] (1)
Firstly, we have to solve the inner parenthesis:
[tex]cos^{-1} (\frac{3}{4})= 41.409[/tex] (2)
Substituting (2) in (1):
[tex]tan (3(41.409))=tan(124.228)[/tex] (4)
Finally we obtain the value:
[tex]tan(124.228)=-1.469[/tex]
Answer:
[tex]tan(3 \times arc \ cos(\frac{3}{4} ))=\frac{\sqrt{7} }{3}[/tex]
Step-by-step explanation:
The given expression is
[tex]tan(3 \times arc \ cos(\frac{3}{4} ))[/tex]
Where
[tex]cos^{-1}(\frac{3}{4} )=x\\[/tex], which means that, [tex]cosx=\frac{3}{4}[/tex]
If we analyse this trigonometric reason in a right triangle, we would find the hypothenuses is 4 and the adjacent leg is 3. Then, using pythagorean theorem, we find the other leg
[tex]y^{2}=4^{2} -3^{2}\\ y=\sqrt{16-9}=\sqrt{7}[/tex]
Which means the opposite leg of our right triangle is the square root of seven.
Finally, using such right triangle, we find the tangent reason, which is the quotient between the opposite leg and the adjacent leg
[tex]tan(radian \ value)=\frac{\sqrt{7} }{3}[/tex]
Therefore, the answer is [tex]\frac{\sqrt{7} }{3}[/tex]
What is the approximate area of the figure
Answer:
option b
137.1 cm²
Step-by-step explanation:
The given figure consist of two shapes
1) half circle
2) rectangle
Formula to use to calculate the area of this figure
half circle + rectangle
1/2πr² + h(b)where r = radius = diameter/2 = 8/2 = 4 cm
h = height = 14 cm
b = base = 8 cm
plug in values in the formula
1/2(3.14)(4)² + (8)(14)
25. 133 + 112
137.13 cm²
Find all Pythagorean triplets of 8.
Answer:
Step-by-step explanation:
There are two Pythagorean Triples containing 8:
6^2+8^2=10^2
8^2+15^2=17^2
PLEASE HELP ME!!!!!!!!!!!!!!In the triangle below, b=___. If necessary, round your answer to two decimal places.
First of all, we can find the angle B by using the fact that the interior angles of a triangle sum up to 180:
[tex]32.5+26.8+B=180 \iff B = 180-32.5-26.8=120.7
[/tex]
Now use the law of sines, which states that the ratio between a side and the sine of its opposite angle is constant. In particular, we have
[tex]\dfrac{\overwrite{BC}}{\sin(A)}=\dfrac{b}{\sin(B)}[/tex]
Plug in the known values and solve for b:
[tex]\dfrac{25}{\sin(32.5)}=\dfrac{b}{\sin(120.7)}\iff b=\dfrac{25\sin(120.7)}{\sin(32.5)}=40.01[/tex]
If the location you want to go is 270 miles away and you want to get there in 4.5 hours, at what constant speed do you need to drive?
the bake star bakery used 2 1/4 cups of raisins to make 4 servings of trail mix. How many cups of raisins are in each serving?
Step-by-step explanation:
Change the mixed fraction into improper fraction:
2 1/4 = 2 (1/4)(25/25) = 2 25/100 = 2.25
Divide 4 with 2.25
2.25/4 = 0.5625
0.5625 or a little over 1/2 cup of raisins are in each serving.
~
Can you Help me with Question 17 Please I’m begging you on my knees I need your help please help me please I’m begging for your help
Answer:
A. 7 more than 2 times m
Step-by-step explanation:
If there's a variable (letter) right next to a coefficient (the number) like in this problem, that means that 2 is being multiplied by m.
Since there's a +7 in the problem, that means thats its being added to or "more than."
Multiplication is "times"
7 is not being multiplied by two or m, it's being added.
So, 2m + 7.
Hope this helps!!!
(1/x-4)• (-x^2+9x-20/x+2)
(Multiplying And Dividing Rational Expressions)
ANSWER
[tex]\frac{5 - x}{x + 2}[/tex]
EXPLANATION
We want to simplify the rational expression:
[tex]( \frac{1}{x - 4)} )( \frac{ - {x}^{2} + 9x - 20}{x + 2} )[/tex]
We split the middle term to obtain:
[tex]( \frac{1}{x - 4)} )( \frac{ - {x}^{2} + 5x + 4x- 20}{x + 2} )[/tex]
We now factor to obtain;
[tex]( \frac{1}{x - 4)} )( \frac{-x(x - 5) + 4(x - 5)}{x + 2} )[/tex]
[tex]( \frac{1}{x - 4)} )( \frac{(x - 5)(4 - x)}{x + 2} )[/tex]
Or
[tex]( \frac{1}{x - 4)} ) ( \frac{ - (x - 5)(x - 4)}{x + 2} )[/tex]
We cancel the common factors to get;
[tex]\frac{ - (x - 5)}{x + 2}[/tex]
[tex] = \frac{5 - x}{x + 2}[/tex]
Which equation represents a line that passes though (-9,-3) and has a slope of -6
Answer:
D
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = - 6 and (a, b) = (- 9, - 3), thus
y - (- 3) = - 6(x - (- 9)), that is
y + 3 = - 6(x + 9)
An investor wants to complain that the stock market continues to drop . What might they do to graph shown to try to convince an audience that this is true
But B is not correct
Answer:
C.
Step-by-step explanation:
The first two questions couldn't be correct. C. Is the only logical answer.
Find the solution to the system of equations given below using substitution.
A. x = -1, y = -7
B. x = 7, y = -1
C. x = 7, y = 1
D. x = -1, y = 7
Answer: OPTION D
Step-by-step explanation:
You can apply the SUBSTITUTION method:
- Solve for x from the second equation and substitute it into the first equation.
- Solve for y:
[tex]x-8y=-57\\x=-57+8y[/tex]
[tex]2(-57+8y)+3y=19\\-114+16y+3y=19\\19y=133\\y=7[/tex]
- Substitute y=7 into any of the original equations ans solve for x. Then:
[tex]x-8(7)=-57\\x-56=-57\\x=-57+56\\x=-1[/tex]
The answer is:
D.
[tex]x=-1\\y=7[/tex]
Why?Substitution method for solving system of equations consists in isolate one variable in terms of the other variable.
So, isolating x in terms of y from the second equation, we have:
[tex]x-8y=-57\\x=-57+8y[/tex]
Then, substituting x into the first equation, we have:
[tex]2(-57+8y)+3y=19\\-114+16y+3y=19\\20y=19+114\\19y=133\\y=\frac{133}{19}=7[/tex]
Now, substituting y into the second equation we have:
[tex]x-8(7)=-57\\x-56=-57\\x=-57+56=-1[/tex]
Have a nice day!
A city received 17 inches of rain last year which was only 37% of what the usually get, how many inches doe it normally get?
Answer:
We have 17 inches = (37/100) · x;
x = 17 ÷ (37/100);
x = 17 · (100/37);
x = 1700 / 37;
x ≈ 46;
Step-by-step explanation:
Final answer:
To find out how much rain a city usually gets, divide the rain it received last year (17 inches) by the percentage of normal rainfall it represented (37%). The city normally receives about 45.95 inches of rain annually.
Explanation:
The student is asking how to calculate the usual annual rainfall for a city if the city received 17 inches of rain last year which was only 37% of their normal rainfall. To find the answer, we want to determine what 100% of their normal rainfall would be. We can use the formula:
Normal Rainfall = (Last Year's Rainfall / Percentage of Normal Rainfall) x 100
Substituting the given values into our formula, we get:
Normal Rainfall = (17 inches / 37%) x 100
Normal Rainfall = (17 / 0.37) inches
Normal Rainfall = 45.95 inches
Therefore, the city usually receives about 45.95 inches of rain annually.
Chad poured a sidewalk that is 42 feet long.He is going to start at the beginning and make a cut every 20 inches.How many cuts will Chad make?
Answer:
26 cuts
Step-by-step explanation:
1. convert 42 feet into inches by multiplying by 12 (12 inches=1 foot)
42*12 = 504 inches
2. divide the total number of inches (504) by 20 (where Chad cuts)
504/20 = 25.2
Since Chad cannot make a partial cut (.2) round up to the next whole number - 26
which expression is equivalent to (3^2)^-2
Answer:
1/(5^6)
Step-by-step explanation:
Which expression is equivalent to (3^2)^-2
Help me show the work please
Answer:
We are working with 2 vertical angles which are ALWAYS equal.
Therefore, 2 + 3x = 62
3x = 60
Therefore, x = 20
Step-by-step explanation:
Write the phrase as an expression 28 divided by 7
Note that result of this division is 4, as 28 divided by 7 equals 4.
How is this so?The phrase "28 divided by 7" can be written as an expression using the division symbol (/) or the fraction bar (÷).
Using the division symbol -
28 / 7
Using the fraction bar -
28 ÷ 7
Both expressions represent the division operation where the number 28 is divided by the number 7.
The result of this division is 4, as 28 divided by 7 equals 4.
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Final answer:
The phrase '28 divided by 7' is written as the expression 28/7, which simplifies to the value 4.
Explanation:
The phrase '28 divided by 7' can be written as an arithmetic expression using the division symbol. The expression is 28 ÷ 7 or using the slash notation, it is 28/7.This is the most concise and universally understood way to express the division in mathematical terms.
When you perform this division, the result is 4, since 28 is evenly divisible by 7. When using a calculator to evaluate similar expressions, such as 337/217, you would get a decimal result.
However, for the phrase provided, no calculator is needed because the division is straightforward.
Which phase describes the algebraic expression r/9
Answer:
The quotient of r and 9
Answer:
Step-by-step explanation:
The quotient of r divided by nine. The quotient is unspecified: you only know that there is one.
Which measurement is most accurate to describe the width of a math book?
8 inches
2 feet
1 yard
2 inches
its 8 inches, because 2 inches is to short, and a yard is too long for the width of a book
Answer:
8 inches
Step-by-step explanation:
2 feet is too long, 1 yard is way too long, and 2 inches is too short
A triangle with measures of x, x, and 2x is a actue, obtuse, or right triangle.
Answer:
right angle triangle.
Step-by-step explanation:
I take it that these are angles and not sides.
x + x + 2x = 180 All triangles have 180 degrees. Combine the left.
4x = 180 Divide by 4
4x/4 = 180/4 Do the division
x = 45
Therefore the angles are
x = 45
x = 45
2x = 90
The triangle is a right triangle because it has 1 angle that is 90 degrees.
What is the surface area of the triangular prism shown?
the answer would be 860 ft²
Answer:
920 ft^2
Step-by-step explanation:
What is the surface area of the triangular prism shown?
Miguel has 125 more baseball cards than chad. Miguel has 405 baseball cards .how many baseball cards does chad have
chad has 280 baseballs because if miguel has 125 MORE than chad then you have to subtract 125 from 405 to get chads baseball cards
To find out how many baseball cards Chad has, subtract 125 from Miguel's total of 405 baseball cards.
Explanation:To find out how many baseball cards Chad has, we can use the information given in the question. It is stated that Miguel has 125 more baseball cards than Chad and Miguel has a total of 405 baseball cards. So, to find out how many cards Chad has, we subtract 125 from Miguel's total:
Chad's total = Miguel's total - 125
Chad's total = 405 - 125 = 280 baseball cards
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In the diagram below P is the circumscribed about quadrilateral ABCD. What is the value of x?
Answer:
Option D. [tex]x=82\°[/tex]
Step-by-step explanation:
Remember that
In a inscribed quadrilateral opposite angles are supplementary
so
In this problem
[tex]m<C+m<A=180\°[/tex]
we have
[tex]m<C=x\°[/tex]
[tex]m<A=98\°[/tex]
substitute the values and solve for x
[tex]x\°+98\°=180\°[/tex]
[tex]x=180\°-98\°=82\°[/tex]
Answer:
82
Step-by-step explanation:
a pex
The two prism below are similar what is the value of x
Answer:
C
Step-by-step explanation:
Since the figures are similar then the ratio of corresponding sides are equal, that is
[tex]\frac{3}{15}[/tex] = [tex]\frac{1}{x}[/tex] ( cross- multiply )
3x = 15 ( divide both sides by 3 )
x = 5 → C
If angle JEK is complementary to angle DFH, then _______. A.
Answer:
D. <JEK = <CFL
Step-by-step explanation:
If angle JEK is complementary to angle DFH,
then <JEK = <CFL
Answer is D.
Answer:
angle JEK is congruent or equal to angle CFL
Step-by-step explanation:
An airplane covers 94 miles in 1/6 of n hour. The plane can cover how many miles in 6 hours
Answer:
3,384 miles
Step-by-step explanation:
If can cover 94 miles in 1/6 of an hour. (1/6 hour)*6 = 1 hour, so multiply 94 by 6 to see how far the plane will travel in 1 hour.
94(6) = 564 miles in one hour
Multiply that by 6 to see how far the plane travels in 6 hours
564(6) = 3,384 miles
The airplane can cover 3,384 miles in 6 hours.
What is the formula for finding distance when the speed and time are given?The formula for finding the distance covered is:
Distance = speed*time
We can find the distance that the plane can cover as follows:It is given that it can cover 94 miles in 1/6 hours.
This should be converted to per hour.
For this, multiply the distance by 6.
94 miles * 6 = 564 miles
The speed of the plane is 564 miles per hour.
The distance that the plane covers in 6 hours = 564 miles per hour * 6 hours
= 3,384 miles.
Therefore, we have found that the plane can cover 3,384 miles in 6 hours.
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