1. What is the solution to the system of equations?
3x + 4y = 12
x + 2y = 10
(a) Show how to solve the system of equations using the linear combination or elimination method.
(b) Show that you can get the same answer by using the substitution method.


Please help worth 93 points

Answer: [tex]x_1=2\\\\x_2=-\frac{1}{2}[/tex]

Step-by-step explanation:

To find the zeros of the quadratic equation given in the exercise, you need to apply the proccedure shown below:

- You must rewrite it as following:

[tex]6x^2-9x-6=0[/tex]

-You can apply the Quadratic formula, which is shown below:

[tex]x=\frac{-b\±\sqrt{b^2-4c}}{2a}[/tex]

In this case:

[tex]a=6\\b=-9\\c=-6[/tex]

- Therefore, when you substitute values, you obtain:

[tex]x=\frac{-(-9)\±\sqrt{(-9)^2-4(6)(-6)}}{2(6)}[/tex]

[tex]x_1=2\\\\x_2=-\frac{1}{2}[/tex]

The riddle 'what asks no questions but must be answered' typically refers to a telephone or a doorbell, both of which signal when someone is attempting to communicate or get attention.

The student's question, "what asks no questions but must be answered," is a type of riddle, which is a question or statement intentionally phrased to require ingenuity in ascertaining its answer. In this context, the answer to the riddle is typically the telephone or a doorbell, as both signal when someone is trying to get in contact or gain attention, and generally, one responds to them. Riddles can form part of the teaching in English, particularly when focusing on language play, word definitions, and understanding semantics. They can encourage students to pay attention to wording and to contemplate why certain expressions carry the meanings they do.

2 and 2, 15tenths is the corret anwser

Answer:

[tex]2\sqrt{2}[/tex]

Step-by-step explanation:

Pythagorean Theorem

[tex]\sqrt{3^2-1^2}\\2\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

Use the distributive property a(b + c) = ab + ac:

8( -10x + 3.5y - 7)

= (8)(-10x) + (8)(3.5y) + (8)(-7)

= -80x + 28y - 42

8(-10x + 3.5y - 7)

= (4)(2)(-10x + 3.5y - 7)

= 4[(2)(-10x) + (2)(3.5y) + (2)(-7)]

= 4(-20x + 7y - 14)

The expression 8(-10x+3.5y-7) equivalent to -80x + 28y - 56.

Let the expression be

8(-10x + 3.5y - 7)

Simplifying the above equation as

[tex]$\ 8\left(-10 x+\frac{35}{10} y-7\right)$[/tex]

Multiplying the equation, then we get

[tex]$-80 x+8 \times \frac{35}{10} y-8 \times 7$[/tex]

[tex]$-80 x+4 \times \frac{35}{5} y-56$[/tex]

[tex]$-80 x+4 \times 7 y-56$[/tex]

- 80x + 28y - 56

Therefore, the correct answer is option (b) - 80x + 28y - 56.

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Answer:

The numbers in decreasing order of their values are:

[tex]\cfrac{19}{3}>\sqrt{37}>6.08171...>6.012[/tex]

Step-by-step explanation:

Before actually comparing, we need to write all of those numbers in decimal form, that will be the only way to actually tell which one is bigger since you are already given numbers in decimal form.

Converting numbers in decimal form.

The first number we are given is [tex]\sqrt{37}[/tex], we know it is a bit higher than 6, since the square root of 36 is 6, so using a calculator we get

[tex]\sqrt{37}=6.0828[/tex]

The second number is a fraction, in decimal form will be:

[tex]\cfrac{19}{3}= 6.3333[/tex]

Writing the decreasing order.

Now that all numbers are in decimal form we can compare them and write them in decreasing order.

[tex]6.3333... > 6.0828...>6.08171...>6.012[/tex]

Lastly we can write the decreasing order using the numbers on their original form.

[tex]\cfrac{19}{3}>\sqrt{37}>6.08171...>6.012[/tex]

Answer:

90% chance that it's not yellow

Step-by-step explanation:

Since there is 1 yellow that mean that 9/10 marbles are a different color

9/10 as a percentage is 90%

Hope this helps and have a blessed day!

Answer:

the answer is

y=(x+1)2+4

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

The zeros of the function are the values of x when the value of y is equal to zero

In this problem

The zeros of the function are the price of a hot dog (in dollars) when the daily profit (in hundreds of dollars) of a hot dog stand are zero

we have

[tex]y=-2(x-3)^{2}+4[/tex]

using a graphing tool

The zeros of the function are

x=$1.59, x=$4.41

so

for these prices the daily profit are zero

see the attached figure

Answer:

The numbers are 25, 20 and 80

Step-by-step explanation:

125=a+b+c

b=a-5

c=4b

c=4(a-5)

c=4a-20

125=a+a-5+4a-20

125=6a-25

150=6a

25=a

b=a-5

b=25-5

b=20

c=4b

c=4(20)

c=80

✓:

80+20+25=125✓

Answer:

Perpindicular ---

construction - the walls need to be build at a perfect shape

interior decorating - things need to be hung on the wall, properly aligned

carpentry - if you want to build a square you need to make a line perpendicular to the first piece of wood, to make a perfect right angle

Step-by-step explanation:

Architects and engineers use parallel and perpendicular lines in technical drawings to ensure accuracy and consistent dimensions, while artists may use these concepts in perspective artwork. Physics calculations involving moments of inertia also apply these principles in determining rotational properties of objects.

Many professions use the concepts of parallel and perpendicular lines. For instance, architects and engineers frequently use parallel and perpendicular lines in their drawings and designs. When architects design buildings with a rectangular plan, they rely on parallel projections, where they scale down a two-dimensional representation of the building while maintaining parallel lines. Engineering drawings, such as those for machine parts, also employ parallel and perpendicular lines to convey the dimensions and orientation of objects accurately.

Artists working in perspective, on the other hand, often employ the concept that parallel lines appear to converge at a vanishing point in the distance, as seen in linear perspective artwork. However, for technical drawings where accuracy and measurement are key, the parallel projection method is crucial as it allows for dimensions to remain consistent.

In physics, moments of inertia calculations for objects like discs and rods often utilize parallel and perpendicular axes theorems to determine rotational properties. And in geometry, constructions frequently involve drawing parallel or perpendicular lines from given points, which is fundamental in defining figures and solving problems.

Answer:

D.) is the answer

Step-by-step explanation:

I know this because the ratio of muffins to donuts is 36:63 but simplified is 4:7

The ratio of muffins to donuts is 4:7 if the bakery has 63 donuts and 36 muffins for sale, option (D) 4 to 7 is correct.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

Number of donuts = 63

Number of muffins = 36

The ratio of muffins to donuts:

36:63

4:7

Ratio is 4 to 7

Thus, the ratio of muffins to donuts is 4:7 if the bakery has 63 donuts and 36 muffins for sale option (D) 4 to 7 is correct.

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Final answer:

The residual for the data point (4,13) given the line of best fit y=5x-2.5 is -4.5, indicating the line overestimates the value of y by 4.5 units.

Explanation:

The student is asking about finding the residual for a data point (4,13) given the line of best fit with the equation y=5x-2.5. To find the residual, you calculate the difference between the actual y value of the data point and the predicted y value from the line of best fit. For the given point, the predicted y value is calculated by substituting x=4 into the line equation, yielding y = 5(4) - 2.5 = 17.5. The residual is the actual y value minus the predicted y value: 13 - 17.5 = -4.5. Therefore, the residual for the point (4,13) is -4.5, indicating that the line of best fit overestimates the actual data value for y by 4.5 units.

Answer:8

Step-by-step explanation:(

x

+

4

)

2

+

(

y

−

7

)

2

=

64

This is the form of a circle. Use this form to determine the center and radius of the circle.

(

x

−

h

)

2

+

(

y

−

k

)

2

=

r

2

Match the values in this circle to those of the standard form. The variable

r

represents the radius of the circle,

h

represents the x-offset from the origin, and

k

represents the y-offset from origin.

r

=

8

h

=

−

4

k

=

7

The center of the circle is found at

(

h

,

k

)

.

Center:

(

−

4

,

7

)

These values represent the important values for graphing and analyzing a circle.

Center:  

(

−

4

,

7

)

Radius:

8

A point has zero dimensions. There's no length, height, width, or volume. Its only property is its location.

One Dimension: Once you connect two points, you get a one-dimensional object — a line segment.

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ Slope = rise/run

rise=2

run=1

Final answer:

2/1 or 2

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

The slope of the line is 4/2, or 2/1, or 2 because if you find the rise over run, you will get either 4/2 or 2/1.

Answer:

Time, t = 1.875 seconds

Step-by-step explanation:

It is given that,

Initial velocity of the ball, u = 30 ft/s

DeSean throws a ball from a platform that is at ground level. The equation of motion when an object is thrown vertically upward is given by the following equation as :

[tex]h(t)=-16t^2+vt+h[/tex]

Here, h = 0 since, the ball is thrown up at the ground level. We have to determine the time when the ball be in air. The quadratic equation becomes :

[tex]-16t^2+30t+0=0[/tex]

t = 1.875 seconds  

So, the ball be in air for 1.875 seconds. Hence, this is the required solution.                                    

Answer:

$541.63

Step-by-step explanation:

To find the balance of Gurindas, we need to break down our values.

Checking Balance = $532.14

Checks = $-46.19 + $-138.32 = $-184.51

Deposit =  $200

Service Charge = $-6

Now to find her new balance, we simply add them all together.

New Balance = 532.14 + -184.51 + 200 + -6

New Balance = $541.63

The first one I believe

Answer: A

Step-by-step explanation: rational numbers \can be turned into a fraction so yea.

Answer:

(-5,0) & (9-14)

Step-by-step explanation:

and or subtract seven from both and... BOOM you got your answer

The conic section is Parabola. It intersects at point (0,5) on the y-axis. The domain of the parabola is all real numbers. The range of the parabola is [tex]y\ |y \ge 5[/tex].

The image appears to be a graph of a parabola. Here's the information:

Type of conic section: Parabola

Center: This parabola doesn't have a center, as parabolas are not symmetrical across both axes.

Intercepts: The parabola intersects the y-axis at the point [tex]$(0, 5)$[/tex]. It doesn't intersect the x-axis.

Domain: The domain of the parabola is all real numbers, as it extends infinitely in both directions to the left and right.

Range: The range of the parabola is all real numbers greater than or equal to 5, as it starts at the point [tex]$(0, 5)$[/tex] and extends infinitely upwards.

The center and intercepts of a conic section vary depending on the specific type. The domain and range also differ based on the nature of the conic section, with some having a limited set of x or y values, while others span all real numbers with exceptions.

To identify the center and intercepts of a conic section, we first need the specific equation of the conic section (circle, ellipse, parabola, or hyperbola). The intercepts are the points where the graph intersects the x-axis and y-axis. The center of a conic section (for circles and ellipses) is the point inside the conic section that is equidistant from all points on the curve. For parabolas, the center does not exist since they are open-ended curves, and for hyperbolas, the center is the midpoint between the vertices of the two branches of the curve.

The domain and range are the set of possible x-values and y-values respectively that the function (conic section) can take. For circles and ellipses, the domain and range are limited to the values within the bounds of those shapes. Parabolas have an infinite domain when the axis of symmetry is vertical and an infinite range when the axis of symmetry is horizontal, except if there is a horizontal directrix, which restricts the range. Hyperbolas have a domain and range all real numbers except for values that fall within the 'gap' created by the asymptotes.

Answer:

5 dollars

Step-by-step explanation:

~Jax

Answer:

0.8p or p - 0.2p

Step-by-step explanation:

You can find the price for any house minus the down payment by writing an expression with a variable. Let p be the price of the house. If you pay 20% then the price will be lowered by 20%. You will pay as your mortgage 80% of the price. You can write it as either the expression 0.8p or p - 0.2p.

Answer:

54

$3 dollar coupons were given

Step-by-step explanation:

We can represent this question as a system of equations

Let

x = number of $1 dollar coupons

y = number of $3 dollar coupons

z = number of $5 dollar coupons

Twice as many $1 coupons were given out as $3 coupons,

x = 2*y

3 times as many $3 coupons were given as $5 coupons.

y = 3*z

The total value of all the coupons given out was $360

x*$1 + y*$3 + z*$5 = $ 360

The system results

x   -   2y   +  0    =  0         (1)

0   +  y     -  3z    = 0         (2)

x    + 3*y      +5*z =   $ 360    (3)

We substitute  equation (2) and (1) into (3)

(2y)   + 3*y    + 5*(y/3) =   $ 360

20*y/3  = 360

y = 54

To determine the number of $3 coupons given out by the bakery, we solved the equation 5x + 3(3x) + 1(2(3x)) = $360, where x represents the number of $5 coupons. We found that x = 18, and since there are three times as many $3 coupons as $5 coupons, the bakery gave out 54 $3 coupons.

The question involves solving a system of linear equations to determine how many $3 coupons were given out by the bakery. Let's define the variables first:

Based on the given information, we can set up the following equations:

Now let's solve the equation:

Once we have x, we know that the number of $3 coupons is 3 times x, so:

3x = 3(18) = 54

Therefore, 54 $3 coupons were given out by the bakery.

Answer:

(0,0) (1,2) (2,4) (3,6)

(0,0) (1,2) (2,4) (3,6)

Answer:

0.25

Step-by-step explanation:

Locate the x value -1.5 along the x-axis. It has a matching output or y value on the curve. Draw a vertical line at x = -1.5. Where the line and curve intersect it the output value. Here it estimates as 0.25.

Answer:

0.223 is the answer

Step-by-step explanation:

Here first we draw the graph of y =[tex]y =e^x[/tex]

and in order to find the value of [tex]e^{-1.5}[/tex]

we draw a line x =-1.5

and the point where this line x =-1.5 intersects with given

graph is the required value

which is y =0.223 at  x =-1.5

Below is the graph given

The answer is (D) 5/8 x 1/2

Answer:

[tex]y=-\frac{3}{5} x+6[/tex]

Step-by-step explanation:

Lets solve the equation [tex]3x+5y=30[/tex] for [tex]y[/tex] step-by-step:

Step 1. Subtract [tex]3x[/tex] from both sides of the equation

[tex]3x+5y=30[/tex]

[tex]3x-3x+5y=-3x+30[/tex]

[tex]5y=-3x+30[/tex]

Step 2. Divide both sides of the equation by 5

[tex]\frac{5y}{5} =\frac{-3x+30}{5}[/tex]

[tex]y=\frac{-3x+30}{5}[/tex]

[tex]y=-\frac{3}{5}x+\frac{30}{5}[/tex]

[tex]y=-\frac{3}{5} x+6[/tex]

We can conclude that the equation that can be used for solve for [tex]y[/tex] is [tex]y=-\frac{3}{5} x+6[/tex]

Answer:

y = -3x/5 + 6

Step-by-step explanation:

Given the equation 3x+5y = 30, to find the equation that can be used to solve for y, we will have to make y the subject of the formula from the given linear equation to have;

3x + 5y = 30

First we will subtract 3x from both sides of the equation to have;

3x+5y-3x = 30-3x

5y = 30-3x

Dividing both sides of the equation by the coefficient of y which is 5 we will have;

5y/5 = 30/5-3x/5

y = 6-(3x/5)

y = -3x/5 + 6

Answer:

[tex]y + 1 = -\frac{2}{5}(x+5)[/tex]

and

2x + 15y = -15

Step-by-step explanation:

To write the point slope form, a point and a slope is required. Find the slope using the two points given and the slope formula.

[tex]m = \frac{y_2-y_1}{x_2-x_1}= \frac{-1 --7}{-5-10}= \frac{6}{-15} = -\frac{2}{5}[/tex]

Substitute -2/5 and the point (-5,-1) into the form. Then convert to make the standard form of the equation.

[tex]y - y_1 = m(x-x_1)\\y --1=-\frac{2}{5}(x--5)\\y + 1 = -\frac{2}{5}(x+5)[/tex]

Now convert to standard form by applying the distributive property and moving terms.

[tex]y + 1 = -\frac{2}{5}(x+5)\\y + 1 = -\frac{2}{5}x - 2\\y + 3 = -\frac{2}{5}x\\\frac{2}{5}x + y +3=0\\2x + 5y + 15 = 0\\2x + 15y = -15[/tex]