HELP CHECK THIS

The work of a student to solve a set of equations is shown:


Equation A: y = 15 − 2z

Equation B: 2y = 3 − 4z



Step 1: −2(y) = −2(15 − 2z) [Equation A is multiplied by −2.]

2y = 3 − 4z [Equation B]

Step 2: −2y = 15 − 2z [Equation A in Step 1 is simplified.]

2y = 3 − 4z [Equation B]

Step 3: 0 = 18 − 6z [Equations in Step 2 are added.]

Step 4: 6z = 18

Step 5: z = 3



In which step did the student first make an error?

Step1

Step 2

Step 3 <<<<<

Step 4

[tex]\underline{\ x|\ \ 0\ \ |\ \ 1\ \ |\ \ 2\ \ |\ \ 3\ \ |\ \ 4\ \ |\ \ 5\ \ |}\\U|500\ |\ 255|\ 130|\ 66\ \ |\ 34\ |\ \ 17\ |\\\\U=a(b)^x\\\\for\ x=0,\ U=500\\\\500=a(b)^0\\\\500=a(1)\to \boxed{a=500}\\\\for\ x=1,\ U=255\\\\255=500(b)^1\\\\255=500b\qquad\text{divide both sides by 500}\\\\b=\dfrac{255}{500}\\\\b=\dfrac{255:5}{500:5}\\\\b=\dfrac{51}{100}\to \boxed{b=0.51}\\\\\text{Therefore we have the equation of the function:}\\\\U=500(0.51)^x[/tex]

[tex]\text{Check for other values of x:}\\\\for\ x=2\\\\U=500(0.51)^2=130.05\approx130\qquad CORRECT\\\\for\ x=3\\\\U=500(0.51)^3=66.3255\approx66\qquad CORRECT\\\\for\ x=4\\\\U=500(0.51)^4=33.826\approx34\qquad CORRECT\\\\for\ x=5\\\\U=500(0.51)^5=17.25125\approx17\qquad CORRECT[/tex]

[tex]Answer:\ \boxed{U=500(0.51)^x}[/tex]

Answer:

27 muffins.

Step-by-step explanation:

We have been given that a baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold.

To find the number of muffins sold by noon let us find 45% of 60.

[tex]\text{The number of muffins sold by noon}=\frac{45}{100}\times 60[/tex]

[tex]\text{The number of muffins sold by noon}=0.45\times 60[/tex]

[tex]\text{The number of muffins sold by noon}=27[/tex]

Therefore, 27 muffins were sold by noon.

Answer:

The true statement is UV < US < SR ⇒ 1st statement

Step-by-step explanation:

"I have added screenshot of the complete question as well as the

diagram"

* Lets revise the hinge theorem

- If two sides of one triangle are congruent to two sides of another

 triangle, and the measure of the included angle between these two

 sides of the first triangle is greater than the measure of the included

 angle of the second triangle then the length of the third side of the

 first triangle is longer than the length of the third side of the second

 triangle

* Lets solve the problem

- The figure has three triangles have a common vertex T

- m∠UTV < m∠UTS < m∠STR

- From the hinge theorem above

∵ The side opposite to ∠UTV is VU

∵ The side opposite to ∠UTS is US

∵ The side opposite to ∠STR is SR

∵ m∠UTV < m∠UTS < m∠STR

∴ UV < US < SR

* The true statement is UV < US < SR

Answer:

VU<US<SR by the hinge theorem

Step-by-step explanation:

Final answer:

Marcus is incorrect, not because the result may not be rational, but because of his reasoning. An integer raised to a negative integer exponent leads to the base being inverted and raised to the positive exponent, but the result is still a rational number.

Explanation:

Marcus is incorrect in stating that any time an integer is raised to an integer exponent, the result is a rational number. To understand why, we should look at the case when an integer is raised to a negative integer exponent. For example, 3-2 is equal to 1 / (32) which simplifies to 1 / 9. A negative exponent inverts the base number and raises it to the positive of that exponent, which means the result is still a rational number, as it's a quotient of two integers. Therefore, the correct statement is that the result of an integer raised to any integer exponent is indeed a rational number, as the quotient of two integers (for negative exponents) is also a rational number.

Answer:

Judy = $5/hr

Ben = $4/hr

Step-by-step explanation:

Judy's hours at work - x

Ben's hours at work - y

8x + 10y = 80

9x + 5y = 65

Given these two equations above, we get:

10y = 80 - 8x, which means y = 8 - 0.8x.

Substitute y in the second equation with 8 - 0.8x, so we have:

9x + 5 (8 - 0.8x) = 65

9x + 40 - 4x = 65

5x = 25

x = 5

Come back to the first equation, substitute x:

8*5 + 10y = 80

10y = 80 - 40

y = 4

Answer:

Its D

Step-by-step explanation:

If p then q. If p is true then q is true.

Answer:

it's number d

Step-by-step explanation:

Answer:

[tex]\frac{x^2}{64} + \frac{y^2}{25} =1[/tex]

Step-by-step explanation:

An ellipse with vertices (-8, 0) and (8, 0)

Distance between two vertices = 2a

Distance between (-8,0) and (8,0) = 16

2a= 16

so a= 8

Vertex is (h+a,k)

we know a=8, so vertex is (h+8,k)

Now compare (h+8,k) with vertex (8,0) and find out h and k

h+8 =8, h=0

k =0  

a minor axis of length 10.

Length of minor axis = 2b

2b = 10

so b = 5

General formula for the equation of horizontal ellipse is

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b} =1[/tex]

a= 8 , b=5 , h=0,k=0. equation becomes

[tex]\frac{(x-0)^2}{8^2} + \frac{(y-0)^2}{5} =1[/tex]

[tex]\frac{x^2}{64} + \frac{y^2}{25} =1[/tex]

Answer:

AC is greater than BC because segment AC is the hypotenuse of right triangle ABC, and the hypotenuse is the longest side of a right triangle.

Answer:

(a-f)/6 = r

Step-by-step explanation:

The total Bonnie must pay is the weekend fee plus the hourly rate times the hours worked

Cost = weekend fee * hourly rate* hours

hours = 6

weekend fee =f

hourly rate = r

Cost = a dollars

Substituting in what we know

a = f+ 6r

We want to solve for r

Subtract f from each side

a-f =f-f +6r

a-f = 6r

Divide each side by 6

(a-f)/6 = 6r/6

(a-f)/6 = r

Answer:

-4 is the simplified form. of the given expression.

Step-by-step explanation:

We have been given an expression:

[tex]-64^\frac{1}{3}[/tex]

We can rewrite 64 as [tex]4^3[/tex]

the given expression will be rewritten as:

[tex](-(4)^3)^\frac{1}{3}[/tex]

powers will get cancel out we get:

[tex]-4[/tex] is the required simplified form.

The selling price of the necklace is calculated by adding a 75% markup to the original purchase price of $150, which results in a selling price of $262.50.

To calculate the selling price of a necklace that a jewelry store purchased for $150 with a 75% markup, you first need to find out how much 75% of the purchase price is and then add that to the original purchase price. To do this, multiply the purchase price, $150, by 75% (or 0.75). This calculation gives you the markup amount:

Markup amount = $150 imes 0.75 = $112.50

After finding the markup amount, you add it to the original purchase price to find the selling price:

Selling price = Original purchase price + Markup amount

Selling price = $150 + $112.50 = $262.50

Therefore, the jewelry store will sell the necklace for $262.50.

The answer: C) (-1, -1)

Answer:

Step-by-step explanation:

Let the length of the rectangular prism = x inches

Width of the rectangular prism = 2 x length = 2x inches

Height of the rectangular prism = 3 inches less than the length = (x -3) inches

Volume of the rectangular prism = length x width x height = 392 cubic inches

= (2x) inches x (x) inches x (x -3) inches = 392 cubic inches

= x2(x-3) = 196 cubic inch

X = 8.59 inch

Length of the rectangular prism = x inches = 7 inch

Width of the rectangular prism = 2 x length = 2 x 7 inch = 14 inch

Height of the rectangular prism = 3 inches less than the length = (x -3) inches =  7 – 3 = 4 inch

The dimensions of the storage container are 7 inches in length, 14 inches in width, and 4 inches in height. The volume equation is solved for length by substituting the relationships between height, width, and length into the formula for volume.

To find the dimensions of a rectangular prism storage container with a volume of 392 cubic inches, we need to set up equations based on the information given. The height (h) of the container is 3 inches less than its length (l), so h = l - 3. The width (w) of the container is twice the length of the container, so w = 2l. Knowing that volume = length * width * height (V = lwh), we can substitute the expressions for h and w into the volume equation to obtain an equation with one unknown:

V = l * (2l) * (l - 3)

Substituting the known volume into the equation, we get:

392 = l * (2l) * (l - 3)

This is a cubic equation that can be solved for l (the length of the container). Once l is found, we can also find h and w since they are defined in terms of l.

Let's solve the equation:

[tex]392 = 2l^2 * (l - 3)[/tex]

Divide both sides by 2 to simplify:

[tex]196 = l^2 * (l - 3)[/tex]

Now we expand and solve for l:

[tex]196 = l^3 - 3l^2[/tex]

Moving all terms to one side gives:

[tex]l^3 - 3l^2 - 196 = 0[/tex]

By trial and error or using a cubic equation solver, we find that l = 7 inches. Now we can find the height and width:

h = l - 3 = 7 - 3 = 4 inches

w = 2l = 2 x 7 = 14 inches

Therefore, the dimensions of the storage container are 7 inches in length, 14 inches in width, and 4 inches in height.

Answer:

Step-by-step explanation:

Start at the end and work backwards to do this one.  Mai scored 5 points.

If Noah scores three times what Mai scores, then:

Noah = 3(5) = 15

If Tyler scores 4 points less than Noah, then:

Tyler = 15 - 4 = 11

If Elena scores twice what Tyler scores, then:

Elena = 2(11) = 22

Set up a proportion:

17 miles in 306 minutes, write as 17/306

X miles in 162 minutes, write as X/162

Now set to equal and solve:

17/306 = x/162

Cross multiply:

17 * 162 = 306 *x

2754 = 306x

Divide both sides by 306:

x = 2754 / 306

x = 9

It will travel 9 nautical miles.

Answer:

62 steps per minute.

Step-by-step explanation:

We have been given that Robert climbed 775 steps in [tex]12\frac{1}{2}[/tex] minutes.

To find the the average steps per minute we will divide 775 by [tex]12\frac{1}{2}[/tex].

[tex]\text{The average steps per minute}=775\div 12\frac{1}{2}[/tex]

Let us convert our mixed fraction into improper fraction.

[tex]\text{The average steps per minute}=775\div \frac{25}{2}[/tex]

Dividing a number by a fraction is same as multiplying the number by the reciprocal of fraction.

[tex]\text{The average steps per minute}=775\times \frac{2}{25}[/tex]

[tex]\text{The average steps per minute}=31\times2[/tex]

[tex]\text{The average steps per minute}=62[/tex]

Therefore, Robert climbed 62 steps per minute.

Answer:

62 Steps per minute. <3

Step-by-step explanation:

Answer:

[tex]13\frac{7}{16}[/tex] laps can Fred run in one hour.

Step-by-step explanation:

Given Statement: Fred is running on the school track. He can run [tex]10\frac{3}{4}[/tex]  laps in [tex]\frac{4}{5}[/tex]  of an hour.

Unit rate are expressed as a quantity of 1, such as 3 feet per second or 7 miles per hour, they are called unit rates

From the given condition we have;

In [tex]\frac{4}{5}[/tex] he can run [tex]\frac{43}{4}[/tex] laps

Unit rate per hour = [tex]\frac{\frac{43}{4} }{\frac{4}{5} }[/tex]

                              =[tex]\frac{43}{4} \times \frac{5}{4} = \frac{215}{16}[/tex] laps

Therefore, Fred can run in one hour is, [tex]13\frac{7}{16}[/tex] laps.

Final answer:

To determine how many laps Fred can run in one hour, we used a proportion equation, converting 10 3/4 laps to an improper fraction and then solving for x. Fred can run approximately 13.44 laps in one hour.

Explanation:

Calculating Laps per Hour

To find out how many laps Fred can run in one hour, we need to perform a simple proportion based on the information given. Fred can run 10 3/4 laps in 4/5 of an hour. To find out how many laps he can run in a full hour (1 hour), we set up the proportion equation:

\[\left(\frac{10 \frac{3}{4}}{\frac{4}{5}}\right) = \left(\frac{x}{1}\right)\]

First, we convert 10 3/4 to an improper fraction, which is \(\frac{43}{4}\). Then we solve for \(x\) by multiplying both sides by 1, which simplifies our proportion to:

\[x = \frac{43}{4} \times \frac{5}{4}\]

Next, we multiply the numerators and then the denominators:

\[x = \frac{43 \times 5}{4 \times 4}\]

\[x = \frac{215}{16}\]

Finally, we divide 215 by 16 to get \(x = 13.4375\), which means Fred can run approximately 13.44 laps in one hour.

Answer:

 the required ratio is: 4:9

Step-by-step explanation:

Quinn has 4 cousins who live in Texas, 3 cousins who live in Nebraska, and 9 cousins who live in Michigan.

We have to find the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan

The required ratio is:

[tex]Ratio=\frac{\text{Number of Quinn's cousins who live in Texas}}{\text{cousins who live in Michigan}}[/tex]

[tex]Ratio=\frac{4}{9}[/tex]

Hence, the required ratio is: 4:9

The ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan is 4:9. This means for every 4 cousins in Texas, there are 9 cousins in Michigan.

The subject of this question is Mathematics. Specifically, it involves calculating ratios. In this case, the student wants to know the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan.

The ratio of something is simply a way to compare quantities. Here, we have 4 cousins in Texas and 9 cousins in Michigan. So, to get the ratio from Texas to Michigan, we simply write it as '4:9' or we can say, 'for every 4 cousins in Texas, there are 9 cousins in Michigan'.

In summary, the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan is 4:9.

https://brainly.com/question/32531170

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Step-by-step explanation:

We have been given that AE=BE and [tex]\angle1\cong \angle2[/tex].

We can see that angle CEA is vertical angle of angle DEB, therefore, [tex]m\angle CEA=m\angle DEB[/tex] as vertical angles are congruent.

We can see in triangles CEA and DEF that two angles and included sides are congruent.

[tex]\angle 1\cong \angle 2[/tex]

[tex]AE=BE[/tex]

[tex]\angle CEA\cong\angle DEB[/tex] or [tex]\angle 3\cong \angle 4[/tex]  

Therefore, [tex]\Delta CEA\cong \Delta DEB[/tex] by ASA postulate.

Since corresponding parts of congruent triangles are congruent, therefore CE must be congruent to DE.

Answer:

92 degrees is x

88 degrees is y

Answer:

x=92.  y= 88

Step-by-step explanation:

all three corners of a tri.  equal 180

so 39+49=88

180-88=92 now y and x= 180 also so y

Answer: (2, 9)

Step-by-step explanation:

[tex]\lbrace^{y=5x-1 }_{2y=3x+12}}[/tex]

Since "y" = "5x - 1", we can replace "y" in the second equation with "5x - 1"

    2y = 3x + 12

⇒ 2(5x - 1) = 3x + 12    substituted "y" with "5x - 1"

⇒ 10x - 2 = 3x + 12     distributed 5x - 1 by 2 on left side

⇒  7x - 2 = 12              subtracted 3x from both sides

⇒  7x = 14                    added 2 to both sides

⇒ x = 2                         divided both sides by 2

Next, let's solve for y by substituting "x" with "2":

y = 5x  - 1

  = 5(2) - 1

  = 10 - 1

  = 9    

Answer

m<3  = 49°

Step-by-step explanation:

It is given that,

M∥n, m∠1 = 50°, m∠2 = 48°, and line s bisects ∠ABC

m<DEF = m<1 + m<2 = 50° + 48° = 98°

Corresponding angle of <DEF is equal to <ABC = 98°

To find m<3

< 4 = <5 = 98/2 = 49° (Since line s bisects ∠ABC)

Therefore,

m<3 = 49°  (< 4 and <3 are vertically opposite angles)

Answer:

m∠3 = 49°

Step-by-step explanation:

We are given that the angles m∠1 = 50° and m∠2 = 48° and the line s bisects ∠ABC.

If m∠1 = 50° and m∠2 = 48°, then ∠DEF = 50 + 48 = 98°

So ∠DEB will be equal to = 180 - 98 = 82°

If ∠DEB = 82°, then the angle from A to B will 180 - 82 = 98°.

We know that the line s bisects ∠ABC, therefore the measure of angle m∠3 will be half of 98 = 49°

Final answer:

Dulcina has 26 refrigerator magnets and Hannah has 52, which is 2 times the number of Dulcina's magnets. They have 78 magnets in total.

Explanation:

The question involves a simple algebra problem. Let's say Dulcina has x refrigerator magnets. According to the problem statement, Hannah has 2 times as many refrigerator magnets as Dulcina, so she has 2x magnets. Together, they have 78 magnets, which means x + 2x = 78. To find out how many refrigerator magnets each has, we need to solve for x.

Combine like terms:
3x = 78

Divide both sides by 3 to solve for x:
x = 26

Now, to find the number of refrigerator magnets Hannah has, we multiply x by 2:
2x = 2 × 26 = 52

Answer: 12 hours

Step-by-step explanation:

1.) add 10 1/4 and 9 1/3. You’ll get 19.75

2.) divide 250 by 19.75. You’ll get something close to 12.6582278481 if you use appendix zeros.

3.) round 12.6582278481 to the nearest whole number. It will be 12. Hope this helps :)

D

Angle 7π/6 is π/6 below the negative x-axis in the 3rd quadrant. Its cosine will be -(√3)/2.

Angle 11π/6 is π/6 below the positive x-axis in the 4th quadrant. Its cosine will be (√3)/2.

The cosines have the same magnitude, but their signs are opposite each other. Jeremy was not correct.

To calculate the height of Lucy's cherry tree, we first convert 3 7/10 to an improper fraction, resulting in 37/10. Then we multiply the height of the lemon tree (6 feet) by 37/10 to get 22.2 feet. Thus, the cherry tree is 22.2 feet tall.

To find the height of Lucy's cherry tree, which is 3 7/10 times as tall as her lemon tree, we start with the known height of the lemon tree, which is 6 feet tall. We then multiply this height by the factor 3 7/10 to determine the height of the cherry tree.

First, let's convert the mixed number to an improper fraction to simplify the calculation:

Next, we'll multiply the height of the lemon tree by this fraction:

6 feet × 37/10 = (6 × 37) / 10 = 222 / 10 = 22.2 feet.
So, the height of Lucy's cherry tree is 22.2 feet tall.

The equation in point slope form is y-y1 = m(x-x1)

The first point given is (-13,9) so this is used for Y1 and X1.

m is the slope which is found by the change in Y over the change in x.

The slope is -3 - 9 / 11 - -13, which equals -1/2

So the equation becomes y-9 = -1/2(x+13)

Answer:

y-9=-1/2(x+13)

Step-by-step explanation:

To find the slope for the line, we use

m = (y2-y1)/(x2-x1)

since we know the points( -13,9) and (11,-3)

m= (-3-9)/(11--13)

   =(-3-9)/(11+13)

  =-12/24

  = -1/2

We can use the point slope form to make the equation for the line

y-y1=m(x-x1)

y-9=-1/2(x--13)

y-9=-1/2(x+13)