Miguel buys eggs and apples at the store.
• He pays a total of $56.97.
• He pays a total of $6.17 for the eggs.
• He buys 8 bags of apples that each cost the same amount.
.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.

Answer:

C

It's a direct variation because you have a constant of 1.25 and no y intercept

Answer:

yes, the Temperature is 5 F

Step-by-step explanation:

-3 + 8 = 5

Answer:

  angle 1 = 108°

Step-by-step explanation:

You want the measure of angle 1, given the measure of angle 4 is 72° in the diagram.

Angles 1 and 4 are a linear pair, so are supplementary:

  angle 1 + angle 4 = 180°

  angle 1 + 72° = 180°

  angle 1 = 108° . . . . . . . subtract 72°

Answer:

Step-by-step explanation:

9*(15/2)[2+14] = 9*15*16 = 2160.

Answer:

Simplifying

y = 6x + -2

Reorder the terms:

y = -2 + 6x

Solving

y = -2 + 6x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying

y = -2 + 6x

Answer:

Ok, for f(x) = x^2 we have only one x-intercept (actually, two equal x-intercepts) at x = 0.

Now, for g(x) = (x - 2)^2 - 3

First, let's analyze the transformations.

When we have g(x) = f(x - a) this means that we moved "a" units to the right (if a is positive)

When we have g(x) = f(x) + a, this means that (if a > 0) we move the graph "a" units up.

In this case we have both those transformations:

g(x) = f(x - 2) - 3

this means that we move 2 units to the right, and 3 units down (because the number is negative)

now we can find the roots of g(x) as:

g(x) = (x - 2)^2 - 3 = x^2 - 4x  + 4 - 3 = x^2 - 4x + 1 = 0

using the Bhaskara's equation:

\(x = \frac{4 +-\sqrt{4^2 - 4*1*1} }{2*1} = \frac{4 +- 3.5}{2}\)

then the roots are:

x = (4 + 3.5)/2 = 3.75

x = (4 - 3.5)/2 = 0.25

Here we have two different x-intercepts

Based on the Law of Cosines; it was proven that:

Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.

Based on the unshaded triangle, we can find that:

cos Θ = x/a

Next, we will prove that: cos (180 - C) = x/a

Remember that:

cos (A + B) = cos A cos B - sin A sin B

Law of Cosines: c² = a² + b² - 2ab. cos C

cos C = - [c² - (a² + b²)] /2ab ... (i)

Then:

cos Θ = cos (180 - C)

cos (180 - C) = cos 180 . cos C - sin 180 . sin  C

We subtitute equation (i):

cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C

cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)

If we focus on the unshaded triangle, we can find an equation of a, where:

a² = h² + x² ... (iii)

And if we combine both triangle into a giant triangle, we can make another equation of c. where:

c² = (x + b)² + h² ... (iv)

We will subtitute equation (iv) into equation (ii):

cos (180 - C) =  [c² - (a² + b²)]/ 2ab

cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab

cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)

We subtitute equation (iii) into equation (v):

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab

cos (180 - C) = [a² + 2bx - a²] / 2ab

cos (180 - C) = 2bx / 2ab

cos (180 - C) = x/a --> PROVEN!

Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.

We know that:

a² + b² - 2ab cos C = c²

c² = (x + b)² + h²

We will try to find the value of cos C:

a² + b² - 2ab cos C = (x + b)² + h²

a² + b² - 2ab cos C = x² + b² + 2bx + h²

a² - 2ab cos C = a² + 2bx

- 2 ab cos C = 2bx

cos C = - x/a

We will subtitute the value of cos C under the Law of Cosines:

c² = a² + b² - 2ab cos C

c² = a² + b² - 2ab (- x/a)

c² = a² + b² + 2bx --> PROVEN!

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Answer:

2.25

Step-by-step explanation:

9 × 250 m = 2250 mL

1 L = 1000 m

2250 mL × (1 L)/(1000 mL) = 2.25 L

Answer:

see explanation

Step-by-step explanation:

(1)

Δ MNK ≅ Δ RTP

to find the congruent triangle to MNK , express the vertices in the same order, that is

M is at the right angle then start with R in the other triangle , followed by

N at the end of the leg and K the third vertex

the same order in the other triangle is R → T → P

then

Δ MNK ≅ Δ RTP

(2)

NM is congruent to TR

TR are the first 2 letters in Δ TRP

the congruent side will be the first 2 letters of Δ NMK , that is NM

then

NM is congruent to TR

(3)

corresponding sides in the 2 triangles are congruent , that is

TR = NM , that is

3x - 1 = 20 ( add 1 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

For the logarithmic function ln(x + y) = 5, the exponential function is obtained as \(e^5 = x + y\).

What is an exponential function?

The formula for an exponential function is \(f(x) = a^x\), where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

To rewrite the equation in exponential function form, we need to recall that the natural logarithm function, ln(x), is the inverse of the exponential function \(e^x\).

In other words, if ln(x) = y, then \(e^y = x\).

Applying this idea to the given equation, we have -

ln(x + y) = 5

\(e^5 = x + y\)

Therefore, the exponential form of the equation is \(e^5 = x + y\).

In this form, we can see that \(e^5\) is the sum of x and y.

The exponential form is useful in situations where we want to solve for x or y, or when we need to simplify expressions involving logarithms.

Therefore, the equation is obtained as \(e^5 = x + y\).

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Answer:

$192

Step-by-step explanation:

Bill: $160.00

Tip: 20%

To figure out 10%, you need to move the decimal point over to the left one place: $16.00

10%: $16.00

16 times 2= $32.00

160.00+32.00= $192.00

Answer:

Ray

Step-by-step explanation:

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray. A ray is named using its endpoint first, and then any other point on the ray

The equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are (b) 2.3p – 10.1 = 6.49p – 4 and (c) 230p – 1010 = 650p – 400 – p

The equation is given as

2.3p – 10.1 = 6.5p – 4 – 0.01p

Evaluate the like terms on the right-hand side

So, we have the following representation

2.3p – 10.1 = 6.49p – 4

The above equation is indicated in option (b)

Multiply through the equation by 100

So, we have:

100(2.3p – 10.1 = 6.5p – 4 – 0.01p)

Evaluate

230p – 1010 = 650p – 400 – p

The above equation is indicated in option (c)

Hence, the equations with the same solution are (b) and (c)

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The expression to represent the average rate of Priya is (5.6×2)÷13 and the average rate is approximately  0.86 miles per hour .

Laura jogs for 2 hours at the rate of 5.6 miles per hour.

Distance travelled = speed × time

= 5.6 × 2

= 11.2 miles

Priya jogs the same distance in 13 hours.

Now to calculate the average rate of Priya we haver to divide the total distance travelled by the total time taken to complete the journey.

Average rate of Priya:

= 11.2 / 13

= 0.86153

≈ 0.86 miles per hour

You will be better able to appreciate the pace of a journey if you are aware of average speed. The speed may occasionally fluctuate while travelling. The need of determining the average speed then increases in order to estimate how quickly the trip will be completed.

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The ordered pairs is a solution to the equation are: (1, -7/5) and (12, 3)

An equation is an expression that shows the relationship between two or more numbers and variables.

We have to find the ordered pair of a solution to the equation:

Equation is 2x - 5y = 9

For ordered pairs: (1, y)

2x - 5y = 9

2(1) - 5y = 9

y = -7/5

For Pair (x,3)

2x - 5y = 9

2(x) - 5(3) = 9

x = 9 + 15 /2

x = 12

Hence, The ordered pairs is a solution to the equation are: (1, -7/5) and (12, 3)

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Answer:

35m³ + 33m² - 38m - 6

Step-by-step explanation:

simplify ( 7m + 1 )( 5m^2 + 4m - 6 )

= 7m * 5m² + 7m * 4m - 7m * 6 + 5m² + 4m - 6

=7 * 5mm² + 7 * 4mm - 7 * 6m + 5m² + 4m

= 35m³ + 33m² - 38m - 6

Answer:

Width = 108 cm

Step-by-step explanation:

Perimeter =  2 x (length + width)

297 = 2 x (length + width)

148.5 = Length + width

Ratio of Length to Width = 3 : 8

Sum of ratio = 11

\(Length = \frac{3}{11} \times 148.5 = 40.5 \ cm\\\\Width = \frac{8}{11} \times 148.5 = 108 \ cm\)

Answer:

See like terms have the same variables

E.g 2x+4y-x+7y

We should take the same variable together with the same signs so here

2x-x will be 1x

4y+7y will be 11 y

So x+11y

Hope it helps!

Answer:

40 pizzas in total

Step-by-step explanation:

10×4=40

Answer:

a)  \(t_{0.035},11=\pm2.201\)

b)  \(t=-2.963\)

c)  \(Reject\ H_0\ when\ \alpha=0.05\)

d)   \(t<t_{\alpha/2},d_t\)

   \(-2.963<2.201\)

Step-by-step explanation:

From the question we are told that:

Sample size \(n=12\)

Mean \(\=x=42.5\)

Standard deviation \(\sigma=3.8\)

Population mean \(\mu=45.75\)

Significance \(\alpha=0.05\)

Generally the hypothesis given by

\(H_0;\mu=45.75\\H_1:\neq =45.75\)

Generally the equation for test statistics is mathematically given by

\(t=\frac{\=x-\mu}{\sigma/\sqrt{n} }\)

\(t=\frac{42.5-45.75}{3.8/\sqrt{12} }\)

\(t=-2.963\)

Generally the Critical value is mathematically given by

\(t_{\alpha/2},d_t\)

\(\alpha=0.05 \\\alpha/2=0.025\\d_t=n-1=11\)

\(t_{0.035},11\)

From table

\(t_{0.035},11=\pm2.201\)

Therefore

\(t<t_{\alpha/2},d_t\)

\(-2.963<2.201\)

\(Reject\ H_0\ when\ \alpha=0.05\)

what's the question?

Answer:

Step-by-step explanation:

what is 12/21 + 18/21 + 14/21

(12 + 18 + 14)/21 =

44/21

Answer:

3x^2-3x+4

Step-by-step explanation:

(-2x^2+x+6)+(5x^2-4x-2)

-2x^2+x+6+5x^2-4x-2

3x^2-3x+4

Answer:

32.1 pounds

Step-by-step explanation:

Given data

Percentage of body fat= 19.8%

Weight= 162pounds

Let us find 19.8% of the persons weight

=19.8/100*162

=0.198*162

=32.076

Therefore, 32.1 pounds of the weight is fat

Answer:

A) y=-4x+20

Step-by-step explanation:

y-y1=m(x-x1)

y-8=-4(x-3)

y=-4x+12+8

y=-4x+20

The mean bonus paid by large companies to their executives is $5 million and the modal class is 3.5-6.5.

To find the mean, we need to find the midpoint of each class and multiply it by the frequency, then add up all of these values and divide by the total frequency:

Class boundaries Midpoint Frequency Midpoint x Frequency

0.5-3.5 2                          11                                         22

3.5-6.5 5                          12                                        60

6.5-9.5 8                           4                                        32

9.5-12.5 11                           2                                       22

12.5-15.5 14                           1                                        14

Total 150  

Mean = (Midpoint x Frequency) / Total Frequency

Mean = 150 / 30

Mean = 5

Therefore, the mean bonus paid by large companies to their executives is $5 million.

To find the modal class, we need to look for the class with the highest frequency. In this case, the class with the highest frequency is 3.5-6.5, with a frequency of 12. Therefore, the modal class is 3.5-6.5.

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Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient

Let f:R⇒S be a surjective homomorphism of rings with identity.

We have to find if R is a PID, prove that every ideal in S is principal.

We know that,

Let I be the ideal of S

Since f is sufficient homomorphism.

So, f⁻¹(I) is an ideal of R.

Since R is PID so ∈ r ∈ R such that

f⁻¹(I) = <r>

I = <f(r)>

Therefore,

Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

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