Solve the system of linear equations by substitution. Check your solution.

Answer:

3. 4x-5=27

4x=27+5

4x=32

x=8

5. 3(2x+3)+3=-2(2-6)

(6x+9)+3=-4+12

6x+9+3=8

6x+12=8

6x=8-12

6x=-4

x=-4/6

x=-2/3

6. 102-4(1+4x)=-4(2-3)

102-4-16x=-8+12

98-16x=4

-16x=4-98

-16x=94

x=94/-16

x=6

x=25,y=15 Not to sure abt this answer but I think I got it

Answer:

\(\frac{7}{10}\)

Step-by-step explanation:

100\(m^{2}\) -5 = 44  Add 5 to both sides

100\(m^{2}\) = 49  Divide both sides by 100

\(m^{2}\) = \(\frac{49}{100}\)

\(\sqrt{m^{2} }\) = \(\frac{\sqrt{49} }{\sqrt{100} }\)

m = \(\frac{7}{10}\)

Evaluating the expression results to

To simplify the given expressions, we substitute the values of A, B, C, and D into the expressions and perform the necessary calculations.

A - 2(B - A) - 3B:

Substituting the values:

8 - 2 * (10 - 8) - 3 * 10

Simplifying the expression inside parentheses

8 - 2(2) - 3 * 10

8 - 4 - 30

Performing subtraction

8 - 4 - 30

-18

Therefore, A - 2(B - A) - 3B simplifies to --18

evaluate the second expression C(4-D)+2CD:

C = 16

D = 11

Substituting the values:

16(4 - 11) + 2(16)(11)

Simplifying

16(-7) + 2(16)(11)

-112 + 352

240

Therefore, the value of the expression C(4-D)+2CD, when C = 16 and D = 11, is 240.

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Answer:B

Step-by-step explanation:

Answer:

Equation 2: y=750-100x

Step-by-step explanation:

Answer:

he values of F(x) between x=1 and x=3 are 1, 4, and 9.

Step-by-step explanation:

To find the value of F(x) between x=1 and x=3, we need to substitute the values of x into the given function F(x) = x^2 and evaluate the function at each value. This gives us:

F(1) = 1^2 = 1

F(2) = 2^2 = 4

F(3) = 3^2 = 9

Therefore, the values of F(x) between x=1 and x=3 are 1, 4, and 9.

Answer:

The new jar is smaller.

Step-by-step explanation:

Like what the statements says, the normal size of coffee is reduced by 1/5 and it become as the new jar which is smaller than the original.

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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Answer:

\(\huge\boxed{\sf r = 5}\)

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

\(\rule[225]{225}{2}\)

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

Answer:

P[ X < 2,4 ]  = 0,1587   or   15,87 %

Step-by-step explanation:

Normal Distribution  N ( 2,6 , 0,2 )

mean = μ₀ = 2,6 ft  and

standard dviation is

σ = 0,2 ft

Samle size 53    n  = 53

2,4 - 2,6 = 0,2

That means the difference between 2,4 and the mean of the sample ( 2,6) is equal to one standar deviation.  The empircal rule establishes that the interval [  μ₀ ± σ]  contans 68,3 % of all values, by symmetry

μ₀ - σ = 68,3/2

μ₀ - σ = 34,15

Then the half of the bell shape curve is 0,5 and  from 0,2 up to 0 ( the normalized μ₀ ) is 34,15 then dfference between

0,5 - 0,3415   =  0,1585  or   15,85% is the probability

Other procedure is:

P[ X < 2,4 ]  = [X  -  μ₀ ] / σ

P[ X < 2,4 ]  = 2,4 - 2,6 / 0,2

P[ X < 2,4 ]  = - 0,2/0,2

P[ X < 2,4 ]  = - 1

And fom z - table we find for z (score) = - 1

P[ X < 2,4 ]  = 0,1587

Answer:

0.0668

Step-by-step explanation:

z=x−μσ=2.3−2.60.2=−1.50

Using the normal distribution tables, we find that the area under the standard normal curve to the left of z=−1.50 is approximately 0.0668. Thus, the probability that an individual man’s step length is less than 2.3 feet is approximately 0.0668.

Answer:

6w = 30

Step-by-step explanation:

We should know that the 30 inches of framing material were used to frame the four sides of the rectangle.

The perimeter of the rectangle is what we should be considering, whenever we are dealing with frames.

This is 2 X (length + width)

From the questions, we can get the dimensions of the rectangle using clues from the various statements made.

From the statement"a rectangular painting length more than twice the width" we can see that the

L = 2w ------------------------- equation 1

substituting this value into the formula for the perimeter of the rectangle we have

30 = 2(2w + w)

30 = 6w

w= 5

from equation 1

L =2 X (5) = 10

Hence, we can set up the equation

6w = 30

However, the closest option to what we have is option D

6w + 6 = 30 - 4

complete question:

Lisa is framing a rectangular painting. The length is three more than twice the width. She uses 30 inches of framing material. What is the length of the printing? Write an equation and solve

Answer:

D.6w + 6 = 30 = 4

Step-by-step explanation:

perimeter = 30 inches

width = w

length = 2w + 3

perimeter of a rectangle = 2l + 2w

where

w = width

l = length

Therefore,

perimeter of a rectangle = 2(2w + 3) + 2w

perimeter of the rectangle = 4w + 6 + 2w

perimeter = 6w + 6

recall

perimeter = 30 inches

6w + 6 = 30

6w = 24

divide both sides by 6

w = 24/6

w = 4

Answer:

a)168.725

b)168.735

168.725≤x<168.735

Step-by-step explanation:

a)168.73 - 0.005

168.725

b) 168.73 + 0.005

168.735

Answer:

x<2

Step-by-step explanation:

2x+6<10

2x<10-6

2x<4

x<4/2

x<2

Answer:

It should be a kilogram.

Gram = too small

milligram = too small

meter = distance

Answer:

19/4

Step-by-step explanation:

Solving the provided question, we can say that the quadratic equation is \((x - 1)(x^{2} + 3x - 4)\) = \(x^{3} + 2x^{2} - 7x + 4\) and the roots of the polynomial are x = 1, -1, 4.

A quadratic polynomial in a single variable is represented by the equation  \(ax^{2}+bx+c=0\). a 0. Since this polynomial is of second order, the Fundamental Theorem of Algebra guarantees that it has at least one solution. There are both simple and complex solutions.

A quadratic equation is just that—quadratic. It has at least one word that has to be squared, as shown by this. One of the often used solutions for quadratic equations is "ax2 + bx + c = 0." where X is an undefined variable and a, b, and c are numerical coefficients or constants.

the quadratic equation is

\((x - 1)(x^{2} + 3x - 4)\) = \(x^{3} + 2x^{2} - 7x + 4\)

On multiplying,

⇒ \(x (x^{2} + 3x - 4) - (x^{2} + 3x - 4)\)

⇒ \(x^{3} + 3x^{2} - 4x - x^{2} - 3x + 4\)

⇒ \(x^{3} + 2x^{2} - 7x + 4\)

∴ We can say that LHS = RHS.

From given equation, the roots of the equation will be  -

\((x - 1)(x^{2} + 3x - 4)\)

⇒ x - 1 = 0

⇒ x = 1

\(x^{2} + 3x - 4 = 0\)

⇒ \(x^{2} - 4x + x - 4\)

⇒ \(x(x - 4) + 1(x - 4)\)

⇒ (x + 1) (x - 4)

⇒ x = -1, x = 4

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Answer:

The very last one is a function

Step-by-step explanation:

The last one is a function because there are no y values that repeat. For example, If the points on one graph are like this; (1, 3) (2, 3); then it cannot be a function, the y values cannot repeat if it is a function.

To make things easier, just try to imagine vertical drawing lines through each point in every graph, if this imaginary vertical line passes more than one point in any graph, then that graph is not a function.

I hope this helps!! :D

Answer:

The last graph represents a function.

Explanation:

A function cannot be one-to-many, i.e., one value of x cannot produce multiple values of y.

In the first graph, when x = 1, y = 3 and y= -2, so it is not a function.

In the second graph, when x = 2, y = 2 and y = -2, so it's not a function.

In the third graph, when x = -3, y = 2 and y = -2, so it's not a function.

∴ In all the graphs except the last, single values of x give multiple values of y on the graph, so they are not functions.

Answer:

Total games played = 25

Step-by-step explanation:

Percentage games won by the basketball team = 36%

Exact number of games won by the team = 9

Let the total games played by the team = x

Therefore, total number of games won = 36% of x

                                                                 = \(\frac{36}{100}\times x\)

Equation which represents the games won by the team will be,

\(\frac{36}{100}\times x=9\)

x = \(\frac{9}{0.36}\)

x = 25

Therefore, total games played by the basketball team are 25.

Answer:

15a+14d

Step-by-step explanation:

I just combined like terms

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Answer:

x = 19.6

Step-by-step explanation:

The sum of the angles of a triangle is 180.

<A + <B+ < C = 180

x + 5x + 4x - 16 = 180

Combine like terms.

10x-16=180

Add 16 to each side.

10x-16+16 = 180+16

10x = 196

Divide each side by 10.

10x/10 = 196/10

x = 19.6

Answer :

Step-by-step explanation :

According to the question It is given that,

We will apply angle sum property in the question.

Angle sum property states that sum of all the angles of triangle is 180°

\(\: :\implies \) ∠A + ∠B + ∠ C = 180

\(\: :\implies \) x + 5x + 4x - 16 = 180

\(\: :\implies \) 10x - 16 = 180

\(\: :\implies \) 10x = 180 + 16

\(\: :\implies \) 10x = 196

\(\: :\implies \) x = 196/10

\(\: :\implies \) x = 19.6

Therefore, The Measure of Angle A is 19.6°

The part of the expression which represents the discounted price before tax is x-35.

The given expression is 0.12x+(x-35).

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

a) The part of the expression represents the discounted price before tax is x-35

b) The part of the expression represent the amount of sales tax in dollars is 0.12x

Hence, the part of the expression which represents the discounted price before tax is x-35.

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We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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Answer:

he will be able to make fewer balls

Step-by-step explanation:

80 times nine is 720 and max only has 700

Answer:

Ann will serve 40 people with 24 bags of salad

Step-by-step explanation:

3,  6,  9,  12,   15,  18,  21,  24

5,  10, 15, 20, 25, 30, 35, 40

Answer:

Step-by-step explanation:

2 over 3 to the power of 2 + 5 × 2 − 4

(2/3)^2 +5×2−4

=4/9 + 10-4

=4/9+10−4

=4/9+6

= \(6 \frac{4}{9} \)

Therefore, 6 4/9 is ur answer

The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Answer:

A) (x-4)(x+16)

Step-by-step explanation:

\(x^2+12x-64\\=x^2-4x+16x-64\\=x(x-4)+16(x-4)\\=(x+16)(x-4)\)

Answer:

12 1/2

Step-by-step explanation:

2 x 5 = 10

1/2 x 5 = 2 1/2

10 + 2 1/2 = 12 1/2