Natalie takes a car to a title loan business to borrow some money. Natalie is given $3,200.00. She must pay back the $3,200.00 in addition to a $1,000.00 fee in 4 months.

What simple interest rate is she being
charged?

Round to the nearest tenth of a percent and don't forget to include a percent sign, %, in your answer.

Natalie is being charged a simply interest rate of ______.

Answer:

11 inches

Step-by-step explanation:

If one inch represents 210 feet, then divide 2310 by 210 to get the number of inches in the scale drawing.

Answer:

11 inches

Step-by-step explanation:

2310/210 = 11

Answer:

5.85369.421.5 does not have a quotient because it is not a mathematical expression.

40.42 ÷ 4.3 = 9.4

15.48 ÷ 0.72 = 21.4

86.4 ÷ 2.4 = 36.0

50.31 ÷ 8.6 = 5.84

Answer:

D = -15g² - 20g

-5g × 3g -5g×4

= -15g² -20g

# to put in ² when typing hold 2 for 5seconds...

#like please

Answer: 8k^2 - 19k + 12

Step-by-step explanation: The way we found this answer was by simplifying the expression.

Step 1 : We want to get (x-2) in the numerator so we could cross it out with the x-2 at the bottom to get our simplified expression.

(8k^3-19k^2+2k+10)/(k-2) = (x-2)(8k^2-17k+5)/(x-2)

You would need to factor out the (x-2)

Step 2: When you cross the (x-2) above with the (x-2) below you end up with 8K^2-17k+5 as the answer.

Answer:

[tex]8k^2-3k-4+\frac{2}{k-2}[/tex]

Step-by-step explanation:

⭐ See the image I attached to my answer to see the working.

⭐ I recommend you look at the image while following along with the steps to understand the steps.

1. See what multiplies with the first term in the divisor to get the first term in the dividend. Then, put that answer in the quotient space.

2. Under the first term in the dividend, write a - sign and open parentheses. Put the first term inside the parentheses.

3. Multiply what you put in the quotient space from step #1 with the second term in the divisor.

4. Put the product from step #3 inside of the parentheses.

5. Subtract the first two terms in the parentheses from the first two terms in the dividend.

. . . . . . . . . . . . . note: in polynomial division, you will not always subtract two terms. we are subtracting two terms here because there are two terms in the divisor.

6. Write the answer from #5 under the parentheses, and bring down another term from the dividend.

7. See what multiplies with the first term in the dividend to get the answer from #5. Then, put that answer in the quotient space.

8. Under step #6, write a - sign and open parentheses. Put the answer from #5 inside the parentheses.

9. Multiply the answer from #7 with the second term in the divisor.

10. Next to the answer from step #8, write the product of step #9.

11. Subtract the terms from step #10 from step #6.

12. Repeat until you have "brought down" all of the terms from the dividend.

After you are done, your remainder will not be 0. Instead, it will be +2. When you have a remainder that isn't 0, you cannot use the quotient as your answer. Instead, you have to write your answer in this format:

[tex]q(x)+\frac{r(x)}{d(x)}[/tex], where q(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

⇒ q(x) = [tex]8k^2-3k-4[/tex]

⇒ r(x) = +2

⇒ d(x) = k -2

⇒ [tex]8k^2-3k-4+\frac{2}{k-2}[/tex]

The correct statement that assigns a random integer between 1 and 10, inclusive, to rn is (D).

int rn = (int) (Math.random() * 10) + 1.

The method Math.random() generates a random number between 0 and 1, inclusive. If we multiply this number by 10, we will get a random number between 0 and 10, exclusive. If we then add 1 to this number, we will get a random number between 1 and 11, exclusive. If we then take the integer part of this number using the (int) cast, we will get a random integer between 1 and 10, inclusive. This is exactly what statement (D) does.

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1. The triangles are congruent based on the SSS congruence theorem.

2. The information is not enough.

3. Both are congruent by the HL congruence theorem.

If two triangles have a pair of congruent hypotenuses and a pair of congruent legs, then both triangles ae congruent to each other based on the HL congruence theorem.

The SSS Congruence Theorem states that if any two triangles have three pairs of corresponding sides that are congruent to each other, then the triangles are congruent.

1. Based on the SSS congruence theorem, the pair of angles in figure 1 are congruent.

2. There is no information available that shows the triangles have a pair of congruent hypotenuses, nor have three pairs of corresponding congruent sides. Th information given is not enough to prove that they are congruent by SSS or HL.

3. Based on the HL congruence theorem,, they are congruent to each other.

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Answer: X= -1± √(-1)² - 4(7)(9)

2(7)

Step-by-step explanation: The correct equation for using the quadratic formula to solve 7x² = 9 + x for x is:

X= -1± √(-1)² - 4(7)(9)

2(7)

The quadratic formula is given by the equation X = -b ± √(b² - 4ac) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, we have a = 7, b = 1, and c = 9, so plugging these values into the formula gives us the equation above.

The equation used to solve Quadratic Equation is -1 ± [√((-1)² - 4(7)(-9])/2(7)

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

we have the Quadratic Equation as:

7x² = 9+ x

7x² -x -9= 0

Using Discriminant method

x = -b ± √(b² -4ac)/2a

x = 1 ± √(1² - 4(7)(-9)/2(7)

x = 1 ± √(1 + 196)/14

Thus, the formula used 1 ± [√(1² - 4(7)(-9])/2(7)

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Answer:

D.

Step-by-step explanation:

Thousandhts

Answer:

d. 7 thousandths

WHY?

0.007 places is a decimal representation of a number. In the decimal system, the value of a digit is determined by its position relative to the decimal point. In this case, the number 0.007 has three digits to the right of the decimal point, so it is said to have three decimal places. The value of each digit in this number is determined by its position: the first digit (0) is in the hundredths place, the second digit (0) is in the thousandths place, and the third digit (7) is in the ten-thousandths place.

A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it. The lateral line receptors are most likely is Mechanoreceptors.

Given that,

A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it.

We have to find according to your understanding of sensory receptors, the lateral line receptors are most likely is.

We know that,

A fish uses its lateral lines, rows of sensory receptors along each side of its body, to sense vibrations in the water around it. According to your understanding of sensory receptors, the lateral line receptors are most likely is Mechanoreceptors.

Mechanoreceptors, also known as Mechanoreceptors, are specialized neurons that react to pressure and deformation caused by mechanical forces. They are surrounded by sensory neurons, which translate external pressure into electrical signals that are sent to the brain.

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Answer: -28

Step-by-step explanation:

Mutiply by 7 on both sides, it cancels out to the left and then -4 (7) equals -28 so n= -28

Answer:

-28

Step-by-step explanation:

Multiply both sides by 7

That cancel outs the denominator 7 out and multiples -4 to -28

now all that's left is 1n or just n = -28

By using algebra equation, the zeros of f(x)f(x) is ;

x = (-4 + 2i) and x = (-4 - 2i)

Given data :

This is a synthetic division shortcut. Write down the real root, then under a division symbol, the coefficients of the variables, 2, 18, 56, and 40. Drop down the 2 first, multiply by the root (-1) and add it to the next coefficient (18). 2*(-1) = -2, -2 + 18 = 16. Drop that one down. Next multiply 16 by the root, (-1) and add that to the next coefficient, 56 + (-16) = 40, drop down the 40, then lastly repeat this, multiply 40 by the root (-1) and add to the last coefficient 40 + (-40) = 0. If the remainder was not 0, then -1 would not have been a real root.

-1 | 2 18 56 40

......0 -2 -16 -40

--------------------

......2 16 40 0

Put these into another equation, (2x2 + 16x + 40)

Factoring out a 2 we get 2(x2 + 8x + 20)

The factors of 20 are 2*10 and 4*5. 2+10 = 12, 4+5 = 9, so we must use the quadratic equation to find our roots.

-8 ± √(64 - 4(20))/2 = -4 ± √(-16)/2 = -4 ± 4i/2 = -4 ± 2i

So the other two roots are x = (-4 + 2i) and x = (-4 - 2i)

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Answer:

y = x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

here m = 1 , then

y = x + c ← is the partial equation

to find c substitute (2, 3 ) into the partial equation

3 = 2 + c ⇒ c = 3 - 2 = 1

y = x + 1 ← equation of line

This question doesn't seem completed to me. Is there anything more after this?

Answer:

[tex]tn = {3 \times \sqrt{2} }^{n - 1} [/tex]

Step-by-step explanation:

since it is geometric sequence we will use the formula

[tex]tn = {ar}^{n - 1} [/tex]

n = 10

r = √2

a = 3

lets first see the result of the 10th term

[tex]t10 = {ar}^{10 - 1} [/tex]

[tex]t10 = {ar}^{9} [/tex]

[tex]t10 = {3 \times \sqrt{2} }^{9} [/tex]

t10 = 3 × 22.63

t10 = 67.89

approximately 68

t10 = 68

for the nth term

Tn = ar^n–1

[tex]tn = {3 \times (\sqrt{2} })^{n - 1} [/tex]

i hope this helps

Answer:

[tex]a_n=3\left(\sqrt{2}\right)^{n-1}[/tex]

[tex]a_{10}=48 \sqrt{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given:

Substitute the given values of a and r into the formula to create an equation for the nth term:

[tex]a_n=3\left(\sqrt{2}\right)^{n-1}[/tex]

To find the 10th term, substitute n = 10 into the equation:

[tex]\implies a_{10}=3\left(\sqrt{2}\right)^{10-1}[/tex]

[tex]\implies a_{10}=3\left(\sqrt{2}\right)^{9}[/tex]

[tex]\implies a_{10}=3 \cdot 2^{\frac{9}{2}}[/tex]

[tex]\implies a_{10}=3 \cdot 2^{4+\frac{1}{2}}[/tex]

[tex]\implies a_{10}=3 \cdot 2^{4} \cdot 2^{\frac{1}{2}}[/tex]

[tex]\implies a_{10}=3 \cdot 16 \cdot \sqrt{2}[/tex]

[tex]\implies a_{10}=48 \sqrt{2}[/tex]

Answer: She needs to invest 6,000 in bonds,6,000inbonds,12,000 in CDs and 2000 in the Savings account to earn a2000intheSavingsaccounttoearna1000 interest.

We follow these steps in order to arrive at the answer:

Let the amount invested in bonds be x

Since the amount to be invested in CDs is twice the investment in bonds, investment in CDs will 2x.

The amount to be invested in the savings bank will be 20000 - (x+2x)20000−(x+2x) or 20,000 - 3x20,000−3x

The interest earned on bonds will be 0.06x0.06x

The interest earned on CDs will be 2x*0.05 = 0.1x2x∗0.05=0.1x

The interest earned on the savings banks accounts will be (20,000-3x)*0.02 = 400-0.06x(20,000−3x)∗0.02=400−0.06x

The total expected interest of $1000 is the sum total of the interest earned from each of the three modes of investment.

Hence total interest is:

1000 = 0.06x + 0.1x+ 400 -0.06x1000=0.06x+0.1x+400−0.06x

Simplifying we get,

1000 -400 = 0.1x1000−400=0.1x

600 = 0.1x600=0.1x

\mathbf{x = 6,000}x=6,000

Since x represents investments in bonds, the investment in CDs will be \mathbf{2x = 2*6,000 = 12,000}2x=2∗6,000=12,000

Finally the investments in savings bank will be \mathbf{20000 - (12,000 + 6,000) = 20,000 - 18,000 = 2,000}20000−(12,000+6,000)=20,000−18,000=2,000

The linear model that could be used to calculate cost of mailing a large envelope is L(x) = 0.88 + 0.2(x – 1) and used to calculate cost of mailing a package is P(x) = 1.71 + 0.17(x – 3). The weight at which the cost a large envelope and a package will cost the same amount to mail is 17 ounces.

Linear models are used to describe a continuous response variable as a function of one or more predictor variables. Let x be the weight in ounces and L be the cost of mailing a large envelope. Based on the provided information, the cost of mailing a large envelope increases with increasing weight. The cost of mailing one ounce is $0.88 and increased by $0.2 for each additional weight. Hence,

L(x) = 0.88 + 0.2(x – 1)

Let x be the weight in ounces and P be the cost of mailing a package. Based on the provided information, the cost of mailing a package remains the same for weight of 1 to 3 ounces at the cost of $1.71, and then increases by $0.17 for each additional weight. Hence,

P(x) = 1.71 + 0.17(x – 3)

The weight at which a large envelope and a package will cost the same amount to mail is determined by equating the two models.

L(x) = P(x)

0.88 + 0.2(x – 1) = 1.71 + 0.17(x – 3)

0.88 + 0.2x – 0.2 = 1.71 + 0.17x – 0.51

0.68 + 0.2 x = 0.17 x + 1.2

0.2x – 0.17x = 1.2 – 0.68

0.03x = 0.52

x = 17.33 ≈ 17 ounces

Note: The question is incomplete. The complete question probably is: Provided table indicates the U.S. Postal Rates for large envelopes and packages of different weights. a) Create a linear model that could be used to calculate the cost to mail a large envelope, given its weight in ounces. Use L to represent the cost to mail a large envelope and x to represent the envelope weight in ounces. Create a linear model that could be used to calculate the cost to mail a package, given its weight in ounces. Use P to represent the cost to mail a package and x to represent the package weight in ounces. Find the weight at which a large envelope and a package will cost the same amount to mail, assuming your linear models still apply to higher weights.

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Since, F value is =19.056 is greater than F critical value =3.3541

Therefore, We have enough evidence that null hypothesis is not rejected

A hypothesis is a theory that is put up to account for a phenomenon. Unless it can be tested through the scientific method, a hypothesis cannot be referred to as a scientific hypothesis. Scientific theories frequently begin with historical observations that cannot currently be fully explained by existing knowledge.

Here,

Null hypothesis,

[tex]H_{0}[/tex]: u1 = u2 =u3

u1,u2,u3 are means of stress  scale for group 1 , group 2 and group 3

Alternate hypothesis,

[tex]H_{A}[/tex] : u1≠u2

The F value is =19.056

Using F critical value α=0.05

df numerator =2 , df denominator = 27

F critical value =3.3541

Conclusion : F value is =19.056 is greater than F critical value =3.3541

Therefore, We have enough evidence that null hypothesis is not rejected

We, conclude that all three groups are equals in terms of mean.

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By using area of trapezium, it can be calculated that-

Length of fencing needed in 15.88m

What is area of trapezium?

Area of trapezium is the total space taken by the trapezium.

If the length of parallel sides be a and b and distance between the parallel sides are d,

Area of trapezium = [tex]\frac{1}{2}\times(a + b) \times (d)[/tex]

Length of the parallel sides = [tex]b_1[/tex] m and 5.28 m

Length of non parallel sides = 3.3 m and 3.3 m

Distance between parallel sides = 3m

Area of trapezium = [tex]\frac{1}{2} \times (b_1 + 5.28) \times 3[/tex]

By the problem,

[tex]\frac{1}{2} \times (b_1 + 5.28) \times 3 = 13.92[/tex]

[tex]b_1 + 5.28 = 13.92 \times \frac{2}{3}\\b_1 + 5.28 = 9.28\\b_1 = 9.28 - 5.28\\b_1 = 4 \m[/tex]

Length of fencing needed = 4 + 5.28 + 3.3 + 3.3 = 15.88 m

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 The answer is -2x² + 8x + 54 = 0.

This refers to a method used to easily solve the task of repeated addition of the same number. It is used when we need to combine groups of equal sizes.

Given in the question:

[tex]\frac{2x +3 }{x^{2}-x}[/tex] *[tex]\frac{4x^{2 } +8x }{10x +30}[/tex]

Multiply the numerators and denominators and equate the two:

(2x + 3) * (4x² + 8x)= ( x² - x) * (10x + 30)

expanding further we have:

(2x + 3) * 4x² + (2x + 3) *8x = ( x² - x) * 10x + ( x² - x) *  30

8x³+12x² +16x² +24x= 10x³ -10x² + 30x² -30x

Resolving the left-hand side of the equation and the right-hand side and equating to zero we have:

8x³- 10x³ + 12x² +16x² +10x² -30x² +24x +30x

2x³ + 8x² + 54x = 0.

Divide through by x, we have:

[tex]\frac{-2x^{3} }{x}[/tex]  + [tex]\frac{8x^{2} }{x}[/tex] +    [tex]\frac{54x}{x}[/tex] = 0

-2x² + 8x + 54 = 0.

Hence the answer is-2x² + 8x + 54 = 0.

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To test the claim that the two samples described come from populations with the same mean, we can use a two-sample t-test.

(a) The degree of freedom is 27

(b) The test statistic is -2.67

(c) Determine the rejection region for the test of H0:μ1−μ2=0 and Ha:μ1−μ2≠0 : we do not reject the null hypothesis.

(d) |t| > 2.70

(1) The degree of freedom for the two-sample t-test is calculated as

(2) The test statistic for the two-sample t-test is calculated as:

Plugging in the values, we get:

(3) To determine the rejection region for the test, we can use a significance level of α = 0.01. For a two-tailed test with α = 0.01, the critical value for t is approximately 2.70. Since our test statistic (-2.67) is less than the critical value, we do not reject the null hypothesis.

(4) For the rejection region, we need to consider values of t that are either greater than or less than the critical value. Therefore, we need to consider |t| values that are greater than 2.70. |t| > 2.70.

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Step-by-step explanation:

⭐ What does it mean for a number (x) to be a multiple of another number (y)?

Thus, we have to show that [tex](2n-5)^2 - 13[/tex] is divisible by 4.

Let's compute [tex](2n-5)^2 - 13[/tex]:

[tex](2n-5) ^2 = 4n^2 -20n + 25[/tex]

[tex]4n^2 - 20n + 25 -13[/tex]

[tex]4n^2 - 20n + 12[/tex]

[tex]4n^2 - 20n + 12[/tex] is the expression we have.

To see if this expression is divisible by 4, we need to divide [tex]4n^2 - 20n + 12[/tex] by 4 and have a remainder of 0.

The given equation (2n-5)² - 13 equals 4² - 20n + 12. Because each term in the simplified equation can be divided evenly by 4, it proves that the equation is indeed a multiple of 4, assuming n is an integer.

The problem is asking to show that the expression (2n-5)² - 13 is a multiple of 4 for all integers. To prove this, we need to expand and simplify the expression and then check whether it can be divided evenly by 4.

Let's start by expanding the expression:

(2n-5)² - 13 = 4n² - 20n + 25 - 13 = 4n² - 20n + 12

Now we can observe that all terms in the equation are divisible by 4:

4n²/4 = n², -20n/4 = -5n, and 12/4 = 3

Because all terms in the equation can be divided evenly by 4, we can say that the entire equation (2n-5)² - 13 is a multiple of 4, assuming n is an integer.

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Since H0 is not rejected so, the mean life of a contain brand of tire used by it's trucks is not less than 35,000 miles.

What is standard deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 35,000 miles.

To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,200 miles with a standard deviation of 1200 miles.

At α = 0.05, test the shipping firm's claim.

Under H0: μ 200  Vs H1: > 200  (Right tailed test)

n = 16, x bar = 205 , s = 14

Null Hypothesis;  H0:  μ = 35000  Vs  H1: < 35000

(Mean life of brand of tire less than 35000 miles).

Under H0 test statistic is

t = (x bar - μ) / (s / √n) ≈ [tex]t_n_-_1[/tex]

Now, n = 18, x bar = 34,200,  s = 12000

t = (34000 - 35000) / (1200 / √18) = -2.8284

t - critical value of α = 0.05 for left tailed at (18 - 1) df = -2.11

Therefore t calculated (= -2.8284) < -2.11

So, we do not reject H0.

Hence, since H0 is not rejected so, the mean life of a contain brand of tire used by it's trucks is not less than 35,000 miles.

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Answer:

Step-by-step explanation:

First, let us substitute x and y values: -7 = -2(-5) + 4

Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).

Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:

14 + b = -7

by simplifying, we can conclude that b = -21

Finally, we can plug in the b-value into our original equation:

y = -2x + 4 - 21

After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).

Answer:

y = -37

Step-by-step explanation:

y = -5 - 8x

y = -5 - 8(4)

y = -5 + ( - 8 x 4 )

y = -5 + ( - 32)

y = -37

Answer:

-3x+y=-5

Step-by-step explanation:

First, find the slope of the equation:

m=(y2-y1)/(x2-x1)  ==> m=slope of equation

(x1, y1), (x2, y2) ==> (x1=3, y1=4), (x2=2, y2=1)

m=(1-4)/(2-3)  ==> plugin x1=3, y1=4, x2=2, and y2=1

m=-3/(-1)

m=3

y=mx+b   ==> slope-intercept equation

1=3(2)+b ==> plugin 3 for m and (2, 1) where x=2 and y=1

1=6+b ==> solve for b

1-6=6-6+b

b=-5

y=3x+(-5)  ==> plugin -3 for m and -5 for b

y=3x-5 ==> simplify

Now, Isolate -5 since it is the only constant

y-3x=3x-3x-5  ==> isolate -5 by subtracting 3x on both sides

-3x+y=-5  ==> simplify and put in Ax+By=C form

y = 3x - 5

sorry can't help with step to step explanation......

The correct answer is System 1: Infinitely many solutionsSystem 2: One solutionSystem 3: No solution

Let's analyze each system of linear equations and determine the number of solutions they have.

y = x + 6 and 3x - 3y = -18

In this system, the first equation is a linear equation in slope-intercept form, and the second equation is a linear equation in standard form. The two equations represent the same line. Since they are the same line, they intersect at infinitely many points. Therefore, this system has infinitely many solutions.

y = -4x + 11 and -6x + y = 11

Both equations in this system are in slope-intercept form. The slopes of the two lines are different (-4 and -6), indicating that the lines are not parallel. Since the lines are not parallel and have different slopes, they intersect at a single point. Therefore, this system has one solution.

y = -2x + 5 and 2x + y = -7

Both equations in this system are in slope-intercept form. The slopes of the two lines are equal (-2 and 2), but their y-intercepts are different. When the slopes are equal and the y-intercepts are different, the lines are parallel and do not intersect. Therefore, this system has no solution.

Matching the systems with the correct number of solutions:

System 1: Infinitely many solutions

System 2: One solution

System 3: No solution

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Answer:

The quen is as following:

ABC is a right triangle at C,

Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1

If CH is an altitude to AB and CL is an angle bisector of ∠ACB, find m∠HCL.

The solution is:  m∠HCL = 30°

Step-by-step explanation:

See the attached figure.

∵The triangle is right at C   ∴∠C = 90°

∴∠A + ∠B = 90° ⇒(1)

∵ Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1

∴∠A = 5 times ∠B

Substitute at (1)

∴ 5 ∠B + ∠B = 90° ⇒⇒⇒ ∴∠B = 15°  and ∠A = 75°

∵CL is an angle bisector of ∠ACB

∴ ∠ACL = 90°/2 = 45°

∵ CH is an altitude to AB ⇒ ∠CHA = 90°

At the triangle AHC:

∠ACH = 180° - (∠CHA + ∠CAH) = 180° - (90° + 75°) = 15°

∴ ∠HCL = ∠ACL - ∠ACH = 45° - 15° = 30°