The triangles are simliar by the:
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The compound inequality 5 \u2264 4x - 1 < 7 results in the solution set [1.5, 2) when solved and graphed. In interval notation, it is expressed as [1.5, 2).

To solve the compound inequality 5 \<= 4x - 1 < 7, we split it into two separate inequalities and solve them individually:

The solution set is the interval [1.5, 2). To graph this solution, plot a closed circle at 1.5 and an open circle at 2, and shade the region in between. In interval notation, the solution set is represented as [1.5, 2).

It will take them 3 hours to meet

Step-by-step explanation:

The given is:

We need to find how long it will take them to meet

Distance = Speed × Time

∵ They will drive toward each other at the same time and meet

   each other somewhere

- That means they will drive for the same time

∵ Jack's average rates 60 mph for t hours

∴ Jack will drive a distance = 60 × t = 60 t  miles

∵ Jill's average rate is 55 mph for t hours

∴ Jill will drive a distance = 55 × t = 55 t  miles

∵ The distance between Jack and Jill is 345 miles apart

- Add their distance above and equate the sum by 345

∴ 60 t + 55 t = 345

∴ 115 t = 345

- Divide both sides by 115

∴ t = 3 hours

It will take them 3 hours to meet

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Answer:

c

Step-by-step explanation:

Final answer:

The area of the trapezoid can be found by decomposing it into a rectangle and two triangles. Using the given dimensions, x = 4 units, y = 5 units, and h = 7 units, the calculated area of the trapezoid is 35 square units.

Explanation:

To find the area of the trapezoid using decomposition, we can break it down into simpler shapes whose area we can calculate more easily. Here, we will break the trapezoid into a rectangle and two triangles.

Let's identify the dimensions of the trapezoid: the top base (x), the bottom base (y), and the height (h). The student has provided that x = 4 units, y = 5 units, and h = 7 units.

The area of the rectangle that forms part of the trapezoid is the product of its base (x) and height (h):

Area of Rectangle = x * h = 4 units * 7 units = 28 square units

Next, we have two right triangles with one of the legs being the difference in the length of the bases (y - x) and the other leg equal to the height (h). The area of one triangle will be:

Area of Triangle = 0.5 * (y - x) * h = 0.5 * (5 units - 4 units) * 7 units = 3.5 square units

Since there are two identical triangles, we double this value:

Total Area of Triangles = 2 * 3.5 square units = 7 square units

Now we can sum the area of the rectangle and the total area of the triangles:

Total Area of Trapezoid = Area of Rectangle + Total Area of Triangles = 28 square units + 7 square units = 35 square units

Therefore, the area of the trapezoid is 35 square units.

Final answer:

The area of the trapezoid can be calculated by decomposing it into simpler shapes and using the formula A = ½(h)(b1 + b2), resulting in 31.5 units² for the given measurements.

Explanation:

To find the area of the trapezoid using decomposition, given that x = 4 units, y = 5 units, and h = 7 units, we need to decompose the trapezoid into simpler shapes like rectangles and triangles.

The area of a trapezoid can be found using the formula A = ½(h)(b1 + b2), where h is the height and b1 and b2 are the lengths of the two parallel bases. As there is no visual provided, and we are given three measurements, we must assume these represent the height and the bases of the trapezoid. The area is then calculated as follows:

Area of Trapezoid = ½(7)(4 + 5) = ½(7)(9) = ½(63) = 31.5 units².

The regular price of the hat is $22.5

We know that the discount price of a hat is $18, so we need to find the regular price of the hat.

Let:

x: Regular price

So:

[tex]\\ \\ Regular \ price \ - \ percentage \ discount \times Regular \ price =discount \ price \\ \\ x-20\%(x)=18 \\ \\ x-0.20x=18 \\ \\ 0.8x=18 \\ \\ x=\frac{18}{0.8} \\ \\ x=22.5[/tex]

Finally, the regular price of the hat is $22.5

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Answer:

5 flowers

Step-by-step explanation:

To get the answer you do 7-2

so she has 5 flowers left.

7-2=5

Answer:

40

Step-by-step explanation:

x = 10

Substitute 10 for x

5 (10) -10

Multiply 5 by 10

50 - 10

= 40

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Answer:40

Step-by-step explanation:

Probability of getting tails on the first flip: 1/2 (because it's one of two possible outcomes).

Probability of getting tails on two consecutive flips: 1/4 (because it's one out of four possible outcomes- tails tails, tails heads, heads tails, heads heads)

A simpler way of thinking about it is 1/2*1/2, because you already have 1/2 for getting tails the first time, and if getting tails the second time were an independent event then the probability would be 1/3, but since it's getting tails twice you multiply the probabilities.

Either way, the answer is 1/4 (or 25%)

If you flip a coin twice the probability that you get tails on the first flip and tails on the second flip is 1/4.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that you flip a coin twice, the probability getting tails on the first flip we have to find the probability that you get tails on the first flip and tails on the second flip.

The probability of getting tails on the first flip is

P(T) = 1/2

When two coins get flipped the total possible outcomes are,

(T, H)(T,T)(H,H)(H,T)

Probability of getting tails on two consecutive flips,

P(T) =1/4

The probability that you get tails on the first flip and tails on the second flip

Thus, if you flip a coin twice the probability that you get tails on the first flip and tails on the second flip is 1/4.

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Answer:

Point C

Step-by-step explanation:

When you graph the two equations, they meet at point c, which is the solution

Answer:

Point C

Step-by-step explanation:

You know the x so you can substitute that into the point:

(4, y)

You don't know y but you can substitute in the x and solve the equation. You would get -3. So the point would be:

(4, -3)

Find that point on the graph and it's Point C.

To determine which line the point lies on, you can just plug in one of the numbers into the equations to see if it equals out.

(2, -1)  I will use the 2 and plug it in for x in the equation.

y = 2x + 1

y = 2(2) + 1

y = 5            The point does not lie on this line because when x = 2, y = 5  (2, 5)

y = x + 5

y = 2 + 5

y = 7          The point does not lie on this line because when x = 2, y = 7  (2, 7)

y = 2x - 5

y = 2(2) - 5

y = 4 - 5

y = -1           The point does lie on this line because when x = 2, y = -1  (2, -1)

y = x - 2

y = 2 - 2

y = 0      The point does not lie on this line because when x = 2, y = 0  (2, 0)

Answer:

C is correct

Step-by-step explanation:

If you plug in the ordered pairs from C, they always work.

Answer:

42

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

Let Joanne age be x

let betty age by y

. ° . x + y = 60

if joanne is 18

y = 18

x + 18 = 60

x = 60 - 18

x = 42

. ° . betty = 42

Answer:

[tex]CE=5.5\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

we know that

According to the Perpendicular Tangent Theorem, tangent lines are always perpendicular to a circle's radius at the point of intersection

That means ----> Triangles ODC and OEC are right triangles

In the right triangle OEC

we have

[tex]OE=OD=4.8\ units[/tex] ----> radius of the circle

[tex]OC=7.3\ units[/tex]

Applying the Pythagorean Theorem

[tex]OC^2=OE^2+CE^2[/tex]

substitute the given values

[tex]7.3^2=4.8^2+CE^2[/tex]

[tex]CE^2=7.3^2-4.8^2\\CE^2=30.25\\CE=5.5\ units[/tex]

Final answer:

The length of the segment CE, which is a tangent to a circle, can be found using the properties of tangents and the Pythagorean theorem. Given OD = 4.8 and OC = 7.3, the length of CE is calculated to be approximately 5.5 units.

Explanation:

The question involves finding the length of segment CE in a configuration where segments CD and CE are tangents to a circle centered at O. Given that OD = 4.8 and OC = 7.3, to find CE, one can use the properties of tangents to a circle. Tangents drawn from the same external point to a circle are congruent. Therefore, the lengths of CD and CE are equal. Since OD and OC form a right triangle with CD (considering triangle OCD), applying the Pythagorean theorem gives us the length of CE directly.

To calculate, let CD = CE = x, hence:

After calculation:

Therefore, the length of CE is approximately 5.5 units.

Answer:

Step-by-step explanation:

so you have 1 red, 2 blue, and 3 red. Together that would be 6 marbles. However it apears that with each draw you gain two marbles. therefore there are 12 possibilities. The likely hood that you will get a green marble then a red marble should be 2/12. In simplified form it is 1/6.

Answer:the answer is 1/5 the other guy got it wrong

Step-by-step explanation:

The measure of angle 5 is 75°.

Step-by-step explanation:

Properties of intersecting lines :

step 1 :

From the figure, the angle (-9x-12) and angle (6x+183) are vertically opposite and are equal.

-9x-12 = 6x+183

⇒ -9x-6x = 183+12

⇒ -15x = 195

⇒ x = -(195/15) = -13

step 2 :

Substitute x= -13 in the angle (-9x-12)

⇒ (-9x-12) = -9(-13)-12

⇒ 117 - 12 = 105°

step 3 :

The measure of angle in a line is supplementary (180°).

Let angle 5 be unknown value "a".

Then, angle (-9x-12) + angle a = 180°

⇒ 105° + a = 180°

⇒ a = 180 - 105

⇒ a = 75°

∴  The measure of angle 5 is 75°

The annual sales after 7 years is $ 855.3556

Solution:

The growth function is given as:

[tex]y = a(1+r)^t[/tex]

Where,

y is the future value

a is the initial value

r is the growth rate

t is the number of years

From given,

a = 650

t = 7

[tex]r = 4 \% = \frac{4}{100} = 0.04[/tex]

Therefore,

[tex]y = 650(1 + 0.04)^7\\\\y = 650(1.04)^7\\\\y = 650 \times 1.315931\\\\y = 855.3556[/tex]

Thus the annual sales after 7 years is $ 855.3556

Answer:

0.1523

Step-by-step explanation:

-1/3 + 5e = 3/7

5e = 3/7 + 1/3

By Elysium

5e = (9 + 7)/21

5e = 16/21

5e = 0.7619

e = 0.7619/5

0.1523

The lowest term is [tex]\frac{75}{4}[/tex].

Solution:

Given expression is [tex]50\times\frac{3}{8}[/tex]

To reduce this term to the lowest term:

[tex]$50\times\frac{3}{8}=\frac{50}{1}\times\frac{3}{8}[/tex]

Multiply the numerator and denominator.

[tex]$50\times\frac{3}{8}=\frac{150}{8}[/tex]

Now, divide the numerator and denominator by the greatest common factor.

Here 150 and 8 both have common factor 2.

So, divide numerator and denominator by 2.

           [tex]$=\frac{150\div2}{8\div2}[/tex]

           [tex]$=\frac{75}{4}[/tex]

[tex]$50\times\frac{3}{8}=\frac{75}{4}[/tex]

Hence the lowest term is [tex]\frac{75}{4}[/tex].

Answer:

The final balance is $10,792.14.

The total compound interest is $2,792.14.

Step-by-step explanation:

Final answer:

Explanation on calculating the amount of $8000 principal at 5% compounded annually after 6 years using compound interest formula.

Explanation:

The question: $8000 principal earning 5% compounded annually after 6 years.

Step-by-step explanation:

Use the compound interest formula: A = P(1 + r/n)^(nt) where A is the amount, P is the principal, r is the rate, n is the number of times interest is compounded per year, and t is the time in years.

Plug in the values: P = $8000, r = 0.05, n = 1 (compounded annually), t = 6.

Calculate: A = $8000(1 + 0.05/1)^(1*6)

A = $10,720.77.

Answer:

Hey "Dixie" heres why: That's why you're being told to flip the second fraction. You're recognizing that dividing by a number is the same as multiplying by the reciprocal. ... Now to multiply fractions, we simply multiply the numerators to get the new numerator and multiply the denominators to get the new denominator.

Hope it helped!

Dividing by a fraction and multiplying by its reciprocal, b/a, yield the same result as division and multiplication interact in such a way. The reciprocal (or flip) of a fraction makes it easier to perform mathematical operations like multiplication and division.

In mathematics, dividing by a fraction a/b is indeed equivalent to multiplying by its reciprocal, which is b/a. This is because of the way division and multiplication operations work.

Here's an example: If you have 4 ÷ (1/2), this can also be seen as 4 multiplied by the reciprocal of 1/2, which is 2/1, or 2. In both cases, the answer would be 8. This shows that dividing by a fraction is the same as multiplying by its reciprocal.

Therefore, when you have any number divided by a fraction, you can simplify the operation by turning it into multiplication by performing the flip (reciprocal) on the fraction you're dividing by.

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The number written in standard form is 24100

Step-by-step explanation:

An object is said to be written in scientific notation when it is written in the following form:

[tex]m\cdot 10^n[/tex]

where

m is the coefficient

n is the exponent of the power of ten

The number can be rewritten in standard form by writing the coefficient and then moving to the right (or to the left) the decimal point by n positions if n is positive (or negative).

In this problem, the number is

[tex]2.41\cdot 10^4[/tex]

So we have

m = 2.41

n = 4

Therefore, we have to write 2.41 and then move the decimal point 4 positions to the right: so we get

[tex]2.41\cdot 10^4 = 24100[/tex]

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Answer:

The answer is 3.06

Step-by-step explanation:

In order to find unit price. You divide the cost per how many units you have.

In this case, you divide 27.54 to 9.

This gives you the answer (3.06)

What is the unit price ?

$27.54 : 9 = $3.06

Juan paid 70.16 % of the original price of the jacket.

Step-by-step explanation:

Step 1:

Given details, Original Selling Price of the jacket = 85.50

New Selling Price of the jacket = 59.99

Step 2:

To determine what percentage of the old price is the new price, we have to use percentage calculation.

[tex]x/100\times 85.50 = 59.99[/tex]

Step 3:

Substitute in the formula, the given values

x = [tex](59.99/85.50) \times 100[/tex]

  = [tex](0.7016) \times 100[/tex]

  = [tex]70.16[/tex]

Therefore, percentage paid is 70.16%

Answer:F(x) is a negative number with a small absolute value

Step-by-step explanation:

The true statement about the graph of f(x) is (a) f(x) is a negative number with a small absolute value

From the given graph, we have the following highlights:

The above means that, when x is a negative number with a large absolute value, then the absolute value of x is a very large positive number.

And so the value of f(x) would be a small absolute value negative number

Hence, the correct option is (a) f(x) is a negative number with a small absolute value

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Answer: 19/20

Step-by-step explanation:

7/10 turns into 14/20

1/4 turns into 5/20

14/20 + 5/20

14 + 5 over 20

= 19/20

19/20 is in simplest form.

[tex]\text{Hey there!}[/tex]

[tex]\mathsf{What\ is\ \dfrac{7}{10}+\dfrac{1}{4}\ in\ simplest\ form?}[/tex]

[tex]\text{First, look for the lowest common denominator (LCD) of the fractions.}\\\text{If you did the calculations correctly, you should've came up with 20 as}\\\text{your LCD}[/tex]

[tex]\mathsf{Here\ is\ how so: \dfrac{7\times2}{10\times2}+\dfrac{1\times5}{4\times5} = \ ?}[/tex]

[tex]\mathsf{7\times2=14\leftarrow first\ numerator}\\\mathsf{10\times2=20\leftarrow first\ denominator}[/tex]

[tex]\mathsf{1\times5=5\leftarrow second\ numerator}\\\mathsf{4\times5=20\leftarrow second\ denominator}[/tex]

[tex]\mathsf{Your\ new\ equation\ SHOULD\ look\ like\ this: \dfrac{14}{20}+\dfrac{5}{20}}[/tex]

[tex]\text{Since, your DENOMINATORS are ALIKE we can KEEP IT}[/tex]

[tex]\mathsf{Which\ leaves\ us\ with\ the\ last\ step\ of\ the\ problem}[/tex]

[tex]\mathsf{ \dfrac{14+5}{20}}}[/tex]

[tex]\mathsf{14+5=19\leftarrow your\ new\ numerator}\\\\\mathsf{20 = 20\leftarrow your\ new\ denominator}[/tex]

[tex]\boxed{\boxed{\bf{Answer: \mathsf{\dfrac{19}{20}}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

K=2J+28

Step-by-step explanation:

Y intercept is 28

Slope is 2

Can you please clarify what you want to ask? Thanks!

Answer:

(- 4, 27 )

Step-by-step explanation:

Equate the right sides of both equations, that is

x² - 2x + 3 = - 2x + 19 ← subtract - 2x + 19 from both sides

x² - 16 = 0 ← in standard form

(x - 4)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 4 = 0 ⇒ x = - 4

Substitute these values into f(x) = - 2x + 19

f(4) = - 2(4) + 19 = - 8 + 19 = 11 ⇒ (4, 11 )

f(- 4) = - 2(- 4) + 19 = 8 + 19 = 27 ⇒ (- 4, 27 )

Answer:

Step-by-step explanation: so u are going to put it like this x- -6 =5

Next u subtract -6 from both sides

x=11

Answer:

x=10

Step-by-step explanation: