If a = 6, then the value of c is...

Answer:

[tex]\sf x = \dfrac{\sqrt{19}+5}{3} \ ; \ x = \dfrac{-\sqrt{19}+5}{3}[/tex]

Step-by-step explanation:

(3x - 5)² = 19

To find the solution for the equation,  take square root on both sides.

    [tex]\sf 3x - 5 = \± \sqrt{19}\\\\ Add \ 5 \ to \ both \ sides \\\\ 3x = \±\sqrt{19} + 5\\\\ Divide \ both \sides \ by 3\\\\ x = \dfrac{\±\sqrt{19}+5}{3}\\\\x = \dfrac{\sqrt{19}+5}{3} \ ; \ x = \dfrac{-\sqrt{19}+5}{3}[/tex]

The correct answer is option A which is segment D which is closer to home.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

From the given graph we can see that in segment D the distance between the home and the person is lesser than all the segments given in the graph.

Therefore the correct answer is option A which is segment D which is closer to home.

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The speed of Aro's paddling and speed of the river will be 1.56 miles per hour and 0.52 miles respectively.

Aro diagrams his river rafting trip, estimating the time it will take him to paddle upstream against the current, and then back downstream with the current. His campsite destination is 5.2 miles upstream. Determine how fast Aro can paddle and how fast the river water is moving. Round to the nearest hundredth as needed. Upstream: Downstream: Let x be the speed of Aro’s paddling and let y be the speed of the river. Upstream: 1.04 = x – y Downstream: 2.08 = x + y Aro can paddle at a speed of miles per hour. The river’s speed is miles per hour.

Based on the information given, the equations will be:

x + y = 1.04

x + y = 2.08

Add both equations together. This will be:

x = 1.56

Now substitute the value of x into equation ii. This will be:

1.56 + y = 2.08

y = 2.08 - 1.56

y = 0.52

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The area is given by f(x) = 10x² + 31x + 15.

The function is a rectangle's area function. We know that a rectangle is a flat, four-sided shape with straight sides and right-angled interior angles. Additionally, the opposing sides are parallel and of the same length.

Rectangle Area = Length * Width

The length of fabric scrap is 5x. So, the rectangular patchwork's length will be 5x + 3.

Since the width of the fabric scrap will be 2x, the rectangular patchwork's width will be 2x + 5.

Then area = f(x) = (5x + 3)(2x + 5) = 10x² + 25x + 6x + 15 = 10x² + 31x + 15

Therefore the area is given by f(x) = 10x² + 31x + 15.

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Answer:

Jane is 11 1/4 years old.

Step-by-step explanation:

Subtract all of the numbers given.

[tex]13\frac{5}{6} -1\frac{1}{3} -1\frac{1}{4}[/tex].

To subtract this, we need to find a common denominator.

A common denominator in this situation is 12. To do this multiply the 5 and the 6 of 5/6 by 2. Multiply the 1 and the 3 of 1/3 by 4. And multiply the 1 and the 4 1/4 by 3.

The new expression will look like this:

[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}[/tex].

Now we can subtract.

[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}=11\frac{3}{12}[/tex]

Reduce the answer.

[tex]11\frac{3}{12}=11\frac{1}{4}[/tex]

In decimal form 11.25

Hope this helps!

If not, I am sorry.

The result of the expression in exponential form is 9^-4

Given the expression below

[tex]9^2 \times 9^{-6}[/tex]

According the product law, since the base are equal, we will add the exponent to have:

[tex]9^2 \times 9^{-6}=9^{-6+2}\\9^2 \times 9^{-6} = 9^{-4}[/tex]

Hence the result of the expression in exponential form is 9^-4

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The relation written as a set of ordered pair is given as: : {(–2, 2), (0, 0), (3, –3)}. (Option D)

An ordered pair is a in math is one that comprises coordinates of one point in the coordinate system where the first is the x coordinate and the other is representative of the y coordinate.

Thus the correct ordered pair is option D. See the graph attached.

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Hello!

Answer:

[tex]\Large \boxed{\sf A. -7}[/tex]

Step-by-step explanation:

We have this inequality:

[tex]\sf -5x - 7 \geq 28[/tex]

Let's solve this inequality:

◼ Add 7 to both sides:

[tex]\sf -5x - 7+7 \geq 28+7[/tex]

◼ Simplify both sides:

[tex]\sf -5x \geq 35[/tex]

◼ Divide both sides by -5, so also change the sign of the inequality

[tex]\sf \dfrac{-5x}{-5} \leq \dfrac{35}{-5}[/tex]

◼ Simplify both sides:

[tex]\boxed{\sf x \leq -7}[/tex]

So the correct answer is A. -7

Answer:

A function is when each input has exactly one output

Step-by-step explanation:

Each input can only have one output, but an output can have multiple inputs.

The probability that the summer solstice will occur on a weekday is equal to 5/7.

Generally, there are seven days in a week and two among these days are weekends while five are weekdays. Thus, this can be represented as follows:

Therefore, the probability that the summer solstice will occur on a weekday is given by:

P = 5/7.

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The area of the trapezoid is calculated as 45.5 feet squared.

What does Area of Trapezoid mean?

The entire area occupied by the sides of a trapezoid is its area. It's important to notice that if we know the lengths of all the sides, we can divide the trapezoid into smaller polygons, such as triangles and rectangles, calculate their areas, and then sum them all together to determine the area of the trapezoid.

If the parallel sides of the trapezoid are known, along with their height, it is possible to determine their area. It is expressed as,

A=[tex]1/2[/tex](a+b) h

where, A= the area of the trapezoid

h= height

'a' & 'b' = parallel side bases

a=5.5 feet , b= 8.5 feet & h=6.5 feet

A=[tex]1/2[/tex](a+b)h

∴A=[tex]1/2[/tex](5.5+8.5)*6.5

⇒A=[tex]1/2[/tex](14)*6.5

⇒A=7*6.5

⇒A=45.5 feet squared

Therefore, the solution is  (b) 45.5 feet squared.

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Step-by-step explanation:

[tex]f(x) = 2 {x}^{2} [/tex]

[tex] \: [/tex]

[tex] = (f \circ f)(x)[/tex]

[tex] = f(f(x))[/tex]

[tex] = 2 {x}^{2} [/tex]

[tex] = 2 {(2 {x}^{2} )}^{2} [/tex]

[tex] = 2( {2}^{2} {x}^{2 + 2} )[/tex]

[tex] = 2(4 {x}^{4} )[/tex]

[tex] = 8 {x}^{4} [/tex]

The answer is A.

Answer:

-28

Step-by-step explanation:

put 3 where is x

f(x) = −5(3)^2 − (3) + 20

exponents flrst

(−5*9) − (3) + 20

-45 -3 +20

-48 + 20

-28

The volume of the second parallelepiped will be 1 cm³. According to the given conditions, α is 50% of a, β is 20% of b and γ is 10% of c.

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

Given condition;

α is 50% of a, β is 20% of b and γ is 10% of c

α =  a/2

β = b/5

γ = c/10

The volume of the first parallelepiped:

V = abc

100cm³=abc

The volume of the second parallelepiped:

[tex]\rm V'= \alpha \times \beta \times \gamma \\\\ \rm V'= \frac{a}{2} \times \frac{b}{5} \times \frac{c}{10} \\\\ V' = \frac{abc}{100} \\\\ V'=\frac{100}{100} \\\\ V' = 1 cm^3[/tex]

Hence, the volume of the second parallelepiped willl be 1 cubic meter.

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Answer: x²-59x+114=0

explanation:

If the roots are 2 and 57, then:-

sum of roots = 2+57 = 59

and, product of roots = 2×57 = 114

the quadratic equation is given by,

x²-(sum of roots)x+(product of roots)=0

so, x²-59x+114=0 will be the desired quadratic equation.

so, none of the options are correct.

the correct answer is x²-59x+114=0.

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Answer:

Inequality Form:

b ≥ 1

Interval Notation:

[1,∞)

Step-by-step explanation:

1) Angles IDO and ILO are congruent, and both measure 122 degrees. So, as angles in a quadrilateral add to 360°, angle LOD measures 360-122-122-32=84°

2) As referred to in the first question, angle ODI measures 122°

3) In a kite, there are two pairs of disjoint congruent sides. This means that in this case, ID=IL=21 and LO=OD. As the perimeter is 74, this means LO=(74-21(2))/2=16

4) LI=ID, so ID=21

The inequality x ≤ 88 represents the situation, and the line graph first represents the solution to the inequality option first is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The missing options are in the picture, please refer to the picture.

We have:

An airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane.

Let's suppose the number of tickets is represented by x

Total number of passengers = 175

The inequality can be framed:

x + 87 ≤ 175

x ≤ 88

Thus, the inequality x ≤ 88 represents the situation, and the line graph first represents the solution to the inequality option first is correct.

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Answer:

EAD

Step-by-step explanation:

Answer:400%

Step-by-step explanation: by the commutativity of multiplication we find (2x)^2=4(x^2)=4(y)

Answer:

3

Step-by-step explanation:

When you divide 27 by 3 it will give you 9 and the square root of 9 gives you a perfect answer indicating that 3 is the least number that must be divided into 27

Answer:

[tex]\fbox {3}[/tex]

Step-by-step explanation:

First, prime factorize 27 :

⇒ 27 = 3 × 3 × 3

If 27 was divided by 3, it would give 3 × 3, which would give 9, a perfect square.

Answer:

175000 km

Step-by-step explanation:

the 1:25000 essentially means that every centimeter represents 25000 kilometers. so the answer is 175000 by multiplying 7 and 25000

The true statement is (b) the random variable is x, the possible values are 0 to 3 and the values are numerical

The table is added as an attachment

From the attached image, we have:

Number of girls (x)          P(x)

0                                         0.125

1                                         0.375

2                                         0.375

3                                         0.125

In the above, the random variable is x, while P(x) represents its probabilities.

Also, the possible values are 0 to 3 as shown in the table.

0 to 3 are numerical digits, and the values are numerical

Hence, the true statement is (b)

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Answer:

Rate of Change = -77.9 feet/year

My interpretation: "Is Bad."

Step-by-step explanation:

The rate of change is the number of feet that Lake Powell dropped, divided by the number of years the drop took place.  We want a value with a unit of feet/year.

Year    Feet

1999     3893

2005    3425.6  

Change

Year = (2005 - 1999)  or 6 years

Feet = (3425.6 - 3893) or -467.4 feet

Rate of Change = (-467.4 feet)/(6 years)

Rate of Change = -77.9 feet/year

=======================

FYI:  Lake Powell is 22.39 feet lower today (June 23, 2022) than it was 1 year ago.

Answer:

width=14 &Length = 70( can add unit behind the answer e.g.cm or mm etc..)

Step-by-step explanation:

we know that in a rectangle not all side are same compare to a square..

therefore:

1) write the formula for perimeter down

perimeter = the sum of all side

perimeter = 2x(width) + 2x(length)

P=2(w)+2(L)

2) substitute into the equation

P =2(w)+2(L)

84=2(w)+2(5*w)

3) perform opposite operation to make w become the subject of the formula inorder to find width

48=2(w)+2(5*w)

48=2w+10w

48=12w

48/12=12w/12( the twelves cancels out)

7=w or the width is 7

4) rewrite the formula and solve

P=2(w)+2(L)

P =2(7) + 2(5*7)

P = 14 + 70

P = 48

Answer:

[tex]\fbox {x = 3}[/tex]

Step-by-step explanation:

Decimal form of the lower and higher limits :

Hence, the best one which lies in the middle of the limits would be 0.3.

Now, equate the middle part :

The equation equivalent to the simple interest formula A = P(1 + rt), that Celo used is P = A/(1 + rt). Hence, the first option is the right choice.

Equivalent equations are the equations that are transformed from one equation to another equation, but the final values they give are equal. It's just the change of the variable on which the equation is derived.

The simple interest equation that Celo used is A = P(1 + rt).

This is currently used to find the final amount A.

On isolating P to one side of the equation in the following ways:

A = P(1 + rt),

or, A/(1 + rt) = {P(1 + rt)}/(1 + rt) {Dividing both sides by (1 + rt)}.

or, A/(1 + rt) = P {Simplifying}.

or, P = A/(1 + rt) {Changing sides}.

Thus, the equation equivalent to the simple interest formula A = P(1 + rt), that Celo used is P = A/(1 + rt). Hence, the first option is the right choice.

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Answer:

The y-coordinates do not change under a horizontal stretch. The x-coordinates do not change under a vertical stretch.

Step-by-step explanation: