For which value of x is the figure a rectangle?
A. x = -1
B. x = 11
C. x = 11.5
D. x = 22.25

We know that the diagonals of rectangle are congruent and bisect each other. So it means the given measurements would be equal to each other. We can set them equal asn solve for x.

8x + 3 = 4x + 7

Subtracting 3 from both sides;

8x + 3 - 3 = 4x + 7 - 3

8x = 4x + 4

Subtracting 4x from both sides;

8x - 4x = 4x + 4 - 4x

4x = 4

Dividing by 4 on both sides;

4x/4 = 4/4

x = 1

Hence, option A is correct i.e. x = 1.

Answer: x=1

Step-by-step explanation:

Split the second term in 4m^2 + 16m + 15 into two terms

4m^2 + 10m + 6m + 15

Factor out the common terms in the first two terms, then in the last two terms

2m(2m + 5) + 3(2m + 5)

Factor out the common term 2m + 5

(2m + 5)(2m + 3)

4m^2 + 16m + 15

With the way the trinomial is, we cannot factor it in it's current state.

We must check to see if splitting the middle term is possible.

List factors of 60

1 * 60

-1 * -60

2 * 30

-2 * -30

3 * 20

-3 * -20

4 * 15

-4 * -15

5 * 12

-5 * -12

6 * 10 (this digits satisfy the criteria for splitting the middle term.)

Split the middle term.

4m^2 + 6m + 10m + 15

Group the polynomials in terms of 2.

(4m^2 + 6m) + (10m + 15)

Factor each binomial.

2m(2m + 3) + 5(2m + 3)

Rearrange the binomials.

(2m + 5)(2m + 3)

The correct answer is:   [B]:    " (x + 5) " .

______________________________

Explanation:

To solve:

_______________________________

Given:

_______________________________

" x²  +  13x + 40 " ;  factor into "two terms" ;

    →  that is;    "factor into 2 (two) binomial expressions" .

____________________________

  What 2 (two) factors of:  "+ 40"  add up to " + 13 " ?  ;

____________________________  

+ 40, + 1  ?? ;  →   +40 + (+1) = +41 ;  →  + 41 ≠  + 13 ;

 - 40 + (-1) ?? ;  →  - 40 + (-1) = - 40 - 1 = - 41 ;  →  - 41  ≠ +13 ;

  +8, + 5 ?? ;     →  + 8 + 5 = + 13 ;  →  + 13  = + 13 .  Yes!

So;  the factors of:  " x²  +  13x + 40 "  ;

are:  " (x + 5) (x + 8) " .

______________________________

        Among this 2 (two) binomial factors:  "(x + 5)"  AND:  "(x + 8)" ;

  one of these:  " (x + 5) "   —   appears among the answer choices provided;

        →  which is:     [B]:    " (x + 5) " .

______________________________

The correct answer is:    [B]:     " (x + 5) " .

______________________________

Hope this helps!

  Best wishes in your academic endeavors — and

     within the "Brainly" community!

______________________________

1.40/3.5=.4

that would be your answer

[tex]-5x+6(4x+15)=242\qquad|\text{use distributive property}\\\\-5x+(6)(4x)+(6)(15)=242\\\\-5x+24x+90=242\qquad|\text{subtract 90 from both sides}\\\\19x=152\qquad|\text{divide both sides by 19}\\\\x=8[/tex]

Hello there!

The answer it should be the the last option "x=8".

[tex]-5x+6(4x+15)=242\\[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓

First you had to expand the form.

[tex]6(4x+15):24x+90[/tex]

[tex]-5x+24x+90=242[/tex]

Then you had to add similar by the elements.

[tex]-5x+24x=19x[/tex]

[tex]19x+90=242[/tex]

You had to subtract by 90 from both sides of the equation.

[tex]19x+90-90=242-90[/tex]

Simplify

[tex]19x=152[/tex]

Divide by 19 from both sides of the equation.

[tex]\frac{19x}{19}=\frac{152}{19}[/tex]

Simplify it should be the correct answer.

[tex]x=8[/tex]

Answer⇒⇒⇒⇒x=8

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

The expression y = kx can be used to find the value of y when x is given. In this case, the value of y when x is 2 is 16.

To find the expression to determine the value of y when x is 2, we need to use the fact that y varies directly as x. This can be represented by the equation y = kx, where k is the constant of variation.

We are given that when x is 6, y is 48. Plugging these values into the equation, we have 48 = k * 6. Solving for k, we find that k = 8.

Now we can use this value of k in our equation to find y when x is 2. Substituting 8 for k and 2 for x, we have y = 8 * 2 = 16. Therefore, the value of y when x is 2 is 16.

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The unit rate is $/Hr.  Since the hours are the unit being considered.

To find the unit rate, divide both sides by three

(Let x = hourly rate)

3x = 15

x = 5

Miguel Makes $5 per Hour

Answer:

He Earns 5 Per Hour

Bob drove 134.5 miles. If you created a comparison between 5/7 and 188.3, do so by using 5/7=x/188.3 . Multiply 7 and x equaling to 7x and 5 with 188.3 to get 941.5 . After that divide 941.5 by 7x, and the answer for x would result in 134.5, the amount he drove

Width=10

Length=20

10 is half of 20

10 × 20 = 200,

The width of the rectangle is 10 centimeters and the length is 20 centimeters. This is determined by using the formula for area of a rectangle, length times width, and substituting the given values.

To solve this problem, we'll use the formula for the area of a rectangle, which is length times width. We're told that the length is 2 times the width and the area is 200 square centimeters.

Let's designate the width as x. So the length is 2x. Since area is length times width, the equation is 2x*x=200. This simplifies to 2x2=200, or x2=100. Therefore, x equals 10 (as we don't consider a negative number for measurement). The width of the rectangle is 10 centimeters and the length, being 2 times the width, is 20 centimeters.

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The answer is C. 3x+5= 5x -8

Correct answer is: difference in their scores is 30

Solution:-

Given that Jeff won a contest play a round golf with Phil.

And Phil's score was -6 where as Jeff score was 24.

Hence difference in the scores = Higher score - lower score

                                                    = 24-(-6) = 30 ( negative of negative will become positive)

Hence difference in their scores is 30.

5

Rounding to whole number is the same number as it is, tenth means to leave one number after the decimal point, hundredths means to leave two numbers after the decimal point and so on.

Answer:

Cutoff for a failing score is 49 and 2.28% students failed.

Step-by-step explanation:

We have been given that scores on a psychology exam were normally distributed with a mean of 57  and a standard deviation of 4.

2 standard deviation below mean would be,

[tex]57-2(4) =57-8= 49[/tex]

Therefore,Cutoff far a failing score is 49.

Now let us find out the z-score for our given values,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{49-57}{4}=\frac{-8}{4} =-2[/tex]

Now let us look up the probability from normal distribution table.

[tex]P(z<-2) =0.02275[/tex]

Therefore, percentage of students failed is 2.28%.

Answer:

Principal = $4,500

Rate of interest=3%

Time = x years

We have to find number of years such that

Amount ≤$7020

Amount ≤ Principal + Simple interest

7020≤4500+ S.I

S.I≥7020-4500

S.I≥$2520

Formula for simple interest

S.I=[tex]\frac{P\times R \times T}{100}[/tex], where P=Principal, R=Rate of interest, T=time

2520≥[tex]\frac{4500 \times 3 \times x}{100}[/tex]

[tex]\frac{2520 \times 100}{4500 \times 3} \leq x[/tex]

x≤[tex]\frac{56}{3}[/tex]

So, the solution set is (0,[tex]\frac{56}{3}[/tex]]

Answer:    

The solution set to the given inequality : 0 < x ≤ 18.67

Step-by-step explanation:

Principal = $4500

Simple Interest Rate = 3%

                                  = 0.03

Time = x year

Amount in the account will be less than or equal to $7020

⇒ Amount ≥ Principal × (1 + Rate × Time)

⇒ 7020 ≥ 4500(1 + 0.03·x)

⇒ 7020 ≥ 4500 + 135·x

⇒ 2520 ≥ 135·x

⇒ 18.67 ≥ x

The solution set to the given inequality : 0 < x ≤ 18.67

AC = CB, hence ΔABC is isosceles

the base angles 34 and x - 5 are therefore equal

x - 5 = 34 ( add 5 to both sides )

x = 39

and 4y = 180 - ( 2 × 34 ) = 112

4y = 112 ⇒ y = 28

Answer:

x=39° ,y=28°

Step-by-step explanation:

In the given figure

Side AC = Side BC

Hence ΔABC is an isosceles triangle.

⇒∠CAB =∠CBA   (∵ angles  opposite to equal sides are equal)

                        ⇒  (x - 5)° = 34°  

                            ⇒  x = 39

Also in Δ ABC

            ∠ABC + ∠ACB + ∠CAB = 180°

                                                    (∵ Sum of all the interior angles of a triangle)

               ⇒   34° + 34° + 4 y = 180°

                 ⇒     4 y =180°-68°

                    ⇒     y=112°÷ 4

                        ⇒y= 28°

Hence, x = 39° , y = 28°

Answer:

7

Step-by-step explanation:

Formula

Total Juice boxes(T) = number of packs(n) * amount in each pack(a)

T = n * a

Givens

T = 84

n = ???

a = 12

Solution

T = n * a      Substitute givens

84 = 12*n    Divide by 12

n = 84 /12  

n = 7            Answer number of packs of 12

y=4/5 x      is a proportional relationship

2. Because it is being reflected across the X axis, the X coordinate would change signs, but the Y coordinate would remain the same sign.

A(-6,-4) would become A'(6,-4)

B(-3,5) would become B'(3,5)

C(1,-1) would become C'(-1,-1)

The answer would be the third choice.

3. Reflected across the Y axis, the X would stay the same sign and the Y would change signs.

P(-2,-4) would become P'(-2,4)

Q(2,-5) would become Q'(2,5)

R(-1,-8) would become R'(-1,8)

The answer would be the second choice.

Answer:

6,8,10

Step-by-step explanation:

Two consecutive even integers would have difference of 2

Hence we can assume the three consecutive integers to be of the form

a-2, a and a+2

Smallest number = a-2 and

Largest number = a+2

Twice the smallest number + 3 times largest number =42 (given)

2(a-2)+3(a+2) = 42

2a-4+3a+6 =42

5a +2 =42

Subtract 2 and then divide by 5

5a = 40 and a = 8

Hence the three numbers are 6,8 and 10

Answer:

6.35 cm

Step-by-step explanation:

Did this exam on FLVS.

02.07 Unit Conversions right?

well hope this helped!!

- The sample size is 64.

- The point estimate of the population proportion is 0.625.

-The margin of error is approximately 16%.

Answer:

Step-by-step explanation:

Given that Katrina randomly selected 64 students out of her school of 400 students and found that 40 of them want school to start at a later time.

Out of the statements given the true statements are :

1) The sample size is 64

2) The point estimate of the population is sample proportion =40/64 =5/8

=0.625

3) Margin of error = std error x 2.58

Std error = sq rt pq/n

p=0.625 and q = 0.375

Hence std error = 0.060

Margin of error = 0.156

Round off to 0.16 = 16%

When three coins are tossed, the probability of two coins landing on heads is 3/8 or 0.375.

In the scenario where three coins are tossed, the total outcomes possible would be 2^3 = 8 (representing Heads/H or Tails/T): HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

Out of these, there are three outcomes where exactly two coins show heads (HHT, HTH, THH), and one coin shows tails. Hence, the probability of getting exactly two heads when three coins are tossed is 3 out of 8 or 3/8 = 0.375.

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[tex]\dfrac{2}{3}(4x-5)=8\qquad|\text{use the division property of equality}\\\\\dfrac{2}{3}(4x-5):\dfrac{2}{3}=8:\dfrac{2}{3}\\\\\dfrac{2}{3}(4x-5)\cdot\dfrac{3}{2}=8\cdot\dfrac{3}{2}\\\\4x-5=4\cdot3\\\\4x-5=12\qquad|\text{use addition property of equality}\\\\4x-5+5=12+5\\\\4x=17\qquad|\text{use the division property of equality}\\\\4x : 4=17:4\\\\x=\dfrac{17}{4}[/tex]

To find the number of gallons of olive oil used during the week, divide the volume of olive oil used in quarts by 4.

To find out how many gallons of olive oil the restaurant used during the week, we need to know the volume of olive oil used and convert it from quarts to gallons. Since there are 4 quarts in a gallon, we can divide the volume of olive oil used by 4 to get the number of gallons. Let's say the restaurant used 20 quarts of olive oil during the week. We divide 20 by 4 to get the answer:

20 quarts ÷ 4 = 5 gallons

Therefore, the restaurant used 5 gallons of olive oil during the week.

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Answer:

Triangle KLM is congruent to triangle ONM.

Step-by-step explanation:

All three angles of triangles are equal, that is both triangles are congruent.

Please share the figure to show the numbering of angle you are using. So that I can describe you which angle is equal to which one.