The larger of two numbers is 9 less than four times the smaller number if the sum of
the two numbers is 26. What is the smaller number?

Answer:

Step-by-step explanation:

If the age of a cat is represented by 'x' and human years by 'y', relation between the age of cat and human years will be,

y = 4x + 16 [multiplying cat's age by 4 and by adding 16]

Now from the given table,

If x = 2,

y = 4×2 + 16

  = 24

If y = 3,

y = 4×3 + 16

  = 28

If x = 4,

y = 4×4 + 16

  = 32

If x = 5,

y = 5×4 + 16

  = 36

If x = 6,

y = 6×4 + 16

  = 40

Cat age             2            3           4            5            6

Human years   24          28        32          36          40

Answer:

[tex]m\angle 3=30^\circ,~m\angle 8=150^\circ[/tex]

Step-by-step explanation:

Angles and Lines

We must recall some properties of angles and lines:

Linear pair of angles: Two angles are linear if they are adjacent angles formed by two intersecting lines. They must add up to 180°.

Corresponding angles: They are angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are congruent, i.e., they have the same measure.

The figure shows two parallel lines a and b, crossed by the line m. These conditions make the following relations be true:

Angles 3 and 4 are linear pair

Angles 8 and 4 are corresponding.

The first relation leads to:

[tex]m\angle 3+m\angle 4 = 180^\circ[/tex]

The second relation leads to:

[tex]m\angle 4 = m\angle 8[/tex]

Since:

[tex]m\angle 3=x[/tex]

[tex]m\angle 8=5x[/tex]

Substituting:

[tex]x + 5x = 180^\circ[/tex]

Simplifying:

[tex]6x = 180^\circ[/tex]

Solving for x:

[tex]x = 180^\circ/6[/tex]

[tex]x = 30^\circ[/tex]

Now,

[tex]m\angle 3=x=30^\circ[/tex]

[tex]m\angle 8=5x=150^\circ[/tex]

[tex]m\angle 3=30^\circ,~m\angle 8=150^\circ[/tex]

Answer:

free 25

Step-by-step explanation:

Answer:

if you ment to say 2 is 12.5% of what number the answer would be 16

Step-by-step explanation:

Write down what you know with x as the number you need to find.

Of is always "multiply"

Choose another way to write 12.5%

2 =12.5% of x

So 2 = 0.125xx

x= 2 *over*0.125

x=16

Answer:

x=16

Step-by-step explanation:

Let the number be x.

if they say 12.5% of a number, this means that 12.5/100 *x which will be :

12.5/100x

make it an equation (a true one)

12.5/100x=2

divide.

2 divided by 12.5/100x would be

x=16!

Cheers, I hope you can understand it well!

Answer:

60

Step-by-step explanation:

Put in Parentheses.

(5 + 1) x 10 =

Solve numbers inside parentheses.

5 + 1 = 6

Now we have 6 x 10.

6 x 10 = 60

Answer:

Step-by-step explanation:

Given:

AB ≅ BC

AK ≅ KC

∠AKE ≅ ∠CKP

To Prove:

ΔAKE ≅ ΔCKP

         Statements                               Reasons

1). AB ≅ BC                                          1). Given

2). ∠BAC ≅ ∠BCA                              2). Property of Isosceles triangles

3). ∠EKA ≅ ∠PKC                               3). Given

4). ΔAKE ≅ ΔCKP                               4). ASA Postulate of congruence

Hence ΔAKE ≅ ΔCKP.

Answer: So if you do 50 dollars - 70% you get, 15 U.S. dollars

Hope this helps :)

Answer:

2139 with a remainder of 1

Step-by-step explanation:

hope this helps :))) have a great day!

Answer:

Step-by-step explanation:

Given the equation

[tex]\frac{1}{5}x-\frac{2}{3}y=30[/tex]

putting y=15

[tex]\frac{1}{5}x-\frac{2}{3}\left(15\right)=30[/tex]

[tex]\frac{1}{5}x-10=30[/tex]

add 10 to both sides

[tex]\frac{1}{5}x-10+10=30+10[/tex]

[tex]\frac{1}{5}x=40[/tex]

[tex]x=200[/tex]

Therefore, the value of x:

Answer:

13/12

Step-by-step explanation:

2(5/3+3/4)_4/3

2(20+9/12)_4/3

2(29/12)_4/3

58/24_4/3

58_32/24

26/24

13/12

Answer:

Following are the solution to the given point:

Step-by-step explanation:

In point a:

[tex]\to 2ty'=8y\to \frac{1}{y} dy = 4 \frac{1}{t} dt\\\\\to \int \frac{1}{y} dy = 4 \int \frac{1}{t} dt \\\\\to \log y = 4 \log t + \log C\\\\\to \log y = \log ct^4\\\\\to y=ct^4 \\\\\to y(-2)=16 \\\\\to 16= c(-2)^4\\\\\to 16= 16c\\\\\to c= \frac{16}{16}\\\\\to c=1\\\\\to r=4[/tex]

In point b:

[tex]\to 2ty' = 8y \\\\\to y'- \frac{4}{t} y=0 \\\\here \ p(t) = \frac{1}{t}[/tex] it's a discontinuous point at t=0, and the largest internal containing -2 since [tex]y=(-2) = 16 \ is\ (-\infty, 0)[/tex]

In point c:

[tex](-\infty,0 ) \cup (0, \infty)[/tex]

Answer:

63

Step-by-step explanation:

36 is approximately 30% of 124 and 42 is approximately 33% of 124, so 30 + 33 = 63

Answer:

Answer, B

Step-by-step explanation:

add the odes and sonnets, and find the percentage of 78/124 which is 62.9% rounded to 63%.

Answer:

they have to pay for school supplies

Step-by-step explanation:

Answer: It would be B 9/50

Step-by-step explanation: if you take 3/7 and x it by 0.1 you get 0.04285714285 and then if you divide that by 5/21 you get 0.18 which equals 9/50 as a fraction

Answer:

-3/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Complete question is;

The diameter of bushings turned out by a manufacturing process is a normally distributed random variable with a mean of 4.035 mm and a standard deviation of 0.005 mm. A sample of 25 bushings is taken once an hour.

a. Within what range should 95 percent of the bushing diameters fall?

b. Within what range should 95 percent of the sample means fall?

c. What conclusion would you reach if you saw a sample mean of 4.020?

Answer:

A) (4.0252, 4.0448).

B) (4.0331, 4.0369).

C) If i saw a sample mean of 4.020, i would conclude that the sample came from a population that did not have a population mean equal to 4.035

Step-by-step explanation:

A) We know that an approximate 95% confidence interval for the item in question has a range of diameter given by the equation;

Range = x¯ ± 1.96σ

Now, since we have a mean of 4.035 mm and a standard deviation of 0.005 mm, we can solve;

Range of bushing diameter = 4.035 ± (1.96 × 0.005) = 4.035 ± (0.0098)

= 4.0252 or 4.0448 and it can be written as;(4.0252, 4.0448).

B) We also know that In the large-sample case, a 95% confidence interval estimate for the population mean is given by the formula;

CI = x¯ ± (1.96s/√n))

Thus, if we solve, we get;

CI = 4.035 ± (1.96 × 0.005 )/√25

CI = 4.035 ± 0.0019

or (4.0331, 4.0369).

c. If i saw a sample mean of 4.020, i would conclude that the sample came from a population that did not have a population mean equal to 4.035 because it doesn't fall into the range of confidence intervals we got earlier.

Answer:

Step-by-step explanation:

-3

perpendicular slope is the negative of the reciprocal

the reciprocal of 1/3 is 3

the opposite of 3 = -3

Answer:

∠AMC  = 75

Step-by-step explanation:

ΔABC,

∠C = 90°  ; ∠B = 30°

∠A + ∠B +∠C  = 180   {Angle sum property of triangle}

∠A + 30 + 90 = 180

       ∠A + 120 = 180

                 ∠A = 180 - 120

                 ∠A  = 60°

In ΔACM,

∠ACM = 90/2  =  45°         { CM is angle bisector}

∠ACM + ∠AMC +∠A =  180   {angle sum property}

   45 +  ∠AMC + 60 = 180

            ∠AMC + 105 = 180

                     ∠AMC = 180 - 105

∠AMC  = 75

Answer:

y>1/3x-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

m = [tex]\frac{rise}{run}[/tex] = [tex]\frac{1}{3}[/tex]

y-intercept is (- 3)

y > [tex]\frac{1}{3}[/tex] x - 3

Answer:

Midpoint (xM, yM)  =  (4, 5)

Hope it helps if it does pls give me brainly :)

Answer:

m∠1 = 37°

General Formulas and Concepts:

Pre-Algebra

Geometry

Step-by-step explanation:

Step 1: Define

m∠3 = 127°

m∠G = 90°

Step 2: Find m∠2

Step 3: Find m∠1

Answer:

x = 20

Step-by-step explanation:

2(x - 5) = 9 - 3x + 6 + 8 + 3x + 7

2x - 10 = 9 - 3x + 6 + 8 + 3x + 7

2x = 10 + 6 + 8 + 7 + 9

2x = 40

x = 40 ÷ 2

x = 20

Thus, x = 20

-TheUnknownScientist

Answer:

the answer is 4(5c-2d)

Answer:

20c-8d

Step-by-step explanation:

As long as you weren't any values for c or d, this expression cannot be simplified any further.

HTH :)

Answer:

Explained below.

Step-by-step explanation:

(A)

Use two-point form to determine the equation for the total monthly cost of the NextFell plan.

[tex](y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\cdot (x -x_{1})\\\\(y-247)=\frac{247-114}{640-260}\cdot (x-640)\\\\(y-247)=0.35x-224\\\\y=0.35x+23[/tex]

(B)

Compute the total monthly cost if 949 minutes are used as follows:

[tex]y=0.35x+23\\\\=(0.35\times 949)+23\\\\=355.15[/tex]

Thus. the total monthly cost if 949 minutes are used is $355.15.

Answer:

-2.5

Step-by-step explanation:

Your want to isolate the x. This is a multiplication problem, so use the inverse operation, which is division. Divide both sides of the equation by

1/4 by multiplying by the reciprocal, 4. (− 5

8)(4) is − 5/2. Use substitution to check the answer. x = − 5/2 :)

Answer: First, you isolate x by dividing 1/4 on both sides.  

1/4x divided by 1/4 equals zero, which just leaves x, and -5/8 divided by 1/4 equals -5/2, so x = -5/2. -5/2 can be simplified to -2.5,  

To check the answer, substitute x for -5/2:

* 1/4 multiplied by -5/2 equals -5/8

* 5/8 = 5/8, so this proves that my answer is correct.