Solve for x. Round to the nearest tenth, if necessary.

Answer:

The length of the shortest side of the triangle is 10 units.

Step-by-step explanation:

Let a be the shortest side of the isosceles triangle and b be the two congruent sides.

The congruent sides b are each one unit longer than the shortest side. Hence:

[tex]b=a+1[/tex]

The perimeter of the isosceles triangle is given by:

[tex]\displaystyle P_{\Delta}=b+b+a=2b+a[/tex]

This is equivalent to the perimeter of a square whose side lengths are two units shorter than the shortest side of the triangle. Let the side length of the square be s. Hence:

[tex]s=a-2[/tex]

The perimeter of the square is:

[tex]\displaystyle P_{\text{square}}=4s=4(a-2)[/tex]

Since the two perimeters are equivalent:

[tex]2b+a=4(a-2)[/tex]

Substitute for b:

[tex]2(a+1)+a=4(a-2)[/tex]

Solve for a. Distribute:

[tex]2a+2+a=4a-8[/tex]

Simplify:

[tex]3a+2=4a-8[/tex]

Hence:

[tex]a=10[/tex]

The length of the shortest side of the triangle is 10 units.

Step-by-step explanation:

 the rational numbers between 1/6 and 2/3 are 2/6 ,3/6 .

Answer:

therefore the rational numbers between 1/6 and 2/3 are 2/6 ,3/6 .........

Answer:

[tex]\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6[/tex]

Step-by-step explanation:

We want to write the equation for a quadratic function in vertex form with vertex at (-1, 6) that passes through the point (-3, 4).

Vertex form is given by:

[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]

Where (h, k) is the vertex and a is the leading coefficient.

Since our vertex is at (-1, 6), h = -1 and k = 6. Substitute:

[tex]f(x)=a(x-(-1))^2+(6)[/tex]

Simplify:

[tex]f(x)=a(x+1)^2+6[/tex]

Next, since the quadratic passes through the point (-3, 4), f(x) = 4 when x = -3. Substitute:

[tex](4)=a(-3+1)^2+6[/tex]

Solve for a. Simplify:

[tex]-2=a(-2)^2[/tex]

Hence:

[tex]\displaystyle -2=4a\Rightarrow a=-\frac{1}{2}[/tex]

Therefore, our function in vertex form is:

[tex]\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6[/tex]

Answer:

(a) is 8 x 7 x 3 = 168

(b) is 8 x 7 = 56

(b2) is weird I don't know what it's asking

Answer:

FOR LETTER A

Volume of prism (expression) = Length x Width/Breadth x Height

Volume of prism (expression) = 8 units x 7 units x 3 units = 168 cubic units

FOR LETTER B

Area of the shaded base = 8 x 7 = 56 square units

Volume of prism = Area of the shaded base x Height

Volume of prism = 56 square units x 3 units = 168 cubic units

Step-by-step explanation:

To find the volume of rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism.

Volume of rectangular prism = length × width × height

To get the area of the shaded base, when the base is in rectangular shape:

Definition: Area of rectangle is the region occupied by a rectangle within it's four sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area. But in the case of a square, since all the sides are equal, therefore, the area of the square will be equal to the square of side-length.

Area of rectangle = Length × Breadth

A = l × b

Answer:

[tex]10x - \frac{1}{x} = 3 \\ 10x = 3 + \frac{1}{x} \\ 10x = \frac{3x + 1}{x} \\ 10x \times x = 3x + 1 \\ 10 {x}^{2} = 3x + 1 \\ 10 {x}^{2} - 3x - 1 = 0 \\ 10 {x}^{2} - 5x + 2x - 1 = 0 \\ 5x(2x - 1) + 1(2x - 1) = 0 \\ (5x + 1)(2x - 1) = 0 \\ \\ 5x + 1 = 0 \\ 5x = - 1 \\ x = \frac{ - 1}{5} \\ \\ 2x - 1 = 0 \\ 2x = 1 \\ x = \frac{1}{2} [/tex]

hope this helps you.

Have a nice day!

Answer:

48 units

Step-by-step explanation:

Work Shown:

sin(angle) = opposite/hypotenuse

sin(F) = EG/FE

sin(F) = 56/65

Refer to the diagram below.

Answer:

Where are the ordered pairs?

Step-by-step explanation:

[tex] \green{\huge{\red{\boxed{\green{\mathfrak{QUESTION}}}}}} [/tex]

What is the slope of y = - x + 7

[tex] \red{ \bold{ \textit{STANDARD \: EQUATION}}}[/tex]

[tex]y = mx + c[/tex]

[tex]WHERE \\ m = SLOPE \\ c = Y - INTERCEPT[/tex]

[tex] \huge\green{\boxed{\huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}}}[/tex]

[tex] \blue{A.T.Q}[/tex]

[tex]y = mx + c \sim y = ( - 1)x + 7[/tex]

[tex] \orange{SO}[/tex]

m= (-1)

which is equal to the slope of the equation .

[tex] \red \star{Thanks \: And \: Brainlist} \blue\star \\ \green\star If \: U \: Liked \: My \: Answer \purple \star[/tex]

Answer:

44

Step-by-step explanation:

Let's say that Devaughn's age is D, and Sydney's age is S.

We know that D is 7 greater than S, so D = 7 + S.

We know that the sum of their ages, or D + S, is equal to 95, so D+S = 95

We have

D = 7 + S

D + S = 95

What we can do is plug D= 7 + S into the second equation to get

D + S = 95

= (7+ S) + S

= 7 + 2 * S

7+2 * S - 95

subtract 7 from both sides to isolate the coefficient and the variable

2 * S = 88

divide both sides by 2 to isolate the variable

S = 44

Sydney is therefore 44 years old

Answer:

7

Step-by-step explanation:

6m = 3m + 21

6m - 3m = 21

3m = 21

m = 21 / 3

m = 7

Answer:

-37

Step-by-step explanation:

-155-20-14-133-73=-395

190+170=360

-395+360=-37

Given:

The gradient of the line passing through A(2,3), B(k,7) is [tex]\dfrac{2}{3}[/tex].

To find:

The value of k.

Solution:

The gradient or slope of a line is:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The gradient of the line passing through A(2,3), B(k,7) is [tex]\dfrac{2}{3}[/tex]. So,

[tex]\dfrac{2}{3}=\dfrac{7-3}{k-2}[/tex]

[tex]\dfrac{2}{3}=\dfrac{4}{k-2}[/tex]

On cross multiplication, we get

[tex]2(k-2)=4(3)[/tex]

[tex]2k-4=12[/tex]

[tex]2k=12+4[/tex]

[tex]2k=16[/tex]

Divide both sides by 2.

[tex]k=\dfrac{16}{2}[/tex]

[tex]k=8[/tex]

Therefore, the value of k is 8.

one is 1800 and another is 1200

Step-by-step explanation:

let no's be A and B

so, A+B =3000

given, 8% = 8/100 = 2/25

12%= 12/100 = 3/25

As per question 8% of A is = 12% of B

so, (2/25)*A = (3/25)*B

now, multiply cross wise

then we get, (A/B) = 3:2

thus two numbers are in the ratio of 3:2

so, let A =3x, B=2x

cause sum of these is 3000 so, A+B =3000

3x+2x =3000

5x = 3000

x= 3000/5

.: x = 600

so, first no is 3x =3*600=1800

2nd no is 2x= 2*600= 1200

Hope this helps you

ANSWER:

10 units

EXPLAINATION:

The measure of the indicated side would be 10 units because the triangle shown here is a equilateral triangle this can be seen by the picture in which all the angles of the triangle are equal.

Answer:

15, The answer is greater than 14 because when you multiply the 2 fractions you get a number that is greater than 15

Step 1: Set up equation

[tex]\frac{25}{1}*\frac{3}{5}[/tex]

Step 2: Cross reduce

you can cross reduce 25 and 5 because they are both share a common divisor

[tex]\frac{5}{1} *\frac{3}{1}[/tex]

Step 3: Multiply numerator and denominator together

[tex]\frac{15}{1}[/tex]

Final Answer:

15

The answer is greater than 14 because when you multiply the 2 fractions you get a number that is greater than 15

Answer:

option 3. (4, -2)

Step-by-step explanation:

For a relation to be a function there should be exactly one output value for a given input.

In the given relation :-

4 has 2 outputs, -2 and 2, so if we remove the pair (4, -2) 4 will have only one output value ,i. e., 2. And hence the relation will be a function.

So the answer is option 3. (4, -2)

Answer:

C. right triangle only

Step-by-step explanation:

Other triangles use other laws such as law of cosines or sines to solve them. Right triangles exclusively use SOH-CAH-TOA because side opposite to 90 degree is always hypotenuse.

Answer:

about 27.6

Step-by-step explanation:

The sum of interior angles for this rectangle is 1080

119+140+124+6x+132+132+102 = 1080 add like terms

749 + 12x = 1080 subtract 749 from both sides

12x = 331 divide both sides by 12

x = 27.6 approximately

Given:

The figure of a triangle.

The perimeter of the triangle ABC is 31.

To find:

The value of x in the given triangle.

Solution:

Three sides of the triangle ABC are AB, BC, AC are their measures are [tex]3b-4,2b+1,b+10[/tex] respectively.

The perimeter of the triangle ABC is 31.

[tex]AB+BC+AC=31[/tex]

[tex](3b-4)+(2b+1)+(b+10)=31[/tex]

[tex]6b+7=31[/tex]

Subtract 7 from both sides.

[tex]6b=31-7[/tex]

[tex]6b=24[/tex]

[tex]b=\dfrac{24}{6}[/tex]

[tex]b=4[/tex]

Now, the measures of the sides are:

[tex]AB=3b-4[/tex]

[tex]AB=3(4)-4[/tex]

[tex]AB=12-4[/tex]

[tex]AB=8[/tex]

[tex]BC=2b+1[/tex]

[tex]BC=2(4)+1[/tex]

[tex]BC=8+1[/tex]

[tex]BC=9[/tex]

And,

[tex]AC=b+10[/tex]

[tex]AC=4+10[/tex]

[tex]AC=14[/tex]

Using the law of cosines, we get

[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]

[tex]\cos A=\dfrac{(AC)^2+(AB)^2-(BC)^2}{2(AC)(AB)}[/tex]

[tex]\cos A=\dfrac{(14)^2+(8)^2-(9)^2}{2(14)(8)}[/tex]

[tex]\cos A=\dfrac{179}{224}[/tex]

Using calculator, we get

[tex]\cos A=0.7991[/tex]

[tex]A=\cos ^{-1}(0.7991)[/tex]

[tex]x=36.9558^\circ[/tex]

[tex]x\approx 37.0^\circ[/tex]

Therefore, the value of x is 37.0 degrees.

Answer:

α = 0.63 radians

Step-by-step explanation:

We are given;

Length of arc; L = 1.6 mm

Radius; r = 2.54 mm

The arc length equation is given by;

L = αr

Where;

L is length of arc

r is radius

α is angle in radians

Thus;

α = L/r

α = 1.6/2.54

α = 0.63 radians

Answer:

(1.6, 6)

Step-by-step explanation:

[tex] ln({e}^{5 - 2x} = 6)[/tex]

[tex]5 - 2x = ln(6) [/tex]

[tex]2x = 5 - ln(6) [/tex]

[tex]x = \frac{5 - ln(6) }{2} [/tex]

y = 6

Answer:

i) 2 + 2x

ii) 154 = 2(2 + 2x + x)

iii) Length = 52m

Breadth = 25m

Step-by-step explanation:

Perimeter of swimming pool = 154m

Breadth = x

Length = 2 + 2x

Formula for finding perimeter = P = 2(l + b)

Therefore,

154 = 2 ( 2 + 2x + x)

154 = 4 + 4x + 2x

154 = 4 + 6x

154 - 4 = 6x

150 = 6x

150/6 = x

25 = x

With the value of x,

we can fInd the length and the breadth

Breadth = x

= 25

Length = 2 + 2x

= 2 + 2(25)

= 2 + 50

= 52

Answer:

19.5 cm

Step-by-step explanation:

the remaining height = 1200 /(12×8)

= 1200/96 = 12.5 cm

so, the height of the tank = 7+ 12.5 = 19.5 cm

[tex]\displaystyle\bf \boxed{V=abh \ ; \ 1dm^3=1litre=1000cm^3} \\\\a=12cm \ ; \ b=8 cm ;\: h_1=7 \; ; \ h_0=h_1+h_2=?\\\\abh_2=1,2litre=1,2dm^3\ = 1200cm^3\\\\ 8\cdot 12 h_2=1200\\\\h_2=12.5 cm\: then \\\\h_0= 7+12,5=19,5 \\\\Answer : the \ height \ of \ the \ tank \ is \ 19,5 cm[/tex]

Answer:

1) Less than

2) greater than

Step-by-step explanation:

Equation of the first line:

(y+7)/(-13+7) = x/-1

(y+7))/-6 = -x

y+7 = 6x

y= 6x - 7

Equation of the second line:

A (4/3,0) ; B (0,8)

y/8 = (x-4/3)/-4/3

y/8 = (x-4/3) * -3/4

y/8 = -3/4x + 1

y = -6x + 8

Answer:

(centre = (3, - 1 ) and radius = 7

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 6x + 2y - 39 = 0 ( collect x/ y terms and add 39 to both sides )

x² - 6x + y² + 2y = 39

Using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 3)x + 9 + y² + 2(1)y + 1 = 39 + 9 + 1

(x - 3)² + (y + 1)² = 49 ← in standard form

with centre (3, - 1 ) and r = [tex]\sqrt{49}[/tex] = 7

Answer:

.14

Step-by-step explanation:

A|B (or A given B)= A and B/B

So

Walk to school | senior= (walk to school and senior)/Senior

walk to school and senior= 5

senior= 25+5+5= 35

5/35= .14