x+y=5
x×y=6
Solve simultaneously with steps

For Janna to prove that △ABC∼△DEF by the SSS similarity theorem, she will use: B. DE/AB = EF/BC = DF/AC = 1/4.

According to the SSS similarity theorem, if the ratio of the corresponding sides of two triangles are equal, then both triangles are similar.

The ratio of the corresponding sides of the triangles given are:

DE/AB = 4/16 = 1/4

EF/BC = 3.25/13 = 1/4

DF/AC = 1.75/7 = 1/4

Therefore, what Janna needs is:

B. DE/AB = EF/BC = DF/AC = 1/4

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I am not 100% sure but I think it is 85 degrees

DO NOT take my word for it

Step-by-step explanation:

I'm not sure but I think it is 75 degree

Answer:

x=4

Step-by-step explanation:

3x=5+7

7+5=12

12/3=4

x=4

Hope this helps!!

Answer:

x=4

Step-by-step explanation:

add like terms

3x =5+7

3x=12

divide both sides by 3

3x=12

3    3

x=4

Answer:

  x ≈ -8.402, 8.502

Step-by-step explanation:

The usual methods of solving quadratic equations apply to this one. Any of them can be used: graphing, factoring, completing the square, quadratic formula.

Often, when the coefficients are non-integers and have no obvious relationship to each other, the most convenient method of solution is the quadratic formula. It tells you the solution to ax²+bx+c=0 is ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Your equation has the coefficients, a = -0.07, b = 0.007, c = 5, so the solutions are ...

  [tex]x=\dfrac{-0.007\pm\sqrt{0.007^2-4(-0.07)(5)}}{2(-0.07)}=\dfrac{-0.007\pm\sqrt{1.400049}}{-0.14}\\\\x=0.05\pm\sqrt{\dfrac{200007}{2800}}=0.05\pm\sqrt{71.4310\overline{714285}}\\\\\boxed{x\approx\{-8.40169,\,8.50169\}}[/tex]

Answer:

[tex]t=8.50, -8.40\:\: \sf (2 \:d.p.)[/tex]

Step-by-step explanation:

Quadratic equations are in the form [tex]ax^2+bx+c=0[/tex],  where [tex]a\neq 0[/tex].

There are three basic methods to solve quadratic equations algebraically:

Given quadratic equation:

[tex]h(t)=-0.07t^2+0.007t+5[/tex]

Method 1 - Factoring

If the trinomial is able to be easily factored, set the equation equal to zero and factor.  Set each factor equal to zero and solve.

As the given example is not easily factored, factoring is not the best method to use on this occasion.

Method 2 - Completing the Square

If the quadratic expression is not able to be easily factored, try completing the square.

Divide all terms by [tex]a[/tex] (-0.07):

[tex]\implies t^2-\dfrac{1}{10}t-\dfrac{500}{7}=0[/tex]

Move the constant to the right side:

[tex]\implies t^2-\dfrac{1}{10}t=\dfrac{500}{7}[/tex]

Add the square of half the coefficient of t to both sides:

[tex]\implies t^2-\dfrac{1}{10}t+\left(-\dfrac{1}{20}\right)^2=\dfrac{500}{7}+\left(-\dfrac{1}{20}\right)^2[/tex]

[tex]\implies t^2-\dfrac{1}{10}t+\dfrac{1}{400}=\dfrac{200007}{2800}[/tex]

Factor the perfect trinomial:

[tex]\implies \left(t-\dfrac{1}{20}\right)^2=\dfrac{200007}{2800}[/tex]

Square root both sides:

[tex]\implies t-\dfrac{1}{20}=\pm\sqrt{\dfrac{200007}{2800}[/tex]

Add 1/20 to both sides:

[tex]\implies t=\dfrac{1}{20}\pm\sqrt{\dfrac{200007}{2800}[/tex]

As decimals to 2 decimal places:

[tex]\implies t=8.50, -8.40\:\:\sf(2 \:d.p.)[/tex]

Method 3 - Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

This can be used to find both real and imaginary or complex solutions.

Identity the variables:

[tex]a=-0.07, \quad b=0.007, \quad c=5[/tex]

Substitute the values into the quadratic formula and solve for t:

[tex]\implies t=\dfrac{-0.007 \pm \sqrt{0.007^2-4(-0.07)(5)} }{2(-0.07)}[/tex]

[tex]\implies t=\dfrac{-0.007 \pm \sqrt{1.400049}}{-0.14}[/tex]

[tex]\implies t=\dfrac{0.007 \pm \sqrt{1.400049}}{0.14}[/tex]

[tex]\implies t=8.50, -8.40\:\: \sf (2 \:d.p.)[/tex]

Finally, a non-algebraic method of solving a quadratic equation is by graphing using a graphical calculator (see attached).  The solutions are the points at which the curve intercepts the x-axis.

Answer:

1:3 is an example and for every two boy there are 5 girls is another example

Edited: I go out Five times as much as My sister does. My sister goes out only 3 times. Which is 15:1

I see 5 blue cars for every 6 red cars. Which is 5:6

Ratio is always represented in terms of ':' like a:b

Examples

#1

The ratio of apples is 2:4 or 1:2

#2

The ratio is 10:7

Answer:

the answer would be no shape.

Step-by-step explanation:

imagine you have the paper in your hands, if you start from the left you would have to fold the paper 3 times, then when it comes to the last 2 squares, you wouldnt be able to close the cube. hope this helps

Answer:

an open cube

Step-by-step explanation:

your welcome

Answer:

12 and 8

Step-by-step explanation:

→ Set up two equations

x - y = 4

[tex]\frac{x+y}{2} =10 \\ \\x + y = 20[/tex]

→ Add the 2 equations together

2x = 24

→ Solve for x

x = 12

→ Substitute into original equation

12 - y = 4

→ Solve

y = 8

The original price is £75

Let the original price be x.

The reduced price is given as:

Reduced =60

So, we have:

Reduced = Original price * (1 - discount)

This gives

x * (1- 20%) = 60

Evaluate the difference

x * 0.8 = 60

Divide by 0.8

x = 75

Hence, the original price is £75

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Answer:

attached

Step-by-step explanation:

The probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 mm is 0.1698 or 16.98%.

Mean length of the population (μ) = 176 mm.

Variance of the population (σ²) = 100.

Therefore, the standard deviation of the population (σ) = √100 = 10.

The sample size (n) = 446.

The mean of the sample = the mean of the population = μ = 176 mm.

The standard deviation of the sample (s) = σ/√n = 0.4735137.

We are asked to find the probability that the sample rods would differ the population mean by greater than 0.65 mm, that is,

either the length of the sample rods is less than (176 - 0.65) =175.35

or the length of the sample rods is more than (176 + 0.65) = 176.65.

This can be shown as P(X < 175.35 or X > 176.65) = 1 - P(175.35 < X < 176.65) = 1 - Normalcdf(175.35,176.65,176,0.4735137) = 1 - 0.8302 = 0.1698 or 16.98%.

Thus, the probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 mm is 0.1698 or 16.98%.

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Answer:

They have none left over and they can make 43 dishes

Step-by-step explanation:

The information given illustrates that the equivalent fraction will be 2/6.

It should be noted that equivalent fraction simply means the fractions that are the same.

In this case, we are given 4/6 and 1/3. They have different numerators and denominators. The question is simply to change 1/3 to another fraction that has a denominator of 6.

This will be illustrated. The equivalent faction to 1/3 will be:

= 1/3 × 2/2

= 2/6

Therefore, the answer is 2/6.

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The model (x+a)(x-a) will represents the factors of 4x²-9 as (2x+3)(2x-3).

The "completing the squares" method aims to construct a quadratic equation of the form where the x variable is entirely covered by a single squared term, which is the square of a linear expression in x, as the name suggests.

The quadratic equation can resemble this:

x²-a² = (x+a)(x-a)

Given equation;

⇒4x²-9

⇒(2x)²-3²

The equation can be modeled as;

(2x+3)(2x-3)

Hence the model (x+a)(x-b) will represents the factors of 4x²-9 as (2x+3)(2x-3).

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The value of f(32) is 3

A function is a mathematical statement used to relate two variables .

It is given that

8f(x) = f((1/8)x)

It is also given that

f(4) = 24

now to determine the value of f(32)

8 * f(32) = f((1/8) *32)

8 *  f(32) = f(4 )

f(32) = 24 /8 = 3

Therefore the value of f(32) is 3

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Answer:

A. 8/17

Step-by-step explanation:

Cosine = adjacent over hypotenuse

Adjacent to angle 62 is 8 (The two angles are said to be adjacent angles when they share the common vertex and side).

The hypotenuse is 17 (opposite of right angle)

Answer:

D

Step-by-step explanation:

(ax + b)² = c

step 1 : take square root of both sides

ax + b = ± [tex]\sqrt{c}[/tex]

step 2 : subtract b from both sides

ax = - b ± [tex]\sqrt{c}[/tex]

step 3 : divide both sides by a

x = - [tex]\frac{b}{a}[/tex] ± [tex]\frac{\sqrt{c} }{a}[/tex]

Answer:

D. Take the square root of both sides

Step-by-step explanation:

Given quadratic equation:

[tex](ax+b)^2=c[/tex]

To solve, square root both sides:

[tex]\implies \sqrt{(ax+b)^2}=\sqrt{c}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{n^2}=n, \quad \textsf{assuming }n \geq 0:[/tex]

[tex]\implies ax+b=\pm\sqrt{c}[/tex]

Subtract b from both sides:

[tex]\implies ax=-b\pm\sqrt{c}[/tex]

Divide both sides by a:

[tex]\implies x=\dfrac{-b\pm\sqrt{c}}{a}, \quad a\neq 0[/tex]

Considering the volume of the given rectangular prism, the height is of 5.03 feet.

The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

In this problem, we have that:

The volume is of 365 cubic feet, hence:

lwh = 365

(2h + 2)(h + 1)h = 365

(2h² + 4h + 2)h - 365 = 0

2h³ + 4h² + 2h - 365 = 0.

Using a cubic equation calculator, the height is of h = 5.03 feet.

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The area of the garden is 33 ft².

The number of tiles required to cover the floor is 17 tiles.

The area of a dog pen is 170/9 square yards.

We need to find the area and perimeter for the given questions.

The formula to find the perimeter of a rectangle=2(Length+Breadth)

The formula to find the area of a rectangle=Length×Breadth.

Given that, a small garden has a perimeter of 24 1/4 ft and the length is 8 ft.

Now, perimeter = 2(8+Breadth)

⇒24 1/4=16+2×Breadth

⇒97/4-16=2×Breadth

⇒Breadth=97-64/4×2=33/8 ft

Now, Area=8×33/8=33 ft²

Therefore, the area of the garden is 33 ft².

Given that, the floor measures 4 1/2 ft by 3 3/4 ft.

The area of a floor=Length×Breadth=9/2×15/4=135/8 ft²

Number of tiles to cover the floor=135/8=16.875

Therefore, the number of tiles required to cover the floor is 17 tiles.

Given that, a dog pen is 3 1/3 yards wide by 5 2/3 yards long.

Now, the area of a dog pen=10/3×17/3=170/9 square yards.

Therefore, the area of a dog pen is 170/9 square yards.

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Answer:

20

Step-by-step explanation:

Long Division, cancel the zeroes, then 80/4 which is 20

Answer:

20

Step-by-step explanation:

8000/400= 20

Answer:

15.

Step-by-step explanation:

Width of the strip + cut = 5/8 + 1/8 = 3/4.

11 3/8 / 3/4

=  91/8 / 3/4

= 91/8 * 4/3

= 91/6

= 15  1/6

So the answer is 15

The location of the fountain based on the information given is (-1, 0.5).

From the graph, the coordinates are (4, 2) and (-4,   -2).

The ratio is given as 5:3.

The coordinates of the fountain will be:

[(5 × -4 + 3 × 4)/(5 + 3), (5 × -3 + 3 × 2)/(5 + 3)]

= (-1, -0.5)

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Answer:

45

Step-by-step explanation:

Use khan acedaemy

Option D: Type I error ("Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15").

Option B: Type II error ("Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15").

Type I​ error:

A. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.

B. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.

C. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.

D. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.

A Type I error is when the null hypothesis is rejected when it is true. In this case, the null hypothesis is that "the proportion of people who write with their left hand is equal to 0.15".

The right option is D (reject the null hypothesis when it is true).

Type II​ error:

A. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.

B. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.

C. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.

D. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.

A Type II error is when the null hypothesis is failed to be rejected when the alternative hypothesis is true. In this case, the null hypothesis is that "the proportion of people who write with their left hand is equal to 0.15".

The right option is B (failed to reject the null hypothesis when it is false).

The options A and C are correct decisions, as reject the null hypothesis when it is false (Option C) and not reject the null hypothesis when it is true (Option A).

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The congruence theorem that can be used is: B. ASA

If we have two triangles that have two pairs of corresponding congruent angles (e.g. ∠LGH ≅ ∠HKJ and ∠LHG ≅ ∠KHJ), and a pair of corresponding congruent sides (e.g. GH ≅ HK), the triangles are said to be congruent triangles by the ASA congruence theorem.

Therefore, triangles GHL and KHL in the image given are congruent triangles by the  ASA congruence theorem.

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Answer: Option 2 or B. ASA

Step-by-step explanation: Trust me!

If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful. Good luck everyone!  :)

Answer:

180

Step-by-step explanation:

For each of the two right triangles, by the Pythagorean theorem, she shared side is of length 15. So, the area of each of the top two rectangles is (½)(8)(15), so their combined area is 120.

Moving onto the trapezoid, we can use the formula for the area of a trapezoid to determine its area is (½)(14+16)(4)=60.

So, the answer is 120+60=180.

Answer:

The solutions of the equation |2 x-3|=17

are x=10

and x=-7

Step-by-step explanation:

Given equations is |2 x-3|=17.

It is required to find out the values of x satisfying the given equation.

To find it out, use the fact that the solution of this type of equation is 2x-3=17.

Or 2x-3=-17 and simplify the equations using simple mathematical operations.

Step 1 of 2

Solve the equation 2x-3=17,

Add 3 on both sides of the equation 2x-3=17,

2x-3+3=17+3

2x=20

Divide by 2 on both sides of the equation 2x=20,

[tex]$$\begin{aligned}&\frac{2 x}{2}=\frac{20}{2} \\&x=10\end{aligned}$$[/tex]

Step 2 of 2

Solve the equation 2x-3=-17,

Add 3 on both sides of the equation 2x-3=-17,

[tex]$2 x-3+3=-17+3$\\ $2 x=-14$[/tex]

Divide by 2 on both sides of the equation 2x=-14,

[tex]$$\begin{aligned}&\frac{2 x}{2}=\frac{-14}{2} \\&x=-7\end{aligned}$$[/tex]

Using translation concepts, the graph of the function y = -|x| is given at the end of this answer.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Graph y = -|x| is a reflection over the x-axis of the function y = |x|, and both functions(|x| in red, -|x| in blue) are given in the graph at the end of this answer.

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The graphs can be described as shown below.

A.) The first graph has the y-intercept at 2. Therefore, the first graph can be described by the equation, y =5x + 2.

B.) For the second graph, the graph passes through the point (-1,0). Therefore, if we substitute the value of y as 0 in the equation y=3x+3, we will get x=-1.

Hence, the equation of the second graph is y=3x+3.

C.) For the third graph, the graph passes through the point (-1.5,0). Therefore, if we substitute the value of y as 0 in the equation y=2x+3, we will get x=-1.5.

Hence, the equation of the second graph is y=2x+3.

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The expressions are not equivalent, even though Ella got the same result when she substituted zero for f. Then the correct option is C.

The equivalent is the expressions that are in different forms but are equal to the same value.

Ella completed the following work to test the equivalence of two expressions.

First expression,                Second expression

⇒ 2f + 2.6                           ⇒ 3f + 2.6

⇒ 2(0) + 2.6                       ⇒ 3 (0) + 2.6

⇒ 0 + 2.6                           ⇒ 0 + 2.6.

⇒ 2.6                                 ⇒ 2.6

The expressions are not equivalent, even though Ella got the same result when she substituted zero for f.

Then the correct option is C.

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