Answer:
(3, 2), (2, 3)
Step-by-step explanation:
x + y = 5
xy = 6
Solve the first equation for x.
x = 5 - y
Substitute 5 - y for x in the second equation.
xy = 6
(5 - y)y = 6
5y - y² = 6
y² - 5y + 6 = 0
Factor.
(y - 2)(y - 3) = 0
y - 2 = 0 or y - 3 = 0
y = 2 or y = 3
Now substitute 2 for y in the first equation and solve for x.
x + y = 5
x + 2 = 5
x = 3
One solution is x = 3; y = 2, or (3, 2).
Now substitute 3 for y in the first equation and solve for x.
x + y = 5
x + 3 = 5
x = 2
Another solution is x = 2; y = 3, or (3, 2).
Answer: (3, 2), (2, 3)
Triangles G H L and K H J are connected at point H. Angles Angles L G H and H K J are congruent. Sides G H and H K are congruent.
Which congruency theorem can be used to prove that △GHL ≅ △KHJ?
SSS
ASA
SAS
AAS
The congruence theorem that can be used is: B. ASA
What is the ASA Congruence Theorem?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.
Learn more about the ASA congruence theorem on:
https://brainly.com/question/2398724
#SPJ1
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! :)
Samual has a collection of toy cars his favorites are the 27 red ones which makes up 60% of his collection how many toy cars dose he have??
Answer:
45
Step-by-step explanation:
Use khan acedaemy
For the following exercises, graph the given functions by hand.
41. y = −| x |
Using translation concepts, the graph of the function y = -|x| is given at the end of this answer.
What is a translation?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.
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
What's the equation of a line that passes through points (–1, –5) and (1, 3)? Question 20 options: y=-2x
y=1/4x-2
y=-x+4
y=4x-1
What 3D shape does this make? I think it's a cube but the only options are rectangular prism, rectangular pyramid, triangular prism, or no shape. Please help!
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
The price of a roll of fabric is reduced by 20%
to £60.
What was its original price?
The original price is £75
How to determine the original price?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
Read more about discount at:
https://brainly.com/question/3541148
#SPJ1
An 11 3/8-inch wide board can be cut into how many strips of width 5/8 inch, if each cut takes 1/8 inch of the width? (Must the answer be a whole
number?)
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
Use the following information to answer the question.
Triangle ABC has side lengths AB=16, BC=13, and AC=7.
Triangle DEF has side lengths DE=4, EF=3.25, and DF=1.75.
Janna needs to prove △ABC∼△DEF.
Which methods can she use to help her prove the triangles are similar by the SSS Similarity Theorem?
Select all that apply.
(The choices are in the image)
For Janna to prove that △ABC∼△DEF by the SSS similarity theorem, she will use: B. DE/AB = EF/BC = DF/AC = 1/4.
What is the SSS Similarity Theorem?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
Learn more about the SSS similarity theorem on:
https://brainly.com/question/4163594
#SPJ1
help asappppp
please
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
What is the equation of a line?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.
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ1
Question 5 of 10
What is the first step in solving a quadratic equation of the form given below?
(ax+ b)² = c
O A. Divide both sides by c
OB. Factor out a common factor
OC. Use the zero product rule
OD. Take the square root of both sides
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]
Question 5
Sam wants to build a toy box in the shape of a rectangular prism that will
hold 36 cubic feet. If the height needs to be 1 foot less than the width and
the length is twice the width, find the height of the toy box.
Considering the volume of the given rectangular prism, the height is of 5.03 feet.
What is the volume of a rectangular prism?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:
h = w - 1 -> w = h + 1.l = 2w = 2(h + 1) = 2h + 2.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.
More can be learned about the volume of a rectangular prism at https://brainly.com/question/17223528
#SPJ1
please help its timed i will give brainlyest
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
In the triangle below, what is the cosine of 62 degrees?
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)
An italian restaurant receive a shipment of 86 veal cutlet.if it takes to make a dish,how many cutlet will the restaurant have left over after making as many dishes as possible?
Answer:
They have none left over and they can make 43 dishes
Step-by-step explanation:
Find the area of each figure. GEOMETRY PLS HELPPPP
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.
Come up with two examples of ratio relationships that are interesting to you.
In mathematics a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other
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
Sam has 2 apples Jane has 4 applesThe ratio of apples is 2:4 or 1:2
#2
dummy stars present at your home =10Stars present in Big dipper =7The ratio is 10:7
For the following exercises, determine whether the functions are even, odd, or neither.
19. Solve |2x − 3 | = 17.
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]
Suppose a batch of steel rods produced at a steel plant have a mean length of 176 millimeters, and a variance of 100. If 446 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by greater than 0.65 millimeters
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%.
Learn more about the probability of sampling distributions at
https://brainly.com/question/15291567
#SPJ4
GUYS HELP QUICK!!!!
Ella completed the following work to test the equivalence of two expressions.
2 f + 2.6. 2 (0) + 2.6. 0 + 2.6. 2.6. 3 f + 2.6. 3 (0) + 2.6. 0 + 2.6. 2.6.
Which is true about the expressions?
The expressions are equivalent because Ella got different results when she substituted zero for f.
The expressions are equivalent because Ella got the same result when she substituted zero for f.
The expressions are not equivalent because Ella would get different results when substituting different numbers for f.
The expressions are not equivalent because Ella would get the same results when substituting different numbers for f.
The expressions are not equivalent, even though Ella got the same result when she substituted zero for f. Then the correct option is C.
What is an equivalent expression?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.
The complete question is attached below.
More about the equivalent link is given below.
https://brainly.com/question/889935
#SPJ1
Identify the type i error and the type ii error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to.
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).
Learn more about Errors on:
https://brainly.in/question/14970496
#SPJ4
Draw an angle that measures 260° in standard position.
Answer:
attached
Step-by-step explanation:
Could use some Geometry help
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
solve this mathematical equation 3x=5+7
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
1. A small garden has a perimeter of 24 1/4 ft. If the lengths is 8 ft, what is the area of the garden.
2. Lynn is putting tiles on her bathroom floor. Each tile measures 1 square foot each. The floor measures 4 1/2 ft by 3 3/4 ft. How many tiles will she need to cover the floor?
3. A dog pen is 3 1/3 yards wide by 5 2/3 yards long. What is the area of the dog pen?
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.
What are the formulas to find the perimeter and the area of a rectangle?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.
To learn more about the area and the perimeter visit:
https://brainly.com/question/11957651.
#SPJ1
Fernando and Maria are at opposite sides of a park. They plan to meet later at a fountain that is located somewhere between them. Maria will arrive at the fountain first, before Fernando even leaves his starting location. The ratio of Maria's starting location to the fountain to Fernando's starting place is 5:3. What is the location of the fountain? Round to the nearest tenth, if necessary.
(, )
The location of the fountain based on the information given is (-1, 0.5).
How to illustrate the location?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)
Learn more about location on:
brainly.com/question/11940101
#SPJ1
Which model represents the factors of 4x^2-9
The model (x+a)(x-a) will represents the factors of 4x²-9 as (2x+3)(2x-3).
What are the quadratic equations in one variable completing the squares method?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).
To learn more about completing the squares method refer to:
https://brainly.com/question/16800259
#SPJ1
HELP! BRainliest +20
A function f is defined such that 8f(x)=f([tex]\frac{1}{8}[/tex]x) for all values of x, and f(4) = 24. What is the value of f(32) ?
The value of f(32) is 3
What is a Function ?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
To know more about function
https://brainly.com/question/12431044
#SPJ1
which 2 number have the mean of 10 and range of 4
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
Fracciones heterogeneas
The information given illustrates that the equivalent fraction will be 2/6.
How to calculate the fraction?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.
Learn more about fractions on:
brainly.com/question/78672
#SPJ1
How do I solve quadratic equations for example,h(t) = – 0.07t2 + 0.007t + 5
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.
SolutionOften, 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:
FactoringCompleting the SquareQuadratic FormulaGiven 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.