[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} A=56 \end{cases}\implies 56=\cfrac{1}{2}bh\implies 112=bh \\\\\\ \boxed{112=2\cdot 2\cdot 2\cdot 2\cdot 7}\to \begin{cases} 16\cdot 7\\ 8\cdot 14\\ 4\cdot 28\\ 2\cdot 56 \end{cases}\qquad or\qquad \begin{cases} 7 \cdot 16\\ 14 \cdot 8\\ 28 \cdot 4\\ 56 \cdot 2 \end{cases}[/tex]
so their product is 112, so tis just a matter of doing some quick prime factoring and combining the factors about.
The triangle with an area of 56 m² can have the base-height pairs: (1, 112), (2, 56), (4, 28), (7, 16), (8, 14), (14, 8), (16, 7), (28, 4), (56, 2), and (112, 1). These pairs satisfy the equation base × height = 112.
The formula for the area of a triangle is 1/2 × base × height. Given that the area of a triangle is 56 m², we can write this as:
Area = 1/2 × base × height
Rearranging for whole number dimensions, we get:
base × height = 2 × Area
Therefore, base × height = 112 m².
Next, we find all pairs of whole numbers (base, height) whose product is 112:
(1, 112)(2, 56)(4, 28)(7, 16)(8, 14)(14, 8)(16, 7)(28, 4)(56, 2)(112, 1)These are all the possible sets of whole number dimensions for the base and height of the triangle with an area of 56 m².
NEED HELP FAST!!!!!!!!!!
Answer:
h = 10 m
Step-by-step explanation:
We are given the following formula of the area of a trapezoid:
[tex]A=\frac{1}{2} (b+c)h[/tex]
where [tex]h[/tex] is the height of the trapezoid and [tex]b[/tex] and [tex]c[/tex] are its bases.
Re-arranging the given formula to solve for h:
[tex]A=\frac{1}{2} (b+c)h[/tex]
[tex]2A=(b+c)h[/tex]
[tex]h=\frac{2A}{(b+c)}[/tex]
Finding the height of the trapezoid given the bases 20 m, 7 m and area 135m^2.
[tex]h=\frac{2 \times 135}{(7+20)}[/tex]
h = 10 m
ANSWER
h=10m
EXPLANATION
The given formula is
[tex]A = \frac{1}{2} (b + c)h[/tex]
We multiply through by 2 to get,
[tex]2A =(b + c)h[/tex]We divide both sides by (b+c) to get,
[tex] \frac{2A}{b + c}=h[/tex]
Or
[tex]h=\frac{2A}{b + c} [/tex]
[tex]h=\frac{2 \times 135}{20 + 7} [/tex]
We simplify to get,
[tex]h=\frac{270}{27} [/tex]
Therefore
[tex]h = 10[/tex]
Now if b=20, c=7 and A=135, then,
An isosceles right triangle has sides that are x+2 units long and a hypotenuse that is 8 units long. What is the length of the missing sides of the triangle
Answer:
In an isosceles right triangle, the hypotenuse is larger than the sides by a factor of the square root of 2.
So, if the hypotenuse is 8 then the sides are 8 / (sq root of 2) = 5.6568542495
Step-by-step explanation:
If f(x) = |x| and g(x)= |x| -4 which translation is applied to f(x) to her g(x)
Answer:
The translation is 4 down.
Step-by-step explanation:
True or False: 3( 12-8 )
______
2.5-4 = 2
Answer: False
Step-by-step explanation:
Which expressions are equivalent to (k^(1/8))^(−1) ?
choose all answers that apply:
a. (k^(-1))^(1/8)
b. (8_/`k)^(-1)
c. k^(-1/8)
d. none of the above
* _/` is a radical with 8 as the index and k as the radicand
The first option is correct: we have
[tex]\left(k^{\frac{1}{8}}\right)^{-1} = \dfrac{1}{k^{\frac{1}{8}}} = \dfrac{1}{\sqrt[8]{k}},\quad \left(k^{-1}\right)^{\frac{1}{8}} = \left(\dfrac{1}{k}\right)^{\frac{1}{8}} = \dfrac{1}{\sqrt[8]{k}}[/tex]
The second option is also correct, because it simply applies the definition
[tex]k^{\frac{1}{n}} = \sqrt[n]{k}[/tex]
The third option is also correct, because it applies the rule
[tex](a^b)^c = a^{bc}[/tex]
The expressions equivalent to (k^(1/8))^(-1) are (k^(-1))^(1/8) and k^(-1/8), matching options a and c from the given choices. These are determined by correctly applying the exponent multiplication rule.
Explanation:The student is dealing with an expression involving exponents and radicals, specifically focused on understanding the rules for combining and simplifying these expressions. The expression in question is (k^(1/8))^(-1), which we'll simplify in a step-by-step fashion.
The rule of exponents we need to apply here is (a^m)^n = a^(m*n). When applying this rule to the given expression we get:
(k^(1/8))^(-1) = k^(1/8 * -1)
Simplify the exponent:
k^(1/8 * -1) = k^(-1/8)
So, the equivalent expression is:
k^(-1/8)
Now let's examine the choices given:
Therefore, the correct answers are a and c.Simplify:
(1/2k)(4k) + 12 =
if i put choices you guys would just guess
Answer:
2k^2 + 12.
Step-by-step explanation:
(1/2k)(4k) + 12
= 1/2 *4 k^2 + 12
= 2k^2 + 12.
Answer:
Step-by-step explanation:
1/2k (4k) + 12= 0
4k/2k + 12 = 0
2k + 12 = 0
2k = -12
Divide by 2 on both sides
K = -6
find the missing term of each pair of equivalent ration 125:80= ____:48
Answer:
The answer would be 75 because of cross multiplication.
Answer:
75
Step-by-step explanation:
125/80=1.5625
48x1.5625=75
Indicate a general rule for the nth term of this sequence.
-6a, -3a, 0a, 3a, 6a. . .
an = 3an + 9a
an = -3an - 9a
an = -3an + 9a
an = 3an - 9a
difference=3a
so an=-6a+(n-1)3a
=3an-9a
Answer:
Option D. [tex]a_{n}=3an-9a[/tex] is the answer.
Step-by-step explanation:
The given sequence is -6a, -3a, 0a, 3a, 6a...........
Since the given sequence is having a common difference d = -3a - (-6a) = -3a + 6a = 3a
Therefore, the given sequence is an arithmetic sequence.
And for an arithmetic sequence general rule or explicit formula is given by
[tex]T_{n}=a+(n-1)d[/tex]
Where a = first term of the sequence
d = common difference
n = number of term which we have to find
Now we put the values from the given sequence
[tex]T_{n}=-6a+(n-1)3a[/tex]
[tex]T_{n}=-6a+3an-3a[/tex]
[tex]T_{n}=3an-9a[/tex]
Option D. [tex]a_{n}=3an-9a[/tex] is the answer.
Enter the product of 8w - 3 and w-1.
Answer:
8w² - 11w + 3
Step-by-step explanation:
(8w - 3)(w - 1)
= 8w² - 8w - 3w + 3
= 8w² - 11w + 3
Answer:
(8w -3) (w -1) =
8w^2-5w+3
Step-by-step explanation:
Can someone help me????
Answer:
in order
Step-by-step explanation:
1) 1
2) 5
3) 2
You are looking for the x values of this "rule". It gives you the y-values so all you have to do is plug the y-values into the rule and solve for x
y = 4 so...
4 = x + 3
4 - 3 = x + (3-3)
1 = x + 0
x = 1
When y is 4 then x is 1
y = 8 so...
8 = x + 3
8 - 3 = x + (3 - 3)
x = 5
When y is 8 then x is 5
y = 5 so...
5 = x + 3
5 - 3 = x + (3 - 3)
2 = x + 0
x = 2
When y is 5 then x is 2
Hope this helped!
~Just a girl in love with Shawn Mendes
Which function has two x-intercepts, one at (0, 0) and one at (4, 0)? f(x) = x(x − 4) f(x) = x(x + 4) f(x) = (x − 4)(x − 4) f(x) = (x + 4)(x + 4)
If you want a polynomial to have the x-intercepts of your choice, you simply have to build a polynomial by multiplying pieces like [tex](x-x_k)[/tex] where [tex]x_k[/tex] is the x-intercept you want.
So, if you want x-intercepts 0 and 4, you have to build the polynomial
[tex](x-0)(x-4) = x(x-4)[/tex]
The function that has x-intercepts at (0, 0) and (4, 0) is f(x) = x (x − 4).
Option A is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The x-intercepts of a function are the points where the graph of the function crosses the x-axis.
At these points, the value of the function is zero.
To have x-intercepts at (0, 0) and (4, 0), the function must be zero when x is equal to 0 and 4.
Let's evaluate the given options:
f(x) = x(x − 4):
This function is zero at x = 0 and x = 4, so it has x-intercepts at (0, 0) and (4, 0).
f(x) = x(x + 4):
This function is zero at x = 0 and x = -4, so it does not have an x-intercept at (4, 0).
f(x) = (x − 4)(x − 4):
This function is zero at x = 4, but it also has a double root at x = 4, so it only has one x-intercept at (4, 0).
f(x) = (x + 4)(x + 4):
This function is zero at x = -4, but it does not have an x-intercept at (0, 0).
Therefore,
The function that has x-intercepts at (0, 0) and (4, 0) is f(x) = x(x − 4).
Learn more about functions here:
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Use substitution to solve the linear system of equations.
equations:
6x + 4y = 14
y = 5
Answer:
Step-by-step explanation:
6x+4y=14
y=5
6x+4(5)=14
6x+20=14
6x=-6
x=-1
Step 1: Where you see a y in the equation 6x + 4y =14 replace it with 5. This will help you find x
6x + 4(5) = 14
6x + 20 = 14
Step 2: Combine like terms by subtracting 20 to both sides
6x + (20-20) = 14-20
6x = -6
Step 3: Isolate x by dividng 6 to both sides
[tex]\frac{6x}{6} = \frac{-6}{6}[/tex]
x = -1
Point of intersection of these two linse is ( -1 , 5 )
Hope this helped!
Help plzzz! I need help with this question. Thx!
The average commute times for employees of a large company is 23 minutes.
The commute time of 12 employees are
25, 33, 26, 29, 17, 29, 42, 19, 15, 52, 11, and 14.
Answer:
Well to find the Mean you Add all of the numbers up and Divide by How many numbers there are
The sample mean is 26 mins and the population mean is 23 mins.
What is sample mean?An average of a group of data is referred to as a sample mean.
What is population mean?The population mean is an average of a group characteristic.
The population mean = 23 minutes(given)
Sample mean = (25 + 33 + 26 + 29 + 17 + 29 + 42 + 19 + 15 + 52 + 11 + 14) / 12
Sample mean = 312 / 12
Sample mean = 26 minutes
Hence, the value of sample mean is 26 minutes and the value of population mean is 23 minutes.
Learn more about mean on:
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Which functions have a y-intercept that is greater than the y-intercept of the function g(x) = |x + 3| + 4? Check three options.
f(x) = –2 (x – 8)2
h(x) = –5 |x| + 10
j(x) = –4(x + 2)2 + 8
k(x)=1/4(x-4)^2+4
m(x)=1/4 |x-8| +6
Answer:
h(x) = –5 |x| + 10
k(x)=1/4(x-4)^2+4
m(x)=1/4 |x-8| +6
Step-by-step explanation:
The given function is:
g(x) = |x + 3| + 4
At y-intercept x=0,
g(0) = |0 + 3| + 4
g(0) = 3 + 4=7
The y-intercept of this function is 7.
We look for the functions with y-intercepts greater than 7.
[tex]f(x)=-2(x-8)^2[/tex]
[tex]f(0)=-2(0-8)^2[/tex]
[tex]f(0)=-128[/tex]
h(x) = –5 |x| + 10
h(x) = –5 |0| + 10=10
[tex]j(x)=-4(x+2)^2+8[/tex]
[tex]j(0)=-4(0+2)^2+8=-8[/tex]
[tex]k(x)=\frac{1}{4}(x-4)^2+4[/tex]
[tex]k(0)=\frac{1}{4}(0-4)^2+4=8[/tex]
m(x)=1/4 |x-8| +6
m(0)=1/4 |0-8| +6=8
Answer with explanation:
The given function is
g(x)=|x+3|+4
The meaning of Y intercept is the distance between origin and Point where the curve cuts Y axis.
In , g(x), put x=0
g(0)=|0+3|+4
=3+4
=7
So, Length of Y intercept =7 unit
2.
f(x)=-2(x-8)²
f(0)=-2×(0-8)²
= -2 × 64
= -128
Length of Y intercept =-128 unit
3.
h(x)=-5|x|+10
h(0)=-5 × |0| +10
=10
Length of Y intercept =10 unit
4.
j(x)=-4(x+2)²+8
j(0)=-4×(0+2)²+8
=-4 × 4+8
= -16 +8
= -8
Length of Y intercept =-8 unit
4.
[tex]\rightarrow k(x)=\frac{1}{4} \times (x-4)^2+4\\\\\rightarrow k(0)=\frac{1}{4} \times (0-4)^2+4\\\\\rightarrow k(0)= 4+4\\\\=8[/tex]
Length of Y intercept =8 unit
5.
[tex]\rightarrow m(x)=\frac{1}{4} \times |x-8|+6\\\\\rightarrow k(0)=\frac{1}{4} \times |0-8|+6\\\\\rightarrow k(0)= 2+6\\\\=8[/tex]
Length of Y intercept =8 unit
⇒ h(x),k(x) and m(x) has y intercept greater than y-intercept of the function g(x) = |x + 3| + 4.
The local hamburger shop sold a combined total of 625 hamburgers and cheeseburgers on Friday . There were 75 fewer cheeseburgers sold than hamburgers how many hamburgers were sold on Friday ?
By setting up a system of equations, it was determined that the local hamburger shop sold 350 hamburgers on Friday.
Explanation:To determine how many hamburgers and cheeseburgers were sold on Friday at the local hamburger shop, we can set up a system of equations based on the information given. Let H represent the number of hamburgers sold and C represent the number of cheeseburgers sold. According to the problem, H + C = 625 and H = C + 75.
To find the number of hamburgers, we replace C in the first equation with H - 75 from the second equation, so we have H + (H - 75) = 625. Simplifying this, we get 2H - 75 = 625. Adding 75 to both sides gives us 2H = 700. Dividing both sides by 2 gives H = 350. Therefore, 350 hamburgers were sold on Friday.
Alan and Samuel each have a 30-year mortgage. Both mortgages were approved at the same time. Alan pays 5 percent interest, while Samuel only pays 3.5 percent.
If Alan and Samuel are the same age and make the same amount of money, why is Alan paying more in interest?
a) Samuel has a better credit score, so his interest rate is lower.
b) Samuel has more credit cards, so he recieves a better rate.
c) Alan has a better credit score, so his interest rate is higher.
d) Alan has a longer credit history, so he recieves a worse rate.
The answer would be c
Answer:
a) Samuel has a better credit score, so his interest rate is lower.
Step-by-step explanation:
Alan and Samuel both are same age and make same amount of money.
They both have a 30-year mortgage. But Alan pays 5 percent interest, while Samuel only pays 3.5 percent.
There correct answer here will be - Samuel has a better credit score, so his interest rate is lower.
When a person has a good credit rating, that means he has never defaulted any payment and has always paid his loan on time. He must be a trusted customer for the bank that is why he got a lower interest rate than Alan.
Which expression is equivalent to 8(u + 3)?
Answer:
8(u + 3) = 8u + 24Step-by-step explanation:
[tex]8(u+3)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(8)(u)+(8)(3)=8u+24[/tex]
What value of x makes this equation true? -1/4x-12=x+3
Answer:
x = -12
Step-by-step explanation:
Step 1: Isolate x
1/4x + x = -12 - 3
Step 2: Combine like terms
5/4x = -15
Step 3: Simplify
x = (-15)(4/5)
x = -12
Answer: -12
Step-by-step explanation:−1 /4 x−12=x+3
Step 1: Subtract x from both sides.
−1 /4 x−12−x=x+3−x
−5 /4 x−12=3
Step 2: Add 12 to both sides.
−5 /4 x−12+12=3+12
−5 /4 x=15
Step 3: Multiply both sides by 4/(-5).
( 4 /−5 )*( −5 /4 x)=( 4 /−5 )*(15)
x=−12
A middle school student is doing a math project in which she has to make a graph of the different ways students get to school. To collect her data, she stands under the bus canopy and asks 100 students how they normally get to school. Is her data valid? Why or why not?
Answer:no
Step-by-step explanation: if they are all under the bus canopy they obviously take the bus make the data bias
Which inequality is true for x = 2? A) 6x + 20 < 29 B) 7x − 10 < 11 C) 14x + 10 < 37 D) 15x − 18 < 12
For this case we must evaluate [tex]x = 2[/tex] in each of the inequalities and verify if the inequality is met or not:
Option A:
[tex]6x + 20 <29\\6 (2) +20 <29\\12 + 20 <29\\32 <29[/tex]
It is not fulfilled!
Option B:
[tex]7x-10 <11\\7 (2) -10 <11\\14-10 <11\\4 <11[/tex]
Is fulfilled!
Option C:
[tex]14x + 10 <37\\14 (2) +10 <37\\28 + 10 <37\\38 <37[/tex]
It is not fulfilled!
Option D:
[tex]15x-18 <12\\15 (2) -18 <12\\30-18 <12\\12 <12[/tex]
It is not fulfilled!
So, option B is correct, inequality is met
ANswer:
Option B
Final answer:
Upon substituting x with 2 in each of the given inequalities, option B (7x − 10 < 11) is the only true inequality, making it the correct answer.
Explanation:
To determine which inequality is true for x = 2, let's substitute x with 2 in each option:
A) 6x + 20 < 29 becomes 12 + 20 < 29, which simplifies to 32 < 29. This is false.B) 7x − 10 < 11 becomes 14 − 10 < 11, which simplifies to 4 < 11. This is true.C) 14x + 10 < 37 becomes 28 + 10 < 37, which simplifies to 38 < 37. This is false.D) 15x − 18 < 12 becomes 30 − 18 < 12, which simplifies to 12 < 12. This is false since 12 is not less than 12.Therefore, option B) 7x − 10 < 11 is the true inequality when x = 2.
A bag has 2 blue marbles, 3 red marbles, and 5 white marbles. Which event have a probability greater than 1/5
Answer:
choosing 1 red marble
choosing 1 white marble, replacing it, and choosing another white marble
and choosing 1 white marble
Help please. Write a formula for the perimeter of an equilateral triangle. Evaluate the formula for the side length of 3.5 cm.
Answer:
A
Step-by-step explanation:
the side of the triangle is 3.5 cm. all 3 sides are the same length because it is an eq. triangle. 3.5*3=9+1.5=10.5
what is 3× + 4 (× +2) +4y
Expand
3x + 4x + 8 + 4y
Collect like terms
(3x + 4x) + 8 + 4y
Simplify
= 7x + 8 + 4y
Answer:
7x + 4y + 8
Step-by-step explanation:
Please be more explicit regarding your goal. "What is ... " could be interpreted in several ways. I will assume you meant, "What is the simplest form of 3x + 4(x + 2) + 4y?" Finally, please use the regular character, " x, " when you mean a variable and use the character " × " for multiplication.
What is the simplest form of 3x + 4(x + 2) + 4y? Do the indicated multiplication. We get: 3x + 4x + 8 + 4y, which in turn is 7x + 4y + 8.
evaluate 4! please help im in a crisis!!!!!!!!
Answer:
24
Step-by-step explanation:
4! means multiply all the number from 4 down to 1
4! = 4*3*2*1
= 24
For this case we have that by definition, the factorial of a number is the product of the "n" consvutive factors from n to 1. The factors are in descending order, that is:
[tex]n! = n (n-1) (n-2) ... 3 * 2 * 1[/tex]
Then, we have the following expression:
[tex]4![/tex]
Applying the definition we have:
[tex]4! = 4 * 3 * 2 * 1 = 24[/tex]
ANswer:
[tex]4! = 24[/tex]
Factor the expression 8x^3y-8x^2y-30xy
Find the Greatest Common Factor (GCF)
GCF = 2xy
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
2xy(8x^3y/2xy + -8x^2y/2xy + -30xy/2xy)
Simplify each term in parenthesis
2xy(4x^2 - 4x - 15)
Split the second term in 4x^2 - 4x - 15 into two terms
2xy(4x^2 + 6x - 10x - 15)
Factor out common terms in the first two terms, then in the last two terms;
2xy(2x(2x + 3) -5(2x + 3))
Factor out the common term 2x + 3
= 2xy(2x + 3)(2x - 5)
-3 < n < 1 what is the possible value of n
Answer:
see explanation
Step-by-step explanation:
Given
- 3 < n < 1
Then possible integer values of n are n = - 2, - 1, 0
A circle with radius of 2cm sits inside a circle with radius of 4cm What is the area of the shaded region
The area of the shaded region between a larger circle with a radius of 4 cm and a smaller circle with a radius of 2 cm is 12π cm². This is calculated by subtracting the area of the smaller circle from the area of the larger circle.
This concerns the area of the shaded area between two circles, one with a radius of two centimetres and the other with a radius of four centimeters.
In order to determine this, we first compute the area of each circle using the formula πr², where r is the circle's radius.
Let's start by calculating the area of the bigger circle: π(4cm)² = 16π cm² is the area.
In a similar manner, we can calculate the smaller circle's area: π(2cm)² = 4π cm² is the area.
The area of the shaded region is equal to the area of the larger circle minus the area of the smaller circle, or area = 16π cm² - 4π cm² = 12π cm².
use an inequality symbol to compare -17 blank -1
[tex]\text{Hey there!!}[/tex]
[tex]\text{Negatives are BELOW 0}[/tex]
[tex]\text{If you have a number line you would see that the negatives goes on the LEFT}[/tex] [tex]\text{SIDE of the number line, while the POSITIVES are on the RIGHT SIDE}[/tex]
[tex]\text{If 17 is GREATER THAN 1 on the number line than -17 is BIGGER THAN -1 in this case}[/tex]
[tex]\boxed{\boxed{\text{Answer:-17}<-1}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
3x2-|y| When x=-5 and y =-2
I'm going to assume you're saying 3x to the power of 2. So first, apply the values of the variables to the equation just as shown:
3(-5)^2 - |-2|
So first, do -5 to the power of 2:
(-5)(-5)=25
Then, multiply 3 to 25:
3*25=75
Now, the absolute value of y is the absolute value of -2. The aboslute value of any number is its positive value, so now we are left with 75-2
75-2=73
73 is your answer.
How many different sleeve/size/color/artwork combination are possible
Answer:
128
Step-by-step explanation:
2*4*4*4= 128
Answer: Option D
( D) 128
Step-by-step explanation: