Answer:
The height of the triangle is four meters.
Step-by-step explanation:
We are given that the area of a triangle is 12 square meters. The base is two meters longer than the height, and we want to determine the height of the triangle.
Recall that the area of a triangle is given by:
[tex]\displaystyle A = \frac{1}{2}bh[/tex]
Since the area is 12 square meters:
[tex]\displaystyle 12 = \frac{1}{2}bh[/tex]
The base is two meters longer than the height. In other words, we can write that:
[tex]b = h + 2[/tex]
Substitute:
[tex]\displaystyle 12=\frac{1}{2}(h+2)h[/tex]
Solve for h. Multiply both sides by two:
[tex]24 = (h+2)h[/tex]
Distribute:
[tex]h^2+2h=24[/tex]
Isolate:
[tex]h^2+2h-24=0[/tex]
Factor:
[tex](h+6)(h-4)=0[/tex]
Zero Product Property:
[tex]h + 6 = 0\text{ or } h -4 =0[/tex]
Solve for each case:
[tex]h = -6\text{ or } h = 4[/tex]
Since the height cannot be negative, we can ignore the first solution.
Thus, the height of the triangle is four meters.
write 1042000 000 m+ in scientific notification
Answer:
1.042 × 109
Step-by-step explanation:
you have to move the decimal from the zero.
Noah had to water 7 plants. Each plant needed 14 ounces of water. Noah multiplied to find out how much water he would need. Which equation shows the addition equation he could use to check his answer?
14 + 14 + 14 + 14 + 14 + 14 = 84
14 + 7 = 21
14 + 14 + 14 + 14 + 14 + 14 + 14 = 98
7 + 7 + 7 + 7 + 7 + 7 + 7 = 49
Answer:
n3 14 + 14 + 14 + 14 + 14 + 14 + 14 = 98
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
x²-2x=8
x² - 2x - 8 = 0
x² - 2x - 4x = 0
(x - 2) (x - 4)=0
x - 2 =0 therefore x = 2
or
x - 4 =0 therefore x = 4
Answer:
x=4 x = -2
Step-by-step explanation:
x²-2x=8
Subtract 8 from each side
x^2 -2x-8 = 8-8
x^2 -2x -8=0
What two numbers multiply to -8 and add to -2
-4*2 = -8
-4+2 = -2
(x-4) (x+2) =0
Using the zero product property
x-4 =0 x+2 =0
x=4 x = -2
At Pontotoc Middle School there are only
7th and 8th graders. There are 15x + 13xy + 10y
students. There are 8x + 8xy + 8y 8th graders.
How many 7th graders are there?
Answer:
So what we need to do is find out how many are left after taking away the 8th graders.
15x - 8x = 7x
so we have part of that
7x
Then 13xy - 8xy
5xy
10y - 8y
2y
this means that for 7th graders its
7x + 5xy + 2y
Step-by-step explanation:
Answer:
7x + 5xy + 2y is the number of 7th graders in the school.
Step-by-step explanation:
We are told that the total number of students is 15x + 13xy + 10y for both, 7th and 8th grade. We are also told that there are 8x + 8xy + 8y 8th graders. Incase you weren't able to figure out by this detail, we need to subtract to find the answer. We need to subtract the total students, 15x + 13xy + 10y, from the 8th graders, 8x + 8xy + 8y.
The steps would look like this:
15x + 13xy + 10y
— 8x + 8xy + 8y
---------------------------
7x + 5xy + 2y
15 - 8 = 7
13 - 8 = 5
10 - 8 = 2
Sofie deposits $45.00 into a new savings account. The account earns 2.5% simple interest per year. No money is added or removed from the savings account for 4 years. What is the total amount of money in her savings account at the end of the 4 years? A. $1.13 C. $49.50 B. $4.50 D. $45
Answer:
$49.50
Step-by-step explanation:
First, let's find how much total interest was made
For every year, 2.5% interest was made
Since we're finding the total for 4 years
It will be 4 x 2.5 = 10% total interest
Now let's find 10% of 45
45 x .1 = 4.5
This means we made $4.5 in those 4 years
Now we just add it to our starting amount
45 + 4.5 = 49.5
What is the reciprocal of 7/9 it’s a fraction by the way
Answer:
9/7
Step-by-step explanation:
Reciprocal means 1 over the number
1 / (7/9)
1 * 9/7
9/7
Answer:
[tex] = \frac{9}{7} [/tex]
Step-by-step explanation:
Reciprocal means inverse:
[tex] {( \frac{7}{9} })^{ - 1} = (\frac{9}{7} ) {}^{1} \\ \\ = \frac{9}{7} [/tex]
If x >0 and y < 0. is the equation x - y >0 sometimes, always, or never true
Prove your answers with two examples.
Answer:
always true because the negative value of y is cancelld by - sign so it becomes x+|y|
examples: x=1, y=-1 then 1-(-1)>0
x=2, y=-5 then 2-(-5)>0
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Which of the following statements is true?
A. Take one sample to best estimate the population average
B. None of these statements are true
C. Choose who is in your sample to make sure that they best model the population being estimated
D. Take multiple samples to better estimate the true population average
Answer:
D. take multiple samples to better estimate the true population average
Answer:
tbh im here for 5 points
Step-by-step explanation:
Suppose h” is continuous at x = 2,h' (2) = 0, and h” (2) < 0.
What can you say about the behavior of h at X = 2?
Answer:
Hello,
Step-by-step explanation:
h(x) has a minimum at x= 2. (h(x) is turning down at x=2)
I have suppose that h''(2 + ) <0 and h''(2 -) <0
Using the intercept method, what are the two points to plot when graphing the line x + 3y = 6?
Answer:
The Slope-Intercept Form is essentially a special case of the Point-Slope Form. It's said that two points determine a line. That truism is used to quickly sketch a line if its equation is given in the Two Intercept-Form ax + by = c. We get the y-intercept by setting x = 0 and solving for y: by = c, y = c b .
Step-by-step explanation:
plzzz make brainlist and follow
Answer:
(0,2) and (6,0)
Step-by-step explanation:
y-intercept, x=0
0+3y=6
y=2
x-intercept, y=0
x=6
What is the standard form of the points (-3,4) (2,-6)
The standard form equation of the line connecting the two points is [tex]2x + y = -2[/tex]
Linear equation in a standard form is given as [tex]Ax + By = C[/tex]
where,
A, B, and C are constants or numbers
x and y are the variables.
To solve this problem, the following steps would be taken:
Step 1: Find the slope of the line connecting points (-3,4) and (2,-6)
[tex]slope (m) = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where,
[tex](x_1, y_1) = (-3,4)\\(x_2, y_2) = (2,-6)[/tex]
Substitute
[tex]slope (m) = \frac{-6 - 4}{2 -(-3)} \\m = \frac{-10}{5}\\m = -2[/tex]
Step 2: Find the y-intercept (b) of the line by substituting [tex](x, y) = (-3,4)[/tex] and [tex]m = -2[/tex] into [tex]y = mx + b[/tex] (slope-intercept form)
[tex]4 = -2(-3) + b\\4 = 6 + b\\4 - 6 = 6 + b - 6\\-2 = b\\b = -2[/tex]
Step 3: Write the equation of the line in slope-intercept form by substituting [tex]m = -2[/tex] and [tex]b = -2[/tex] into [tex]y = mx + b[/tex]
[tex]y = -2x + (-2)\\y = -2x - 2[/tex]
Step 4: Rewrite the equation in standard form [tex](Ax + By = C)[/tex]
[tex]y = -2x - 2\\[/tex]
Add [tex]2x[/tex] to both sides
[tex]2x + y = -2x - 2 + 2x\\2x + y = -2[/tex]
The standard form equation of the points (-3,4) and (2,-6) is [tex]2x + y = -2[/tex]
Learn more about standard form of two points of a linear equation here:
https://brainly.com/question/18446164
Where did term “infinity” come from
Find the value of x.
A.124
B.57
C.72
D.90
9514 1404 393
Answer:
x = 90°
Step-by-step explanation:
Half the sum of x and 120° is the angle where the chords cross, 105°. Then ...
105° = (1/2)(x +120°)
210° = x + 120°
210° -120° = x = 90°
_____
Additional comment
z is the arc that finishes the circle: 360° -90° -68° -120° = 82°.
Select the correct answer. Consider this system of equations, where function f is quadratic and function g is linear:
y = f(x)
y = g(x)
Which statement describes the number of possible solutions to the system?
A. The system may have no, 1, 2, or infinite solutions.
B. The system may have no, 1, or infinite solutions.
C. The system may have 1 or 2 solutions.
D. The system may have no, 1, or 2 solutions
Answer:
C is the answer
Step-by-step explanation:
Quadratic equations have at most 2 solution, and linear equations only have 1 solution, and since y is equal to both of them, it can only have 1 or 2 solutions.
The correct answer is option D. The system may have no, 1, or 2 solutions
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
f(x) is a quadratic function and g(x) is linear function
y=f(x)
y=g(x)
Quadratic equations have at most 2 solution
linear equations only have 1 solution,
f(x)=g(x)=y
y is equal to both of them, it can only have 1 or 2 solutions.
A line and a parabola can intersect zero, one, or two times
Therefore, a linear and quadratic system can have zero, one, or two solutions
Hence, the correct answer is option D. The system may have no, 1, or 2 solutions
To learn more on Quadratic equation click:
https://brainly.com/question/17177510
#SPJ2
5x2y and 7xy2 are like terms.
True
False
Answer: False
The variable portions x^2y and xy^2 are slightly different, so that's why we don't have like terms here.
Answer:
False
Step-by-step explanation:
Like terms are those terms where they have the same variable
so here
5x2y variables are = 5x and 2y
7xy2 variables are = 7x and y2
you can observe that x variable is same but y variable is not same as 5x3y have 2y whereas 7xy2 have y2#
so the answer is FALSE
3/4 - 3/5
please give me answer
Hey there! I believe these are the two correct options!
Decimal form: 0.15
Fraction form: [tex]1 \frac{7}{10}[/tex]
Hope this helps!
3/4 - 3/5
Take LCM 20
So 3/4×5/5 and 3/5×4/4
= 15/20 - 12/20
= 3/20
Must click thanks and mark brainliest
Write the equation of the line in fully simplified slope - intercept form
Answer:
y = -2/5x - 4
Step-by-step explanation:
Please help!!! i’ll mark brainliest
6 + (-47) =
Because it's +-, the - cancels out the +.
We can rearrange the equation to 6-47.
Or -47+6.
Then the answer is -41
If this was helpful hit the thanks :D
6+(-47)
Remove the parentheses
6-47
= -41 as your answer
What is the value of x (Khan Academy question)
Answer:
72
Step-by-step explanation:
Use cross multiplication.
60/20 = x/24
That simplifies to
20x=60(24)
20x=1440
Divide by 20 on both sides to isolate x
x = 1440/20
x = 72
Miles is putting a fence around his garden. The total area of the garden is 4,864 square feet. The length of the garden is 152 feet. How many feet of fencing does he need to go around the whole garden?
Help pls!!
Fencing required to go around the whole garden = 368 feet
To calculate the fencing needed, given measures in the question,
Total area of the garden is 4864 square feet.Length of the garden is 152 feet.Since, area of a rectangular garden is given by the expression,
Area = Length × Width
4864 = 152 × Width
Width = [tex]\frac{4864}{152}[/tex]
= 32 feet
Since, length of the fence needed = Perimeter of the garden
And Perimeter of a rectangular garden is given by the expression,
Perimeter = 2(length + width)
By substituting the values of length and width of the garden in the expression,
Perimeter = 2(152 + 32)
= 368 feet
Therefore, 368 feet of the fence will be required to go around the whole garden.
Learn more,
https://brainly.com/question/22073676
simplify
(-3y)*(-7y)
Answer:
answer of this question is
21y^2
If you randomly choose a number from 1 to 10 and multiply them together, what is the probability that the number ends in a 0?
(3x)2 – 7y2, when x = 3 and y = 2
[tex]3 \times 3 \times 2 - 7 \times 2 \times 2 \\ 18 - 28 \\ - 10[/tex]
Answer:
115
Step-by-step explanation:
(3x)^2 – 7y^2
Plug in:
(3×3)^2 – 7×2^2
9^2 - 14^2
81 - 196
115
Hope this helped.
what is
4c ÷ 3 if c=6
Answer:
8
Step-by-step explanation:
4c ÷ 3
Plug in:
4c ÷ 3
4(6) ÷ 3
24 ÷ 3 = 8
Hope this helped.
Answer:
8
Step-by-step explanation:
4(6)/3 = 24/3 = 8
4 times 6 is done first because you do multiplication/division first from left to right according to PEMDAS.
17
Ax+2y=12
8x +32 y=144
For what value of A will the system of equations above
have no solutions?
Answer:
Hello,
a=0.5
Step-by-step explanation:
[tex]\left \{ \begin{array}{ccc}ax+2y&=&12\\8x+32y&=&144\\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}ax+2y&=&12\\x+4y&=&18\\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}(1-2a)x&=&-6\\x+4y&=&18\\\end{array}\right.\\\\if\ 1-2a\neq 0\ (or\ a\neq \dfrac{1}{2} )\ then\\\left \{ \begin{array}{ccc}x&=&\dfrac{6}{2a-1}\\\\y&=&\dfrac{18-\dfrac{6}{2a-1}}{4} \\\end{array}\right.\\\\[/tex]
[tex]\Longleftrightarrow\ \left \{ \begin{array}{ccc}x&=&\dfrac{6}{2a-1}\\\\y&=&\dfrac{ 3(3a-2)}{2a-1} \\\end{array}\right.\\\\[/tex]
else\
[tex]a=\dfrac{1}{2} \\\Longleftrightarrow\ \left \{ \begin{array}{ccc}\dfrac{1}{2} x+2y&=&12\\\\x+4y&=&18 \\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}x+4y&=&24\\\\x+4y&=&18 \\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}0=6\ !!!!!\\\end{array}\right.\\\\Syetem\ has\ no\ solution\\[/tex]
given m||n, find the value of x and y
Answer:
x = 145, y = 35
Brainliest, please!
Step-by-step explanation:
y = 35 degrees because it and the original 35 degree angle are alternate interior angles. Alternate interior angles are congruent, or the same.
x is supplementary to y. x + y = 180. x + 35 = 180. x = 180 - 35. x = 145
If you save a hundred dollars every two weeks for five years how much money would you have?
Answer:
$13,000
Step-by-step explanation:
52 weeks in a year means 26 two week periods (fortnights, if you feel it is important in social studies). This means 2600 dollars per year. Multiplty by 5 to get $13,000. Hope this helps!
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The difference between the largest and smallest values in a data set is the ______________.
A. mean
B. mode
C. median
D. range
Answer:
the answer is D. range......
MP=300sp=245 find discount
Answer:
55
Step-by-step explanation:
we know ,
discount = M.P - S.P
=300 - 245
= Rs 55
Answer:
22.45%
Step-by-step explanation:
300-245=55
then do like in the pic
What percentage is 420 grams of 750 grams?
%
