The area of the triangle is = 19.4 cm²
What is the area of triangle?Triangle's area is equal to 1/2 (b × h) square units.
where the triangle's base and height, respectively, are denoted by b and h. Let's now examine how to use the provided formula to get a triangle's area.
Area of triangle = 1/2 × B × H
We will calculate the height of the triangle with the help of Pythagoras theorem.
Consider a straight line representing the height of the triangle.
⇒ base = 4cm, half of base = 2cm
⇒ hypotonus = 10cm
(h²) = b² + a²
⇒ 10² = 2² + a²
⇒ 100 = 4 + a²
⇒ √96cm = a
a = 9.7cm
area of triangle = 1/2 × 4 × 9.7
= 19.4 cm²
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1.2 x (-5) =
I had -60 but it says the answer was incorrect and I’m not sure what I’m doing wrong. Any explanation on what I’m doing wrong?
Answer: -6, not 60
Step-by-step explanation:
Negative+Positive=Negative
Positive+Positive=Negative
Negative+Negative=Positive
Which function has the following domain and range?
Domian {-12, -7, 0, 4, 12}
Range { 0, 1, 2}
A) {(-12, 12), (0,2)}
B) (0,4), (2,12), (1,-7), (0,-12), (1,0)}
C) {(-12,0), (-7,1), (0,2), (-4,5), (3,-1)}
D) {(4,1), (-7,0), (12,2), (0,0), (-12,1)}
D. The function {(4,1), (-7,0), (-12,2), (0,0), (-12,1)} has the given domain {-12, -7, 0, 4, 12} and range { 0, 1, 2}.
What is domain and range ?The domain is the set of all inputs which has an output or range.The range of a function is the set of all outputs form which the domain is defied.
According to the given question domain and range of a function are given they are { -12, -7, 0, 4, 12 } and { 0, 1, 2 }.
This can be written an an ordered pair as { (-12,0), (-12,1), (-12,2), (-7,0), (-7,1), (-7,2), (0,0), (0,1), (0,2), (4,0), (4,1), (4,2), (12,0), (12,1), (12,2) }.
From the given options we can observe that in option D. which has ordered pairs { (4,1), (-7,0), (-12,2), (0,0), (-12,1) }.
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the formula for the volume of a rectanglular prism is given by
V=lwh
where V is volume, l is length, w is width, and h is height.
a) solve for L if V=120, w=6, and h=4
l=
b) solve for L in general.
l=
Answer:
Step-by-step explanation:
V=lwh
120=l(6)(4)
120=24I
[tex]\frac{120}{24} =\frac{24I}{24} \\I=5[/tex]
Answer:
V=lwh
120=l(6)(4)
120=24I\begin{gathered}\frac{120}{24} =\frac{24I}{24} \\I=5\end{gathered}
Create an equivalent expression for 9−7 • 95.
−9^2
one over nine raised to the second power
one over nine raised to the power of negative two
9^2
The equivalent expression of 9^-7 * 9^5 is 1/9^2
How to create an equivalent expression?The expression is given as
9^-7 * 9^5
Apply the law of indices.
So, we have
9^-7 * 9^5 = 9^(-7 + 5)
Evaluate the sum
9^-7 * 9^5 = 9^-2
Rewrite as
9^-7 * 9^5 = 1/9^2
Hence, the equivalent expression of 9^-7 * 9^5 is 1/9^2
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A student takes out 2 loans to pay for college. One loan at 9% interest and the other at 12% interest.
The total amount borrowed is $65,000, and the interest after 1 year for both loans is $6,360.
Find the amount of each loan.
The loan amount at 9% interest is $48,000.
The loan amount at 12% interest is $17,000
What are the loan amounts?The first step is to form a system of equations that can be used to determine the required values:
0.09a + 0.12b = $6,360 equation 1
a + b = $65,000 equation 2
Where:
a = amount of the loan at 9% interest
b = amount of the loan at 12% interest
What is each loan amount?Multiply equation 2 by 0.09
0.09a + 0.09b = 5850 equation 3
Subtract equation 3 from equation 2
0.03b = 510
Divide both sides of the equation by 0.03
b = 510 / 0.03
b = $17,000
Subtract 17,000 from 65,000
a = 65,000 - 17,000
a = $48,000
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The account balance of each of three children at the end of a month is shown below:
Kyle has −$2.25
Jason has −$2.00
Sue has as much savings in her account as the amount Kyle owes the bank.
Part A: On a blank paper, draw a number line from −4 to +4. Plot points on the number line to show the account balances of the three children. Label the points using the name of each child. Describe in detail how you created and labeled this number line, and what it looks like in detail. (5 points)
Part B: Determine whether Kyle or Jason owes the bank more. Use absolute values and inequalities to write statements that justify your conclusion. (5 points)
The drawing of the number line representing the bank balances is attached below . Kyle owes the bank more money than Jason.
The number line a physical representation of all real numbers. A number line is basically a graph of all real numbers. A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
On the number line all the values of the bank balances of the 3 siblings are given.
Kyle owes the bank $2.25 , therefore Sue has $2.25 in her bank account.
Now we can see in the number line that -2.25 is to the left of -2.0 ,
therefore we can say that:
|-2.25| > |-2.00|
as the absolute value of the given balance .
But -2.25 < -2.00
Hence Kyle owes more money to the bank as represented on the number line.
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A picture frame has a width of 2 inches. If the area of the frame is 128 square inches, and if the picture
itself is 4 inches longer than it is wide, what are the dimensions of the Picture
The dimensions of the picture will be 60 inches and 2 inches.
We are given that:
The width of the frame is = 2 inches.
The area of the frame is 128 inches².
Let the length of the frame be x.
So, according to the question, we get the length of the picture as:
length = x + 4
Area of picture frame = l × b
128 = (x + 4) × 2
128 = 2 x + 8
2 x = 128 - 8
2 x = 120
x = 120 / 2
x = 60 inches.
Therefore, the dimensions of the picture will be 60 inches and 2 inches.
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Which linear equation shows a proportional relationship?
y equals negative 2 times x minus one third
y equals one third times x minus 1
y equals five sixths times x
y equals 5 times x plus 3
The proportional relation is the third one.
y = (5/6)*x
Which linear equation shows a proportional relationship?A general linear equation in the point-slope form is written as:
y = a*x + b
Where the a is the slope, and b is the y-intercept.
Particularly, a proportional relation is a linear equation where the y-intercept is equal to zero
y = a*x
And in this case, the slope is also called a constant of proportionality.
Then from the given options, the one that is a proportional relation is:
y = (5/6)*x
Which is the third option, counting from the top.
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Write the Write the rational number -3.5
using quotients of the form
. Use the integers below.rational number using quotients of the form . Use the integers below.
The quotient form of given rational number is -7/2.
Given the rational number is -3.5.
Here, we want to write the quotient form of the given rational number.
rational numbers, in arithmetic, a number that can be expressed as the quotient p/q of two integers such that q ≠ 0.
Number 3.5 is a rational number. As we know rational numbers can also be expressed as decimals with repeating digits after the decimal point. The number7/2 is the ratio of two integers that are 7 integers divided by 2 integers and expressed in fraction (as p/q where q is not equal to 0).
Hence, the quotient form of the given rational number -3.5 is -7/2.
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What are the coordinates of the y intercept of the function y=|3x-10|+1
Answer: (0,11)
Step-by-step explanation:
The y-intercept is when x is equal to 0, so we can just plug that into get the y-coordinate.
y = |3x - 10| + 1
y = |-10| + 1
y = 10 + 1
y = 11
Leon draws there height shown in the parallelogram. He estimates that the height is about 5 units long. Is Leon’s estimate reasonable? Explain.
Based on the given parallelogram, a height of 5 units long as estimated by Leon is not reasonable.
What is the height of the parallelogram?The height of the parallelogram can be found by counting the number of squares from the base of the parallelogram to the top. The squares are given in the graph which is shown attached.
When this counting is done, we get 6 squares.
6 units is therefore the height of the parallelogram which means that Leon's estimate of 5 units is therefore not reasonable.
In conclusion, Leon's estimate is not a reasonable estimate.
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Diana, Elsa, Flora and Hannah agreed to share the cost of a present equally for their mother. Hannah did not bring her money so the other 3 sisters paid for her share. Flora paid 4/5 of what Diana and Elsa paid. Diana paid $10 less than Elsa. The ratio of Diana and Elsa share is 1:4. When they reached home, Hannah returned her sisters' their share of money. Hannah returned Flora $84. (a) How much did Diana and Elsa pay altogether? (b) How much did Hannah pay Diana?
Using proportions, it is found that:
a) Diana and Elsa paid $105 altogether.
b) Hannah paid Diana $21.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Hannah returned Flora $84, and Flora paid 4/5 of what Diana and Elsa paid, hence the amount Diana and Elsa received by Hannah is given as follows:
4/5x = 84
0.8x = 84
x = 84/0.8
x = 105.
Hence Diana and Elsa paid $105 altogether.
For item b, we have that the ratio of Diana and Elsa share is 1:4, hence Diana got 1/5 of the amount paid by Hannah, hence:
1/5 x 105 = 21.
Hannah paid Diana $21.
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PLEASE HELPPP!!! Which expression is equivalent to sum of quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity?
A. negative twenty nine sixths times n minus one twelfth (-29/6n- 1/12)
B.negative twenty nine sixths times n plus one twelfth( -29/6n + 1/12)
C. negative eleven sixths times n minus one twelfth (-11/6n-1/12)
D.negative eleven sixths times n plus five twelfths ( -11/6n + 5/12
The given expression is equivalent to the expression - 11/6 n - 1/12. Then the correct option is C.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The sum of capacity minus three and one-third times n plus one-sixth ended capacity + capacity one and three-sixths times n minus three-twelfths end quantity.
Let n be the number. Then the expression will be
⇒ -(3 1/3)n + 1/6 + (1 3/6)n - 3/12
Simplify the equation, then we have
⇒ -(3 1/3)n + 1/6 + (1 3/6)n - 3/12
⇒ -10/3 n + 3/2 n + 1/6 - 1/4
⇒ -11/6 n - 1/12
The given expression is equivalent to the expression - 11/6 n - 1/12. Then the correct option is C.
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A jar has marbles in these three colors only: 5 green, 3 blue, 7 red.
What is the probability of randomly choosing a red and then a green marble? You
keep the red marble after choosing it.
Answer:
Probability of choosing a red marbles = 7/15
Probability of choosing a green marble = 5/15
Step-by-step explanation:
Formula = Marble/Total of the whole marble
= red marbles /Total of the whole marble
= 7/15
ANDgreen marble/Total of the whole marble
= 5/15
The zeros of a 5-th degree polynomial are 2,i,-2i. Find the remaining zeros.
Answer:
-i,2i
Step-by-step explanation:
zeros(2,i,-2i {5th degree}
then the conjugate zeroes are,
I,2i {conjugate zeros}
so the answer is i, 2i
rewrite 100 as a base and exponent without using an exponent of 1
Answer:
10^2
Step-by-step explanation:
please help, it would mean a lot to me! :) I need to understand these type of math problems and I need help on this one! I am having a test next week!
Answer:
2A/h = b
Step-by-step explanation:
To get b by itself, you have to reverse each operation for the other variables.
h is being multiplied by b here, so to reverse it, you would divide h on both side of the equation. This will give you...
A/h = 1/2b (h is not on the right side anymore because it got canceled out.)
Next you will get rid of the 1/2 by multiplying both sides of the equation with the reciprocal. The reciprocal of 1/2 is 2/1. This will give you..
2A/h = b (1/2 is not on the right side anymore because it got canceled out by 2/1 (1/2 x 2/1 = 1))
Step-by-step explanation:
this is the formula for the area of a triangle :
half off the baseline times the height (to this baseline).
to solve an equation for one variable involved means to end up with only that variable on one side, and everything else on the other side.
the whole time we keep the equality alive, so any change done on one side has to be done on the other side as well.
A = 1/2 × b × h
to solve for b means we want to get rid of the 1/2 and the h factor.
let's start with the 1/2 factor : we multiply both sides by 2.
2A = b × h
and to get rid of h, we need to divide both sides by h :
2A/h = b
and that's it.
Melissa bought 36 pine seedlings and 30 juniper seedlings to plant in rows on her tree farm. She wants each row to have the same number of seedlings. She wants only one type of seedling in each row. What is the greatest number of seedlings she can plant in each row? How many rows of each type of tree will there be? Each row will contain rows of juniper seedlings. seedlings.
She can plant maximum of 6 seedlings in each row. There can be 6 rows of pine seedlings and 5 rows of juniper seedlings.
The Highest Common Factor (HCF) of two numbers is the highest possible number that divides both the numbers completely.
Given: 36 pine seedlings and 30 juniper seedlings and Melissa wants each row to have the same number of seedlings with only one type of seedling in each row.
The greatest number of seedlings that can be planted in each row can be calculated by HCF.
HCF of 36 and 30:
36= 2*2*3*3
30=2*3*5
HCF is 2*3=6
Number of rows of pine seedlings= [tex]\frac{36}{6}[/tex]
=6
Number of rows of juniper seedlings= [tex]\frac{30}{6}[/tex]
=5
Hence, she can plant 6 seedlings in a row. There will be 6 rows of pine seedlings and 5 rows of juniper seedlings.
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A bag contains 2 gold marbles, 7 silver marbles, and 21 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?
The expected value if i play this game is 1/30 dollars.
What is probability ?Probability is the occurrence of a certain event out of the total events that can happen on a given satiation.
According to the given question A bag contains 2 gold marbles, 7 silver marbles, and 21 black marbles.
No. of sample space N(s) = 2 + 7 + 21 = 30.
No. of gold marbles N(g) = 2.
No. of silver marbles N(sil) = 7.
No. of black marbles N(b) = 21.
We know,
P(g) = N(g)/N(s) = 2/30 = 1/15.
P(sil) = N(sil)/N(s) = 7/30.
P(b) = N(b)/N(s) = 21/30 = 7/10.
Given if it is gold, you win 4dollars. If it is silver, you win 2 dollars. If it is black, you lose 1 dollars.
The expected value if you play this game is
= 4P(g) + 2P(sil) - 1P(b)
= 4(1/15) + 2(7/30) - 1(7/10).
= 4/15 + 14/30 - 7/10.
= (8+14-21)/30.
= 1/30 dollars.
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Determine whether the following possible responses should be classified as interval, nominal, ratio or ordinal data The starting salaries of new phd graduates from a statistics program
The starting salaries of new phd graduates from a statistics program illustrates a ratio data.
How to explain the information?The four basic levels of measuring scales—nominal, ordinal, interval, and ratio are used to collect data in the form of multiple-choice questions on surveys and questionnaires.
Each scale serves the same purpose as the preceding scale, and all survey question scales are incremental levels of measurement.
Nominal: the data can only be categorized.
Ordinal: the data can be categorized and ranked.
Interval: the data can be categorized and ranked, and evenly spaced.
Ratio: the data can be categorized, ranked, evenly spaced and has a natural zero.
Therefore, the starting salaries of new phd graduates from a statistics program illustrates a ratio data.
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What are the correct answers?
Answer:
It has only one answer which is 'The decimal is non-terminating'
A ball is accidentally dropped from the top of a tall building. It took 3.0 secs for the ball to hit the ground. The acceleration of gravity is g = 10 m/sec². Find the initial height from which the ball was dropped.
Answer:
[tex]{ \rm{s = ut + \frac{1}{2} {at}^{2} }} \\ \\ { \rm{h = 0 + \frac{1}{2} \times 10 \times {3}^{2} }} \\ \\ { \tt{h = 5 \times 9}} \\ { \tt{h = 45 \: m}}[/tex]
What is the value of g(1) for the function g(x) = 2x + 5?
Α. 7
B. 8
C. 26
D. 27
Find the perimeter or circumference and area of each figure if each unit on the
graph measures 1 centimeter. Round answers to the nearest tenth, if necessary.
The perimeter or circumference and area of each figure if each unit on the graph measures 1 centimeter is 18.
The area of a circle is π[tex]r^2[/tex]
The area of a triangle is 1/2×base×height
The area of the rectangle is length×breadth
The perimeter of a circle is 2πr
so, Area of Triangle =1/2×b×h
1/2×4×9=18
A rectangle is a quadrilateral with all angles equal and opposing sides equal and parallel. There are numerous rectangular items all around us. Each rectangle shape has two dimensions: length and breadth. The length of the rectangle is known as the length, while the width is known as the width.
A rectangle is a closed two-dimensional shape with four sides. A rectangle's opposite sides are equal and parallel, and all of its angles are 90°. Examine the rectangle below to observe its form, sides, and angles.
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Kyle wants to buy a television on a hire purchase agreement. The cash price of the television is R5 600 R5 600. She is required to pay a deposit of 15%
15% and pay the remaining loan amount off over 24 24 months at an interest rate of 14% 14% p.a.
What are Kyle's monthly repayments?
The monthly repayment Kyle has to pay on the television based on the hire purchase agreement is R229.
What is the monthly repayment?The monthly repayment is the amount to be paid monthly with interest on the given loan amount.
We have,
Price of the television = R5600
Deposit amount:
= 15% of 5600
= 15/100 x 5600
= 0.15 × 5600
= 840
Now,
The remaining amount:
= 5600 - 840
= 4760
The monthly repayment amount of 14% per annum is:
A = [ P( R/12 )( 1 - R/12 [tex])^{n}[/tex] ] / ( 1 + r/12 [tex])^{n}[/tex] - 1
A = [ 4760 ( 0.14/12 )( 1 - 0.14/12 [tex])^{24}[/tex] ] / [ ( 1 + 0.14/12 [tex])^{24}[/tex] - 1 ]
A = 228.54
A ≅ 229
Thus the monthly repayment Kyle has to pay on the television based on the hire purchase agreement is R229.
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Simplify by reducing the index of th
21/ 15
√X
Answer:
simplify the reducing the index of the
21/15√x
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
I need help to answer this question please 3(4x−1)=21
Answer: x=1.75
Step-by-step explanation:
Multiply: 12x-3=21
Subtract: 12x=21
Divide: 21/12= 1.75
Final Answer: X = 1.75
Which one is function?
Answer:
a
Step-by-step explanation:
there are not two points on the same line.
im confused on this !
Answer:
P = 35x + 18(140-x)
Step-by-step explanation:
I think they are just asking for the expression, not to solve it. We would need more info (like the total profit) to solve it.
Multiply these polynomials using the FOIL method and the answer should be a polynomial as well.
[tex]( m^{\frac{1}{3} } + y^{-\frac{1}{2} } )^{2}[/tex]
The answer to the expression is m^2/3 + 2 * m^1/3 * y^(-1/2) + 1/y
What is FOIL?FOIL is a mnemonic for the standard method of multiplying two binomials, hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: First (“first” terms of each binomial are multiplied together)
given:
(m^1/3 + y^(-1/2))^2
we can write it as
(m^1/3 + y^(-1/2))*(m^1/3 + y^(-1/2))
=m^1/3 * m^1/3 + m^1/3 * y^(-1/2) + y^(-1/2) * y^(-1/2) + y^(-1/2)*m^1/3
=m^2/3 + m^1/3 * y^(-1/2) + 1/y + y^(-1/2)*m^1/3
= m^2/3 + 2 * m^1/3 * y^(-1/2) + 1/y
Hence, the answer to the expression is m^2/3 + 2 * m^1/3 * y^(-1/2) + 1/y
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