The given system of equations : 6x - y = 2 and 4x - y = -8.
6x - y = 2 ( 1 )
4x - y = -8 ( 2 )
for the value of y, use substitution method:
Solve the equation (1) for y :
6x - y = 2
y = 6x - 2
Susbtitute the value of y in the equation ( 2 )
4x - y = - 8
4x - (6x - 2) = - 8
4x - 6x + 2 = - 8
4x -6x = - 8 - 2
-2x = -10
Divide both side by ( -2)
-2x/(-2) = -10/(-2)
x = 5
Substitute x = 5 in the equation ( 1 )
6x - y = 2
6( 5 ) - y = 2
30 - y = 2
y = 30 - 2
y = 28
So, the value of y is 28
Answer : y = 28
Evaluate. 0⁴= please
A right isosceles triangle has an area of 40.5 cm2. How tall is it?
Area = 40 cm^2
base = ?
height = x
Area = base * height / 2
bh = 2(40.5)
bh = 81 cm^2
81 3
27 3
9 3
3 3 height = 3 x3 x 3 base = 3
1
The height must be 27 cm and the base 3 cm.
Solve the following system of equations using elimination. 2x + 5y = 12 -2x + 3y = 4
To solve a system of equation using elimination:
1. If it is necesary multyiply one of both equations for a number that makes each equation have an opposite term to the other equation.
In this case the equations already have opposite terms (2x and -2x)
2. Add equations:
3. Solve the variable in the result of substraction:
[tex]\begin{gathered} 8y=16 \\ y=\frac{16}{8} \\ \\ y=2 \end{gathered}[/tex]4. Use the value of the variable you get in the previus step to solve the other variable:
[tex]\begin{gathered} 2x+5y=12 \\ y=2 \\ \\ 2x+5(2)=12 \\ 2x+10=12 \\ 2x=12-10 \\ 2x=2 \\ x=\frac{2}{2} \\ \\ x=1 \end{gathered}[/tex]Then, the solution for the system of equations is x=1 and y=2An automobile travels 415 miles on 16 2/3 gallons of gasoline.
a) How many miles per gallon does the car get on the trip? (Enter your answer as a simplified mixed number.)
b) How many gallons would be required for the car to travel 498 miles?
Aisha is trying to determine if △LMN and △PQR are similar, congruent, or neither using the information in the diagram.
Triangles L M N and P Q R are shown. The length of side L M is 11 and the length of P Q is 22. The length of M N is 7 and the length of Q R is 12. The length of N L is 6 and the length of R P is 12.
Which statement is true?
The statement that is true about the triangle is that D. The triangles are similar by the SSS similarity theorem.
How to illustrate the information?It should be noted that congruence simply refers to a scenario where there are the same triangles.
The SSS Similarity Theorem states that two triangles are similar if all three pairs of matching sides are proportionate.
Compare the shortest sides first, followed by the longest sides, when applying the SSS Similarity Theorem. Two triangles are similar if their corresponding side lengths are proportionate to one another.
Therefore, triangle LMN and PQR are the same.
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The triangles are not similar, but they are congruent.
The triangles are neither similar nor congruent.
The triangles are similar by the SAS similarity theorem.
The triangles are similar by the SSS similarity theorem.
Answer:
d) The triangles are similar by the SSS similarity theorem.
Use the diagram to answer the question. 15 ft 120 ft2 10 ft A rectangular yard contains a 120-square-foot garden. If seeds are scattered uniformly over the yard, what is the probability that a seed lands in the garden?
area of the rectangle
[tex]\begin{gathered} \text{area}=\text{length}\times width \\ \text{area}=15\times10=150 \end{gathered}[/tex]area of rectangle is 150 sq ft, therefore the probability that a seed lands in the garden is
[tex]\frac{area\text{ garden}}{area\text{ rectangle}}=\frac{120}{150}=\frac{4}{5}[/tex]answer: 4/5
Complete Complete the following tick -tac-toe board to find the three in a row there is only one correct way to make the tick-tac-toe, three in row! The code to unlock the puzzle will be the product of the three the following three puzzle Tic tac toe
GARDENING Molly's school is planning a school-based community garden with the diagram shownIf the school has 64 yards of fencing for the rectangular garden, use a system of equations and a graphing calculator to find the value of Then find the dimensions of the garden.
The value of x is 5 yards and the length and width of the garden is 20 yards and 12 yards respectively.
Given, the school has 64 yards of fencing for the rectangular garden.
we know that, the perimeter of the rectangle is the sum of twice the length and twice the width.
length (l) = x²-5
width (w) = 4x-8
therefore, 2(l+w) = 64
⇒ 2(x²-5+4x-8) = 64
⇒ 2(x²+4x-13) = 64
⇒ 2x²+8x-26 = 64
⇒2x²+8x-26-64 = 0
⇒2x²+8x-90 = 0
divide the equation by 2.
⇒ x²+4x-45=0
⇒ x²+9x-5x-45 = 0
⇒ x(x+9) - 5(x+9) = 0
⇒ (x+9) (x-5)
⇒ x = -9 or x = 5
therefore, x cannot be negative,
hence x = 5 yards.
therefore, l = x²-5
l = 5² - 5
l = 25-5
l = 20 yards.
w = 4x-8
w = 4(5) - 8
w = 20-8
w = 12 yards.
Hence we get the value of x as 5 yards and the dimensions of the garden as 20 yards by 12 yards,
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Koharu pie dough recipe uses 6 oz of flour, 4 oz of butter, and 2 oz of water. Complete the sentences to describe the ratios in her recipe. The ratio of ____ to ____ is 3:2
Answer:
The ratio of flour to butter is 3:2
Step-by-step explanation:
:]
a Is it possible to construct a triangle with lengths of 7, 54, and 45? EXPLAIN why or why not?
For a, b, and c to be the lengths of a triangle they must satisfy the following system of inequalities:
[tex]\begin{gathered} a+b>c, \\ a+c>b, \\ b+c>a\text{.} \end{gathered}[/tex]Now, notice that:
[tex]\begin{gathered} 7+54>45, \\ 45+54>7,\text{ } \\ 45+7=52<54. \end{gathered}[/tex]Since the given numbers do not satisfy the last inequality, then they cannot be the lengths of a triangle.
Answer: No it is not possible to construct a triangle with lengths 7, 54 and 45, because:
[tex]45+7<54.[/tex]Find the least common denominator of
8/x²+11x+28
and
-2/x^2+4x
The least common denominator of 8/( x²+11x+28 ) and -2/ (x^2+4x) is (x+4).
We have to find the least common denominator of 8/x²+11x+28 and -2/x^2+4x. We can solve this problem by following a few steps.
The denominator of both terms is, x²+11x+28 and x²+4x.
First of all, we have to find the factors of these two terms.
Let's find the factors of x²+11x+28.
x²+11x+28 = x²+11x+28
Or, x²+11x+28 = x²+ 4x+ 7x+ 28 [ we have to break the middle term in such a way as the product of consecutive terms must be 28 ]
Or, x²+11x+28 = x (x+4) +7 (x-4) [ we have to take ( x+ 4) as acommon ]
Or, x²+11x+28 = ( x+4 )( x+7 ).................(1)
Now find the factors of x²+4x.
x²+4x = x (x+4)..................(2) [ We have to take x as a common ]
Therefore, the common term between (1) and (2) is ( x+4 ). So, the least common denominator is ( x+4 ).
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2 The model shown below is a composite of tworectangular prisms.What is the volume of the model in cubic units?F 640 H 960G 512 J 1,280
Answer
Volume of the prism = 960 cubic units
Explanaion:
Step 1: Divide the two prism
Volume of a rectangular prism is
l x w x h
Where l = length, w= width, and h = height
The volume = full prism - cut prism
Full prism = 16 * 10 * 8
Full prism = 1280 cubic units
Cut prism = 8 * 10 * 4
Cut prism = 320 cubic units
Volume = 1280 - 320
Volume = 960 cubic units
5/6x-2/3(x-2) + 1/2 please helppp
Answer:38
Step-by-step explanation:
An equality that represents numbers that are not a solution of x-1.2>2.8
The solution is x> 4 or x ∈(4,∞)
Here equality given is
x - 1.2> 2.8
Rearrange the variable to the left side of the equation
x > 2.8 + 1.2
Calculate the sum
x > 4
Or we can also say
x ∈ (4,∞)
Therefore the range of x is x∈ (4,∞).
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The result obtained from measuring length is called a/an __________ measurement and is stated in __________ units.
The result obtained from measuring length is called a linear measurement and is stated in linear units.
The linear measurement is the distance between the two objects or points. The linear measurement is a single dimension measurement
The unit of the measurement of the length is called linear units. In US system of measurements the linear units are feet, yard and inch etc..,In metric system the linear units are meter, centimeter, decimeter etc..
Therefore the result obtained from measuring length is called a linear measurement and is stated in linear units.
Hence, the result obtained from measuring length is called a linear measurement and is stated in linear units.
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What is the range shown in the graph below ?
Take into account that the range are all availables values of the function, that is, available values of the y coordinate in the graph.
As you can notice, such values are in the following interval:
range: (-∞,8]
Put the correct number in each box 1/7 = 4/? = ?/56
Answer: 1/7 = 4/28 = 8/56
Step-by-step explanation: 7 timestables
Answer:
1/7=4/28=8/56
Step-by-step explanation:
From the pattern of the question we can see that the numerator of the second fraction is 4 and the previous fraction's numerator is 1 that means the fraction has been multiplied by 4. Therefore multiplying the numerator and denominator results in the answer 4/28. For the last fraction we can see that the denominator is 56 and is the double of 28 therefore doubling the whole second fraction we get our answer as 8/56. Overall equating all the three fractions we get the same answer 1/7 after minimizing the fraction.
Username: TNakashrai
What must x equal if a ∥ b? Explain.
The value of x should be equal to 23
Given
Angle at the top is 86
also equation 3x + 17
The lines are parallel
We know if a transverse line is drawn across two parallel lines then 3 types of angles would form namely Corresponding angle, alternate angle, Opposite angle.
From the geometry the angle 86 and the equations 3x + 17 are alternative angles.
Since alternative angles are equal 86 will be equal to 3x + 17
Now equating both
86 = 3x + 17
86 - 17 = 3x
69 = 3x
x = 23
Hence the value of x is equal to 23
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Answer: x=23
Step-by-step explanation:
Im not going to bore you with long algebra but basically 86-17=3x
69=3x inverse you get 23
please help me solve. I have 81 for blank 1 and 9 for blank 2. it is incorrect
We can further simplify
[tex]\sqrt[]{27}[/tex][tex]\begin{gathered} \sqrt[]{27}\text{ = }\sqrt[]{3\text{ x 9}} \\ \sqrt[]{27}\text{ = }\sqrt[]{3}\text{ x }\sqrt[]{9} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{27}\text{ = }\sqrt[]{3}\text{ x 3 = 3 x }\sqrt[]{3} \\ \sqrt[]{27}\text{ = 3 }\sqrt[]{3} \end{gathered}[/tex][tex]\sqrt[]{3}\text{ x }\sqrt[]{27\text{ }}\text{ = }\sqrt[]{3}\text{ x 3}\sqrt[]{3}[/tex]The answers for the blank spaces are
[tex]\sqrt[]{3}\text{ and 3}\sqrt[]{3}[/tex]Factor 3z^2(8z^2-14z+3)
Answer:
3z²(4z-1)(2z-3)
Step-by-step explanation:
Factor 8z²-14z+3
8z²-14z+3 = (4z-1)(2z-3)
So 3z² (8z²-14z+3)
= 3z²(4z-1)(2z-3)
Choose the correct ordering of the numbers below from greatest to least.L. 779.56M. 29.7023N. 7.8695O. 0.8436P. 70.7540
When you order a number, you must check the number most in the left. The number L and the number M for example,
L. 779.56
M. 029.7023
In the hundreds place, L has a '7', and M has a '0', this means L is bigger than M.
Doing the same procedure with the other, we get the following order:
[tex]\begin{gathered} 779.56>70.7540>29.7023>7.8695>0.8436 \\ L>P>M>N>O \end{gathered}[/tex]Box A weighs 212.04 kilograms. Box B weighs 212 1/4 kilograms Which statement is true?A) the box weigh the same amountB) Box B weighs 0.10 of a kilogram more than Box AC) Box A weighs 0.15 of a kilogram more than box BD) Vox b weighs 0.21 of a kilogram more than Box A
To be able to compare the weight of the boxes, we need to have their weight in decimal form:
Box A --> 212.04 kilograms
Box B --> 212 1/4 kilograms
Convert 212 1/4 to decimal:
[tex]\begin{gathered} \text{SINCE }\frac{1}{4}=0.25 \\ 212\frac{1}{4}=212.25 \end{gathered}[/tex]Box B --> 212.25
We can see that the weight of box B is more than the weight of box A, so we discard options A and C.
To find how much more is the weight of box B, we subtract the quantities:
[tex]212.25-212.04=0.21[/tex]Answer: Box B weighs 0.21 of a kilogram more than box A
MapsQuestion 120 ptsIf a recipe calls for 58 ounces of pecans andthere are 16 ounces in 2 cups, how many pecanswill you need?
the recipe needed = 58 ounces of pecans
we have 16 ounces in 2 cups,
so we need
58 - 16 = 42 ounces
so we need 42 ounces of pecans.
Find the intersection points of f(x) = (x + 7)(x - 5) and g(x) = x-5.
510
Answer:
-7
Step-by-step explanation:
all answers are in the picture
how do i do square root of 24 on the simplified radical form
Re-write the question as :
[tex]\sqrt{24}[/tex]This can further be written using factors of 24 as;
[tex]\sqrt{6\ast4}[/tex]Separate as :
What is the answer with a posible fraction remainder3.8/21.85
The solution with a potential fraction remainder for the given fraction, 3.8/21.85, is 0.
How to find the remainder?By shifting the decimal point 1 places to the right, you can convert the divisor 3.8 to a whole number. Then, move the decimal point in the dividend by one place to the right, keeping the same position.
what do you understand by remainder ?The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.
These equations follow:
218.5 ÷ 38 = 5.750
because of this:
21.85 ÷ 3.8 = 5.750
To three decimal places, both calculations.
0 0 5. 7 5 0
3 8 √2 1 8. 5 0 0
− 0
2 1
− 0
2 1 8
− 1 9 0
2 8 5
− 2 6 6
1 9 0
− 1 9 0
0 0
− 0
0
The answer is 0.
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The pentagons ABCDE and PQRST are similar.
Find the length x of TP.
Answer:x=3
Step-by-step explanation: if they are similar lets say for instance BD is congruent to QS.
so TP is congruent to AE and AE is three so TP has to be three.
hope this helps!
A grocery store sells a bag of 3 oranges for $2.16. What is the cost of oranges, in dollars per orange?
Answer:
0.72
Step-by-step explanation:
The answer is that because all you have to do is just 2.16 divided by 3. Equalling to 0.72. Now we just have to do 0.72 + 0.72 + 0.72 and that would equal $2.16.
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Hello! Vectors u and v are shown in the graph. What is -3(u x v)?
Explanation
The values of the vectors are shown below
Thus
[tex]\begin{gathered} u=(6,5) \\ v=(-6,-10) \end{gathered}[/tex]Thus to get -3(u.v) will be
[tex]\begin{gathered} step\text{ 1} \\ find\text{ the dot product} \\ u.v=6(-6)+5(-10) \\ u.v=-36-50 \\ u.v=-86 \end{gathered}[/tex]The next step will be
[tex]\begin{gathered} -3(u.v)=-3\times-86=258 \\ \\ -3(u.v)=258 \end{gathered}[/tex]The answer will be
Evaluate the polynomial function for the given values of the variable
ANSWERS
• P(2) = 11
,• P(-1) = 14
,• P(0) = 7
EXPLANATION
Every time we have to evaluate a function, what we have to do is replace the variable with the value and solve the operations.
Let's solve P(2),
[tex]P(2)=3(2)^2-4(2)+7[/tex]Solve the powers first,
[tex]P(2)=3\cdot4-4\cdot2+7[/tex]Then the products,
[tex]P(2)=12-8+7[/tex]And then the additions/subtractions,
[tex]P(2)=11[/tex]The process is the same for the other two values,
[tex]P(-1)=3(-1)^2-4(-1)+7=3\cdot1-4(-1)+7=3+4+7=14[/tex]And,
[tex]P(0)=3(0)^2-4(0)+7=3\cdot0-4\cdot0+7=0+0+7=7[/tex]Hence, P(2) = 11, P(-1) = 14 and P(0) = 7.