Answer:
Step-by-step explanation:
x+2y=7
Final answer:
To write an equation with (1,3) as a solution, choose an arbitrary slope and use the given point to solve for the y-intercept, forming a complete linear equation.
Explanation:
To write an equation in two variables that has (1,3) as a solution, you start by understanding linear equations in the form y = mx + b, where m is the slope, and b is the y-intercept. Given the point (1,3), we can choose an arbitrary slope (for example, 2) and plug the point into the equation to solve for b.
Note: y = 2x + b, and with the point (1,3), substituting x with 1 and y with 3 gives 3 = 2(1) + b, which simplifies to b = 1. Therefore, an example equation that fits the criteria is y = 2x + 1.
Daniel gets a paycheck every 444 weeks. He works xxx hours each week.
How many hours does Daniel get paid for on each paycheck?
Answer:4 divided by x hours
Step-by-step explanation:
The number of hours that Daniel gets paid for on each paycheck will be 4x.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Every 4 weeks, Daniel receives a paycheck. He puts in x hours a week at work.
The number of hours that Daniel gets paid for on each paycheck is given as,
⇒ 4 · x
⇒ 4x
The number of hours that Daniel gets paid for on each paycheck will be 4x.
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Solve the equation 15=7-|2x|
Answer:
4
Step-by-step explanation:
15 = 7 - /2x/
Subtract 7 from both sides ( if it was negative you would add it)
(15-7) = (7 - 7) -/2x/ now the seven is no longer there
8 = -/2x/
Now divide 2 from both sides
( 8 / 2 ) = - /(2 / 2)x/
4 = -/x/
4 = -x
Now the two is no longer there but the x would still be there because you divided it by 2 and not 2x
To solve the equation 15 = 7 - |2x|, consider two cases: 2x ≥ 0 and 2x < 0. In case 1, x = -4. In case 2, x = 4.
Explanation:To solve the equation 15 = 7 - |2x|, we need to eliminate the absolute value. To do this, we can consider two cases: when 2x is positive and when 2x is negative.
Case 1: 2x ≥ 0
In this case, the equation becomes 15 = 7 - 2x, which simplifies to 2x = -8. Solving for x, we get x = -4.
Case 2: 2x < 0
In this case, the equation becomes 15 = 7 + 2x, which simplifies to 2x = 8. Solving for x, we get x = 4.
Therefore, the solution to the equation 15 = 7 - |2x| is x = -4 or x = 4.
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Given: Angle T S R and Angle Q R S are right angles; Angle T Is-congruent-to Angle Q
Prove: Triangle T S R Is-congruent-to Triangle Q R S
Triangles T S R and Q R S share side S R. Angles T S R and S R Q are right angles. Angles S T R and S Q R are congruent.
Step 1: We know that Angle T S R Is-congruent-to Angle Q R S because all right angles are congruent.
Step 2: We know that Angle T Is-congruent-to Angle Q because it is given.
Step 3: We know that Line segment S R is-congruent-to line segment R S because of the reflexive property.
Step 4: Triangle T S R Is-congruent-to Triangle Q R S because
of the ASA congruence theorem.
of the AAS congruence theorem.
of the third angle theorem.
all right triangles are congruent.
Answer:
B. of the AAS congruence theorem.
Step-by-step explanation:
Triangles TSR and QRS share side SR
SR=RS
Angle TSR and Angle QRS are right angles, so
∠S= ∠R
Angle T Is-congruent-to Angle Q, so
∠T= ∠Q
From these data, we have one congruent side and two congruent angles. The possible congruence theorem that we can apply will be either ASA or AAS. In the ASA theorem, the congruence side must be between the two congruent angles.
The congruence side required for the ASA theorem for this triangle is ST = RQ. It is wrong because the congruent side we have is SR=RS. The correct option is the AAS theorem.
What is the equation of the function that is graphed as line a?
y = 2x - 1
y = -x - 1
y = -x
y = 3x
Answer:
[tex]y = - x-1[/tex]
Step-by-step explanation:
The line a passes through th points (-1,0) and (0,-1)
The equation of line which is passes through the point [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex](y-y_1)= \frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Therefore the equation of line which passes through the points (-1,0) and (0,-1)
is
[tex]y-0=\frac{-1-0}{0-(-1)} [x-(-1)][/tex] [ [tex]x_1 = -1, y_1= 0[/tex] [tex]x_2 = 0[/tex] and [tex]y_2 = -1[/tex]]
[tex]\Leftrightarrow y = -1 (x+1)[/tex]
[tex]\Leftrightarrow y = - x-1[/tex]
Answer:
b
Step-by-step explanation:
3 and 5/6 times 1 and 2/4
Step-by-step explanation:
3 5/6 = 3 × 6 + 3 = 23 = 23/6
1 2/4 = 1 × 4 + 2 = 6 = 6/4
23 × 6 = 138
6 × 4 = 24
138/24÷2=68/12÷2=34/6÷2=17/3
since 17 and 3 are prime numbers we cannot simplify any further but 17/3 is an improper fraction so we convert it back to a mixed fraction
3÷17=5 R2 = 5 2/3
What is the approximate area of a circle with a diameter of 14 inches
what is the equivalent decimal to this praction 5/45
Answer:
[tex]0.\overline{1}[/tex]
Step-by-step explanation:
The fraction reduces to 1/9. Since you're familiar with the decimal equivalents of fractions with denominators less than 10, you know this has the decimal equivalent:
1/9 = 0.11111111...(repeating)
_____
Even if you're not familiar with the equivalent of 1/9, you probably know that ...
1/3 = 0.33333...(repeating)
and
2/3 = 0.66666...(repeating)
Of course, 1/3 = 3/9, so dividing 0.333... by 3, we get 1/9 = 0.111....
_____
The attachment shows the long division. It gets boring quickly.
Final answer:
The equivalent decimal of the fraction 5/45 is approximately 0.1111
Explanation:
To find the equivalent decimal of the fraction 5/45, we can start by simplifying the fraction. Since both the numerator (5) and the denominator (45) are divisible by 5, we can reduce the fraction to 1/9.
To convert this simplified fraction into a decimal, we divide 1 by 9.
1 ÷ 9 = 0.111...
The decimal 0.111... means that the 1 repeats indefinitely, which is known as a repeating decimal.
If we want to convert this repeating decimal into an approximation with a specific number of decimal places, we could round it. For example, we could say 0.111... is approximately 0.111 when rounded to three decimal places.
(ASAP: Will give Brainly to whoever answers first) Which expression shows how 6⋅45 can be rewritten using the distributive property?
A. 6⋅4+6⋅5
B. 20⋅6+20⋅5
C. 6⋅40+6⋅5
D. 6⋅40+6
Answer:
C)
Step-by-step explanation:
Susan plans to add $4.23 per week to her savings . how much money will she have after 12 weeks? Create a table showing how much she saves every two weeks up until you get to 12 . Create a graph using your table and write out one equation using your table
Week 1: 4.23
———————
Week 2: 8.46
Week 4: 16.92
Week 6: 25.38
Week 8: 33.84
Week 10: 42.30
Week 12: 50.76
I can’t draw a graph on here but it’s basically a straight line.
Equation: y=4.23x
y is the amount of money she has at x weeks
Answer:
week one 4.23
week 2 8.46
week 3 12.
Step-by-step explanation:
A polynomial function has a root of 0 with multiplicity 1, and a root of 2 with multiplicity 4. If the function
has a negative leading coefficient, and is of odd degree, which of the following are true?
The function is positive on (-0, 0).
The function is negative on (0, 2).
The function is negative on (2,).
The function is positive on (0,0).
Answer:
A, B, and C are true
Step-by-step explanation:
Using the Factor Theorem to find the function, the correct statement is:
The function is positive on (0,∞).
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots
x1, x2,...xn is given by:
f(x) = a(x-x1)(x-x2).....(x-xn)
In which a is the leading coefficient.
here, we have,
The described roots means that:
x1 = 0, x2 = x3= x4 =x5 = 2
Hence the function is:
f(x) = x(x - 2)^4
(x - 2)^4 is always positive, hence the sign depends on the sign of x, which means that the correct statement is:
The function is positive on (0,∞).
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simplify (-4)+(-3)+10 (-1)
Answer:
hope this will help u . ..... plz mark me brainliest
Answer:
-17
Step-by-step explanation:
-4 - 3 - 10 = -17
Find the area of the triangle below. Show as much work as possible. Label your answer appropriately
Answer:
[tex]\frac{5x^{2} }{6}[/tex]
Step-by-step explanation:
Given: Base of triangle= [tex]\frac{5x}{3}[/tex]
Height of triangle= x
Now, finding the area of triangle.
We know area of triangle= [tex]\frac{1}{2} \times base\times height[/tex]
Subtituting the value of base and height in the formula.
⇒[tex]Area\ of\ triangle= \frac{1}{2} \times \frac{5x}{3} \times x[/tex]
Solving it to find area of triangle
∴ [tex]Area\ of\ triangle= \frac{5x^{2} }{6}[/tex]
Hence, area of triangle is [tex]\frac{5x^{2} }{6}[/tex]
Answer:
A=5x^2/6
Step-by-step explanation:
Bill earns $5 for every car he washes. If he earns at least $45, how many cars did Bill wash?
a) define the variable: ____=______________________
b)Write an inequality to represent the scenario:_______________
c) solve the inequality:
d) graph the solution of the inequality on a line graph
hellppp 70 pointsss
what is the equation of the quadratic function shown in the graph ?
f(x)=___ (x + ___) (x-___)
y=a.(X-x1)(X-x2)
x1 and x2 are x-intercepts
x1=-3
x2=1
other points: (-1,8) and (0,5)
y=a.(x+3).(x-1)
a=-2
f(x)= -2.(x+3)(x-1)
The equation is [tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]
How to get the equationGiven the quadratic equation in the form \(y =[tex]a \cdot (X - x_1)(X - x_2)\), where \(x_1\) and \(x_2\)[/tex]represent the x-intercepts, and the given x-intercepts are[tex]\(x_1 = -3\) and \(x_2 = 1\).[/tex]
Using the given x-intercepts [tex]\(x_1 = -3\) and \(x_2 = 1\)[/tex], the equation becomes [tex]\(y = a \cdot (x + 3)(x - 1)\).[/tex]
We are also provided with two other points: (-1, 8) and (0, 5).
We can substitute the point (-1, 8) into the equation to solve for \(a\):
[tex]When \(x = -1\) and \(y = 8\):\[8 = a \cdot ((-1) + 3)((-1) - 1)\]\[8 = a \cdot (2)(-2)\]\[8 = -4a\]\[a = -2\][/tex]
Therefore, the value of \(a\) is -2.
Substituting [tex]\(a = -2\) into the equation \(y = a \cdot (x + 3)(x - 1)\), we get:\[y = -2 \cdot (x + 3)(x - 1)\][/tex]
[tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]
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The perimeter of a rectangular painting is 344 centimeters. If the length of the painting is 91 centimeters, what is its width?
Answer:b = 81
Step-by-step explanation:
perimeter = 2(l+b)
344= 2(91 + b)
344 =182 + 2b
344 -182 =2b
162 = 2b
b = 162/2
b= 81
Answer:
perimeter = 2(l+b)
344= 2(91 + b)
344 =182 + 2b
344 -182 =2b
162 = 2b
b = 162/2
b= 81
Step-by-step explanation:
What is the slope of y = 4 - 2.x?
Answer:
The slope of y=4-2x is -2.
what is the solution to this problem
x+5y=4
3x-7y=-10
To solve the given system of linear equations, we use the elimination method to find the solution, which is (x, y) = (-1, 1).
The student is asking how to find the solution to a system of linear equations:
x + 5y = 4
3x - 7y = -10
To solve this system, one can use the method of elimination.
Multiply the first equation by 3 and the second equation by 1 to align the coefficients of x.
The resulting equations are:
3x + 15y = 12
3x - 7y = -10
Subtract the second equation from the first to eliminate x:
22y = 22
Divide by 22 to find y:
y = 1
Substitute y = 1 into the original first equation:
x + 5(1) = 4
Solve for x:
x = -1
The solution to the system is (x, y) = (-1, 1).
A triangular prism has a base area of 7.3 square cm and a volume of 71.54 cubic cm. The height of the prism must be?
Answer:
Multiply or divide 7.3 times or divided by 71.54
Height of the prism is 9.8 cm
Given that;
Triangular prism base area = 7.3 square cm
Volume of prism = 71.54 cubic cm
Find:
Height of the prism
Computation:
Height of the prism = Volume of prism / Triangular prism base area
Height of the prism = 71.54 / 7.3
Height of the prism = 9.8 cm
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which function has a simplified base of 4^3√4?
Answer:
The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].
Step-by-step explanation:
We have to choose from options the exponential function which has a simplified base of 4∛4 i.e. ∛(256).
Now, the exponential function in the option III will be the answer.
The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].
So, the base is [tex](\sqrt[3]{16} )^{2}[/tex] = [tex]\sqrt[3]{16^{2}} = \sqrt[3]{256} = 4\sqrt[3]{4}[/tex]. (Answer)
The general formula of an exponential function is [tex]f(x) = a(b)^{x}[/tex] , where b is called the base of the function.
The function that has a simplified base of (4∛4) is;
Option C; 4(∛16)^(2x)
From the general formula of an exponential function, we know that;
f(x) = a(b)^(x)
Now, we have;
f(x) = (4∛4)^(x)
Thus, looking at the options, option C is correct because;
In 4(∛16)^(2x), the base is (∛16)² and when we simplify it, we will get 4³(√4) because;
(∛16)² = √(16^(⅔))
>> 256^(⅓)
>> 4∛4
This is the same as our initial value.
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half an avocado has about 160 calories. how many calories do a dozen have?
Answer:
3,840 calories
Step-by-step explanation:
a = an avocado's calories
Given: 1/2a = 160 calories
Multiply both sides of the equation by 2
a = 320 calories
We need to find the amount of calories in a dozen (12) avocados so multiply both sides of this equation by 12
12a = 3,840 calories
Hope this helps :)
Glenda lives in Ohio, which has a sales tax of 5.5%. She just bought a grill whose full price was $220, but she got 40% off, because the store was having a sale. What was the total amount that Glenda paid?
A. $139.26
B. $92.84
c. $88.00
D. $132.00
Answer:A ($139.26)
Step-by-step explanation:
find a formula for the nth term in this arithmetic sequence: a1=0, a2=0.5, a3=1, a4=1.5...
Answer:
0.5
Step-by-step explanation:
2-8x=10
looking for solution
Answer:
x=-1
Step-by-step explanation:
2-8x=10 subtract both sides by 2
-8x=8 divide both sides by -8
x=-1
Answer:
x = -1
Step-by-step explanation: 2 - 8x = 10
-2. -2
-8x. 8
Divide -8. -8
x = -1
How can you solve the equation 4x= 2X-2 graphically?
On Thursday, 13,450 people attended a baseball game. Only 11,350 people attended the game. Only 11,350 people attended the game on Friday. How many more people attended the game on Thursday than the game on Friday explain how to use mental math to slove.
By using mental math and breaking down the numbers into parts, you find that 2,100 more people attended the baseball game on Thursday than on Friday.
Explanation:The subject of this problem is subtraction. To find out how many more people attended the baseball game on Thursday than on Friday, you need to subtract the number of people who attended on Friday from the number who attended on Thursday. In math terms, this would be 13,450 (Thursday's attendance) - 11,350 (Friday's attendance).
To make this easier using mental math, you might notice that both numbers end in 50. You could subtract these separately: 13,000 - 11,000 = 2,000 and 450 - 350 = 100. Adding these results together, you get 2,000 + 100 = 2,100.
So, the answer is that 2,100 more people attended the baseball game on Thursday than on Friday.
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If RSU~VST, then the triangles are similar by:
show work for brainlist
Step-by-step explanation:
[tex] \because \triangle \: RSU \sim \: \triangle VST \\ \\ \therefore \: \frac{RS}{VS} = \frac{7}{14} = \frac{1}{2} ....(1) \\ \\ \angle RSU \cong \: \angle VST ....(2) \\ (vertically \: opposite \: angles) \\ \\ \frac{US}{TS} = \frac{4}{8} = \frac{1}{2} ....(3) \\ \\ from \: equations \: (1) \: (2) \: and \: (3) \\ it \: is \: clear \: that: \\ \triangle \: RSU \sim \: \triangle VST\\ ..(by \:SAS\:similarity\:postulate) [/tex]
Thus, given triangles are similar by SAS similarity postulate.
When the triangles RSU and VST are said to be similar, it means the corresponding sides and angles are proportional and equal respectively, which is known as the Angle-Angle criterion for similarity.
Explanation:If the triangles RSU and VST are similar (RSU ~ VST), it means the corresponding sides and angles of the two triangles are proportional, and the corresponding angles are equal. This is also known as the Angle-Angle (AA) criterion for similarity. The order of the letters signifies the corresponding parts of the triangles. R corresponds to V, S to S, and U to T. So, the angles R and V are congruent, as are the angles U and T. Because we have two pairs of congruent angles, we can say that the triangles are similar by the AA criterion.
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Explain how you can use a table or graph to find the slope. What does the slope
represent in the problem?
I’m a given rectangle the shorter side is 2 units less than the longer side. If we let the longer side be represented as the variable x create an expression that represents the perimeter of the rectangle.
Answer:
4(x-1)units
Step-by-step explanation:
In a given rectangle, the length of the rectangle is the shorter side while its breadth is the longer side.
Since we have 2 lengths and 2 breadths in a rectangle, the perimeter of the rectangle will be 2L+2x where
L is the length(shorter side) and x is the breadth (longer side).
According to the question, the shorter side(L) is 2 units less than the longer side(x). Mathematically,
L = x-2
Substituting L = x-2 into the formula of perimeter of a rectangle we have,
P = 2(x-2) + 2x
P = 2x-4+2x
P = 4x-4
P = 4(x-1)
The perimeter of the rectangle will be 4(x-1)units
Harry solves the equation 1/3t=15. He says the solution is 30. Is his solution correct.
Harry can first substitute (blank) for t. He can the multiply 1/3 by (blank) to get a product of (blank). Since 15 (blank) equal to (blank), Harry's solution (blank) correct
Answer:
Harry's solution is incorrect.
Harry can first substitute (30) for t. He can the multiply 1/3 by (30) to get a product of (10). Since 15 (≠) equal to (10), Harry's solution is (not) correct.
Step-by-step explanation:
Given:
Equation = [tex]\frac{1}{3}(t) =15[/tex]
Solution of the equation = [tex]30[/tex]
Lets check the equation whether both sides of the equation gives same result by plugging the values of t = 30.
⇒ [tex]\frac{1}{3}(t) = 15[/tex]
⇒ [tex]\frac{1}{3}(30) = 15[/tex]
⇒ [tex]\frac{30}{3} =15[/tex]
⇒ [tex]10=15[/tex]
We know that 10 ≠ 15 so the solution is incorrect.
According to the question :
Harry can first substitute (30) for t. He can the multiply 1/3 by (30) to get a product of (10). Since 15 (≠) equal to (10), Harry's solution is (not) correct.
Harry's solution is incorrect.
We have an upcoming test on Logorithms and my teacher forgot to go over how to solve logorithms with different bases. How would you solve them? for example,
3log[tex]_{4}[/tex] 2 +log[tex]_{5}[/tex] 512
The value of [tex]3log_{4}(2)+log_{5}(512)[/tex] is about 5.376
Step-by-step explanation:
Let us revise some rules of logarithm
[tex]log(a)^{n}=n.log(a)[/tex] [tex]log_{b}(a)=\frac{log(a)}{log(b)}[/tex]∵ The expression is [tex]3log_{4}(2)+log_{5}(512)[/tex]
- By using the 1st rule in the first term
∵ [tex]3log_{4}(2)=log_{4}(2)^{3}[/tex]
∵ 2³ = 8
∴ [tex]log_{4}(2)^{3}=log_{4}(8)[/tex]
- By using the second rule
∵ [tex]log_{4}(8)=\frac{log(8)}{log(4)}=1.5[/tex]
∵ [tex]log_{5}(512)=\frac{log(512)}{log(5)}=3.876[/tex]
- Add the two answers
∴ [tex]3log_{4}(2)+log_{5}(512)[/tex] = 1.5 + 3.876
∴ [tex]3log_{4}(2)+log_{5}(512)[/tex] = 5.376
The value of [tex]3log_{4}(2)+log_{5}(512)[/tex] is about 5.376
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