Answer:
X=3
Y=1
Step-by-step explanation:
In solving simultaneous equations, there are three methods, we have the elimination method, substitution method or graphical method. But for the purpose of this question, we would be using Elimination method.
5y-4x =-7 Equation 1
2y+4x=14 Equation 2
Since x has the same coefficient, it's easy to eliminate by adding up the two equations
5y+2y=7y
-4x+(+4x)=0
-7+(+14)=7
We have 7y=7
Divide both sides by 7,
y=7/7
y=1
Substituting for y in equation 2.
2(1)+4x=14
2+4x=14
4x=14-2
4x=12
x=12/4
x= 3
Which equation has real zeros corresponding to
the x-intercepts of the graph?
y = log3(x) – 1
y = 3x - 3
y=-3(x - 1) + 3
y = log3(2x) - 2
Answer:
A
Step-by-step explanation:
y = log3(x) – 1
I don't know why but this is the correct answer.
[tex]y = \log_{3}x - 1[/tex] is the equation with real zeros corresponding to the x-intercepts of the graph.
How to find a function based on a graphAccording to the statement, we must find a function such that all values of [tex]x[/tex] so that [tex]y(x) = 0[/tex] and are the same of the graph. A quick approach consists in solving on each expression:
Expression A
[tex]\log_{3}x-1 = 0[/tex]
[tex]\log_{3}x = 1[/tex]
[tex]x = 3[/tex]
Expression B
[tex]3\cdot x - 3 = 0[/tex]
[tex]3\cdot x = 3[/tex]
[tex]x = 1[/tex]
Expression C[tex]-3\cdot (x-1) + 3 = 0[/tex]
[tex]-3\cdot x +6 = 0[/tex]
[tex]x = 2[/tex]
Expression D[tex]\log_{3}2x - 2 = 0[/tex]
[tex]\log_{3}2x = 2[/tex]
[tex]2\cdot x = 9[/tex]
[tex]x = \frac{9}{2}[/tex]
Hence, we conclude that [tex]y = \log_{3}x - 1[/tex] is the equation with real zeros corresponding to the x-intercepts of the graph. [tex]\blacksquare[/tex]
Remarks
The graph is missing and all functions are poorly formatted. Correct statement is shown below:
Which equation has real zeros corresponding to the x-intercepts of the graph?
A. [tex]y = \log_{3} x - 1[/tex]
B. [tex]y = 3\cdot x -3[/tex]
C. [tex]y = -3\cdot (x-1) + 3[/tex]
D. [tex]y = \log_{3}2x -2[/tex]
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Use the equation to answer the question.
12a+9b=k(2a+32b)
Which value of k makes the equation true?
a.6
b.2
c.4
d.3
To find the value of k that makes the equation true, we can start by expanding both sides of the equation. Then, rearrange the equation to isolate the terms with a on one side and the terms with b on the other side. Finally, solve for k to find the value that makes the equation true.
Explanation:To find the value of k that makes the equation true, we can start by expanding both sides of the equation:
12a + 9b = k(2a + 32b)
12a + 9b = 2ka + 32kb
Next, we can rearrange the equation to isolate the terms with a on one side and the terms with b on the other side:
12a - 2ka = 32kb - 9b
This simplifies to:
(12 - 2k)a = (32k - 9)b
To make this equation true, the coefficient of a must be equal to the coefficient of b. Therefore, we can set up an equation:
12 - 2k = 32k - 9
Solving for k:
12 + 9 = 32k + 2k
21 = 34k
k = 21/34
Therefore, the value of k that makes the equation true is 21/34.
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Find the area of the circle with the center C (1, -2) and passes through the point (4, 2). Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
r=√((4-1)²+(2+2)²)=√(9+16)=5
area of circle=π r²=3.14×5²=78.50=78.5
The area of the circle is found by calculating the radius using the distance formula and then applying the formula A = πr². Using the common approximation of π as 3.14, the area is found to be approximately 78.5 square units when rounded to the nearest tenth.
The first step in finding the area of the circle is to determine its radius. The radius can be found by calculating the distance between the center of the circle, C (1, -2), and a point on the circle, (4, 2). Using the distance formula, we get the radius r = √((4-1)² + (2-(-2))²)} = √{(3)² + (4)²} = √{9 + 16} = √{25} = 5 units. Next, we use the formula for the area of a circle, which is A = πr². Substituting the radius in, we find A = π(5)² = 25π. The approximation on the circle for π is 3.14, thus the area of the circle is approximately A = 25 * 3.14 = 78.5 square units, which should be rounded to the nearest tenth.
It is also noteworthy that any approximation on the circle may vary slightly depending on the value chosen for π, but using 3.14 is commonly accepted for most calculations. So our final answer is, rounding to the nearest tenth, the area of the circle is approximately 78.5 square units.
Write the sentence as an equation.
19 increased by d is 234
Answer:
19+d=234
Step-by-step explanation:
"increased by d" is addition. "is" is equal. So Putting these together it would be 19+d=234.
Hope this helped!
3 4/6 - 2 1/4 please help me
Answer:1 5/12
Step-by-step explanation:
3 4/6 - 2 1/4
Change to improper fraction we have
22/6 - 9/4
(2x22-3x9)/12
(44-27)/12
17/12=1 5/12
Answer:
1 5/12
Step-by-step explanation:
3 4/6 - 2 1/4
3 2/3 - 2 1/4
11/3 - 9/4
Lcm is 12
(11×4 - 9×3)/12
(44 - 27)/12
17/12
1 5/12
A polynomial function can be written as (x - 2)(x - 3)(x + 5). What are the x-intercepts of the
graph of this function?
a. (2,0), (3, 0), (-5,0)
b. (-2,0), (-3,0), (5,0)
c. (2,0), (3, 0), (5,0)
d. (-2, 0), (-3,0), (-5,0)
Answer:
a) : (2,0), (3,0), (-5,0)
Step-by-step explanation:
(x - 2)(x - 3)(x + 5)=0 (y=0)
x-2=0, x-3=0, x+5=0
x=2, x=3, x=-5
x-intercepts: (2,0), (3,0), (-5,0)
What does 5.9E4 mean?
Answer:
59,000
Step-by-step explanation:
That is scientific notation, as used in a calculator, for example, to mean
5.9 * 10^4
5.9 * 10^4 = 5.9 * 10,000 = 59,000
solve 4(3)+5(6+1) wut is dis
Answer: 47
Step-by-step explanation:
Answer:
47 is the answer
Step-by-step explanation:
When a function goes through the origin how can I find the slope
Answer:
m= y/x
Step-by-step explanation:
The equation to find the slope (m) is to determine 2 points then divide the difference of y-coordinates with the x-coordinates.
The equation will look like this:
m= (y2-y1)/(x2-x1)
When a function goes through the origin(0, 0), that means the line doesn't have c variable, the equation of the line will be as simple as y=mx
Then the equation to find the slope(m) will be:
y=mx
m=y/x
You can directly divide y-coordinate with x-coordinate to find the slope.
Finding Side Lengths
2 in.
xin.
These two figures are the image and pre-image of a
dilation
Find the lengths of the missing sides.
4 in.
5 in.
Answer:
x = 2.5y = 5Step-by-step explanation:
As the two figure are the image and pre-image of a dilation.
Considering the left sided triangle is original and right sided triangle ( smaller one) is the image.
As one of the sides of the left triangle (original figure) is 4 in. And the corresponding length of the side on the right triangle (image of the figure) is 2 in.
It means the image of the side (2 in) is obtained when the side (4 in) of the original object is dilated by a scale factor of 1/2. In other words, the side of the image (2 in) is obtained multiplying the side (4 in) of original figure by 1/2. i.e. 4/2 = 2 in
Lets determine the missing side of the right side triangle by the same rule.
As the original object has one of the sides is 5 in and the corresponding side of the image has x in. As the original figure is dilated by a scale factor of 1/2. so the missing side of x will be: x = 5/2 = 2.5
So, the value of x will be 2.5
Similarly, the original object has one of the sides with length (y + 1 in). As the As the original figure is dilated by a scale factor of 1/2. As the corresponding length of the side of the image triangle is 3 in.
so
y + 1 = 2(3) ∵ 3 in (image side) is multiplied by 2
y + 1 = 6
y = 6 - 1
y = 5
So, the value of y = 5
Therefore,
x = 2.5y = 5Answer:5.5
6
Step-by-step explanation:
what is the perimeter?
Answer:
18 yards
Step-by-step explanation:
6+5+3+4= 18
25 points plz help!!! Calculate the equation of the line through the points (-1, 1), (4, 0), and (24, -4)
The equation of the line is y=-1/5x+4/5.
Calculating m, the slope we subtract two of the points,
(-1, 1)
(4, 0)
This equals 0-1/4+1, which simplifies to -1/5
The slope is -1/5 and we can put that into the slope-intercept form along with a point to get b, the y-intercept.
So, y=-1/5x+b
Substituting x and y with a point.
1=-1/5(-1)+b
1=1/5+b
b=4/5
So, the equation is y=-1/5x+4/5.
What is the Equation of a Line?The equation of a line is a single illustration of numerous points on the line. the general form of the equation of a line is of the form ax + via + c = zero and any factor on the road satisfies this equation. these two minimal requirements to shape the equation of a line are the slope of the road and a factor on the line.
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joyce has between 25 to 75 coloured beads. when she makes them into groups of 9, 8 beads are left out. when she groups into groups of 8, 6 beads are left out,how many beads are left
Answer:
Joyce has total 62 colored beads.
Step-by-step explanation:
For making groups of 9, let the number of beads be x.
total beads = 9x + 8
For making groups of 8, let the number of beads be y.
total beads = 8y + 6
As the total number of beads in both cases are same so,
9x + 8= 8y + 6
or, 9x-8y = -2
Now lets check the values through hit and trial;
First check; x=6, y=7
9*6 - 8*7 = -2
or, 54- 56 = -2
or, -2 =-2
This satisfies our equation.
Hence; Total beads = 9*6 + 8 = 62
The total number of beads joyce had is 62.
Number of beads she have is 62 .
Step-by-step explanation:
Here we have , joyce has between 25 to 75 colored beads. when she makes them into groups of 9, 8 beads are left out. when she groups into groups of 8, We need to find how many beads are left . Let's solve this:
when she makes them into groups of 9, 8 beads are left out equation is
[tex]9x+8[/tex]
when she groups into groups of 8 , 6 beads are left out, equation is
[tex]8y+6[/tex]
Equating both equation's we get:
⇒ [tex]9x+8 = 8y+6[/tex]
⇒ [tex]9x-8y = -2[/tex]
By hit & trial method , we put x = 6 & y=7:
⇒ [tex]9(6)-8(7) = -2[/tex]
⇒ [tex]54-56= -2[/tex]
⇒ [tex]-2= -2[/tex]
Since , LHS = RHS x = 6 & y=7 satisfies the equation [tex]9x+8 = 8y+6[/tex] . So putting value of x=6 in [tex]9x+8[/tex] we get:
⇒ [tex]9x+8[/tex]
⇒ [tex]54+8[/tex]
⇒ [tex]62[/tex]
Therefore, Number of beads she have is 62 .
Find the measure of < B
The measure of angle b is 25°.
Solution:
Given data:
The "L" shape angle is a right angle.
Right angle is splitted by another line and two angles are formed.
One angle is 65° and the other angle is b.
Let us find the other angle b.
65° + m∠b = 90°
Subtract 65° from both sides of the equation.
m∠b = 90° – 65°
m∠b = 25°
Hence the measure of angle b is 25°.
If you dissolve 10 grams of sugar in 30 grams of water you will make __ grams of __% sugar syrup
Answer:
25%
Step-by-step explanation:
Sugar Syrup = 40 grams
10 grams / 40 grams = 1/4
1/4 = 25%
Answer:
40 grams of 25% sugar syrup
Step-by-step explanation:
A block of clay weighing 5 pounds is divided into 9 equal pieces.How muck does each piece way
Answer:
5/9 pounds or rounded 0.5555... pounds
Step-by-step explanation:
Step 1: Make an equation
5 / 9 = x
Step 2: Solve
5 / 9 = x
5/9 pounds or rounded 0.5555... pounds
Answer: 5/9 pounds or rounded 0.5555... pounds
Answer:
5/9 of a pound
Step-by-step explanation:
5 pounds of clay is divided into 9 equal pieces
5 ÷ 9
This can be written as a fraction
5/9
Each block weighs 5/9 of a pound
Hope this helps :)
g(x) = 4x2 – 3x + 7
Find g(3)
Answer:
g(3)=34
Step-by-step explanation:
Just plug in 3 for x:
4(3)^2-3(3)+7
4(9)-9+7
36-9+7
27+7
34
So g(3)=34
At a baseball game, a vendor sold a combined total of 232
sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Answer:
Step-by-step explanation:
sodas ----x
hot dogs ---- y
x = 2y
x+y = 192
2y + y = 192
3y=192
y = 64
64 hotdogs and 128 sodas
A mug is 2/3 full. The mug contains 5/6 of a cup of water. Find the capacity of the mug.
We want to find the total capacity of the mug given that we know how much liquid there is in a 2/3 full mug.
We will find that the capacity of the mug is 1.25 cups.
We know that when the mug is 2/3 full, it has 5/6 cups.
Then if we define C as the total capacity of the mug, we can write:
(2/3)*C = 5/6 cups.
Now we can solve the above equation for C:
C = (3/2)*(5/6) cups = 1.25 cups.
The capacity of the mug is 1.25 cups.
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The value of 3over2 + 3over3 = ___.
Answer:
15/6 or 2.5
Step-by-step explanation:
Step 1: Convert words into an expression
The value of 3over2 + 3over3 = ___.
3/2 + 3/3 = ?
Step 2: Make common denominators
3/2 * 3/3 = 9/6
3/3 * 2/2 = 6/6
Step 3: Add
9/6 + 6/6
15/6
Answer: 15/6 or 2.5
6. On day 1 of a bake sale, the group sold 125 chocolate chip cookies and 75 oatmeal cookies. They also received donations that
totaled $46. They raised $196 on day 1. Both types of cookies were sold for the same price. Write and solve an equation to find
how much they charged for each cookie.
Answer:$1.33
Step-by-step explanation: What I did is I subtracted the 46 dollars in donations from the total they raised on day 1 to get the amount for just the cookies $150. Then I added the amount of the 2 total of cookies sold = 200. Then, I took the amount of cookies sold and divided it by the amount they made selling the cookies = 1.33. 200 ÷ 150 = 1.33
I hope this helps
Solve for x
3.5x=24.5
Answer:
8.166666666666666666666666666666666666666666
Step-by-step explanation:
Question 1
Graph the line that passes through the two points.
(−
3
2
,−
3
2
), (
3
2
,
3
2
)
Answer:
The equation of the line is y=1x and I will show you a picture of a graph with your points and a line of that equation.
Step-by-step explanation:
Of 140 seventh graders, 15% earn the presidential fitness award. How many students earn the award?
Answer:
119
Step-by-step explanation:
Hope this helps! Brainliest is appreciated.
George is playing cards what is probability of pulling an ace or Jack from the deck
Answer: 4/52 or 1/13 (simplified)
Step-by-step explanation: There are 52 cards in a deck and 4 aces
Answer:
1/13
Step-by-step explanation:
There are 13 types of cards in a deck and there are 4 cards in each. So if you wanted to pull a ace or jack from the deck it would be 1/13
=
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If the measure of one exterior angle of a regular polygon is 40 degrees, how many sides does the polygon have?
Answer:
The polygon has 9 sides
Step-by-step explanation:
we know that
A regular polygon has equal length sides and equal interior angles
step 1
Find the measure of the interior angle
Remember that
The interior angle plus the exterior angle must be equal to 180 degrees (form a linear pair)
Let
x ----> the measure of each interior angle in the regular polygon
so
[tex]x+40^o=180^o[/tex]
solve for x
[tex]x=180^o-40^o=140^o[/tex]
step 2
Find the number of sides of the regular polygon
we know that
The measure of each interior angle in a regular polygon is given by the formula
[tex]x=\frac{(n-2)180^o}{n}[/tex]
where
n is the number of sides of the polygon
substitute the given values
[tex]140^o=\frac{(n-2)180^o}{n}[/tex]
solve for n
[tex]140n=180n-360\\180n-140n=360\\40n=360\\n=9\ sides[/tex]
therefore
The polygon has 9 sides
A factory that is working at 90% capacity is shipping 450 cars per week. If the factory works 100% capacity, how many cars can it ship per week
Answer:
500
Step-by-step explanation:
450/90 × x/100
how to solve x
100÷90=1.11111111111
1.11111111111×450
find the mean:
23,91,83,31,49,11,60,92
Answer:
55
Step-by-step explanation:
For the mean you add together all of the values, and then divide the sum by the number of digits there are.
23+91+83+31+49+11+60+92 = 440
440/8 = 55
23 + 91 + 83 + 31 + 49 + 11 + 60 + 92 = 440/8 = 55
Mean: 55.
Find the discrimanant and the number of real roots for this equation 9x^2+12x+4=0
For this case we have that by definition, the discriminant of a quadratic equation [tex]ax ^ 2 + bx + c = 0[/tex], is given by:
[tex]d = b ^ 2-4 (a) (c)[/tex]
[tex]d> 0[/tex]: Two different real roots
[tex]d = 0[/tex]: Two equal real roots
[tex]d <0[/tex]: Two different complex roots
If we have [tex]9x ^ 2 + 12x + 4 = 0[/tex], then:
[tex]a = 9\\b = 12\\c = 4[/tex]
Substituting the values:
[tex]d = 12 ^ 2-4 (9) (4)\\d = 144-144\\d = 0[/tex]
Thus, we have two equal real roots.
ANswer:
We have two equal real roots.
The hypotenuse of a 30°-60°-90°
triangle has a length of 12 cm.
Which could be the length of a leg
of the triangle?
Answer: Below
Step-by-step explanation:
If you don't know Trigonometry, in a 30-60-90 triangle, the hypotenuse is always twice as long as the side opposite the 30° angle and the side opposite the 60° angle is √3 times as long as the side opposite the 30° angle.
So, since the hypotenuse has length 12 cm,
side opposite 30° angle (shorter leg) = 6 cm
side opposite 60° angle (longer leg) = 6√3 cm
The possible lengths of the legs are 6 and 6√3
How to determine the length of a leg?The triangle is given as:
30-60-90 triangle
And we have:
Hypotenuse = 12 cm
A 30-60-90 triangle is a unique triangle with the following parameters
Opposite = Hypotenuse/2
Adjacent = Hypotenuse/2 * √3
So, we have:
Opposite = 12/2
Adjacent = 12/2 * √3
Opposite = 6
Adjacent = 6√3
Hence, the possible lengths of the legs are 6 and 6√3
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