WXY is an isosceles triangle with line WX congruent to line WY. if WX is 3 more than four times x, XY is 7 less than five times x, and WY is 66 less than seven times x, find x and the measure of each side.
Answer:
x=10
Step-by-step explanation:
part 1:
4x+3=5x-7
(subtract 4x from 5x to get 1x and add 7 to 3 to get 10)
1x=10
x=10
part 2:
WX=4(10)+3=43
XY=5(10)-7=43
WY=7(10)-66=4
An isosceles triangle, have two congruent sides.
The value of x is 23The measure of each side is 95, 95 and 108From the question, we have the following highlights
[tex]\mathbf{WX = WY}[/tex]
[tex]\mathbf{WX = 3 + 4x}[/tex]
[tex]\mathbf{XY = 5x - 7}[/tex]
[tex]\mathbf{WY = 7x - 66}[/tex]
(a) Find x
We have:
[tex]\mathbf{WX = WY}[/tex]
Substitute values for WX and WY
[tex]\mathbf{3 + 4x = 7x - 66}[/tex]
Collect like terms
[tex]\mathbf{7x - 4x = 3 + 66}[/tex]
[tex]\mathbf{3x = 69}[/tex]
Divide both sides by 3
[tex]\mathbf{x = 23}[/tex]
Hence, the value of x is 23
(b) The measure of each side
Substitute 23 for x in:
[tex]\mathbf{WX = 3 + 4x}[/tex]
[tex]\mathbf{XY = 5x - 7}[/tex]
[tex]\mathbf{WY = 7x - 66}[/tex]
[tex]\mathbf{W = 3 + 4 \times 23}[/tex]
[tex]\mathbf{W = 95}[/tex]
[tex]\mathbf{XY = 5x - 7}[/tex]
[tex]\mathbf{XY = 5 \times 23 - 7}[/tex]
[tex]\mathbf{XY = 108}[/tex]
[tex]\mathbf{WY = 7x - 66}[/tex]
[tex]\mathbf{WY = 7 \times 23 - 66}[/tex]
[tex]\mathbf{WY = 95}[/tex]
Hence, the measure of each side is 95, 95 and 108
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Write (9 + 6i) − (1 + 3i) as a complex number in standard form.
Answer
8+3i
Step-by-step explanation:
(9 + 6i) − (1 + 3i)
(8+6i)-(3i)
8+3i
7 divided by something = 1204
Explain the axis of symmetry for f(x)=-2(x-4)^2+2
Identify the relative minimum point of the graph. Select all that apply.
What does it mean to be “in the black?”
Answer: c you have more credits then debts
Step-by-step explanation:
If your car travels 290 miles and uses 8.2 gallons, how many miles per gallon did you get? (round your answer to three decimal places.)
1. algebraic expression
2. coefficient
3. constant
4. expression
5. variable
A. the constant preceding the variables in a product
B. a letter or symbol used to represent an unknown
C. a mathematical expression containing one or more variables
D. a numerical value
E. a mathematical phrase that cannot be determined true or false
Answer:3. constant - D. a numerical value
2. coefficient - A. the constant preceding the variables in a product
4. expression -E. a mathematical phrase....
5. variable - B. a letter... representing an unkown
1. algebraic expression - C. a mathematical expression...
hope this helps
Step-by-step explanation:
A valid opinion poll requires random sampling which means
Simplify square root of negative 48.
a) negative 4 square root of 3
b) 4 square root of negative 3
c) 4 i square root of 3
d) 4 square root of 3 i
Answer:
C. 4 i square root of 3
Step-by-step explanation:
In a salsa recipe, the number of tomatoes added is proportional to the amount of salt added. This graph shows the relationship.
What is the unit rate for the number of tomatoes to the tsp of salt?
Answer:
The unit rate for the number of tomatoes to the tsp of salt is 3.
Step-by-step explanation:
Consider the provided graph.
The equation of the line is [tex]y=3x[/tex]
A unit rate is a rate with 1 in the denominator.
Here, the meaning of unit rate is how much tomatoes to the tsp of salt.
As we know the slope intercept form is:
[tex]y = mx + b[/tex]
Where, m is the slope of the line or rate and b is y intercept.
By the comparison we can say that the slope of the line is 3. Here, the denominator is 1.
This shows that 3 tomatoes are added for each teaspoon of salt.
Hence, the unit rate is 3.
A giraffe can run 32 miles per hour. What is this speed in feet per second? Round your answer to the nearest tent.
Speed is the rate of change of distance over time.
The speed in feet per seconds is 46.9
The speed of the giraffe is given as:
[tex]\mathbf{Speed = 32 miles/hour}[/tex]
Start by converting miles to feet
To do this, we multiply 32 by 5280.
So, we have:
[tex]\mathbf{Speed = 32 \times 5280feet/hour}[/tex]
[tex]\mathbf{Speed = 168960feet/hour}[/tex]
Next, convert hour to seconds
To do this, we divide by 36000.
So, we have:
[tex]\mathbf{Speed = \frac{168960}{3600} feet/seconds}[/tex]
[tex]\mathbf{Speed = 46.9 feet/seconds}[/tex]
Hence, the speed in feet per seconds is 46.9
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25 POINTS PLS HURRY!!!
How does the graph of g(x)=0.25⌊x⌋ differ from the graph of f(x)=⌊x⌋?
Multiplying by 0.25 shifts the graph of g(x)=0.25⌊x⌋ up 0.25 unit.
Multiplying by 0.25 shifts the graph of g(x)=0.25⌊x⌋ right 0.25 unit.
Multiplying by 0.25 shifts the graph of g(x)=0.25⌊x⌋ down 0.25 unit.
Multiplying by 0.25 compresses the graph of g(x)=0.25⌊x⌋ vertically by a factor of 0.25.
Answer:
The answer is d
Step-by-step explanation:
the sum of three consecutive integers is 105 which equation could you use to find the three integers?
Equation: n + (n +1) + (n+2) = 105
solution:
n + (n +1) + (n+2) = 105
3n +3 = 105
3n = 102
n = 102/3
n = 34
34 +1 = 35
34+2 = 36
34 +35 +36 = 105
Find the value of ‘x' and the length of segment ab. if b is between a and c, and ab = 3x – 3 and bc = 4x + 8, and ac = 75, then find the value of ‘x' and ab. answer
To solve for 'x' and the length of segment AB, we use the equation AB + BC = AC, which simplifies to (3x - 3) + (4x + 8) = 75, revealing that 'x' = 10 and the length of AB is 27 units.
Explanation:The question requires us to find the value of 'x' and the length of segment AB given that B is between A and C, with AB = 3x – 3, BC = 4x + 8, and the total length AC = 75. To solve this, we set up an equation using the given lengths of segments AB and BC to equal the total length AC. This gives us the equation AB + BC = AC, which simplifies to (3x – 3) + (4x + 8) = 75.
First, we simplify the equation: 3x + 4x – 3 + 8 = 75, which reduces to 7x + 5 = 75. Subtracting 5 from both sides gives us 7x = 70. Dividing both sides by 7, we find that x = 10. With the value of x, we can find AB by substituting x back into its equation: AB = 3(10) – 3 = 30 – 3 = 27.
Therefore, the value of 'x' is 10 and the length of segment AB is 27 units.
PLS HELP!!!
A copy center offers its customers two different pricing plans for black and white photocopies of 8.5 in. by 11 in. pages. Customers can either pay $0.08 per page or pay $7.50 for a discount card that lowers the cost to $0.05 per page. Write and solve an equation to find the number of photocopies for which the cost of each plan is the same.
.08c = .05c + 7.50; c = 250
.05c = .08c + 7.50; c = 22.5
.08c = .05c – 7.50; c = 250
7.50 = .08c + .05c; c = 58
Answer:
.08c=.05c-7.50; c=250
Step-by-step explanation:
What is the lowest common multiple of (3^2 x 8^4) and (3^3 and 8^3) ?
Help me and how to do this??
A=11+4b-4c. Solve for C.
Answee Choices:
A. C=a-4b-11/-4
B. C=a+b-11/-4
C. C=a+4b+11/-4
D. C=a-b+11/-4
Can someone please explain this with steps? I don't understand this problem. Thanks!
Two expressions with equal sign is equation. C=a-4b-11/-4 is the solution for c when given equation is A=11+4b-4c. Option A is correct.
What is equation?Two expressions with equal sign is called as equation.
Given equation,
a= 11 + 4b - 4c
We need to separate c from equation,
-4c = a - 11 - 4b
Divide both sides by -4
c=(a-11-4b)/-4
Therefore option A is correct for equation A=11+4b-4c.
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What are the slope and the y-intercept of the linear function that is represented by the equation y=9x-2?
1.)The slope is –2, and the y-intercept is 9.
2.)The slope is 2, and they y-intercept is 9.
3.)The slope is 9, and the y-intercept is –2.
4.)The slope is 9, and the y-intercept is 2.
Answer with explanation:
The equation of line in slope intercept form is :
y= m x +c
Where,m =Slope
c=Y intercept =Distance between origin and point where the line cuts the Y axis
The equation of line is
y= 9 x-2
Comparing with the above equation of line in slope intercept form
Slope =9
Y intercept =2
Option 4
The slope is 9, and the y-intercept is 2.
Decide which of the two points lies on the graph of the line
X= -3
A. 2,-3
B. -3,2
Jonathon created a graph that shows the number of exercises he completes in his workout routine
Which statement summarizes his exercise routine?Jonathon does 3 crunches for every 2 push-ups.Jonathon does 2 push-ups for every 3 crunches.Jonathon does 2 push-ups for every 15 crunches.Jonathon does 15 push-ups for every 2 crunches.
Answer: Hello mate!
in the graph you can see that:
Jonathon does 2 pushups when he does 15 crunches.
then he does 4 = ( 2+ 2) pushups when he does 30 = (15 + 15) crunches
this means that he does 2 pushups more than before, and 15 crunches more than before.
and 6= (2 + 2 +2) pushups when he does 35 =(15 + 15 + 15) crunches.
this, again, means that he does 2 pushups more than before, and 15 crunches more than before.
then you can see that he does 2 pushups for every 15 crunches.
What is the value of 5^3? A.125 B.25 C.15 D.8
Which set represents a pythagorean triple (1 point)?
Write the next three terms and write a rule to describe the number pattern. 0.57, 0.66, 0.75, 0.84, . . .
The next three terms in the number pattern 0.57, 0.66, 0.75, 0.84 are 0.93, 1.02, and 1.11. The rule for the pattern is that each term increases by 0.09 from the previous term.
Explanation:The given sequence is: 0.57, 0.66, 0.75, 0.84, ... The step or difference between each consecutive term is 0.09. Therefore, the next three numbers in the sequence would be: 0.84 + 0.09 = 0.93, 0.93 + 0.09 = 1.02, 1.02 + 0.09 = 1.11. So the answer is 0.93, 1.02, 1.11.
The generalized rule for this series is that each term increases by 0.09 from the previous term. In mathematical terms, if we denote the nth term as Tn, then Tn+1 = Tn + 0.09. This rule tells us that the number pattern involves adding 0.09 for each subsequent term in the sequence.
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2/3 x 5/7 =? A. 7/10 B. 14/15 C. 10/21 D. 7/21
HELP ME
2/3 * 5/7 =
multiply the 2 top numbers and then the 2 bottom numbers
2*5 =10
3*7 = 21
so you get 10/21
answer is C
Factor -8x^3-2x^2-12x-12x-3
How do you find the quadratic equation of a parabola with the vertex and x intercept?
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 648 feet of fencing is used. find the dimensions of the playground that maximize the total enclosed area.
Find x if:
64x^3=a^6
The answer will be (a/2) to the power of 2.
What is the relationship between the sine and cosine of complementary angles in a right triangle? Please give an example to support your answer.
Final answer:
The sine and cosine of complementary angles in a right triangle are equal to each other but reversed, because the opposite side for one angle is the adjacent side for the other, relative to the hypotenuse.
Explanation:
The relationship between the sine and cosine of complementary angles in a right triangle is that they are equal to each other but reversed. If one angle is x and its complementary angle is 90° - x (because complementary angles add up to 90°), then the sine of x is equal to the cosine of its complementary angle, and vice versa.
This is because, in a right triangle, the side that is the opposite side for one angle becomes the adjacent side for the complementary angle, relative to the hypotenuse which remains the same for both angles.
For example, in a right triangle with one acute angle of 30°, its complementary angle is 60°. The sine of 30° is 1/2, and the cosine of 60° is also 1/2. Similarly, the cosine of 30° is [tex]\sqrt{3/2[/tex], and the sine of 60° is [tex]\sqrt{3/2[/tex] shows a complementary relationship.