The simplified product is 7x² + 28x.
Option B is the correct answer.
We have,
To simplify the product 7 x (x + 4), we need to distribute the 7x to both terms inside the parentheses.
The distributive property states that for any numbers a, b, and c,
a x (b + c) = a x b + a x c.
Applying this property to the given expression, we have:
(7x) x (x) + (7x) x 4
Multiplying 7x by x gives us 7x², and multiplying 7x by 4 gives us 28x.
So the simplified expression becomes:
7x² + 28x
Therefore,
The simplified product is 7x² + 28x.
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In the figure, TU is tangent to the circle at point U. Use the figure to answer the questions.
(a) Describe the relationship among the lengths of the segments formed by the secant, RT, and the tangent segment, TU. You may use words and/or an equation.
(b) Suppose RT = 9 in. and ST = 4 in. Is it possible to find the length of TU? If so, show how to find the length. If not, explain why not.
Both the parts of this question require the use of the "Intersecting Secant-Tangent Theorem".
Part A
The definition of the Intersecting Secant-Tangent Theorem is:
"If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment."
This, when applied to our case becomes, "The length of the secant RT, times its external segment, ST, equals the square of the tangent segment TU".
Mathematically, it can be written as:
[tex] RT\times ST=(TU)^2 [/tex]
Part B
It is given that RT = 9 in. and ST = 4 in. Thus, it is definitely possible to find the value of the length TU and it can be found using the Intersecting Secant-Tangent Theorem as:
[tex] RT\times ST=(TU)^2 [/tex]
Thus, [tex] (TU)^2=9\times 4=36 [/tex]
[tex] \therefore TU=\sqrt{36}=6 [/tex]
Thus the length of TU=6 inches
The graphs below have the same shape. What is the equation of the blue
Answer: The correct option is B.
Explanation:
From the given figure it is noticed that the parent function is,
[tex]f(x)=x^2[/tex]
The graph of f(x) shifts 5 units right.
The transformation is defined as,
[tex]g(x)=f(x+a)+b[/tex]
Where, a shows the horizontal shifts and b shows the vertical shift.
If a<0 then the graph of f(x) shifts right side by a units and if a>0 then the graph of f(x) shifts left side by a units.
If b<0 then the graph of f(x) shifts downward by b units and if b>0 then the graph of f(x) shifts upward by b units.
Since the graph of parent function is shifts only right side by 5 units, therefore
[tex]g(x)=f(x-5)+0[/tex]
Since [tex]f(x)=x^2[/tex]
[tex]g(x)=(x+5)^2[/tex]
Thus, the correct option is B.
The function in option A represents the left shift of f(x) by 5 units. The option C represents the downward shift of f(x) by 5 units. The option D represents the upward shift of f(x) by 5 units.
prove that an isosceles trapezium is always cyclic
helppppppppppppppppppp
A street promotion worker gets paid $0.10 for each flyer he hands out. His goal is to make $15 an hour. How many flyers must he hand out each hour?
A. 45
B. 1500
C. 150
D. 15
The street promotion worker must hand out 150 flyers each hour to make $15.
Explanation:To determine how many flyers the street promotion worker must hand out each hour to make $15, we need to use the equation:
Number of flyers × Payment per flyer = Total payment
Since the worker wants to make $15 an hour, the equation becomes:
Number of flyers × $0.10 = $15
To solve for the number of flyers, we divide both sides of the equation by $0.10:
Number of flyers = $15 ÷ $0.10
Number of flyers = 150
Therefore, the street promotion worker must hand out 150 flyers each hour to make $15.
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the sum of 5 consecutive odd number is 145
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
Answer:
C
Step-by-step explanation:
The very first term would result in 2 having an exponent in 0 making the equation -3 * 1 which is just -3 and C is the only option.
To further prove this -3 * 2^3 is -24. n is the term that you are looking for. So finding the fourth term would mean you would take 4-1 which is 3 thus making the exponent 3.
Which sequence of transformations creates a similar, but not congruent, triangle? ((will medal for correct answer))
Dilation and rotation
Rotation and translation
Reflection and rotation
Translation and reflection,
Help please what is the sum?
Please help thank you.
PLEASE HELP! BRAINIEST GETS 50 POINTS!
14. The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows: y = 4 + 2x. What does the y-intercept of this function represent?
A) The original height of the plant was 4 mm.
B) The original height of the plant was 2 mm.
C) The height of the plant increases by 2 mm for every hour of sunlight it receives.
D) The height of the plant increases by 4 mm for every hour of sunlight it receives.
16. The table below shows the values of y for different values of x:
x 7 8 9 10 11 12 13
y 3 5 7 9 10 13 14
The correlation coefficient for the data is 0.9976. Which statement is true about the data in the table?
A) There is a strong positive relationship between x and y.
B) There is a strong negative relationship between x and y.
C) There is a weak positive relationship between x and y.
D) There is a weak negative relationship between x and y.
10. Two groups of students were asked how far they lived from their school. The table below shows the distances in miles:
Group A (distance in miles) 1 1.5 3 3.2 2.8 1.5 1.8 2.5 2.2
Group B (distance in miles) 2 2.5 3.2 3 1.8 2.4 3 1.5 1.8
Which statement best compares the mean distances for the two groups?
A) It is equal for Group A and Group B.
B) It is greater for Group B than Group A.
C) Its value for Group A is double its value for Group B.
D) Its value for Group B is double its value for Group A
DONT ANSWER IF YOU'RE NOT 100% CERTAIN...I NEED TO PASS
Answer:
Ok so the first one, your answer will be C. The height of the plant increases by 2 mm for every hour of sunlight it receives. For the second one, It is B.There is a strong negative relationship between x and y. And the last one is B. It is greater for Group B than Group A.
Step-by-step explanation: Hopes this helps!!! :)
At the end of the first round in a quiz show, Jeremy has at most negative 20 points. Write an inequality that means “at most negative 20.”
The sin 215° is ____
●A positive value
●0
●A negative value
The sin 215 degrees is a positive value. (Soh Cah Toa - Sin Cos Tan)
Answer: A positive value
believe; live
Consider the two triangles shown.
If f(x) = 1 + 5x, and g(x) = x3, find (f∘g)(x)
A.
1 + 5x3
B.
1 – 3x3
C.
1 + 8x
D.
5x3
Class 10R sat a test. The mean mark of the class was 70%. There are 30 students in class 10R, 20 of whom are boys. The mean mark for the boys in the test was 62%.Work out the mean mark for the girls.
86%
70X30=2100
20X62=1240
2100-1240 = 860
860/10=86
Answer:
Mean mark for the girls is [tex]86%[/tex].
Step-by-step explanation:
Given information:
Number of total students in the class=[tex]30[/tex]
Number of boys in the class=[tex]20[/tex]
Then, number of girls will be=[tex]30-20[/tex]=[tex]10[/tex]
The mean mark of the class=[tex]70\times30=2100[/tex]
The mean mark for the boys is [tex]62[/tex]
Then, mark for the boys[tex]=62\times20=1240[/tex]
The mark for the girls=[tex]2100-1240=860[/tex]
Then mean mark of the girls will be [tex]\frac{860}{10}=86[/tex]
Hence, mean mark for the girls is [tex]86%[/tex].
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Let f(x)=25x2−2 .
The function g(x) is a vertical stretch of f(x) by a factor of 2.
What is the equation of g(x)?
Enter your answer in the box.
g(x) =
We are given function f(x) = 25x^2 -2.
g(x) is a vertical stretch of f(x) by a factor of 2.
We know, the transformation rule
y= k f(x), vertical stretch by a factor k. For k>0.
Because function f(x) is being vertical stretched by a factor of 2. So, we need to multiply f(x) function by 2.
Therefore, g(x) = 2 f(x) = 2*(25x^2-2).
Therefore, g(x) = 2*(25x^2-2) or g(x) = 50x^2-4.
Answer:
The Given function is
f(x)= 25 x² -2
Now, a function g(x) is obtained when the function f(x) is stretched by a factor of 2.
Consider point (x,y) on f(x).When function is stretched vertically by a factor of 2 ,it means, the coordinate changes from (x,y) to (x,2 y).
Since we have to stretch the function as whole, we will multiply original function by 2.
So, g(x)= 2× [25 x² - 2] =50 x² -4
g(x)=50 x²- 4
Which absolute value function has a graph that is wider than the parent function when graphed represents the parent function f(x)=|x| reflected over the x-axis and translated 1 unit to the right
A. F(x) = -|x|+1
B. F(x) = -|x-1|
C. F(x) =|-x|+1
D. F(x) =|-x-1|
Answer:
B.[tex]F(x)=-\mid{x-1}\mid[/tex]
Step-by-step explanation:
We are given that a function
[tex]f(x)=\mid x\mid[/tex]
We have to find absolute value of function when parent function reflected over the x- axis and translated 1 unit to the right.
The transformation rule when the point (x,y) is reflected over x- axis is given by
[tex](x,y)\rightarrow (x,-y)[/tex]
Apply the reflection on function over x- axis then, we get
[tex]g(x)=-\mid x\mid[/tex]
Transformation rule when the point (x,y) is shifted a units towards right is given by
[tex](x,y)\rightarrow (x-a,y)[/tex]
When the graph is translated 1 units towards right then , obtained function is given by
[tex]F(x)=-\mid{x-1}\mid[/tex]
Jade buys a blouse and a skirt for 34 of their original price. Jade pays a total of $31.50 for the two items. If the original price of the blouse is $18, what is the original price of the skirt? Enter your answer in the box.
Answer:
The original price of the skirt is $24
Step-by-step explanation:
The question must be 3/4 of their original price. So, I will solve this using 3/4 as 34 is unclear and does not suit the question.
Lets assume that the price of the blouse be = x
Lets say the price of the skirt is = y
Now, given is that 3/4 of the price together for both items is $31.5 0
This means,
[tex]\frac{3}{4}(x+y)=31.50[/tex] ..... (1)
The original price of the blouse is $18 so, x= 18 .............(2)
Putting x=18 in equation (1)
[tex]\frac{3}{4}(18+y)=31.50[/tex]
[tex]3(18+y)=31.50*4[/tex]
[tex]3y+54=126[/tex]
[tex]3y=72[/tex]
y=24
Hence, the original price of the skirt is = $24.
Check:
Original price of both items = [tex]18+24=42[/tex]
And 3/4 of 42 is [tex]\frac{3}{4}*42= 31.50[/tex]
So, the correct answer is $24.
Please help, what effect does doubling the radius of a cone's base have on the cone's volume? Thank you! :),
It has 3 more vertices than a triangle
Wendy enjoys listening to hip hop and downloads music regularly from the internet. She already has four hours of hip hop in her collection. From the second month onward, the number of hours of hip hop music she downloads each month is nine percent greater than the number of hours of hip hop music she had downloaded the previous month. Which function best shows the total number of hours of hip hop music Wendy has in her collection f(x) after x months? f(x) = (1.09)x + 3 f(x) = 3(1.09)x f(x) = (1.09)x + 2 f(x) = (1.09)x - 2
The second step in the process for factoring the trinomial x^2-3x-40 is to
Answer:
Second step x( x +5 ) -8 (x+ 5 ) in process of factoring .
Step-by-step explanation:
Given : Trinomial x²-3x-40 .
To find : The second step in the process for factoring .
Solution : We have x²-3x-40 .
On factoring x²+ 5x - 8x - 40 .
Taking common x from first two terms and -8 from last two terms.
x( x +5 ) -8 (x+ 5 ) .
Therefore , Second step x( x +5 ) -8 (x+ 5 ) in process of factoring .
Miguel had 63 lemons to make lemonade at his stand. He used some lemons to make lemonade. Now he has 25 lemons. How many lemons did Miguel use?
Miguel used ___lemons to make lemonade.
Answer: He used 38 lemonsssssssssssss
Step-by-step explanation:
What is the approximate value of the function at x = 0?
a) -3
b) -4
c) -5
d) -4.5
Johanna’s parents give her $10 per week for lunch money. She cannot decide whether she wants to buy or pack her lunch. If a hot lunch at school cost $2, write and solve an inequality to finding the maximum number of times per week Johanna can buy her lunch
Rectangle M was dilated to form rectangle M’. What ratio is the scale factor?
1/2
2/3
4/3
3/2
Solution:
we are given that
Rectangle M was dilated to form rectangle M’.
we have been asked to find
What ratio is the scale factor?
we can find the required ratio by dividing the corresponding sides of the given rectangles as below:
[tex] Ratio=\frac{6}{4}=\frac{2}{4/3}\\
\\
[/tex]
[tex] Ratio=\frac{3}{2}=\frac{6}{4} \\
\\
\
Ratio=\frac{3}{2}=\frac{3}{2}\\ [/tex]
Hence the required ratio is 3/2.
Answer:(d or 3/2
Step-by-step explanation: I took the test
viola makes gift baskets for valentine's day.she has 13 basket left over from last year, and she plans to make 12 more each day. if there are 15 work days unitl the day she begins to sell the baskets, how many baskets will she have to sell?
193 baskets
156 baskets
205 baskets
181 baskets
20 POINTS! What is the distance between the points (2, 3) and (5, -4)?
An object is traveling around a circle with a radius of 10 cm. If in 20 seconds a central angle of 1/3 radian is swept out, what is the linear speed of the object?
I think I've set my formula up right (v=Δ20/Δ1/3 radian), but I don't know what to do with the Δ thing. Once I know how to do that I should be able to like, actually figure it out.