Answer
Ratio of borax solution to glue = (1/3)
Ratio of glue to borax solution = (3/1)
Part B
The ratio table
B - Borax solution
G - Glue
B | G
1 | 3
2 | 6
3 | 9
4 | 12
5 | 15
Explanation
The recipe calls for
1 part borax solution to 3 parts glue
Ratio of borax solution to glue = (1/3)
Ratio of glue to borax solution = (3/1)
Part B
Since we know that 1 part of borax solution = 3 parts of glue, we just need to multiply the amounts of borax solution by 3 to obtain the amount of glue.
The ratio table
B - Borax solution
G - Glue
B | G
1 | 3
2 | 6
3 | 9
4 | 12
5 | 15
Hope this Helps!!!
Which of the following are true about the graph of y = (x - a)(x - b)2(x - c)3I) The graph travels through the point x = aII) The graph "bounces off" the point x = bIII) The graph "bounces off" the point x = c
Consider the given equation,
[tex]y=(x-a)(x-b)^2(x-c)^3[/tex]Put x = a in the equation,
[tex]\begin{gathered} y=(a-a)(a-b)^2(a-c)^3 \\ y=(0)(a-b)^2(a-c)^3 \\ y=0 \end{gathered}[/tex]So the graph of the function passes through (a,0), which is a valid point.
So, option (I) is correct.
Similarly, when substituting the other values, it is obtained that the curve of the given function passes through points (b,0) and (c,0).
But this contradicts with the statements in (II) and (III) respectively.
Therefore, it can be concluded that only statement (I) is correct.
Find the missing side length and angles of ABC given that m A = 41°, b = 4, and c = 10.
To solve this question, we would use cosine rule which is given as
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Our values have been defined for us and we will proceed to evaluate
[tex]\begin{gathered} a^2=4^2+10^2-2(4)(10)\cos 41 \\ a^2=16+100-80\cos 41 \\ a^2=116-60.376 \\ a^2=55.624 \\ \text{take the square root of both sides} \\ a=\sqrt[]{55.624} \\ a=7.458\approx7.5 \end{gathered}[/tex]From the calculations above, the value of the missing side a is 7.5 units
To find angle B,
we can use sine rule
[tex]\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B} \\ \frac{7.5}{\sin 41}=\frac{4}{\sin B} \\ \sin B=\frac{4\times\sin 41}{7.5} \\ \sin B=0.3498 \\ B=\sin ^{-1}0.3498 \\ B=20.5^0 \end{gathered}[/tex]We can still approach C with sine rule or sum of angle in a triangle
[tex]\begin{gathered} A+B+C=180 \\ 41+20.5+C=180 \\ c=118.5^0 \end{gathered}[/tex]From the calculations above, the value of a = 7.5 , B = 22⁰ and C = 118.5⁰ respectively which is option B
Select the correct answer from each drop-down menu.A carpenter is building a triangular frame. She has three pieces of wood measuring 5 feet. 6 feet, and 12 feet.The carpenter build the triangular frame with the three pieces of wood. She could cut the to create a triangular frame.piece byNext
Explanation
Answer:
The carpenter can build the triangular frame by cutting the 12 foot piece by 2foot
give the function f(x)=-2x-5 determine the value of f(-3)
We have the next function
[tex]f(x)=-2x-5[/tex]And we must calculate f (-3).
To calculate it we must replace x = -3 in the function.
[tex]f(-3)=-2(-3)-5[/tex]Finally, we must simplify the answer
[tex]f(-3)=6-5=1[/tex]So, the answer is
[tex]f(-3)=1[/tex]Find the value of x that will make A B5x + 20А.B3x + 60x = [?]
x = 20
Using the alternate exterior angles theorem, it was stated the exterior ang
What is the inequality shown?
The inequality shown is -4 ≤ x ≤ 3.
In graph, as we can see the dots are solid that means inequality is not strict which leads to use of equal sign as well.
In graph, the line is from -4 to 3, that means the number exists between or equals to -4 and 3.
Hence, inequality is -4 ≤ x ≤ 3.
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I tried everything I could to answer this question but I couldn’t get it
We need to use some properties of the kyte:
· The opposite obtuse angles are equal. In the figure, this means ∠WZY = ∠WXY
· The large diagonal bisects the angles ∠ZWX and ∠XYZ
56 ask us to find m∠XYZ. We can note that the angles ∠ZXY and ∠XZY are congruent. And we know that the interior angles of the triangle XYZ add to 180º.
m∠VXY = m∠VZY = 58º
Then:
[tex]\begin{gathered} m∠ZXY+m∠XZY+m∠XYZ=180º \\ 58º+58º+m∠XYZ=180º \\ m∠XYZ=64º \end{gathered}[/tex]The answer to 56. is 64º
57 ask us to find m∠ZWV, we can use the second property listed above. The large diagonal bisects the angle ∠ZWX. Since we know ∠ZWX = 50º, then:
[tex]\begin{gathered} m∠ZWV=\frac{1}{2}\cdot m∠ZWX \\ . \\ m∠ZWV=\frac{1}{2}\cdot50º=25º \end{gathered}[/tex]The answer to 57 is 25º
58 ask us to find m∠VZW. We know that the sum of all internal angles of a kite (or any quadrilateral), is 360º.
We know:
m∠ZWX = 50º
m∠WZY = m∠WXY
m∠XYZ = 64º
Then:
[tex]\begin{gathered} m∠ZWX+m∠WZY+m∠WXY+m∠XYZ=360º \\ 50º+2m∠WZY+64º=360º \\ 2m∠WZY=360º-114º \\ m∠WZY=\frac{1}{2}\cdot246º \\ m∠WZY=123º \end{gathered}[/tex]And:
[tex]m∠WZY=m∠VZW+m∠VZY[/tex]Now replace the known values of m∠WZY = 123º and m∠VZY = 58º:
[tex]\begin{gathered} 123º=m∠VZW+58º \\ m∠VZW=123º-58º=65º \end{gathered}[/tex]The answer to 58 is 65º
59 ask us to find m∠WZY, we sis it in 58 to find m∠VZW.
The answer to 59 is 123º
Louis wants to bake 10 cakes for the church festival. She needs 1 3/4cups of flour and 2 1/2 cups of sugar for each cake. How much flourwill she need for the 10 cakes?Enter your answer as an improper fraction.
Total = 10 cakes
Flour = 1 3/4
Sugar = 2 1/2
Change the fractions to improper fractions
Flour = 1 3/4 = 7/4
Sugar = 2 1/2 = 5/2
Multiply each numbher by 10
Flour = 7/4 x 10 = 70/4
Sugar = 5/2 x 10 = 50/2
Change to proper fractions
Flour = 17 1/2 cups
Sugar = 25 cups
Identify an equation in point-slope form for the line parallel to y = 1/2x - 7 thatpasses through (-3,-2).
ANSWER:
D.
[tex]y+2=\frac{1}{2}(x+3)[/tex]EXPLANATION:
Given:
[tex]y=\frac{1}{2}x-7[/tex]Recall that the slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where;
m = slope of the line
b = y-intercept of the line
Comparing both equations above, we can see that the slope(m) of the line is 1/2 and the y-intercept(b) is -7
Recall that parallel lines have the same slope. So the line that is parallel to the given line will have the same slope(m) of 1/2
Given the point (-3, -2), we can go ahead and write the equation of the parallel line in point-slope form as seen below;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=\frac{1}{2}[(x-(-3)] \\ y+2=\frac{1}{2}(x+3) \end{gathered}[/tex]100 + (n - 2) ^ = 149 how do I solve this what is the first step??
The given expression is
[tex]100+(n-2)^2=149[/tex]First, we have to subtract 100 on each side
[tex]\begin{gathered} 100-100+(n-2)^2=149-100 \\ (n-2)^2=49 \end{gathered}[/tex]Hence, the answer is the first option, that's the first step.The reason for this first step is because we can't take a square root without getting rid of the terms 100, otherwise, the process would be wrong.
Can you help me with this question? I have no other information.
Given,
The number of lawn mowed by Thomas is 35.
The amount of tip thomas got is $150.
The number of lawn mowed by Candice is 30.
The amount of tip Candice got is $275.
They charged equal price to mow each lawn.
Consider,
The amount of mowing the one lawn is x.
According to the question,
[tex]undefined[/tex]The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is 4 ft long with a diameter of 1.6 ft. Suppose gas is poured into the tank at a rate of 1.9 ft^3 per minute. How many minutes does it take to fill the empty tank?
Use the value 3.14 for pi, and round your answer to the nearest minute. Do not round any intermediate computations.
Hence, the minutes it take to fill the empty tank is [tex]8.0384min[/tex].
What is the volume of cylinder?
The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold.
In geometry, there is a specific volume of a cylinder formula that is used to measure how much amount of any quantity whether liquid or solid can be immersed in it uniformly.
Here given that,
The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is [tex]4[/tex] ft long with a diameter of [tex]1.6[/tex] ft. Suppose gas is poured into the tank at a rate of [tex]1.9ft^3[/tex] per minute.
Here,
[tex]d=1.6ft\\r=0.8ft\\h=4ft[/tex]
The general formula for the volume of cylinder is
[tex]V=\pi r^2h\\V=(3.14)(0.8)^2(4)\\V=(3.14)(0.64)(4)\\V=8.0384min[/tex]
Hence, the minutes it take to fill the empty tank is [tex]8.0384min[/tex].
To know more about the cylinder
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Which of the following represents the synthetic division form of the long division problem below? x - 3x+4/ x-5
The number on the left in the synthetic division form is the root of the divisor polynomial. The root of x-5 is 5
The numbers on the right are the coefficients of the dividend polynomial: 1 -3 4
The correct answer is option B
If you toss two dice, what is the probability that the sum of the dots is either 7 or 11?
sum of 7:
there are 6 combinations: (1,6) (6,1) (2,5) (5,2) (3,4) and (4,3)
[tex]=6\times\frac{1}{36}=\frac{6}{36}[/tex]sum of 11:
there are 2 combinations: (5,6) and (6,5)
[tex]=2\times\frac{1}{36}=\frac{2}{36}[/tex]thus the probability is
sum of 7 + sum of 11
[tex]\begin{gathered} =\frac{6}{36}+\frac{2}{36} \\ =\frac{8}{36} \\ =\frac{2}{9} \end{gathered}[/tex]therefore = 22%
To solve the equation 2x - 6 = 30 by balancing, what would be step?
Given the equation
[tex]2x-6=30[/tex]To solve the equation means to determine the value of x, so your objective will be to isolate the x term in one side of the equal sign.
To do this using the balancing method, you have to "pass" all unrelated terms to the other side if the equal sign by performing the oposite operation.
So, first step is to pass -6 to the other side by adding it to both sides of the equation
[tex]\begin{gathered} 2x-6+6=30+6 \\ 2x=36 \end{gathered}[/tex]Next, the x term is being multiplied by 2, to cancel this multiplication you have to divide it by 2. And, to keep the equality valid, any operation performed in one side of the equal sing must be performed on the other side so, divide 36 by 2 too.
[tex]\begin{gathered} \frac{2x}{2}=\frac{36}{2} \\ x=18 \end{gathered}[/tex]The temperature was 55 degrees when i left my house this morning at 7am. At 4pm the temperature was 82 degrees. What was the percent change in temperature?
Answer:
27/55 × 100 = 49.0909090909 %
Drag the red and blue dots along the x-axis and y-axis to graph 8x+2y=10
Solution
Writing in the form
[tex]\begin{gathered} y=mx+x \\ \\ \Rightarrow4x+y=5 \\ \\ \Rightarrow y=-4x+5 \end{gathered}[/tex]Needing help with this practice problem please. Also, I need to show all work
ANSWER
L = 24 inches
W = 14 inches
EXPLANATION
Given tat
The length of the rectangular painting is 10 inches more than the width
Let the width of the rectangular painting be x
Recall, that the frame is 2 inches thick. This implies that there re 2 inches to the left ogf the length and 2 inches to the right of the length. So, there are more 4 inches to the length of the picture
Hence, the new length is
L = (x + 10) + 4
L = x + 10 + 4
L = x + 14
Also, for the width of the painting, we have
w = x + 4
Recall, that the area of a rectangle is given below as
Area = L x W
[tex]\begin{gathered} \text{ Area of a rectangle = L x W} \\ \text{ L = x + 14, and W = x + 4, and A = 336 in}^2 \\ \text{ 336 = \lparen x }+\text{ 14\rparen \lparen x }+\text{ 4\rparen} \\ \text{ Open the parentheses} \\ \text{ 336 = x}^2\text{ + 4x + 14x + 56} \\ \text{ 336 = x}^2\text{ + 18x + 56} \\ \text{ x}^2\text{ + 18x + 56 = 336} \\ \text{ x}^2\text{ + 18x + 56 - 336 =0} \\ \text{ x}^2\text{ + 18x - 280 = 0} \end{gathered}[/tex]Find the value of x by using factorizatin method
[tex]\begin{gathered} \text{ x}^2\text{ }+\text{ 28x - 10x - 280 = 0} \\ \text{ x\lparen x + 28\rparen - 10\lparen x + 28\rparen = 0} \\ \text{ \lparen x - 10\rparen \lparen x + 28 \rparen = 0} \\ \text{ \lparen x - 10\rparen = 0 or \lparen x + 28\rparen = 0} \\ \text{ x = 0 + 10 or x = 0 - 28} \\ \text{ x = 10 or x = -28} \end{gathered}[/tex]Find the length and the width of the rectngular painting
L = x + 14
L = 10 + 14
L = 24 inches
width
W = x + 4
W = 10 + 4
W = 14 inches
The total points scored in the games of an NBA playoff series:195 177 215 200 189 232 201 199 192 201 Round any of the following answers to 1 decimal if needed. If there is no mode type NONE in the answer box.Mean = Median = Mode = Maximum = Minimum =
Solution
Step 1:
Arrange the number in ascending order of magnitude.
177, 189, 192, 195, 199, 200, 201, 201, 215, 232
Step 2:
[tex]\begin{gathered} Mean=\frac{177+189+192+195+199+200+201+201+215+232}{10} \\ \\ Mean\text{ = }\frac{2001}{10} \\ \\ Mean\text{ = 200.1} \end{gathered}[/tex][tex]\begin{gathered} Median\text{ = }\frac{199+\text{ 200}}{2}\text{ } \\ \\ Median\text{ = }\frac{399}{2} \\ \\ Median\text{ = 199.5} \end{gathered}[/tex]Mode is the most occurring number.
Mode = 201
Maximum = 232
Minimum = 177
Hi, can you help me answer this question, please, thank you!
Given:
mean, u = 0
standard deviation σ = 1
Let's determine the following:
(a) Probability of an outcome that is more than -1.26.
Here, we are to find: P(x > -1.26).
Apply the formula:
[tex]z=\frac{x^{\prime}-u}{\sigma}[/tex]Thus, we have:
[tex]\begin{gathered} P(x>-1.26)=\frac{-1.26-0}{1} \\ \\ P(x>-1.26)=\frac{-1.26}{1}=-1.26 \end{gathered}[/tex]Using the standard normal table, we have:
NORMSDIST(-1.26) = 0.1038
Therefore, the probability of an outcome that is more than -1.26 is 0.1038
(b) Probability of an outcome that
what is the prescribed dosage for a 4 yr old child, if the adult dosage is 180 milligram
In order to calculate the child's dosage, let's use the value of n = 4 and M = 180 in the formula, then we calculate the value of D:
[tex]\begin{gathered} D=\frac{n}{n+12}\cdot M \\ D=\frac{4}{4+12}\cdot180 \\ D=\frac{4}{16}\cdot180 \\ D=\frac{1}{4}\cdot180 \\ D=\frac{180}{4} \\ D=45 \end{gathered}[/tex]So the child's dosage is 45 milligrams.
Express the answer in terms of a natural logarithm. Y= (do not simplify)
Solution
Exponential expressions with natural base e are of the form
[tex]y=a.e^{kx}[/tex]The value of 'a' is already set to be 96 since this is the coefficient of the given equation. We just need to find k
so set 3.8^x as e^kx and solve for k
[tex]\begin{gathered} 3.8^x=e^{kx} \\ 3.8^x=(e^k)^x \\ 3.8=e^k \end{gathered}[/tex]The two sides have the same exponent of x. So the two bases are 3.8 and
e^k must be equal to
[tex]\begin{gathered} e^k=3.8 \\ k=ln(3.8) \\ k=1.335 \end{gathered}[/tex]This means
[tex]e^{kx}=e^{1.335x}[/tex]and we replace the
[tex]3.8^x=e^{1.335x}[/tex]to go from
[tex]y=96(3.8)^x[/tex]to
[tex]y=96.e^{1.335x}[/tex]Therefore the correct answer is
[tex]y=96.e^{1.335x}[/tex]INSTRUCTIONS: JCTIONS: e slope of the line er it here:m=1/3 Find the slope of the line and enter it here: 4 ey-intercept of & enter it Find the y-intercept of the line & enter it here: Write the equation of the line in form y=mx+b + he equation of in form y=mx +b /3x + 2 30 म
The equation of a line in the slope intercept form is expressed as
y = mx + b
where
m represents slope
b represents y intercept
The formula for finding slope is
m = (y2 - y1)/(x2 - x1)
From the graph,
When x1 = 1, y1 = - 2
when x2 = 2, y = 1
Slope = (1 - - 2)/(2 - 1) = 3/1
Slope = 3
The y intercept is the value of y at the point where the line cuts through the y axis. Thus, y intercept = - 5
To write the equation of the line, we would substitute m = 3 and b = - 5 into the slope intercept equation. Thus, the equation of the line is
y = 3x - 5
Identify the function shown in this graph. 5 4 3 2 과 2 பான் O A. y = x + 4 ос B. y=-x+4 C. y= x-4 D. y=-x-4
Given the graph of the line passes through the points ( -4 , 0 ) and ( 0 , 4 )
The general form of the line is : y = mx + b
where m is the slope and b is y-intercept
The slope will be calculated as following:
[tex]\text{slope}=m=\frac{y2-y1}{x2-x1}=\frac{4-0}{0-(-4)}=\frac{4-0}{0+4}=\frac{4}{4}=1[/tex]b = y intercept = ( the value of y when x = 0 )
So, as the line pass through the point ( 0 , 4 )
b = 4
so, the equation of the line is:
[tex]y=x+4[/tex]Write the rate as a unit rate.980 cars in 280 households?
under which of these conditions will the law of sines not give additional information about the triangle?A. two sides and the included angle are given B. two angles and a side opposite one of them are given C. two sides and an angle opposite one of them are given
We will have that the law of sines won't give us any more information under the following situation:
*Two sides and the included angle are given. [Option A]
identify the type of function represented by the equation y=-3x
y = -3x is the equation of a line, with a slope of -3 and a y-intercept of 0
write an equation for the graph below in terms of xy=______
Given the graph of a line.
We will write the equation of the line using two points lying on the line
As shown, the line passes through the points (0, 1) and (-1, 3)
The general equation of the line is: y = m * x + b
Where (m) is the slope and (b) is the y-intercept
We will find the slope as follows:
[tex]slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{-1-0}=\frac{2}{-1}=-2[/tex]And the value of b = the value of (y) when x = 0
So, b = 1
So, the answer will be, the equation of the line:
[tex]y=-2x+1[/tex]For questions 7-8: P is the center of a circle with diameter KR.7. If P(7,-5) and R(4,-2), find the coordinates of point K.8. What is the length of the radius to the nearest hundredth?
Answer:
7.) The coordinates of point K are (10,8)
8.) The length of the radius, to the nearest hundreth, is of 4.24 units.
Step-by-step explanation:
P is the center of a circle with diameter KR:
This means that P is the midpoint between K and R.
I will see that the points are:
[tex]P(x_P,y_P),K(x_K,y_K),R(x_R,y_R)[/tex]Since P is the midpoint:
[tex]x_P=\frac{x_K+x_R}{2},y_P=\frac{y_K+y_R}{2}[/tex]P(7,-5) and R(4,-2)
This means that:
[tex]x_P=7,y_P=-5,x_R=4,y_R=-2[/tex]7. If P(7,-5) and R(4,-2), find the coordinates of point K
[tex]x_P=\frac{x_K+x_R}{2}[/tex]Substituting:
[tex]7=\frac{x_K+4}{2}[/tex][tex]x_K+4=14[/tex][tex]x_K=10[/tex]Now we do the same for y:
[tex]y_P=\frac{y_K+y_R}{2}[/tex]Replacing with what we have
[tex]-5=\frac{y_K-2}{2}[/tex][tex]y_K-2=-10[/tex][tex]y_K=-8[/tex]The coordinates of point K are (10,8)
8. What is the length of the radius to the nearest hundredth?
The radius is half the diameter(distance between KR divided by 2). It can also be the distance between an endpoint of the circle and the centre(Distance between P and K, or between P and R).
I am going to calculate the distance between P and R.
P(7,-5) and R(4,-2). So
[tex]R=\sqrt{(7-4)^2+(-5-(-2))^2}=\sqrt{3^2+(-5+2)^2}=\sqrt{9+9}=\sqrt{18}=4.24[/tex]The length of the radius, to the nearest hundreth, is of 4.24 units.
write an equation of each line shown below in slope- intercept form
Step-by-step explanation:
red: y=2x-1
blue: y=-2/5x-1